# embeddings_queue

created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41014-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 5, "chroma:document": "6 DETERMINATION OF FRACTURE PARAMETERS FROM FRACTURING PRESSURE DECLINE SPE 8341 \nAs a result, the average width, w, is related to the \nmaximum width at the wellbore, W, by \n7T ss W: shut-in w = 4 (33) \n7T \nsP W: pumping w = 4 (34) \nDuring the period of shut-in, w is essentially constant \nand (33) and (34) relate the change of W during this \nshort period before to after shut-in. From the defini\u00ad\ntion of fluid efficiency \n(35) \nCombining (32) and (35), and substituting into (25) \ngives \nw = TICH it (1 + p) (eff)/H (36) p 0 \nand substituting (28) yields, at the end of pumping, \nw = 7TC1 It p \n0 \nC' = CH /H p (37) \nin which C' is the average fluid loss coefficient with \nrespect to the total fracture height, and p is the \ndecline pressure ratio given in. (26) or (27). \nFrom (34), the maximum width at the wellbore, at \nthe end of pumping, is \n4 w w = -;s \np \nwith w given by (37). (38) \nThe time for a fracture to close after shut-in is \ngiven in Appendix B and is found by integrating (9)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4108c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 5, "chroma:document": "given in Appendix B and is found by integrating (9) \nfrom shut-in to the time to close using f1 (~t/t ) of \n(13). As a result, the following express~on is0deter\u00ad\nmined in Appendix B, \ng (!J.t/t ) = ---'w-'----\n0 2C' /t (39) \n0 \nwhere the time to close, !J.t, is the value of g(!J.t/t ), \ndefined in (16), which equals the right-hand side o~ \n(39). This expression assumes that the average width \nand average fluid loss coefficient can be estimated \nthrough the fracture design process. \nAnother expression for closure time can be obtained \nfrom pressure decline data shortly after the fracture \ntreatment which would be useful for estimating the \nadditional time for the fracture to close. This expres\u00ad\nsion is obtained by combining (37) and (39). \ng(!J.t/t ) = _:~!\u00a3_ \n0 2 (40) This expression depends only on the pressure decline \nratio given in (26) or (27). \nUsing symbolic notation, in terms of the inverse \nfunction of g, i.e., g-1, (39) and (40) can be rewritten \nfor the dimensionless closure time as \nt:.t/t \n0"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41104-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 5, "chroma:document": "for the dimensionless closure time as \nt:.t/t \n0 \nt:.t/t \n0 \nAPPLICATIONS g-1 [ w ] \n2C'/t \n0 (41) \nIn this section the expressions derived previously \nwill be applied to fracturing pressure decline data for \ntreatments of three wells. More specific information \non the treatments is given in Table I. \nCase 1: This was a calibration treatment of 500 \nbbls in the Muddy J sand of the Denver Basin. The \ncalibration treatment was pumped without proppant to \ndetermine information on the tendency of fracture \nheight to increase with respect to volume and pressure, \nand on fluid-loss behavior of the zone. The treatment \nconsisted of polymer-emulsion fluid consisting of two\u00ad\nthirds condensate and one-third water with 50 lbs of \npolymer per 1000 gals. \nFigure 6 shows the SP log from which a fluid-loss \nheight of 32 feet over the height of the fracture was \nestimated, and the post-fracture temperature log from \nwhich a fracture height of 60 ft. was estimated. \nFigure 7 shows a \"pump-in/flow-back\" determination of"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4117c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 5, "chroma:document": "Figure 7 shows a \"pump-in/flow-back\" determination of \nclosure pressure (discussed in next section) and the \nsurface pressure decline, after shut-in. The left-hand \nside of Fig. 8 shows a pressure difference plot con\u00ad\nstructed from the decline data and compatible with \nEq. 15 and Fig. 3. The right-hand side of Figure 8 \nshows a \"curve match\" of the master curves, Fig. 3, \nwith the field data from which a P~\\' value of 350 psi \nwas.obtained. The master curves are shown as dashed \nlines in Fig. 8. A discussion of the \"curve match\" \ninterpretation will be given in a later section. Using \nthe data from Table 1 and Eq. 18, the fluid-loss \ncoefficient is estimated to be \nc \nE'H /t p 0 .00053 ft/lmin \nFrom Fig. 7, the instantaneous shut-in pressure above \nclosure pressure and the pressure decline difference \nbetween o=.S and 1.0 can be obtained as 800 and 210 \npsi, respectively. From Fig. 3, the value of \nG(.S,l.)=O.S9, and from Fig. 2 the S /S ratio is \nobtained as .88 for estimated valuespofsn=.75 and"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae411fe-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 5, "chroma:document": "obtained as .88 for estimated valuespofsn=.75 and \na=l.O. Using the above data and Eq. 27, the pressure \ndecline ratio is \np 0.98 \nFrom Eq. 28, the fluid efficiency is \neff = 0.49 Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4126c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 6, "chroma:document": "0 SPE 8341 K. G. NOLTE \nFrom the data above and Table I, the fracture length \n(tip to tip) can be estimated from Eq. 25 as \nL = 2700 ft \nFor Eq. 25, the injected volume, Qt , must be converted \nto ft.3 fo~ compatibility of units Rsed above and in \nTable I. Eq. 37 can be used to estimate the average \nwidth across the height and length from the above data, \nand yields \nw = 0.0094 ft 0.11 inch can be estimated. Forming a ratio of P<'~, Hz, and \n~ for the two cases gives \n0 \n(25'300 =.; 250150 = \u202263 \nH1 = .sox H2 = .80 x 150 120 ft \nfor the fracture height at the time of the pad shut-in \nThe maximum width can be found from w and Eq. 34 and is and indicates the fracture height changed very little \nW = 0.24 inch \nThe dimensionless time for the fracture to close is \ngiven by Eq. 41 and for p=0.98 is \n-1 0 = g (1.54) = 1.6 \n6t = ~ t = 1.6 X 100 \n0 160 min. \nwhere Fig. 1 can be used to evaluate g-1\u2022 The actual \nclosure time from Fig. 7 was 150 min. This is the only"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae412da-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 6, "chroma:document": "closure time from Fig. 7 was 150 min. This is the only \nparameter of those determined above which can be check\u00ad\ned with data. \nCase 2: This treatment consisted of 700,000 lbs \nof 20/40 sand and 300,000 gals of a cross-linked, \nwater-base fluid with 40 to 60 lb/1000 gals of polymer \nand a 5% hydrocarbon phase to reduce leakoff. The \ntreatment was stopped after 30,000 gals for about \n80 min. The data used in the following calculations \nneglects this first part of the treatment. The zone \ntreated was the same as for Case 1. A fluid-loss \nheight of 70 ft and fracture height of 150 ft were \nestimated from the appropriate logs for the treatment. \nThe surface pressure decline data is shown in Fig. 9 as \nis the pressure-difference \"curve match\". The master \ncurves are shown as dashed lines. Using the same \nequations as in Case 1, the following parameters are \nestimated for this treatment. \nP* = 300 psi \nC = .00076 ft/lmin \np = 2.4 \neff = 0.59 \nL = 4600 ft \nw 0.43 in \nW = 0.86 in \n0 = 5.5; 6t = oto"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4133e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 6, "chroma:document": "L = 4600 ft \nw 0.43 in \nW = 0.86 in \n0 = 5.5; 6t = oto \n6t = 5.5 x 250 = 1380 min = 23 hrs \nThe well was flowed back before closure and, therefore, \nthe 23-hour closure estimate cannot be compared with \nactual data for this case. \nAs stated above, this treatment was stopped during \nthe pad, i.e., shut-in, after 30,000 gals and a pump \ntime of 25 minutes. An analysis of the decline data \n(not given here) after the pad shut-in gave a P* value \nof 150 psi. Using Eq. 17, and assuming that all param\u00ad\neters, except the pump time, t , and the height are the \nsame for the pad shut-in and tRe shut-in after the \ntreatment, the height at the time of the pad shut-in during the major portion of the treatment. \nCase 3: the final example uses data on pressure \ndecline reported by Novotny.5 The reported data is \nsummarized in Table 1. This treatment was 400 bbl of a \npolymer-emulsion fluid. From the decline data in this \nreference, a rate of decline of dP/dt=4.5 psi/min is"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae413ac-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 6, "chroma:document": "reference, a rate of decline of dP/dt=4.5 psi/min is \ninferred at a shut-in time of 40 minutes (i.e., o=l for \na 40-minute pump time). Equation 9 will be used to \nestimate the fluid-loss coefficient with a value of \nf(o=l)=0.78 from Fig. 1 and a B value from Fig. 2 of \n0.67 (assuming values of a=.75 ~nd n=.75). This equa\u00ad\ntion gives \nc nH2B s rt:\" dP \n4H Ef(o) dt = 0.00035 \np \nFrom the referenced decline data, an inferred value of \ninstantaneous shut-in pressure above closure pressure \nof P=780 psi is obtained, and from Fig. 2 a B /Bs \nvalue of 0.88. Using the above data, the pregsure \ndecline ratio is \n2B P/t \nP = f ( 0 ) n B P dP I~ t = 1. 8 7 \ns \nThe fluid efficiency, from Eq. 28 is \neff _P_ = .65 \n1 + p \nand estimating the length from Eq. 31 gives \nL Qt\n0(1-eff) \nnCH It p 0 5600 ft \nThe average width, over the height and length, and \nmaximum width at the wellbore, obtained from Eqs. 37 \nand 38, are \nw .0043 ft = 0.052 inch"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4141a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 6, "chroma:document": "and 38, are \nw .0043 ft = 0.052 inch \nw 0.11 inch 7 Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41488-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "8 DETERMINATION OF FRACTURE PARAMETERS FROM FRACTURING PRESSURE DECLINE SPE 8341 \nThe time for the fracture to close is obtained from \nEq. 36 and Fig. 1 as \n6t = at = 4.0 X 40 = 160 min. \n0 \nThe estimated closure time of 160 min. and fluid effi~ \nciency are in reasonable agreement with that obtained \nfrom the referenced data. However, the above length is \nsignificantly greater and the above width is signifi\u00ad\ncantly less than those esimated in the cited reference. \nThese values can be brought in closer agreement by \nreducing the modulus for the referenced data from 107 \nto 6 x 106 psi, (i.e., similar to the value for the \nprevious cases). For the reduced modulus, the above \nparameters which would change and their resulting \nvalues are listed below \nc = .00055 ft/lmin \nL = 3400 ft -w = .087 in \nw = 0.18 in \nFor the reduced modulus, the above value of W is in \nreasonable agreement to the referenced value of 0.21. \nHowever, the referenced value of L=852 ft. is still"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41500-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "However, the referenced value of L=852 ft. is still \nsigni~icantly different than the above value. It is \nnoted that the referenced values of fluid pumped, \nefficiency, and wellbore width are not consistent with \nthe referenced value of height. \nDISCUSSION OF APPLICATIONS \nThe \"curve match\" for Case 1, shown in Fig. 8, \nindicates that the data curve for 8=.25 is larger than \nthe theoretical pressure difference curve for 8=.25. \nThis indicates that the average rate of pressure \ndecline between 8=.25 and subsequent times is greater \nthan predicted by fluid loss to the formation alone. \nAn expianation is that the fracture is still extending \nafter time 8=.25. This explanation is supported by a \nnumerical simulator for fractures (similar to that \ndiscussed in Ref. 4) which has been extended to include \nfracture closure as well as extension. The continued \nextension for some time after shut-in is contrary to \nthe assumption used to derive the expressions in this"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41578-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "the assumption used to derive the expressions in this \npaper. However, the assumption of extension stopping \nat shut-in provides conservative estimates in that the \ndetermined fluid-loss coefficient will be greater and \nthe length less than in reality. This follows because \ncontinued extension creates larger rates of pressure \ndecline (proportional to estimated value of C) than for \nno extension, because the increased length reduces the \naverage fracture width (for a fixed volume of fluid) \nand thus reduces the pressure. Also, the additional \nextension creates new fracture area (i.e., fluid-loss \narea) not accounted for by the analysis which assumes \nno extension after shut-in. \nOther possible deviations from the assumptions, \nwhich would lead to conservative estimates of the \nfluid-loss coefficient and length, are interference \nfrom proppant and variable fracture height. If the \nfracture height is not essentially constant, it will \ntend to decrease away from the wellbore. This follows"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae415f0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "tend to decrease away from the wellbore. This follows \nbecause the pressure decreases toward the tip as a \nresult of the pressure gradient required to maintain \nfluid flow; and since an increase in fracture height \nmost likely results from an increase in pressure, the \nfracture height will tend to decrease toward the tip. Therefore, the average fracture height will most likely \nbe equal to or less than that determined at the well\u00ad\nbore. The effect of proppant on fracture closure is to \nmake the system effectively stiffer which is equivalent \nto increasing the formation modulus. Either a stiffer \nfracture system than would actually occur without \nproppant, or a smaller than estimated average-fracture\u00ad\nheight would increase the pressure decline rate and \nlead to estimating a larger than actual fluid-loss \ncoefficient. Since the effect of proppant is to \nincrease the decline rate, an indication of the effect \nof proppant on the match curves would be for the data"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41668-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "of proppant on the match curves would be for the data \nvalues to deviate toward larger values than indicated \nby the theoretical curves. \nThe match curves in Fig. 8 also show that all the \ndata curves, except 8=.25, tail off to lower values \nthan the theoretical curves for times greater than 125 \nminutes. This indicates that the rate of fluid loss \nafter 125 minutes is less than predicted. An inter\u00ad\npretation of this observation is that for times greater \nthan 125 minutes the fracture walls are closing to\u00ad\ngether from the tip toward the wellbore, since there \nwas no proppant in this case. The closing of the \nunpropped fracture reduces the area for fluid loss in \nthe relatively high loss area of the tip and conse\u00ad\nquently reduces the net rate of loss and pressure \ndecline. \nThe match curves for Case 2 also indicate fracture \nextension after 8=.25, or 63 minutes, but none after \no~0.5, or 125 minutes. The curves for this case do not \ntail-off to the same degree as for Case 1."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae416d6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "tail-off to the same degree as for Case 1. \nFor Cases 1 and 2, a fracture closure pressure is \nrequired to determine the net fracture pressure above \nclosure, denoted by P. The closure pressures were \ndetermined for these cases by a procedure prior to the \ntreatments which consists of creating a fracture with a \nrelatively small amount of fluid and flowing the fluid \nback out of the fracture at a controlled rate through a \nchoke. The decline curve for the flow-back stage \n(e.g., Fig. 7) shows a recognizable dogleg of an in\u00ad\ncrease rate of decline at the closure pressure due to \nthe restriction to flow out of the fracture introduced \nas the fracture closes at the wellbore. \nSUMMARY OF APPLICATIONS \n1. The example cases given in this paper illustrate \nthat the parameters which describe the geometry of \na fracture can be obtained simply and directly \nfrom the pressure decline data after a treatment. \n2. Using the parameters determined from an actual or \ncalibration treatment (e.g., Case 1) improved"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4174e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "calibration treatment (e.g., Case 1) improved \ndesigns can be achieved for future treatment in a \ngiven pay zone. \n3. In particular, the\"fluid-loss coefficient should \nbe similar for all treatments of a given zone for \nsimilar fluids. As a result, using a \"calibrated\" \nfluid-loss coefficient and using decline data from \nsubsequent treatments, the fracture height or the \nformation modulus, and the fracture length can be \nestimated for these treatments. \n4. The decline pressure ratio, p, obtained from \ndecline data only, provides estimates of the fluid \nefficiency and fracture closure time. \n5. The only direct check on the accuracy of the \nestimates provided by this analysis is the time \nfor the fracture to close. In the two cases where Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae417bc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 8, "chroma:document": "SPE 8341 K. G. NOLTE 9 \nclosure time data exis.ted, the predicted time Wq1;1. \nin good agreement with the data. \nNOMENCLATURE \nA = cross-sectional area of fracture \nC = fluid-loss coefficient \nE' = plane strain modulus \n= E/(l-v2) \nE =Young's Modulus \neff = fluid efficiency \nf(o) =dimensionless pressure decline function, Eq. 7. \nG(o,o\n0) = dimensionless pressure \ndifference function, Eq. 16. \ng(o) = avg. decline rate function, Eq. 16. \nH = fracture height \nH = fluid-loss height p \nL = fracture length \nP = fracture pressure, above closure pressure, \nat wellbore and at shut-in \nP* =match pressure, Eq. 17. \n6P(o\n0,o) = pressure decline difference \ndP/dt = pressure decline rate \np = pressure at some point in fracture. \np = average pressure over length of fracture. \nQ = pump rate. \nt = time variable. \nt\n0 = pump time. \n6t = time since shut-in. \nw = maximum fracture width \nw = maximum fracture width \nin the fracture. \n-at \nat \nw = average width over height well bore. \nsome point \nand length."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41834-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 8, "chroma:document": "some point \nand length. \nz = distance v~riable down fracture. \na = denotes proportionality \nS = ratio of average and wellbore pressure. \nsp = value of s while pumping. \nSs = value of S while shut-in. \no = dimensionless shut~in time = 6t/t \n0 \n8\n0 = reference shut-in time for pressure \ndifferences. \nA = fluid loss per unit fracture length. \nv =Poisson's ratio. \nT = time of local fracture creation. \n!REFERENCES \n1. Khristianovic, S. A. and Zheltov, Y. P., \"Forma\u00ad\ntion of Vertical Fractures by Means of Highly \nViscous Liquid,\" Proc. Fourth World Pet. Gong., \n\u00b7Rome (1955). 2. \n3. \n4. \n5. \n6. Perkins, T. K., and Kern, L. R., \"Widths of \nHydraulic Fractures,\" J. Pet. Tech. (Sept., 1961). \nNolte, K. G., and Smith, M. B., \"Interpretation of \nFracturing Pressures,\" 54th Annual Tech. Con\u00a3. and \nExhib., Las Vegas (Sept., 1979). \nNordgren, R. P., \"Propagation of a Vertical \nHydraulic Fracture, ll Soc. Pet. Eng. Jour. (August, \n1972). \nNovotny, E. J., \"Proppant Transport,\" 52nd Annual"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae418a2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 8, "chroma:document": "1972). \nNovotny, E. J., \"Proppant Transport,\" 52nd Annual \nTech. Conf. and Exhib., Denver (October, 1977). \nDobkins, T. A., \"Methods to Better Determine \nHydraulic Fracture Height,\" 54th Annual Tech. \nCon\u00a3. and Exhib., Las Vegas (Sept., 1979). \nAPPENDIX A \nFluid Flow in a Vertical Fracture \nIn the following, the power-law flow model will be \na.ssumed to represent the flow behavior of a fracturing \nfluid over the range of conditions generally encount\u00ad\nered in fracturing applications. The parameters for \nthis model, as used \u00b7in the following, are \nShear stress = k(shear rate)n \nFor this assumption, the pressure gradient2 is \n~ \ndz n \n=2k~ 2n+l w \nm = (2n+l)/n (1) \nfor flow of q (volumetric flow rate per unit height) \nbetween walls separated by the width w. The total flow \nrate, Q, down both wings of the fracture is twice the \nrate down either wing and is found by rearranging (1) \nand integrating over the cross section. \nH/2 1/n Jq 1 Cdp L) Q = 2 dy = -m dz 2k \n-H/2 \nH/2 \nX J wm dy \n-H/2 \nor \n1/n"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41924-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 8, "chroma:document": "-H/2 \nH/2 \nX J wm dy \n-H/2 \nor \n1/n \nQ = cL dp) Hifl cp (n) \n2k dz m (2) \nwhere \n1/2 m \n<j>(n) = J c~r d (Y) w H (3) \n-1/2 \nm = (2n+l)/n Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae419a6-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 9, "chroma:document": "10. DETERMINATION OF FRACT'ORE PARAMETERS FROM FRACTURING PRESSURE DECLINE SPE 8341 \nand W is the maximum cross-sectional width. In (2) the Also from (8), the pressure at the wellbore is \nassumptions were made that k and n are constant across \nthe section and that dp/dz is also constant across the \nsection, i.e., one-dimensional flow. Rearranging (2) \nyields the proportionality \ndp = Mk~t ~ \ndz HnW2n+l a w2n+l \nn \nM = 2 (<P (:)) m (2n+l) /n (4) 1 \np (11) \nForming the ratio of p, from (9), to the pressure at \nthe wellbore, P from (11), gives \np/P = ___ 1 ___ = 2n+2 = 8 (e+l) 2n+bn+a+3 \np = 8P (12) \nfor the pressure gradient down a constant height frac- Without a detailed discussion, it has been found from \nture. If the fracture responds elastically to internal a numerical fracture simulator (similar to that \npressure discussed in Ref. 4) that the appropriate approxima\u00ad\ntions for flow rate in (7) or (12) are \np sw (5) \nwhere Sis the fracture stiffness (i.e., S = E'/2H for"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41a28-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 9, "chroma:document": "where Sis the fracture stiffness (i.e., S = E'/2H for \na constant-height fracture in a homogeneous, infinite, \nelastic medium), (4) and (5) yield \np2n+l dp a kQn dz (6) \nfor which the fracture stiffness is assumed to be \nconstant. For the assumption of a homogeneous elastic \nmedium, the fracture cross section is elliptical2 with \na minor axis of W and a major axis of H. For this case \na numerical integration for <P(n) and M defined in (3) \nand (4) is possible and is shown graphically in \nFig. 10. \nAssuming k and Q have the exponential relation\u00ad\nships \nk k (2z/L) a \n0 (7) \nQ Q (2z/L)b \n0 \nalong the fracture, and integrating (6) from the tip \n(p=O, z=O) to some distance z toward the wellbore \nyields \n-(8) \nfor which n was assumed effectively to be constant. \nThe average value of p, along the length L of the \nfracture, from (8) is \nL \np = f J p (z) dz \n0 \n(e+l) \ne = (a+bn+l)/(2n+2) (9) \n(10) b = 0 shut-in \nss 2n+2 \n2n+3+a \n(13) \nb = 1 pumping \nsP 2n+2 \n3n+3+a \nimplying a nearly constant flow rate, greater than"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41aa0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 9, "chroma:document": "3n+3+a \nimplying a nearly constant flow rate, greater than \nzero, down the fracture for shut-in even though the \nflow rate is zero at the wellbore and fracture tip; \nand a linearly varying flow rate while pumping of Q \nat the wellbore to essentially zero at the fracture0 \ntip. From (7) the variation of k, or equivalently \nthe viscosity, can be represented as \na = 0 constant viscosity \na = 1 medium degradation (14) \na = 2 strong degradation \nwhere \"a\" reflects the \"order of magnitude\" decrease \nin fluid viscosity down the fracture due to tempera\u00ad\nture, shear and time degradation of fluid system. \nThe ratio of 8 for pumping, 8 , to that for \nshut-in, 8 , is found from (13) asp s \n8 _E.. = 2n+3+a = 1 _ n \n8s 3n+3+a 3n+3+a (15) \nFor the sake of completeness, the actual equality for \n(11) is \n1 \n{ s2n+l k Qn 1} 2n+2 \np(L) M' o 0 (16) \n(a+bn+l) Hn \nwhere \n1"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41b22-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 9, "chroma:document": "{ s2n+l k Qn 1} 2n+2 \np(L) M' o 0 (16) \n(a+bn+l) Hn \nwhere \n1 \nM' [ (2n+2)M] 2n+Z Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41ba4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 10, "chroma:document": "SPE 8341 K. G. NOLTE \nwith M defined in (4). By using the relationship for \nM in terms of n in Fig. 10, it can be shown, surpris\u00ad\ningly, that M' in (16) is essentially independent of \nnand is equal to 2.53 \u00b1 0.5% over the range of n=0.4 \nto 1.0. In (16), Q is the total flow rate into both \nfracture wings, L i~ the length of a fracture wing, \nand Sis defined by (5). \nAPPENDIX B \nTime for Fracture to Close \nThe time for a fracture to close can be found \nfrom Eq. 9 of the text. Rewriting this equation\u00b7 \nresults in \n2H dP 8CHP f(t) \nE' dt = \nTIH S /t s 0 (1) \nand integrating over the shut-in time 6t (time for \npressure to go to zero) gives \n2H p \nE' (2) \nwhere P is the pressure at shut-in. Noting that the left-hand side of (2) is the maximum width W at the \nwellbore,2 and rewriting yields \n0 \nC' 6t/t \n0 f t CL.lt/t ) d6t = ci ws ) -1-\u00ad\no to s 2C'/t \n0 (3) \nThe integral can be shown to be equal to g(6t/t ) \ngiven in (16) of the text, if (13) of the text ~s \nused for f. C' is the average fluid-loss coefficient"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41c1c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 10, "chroma:document": "used for f. C' is the average fluid-loss coefficient \nover the fracture height, and using (33), the term in \nparentheses on the right-hand side can b~ expressed \nin terms of the average fracture width, w, at shut\u00ad\nin. Therefore, (3) can be rewritten as \ng(6t/t ) \n0 = __ w __ \n2C'/t \n0 (4) \nTable 1 \nData for Example Well Analysis \nCase 1 Case 2 Case 3 (Ref. 5) \nTreatment Vol. (bbl) 500 6,400 400 \nTreatment Rate (BPM) 5 30 10 \nTreatment Time (min.) 100 250 40 \nFluid Type Poly. -Em. Cross-Lk. Poly. -Em. \nReservoir Depth (ft.) ?,900 8,000 10,000 \nTemperature (\u00b0F) 265 265 200 \nPermeability, (md) .01 .01 1.0 \nFracture Height (ft.) 60 150 60 \nFluid-Loss Height (ft.) 32 70 20 \nFormation Modulus (106 psi) 5 6 10 \nTime to Close (min.) 150 130 \nProppant No Yes Yes 11 Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41ca8-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 11, "chroma:document": "4 \n3 \n\u00a7: 2 = \n1 \n0 0.25 0.5 0. 75 1.0 1.5 2.0 3.0 4.0 6.0 \n1.5 \no = ~t/t0, Dimensionless Shut-in Time \nFig. 1 -Dimensionless time function versus rlimensionless time. \n0 2 0 2 0 21.0 \n/3p f3s 0.9 0.9 \n(Pumping) (Shut-in) \n0.8 0.8 \nco.. \n0 0.7 0.7 0.7 \nG) \nf3r/f3s :I 'i > 0.6 0.6 0.6 \n0.5 0.5 0.5 \n0.4 0.4 \n0 2 0 2 0 2 \nViscosity Exponent, a \nFig. 2 -Variation of S with viscosity exponent, Eq. 7 -Appendix A. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41d2a-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 12, "chroma:document": "-0 \"0 .. \"0 \n(!} \n.. c \n0 ... \n(.J c \n::::J 1 LL. \nQ) .8 (.J c .6 Q) .... \nQ) = c .4 \nQ) .... \n::::J en en .2 Q) .... \nCl. 0.25 0.5 1.0 1.5 2.0 3.0 5.0 \n0 -o-\n0.25 \n0.5 \n0.75 \n1.0 \n0.25 0.5 1.0 1.5 2.0 3.0 5.0 \nDimensionless Shut-in Time, o -~t/t0 \nFig. 3 -Master curves for pressure differences. \nPressure Decline Ratio, p, Eqs.26 & 27 \n/ / \n/ \n/ \n/(Slope / \np P/t0 P Proportional to --or -\ndP/dt ~P \n-------T \n~P (8o, o) \n-~ / 1 / = Plt0 \nz ~-~ Fracture _ _ _ _ _ :\\ _ dP I Slope ~Cit Closure Pressure I \n~t 0 - = 8=0 0.5 \u2022 t0 ~~----L---~1----L---~J \n~t == 0 0.5t0 t0 I I I ~ 1.0 \n0 t0 1 .5 t0 2t0 t, time \n1~\u2022--Pumping------+--Shut-in ---\nFig. 4 -Illustration of pressure terms for decline analysis. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41dac-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 13, "chroma:document": "..J \n........ \nN 1.0 \n/% / / /Upper bound, Eq.12 \n/...,._, z/L = t/t0 / \n/ 't (z) \n~------~A~-------r Lower Upper' \nbound Actual bound \nlog t/t0 1.0 \nFig. 5 -Bounds for rate of fracture extension and time \nof fracture creation. \nSP-Log \nFluid Loss 7850 \n..... -..c: ..... c. \nQ) c Post-Fracture \nTemperature Log \n7950 *See Ref.6 \nFig. 6 -Input data for analysis of case 1. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41e2e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 14, "chroma:document": "Pressure Decline After Fracturing-\n1800 \n'iii c. \nen 1400 \n\"-::I \nCl) \nCl) \nen \n\"-1200 a. \nen \nC.) \nca -1000 \"-::I en \n800 \n600 \n0 25 11 \n~P=210 Cl) \u2022 \n': 1000 \nQ) \n\"-Pump-in/ \nFlow-back \n::::1 \nCl) \nCl) \nQ) 0:: Closure \na, Pressure \n~ 600 ~750 psi \n~ ~~~~-\n::::1 0 en 2,min. \nJf--~---\nLOj OJ ol ~ Closure ill ~~ Pressure \n50 75 100 ~ 25 150 \nTime Since Shut-In, min. \nFig. 7 -Pressure decline for case 1. \nPressure Differences for Data Match of Data and Master Curves \n..lt . '[ 8001- o 25mm. \nIll 6001-\u2022 50 \n~ c 75 \n~ 400 ~ \u2022100 ... .! \n- 0 c \n~ 200-\n:::1 \nIll \nIll \nQ) ... 1-\n~ 100 r-\n~ \n(J \nQ) 0 \n\u2022 0 0 \n0 \n0 \n0 \u2022 a \u2022 0 \na \u2022 \u2022 a \u2022 \n\u2022 \n0 \u2022 100 +a=1 \nI ~0;6; \nI 0/ /./ p. =350 o / /e /I - ---/-\"-lei-- j I /, I \n0 /1 ' 0/ ( 1 ,t 1\u2022 G(o,o0l= 1 \nI \u2022 I I \no I '! f t\u2022 I I I !. \nI I I. I \nI ,\u2022 01 I \nI I I \u2022 \nI I 1 \n100 c I I I 50 ......_--'---!..----L---'-----'----....1 \n50 75 100 150 200 50 75 100 150 200 50 \nShut-in Time , min Shut-in Time, Min."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41ea6-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 14, "chroma:document": "Shut-in Time , min Shut-in Time, Min. \nFig. 8 -Match of pressure differences for case 1. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41f28-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 15, "chroma:document": "Match of Data and Master Curves \n1/) a= 1.0 0. \nI o} ' r.n \n~ 0~ 0 o/ /. c: 400 p\u2022 =300 ~ / / \u2022\u2022 ~ \n1/) Q; ----o /1' -;\u2022-/J- 0. -\n~\u00b7 ~ \"-' ~\u00b7 I \u2022 a 0 \"\"7~~~~~. 1 .5 ~ o r.o\"' ' /a!. G(o,o0)=1 (3 ... 1.()\u2022 \n~ :I \n0 1/) \n1/) / ~~c\u00a7'0o/ I ..... r~. \n~ 2000 ~ \n'r::!\n0/y .1 J 1 ... \nll. Y ~ ~o I :I \n1/) \n1/) \n~ ... \nll. \n~ \n0 \nca 't :I \n(/) ~ c: \"'I o. (j o\u00b7l.-\u00b71 \n~ t = 250 0 50 0 \n0 100 400 \nShut-in Time, Min. \nFig. 9 -Decline data and pressure difference match for case 2. \n10 \n8 \nc \n~ 6 \n4 \n0.4 \n0.60 \n0.58 \nc 0.56 \n-$. \n0.54 \n0.52 \n0.4 37r \n16 0.6 0.8 \n~-------\nL Value Assumed \nin Ref.2 \n0.6 0.8 \nPower Law Exponent, n 1.0 \n1.0 \nFig. 10 -Dependence of geometry variables on exponent n. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae41fa0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 0, "chroma:document": "SPE-187038-MS\nFracture Closure Stress: Reexamining Field and Laboratory Experiments of\nFracture Closure Using Modern Interpretation Methodologies\nD. P. Craig, DFITpro.com; R. D. Barree, Barree & Assocs. LLC; N. R. Warpinski, Retired and T. A. Blasingame,\nTexas A&M University\nCopyright 2017, Society of Petroleum Engineers\nThis paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, USA, 9-11 October 2017.\nThis paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents\nof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect\nany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae42022-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 0, "chroma:document": "consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may\nnot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.\nAbstract\nDuring the 1990s, field and laboratory experiments measured hydraulic fracture creation, propagation,\nand closure, and the archived data represent the finest collection of measurements that can be used to\nevaluate fracture models and fracture closure interpretation methodologies. None of the current fracture\nclosure interpretation methods, including G-function derivative analysis, log-log storage diagnostics, and\nthe changing-compliance method have been evaluated versus the field and laboratory measured data.\nRecent papers have proposed fracture closure pressure interpretations that differ from established\nmethodologies, and under some circumstances, will result in a closure pressure that is higher than"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae420a4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 0, "chroma:document": "traditionally accepted. Thus, it seems an opportune time to reexamine the field and laboratory fracture\nclosure data using interpretation methodologies developed over the last twenty years.\nAdditional issues cloud closure pressure interpretations, including different definitions of fracture closure\nused in numerous publications, like mechanical fracture closure, hydraulic fracture closure, progressive\nfracture closure, and complete fracture closure. Evidence from downhole tiltmeters and finely-instrumented\nlaboratory experiments of fracture propagation and closure all demonstrate that residual width is retained\nafter closure. Consequently, closure is somewhat of a misnomer, and if a \"closed\" fracture remains open,\nthe relationship between what we interpret as fracture closure and the minimum horizontal stress needs to\nbe clearly defined based on measurements as opposed to simulation.\nBased on field tiltmeter deformation and pressure measurements in hard rock formations, we find that"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4214e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 0, "chroma:document": "G-function derivative analysis and the log-log storage diagnostic plot interpretations together provide a\nfracture closure pressure that is consistent with the minimum horizontal stress identified using tiltmeter-\nmeasured rock deformation. Additionally, the closure pressure interpretations, and corresponding minimum\nhorizontal stress, are invariant over multiple injection/falloff sequences of varying volume and time.\nField experiments exhibiting variable-storage/changing-compliance signatures were also observed, and the\nchanging-compliance method interpretations of fracture closure pressure are inconsistent with tiltmeter-\nmeasured rock deformation. Finally, we find the fracture re-opening pressure identified using tiltmeter\ndeformation and the fracture closure pressure interpreted using pressure falloff data are essentially equal."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae421c6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 1, "chroma:document": "2 SPE-187038-MS\nBased on laboratory measurements of fracture closure and pressure, we find that G-function derivative\nanalysis and the log-log storage diagnostic plot together provide a fracture closure interpretation generally\nconsistent with measured fracture closure, but despite attempts to define an objective closure identification\nmethodology, fracture closure signatures are often non-distinct and interpretations are subjective. In soft\nrock reservoirs, like unconsolidated sand, the fracture closure pressure interpretation does not correspond\nto the minimum horizontal stress, but in hard rock reservoirs, the fracture closure pressure identified using\nG-function derivative analysis and log-log storage diagnostic interpretations are approximately equal to the\nimposed minimum horizontal stress.\nIntroduction\nHydraulic fracture closure has been studied for decades by researchers inside and outside of the petroleum"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae42248-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 1, "chroma:document": "industry. Even after decades of study, opinions vary widely with respect to the fracture closure process,\nthe identification of fracture closure pressure, and the relationship between hydraulic fracture closure\npressure and the minimum horizontal stress. Hydraulic fracture closure pressure is typically inferred from\npressure data during fracture initiation, re-opening, or falloff. While we recognize small-volume stress tests,\nfracture step-rate tests, fracture-injection/flow back tests, and fracture pulse tests are all used to infer closure\npressure, we focus our study on fracture closure interpretations from the analysis of pressure and time data\nduring a fracture-injection/falloff test (DFIT).\nNumerous models and methods exist for identifying fracture closure pressure from pressure versus time\ndata recorded during injection/falloff sequences. In geophysics and rock engineering, Hayashi and Haimson\n(1991) provided a summary of commonly-used methods outside of petroleum engineering, and the authors"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae422c0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 1, "chroma:document": "described a fracture closure process based on observations of laboratory fracture closure experiments.\nHayashi and Haimson suggested a 3-stage fracture closure process during the shut-in period following a\nfracture inducing or dilating injection. Stage 1 of the process begins at the end of fracture-tip extension after\nshut-in and as aperture along the entire fracture half-length decreases. According to Hayashi and Haimson,\nfracture closure begins at the fracture tip, which defines Stage 2 of the closure process, and continues as the\nopen width and fracture length decrease from the fracture tip back to the wellbore. Stage 3 of the process is\ndefined by \"complete\" closure of the hydraulic fracture, where complete closure allows for the possibility of\nresidual fracture width. Hayashi and Haimson define the pressure observed at fracture-tip closure (Stage 2)\nas the minimum horizontal stress. Although Hayashi and Haimson based their model on observed field and"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae42338-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 1, "chroma:document": "laboratory closure data, they did not present fracture dimensions during closure to validate their proposed\nfracture closure process.\nSeveral derivative works have followed from the work of Hayashi and Haimson (1991), notably Raaen,\nSkomedal, Kj\u00f8rholt, Markstead, and \u00d8kland (2001) who recognized that a change in fracture compliance\nshould be observed as fracture closure begins at the fracture tip, and suggested a fracture-injection/flow\nback test and interpretation methodology to identify closure pressure from a change in fracture compliance.\nMcClure, Jung, Cramer, and Sharma (2015) extended the work of Raaen et al., and using simulations\nof synthetic cases and interpretations of field data, described a changing fracture-compliance method for\nidentifying fracture closure from pressure falloff data in the absence of flow back. Recently, Zanganeh,\nClarkson, and Hawkes (2017) have suggested a fracture closure process and closure pressure identification"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae423ba-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 1, "chroma:document": "analogous to that of Hayashi and Haimson (1991). Zanganeh, Clarkson, and Hawkes also suggest that the\nfracture closure pressure corresponding to the minimum horizontal stress is observed at the start of tip\nclosure, and base their conclusions on finite-element modeling of synthetic cases and interpretations of\nfield data.\nClassical fracture closure pressure interpretation methods include plotting the shut-in pressure and\npressure derivative versus the square root of time, which have been described by Middlebrook, Aud,\nHarkrider, and Hansen (1997). Perhaps the best known fracture closure pressure interpretation methodology"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae42432-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 2, "chroma:document": "SPE-187038-MS 3\nis G-function analysis, which was initially presented by Nolte (1979), and expanded to include G-function\nderivative analysis by Castillo (1987) and Barree and Mukherjee (1996). A \"holistic\" approach to fracture\nclosure interpretation that included a square-root of time plot, G-function derivative analysis, and a log-log\nstorage diagnostic plot was also presented by Barree, Barree, and Craig (2009). We assume for the purposes\nof this research that the de facto standard for closure pressure interpretation from fracture-injection/falloff\ndata is G-function derivative analysis combined with the log-log storage diagnostic plot.\nThe G-function is defined as follows\n(1)\nwhere the dimensionless loss-volume function at the end of pumping is defined by Valk\u00f3 and Economides\n(1999) as\n(2)\nand \u03b1N is Nolte's power-model growth exponent (\u00bd \u2264 \u03b1N \u2264 1) and \u0393 is the Euler gamma function. The\ndimensionless loss-volume function is defined at any time after the end of pumping and written as\n(3)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae424b4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 2, "chroma:document": "(3)\nwhere F is the hypergeometric function, dimensionless time is defined as \u0394tD = (t \u2013 te)/te, and te is the time\nat the end of pumping.\nClosure Interpretation and Leakoff Types\nG-function derivative analysis requires a Cartesian plot of three curves: bottomhole pressure versus the G-\nfunction; the derivative, dp w/dG, versus the G-function, and the derivative, Gdp w/dG, versus the G-function.\nG-function derivative analysis can be used to identify hydraulic fracture closure and has been classically\nused to identify several non-ideal leakoff types, including pressure-dependent leakoff, fracture-height\nrecession/transverse or variable storage, and fracture tip extension. Examples of the leakoff types commonly\nobserved have been provided by Barree, Barree, and Craig (2009) and Craig, Eberhard, and Barree (2000).\nFig. 1 contains graphs of the four common leakoff types and has been updated from that of Craig, Eberhard,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae42536-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 2, "chroma:document": "and Barree to include variable storage/changing compliance. A brief review of the classical leakoff types\nis as follows.\nNormal leakoff  behavior occurs when fracture area is constant during shut-in and leakoff is through\na homogeneous rock matrix. With G-function derivative analysis, normal leakoff is indicated by a\nconstant derivative and when the derivative Gdp w/dG lies on a straight line extending from the origin.\nFracture closure is identified when the Gdp w/dG data deviate downward from the straight line.\nPressure-dependent leakoff  from dilated fractures/fissures is indicated by a characteristic \"hump\" in\nthe Gdp w/dG derivative that lies above an extrapolated straight line from the origin through the normal\nleakoff data. The fissure opening pressure is identified at the end of the hump when the Gdp w/dG\nderivative data begin to follow the extrapolated straight line. A period of normal leakoff behavior"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae425ae-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 2, "chroma:document": "is generally observed before fracture closure is identified when the Gdp w/dG derivative data deviate\ndownward from the extrapolated straight line.\nFracture height recession or transverse storage or variable storage or changing compliance  during\nshut-in are indicated by G-function derivative analysis when the Gdp w/dG derivative data fall below\na straight line extrapolated through the normal leakoff data. Traditionally, hydraulic fracture closure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae42630-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 3, "chroma:document": "4 SPE-187038-MS\nis identified when the Gdp w/dG derivative data deviate downward from the straight line; however,\nMcClure, Jung, Cramer, and Sharma (2015) argue that fracture closure should be identified as the\npressure corresponding to the beginning of variable storage or changing compliance. Storage and\ncompliance are related to system stiffness by a reciprocal relationship. For example, Craig and\nBlasingame (2005, 2006) and Craig (2014) define storage during fracture propagation and closure as\n(4)\nwhere C is the storage coefficient, cw is the wellbore-fluid compressibility, cf is fracture-fluid\ncompressibility, Vw is the volume of the wellbore, Vf is the volume of one wing of the fracture, Af is\nthe area of one wing of the fracture, and Sf is the fracture stiffness, which can be written in a general\nform for 2D-analytical expressions of fracture stiffness as\n(5)\nwhere c is constant, E' is the plane-strain modulus, and Lc is a characteristic length. McClure, Jung,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae426b2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 3, "chroma:document": "Cramer, and Sharma (2015) frame their discussion of closure around system stiffness, which is the\nreciprocal of storage, that is, using the definitions of storage in Eq. 4, system stiffness is defined as\n(6)\nwhere Seff is a system stiffness. In another recent work, van den Hoek (2016) frames his discussion\nof fracture closure in terms of total compliance, which using the definitions in Eq. 4, he defines as\n(7)\nwhere Ct is a system compliance and Cf is a time-dependent fracture compliance, which van den\nHoek defined as\n(8)\nwhere h is the fracture height, L is the fracture half length, and E(m) is complete elliptical integral. van\nden Hoek (2016) provided an interesting modification in that he allowed a time-dependent fracture\ncompliance during the falloff. In other words, van den Hoek's solution, which was formulated based\non laboratory experiments of fracture closure, explicitly allows fracture height and or length recession\nbefore hydraulic fracture closure is observed."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae42734-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 3, "chroma:document": "before hydraulic fracture closure is observed.\nIt should be clear that discussions of variable storage, effective stiffness, and changing total\ncompliance all refer to the same phenomena during a fracture-injection/falloff sequence. In Fig.\n1, the graph labeled \"Fracture Height Recession/Transverse or Variable Storage\" illustrates the\nGdp w/dG derivative response during the closure process with variable storage, compliance, or"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae427c0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 4, "chroma:document": "SPE-187038-MS 5\nstiffness. Additionally, the figure illustrates the different interpretations of fracture closure based\non the changing fracture compliance method or the classical Gdp w/dG derivative interpretation\u2014a\ndifference of about 500 psi between the two interpretations in the Fig. 1 example.\nFracture tip extension , which occurs when a fracture continues to grow after injection is stopped, is\nindicated when the Gdp w/dG derivative data lie along a straight line that extrapolates above the origin.\nFigure 1\u2014Classical G-function derivative analysis qualitative interpretations.\nAs noted, Fig. 1 shows the traditional interpretation of leakoff types during a falloff, but other effects\ncan result in a non-linear Gdp w/dG derivative response. Barree and Miskimins (2016) summarized several\nadditional possibilities to explain Gdp w/dG derivative deviation from a \u2018normal\u2019 leakoff signature, and\nin some cases, the root cause of the Gdp w/dG derivative deviation from normal leakoff may be either"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae42842-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 4, "chroma:document": "unknown or ambiguous. Additionally, combinations of the above leakoff-types can be observed in some data\nsets. Fracture-injection/falloff tests conducted at the toe of horizontal wells predominately exhibit variable\nstorage or changing compliance during the falloff, so the correct fracture closure interpretation is important\nfor determining a representative minimum horizontal stress.\nThe holistic analysis method (Barree, Barree, and Craig 2009) also requires a log-log plot of the derivative\ntd[p e \u2013 pw(t)]/dt plotted versus time, t, which we refer to here as the log-log storage diagnostic. Craig (2014)\nhas proved that the derivative td[p e \u2013 pw(t)]/dt is related to a constant-rate pressure transient solution as\nfollows.\n(9)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae428c4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 5, "chroma:document": "6 SPE-187038-MS\nwhere pi is the initial reservoir pressure, pwsD is the slug-test pressure difference, and dimensionless pressure,\ndimensionless time, and the dimensionless storage coefficient are defined as\n(10)\n(11)\n(12)\nThe fracture closure process is a storage phenomenon, so storage consists of both wellbore and\nfracture storage components. In general, an observed deviation of the Gdp w/dG derivative off of the\nextrapolated straight line, for example, pressure-dependent leakoff, will result in an observed deviation of\nthe td[p e \u2013 pw(t)]/dt derivative on the log-log storage diagnostic plot, which signals a change in fracture\nstorage. Additionally, the deviation of the Gdp w/dG derivative identified as fracture closure coincides with\ndissipation of storage distortion of the pressure falloff data identified by the log-log storage diagnostic in\nsoft and hard rock types.\nThe above discussion of the fracture closure process and fracture closure identification are all based"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae42950-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 5, "chroma:document": "on analytical or numerical models, and although the models are based on fundamental physics and sound\nprinciples, their validation is often based on interpretation, which can be ambiguous. Both laboratory\nand field experiments of hydraulic fracture propagation and closure have been completed over the last\ntwo decades; however, the results of fracture closure models have not been routinely tested against the\nexperimental observation.\nAnalysis and Interpretation of Data\nWe examined both field and laboratory data with the intent of validating fracture closure interpretation\nmodels and methodologies with known or carefully measured results. The field data include virtually all\nthe time, rate, pressure, and deformation measurements from the M-Site project that has been summarized\nby Peterson, et al (1996) and Warpinski, et al (1998). We recognize that we are not the first to analyze\nall, or portions, of the M-Site field measurements. The original interpretations relied on fracture closure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae429dc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 5, "chroma:document": "identification methods that preceded the development of G-function derivative analysis and the log-log\nstorage diagnostics; consequently, the original interpretations were often inconsistent between data sets and\nanalysts. Subsequent analysis of the M-Site field data, for example, the study presented by Gulrajani, Nolte,\nand Romero (2001), also noted inconsistent interpretations of the multiple data sets, which the authors\nrationalized was caused by repeated injections of increasing volume connecting higher-stress reservoir rock\nto the wellbore.\nOur intent is to provide a consistent interpretation of all relevant time, rate, pressure, and deformation\ndata recorded at the M-Site. Additionally, our objective is to use the downhole tiltmeter fracture re-opening\nand fracture closing deformation measurements to define the minimum horizontal stress. With the minimum\nhorizontal stress defined independently, we then compare fracture closure pressure interpretations from the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae42f2c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 5, "chroma:document": "different methodologies to validate a closure model.\nMany laboratory experiments have also been completed of hydraulic fracture creation, propagation, and\nclosure. We use publicly-available laboratory data, where the minimum horizontal stress is experimentally\nimposed, to compare fracture closure pressure interpretations with the known solution to validate a closure\nmodel. Additionally, some publicly available data includes measurements of fracture dimensions that were\nrecorded during closure, so the effect of changing storage (or changing compliance) can be evaluated with\nrespect to the fracture closure interpretations. Finally, we include a never-published laboratory experiment"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4304e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 6, "chroma:document": "SPE-187038-MS 7\nwhere the minimum horizontal stress is experimentally imposed, and a blind test is used to compare the\ninterpreted fracture closure pressure to the known minimum horizontal stress.\nField Experiments of Fracture Closure\nPerhaps the most comprehensive, best-documented, and publicly available field data set of fracture closure\nwas recorded at the M-Site in the mid-1990s. While the scope of the M-Site project was much more\ncomprehensive than simply fracture closure determination, two separate hard rock, tight-gas sandstone\nformations were tested during the field experiments, and the results provide insight into the fracture\nclosure process and fracture closure pressure determination. Experiments in both sands included multiple\ninjections of varying injection volume, injection rate, falloff time, flow back periods, time between\ninjections, and observations of hydraulic fracture closure. Many injections were monitored by downhole"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae430e4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 6, "chroma:document": "tiltmeters cemented in place in an offset wellbore along with microseismic imaging of fracture propagation\nfrom two arrays in adjacent wellbores. Fig. 2 shows a plan view of the surface location of the M-Site\nwells. The Monitor Well shown in Fig. 2 held six tiltmeters and a microseismic array cemented in place\nwhile a wireline-run microseismic array monitored events from MWX-3. Fig. 3 contains the location and\norientation of the tiltmeters in the Monitor Well along with the location of the triaxial seismic receivers\nwith respect to the B-Sand and C-Sand in the MWX-2 treatment well. Within Fig. 3, the measurement-\naxis orientation is shown for each tiltmeter, and for all tiltmeters the y-axis is essentially normal to the\nprimary fracture orientation in the treatment well, which is shown in Fig. 2. With the tiltmeter y-axes\nessentially normal to the primary fracture plane, the tiltmeters have proven to be extremely sensitive"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43238-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 6, "chroma:document": "to the rock deformation resulting from small fracture-width changes in the treatment well. Additionally,\nthe deformation and tiltmeter response is virtually immediate with respect to rate or pressure changes in\nthe treatment well once the treating pressure exceeds the minimum horizontal stress. Additional M-Site\nwellbore configuration, experimental measurements, and experimental procedures have been exhaustively\ndocumented by numerous authors, including Warpinski et al (1995, 1996, 1997, 1998), Peterson, et al\n(1996), and Branagan, et al (1996a, 1996b, 1997a, 1997b).\nFigure 2\u2014Plan view of M-Site, including locations of treatment well\n(MWX-2) and Monitor Well (downhole tiltmeters). After Branagan, et al. 1996."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae432d8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 7, "chroma:document": "8 SPE-187038-MS\nFigure 3\u2014Tiltmeter placement within Monitor Well, and tiltmeter axis orientation. After Branagan et al. (1996).\nFor the purposes of this paper, the pressure, rate, and time data recorded during the injection/falloff\nsequences are interpreted using G-function derivative analysis and the log-log storage diagnostic plot\nto infer hydraulic fracture closure, and where relevant tiltmeter measurements are available, closure-\nstress interpretations are compared with tiltmeter-measured rock deformation. As noted, the downhole\ntiltmeters are extremely sensitive to deformation created by an opening or closing fracture; thus, the tiltmeter\nmeasurements provide the best direct indication of hydraulic fracture width changes in field experiments.\nInjection/falloff sequences were completed in both the B-sand and the C-sand. In the B-sand, a total of\n10 injection/falloff, or injection/falloff/flowback, sequences were recorded over a period of nine months"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4335a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 7, "chroma:document": "with different fluid types, volumes, injection rates, falloff period, and flowback period. The first three\ninjection/falloff sequences were three small volume and low rate classical stress tests to establish an\nestimated minimum horizontal stress. In the C-sand, a total of 8 injection/falloff, or injection/falloff/\nflowback, sequences were recorded with different fluid types, volumes, injection rates, falloff period, and\nflowback period. No small-volume stress tests were pumped in the C-sand in the MWX-2 wellbore.\nFracture re-opening experiments were pumped in both the B-Sand (Injection 4B) and the C-Sand\n(Injection 4C). Prior injections in both sands had created and propagated a hydraulic fracture, so the re-\nopening experiments were pumped at very low rates to observe the dilation of an existing fracture, which\nwould be indicated by the rock deformation measured by the tiltmeters. As previously noted, an existing"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae433d2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 7, "chroma:document": "fracture should dilate (open) as the pressure within the fracture exceeds the minimum horizontal stress.\nConversely, an existing fracture should contract (close) during a falloff to a residual-width. In hard rock (E\n> 1.8 \u00d7 106 psi [12.5 GPa]), the pressure observed at fracture closure (residual width) corresponds to the\nminimum horizontal stress. Thus, in both the B-Sand ( E = 4.57 \u00d7 106 psi [31.5 GPa]) and C-Sand (E = 5.25"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43454-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 8, "chroma:document": "SPE-187038-MS 9\n\u00d7 106 psi [36.2 GPa]) fracture re-opening and fracture closure should occur at the same pressure, which is\nequivalent to the minimum horizontal stress (within experimental error). In soft rock (E < 7.25 \u00d7 105 psi [5.0\nGPa]), which includes unconsolidated sand formations, fracture closure to a residual width can be observed\nat a pressure below the minimum horizontal stress (Dong and de Pater 2007).\nB-Sand Stress Tests and Fracture Closure Experiments\nB-Sand experiments at the M-Site began with three stress tests in November 1994. Fig. 4 shows graphs\nfor each of the three stress tests, which are labeled within each graph \"Stress Test #1,\" \"Stress Test #2,\"\nand \"Stress Test #3.\" For each injection/falloff sequence, Fig. 4 shows graphs of bottomhole pressure and\ninjection rate versus time; bottomhole pressure, the derivative of bottomhole pressure with respect to the G-\nfunction, dp w/dG, and the product of the G-function and the derivative of bottomhole pressure with respect"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae434d6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 8, "chroma:document": "to the G-function, Gdp w/dG, plotted versus the G-function during the shut-in period; and a log-log storage\ndiagnostic graph of the fracture-pressure difference, pe \u2013 pw(t), and the product of time and the derivative of\nthe fracture-pressure difference with respect to time, td[p e \u2013 pw(t)]/dt, plotted versus time since the beginning\nof the injection.\nFigure 4\u2014MWX-2 stress tests recorded in November 1994."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43580-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 9, "chroma:document": "10 SPE-187038-MS\nStress Test #1 was a very small injection of 41-gal of water pumped at injection rates of less than 20\ngal/min. For Stress Test #1 the 1994 interpretation of closure of (p c)1994 = 3,020 psi is shown along with\na new interpretation of the fissure-opening pressure, (p fis)2017 = 2,941 psi, and fracture closure pressure,\n(pc)2017 = 2,886 psi using G-function derivative analysis. The log-log storage diagnostic graph shows that\nthe fracture closure time interpreted using G-function derivative analysis corresponds to the dissipation of\nstorage distortion of the pressure falloff data.\nStress Test #2 was a slightly larger injection of 47-gal of water pumped at injection rates of less than 20\ngal/min. For Stress Test #2, the new interpretation includes a fissure opening pressure of ( pfis)2017 = 2,915\npsi, and hydraulic fracture closure pressure of (p c)2017 = 2,893 psi.\nStress Test #3 was again a slightly larger injection of 51-gal of water pumped at injection rates of less"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae435f8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 9, "chroma:document": "than 20-gal/min, but the test included a step-down in injection rates. G-function derivative analysis shows a\nfissure-opening pressure, (p fis)2017 = 2,960 psi, but the final recorded pressure during the falloff was ( pw)final\n= 2,938 psi, and G-function derivative analysis confirms that hydraulic fracture closure was not observed,\nwhich is indicated by the increasing Gdp w/dG derivative through the end of the recorded pressure data. The\nlog-log storage diagnostic also demonstrates that the end of storage distortion was not observed during the\nrecorded falloff, which is also indicated by the increasing derivative, td[p e \u2013 p w(t)]/dt.\nAfter a 19-bbl borate crosslinked-gel injection (Injection 1C) was completed, the fracture diagnostics\ncontinued with Injection 2B, Injection 3B, and Injection 4B, and the fracture closure diagnostic graphs are\nshown in Fig. 5 with each injection/falloff sequence labeled \"Injection 2B,\" \"Injection 3B,\" and \"Injection"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43670-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 9, "chroma:document": "4B,\" respectively. Injection 2B consisted of 27.1 bbl of 2% KCl-treated water injected in step rates up\nto 3.3 bbl/min. There are several important features of Injection 2B to note. First, the step-rate injection\ncan theoretically be used to interpret fracture closure pressure from a graph of bottomhole pressure versus\ninjection rate; however, close examination of the bottomhole pressure and injection rate versus time graph\nfor Injection 2B clearly shows the pressure response was not smooth or constant at the lowest injection rate\nof 0.5-bbl/min; consequently, an interpretation of the fracture closure stress from the step-rate pressure data,\nlike that presented by Gulrajani, Nolte, and Romero (2001), is highly questionable."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae436e8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 10, "chroma:document": "SPE-187038-MS 11\nFigure 5\u2014MWX-2 Injections 2B (27 bbl), 3B (104 bbl), 4B (215 bbl) April 1995.\nSecond, the G-function derivative analysis graph clearly shows the \"sudden\" appearance of variable\nstorage or changing compliance during the falloff, which was not observed in any of the stress tests recorded\nbefore the crosslinked-gel Injection 1B. The fracture-compliance method interpretation suggests a fracture\nclosure pressure of (p c)\u0394Cbc = 3,208 psi, where the subscript \u2018\u0394Cbc\u2019 denotes variable storage/compliance\nbefore closure. Since the final recorded pressure before beginning flow back was ( pw)final = 2,893 psi, fracture\nclosure was not observed during the falloff based G-function derivative analysis. Additionally, the log-\nlog storage diagnostic clearly shows storage distortion is observed through the end of the recorded falloff\ndata; thus, hydraulic fracture closure was also not observed during the falloff based on the log-log storage\ndiagnostic."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43760-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 10, "chroma:document": "diagnostic.\nInjection 3B was a 104-bbl injection of 2% KCl-treated water, which except for a brief shut-down early\nin the test, was injected at a constant rate. The bottomhole pressure and injection rate versus time plot shows\nthe final recorded pressure during the falloff was (p w)final = 2,972 psi. The G-function derivative analysis\ngraph once again suggests variable storage/changing compliance was observed during the falloff. Using the\nfracture-compliance method, the fracture closure is (p c)\u0394Cbc = 3,308 psi. Fracture closure was not observed"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae437d8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 11, "chroma:document": "12 SPE-187038-MS\nbased on G-function derivative analysis as indicated by the increasing derivative, Gdp w/dG, and based on the\nlog-log storage diagnostic plot, which shows an increasing derivative, td[p e \u2013 pw(t)]/dt, and corresponding\nstorage distortion of the pressure falloff.\nInjection 4B was a 214.7 bbl injection of 2% KCl-treated water with a brief shut-down during the\ninjection, but with a hydraulic fracture re-opening experiment included at the beginning of the injection.\nAs was observed in Injection 2B and Injection 3B, the G-function derivative analysis plot shows a strong\nindication of variable storage/changing compliance, and the fracture-compliance method closure pressure is\n(pc)\u0394Cbc = 3,330 psi. Conversely, fracture closure was not observed based on G-function derivative analysis\nand the log-log storage diagnostic plots, which both show increasing derivatives, Gdp w/dG and td[p e \u2013 pw(t)]/\ndt, respectively, through the end of the falloff data."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4385a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 11, "chroma:document": "dt, respectively, through the end of the falloff data.\nAlthough the low-volume stress tests should have established a fracture closure pressure corresponding\nto the minimum horizontal stress, the test analyses remain pressure interpretations of fracture closure and\nare not a direct observation of closure. The tiltmeters, however, are a measurement of rock deformation\nas a function of increasing hydraulic fracture width. Consequently, a re-opening experiment where 2%\nKCl-treated water is slowly injected into an existing fracture, and the pressure gradually increases, should\nindicate measurable rock deformation as the pressure within the fracture exceeds the minimum horizontal\nstress (closure pressure) and the hydraulic fracture dilates.\nFig. 6 contains plots of bottomhole pressure and y-axis deformation of the tiltmeters at 4,628-ft (below\nthe B-Sand), 4,558-ft (within the B-Sand), 4,487-ft (above the B-Sand). In each figure, the tiltmeter"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae438dc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 11, "chroma:document": "measurements are essentially constant before the injection begins and as pressure starts to increase. As\nbottomhole pressure exceeds approximately 2,800 psi, deformation is observed in every tiltmeter. The\ntiltmeter measurements suggest existing-fracture dilation begins at approximately (p c)ReOpen  \u2248 2,800 psi,\nwhich may be the fracture opening pressure corresponding to the minimum horizontal stress. Each figure\nshows a vertical red dashed line that corresponds to the fracture closure pressure interpreted from the stress-\ntest data, 2,855 psi \u2264 (p c)2017 \u2264 2,893 psi and the black dashed line corresponds to the fracture closure stress\ninterpreted using the fracture-compliance method, which is 3,208 psi \u2264 (p c)\u0394Cbc \u2264 3,330 psi.\nFigure 6\u2014MWX-2 B-Sand Injection 4B re-opening experiment tiltmeters identifying deformation and fracture opening.\nUnfortunately, tiltmeter re-opening experiments also have uncertainty, for example, if the re-opening"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4394a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 11, "chroma:document": "injection rate is too high, deformation may be observed before reopening. The tiltmeter measurements\nare, however, consistent with the fracture closure pressure interpreted from G-function derivative analysis\nand log-log storage diagnostic. Additionally, the tiltmeter measurements seem to validate that the fracture\nclosure pressure interpretations based on identifying the dissipation of storage distortion correspond to the\nminimum horizontal stress. Conversely, the tiltmeter measurements are inconsistent with the findings of the\nfracture-compliance method for closure identification, that is, the fracture-compliance method interpreted\nclosure pressure may not correspond to the minimum horizontal stress. Fig. 6 does show a significant"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae439c2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 12, "chroma:document": "SPE-187038-MS 13\nincrease in deformation as the pressure exceeds approximately 3,100 psi, but the initial deformation is\nobserved as bottomhole pressure increases above approximately (p c)ReOpen  \u2248 2,800 psi.\nInjections 5B and 6B were both 400-bbl 40-lb/1,000-gal linear gel injections, and the pressure falloff did\nnot extend through hydraulic fracture closure for either injection/falloff sequence. Injection 7B consisted\nof the final KCl-treated water injection/falloff in the B-Sand, and the falloff did extend through hydraulic\nfracture closure. Fig. 7 shows the Injection 7B diagnostic plots, and the bottomhole pressure and injection\nrate versus time graph show that the injection consisted of 30.5-bbl of 2% KCl treated water at injection\nrates up to 19 bbl/min. Unlike Injection 2B, Injection 3B, and Injection 4B, but like the three stress tests, the\nleakoff-off type identified using G-function derivative analysis is pressure-dependent leakoff with a fissure-"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43a30-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 12, "chroma:document": "opening pressure of (p fis)2017 = 2,893 psi. G-function derivative analysis shows no indication of variable\nstorage/changing compliance, but it does indicate fracture closure was observed at ( pc)2017 = 2,855 psi, which\nis consistent with the three stress tests and validated by the tiltmeter measurements from the Injection 4B re-\nopening experiment. The log-log storage diagnostic also shows storage distortion dissipates as the fracture\ncloses, which is indicated by the decreasing derivative td[p e \u2013 p w(t)]/dt, after closure.\nFigure 7\u2014MWX-2 B-Sand Injection 7B -- 31 bbl KCl water prefrac DFIT August 1995.\nThe tiltmeter measurements during the re-opening experiment provided a clear indication of hydraulic\nfracture re-opening and dilation during the injection, but the measurements are not as definitive during\nclosure. For example, Fig. 8 contains a graph of bottomhole pressure and tiltmeter deformation recorded"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43aa8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 12, "chroma:document": "during the pressure falloff for the tiltmeter located at 4,487-ft (above the B-Sand). Notice that as bottomhole\npressure falls below the re-opening pressure and falloff-interpreted fracture closure pressure, the tiltmeter\nmeasurements continue to show decreasing deformation, which suggests fracture width continues to\ndecrease. Examination of the tiltmeter measurements also shows that the data are relatively noisy; however,\nthe shape of the tiltmeter-measured deformation curve is similar to the pressure falloff curve, and the\ntiltmeter-measured deformation might follow relationships known to exist for fracture pressure falloff data."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43b2a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 13, "chroma:document": "14 SPE-187038-MS\nFigure 8\u2014MWX-2 B-Sand Injection 7B bottomhole pressure and tiltmeter (4,487 ft) falloff during shut-in.\nAs previously noted, Craig (2014) demonstrated that the derivative, td[p e \u2013 pw(t)]/dt, is related to a general\npressure transient solution as follows.\n(13)\nGenerally, an analytical solution for a fractured well is used to generate the pressure transient derivative,\nand the observed DFIT data are matched to an appropriate solution. The method is general, and any\nappropriate transient solution, including flow from an infinite- or finite-conductivity fracture, dual porosity\nreservoir, anisotropic reservoir, multiple producing fractures, etc., can be used in the matching process. For\nthe purposes of the current paper, it's important to note the behavior of the pressure-transient derivative,\nwhich is shown in Fig. 9. In Fig. 9, the increasing derivative is indicative of wellbore and fracture storage"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43bac-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 13, "chroma:document": "distortion. Wellbore and fracture storage distortion dissipates as the curve reaches the apex and begins to\nfall. A closing fracture is a type of storage ( Craig and Blasingame 2005, 2006), and in most cases, fracture\nstorage affects the falloff data long after wellbore storage has dissipated. Thus, when the derivative, td[p e\n\u2013 p w(t)]/dt, is increasing, the fracture is still closing.\nFigure 9\u2014Pressure transient solution derivative versus dimensionless time."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43c24-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 14, "chroma:document": "SPE-187038-MS 15\nIn terms of the tiltmeter response, tiltmeter measurements peaked at the end of pumping, that is, the\nhydraulic fracture maximum width was observed at the end of pumping and pressure pe. Since tiltmeter\ndeformation is proportional to the fracture width, and the fracture width changes over time are a function\nof pressure, it's anticipated that the tiltmeter deformation-difference derivative, td[(u y)e \u2013 uy (t)]/dt, curve\nshould mirror the fracture pressure-difference derivative curve. In other words, we postulate that in a\nhomogeneous reservoir with normal leakoff, the tiltmeter deformation-difference derivative, td[(u y)e \u2013 uy(t)]/\ndt, will increase through hydraulic fracture closure. Similarly, if pressure-dependent leakoff is observed,\nthe tiltmeter deformation-difference derivative should show a positive \"hump,\" like the fracture pressure-\ndifference derivative.\nOne issue, however, in attempting derivative analysis of tiltmeter data is the noise noted in Fig. 8. If finite-"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43c9c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 14, "chroma:document": "difference differentiation of the noisy tiltmeter data is attempted, the noise will be amplified by the derivative\ncalculation, and the derivative may be of limited value. An alternative technique for calculating a \"noiseless\"\nunderlying derivative of noisy experimental data was developed by Chartrand (2011) and is called total\nvariation regularization. Fig. 10 illustrates the derivative calculation of the tiltmeter measurements (4,487\nft) using both \"smoothed\" central-difference calculations and total variation regularization. With a smooth\nderivative calculation, the tiltmeter deformation-difference derivative, td[(u y)e \u2013 uy (t)]/dt, should show\ntrends similar to the fracture pressure-difference derivative, td[p e \u2013 p w(t)]/dt.\nFigure 10\u2014MWX-2 B-Sand Injection 7B tiltmeter du y/dt derivative\ncalculated with central-difference and total variation regularization.\nFig. 11 shows a log-log graph of the tiltmeter deformation-difference derivative versus time since the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43d14-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 14, "chroma:document": "beginning of pumping for the tiltmeters at 4,487-ft (above B-Sand), 4,558-ft (within B-Sand), and 4,628-\nft (below B-Sand). All three tiltmeter derivative curves have a similar behavior that includes a pressure-\ndependent leakoff \"hump\" followed by an increasing derivative until fracture closure is observed. Fig. 11\nalso contains a log-log plot of both the fracture pressure-difference derivative and the tiltmeter deformation-\ndifference derivative (4,558-ft within B-Sand), and shows how both exhibit a pressure dependent hump and\nan increasing derivative before hydraulic fracture closure is interpreted. Figs. 10 and 11 demonstrate that\na characteristic tiltmeter deformation-derivative signature was observed and is consistent with pressure-\ninferred hydraulic fracture closure. While the tiltmeter deformation-derivative curves may not provide an\neasily-identified and definitive closure event, the tiltmeter deformation-difference derivative interpretation"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43d8c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 14, "chroma:document": "along with the analog fracture pressure-difference derivative methodology provide convincing evidence of\nhydraulic fracture closure, and the closure pressure is consistent with the fracture re-opening and pressure-"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43e0e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 15, "chroma:document": "16 SPE-187038-MS\nfalloff inferred fracture closure pressure. To our knowledge, a relationship between the deformation-\ndifference derivative and the pressure-difference derivative has not been studied. The trends observed in the\ntiltmeter and pressure data suggest additional research is warranted to mathematically define a relationship\nif one exists.\nFigure 11\u2014Comparison of tiltmeter deformation-difference derivatives, td[(u y)e-uy(t)]/dt, and comparison of\ntiltmeter deformation-difference derivative (4,558 ft) with observed fracture pressure-difference derivative, td\u0394p/dt.\nFracture Re-Opening Experiment \u2013 C-Sand\nThe C-Sand is located between 4,303-ft and 4,390-ft in the MWX-2 wellbore, and the experiments of interest\nfor the present paper are Injection 3C and Injection 4C, which includes a fracture re-opening experiment.\nInjection 1C, like Injection 1B in the B-Sand, was a 95-bbl injection of 40-lb/1,000-gal borate-crosslinked"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43e86-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 15, "chroma:document": "gel, and Injection 2C was a 40-lb/1,000-gal linear gel injection. Injection 3C was a 247-bbl injection of\n40-lb/1,000-gal linear gel, with a significant falloff period; however, fracture closure cannot be interpreted\nfrom the falloff data using G-function derivative analysis and the log-log storage diagnostic plot.\nFig. 12 contains a graph of bottomhole pressure and injection rate versus time, the G-function derivative\nanalysis plot, and the log-log storage diagnostic graph. The graph of bottomhole pressure and injection rate\nversus time shows a maximum injection rate of 19-bbl/min and a falloff that was recorded through a final\nbottomhole pressure of (p w)final = 2,956 psi. G-function derivative analysis suggests fracture closure was not\nobserved through the end of the falloff, and the log-log storage diagnostic also shows an increasing fracture\npressure-difference derivative through the end of the falloff, which confirms storage was still distorting the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43efe-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 15, "chroma:document": "pressure falloff and suggests the fracture was still closing."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43f76-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 16, "chroma:document": "SPE-187038-MS 17\nFigure 12\u2014MWX-2 C-Sand Injection 3C DFIT Analysis.\nA fracture re-opening experiment was also conducted in the C-Sand, and Fig. 13 contains a graph of\nbottomhole pressure and injection rate during the re-opening. The injection rates were kept lower during\nre-opening as compared to the B-Sand re-opening experiment; thus, the tiltmeter re-opening deformation\nmeasurements may provide a more definitive fracture re-opening pressure. As shown in Fig. 13, the injection\nrates were maintained at generally less than 10-gal/min until fracture opening was observed. Fig. 14 contains\ngraphs of bottomhole pressure and tiltmeter deformation for the tiltmeters at 4,418-ft (below the C-Sand),\n4,348-ft (within the C-Sand), and 4,273-ft (above the C-Sand). Even with the noise in the tiltmeter-recorded\ndeformation, a fracture re-opening pressure of approximately (p c)ReOpen  \u2248 2,900 psi was observed. Pressure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae43ff8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 16, "chroma:document": "falloff analysis of the entire Injection 4C injection/falloff sequence is shown in Fig. 15. The final recorded\npressure during the falloff was (p w)final = 3,108 psi, which is clearly above the hydraulic fracture re-opening\nstress, and both G-function derivative analysis and the log-log storage diagnostic confirm that hydraulic\nfracture closure was not observed during the falloff, which is indicated by the increasing derivatives, Gdp w/\ndG and td[p e \u2013 p w(t)]/dt, respectively, through the end of the falloff data.\nFigure 13\u2014MWX-2 C-Sand Injection 4C Reopening Experiment."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4407a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 17, "chroma:document": "18 SPE-187038-MS\nFigure 14\u2014MWX-2 C-Sand Injection 4C Reopening Experiment.\nFigure 15\u2014MWX-2 C-Sand Injection 4C DFIT Analysis\nSummarizing the findings from both the B-Sand and C-Sand injection/falloff and fracture re-opening\nexperiments, we observed the following.\n\u2022Fracture re-opening experiments using bottomhole pressure and tiltmeter deformation\nmeasurements suggest a B-Sand fracture re-opening pressure of (p c)ReOpen  \u2248 2,800 psi and a C-Sand\nre-opening pressure of (p c)ReOpen  \u2248 2,900 psi.\n\u2022Fracture closure pressure interpretations using G-function derivative analysis and the log-log\nstorage diagnostic suggest a fracture closure pressure approximately equivalent to the fracture re-\nopening pressure. In the B-Sand, the falloff-interpreted closure pressure was 2,855 psi \u2264 ( pc)2017 \u2264\n2,893 psi. However, the C-Sand injection/falloff sequences did not allow bottomhole pressure to\ndecline below pw(t) = 2,956 psi, but we can confidently state that the falloff analysis in the C-Sand"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae440f2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 17, "chroma:document": "suggests a fracture closure pressure of (p c)C-Sand < 2,956 psi.\n\u2022Fracture closure pressure when interpreted using G-function derivative analysis and the log-\nlog storage diagnostic was invariant over multiple injection/falloff sequences, including different\nfluids, fluid volumes, and rates, and invariant over time.\n\u2022The fracture-compliance method interpretations of the G-function derivative, Gdp w/dG, in the B-\nSand injections suggested a fracture closure pressure of 3,208 psi \u2264 ( pc)\u0394Cbc \u2264 3,330 psi, which\nare inconsistent with the small-volume stress tests, holistic G-function derivative analysis, and the\nfracture re-opening experiments.\n\u2022Tiltmeter measurements during a pressure falloff do not exhibit an easily-identifiable and definitive\nclosure event."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44160-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 18, "chroma:document": "SPE-187038-MS 19\n\u2022Tiltmeter deformation-difference derivative curves are generally similar in shape and behavior to\nfracture pressure-difference derivatives; consequently, the deformation-difference derivative can\npotentially validate fracture closure and the end of storage distortion identified using G-function\nderivative analysis and the log-log storage diagnostic.\nLaboratory Experiments of Fracture Closure\nNumerous researchers have reported experiments of fracture propagation and closure under controlled\nlaboratory conditions. Cheung and Haimson (1989) looked at existing fracture closure interpretation\ntechniques, while also developing a new model of their own, for identifying fracture closure pressure\nfrom pressure falloff data. Their experimental method required multiple injection-falloff sequences with\nthe wellbore pressure falling to below 1 MPa before each subsequent injection, and their experiments"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae441ce-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 18, "chroma:document": "focused as much on identifying the fracture re-opening pressure as the fracture closure pressure. Fig. 16\ncontains a graph of pressure and the Gdp w/dG derivative for injection \u2018a\u2019 of Test #10 for a Niagara dolomite\n(E > 6.3 \u00d7 106 psi [43.7 GPa]) fracture closure experiment. Injection \u2018a\u2019 was the first fracture-injection/\nfalloff in the sample, and it was the only injection/falloff sequence with sufficient analyzable before-\nclosure data. For example, only about 10 seconds of before-closure pressure data are available for analysis\nin Fig. 16, which is barely sufficient to identify trends. The raw experimental data were not available;\nhowever, Cheung and Haimson's Fig. 2 was digitized using publicly-available software (Rohatgi 2017),\nwhich provided the pressure and time data required to construct Fig. 16. While digitizing historical publicly-\navailable experimental data is sometimes necessary (and worthwhile), there is inevitably a loss of resolution;"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44250-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 18, "chroma:document": "consequently, the data scatter shown in Fig. 16 may not have existed in the original raw pressure and time\nrecording.\nFigure 16\u2014Niagara Dolomite Test #10 Injection \u2018a\u2019. After Cheung and Haimson (1989).\nThe graph illustrates a clear \"hump\" in the Gdp w/dG derivative, which based on Fig. 1, is interpreted\nas pressure-dependent leakoff. de Pater et al (1994) have found pressure-dependent leakoff in laboratory\nfracturing experiments of moderately hard sandstone, so the result is anticipated even though the sample\ncontains no obvious natural fractures or fissures. The closure pressure is interpreted to be 13.2 MPa, which\nis within 12% of the imposed 15 MPa minimum horizontal stress. While the interpretation reasonable, it is\nnonunique because of limited before-closure data and a noisy Gdp w/dG derivative. With very few before-\nclosure data points, and since virtually all the before-closure data is affected by pressure-dependent leakoff,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae442c8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 18, "chroma:document": "the log-log storage diagnostic is of limited value for a fracture closure interpretation in this case."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44340-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 19, "chroma:document": "20 SPE-187038-MS\nWhen reviewing laboratory data, it is useful to have fracture dimensions measured during closure to help\ncorrelate the pressure falloff to measured fracture dimensions. While Cheung and Haimson reported acoustic\nemissions during closure, fracture dimensions during closure were not reported. de Pater, Desroches,\nGroenenboom, and Weijers (1996) presented measurements of both pressure falloff and fracture dimensions\nwith respect to time for both sandstone (E \u2245 3 \u00d7 106 psi [20.4 GPa]) and cement paste. Fig. 17 contains a\ngraph of pressure, dp w/dG, and Gdp w/dG versus the G-function and a graph of fracture width at the wellbore,\nfracture radius, and Gdp w/dG versus the G-function. The data were digitized from Fig. 3 and Fig. 10 of de\nPater, Desroches, Groenenboom, and Weijers (1996) for the sandstone sample.\nFigure 17\u2014G-function derivative analysis and fracture dimensions during closure for SNV03. After de Pater, et al (1996)."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae443b8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 19, "chroma:document": "G-function derivative analysis suggests fracture closure was not observed through the end of the recorded\npressure falloff data as indicated by the Gdp w/dG derivative following a straight line extrapolated from the\norigin. The imposed stress was 23 MPa, which coincides with the last recorded pressure. A definitive closure\nidentification using G-function derivative analysis would have required recording the pressure falloff below\n23 MPa; however, the Gdp w/dG derivative curve is consistent with the observed closure. In other words,\nclosure was not observed during the falloff, which is confirmed by the Gdp w/dG derivative curve.\nPressure-dependent leakoff is once again indicated during the falloff of the sandstone sample by the\nGdp w/dG derivative \"hump.\" Fig. 17 also shows that during the Gdp w/dG derivative pressure-dependent\nleakoff signature, both the fracture width and fracture radius were decreasing. As previously discussed, a"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4443a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 19, "chroma:document": "decreasing radius during the falloff increases fracture stiffness, which should result in decreasing storage\nand a changing compliance signature of the Gdp w/dG derivative, which is opposite of what is observed. In\nboth the Niagara dolomite and the Colton sandstone samples, any variable storage/changing compliance\nsignature that should be observed in the Gdp w/dG derivative, is masked by the pressure-dependent leakoff.\nThe fracture width change and radius change during closure confirm that the fracture was indeed closing\nfrom the fracture tip back to the wellbore, which is consistent with the closure process defined by Hayashi\nand Haimson (1991) and \"progressive fracture closure\" as defined Zanganeh, Clarkson, and Hawkes (2017).\nHowever, the experiment also clearly shows that the minimum horizontal stress is not equivalent to the\npressure at tip-closure. At fracture-tip closure, the experimental data show a pressure of about 30 MPa, but"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae444b2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 19, "chroma:document": "the imposed horizontal stress was only 23 MPa; thus, the conclusions of Zanganeh, Clarkson, and Hawkes\nare not supported by experimental data in a hard rock sample. In hard rock, a fracture closure pressure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44520-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 20, "chroma:document": "SPE-187038-MS 21\ncorresponding to the minimum horizontal stress is correctly identified by the traditional Gdp w/dG derivative\ninterpretation and the log-log storage diagnostic when the fracture closes to essentially the residual width\nat the wellbore.\nDong and de Pater (2007) presented a fracture closure experiment of a soft unconsolidated sand (E \u2245\n250,000 psi [1.7 GPa]), which makes a very interesting comparison with the hard-rock cases noted above.\nFig. 18 contains a graph of pw, dp w/dG, and Gdp w/dG versus the G-function along with a log-log graph of\nthe td[p e \u2013 pw(t)]/dt derivative versus time. A Gdp w/dG derivative interpretation suggests fracture closure\nis observed at G = 2.09 and a closure pressure of 3 MPa after periods of pressure-dependent and normal\nleakoff; however, the imposed stress during the experiment was 7 MPa. The td[p e \u2013 pw(t)]/dt derivative also\nshows the effects of pressure-dependent leakoff and fracture storage distortion until fracture closure was"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44598-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 20, "chroma:document": "observed. Fig. 19 is reproduced from Dong and de Pater (2007) and shows several CT scans of the hydraulic\nfracture during the pressure falloff. The CT scans shows that the fracture remains open with perhaps a small\ndecrease in aperture as the pressure declines below the imposed horizontal stress; however, it also shows\nthat the fracture closes as the pressure decreases to about 3 MPa. After the pressure falls below the imposed\nminimum horizontal stress, fracture closure begins at the tip and proceeds back to the wellbore until a\nresidual fracture width is observed. The CT scans graphically demonstrate that the Gdp w/dG derivative and\nthe log-log td[p e \u2013 pw(t)]/dt derivative accurately reflect fracture closure, that is, the methods can identify the\ndecrease to a residual fracture width and volume, but for soft rock, the closure pressure does not correspond\nto the minimum horizontal stress.\nFigure 18\u2014Soft unconsolidated sand closure experiment CTC08. After Dong and de Pater 2007."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44624-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 21, "chroma:document": "22 SPE-187038-MS\nFigure 19\u2014CT scans of fracture closure in a soft unconsolidated sand. After Dong and de Pater (2007).\nFig. 19 is also an excellent visualization of fracture-storage distortion. As previously noted, during\na fracture-injection/falloff test, storage has both wellbore and fracture components. In the laboratory\nexperiments, wellbore storage is minimized, so the primary contributor to storage distortion of the falloff\ndata is fracture closure when fluid is \"squeezed\" from the fracture into the formation as closure proceeds.\nFigs. 18 and Fig. 19 viewed in conjunction demonstrate that the storage distortion observed in the td[p e\n\u2013 pw(t)]/dt derivative is purely a function of the closing fracture. When the fracture finally closes, storage\ndistortion of the pressure falloff dissipates. The observation holds for field and laboratory data and is\nindependent of rock hardness.\nFig. 20 is an example provided by van Dam and de Pater (2017) of a closure experiment in a harder"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4469c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 21, "chroma:document": "sample (E \u2245 1.3 \u00d7 106 psi [8.9 GPa]). The example was provided as a \"blind test\" where the imposed\nstress remained unknown until after an analysis was completed, and the examples illustrates the difficulty\nof interpreting fracture closure from laboratory data. The Gdp w/dG derivative shows a pressure-dependent\n\"hump,\" a variable storage/changing compliance \"dip,\" and a period of normal leakoff. A changing-\ncompliance interpretation results in a closure pressure of 20.16 MPa, which is 26% too high, and as was\ndemonstrated in the field experiments, a strict changing-compliance closure interpretation as advocated by\nMcClure, Jung, Cramer, and Sharma (2015), does not provide the correct closure pressure and minimum\nhorizontal stress. A classical interpretation resulted in a closure pressure of 14.32 MPa, and while the\nclassical interpretation is within 10.5% of the correct answer (16 MPa), it illustrates the difficulty in drawing"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4471e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 21, "chroma:document": "the correct Gdp w/dG derivative straight line during a G-function derivative analysis without a clear and\ndistinct deviation of the Gdp w/dG derivative off the straight line. It also shows that picking the end of storage\ndistortion using the td[p e \u2013 pw(t)]/dt derivative is helpful, but it is also not distinct since closure is observed\nas storage distortion dissipates and not necessarily at the apex of the td[p e \u2013 pw(t)]/dt derivative. In other\nwords, despite all attempts to make fracture closure identification objective using the Gdp w/dG and td[p e \u2013\npw(t)]/dt derivatives, the pressure falloff trends from laboratory experiments are often non-distinct and the\ninterpretation subjective, which can introduce some interpretation error\u2014for example, 12.5% for the hard\ndolomite and 10.5% for the hard sandstone."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae447a0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 22, "chroma:document": "SPE-187038-MS 23\nFigure 20\u2014Laboratory fracture-closure experiment (GNV06b) in moderately hard rock (E = 1.3 \u00d7 106 psi [8.9 GPa] and v = 0.21).\nConclusions\nBoth laboratory and field experiments of hydraulic fracture closure with measurements of fracture\ndimensions during the pressure falloff have been examined and the results compared to interpretations of\nclosure pressure from the pressure falloff and the relationship to the minimum horizontal stress. In two\nhard-rock microdarcy sandstone reservoirs, field experiments of fracture closure monitored by downhole\ntiltmeters suggested the following.\n\u2022Fracture re-opening experiments using bottomhole pressure and tiltmeter deformation\nmeasurements suggest a B-Sand fracture re-opening pressure of (p c)ReOpen  \u2248 2,800 psi and a C-Sand\nre-opening pressure of (p c)ReOpen  \u2248 2,900 psi.\n\u2022Fracture closure pressure interpretations using G-function derivative analysis and the log-log"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44822-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 22, "chroma:document": "storage diagnostic suggest a fracture closure pressure approximately equivalent to the fracture re-\nopening pressure. In the B-Sand, the falloff-interpreted closure pressure was 2,855 psi \u2264 ( pc)2017 \u2264\n2,893 psi. However, the C-Sand injection/falloff sequences did not allow bottomhole pressure to\ndecline below pw(t) = 2,956 psi, but we can confidently state that the falloff analysis in the C-Sand\nsuggests a fracture closure pressure of (p c)C-Sand < 2,956 psi.\n\u2022Fracture closure pressure when interpreted using G-function derivative analysis and the log-\nlog storage diagnostic was invariant over multiple injection/falloff sequences, including different\nfluids, fluid volumes, and rates, and invariant over time.\n\u2022The fracture-compliance method interpretations of the Gdp w/dG derivative in the B-Sand injections\nsuggested a fracture closure stress of 3,208 psi \u2264 ( pc)\u0394Cbc \u2264 3,330 psi, which are inconsistent with\nthe small-volume stress tests, holistic G-function derivative analysis, and the fracture re-opening"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae448a4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 22, "chroma:document": "experiments.\n\u2022Tiltmeter measurements during a pressure falloff do not exhibit an identifiable and definitive\nclosure event.\n\u2022Tiltmeter deformation-difference derivative curves are generally similar in shape and behavior to\nfracture pressure-difference derivatives; consequently, the deformation-difference derivative can\npotentially validate fracture closure and the end of storage distortion identified using G-function\nderivative analysis and the log-log storage diagnostic.\nLaboratory experiments of fracture closure in soft rock (E < 7.25 \u00d7 105 psi [5.0 GPa]) through hard\nrock (E \u2245 6.3 \u00d7 106 psi [43.7 GPa]) demonstrate that G-function derivative analysis and the log-log storage\ndiagnostic interpretations of pressure falloff data can generally identify hydraulic fracture closure although"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4491c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 23, "chroma:document": "24 SPE-187038-MS\nthe trends in the falloff data are sometimes non-distinct and the interpretations subjective. Examination of\nlaboratory experiments of fracture closure also suggest the following.\n\u2022Measurements of fracture dimensions and pressure during closure show that fracture closure begins\nat the fracture tip and proceeds to the wellbore, which confirms the closure process of Hayashi and\nHaimson (1991); however, the pressure at tip closure did not correspond to the minimum horizontal\nstress.\n\u2022Although changing compliance was observed in samples based on measurements of fracture\ndimensions and pressure, the fracture closure pressure corresponding to changing compliance did\nnot correspond to the minimum horizontal stress.\n\u2022Fracture closure is observed as storage distortion of the pressure falloff dissipates, which\ncorresponds to closure at the wellbore and a near-residual fracture volume.\n\u2022In soft rock, like unconsolidated sand, G-function derivative analysis and the log-log storage"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4499e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 23, "chroma:document": "diagnostic correctly interpret fracture closure, but the closure pressure does not correspond to the\nminimum horizontal stress.\n\u2022In hard rock, G-function derivative analysis and the log-log storage diagnostic correctly interpret\nfracture closure, and the fracture closure pressure is approximately equal to the minimum horizontal\nstress.\nAcknowledgment\nWe appreciate Hans de Pater providing the raw pressure and time data for CTC08 and the blind test.\nNomenclature\nAf= fracture area, L2\nB= formation volume factor, L3/L3\ncf= compressibility of fluid in fracture, Lt2/m\ncw= compressibility of fluid in wellbore, Lt2/m\nC= wellbore and fracture storage, L4t2/m\nCf= time-dependent fracture compliance, L4t2/m\nCs= slug-test storage coefficient, L4t2/m\nCt= system compliance, L4t2/m\nE= Young's modulus, m/Lt\nE'= Plane-strain modulus, m/Lt2\nE(m) = complete elliptical integral, dimensionless\nF= hypergeometric function, dimensionless\ng= loss-volume function, dimensionless\nG= G-function, dimensionless\nh= height, L, ft"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44a20-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 23, "chroma:document": "G= G-function, dimensionless\nh= height, L, ft\nhf= fracture height, L, ft\nk= permeability, L2, md\nLf= fracture half-length, L, ft\np= pressure, m/Lt2\npws= wellbore pressure with variable flow rate, m/Lt2\npwc= wellbore pressure with constant flow rate, m/Lt2\nq= flow rate, L3/t\nSf= fracture stiffness, m/L4t2\nSeff= system stiffness, m/L4t2"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44a98-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 24, "chroma:document": "SPE-187038-MS 25\nsfs= fracture-face skin, dimensionless\nt= time, t\ntLfD= Dimensionless time, dimensionless\nVw= wellbore volume, L3\nVf= fracture volume one wing, L3\nGreek\n\u03b1N= fracture growth exponent, dimensionless\n\u0394= difference, dimensionless\n\u03bc= viscosity, m/Lt, cp\n\u03c4= variable of substitution, dimensionless\n\u03d5= porosity, dimensionless\n\u0393= Euler gamma function, dimensionless\nSubscripts\nc= constant-rate\n\u0394Cbc = changing-compliance closure\nD= dimensionless\ne= end of injection\nfinal = last recorded\ni= property evaluated at initial conditions\n0= end of injection\ns= slug test\nw= wellbore\nr= reservoir\nReOpen = observed re-opening\nReferences\nBarree, R.D., Barree, V .L., and Craig, D.P. 2009. Holistic Fracture Diagnostics: Consistent Interpretation of Prefrac\nInjection Tests Using Multiple Analysis Methods. SPE Prod & Opers 29 (03). https://doi.org/10.2118/107877-PA\nBarree, R.D. and Mukherjee, H. 1996. Determination of Pressure Dependent Leakoff and Its Effects on Fracture Geometry."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 24, "chroma:document": "Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, USA, 6-9 October. SPE-36424-\nMS https://doi.org/10.2118/36424-MS\nBarree, R.D. and Miskimins, J.L. 2016. Physical Explanation of Non-Linear Derivatives in Diagnostic Fracture Injection\nTest Analysis. Presented at the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, USA, 9-11\nFebruary. SPE-179134-MS https://doi.org/10.2118/179134-MS\nBranagan, P.T., Warpinski, N.R., Engler, B., and Wilmer, R. 1996a. Measuring the Hydraulic Fracture-Induced\nDeformation of Reservoirs and Adjacent Rocks Employing a Deeply Buried Inclinometer Array: GRI/DOE Multi-Site\nProject. Presented at the SPE Annual Technical Conference and Exhibition, Denver, Colorado, U.S.A., 6-9 October.\nSPE-36451-MS. https://doi.org/10.2118/36451-MS\nBranagan, P.T., Peterson, R.E., Warpinski, N.R., Wright, T.B. 1996b. Characterization of a Remotely Intersected Set"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 24, "chroma:document": "of Hydraulic Fractures: Results of Intersection Well No. 1-B, GRI/DOE Multi-Site Project. Presented at the SPE\nAnnual Technical Conference and Exhibition, Denver, Colorado, U.S.A., 6-9 October. SPE-36452-MS. https://\ndoi.org/10.2118/36452-MS\nBranagan, P.T., Peterson, R.E., and Wilmer, R. 1997a. Measurements of Well-to-Well Conductivity Through a Propped\nHydraulic Fracture. Presented at the 1997 SPE Rocky Mountain Regional Meeting, Casper, Wyoming, U.S.A., 18-21\nMay. SPE-38375-MS. https://doi.org/10.2118/38375-MS\nBranagan, P.T., Warpinski, N.R., Peterson, R.E., Hill, R.E., and Wolhart, S.L. 1997b. Propagation of a Hydraulic Fracture\ninto a Remote Observation Wellbore: Results of C-Sand Experimentation at the GRI/DOE M-Site Project. Presented\nat the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, U.S.A., 5-8 October. SPE-38574-MS.\nhttps://doi.org/10.2118/38574-MS"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 25, "chroma:document": "26 SPE-187038-MS\nCastillo, J.L. 1987. Modified Fracture Pressure Decline Analysis Including Pressure-Dependent Leakoff. Presented\nat the Low Permeability Reservoirs Symposium, Denver, Colorado, USA, 18-19 May. SPE-16417-MS https://\ndoi.org/10.2118/16417-MS\nChartrand, R. 2011. Numerical differentiation of noisy, nonsmooth data,\" ISRN Appl. Math., vol. 2011, https://\ndoi.org/10.5402/2011/164564\nCheung, L.S. and Haimson, B.C. 1989. Laboratory Study of Hydraulic Fracturing Pressure Data\u2014How Valid is Their\nConventional Interpretation. Int. J. Rock Mech. Min. Sci. & Geomech. 26 (6) 595-604.\nCraig, D.P. 2014. New Type Curve Analysis Removes Limitations of Conventional After-Closure Analysis of DFIT\nData. Presented at the 2014 SPE Unconventional Resources Conference \u2013 USA, The Woodlands, Texas, 01-03 April.\nSPE-168988-MS https://doi.org/10.2118/168988-MS\nCraig, D.P. and Blasingame, T.A. 2005. A New Refracture-Candidate Diagnostic Test Determines Reservoir Properties"}


created_at: 2023-11-17 19:17:23
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 25, "chroma:document": "and Identifies Existing Conductive or Damaged Fractures. Presented at the 2005 SPE Annual Technical Conference\nand Exhibition, Dallas, Texas, USA, 9-12 October. SPE-96785-MS. https://doi.org/10.2118/96785-MS\nCraig, D.P.and Blasingame, T.A. 2006. Application of a New Fracture-Injection/Falloff Model Accounting for\nPropagating, Dilated, and Closing Hydraulic Fractures. Presented at the 2006 SPE Gas Technology Symposium,\nCalgary, Alberta, Canada, 15-17 May. SPE-100578-MS. https://doi.org/10.2118/100578-MS\nCraig, D.P., Eberhard, M.J., and Barree, R.D. 2000. Adapting High Permeability Leakoff Analysis to Low Permeability\nSands for Estimating Reservoir Engineering Parameters. Presented at the 2000 SPE Rocky Mountain Regional/Low-\nPermeability Reservoirs Symposium and Exhibition, Denver, Colorado, USA, 12-15 March. SPE-60291-MS. https://\ndoi.org/10.2118/60291-MS\nde Pater, C.J., Weijers, L. Savic, M., Wolf, K.H.A.A., van den Hoek, P.J., and Barr, D.T. 1994. Experimental Study of"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 25, "chroma:document": "Nonlinear Effects in Hydraulic Fracture Propagation. SPE Prod & Facilities 9 (04). https://doi.org/10.2118/25893-PA\nde Pater, C.J., Desroches, J., Groenenboom, J., and Weijers, L. 1996. Physical and Numerical Modeling of Hydraulic\nFracture Closure. SPE Prod & Facilities 11 (02). https://doi.org/10.2118/28561-PA\nvan Dam, D.B. and de Pater, C.J. 2017. Personal communication.\nDong, Y . and de Pater, C.J. 2007. Closure of Hydraulic Fractures Visualized by X-ray CT Technique in Sand. Presented\nat the 1st Canada \u2013 U.S. Rock Mechanics Symposium, Vancouver, Canada, 27-31 May. ARMA-07-082.\nGulrajani, S.N., Nolte, K.G.,, Romero, J. 2001. Evaluation of the M-Site B-Sand Fracture Experiments: Evolution of a\nPressure Analysis Methodology. SPE Prod & Facilities 16 (01). https://doi.org/10.2118/69206-PA\nHayashi, K. and Haimson, B.C. 1991. Characteristics of Shut-in Curves in Hydraulic Fracturing Stress Measurements\nand Determination of in Situ Minimum Compressive Stress. Journal of Geophysical Research 96 (B11) 18,311-321."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 25, "chroma:document": "https://onlinelibrary.wiley.com/doi/10.1029/91JB01867\nMcClure, M.W., Jung, H., Cramer, D.D., and Sharma, M.M. 2015. The Fracture-Compliance Method for Picking Closure\nPressure From Diagnostic Fracture-Injection Tests. SPE Journal 21 (04). https://doi.org/10.2118/179725-PA\nMiddlebrook, M.L., Aud, W.W., Harkrider, J.D., and Hansen, J.T. 1997. An Evolving Approach in the Analysis of Stress-\nTest Pressure-Decline Data. SPE Production & Facilities 12 (03). https://doi.org/10.2118/29599-PA\nNolte, K.G. 1979. Determination of Fracture Parameters From Fracturing Pressure Decline. Presented at the 1979 SPE\nAnnual Technical Conference and Exhibition, Las Vegas, Nevada, USA, 23-26 September. SPE-8341-MS https://\ndoi.org/10.2118/8341-MS\nPeterson, R.E., Wolhart, S.L., Frohne, K.W., Branagan, P.T., Warpinski, N.R. and Wright, T.B. 1996. Fracture\nDiagnostics Research at the GRI/DOE Multi-Site Project: Overview of the Concept and Results. Presented at the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44e12-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 25, "chroma:document": "SPE Annual Technical Conference and Exhibition, Denver, Colorado, U.S.A., 6-9 October. SPE-36449-MS. https://\ndoi.org/10.2118/36449-MS\nRaaen, A.M., Skomedal,, E., Kj\u00f8rholt, H., Markstead, P., and \u00d8kland,D. 2001. Stress determination from hydraulic\nfracturing tests: the system stiffness approach. Int. Journal of Rock Mechanics & Mining Science 38 (2001) 529-541.\nRohatgi, A. 2017. WebPlotDigitizer. V3.12. June 2017. Austin, Texas, USA http://arohatgi.info/WebPlotDigitizer\nValk\u00f3, P.P. and Economides, M.J. 1999. Fluid-Leakoff Delineation in High-Permeability Fracturing. SPE Production &\nFacilities 14 (02) May. https://doi.org/10.2118/56135-PA\nvan den Hoek, P. 2017. A Simple Unified Pressure-Transient-Analysis Method for Fractured Waterflood Injectors and\nMinifractures in Hydraulic-Fracture Stimulation. SPE Production & Operations https://doi.org/10.2118/181593-PA\nWarpinski, N.R., Engler, B.P., Young, C.J., Peterson, R., Branagan, P.T., and Fix, J.E. 1995. Microseismic Mapping of"}


created_at: 2023-11-17 19:17:23
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 25, "chroma:document": "Hydraulic Fractures Using Multi-Level Wireline Receivers. Presented at the SPE Annual Technical Conference and\nExhibition, Dallas, Texas, U.S.A., 22-25 October. SPE-30507-MS. https://doi.org/10.2118/30507-MS\nWarpinski, N.R., Wright, T.B., Uhl, J.E., Engler, B.P., Drozda, P.M., Peterson, R.E., and Branagan, P.T. 1996. Microseismic\nMonitoring of the B-Sand Hydraulic Fracture Experiment at the DOE/GRI Multi-Site Project. Presented at the\nSPE Annual Technical Conference and Exhibition, Denver, Colorado, U.S.A., 6-9 October. SPE-36450-MS. https://\ndoi.org/10.2118/36450-MS"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 26, "chroma:document": "SPE-187038-MS 27\nWarpinski, N.R., Branagan, P.T., Peterson, R.E., Fix, J.E., Uhl, J.E., Engler, B.P. and Wilmer, R. 1997. Microseismic\nand Deformation Imaging of Hydraulic Fracture Growth and Geometry in the C Sand Interval, GRI/DOE M-Site\nProject. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, U.S.A., 5-8 October.\nSPE-38573-MS. https://doi.org/10.2118/38573-MS\nWarpinski, N.R., Branagan, P.T., Peterson, R.E., Wolhart, S.L. 1998. An Interpretation of M-Site Hydraulic Fracture\nDiagnostic Results. Presented at the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium,\nDenver, Colorado, U.S.A., 5-8 April. SPE-39950-MS. https://doi.org/10.2118/39950-MS\nZanganeh, B., Clarkson, C.R., and Hawkes, R.V . 2017. Reinterpretation of Fracture Closure Dynamics During Diagnostic\nFracture Injection Tests. Presented at the 2017 SPE Western Regional Meeting, Bakersfield, California, USA, 23 April.\nSPE-185649-MS. https://doi.org/10.2118/185649-MS"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44f84-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 0, "chroma:document": "SPE 16417 SPE/DOE \nSociety of \nPetroleum Engineers U.S. Department \nof Energy \nModified Fracture Pressure Decline Analysis Including \nPressure-Dependent Leakoff \nby J. L. Castillo* Dowell Schlumberger \n*Member SPE \nCopyright 1987, Society of Petroleum Engineers \nThis paper was prepared for presentation at the SPE/DOE Low Permeability Reservoirs Symposium held in Denver, Colorado, May 18-19, 1987. \nThis paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the \nauthor(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the \nauthor(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers \npresented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae44ffc-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 0, "chroma:document": "restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of \nwhere and by whom the paper is presented. Write Publications Manager, SPE, P.O. Box 833836, Richardson, TX 75083-3836. Telex, 730989 SPEDAL. \nABSTRACT \nNolte developed an analysis of the pressure \ndecline following a fracturing treatment to provide an \nestimate of fluid efficiency, fluid loss coefficient, \nand fracture geometry. This analysis has become an \nindustry standard for evaluating and improving the \ndesign of fracturing treatments. The derivations by \nNolte assume the leakoff coefficient is a pressure\u00ad\nindependent constant. This assumption is valid when \nleakoff is controlled by a compressible filter cake. \nIn cases where leakoff is primarily controlled by \nfiltrate viscosity, by an incompressible filter cake, \nor by reservoir permeability and compressibility, the \nleakoff coefficient is pressure dependent, and, there\u00ad"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4506a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 0, "chroma:document": "leakoff coefficient is pressure dependent, and, there\u00ad\nfore, declines during the closure period. Under these \ncircumstances, direct application of the Nolte tech\u00ad\nnique may not be appropriate, and could cause an \noptimistic estimate of fluid efficiency and leakoff \ncoefficient. \nThis paper introduces a new plot for fracture \npressure decline analysis that determines the pressure \nparameters (ISIP, Pc, P*) required in the Nolte leak\u00ad\noff calculations. The derivative of this plot may be \nused to identify the extension period, the closure \nperiod, and to assess the influence of pressure depen\u00ad\ndent 1 eakoff on fracture pressure decline. In order \nto account for pressure dependent 1 eakoff, equations \nare presented where the leakoff coefficient is treated \nas a mathematical variable.\u00b7 The equations describe \nsimple linear relations applicable to the fracture \nclosure period. When these relations are plotted on \nReferences and illustrations at end of paper. Cartesian coordinates, the closure period is recog\u00ad"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae450e2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 0, "chroma:document": "nized by a straight line with slope proportional to \nthe 1 eakoff coefficient. As shown in the examples, \nthis modified approach is easily applied and provides \nnew insight to the fracture closure period. \nINTRODUCTION \nThe methodology currently used in fracture pres\u00ad\nsure decline analysis employs type-curve matching to \ndetermine a match pressure (P*) that is proportional \nto the leakoff coefficient.1'2 Data used in the curve \nmatch must correspond to the closure period. This \nperiod is usually interpreted as the 11linear11 region \nof a square-root of time plot or as the half-slope \nregion of a log-log plot.3,4 Analysis of the square\u00ad\nroot plot or the log-log plot, however, is often \ninconclusive. To aid identification of the closure \nperiod, the closure pressure is usually determined \nprior to a calibration treatment from a stress test \n(e.g. pump-in flow-back test). \nA new plot is introduced that has the unique \nadvantage of providing all of the pressure variables"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45164-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 0, "chroma:document": "advantage of providing all of the pressure variables \n(ISIP, Pc, P*) required in decline analysis. This \nplot is more easily applied than the Nolte type \ncurves, and is superior to the square-root of time \nplot because it uses a more precise relationship \nbetween decline pressure and time. When the deriva\u00ad\ntive of this plot is graphed against time, fracture \nextension after shut-in, fracture closure, and pres\u00ad\nsure dependent 1 eakoff can be observed. This plot \nenhances interpretation and identification of the \nclosure period. However, by no means should use of \nthis plot replace stress tests. \nWhen analysis of the derivative plot indicates a \ndependence of leakoff rate on pressure, a technique is \npresented to account for a declining leakoff coeffi\u00ad\ncient during closure. \n273 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45268-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "2 MODIFIED FRACTURE PRESSURE DECLINE ANALYSIS \nINCLUDING PRESSURE-DEPENDENT LEAKOFF SPE 16417 \nDEVELOPMENT OF THE 11G-FUNCTION11 PLOT \nNolte1'2 has shown that, during closure, the \npressure difference between two shut-in times can be \nexpressed as \n1r\u2022C\u2022f \u2022It \n__ ...__P _ _._p \u2022 G(to,t*o) \n2 \u2022cf \n(l~t> ~t*) ( 1) \nwhere, ~t* is a reference time since shut-in, C is the \nleakoff coefficient, fp is the ratio of permeable area \nto gross area, tp is pump time, and t0 is dimension\u00ad\nless time (M/t ). Equations for cf (fracture's \ncompliance for wfdth) and G (dimensionless difference \nfunction) are given in Appendix A. \nA Nolte type-curve1 is constructed by selecting a \ndimensionless reference time (t11*) prior to closure \nand plotting G against t0 on log-log coordinates. The \nsame reference time is used to plot ~p against ~t \u00b7 on \nlog-log coordinates. A curve match is obtained by \noverlaying the curves, aligning the x axes so that ~t \ncorresponds to t0, and shifting along the y axis."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae452ea-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "corresponds to t0, and shifting along the y axis. \nOnce a match is obtained, a match point is selected, \nand the Nolte match pressure (P*) is computed from \n~P/G. The match pressure is equivalent to \nTI\u2022C\u2022f \u00b7It P* = p . p (2) \n2\u2022cf \nWhen compliance can be inferred, the leakoff \ncoefficient can be estimated from Equation 2. \nThe new plot proposed here makes note of the fact \nthat Equation 1 is a linear equation. Substituting \nEquation 2 into Equation 1, and selecting a reference \ntime of ~t* = 0.0 results in \nP(~t) = P*\u2022G(tD,O) + P(~t* = 0) (3) \nThis equation is in the familiar form of y = mx + \nb. Thus, a Cartesian plot of decline pressure against \nG (referred to below as the 11G-Function11 plot) should \nresult in a straight line during the closure period \nwith slope equal toP* andy-intercept equal to a \ntheoretical pressure at shut-in. The closure period \nis recognized by linearity; deviation from linearity \nidentifies the closure pressure. From this single"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4536c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "identifies the closure pressure. From this single \nplot, then, all of the pressure parameters ( Pc, P*, \n!SIP) required in the analysis calculations are \ninferred. \nInterpretation of the G-Function plot is enhanced \nby differentiating Equation 3 to give \ndP \nP* (4) \ndG \nA graph of dP/dG against ~t (referred to as the \nG-Function derivative plot) should provide a horizon\u00ad\ntal line during the closure period with a constant y\u00ad\naxis value of P*. The derivative, dP/dG, may be \ncomputed by using linear regression on a small number \nof data points (e.g. 5); the ~t value that corresponds \nto dP/dG is a time average of the points used. Example 1 \nFigures 1 and 2 are the G-Function and G-Function \nderivative plots, respectively, for a case where a \ncrosslinked HPG fluid was used in a gas well. Figure \n2 shows the G-Funct ion plot is 1 i near ( i .e. constant \nslope) from 10 to 32 minutes. The non-linearity from \nshut-in to 10 minutes is interpreted as fracture \nextension after shut-in, while the non-linearity after"}


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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "extension after shut-in, while the non-linearity after \n32 minutes implies that the fracture is closed. \nAn estimate of a theoretical !SIP is obtained by \ndrawing a line through the linear portion of the G\u00ad\nFunction plot and extrapolating to the y-axis (as \nindicated in Figure 1). The difference between the \ntheoretical !SIP and the observed !SIP corresponds to \na decrease in fracture width resulting from continued \nfracture extension after shut-in. Use of the theoret\u00ad\ni c a 1 I S I P i n t he Nolte e f f i c i en c y c a 1 c u 1 at i o n 2 s h o u 1 d \nprovide a lower bound estimate of fluid efficiency. \nFigure 3 is the square-root of time plot using \nthe same data as above; Figure 4 is the derivative \nplot of the square-root of time. As shown by Figure \n4, the square-root plot is never linear. Instead, the \nsquare-root plot exhibits an inflection when fracture \nclosure occurs. The inflection is observed as a \nchange in slope (from + to -) in the square-root"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45470-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "change in slope (from + to -) in the square-root \nderivative plot. The implication of this example is \nthat the square-root of delta time is not directly \nproportional to the pressure decline during fracture \nclosure. \nThe G-Functi on plot, therefore, represents the \nclosure period more accurately than the square-root of \ntime plot since G is linearly related to the pressure \ndecline. Both the G-Function plot and the square-root \nof time plot are enhanced by plotting their deriva\u00ad\ntives against time. \nPRESSURE DEPENDENT LEAKOFF \nNolte1'2 developed Equation 1 from an assumption \nthat the leakoff coefficient is independent of varia\u00ad\ntions in pressure. This assumption was shown to be \nvalid when leakoff is controlled by a compressible \nfilter cake.2 When leakoff is primarily controlled by \nan incompressible filter cake, by filtrate viscosity, \nor by the reservoir, the leakoff coefficient is depen\u00ad\ndent on pressure.2,s During fracture closure, there\u00ad\nfore, the leakoff coefficient declines as the pressure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae454f2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "fore, the leakoff coefficient declines as the pressure \nin the fracture declines. As indicated by Equations 2 \nand 4, a declining 1 eakoff coefficient should result \nin a declining G-Function derivative plot. \nExample 2 \nFigures 5 and 6 are a G-Functi on plot and a G\u00ad\nFunction derivative plot, respectively, for a case \nwhere an oil reservoir was fractured with a waterfrac \nfluid (10 lb polymer per 1,000 gallons). The leakoff \ncontrol in this case is primarily due to the reser\u00ad\nvoir's compressibility and permeability; thus, the \n1 eakoff coefficient is pressure dependent. Ex ami na\u00ad\ntion of the G-Function derivative plot in Figure 6 \nindicates a slope change at five minutes that corres\u00ad\nponds to fracture closure. The square-root plot in \nFigure 7 also exhibits an inflection at five minutes \n(as indicated in Figure 8). Observe that the G-Func\u00ad\ntion derivative plot in Figure 6 is not horizontal \nduring the closure period. This implies that, when"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4557e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "during the closure period. This implies that, when \n274 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae455f6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 2, "chroma:document": "SPE 16417 J. L. CASTILLO 3 \n1 eakoff is pressure dependent, the 1 i near relation \nbetween decline pressure and the G-Function does not \nhold. In these cases, Equation 3 falls short of \naccurately predicting fracture pressure decline. \nEquations that account for pressure dependence \nare presented in the next section. These equations \nwere developed from an assumption of a direct rela\u00ad\ntionship between leakoff rate and a pressure-dependent \nleakoff coefficient. A more comprehensive relation\u00ad\nship, however, between leakoff rate and pressure \nshould be derived using superposition of the total \npressure hi story in the fracture. 6 Thus, the tech\u00ad\nnique proposed below provides a first-order correction \nfor pressure-dependent leakoff. \nSUMMARY OF EQUATIONS FOR PRESSURE DEPENDENT LEAKOFF \nDetermination of Pressure Dependent Leakoff \nCoefficient \nThe general form of the 1 eakoff coefficient as a \nfunction of fracture pressure above reservoir pressure \ncan be expressed as,s \nC(z,t) = M \u2022 (~Pf,r(z,t) )u (5)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45678-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 2, "chroma:document": "can be expressed as,s \nC(z,t) = M \u2022 (~Pf,r(z,t) )u (5) \nThe ~pf r(z,t) term is the difference between \nfracture pres~ure (Pf) and reservoir pressure (Pr) at \na given position in the fracture (z) at a given time \n(t), i.e.: \n~pf r(z,t) = Pf(z,t) -Pr = , \nPn(z,t) + Pc -Pr \nwhere, \nPn = net pressure above closure \nPc = closure pressure (6) \nThe coefficients, M and u, are functions of the \nleakoff mechanism, and are given below for three cases \nof 1 eakoff control where pressure-dependence is si g\u00ad\nnificant:2,5 \nI: Reservoir Permeability and Compressibility \nu = 1 \nM = .001183 \u2022 lkr \u2022 $r \u2022 cr I ~r \nwhere, \nkr = permeability to reservoir fluid, md \n$r = porosity containing reservoir fluid \ncr = compressibility of reservoir fluid, \n~r = reservoir fluid viscosity, cp \nII: Viscosity of Fluid Filtrate \nu = 112 \nM = .001483 \u2022 v'kf \u2022 $f I ~f psi-1 where, \nkf =permeability to fracture fluid filtrate, md \n$f =porosity containing fracture fluid filtrate \n~f = fracture fluid filtrate viscosity, cp"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae456f0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 2, "chroma:document": "~f = fracture fluid filtrate viscosity, cp \nIII: Incompressible Filter Cake \nu = 112 \nM = function of filter cake properties \nAn estimate of the total effective leakoff coef\u00ad\nficient as a function of wellbore net pressure (Pnw) \ncan be approximated by \nC( t) = M \u2022 ( Pnw( t) \u2022 8 + pc -pr )u (7) \nwhere the 8 term is defined by Nolte as the ratio of \naverage net pressure in the fracture to well bore net \npressure.1'2 Values for 8 are provided in Appendix A \n(8 = 8p during pumping, 8 = 8s during shut-in). \nEquation 7 can be used to estimate C when M and u have \nbeen determined. The exponent u is selected based on \nthe supposed primary 1 eakoff mechanism. The coeffi\u00ad\ncient M may be graphically determined as discussed in \nthe next sections. \nDetermination of M for Reservoir Leakoff Control \nThe linear equation below was derived (see Appen\u00ad\ndix B) for the case where the primary mechanism of \n1 eakoff control is from the reservoi r\u2022 s permeabi 1 ity \nand compressibility (i.e. u = 1): \n-1r\u2022M\u2022f \u20228s\u00b7lf"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45768-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 2, "chroma:document": "and compressibility (i.e. u = 1): \n-1r\u2022M\u2022f \u20228s\u00b7lf \nln[Pnw( ~t) \u20228s + Pc -Pr] = p p \u2022 G(t0,0) \n2 \u2022Cf \n+ ln[Pnw(O) \u2022Ss + Pc -Pr] (8) \nA plot of ln[Pnw(~t)\u20228s + Pc -Pr] against G \nshould yield a straight line during closure with slope \nproportional to M and a y-intercept from which a \ntheoretical ISIP can be inferred. After determining \nthe slope and y-i ntercept of this plot, M can be \ncalculated from \nM - -SLOPE \u20222 \u2022cf \nlT\u2022f 0 8S \u2022ft p p \nand a theoretical ISIP can be calculated from \nexp(yint) -Pc + Pr \nISIP = -------- + Pc \n8S (9) \n(10) \nNotice that calculation of the term ln[Pnw(~t) \u20228s \n+ Pc -Pr] requires an estimate of closure pressure \nand reservoir pressure. Ideally, closure pressure \nwill have been estimated from a stress test and reser\u00ad\nvoir pressure wi 11 have been estimated from a tran\u00ad\nsient pressure test. \nDetermination of M for Filtrate Viscosity or Incom\u00ad\npressible Filter-Cake Leakoff Control \nThe equation below was derived (see Appendix B) \nfor the case where the primary mechanism of 1 eakoff"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae457d6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 2, "chroma:document": "for the case where the primary mechanism of 1 eakoff \n275 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4584e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 3, "chroma:document": "4 MODIFIED FRACTURE PRESSURE DECLINE ANALYSIS \nINCLUDING PRESSURE-DEPENDENT LEAKOFF SPE 16417 \ncontrol is from the viscosity of fracture fluid fil\u00ad\ntrate or from an incompressible filter cake (i.e. u ~ \n1/2): ~ \n[Pnw(~t)\u2022as + Pc-Pr]1/2 = \n+ [Pnw(O)\u2022as + Pc ~ Pr]1/2 ( 11) \nA plot of [Pnw(~t) \u2022as + Pc -Pr]1/2 against G \nshould yield a straight line during closure with slope \nproportional to M and a y-intercept from which a \ntheoretical ISIP can be inferred. After determining \nthe slope and y-i ntercept of this plot, M can be \ncalculated from \nSLOPE\u20224\u2022cf \nM = -~~~--..:.-\n'JT\u2022f \u2022as\u00b7lt p p (12) \nand a theoretical ISJP can be calculated from \n2 (yint) -Pc + Pr \nISIP = -----....,..-.- + Pc (13) \nas \nNotifh that cal cul ati on of the term [Pnw( 4t) \u2022 as + \nPc -PrJ requires an estimate of closure pressure \nand reservoir pressure. \nFluid Efficiency \nThe following equation was derived to include \npressure dependent l eakoff effects in Nol te\u2022 s fluid \nefficiency calculation 2 based on dimensionless closure \ntime (t0c):"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae458d0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 3, "chroma:document": "time (t0c): \n.,.b -~2 -4ac \neff = (14) \n2a \nwhere, \na gdl gdu \nb gdu 2. gdl + 1 -Ks/ j c = gdl 1 (15) \nand, \ngdl gl(tDc) \n--\"--~ and gdu (16) \ngl ( O) \nKs = Nolte\u2022s correction for spurt (usually 1.0) \nAlso, \nj (17) Pnws = wellbore net pressure at shut-in \nm = slope of Nolte-Smith plot \nPc = closure pressure \nPr = reservoir pressure \nThe terms g1 and gu are the lower and upper \nbound, respectively, for Nolte\u2022s dimensionless loss\u00ad\nvolume function.1'2 Equations for these functions can \nbe found in Appendix A. Note that when pressure\u00ad\ndependence becomes negligible, the exponent u ap\u00ad\nproaches 0 and j in Equation 17 approaches unity. \nAPPLICATION \nRecall that Example 2 was characterized by a \ndeclining leakoff coefficient during closure (Figure \n6). Since the reservoir in this example was liquid \nfilled, and since the wall-building properties of the \nfluid were negligible, it was inferred that leakoff \ncontrol was primarily due to the reservoir. There\u00ad\nfore, Equation 8 was used to construct the specialized"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45948-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 3, "chroma:document": "fore, Equation 8 was used to construct the specialized \nplot in Figure 9. The derivative plot (Figure 10) \nshows that Figure 9 is linear during the closure \nperiod. This implies that Equation 8 pro vi des a \nlinear relation during closure between functions of \npressure and time when leakoff is reservoir con\u00ad\ntrolled. Table 1 compares analysis results between \nEquations 1 and 2 (pressure independence) and Equa\u00ad\ntions 7, 8, and 9 (pressure dependence). Notice that \nif data near closure had been used in the Nolte type\u00ad\ncurve match, a P* value of 1,270 psi would have been \nestimated resulting in a C value of .0038. This value \nis 25% less than the value calculated from Equation 7 \nwhen pressure-dependence is considered. \nCONCl-USIONS \nA new plot (G-Function plot) has been introduced \nthat is superior to the square-root of time plot. The \nsquare-root plot uses an approximate relationship \nbetween pressure and time, whereas the G-Function plot \nuses a more precise relationship (gquation 5), When"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae459ca-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 3, "chroma:document": "uses a more precise relationship (gquation 5), When \nthe derivative of the G-Function plot is graphed \nagC!i nst time, phenomena such as fracture extension \nafter shut-in, fracture closure, and pressure-depen ... \ndent 1 eakoff can be observed, To account for pres\u00ad\nsure-dependence, first-order approximation functions \nare provided (Equations 8, 11) to correct for a de\u00ad\nclining leakoff coefficient during closure. These \nfunctions tend to linearize the relation between \npressure and time during the closure period. As shown \nin Example 2, ignoring pressure dependence can result \nin an optimistic estimate of the leakoff coefficient. \nNOMENCLATURE \na = viscosity degradation coefficient \nAf = fracture area, ft2 \ncf = fracture compliance for width, ft/psi \nC = leakoff coefficient, ft/lrnln \nE1 = plane-strain modulus, psi \neff = \nf = p \nf(tp) \ng (to) = fluid efficiency \nratio of permeable area to gross area \ndimensionless loss-rate function \ndimensionless loss-volume function"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45a56-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 3, "chroma:document": "dimensionless loss-volume function \n276 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45ad8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 4, "chroma:document": "SPE 16417 J. L. CASTILLO 5 \nG(t0,t*0) dimensionless difference function \nHg =gross fracture height, ft \n!SIP = instantaneous shut-in pressure, psi \nk = permeability, md \nL = fracture half-length, ft \nM = leakoff proportionality constant \nn\u2022 behavior index of fracturing fluid \nP pressure, psi \nPc closure pressure, psi \nPr = reservoir pressure, psi \nPn = net pressure above closure, psi \nPnw = wellbore net pressure, psi \nP* = Nolte Match Pressure, psi \n~t = delta time since shut-in, minutes \n~t* = reference time since shut-in, minutes \nt = p pump time, minutes \nto = dimensionless delta time ( t.t/tp) \nu = exponent for leakoff \nVi = injected volume , ft 3 \nw = average fracture width, ft \nz ::: position in fracture \nS = ratio of average net pressure to wellbore \nnet pressure \n~P(~t,~t*) = pressure difference between ~t and ~t* \n~Pf,r =difference between fracture and reservoir \npressure \n~s = Nolte\u2022s correction for spurt \n~ = porosity \n~ = viscosity, cp \nREFERENCES"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45b5a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 4, "chroma:document": "~ = porosity \n~ = viscosity, cp \nREFERENCES \n1. Nolte, K. G.: 110etermination of Fracture Parame\u00ad\nters from Fracturing Pressure Decline Analysis, .. \npaper SPE 8341 presented at the 1979 SPE Annual \nTechnical Conference and Exhibition, Las Vegas, \nSept. 23-26. \n2. Nolte, K. G.: 11A General Analysis of Fracturing \nPressure Decline Analysis With Application to \nThree Models,11 SPEFE (Dec. 1986) 571-583. \n3. \n4. \n5. Elbel, J. L. et al.: 11Stimulation Study of Cot\u00ad\ntage Grove Formation, .. J. Pet. Tech. (July 1984) \n1199-1205. \nNolte, K. G.: 11Fracture Design Considerations \nBased on Pressure Analysis ,11 paper SPE 10911 \npresented at the SPE Cotton Valley Symposium, \nTyler, May 1982. \nHoward, G. C. and Fast, C. R.: \ning, Monograph Series, SPE, \n( 1970) , Vo 1 \u2022 2. Hydraulic Fractur\u00ad\nRichardson, Texas \n6. Nolte, K. G.: Personal communication, Feb. 1987. APPENDIX A \nCalculation of Fracture Compliance (cf): \nThe fracture\u2022s compliance for width is given by \nNolte as: \n'IT. ss \ncf = -~ \u2022 \n2 \u2022E I r- -\nHg PK \n2 \u2022L"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45bdc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 4, "chroma:document": "Nolte as: \n'IT. ss \ncf = -~ \u2022 \n2 \u2022E I r- -\nHg PK \n2 \u2022L \n32 \n--z\u2022L \n31T --KGD \nRadial (A1) \nwhere E1 is the plane-strain modulus, Hg is gross \nfracture height, Lis hydraulic half-length, and Sis \nthe ratio of average net pressure in the fracture to \nthe well bore net pressure at shut-in. Nolte reports \nvalues of s during closure (ss) and during pumping \n( Sp) as f o ll ows : \n[2n+2)./(2n.+3+a~\u00b7 PK Ss 0. 9 KGD \n0.925 Radial \nand, \nn\u2022 \na ~2n+2)/(3n+3+aJ.\u00b7 PK\u00b7. Sp = ~ 0.85 KGD \n? Radial \nBehavior index of fracture fluid \nNolte viscosity degradation correction \n0 for no degradation \n1 for moderate degration \n2 for severe degradation (A2) \n(A3) \nThe Sp value for the radial model is expected to \nbe much less than unity.2 \nOnce efficiency has been determined, the following \nequation from Nolte2 can be used to estimate fracture \nhalf-length (L): \nr-2 ~ \nHg \u2022L PK \nVi \u2022eff\u2022E1 2 \nss . 2 \u2022Hg \u2022L KGD (A4) \n16 3 -\u00b7L Radial \n31T \nwhere, '---\ninjected vo 1 ume \nnet pressure immediately after shut-in"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45cae-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 4, "chroma:document": "injected vo 1 ume \nnet pressure immediately after shut-in \nOnce compliance has been determined, average \nhydraulic width in the fracture at shut-in can be \nestimated from: \n(A5) \nCalculation of the G-Function: \nThe G-Function is calculated from Nolte\u2022sl,2 \ndimensionless loss-volume function (g) as follows: \n4 \n\u2022 [g(t0) .. g(O)] (A6) \n'IT \n277 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45d30-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 5, "chroma:document": "6 MODIFIED FRACTURE PRESSURE DECLINE ANALYSIS \nINCLUDING PRESSURE-DEPENDENT LEAKOFF SPE 16417 \nwhere g is defined as \n(A7) \nThe upper bound (gu) and lower bound (g1) for g are \ngu(X) 4/3{(l+X)1\u20225 -x1\u20225} (eff+l) \n(AB) \ng1(x) (l+X)sin-l(l+X)-.5 + x\u00b75 (eff+O) \nAPPENDIX B \nDetermination of the M Coefficient: \nNolte2 developed the following equation for calcu\u00ad\nlating leakoff rate during closure: \n2\u2022C\u2022f \u2022Af \nq( t) p \n~ \neff+l \n(Bl) \neff+O \nBy substituting Equation 7 for C and replacing the \nbracketed term in Equation Bl by f(tD) results in \nq(t) = \n2\u2022M\u2022{Pnw(t)\u2022Ss + Pc-Pr}u \u2022f \u2022A -------------l.:...p____;_f \u2022 f(tD) \n~ (B2) If fracture area (Af) is assumed to remain essen\u00ad\ntially constant during closure such that leakoff area \ndoes not change, and such that the fracture\u2022 s com\u00ad\npliance for width remains constant, then the rate of \nchange of fracture volume can be related to the rate \nof change of average fracture width (w): \ndw \n-Af \u00b7-= q(t) \ndt (B3) \nBased on Nolte\u2022 s definition of compliance, the"}


created_at: 2023-11-17 19:17:23
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id: 9ae45db2-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 5, "chroma:document": "dt (B3) \nBased on Nolte\u2022 s definition of compliance, the \nrate of change in average fracture width can be re\u00ad\nlated to the rate of change in net pressure: \ndw dPnw \n(B4) \ndt dt \nSubstituting B3 and B4 into B2 cancelling Af, and \nrearranging terms results in an equation that relates \nrate of change in pressure to dimensionless time: \n-dPnw \ndt 2\u2022M\u2022fp\u2022{Pnw\u2022Ss + Pc-Pr}u \nCf\u2022~ \nSeparating variables results in: \n-dPnw 2\u2022M\u2022f \u00b7It \n_ ____.,P _ _._P \u2022 f ( t D) d t D \ncf {Pnw\u2022Ss + Pc -Pr}u (B5) \n(B6) \nIntegrating B6 between shut-in (tD=O) and some \nlater time using u=l and u=l/2 provides the relations \npresented in this paper. \n278 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45e3e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 6, "chroma:document": "SPE 1 6 4 1 ~ I \nTABLE 1 \nPKN MODEL \nPressure Pressure \nParameter Independence Dependence \nefficiency 0.137 0.113 \nderivative 1,510 psi 0.73 \n@ shut-in (see Figure 6) (see Figure 10) \nderivative 1,270 psi 0.73 \n@ closure (see Figure 6) (see Figure 10) \n.0038 ( ft/ /min) \n(near closure) \nLeakoff Coeff. .0051 ( ft/ /min) \n(C) \n.0045 (ft/lmin) \n(near shut-in) \nHalf-Length 154 ft 127 ft \n(see Equation A4) (see Equation A4) \nMean Width .112 in. .112 in. \n@ shut-in (see Equation A5) (see Equation A5) \n279 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45ec0-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 7, "chroma:document": "6,000 \n5,aoo \n,_ \n\u00b7;;; \n~ 5,600 \nLaJ \nl:t: \n::::> \nVl 5,400 \nVl \nLaJ \nl:t: a.. \n5,200 \n5,000 \n0 0.5 1.0 1.5 2.0 \nG FUNCTION \nFigure 1. Pressure vs. the G-Function (Example 1). \n~ 600 \na. End of -Extension Fracture Closed \nLaJ / > \n~ 500 \n> \n~ \nLaJ c \n1-400 \nz \n0 a.. \nI \nLO 300 \n(!) \n\"C \n\"200~----~----~------~----~----~----~ \n~ 0 10 20 30 40 50 \n\u00b7DELTA TIME SINCE SHUT-IN (min) \nFigure 2. G-Function Derivative Plot (Example 1). \n5,aoo \n,_ \n-;;; \n~ 5,600 \nLaJ \nl:t: \n:::::J \n~ 5,400 \nLaJ \nl:t: a.. \n5,200 60 \n5,ooo o'-----'-----2~---'-3 ---.l...4----.J...5 ___ .J...6 ___ _._7 _ ____. a \nSQUARE ROOT OF DELTA TIME \nFigure 3. Square-Root Plot (Example 1). SP\u00a3 1 6 4l7i I \n1-200 a \n....J \nD.. Fracture Closed \n1-a:= a I \nVl \n1.&.. 150 \na \nLaJ > i= \n~ > 100 ~ \nLaJ c \n1-z \n0 a.. \nI \nLO 10 20 30 40 50 60 \nDELTA TIME SINCE SHUT-IN \nFigure 4. Square-Root Derivative Plot (Example 1). \n6,200 \n6,000 \n,_ \n\"iii \n~ 5,aoo \nLaJ \nl:t: \n::::> \nVl 5,600 Vl \nLaJ \nl:t: a.. \n5,400"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45f42-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 7, "chroma:document": "~ 5,aoo \nLaJ \nl:t: \n::::> \nVl 5,600 Vl \nLaJ \nl:t: a.. \n5,400 \n5,200 L..._ __ ___l ____ __.J.. ___ .....J.... __ .....J._ ___ ~---...l------' \n0 0.1 0.2 0.3 0.4 .0.5 0.6 0. 7 \nG FUNCTION \nFigure 5. Pressure vs. the G-Function (Example 2). \n~ 2,500 .--..----------------------------------, \na. -\nLaJ > i= 2,000 \n~ \n~ \nLaJ c \n1-1,500 \nz \n0 a.. \nI \nLO 1,000 \n(!) \n\"C ' 500 a.. \n\"C 0 \nFigure 6. Fracture Closed \n2 3 4 5 6 7 a 9 10 11 12 \nDELTA TIME SINCE SHUT -IN (min) \nG-Function Derivative Plot (Example 2). \n280 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae45fc4-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 8, "chroma:document": "6,000 -\"iii \n~ 5,800 \nLW \n~ \n:::J \nVl 5,600 Vl \nLW \n[t: \nD... \n5,400 \n..... 350 0 \n.....1 \nD... \n..... [t: \n0 300 Vl \nLa.. \n0 \nw 250 > \n~ ct > \n~ w 200 c \n..... :z \n0 \nD... \nI Ill \nFigure 0.5 1.0 1.5 2.0 2.5 3.0 3.5 \nSQUARE ROOT OF DELTA TIME \nFigure 7. Square-Root Plot (Example 2). \n2 3 4 5 6 7 a 9 10 11 12 \nDELTA TIME SINCE SHUT -IN \n8. Square-Root Derivative Plot (Example 2). \n281 SP'E 1 6 4 1 ?1 ~ \n7.5 :z \n0 \n~ 7.4 u :z \n:::J \nLa.. \n..... 7.3 \n:z-wu \n~:::J 7.2 \nW~:t: n...o \n~La.. 7.1 \nw \n[t: \n:::J 7.0 Vl \nVl w \n[t: 6.9 a.. 0 0.1 0.2 0.3 0.4 0.5 0.7 0.6 \nG FUNCTION \nFigure 9. Pressure Function (u=l) vs. the G-Function \n(Example 2) \u2022 \nz 1.4 \n0 \n~ u z 1.2 :::J \nLa.. \nLa.. \n0 1.0 \nWll \n>:::J \n~[t: \n~0 o.a \n~I.&.. \nw c \n..... 0.6 z \n0 \nD... \nI 0.4 Ill 0 \nFigure 10. 2 3 4 s s 7 a 9 10 11 12 \nDELTA TIME SINCE SHUT -IN (min) \nPressure Function (u=l) Derivative Plot"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-16417-ms.pdf", "page": 8, "chroma:document": "Pressure Function (u=l) Derivative Plot \n( Ex amp 1 e 2 ) \u2022 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae460c8-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 0, "chroma:document": "SPE-215017-MS\nBest Practices in DFIT Interpretation - Comparative Analysis of 80 DFITs in\nthe Canadian Montney Shale Play\nClaudio Virues , Alexandra Robertson, and Bruce Sendecki , Alberta Energy Regulator\nCopyright 2023, Society of Petroleum Engineers DOI 10.2118/215017-MS\nThis paper was prepared for presentation at the 2023 SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, USA, 16 - 18 October 2023.\nThis paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents\nof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect\nany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4614a-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 0, "chroma:document": "consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may\nnot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.\nAbstract\nCurrent practice for conducting minifrac or diagnostic fracture injection tests has been changing with time.\nThe Alberta Energy Regulator (AER) has a pressure and deliverability testing directive that has guidance\non those tests. This guidance was updated in late 2021. Many operators from the Canadian Montney shale\nplay submit minifracs to AER, 80 of these minifracs were summarized statistically in this paper. Closure,\nreservoir pressure, and permeability were the main analyzed parameters in the paper scope.\nRequirements for pressure and deliverability tests are set out by this newly updated directive. Industry\nuses minifrac in horizontal wells with multistage fracture treatments when developing unconventional"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae461cc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 0, "chroma:document": "reservoirs. Closure, initial reservoir pressure is commonly being determined with the common well test.\nHolistic or tangent vs. compliance method are compared for closure pressure in this paper. Readers are\neager to replicate results, so for After Closure Analysis (ACA) methods equations that govern the analysis\nare provided in detail.\nPublished or commercially available holistic and compliance models are compared for closure pressure.\nPublished or commercially available ACA Soliman and Nolte methods are compared for permeability\nand reservoir pressure. Horizontal wells in 80 unconventional shale field case studies are presented. The\nfact that the signature of closure pressure is not apparent is a significant finding. Similarity of closure\npressure outcomes or estimates for tangent vs compliance is remarkable. Differentiation of reservoir\npressure determination for either linear or radial flow are observed. Interpretation on net pressure impact is"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae46244-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 0, "chroma:document": "evaluated and ultimately differentiation on ACA permeability determination is assessed. Analogous shale\nplays operators in USA and current Canadian Montney Shale play operators will find practical and direct\nimplications. To calculate effective fracture half length and optimize fracture design and well spacing\naccurate permeability values are needed. To design hydraulic fractures with geomechanics applications\naccurate closure pressure values are essential. To conduct Rate Transient Analysis (RTA) for resources and\nreserves assessment in similar unconventional shale plays accurate initial reservoir pressure as an input is\nfundamental.\nComparing analytically closure pressure methods in unconventional shale plays is novel. In addition,\npracticing engineers or well testing interpreters will find the comparison of different after closure analysis"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae462c6-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 0, "chroma:document": "relevant.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4633e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 1, "chroma:document": "2 SPE-215017-MS\nIntroduction\nThe AER requires pressure data to better manage the Montney resource play by understanding regional\npressure trends. Pressure analysis is also important to confirm the resource estimate used for annual reserves\nreporting in ST98 Alberta Energy Outlook. As part of contributions towards modernization, the AER has\nrevised the pressure and deliverability testing of oil and gas wells directive to include a minifrac testing and\nsubmission requirement. To ensure licensees and operators could submit minifrac results and data, AER\nrevised the PAS file in early 2020.\nHorizontal multistage wells with important volumes of treatment fluids are being used by industry in\nthe development of unconventional or tight reservoirs. In these reservoirs, build up tests are not providing\na representative initial reservoir pressure post-completion mainly due to extended shut-in time needed.\nInstead, minifrac, fracture injection or fall-off test has become the go to well test as far as determination of"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae463c0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 1, "chroma:document": "initial reservoir pressure in unconventionals.\nProppant-less minifracs are normally executed before the principal hydraulic fracture treatment.\nMinifrac's intent is generate a short fracture while injecting in order for the formation to be broken down.\nTherefore, while the pressure is falling down, the closure of the short fracture could be observed. Small\ninjected volumes of typically water, normally less than 16 m3, are used in these low rate tests. Less than\n15 minutes are normally used for total injection to be concluded, with the pressure falling (fall-off) over\ntypically a period of two weeks.\nDuring injection and fall-off periods the data on pressure is collected. Pressure is uploaded, smoothed\nand filtered for analysis in order to extract stress estimates, pore pressure and permeability. While assisting\nproduction and pressure analysis, being inputs for reservoir models, aiding to reserves quantification or"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae46442-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 1, "chroma:document": "stimulation assessment, determination of pore pressure and permeability is extremely important. Once\npressure data is analyzed and interpreted, leak-off coefficients, gradient of fracture pressure and closure of\nfracture pressure or minimum principal stress (or S min) could aid fracture design.\nGeology of Montney\nIn late 2013, NEB, AER and BC MoNGC assessed collaboratively the Montney geological formation's\nsaleable, and not conventional oil resources.\nIn Alberta and British Columbia in the 1950's, industry was focusing only on dolostone/sandstone\nMontney reservoir for oil and gas discovery. Siltstone, which has far greater volume of rock with oil and\ngas in it but less permeable, surrounded the standard dolostone/sandstone reservoir at the time. Montney\nsiltstones had to wait until 2005 to be developed, when drilling horizontals and multistage hydraulic\nfracturing came roaring.\nThe Montney geological formation (Lower Triassic) is vast, approximately ~131,000 km2 (Figure 1)."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae464c4-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 1, "chroma:document": "Its thickness is roughly on average 200 m, while thinning out at its eastern and northeastern flanks while\nspreading to over 300 m on the west before commencing with outcrops in the Rocky peaks.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4653c-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 2, "chroma:document": "SPE-215017-MS 3\nFigure 1\u2014Position of the Montney Formation in the subsurface of Alberta and British\nColumbia. (Source: The Ultimate Potential for Unconventional Petroleum from the\nMontney Formation in Alberta and British Columbia energy briefing note, November 2013)\nMethods\nThe minifrac analysis is performed before and after closure:\n\u2022Pre or before Closure Analysis (PCA)\n\u2022(ACA) or After Closure Analysis\nPre-Closure Analysis (PCA)\nThe subsequent parameters are extracted from the Before Closure Analysis:\n\u2022Closure Pressure of the fracture (p c)\n\u2022Instantaneous Shut-In Pressure (ISIP)\nISIP = Final Bottomhole Injection Pressure minus Friction Component\n\u2022Gradient of ISIP\nGradient of ISIP = ISIP divided by Depth of the Formation\n\u2022Net of the Fracture Pressure (\u0394p net)\n\u0394p net = ISIP minus Closure PressureDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae465be-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 3, "chroma:document": "4 SPE-215017-MS\n\u2022Fluid Efficiency: accumulated volume within the fracture divided by the total fluid injected.\nThis paper will review two methods to pick closure:\n1.McClure et al (2019)\n2.Barree et al (2009)\nAfter Closure Analysis (ACA)\nAfter Closure Analysis is completed on fall-off data compiled after fracture closure. The workflow is akin\nto conventional pressure transient analysis.\nThere are two ACA techniques discussed in this paper: Nolte and Soliman/Craig\nPre-Closure \u2013 \"Compliance\" procedure from McClure et al. (2019)\nFigure 2  shows field and simulation data with indication of closure from the tangent method (blue) and\nindication of closure from the fracture-compliance method (orange).\nFigure 2\u2014Identification of closure from the tangent and compliance\nmethod in field and simulation data (Source: SPE Journal 21)\nDiagnostic plots.   Figure 3  (left) reveals a DFIT conducted in the Montney formation. The plot shows"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae46640-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 3, "chroma:document": "measured calculated bottomhole pressure (BHP). When calculating fracture closure pressure, a hydrostatic\nadjustment would be added to convert from wellhead pressure (WHP) to BHP.\nFigure 3\u2014BHP Pressure (blue) and injection rate (orange) versus elapsed\ntime in hours (left) and BHP (blue) and dP/dG (red) versus G-time (right)Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae466cc-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 4, "chroma:document": "SPE-215017-MS 5\nFigure 3  (left) reveals pressure (blue) and injection rate (orange) versus time during injection and initial\nshut-in.\nFigure 3  (right) reveals pressure BHP (blue) and dP/dG (orange) versus G-time.\nData requirements for applying the procedure from McClure et al. (2019)\nIdentifying the contact pressure.   Figure 4 exhibits 2 cases of G-function plots where this key signature\nis clear or \"adequate\" or \"strong.\"\nFigure 4\u2014G-function plots where McClure closure signature is clear.\n(\"Adequate\" (left) vs. \"Strong\" (right) indication of McClure closure.\nFigure 5  indicates G-function plots from two Montney DFITs. The DFIT on the left can be classified as\ndisplaying \"weak\" indication of closure. The separation between the minimum and maximum dP/dG is not\ngood. Appraising stress with these types of tests is considered best practice.\nFigure 5\u2014\"Weak\" (left) vs. \"No\" (right) indication of McClure closure\nThe plot on the right can be characterized as displaying \"no\" indication of closure. The dP/dG plot is"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4674e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 4, "chroma:document": "diminishing monotonically downward without modulating upward. Best practice is not to carry on with\nestimating stress from these types of tests.\nEstimating effective Instantaneous Shut-in Pressure (ISIP).   Figure 6  displays how to detect contact\npressure and determine effective ISIP.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae467d0-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 5, "chroma:document": "6 SPE-215017-MS\nFigure 6\u2014Identification of contact pressure and effective ISIP (Source: URTeC-2019-123)\nMinifrac Observations from real data \u2013 McClure et al (2019)\nEstimating effective ISIP and S min.   In Figure 7 , contact happens around G-time of ~7.8, contact pressure\nor closure pressure estimation is 53,908 kPa and for the S min estimation a subtraction of 515 kPa (75 psi)\nfrom fracture closure will be required. The effective ISIP, ~56,000 kPa, is assessed by identifying the point\nof minimum dP/dG and extrapolating the pressure versus G-time curve back to zero from this point. The\neffective ISIP is an assessment for the pressure in the far-field fracture at shut-in. This is the pressure actually\npresent in the fracture that is opening up and spreading the crack.\nFigure 7\u2014Well 6 \u2013 Identification of contact pressure, minimum dP/dG and effective ISIP\nPre-Closure \u2013 \"Holistic\" procedure from Barree et al. (2009)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae46852-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 5, "chroma:document": "Pre-Closure \u2013 \"Holistic\" procedure from Barree et al. (2009)\nEstimating closure pressure and Smin.   Barree et al. (2009) proposed penciling in a straight line from\nthe origin to the tangent to the curve, near the peak, and recognizing this as the time of fracture \"closure\",\nbelieved to be equal to S min (see Figure 8 ). This is the so-called \"tangent\" method. Closure event is also\nmarked by a straight vertical dashed line in Figure 8 .Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
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id: 9ae468ca-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 6, "chroma:document": "SPE-215017-MS 7\nFigure 8\u2014G-function plot (Source: SPE 107877)\nSupplementary pre-closure interpretations from the \"tangent\" method.\nLeak-off types.\n1.Normal Leak-off (NL)  (Figure 9 , left)\n2.Transverse Fracture Storage/Fracture Height Recession (TFS/FHR) ( Figure 9, right)\n3.Pressure Dependent Leak-off (PDL): (Figure 10, left)\n4.Fracture Tip Extension (FTE)  (Figure 10 , right).\nTable 1  shows a summary of the leak-off types for all 80 field case studies.\nFigure 9\u2014Normal leak-off (left) and transverse fracture storage/fracture height recession leak-off (right) \u2013 Source: S&P GlobalDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 7, "chroma:document": "8 SPE-215017-MS\nFigure 10\u2014Pressure dependent leak-off (left) and fracture tip extension leak-off \u2013 Source: S&P Global\nTable 1\u2014Summary of the leak-off types and whether McClure Closure was observed.\nLeak-Off Type McClure Closure Pressure\nWell 1 TFS / FHR n/a\nWell 2 NORMAL (NL) YES\nWell 3 TFS / FHR YES\nWell 4 TFS / FHR n/a\nWell 5 PDL n/a\nWell 6 TFS / FHR YES\nWell 7 TFS / FHR YES\nWell 8 TFS / FHR YES\nWell 10 PDL n/a\nWell 11 TFS / FHR YES\nWell 12 TFS/FHR n/a\nWell 13 PDL n/a\nWell 14 PDL n/a\nWell 15 PDL n/a\nWell 16 PDL n/a\nWell 17 PDL n/a\nWell 18 TFS / FHR n/a\nWell 19 TFS / FHR n/a\nWell 20 TFS / FHR n/a\nWell 21 PDL n/a\nWell 22 TFS / FHR n/a\nWell 25 TFS / FHR YES\nWell 26 TFS / FHR n/a\nWell 27 TFS / FHR YES\nWell 28 PDL n/a\nWell 29 TFS / FHR n/a\nWell 30 TFS / FHR n/aDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 8, "chroma:document": "SPE-215017-MS 9\nLeak-Off Type McClure Closure Pressure\nWell 31 TFS / FHR YES\nWell 32 TFS / FHR YES\nWell 33 NORMAL (NL) n/a\nWell 35 TFS / FHR n/a\nWell 36 TFS / FHR n/a\nWell 37 TFS / FHR YES\nWell 38 TFS / FHR n/a\nWell 39 TFS / FHR n/a\nWell 40 TFS / FHR n/a\nWell 41 NORMAL (NL) n/a\nWell 42 TFS / FHR n/a\nWell 44 NORMAL (NL) n/a\nWell 45 TFS / FHR n/a\nWell 46 NORMAL (NL) n/a\nWell 47 TFS / FHR n/a\nWell 48 TFS / FHR YES\nWell 49 TFS / FHR YES\nWell 50 NORMAL (NL) YES\nWell 52 TFS / FHR YES\nWell 53 TFS / FHR YES\nWell 54 FTE YES\nWell 55 TFS / FHR YES\nWell 56 TFS / FHR YES\nWell 57 TFS / FHR YES\nWell 58 TFS / FHR YES\nWell 59 NORMAL (NL) n/a\nWell 60 TFS / FHR YES\nWell 61 TFS / FHR YES\nWell 62 TFS / FHR YES\nWell 63 TFS / FHR YES\nWell 64 TFS / FHR YES\nWell 65 TFS / FHR YES\nWell 66 FTE YES\nWell 67 TFS / FHR YES\nWell 68 TFS / FHR YES\nWell 69 TFS / FHR YES\nWell 70 TFS / FHR YES\nWell 71 TFS / FHR YES\nWell 72 TFS / FHR YES"}


created_at: 2023-11-17 19:17:23
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 8, "chroma:document": "Well 71 TFS / FHR YES\nWell 72 TFS / FHR YES\nWell 73 TFS / FHR YESDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 9, "chroma:document": "10 SPE-215017-MS\nLeak-Off Type McClure Closure Pressure\nWell 74 TFS / FHR YES\nWell 75 TFS / FHR YES\nWell 76 TFS / FHR YES\nWell 77 TFS / FHR YES\nWell 78 TFS / FHR YES\nWell 79 TFS / FHR YES\nWell 80 TFS / FHR YES\nThe pivot chart in Figure 11  shows how many leak-off types show indication of McClure closure pressure\nvs. when it is not available (n/a). McClure closure is not found in pressure dependent leak-off.\nFigure 11\u2014Pivot chart for leak-off types\nMinifrac Observations from real data - Barree et al. (2009)\nWell 44 - Normal Leak-off G-function Analysis.   The field case in Figure 12 reveals some minor deviation\nfrom the perfect constant leak-off but is a notable example of the anticipated curve shape with a clear-cut\nindication of closure at Gc = 7.157.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 10, "chroma:document": "SPE-215017-MS 11\nFigure 12\u2014Well 44 - G-function\nWell 44- Normal Leak-off Sqrt(t) Analysis.   The plot in Figure 13 , reveals that the slope of the pressure\ncurve begins low, then rises and gets a maximum rate of decline at the inflection point, then diminishes\nagain after closure.\nFigure 13\u2014Well 44 - Sqrt(t) plot\nResults\nEstablished industry methodologies were compared. No one method is recommended over another. The\nanalysis performed demonstrates the ranges of outcomes between the alternative approaches.\nThe results are summarized in Table 2 . Thereafter, we discuss the clarity of the compliance closure\nresponse, a comparison between closure and net pressure from holistic vs. compliance method, estimation\nof permeability and pressure, and rate transient analysis implications.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 11, "chroma:document": "12 SPE-215017-MS\nTable 2\u2014Summary of the statistical comparisons, conditions for inclusion of a test in the comparison, and key findings\nComparisons Condition for Inclusion Key Findings\nComparison of DFITs showing strong,\nadequate, weak, or no \"compliance\" method\nindication of closureNo condition; all DFITs were\nincluded20% showed strong indication of closure,\n~24% showed adequate indication of closure,\n~9% showed weak indication of closure and\n~48% showed no indication of compliance\nclosure.\nComparison of closure pressure\nestimated from \"compliance\" versus\n\"tangent\" methodsMust have strong, adequate \"compliance\"\nindication of closureThe tangent method and compliance\nmethods provide similar closure pressure within\n8% difference.\nComparison of net pressure Must have strong or adequate\n\u2018compliance\u2019 indication\nof closureThe net pressure estimated using tangent\nclosure and ISIP is 10x higher than that estimated\nbased on compliance closure and effective\nISIP, or an average of ~17,000 kPa."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 11, "chroma:document": "ISIP, or an average of ~17,000 kPa.\nComparison of permeability Must have either achieved radial\nand/or linear flowsPermeabilities estimates were of the same\norder of magnitude for Nolte and\nSoliman/Craig.\nComparison of pore pressure Must have either achieved radial\nand/or linear flowsPore pressure estimates were of the same\norder of magnitude for Nolte and\nSoliman/Craig.\nComparison of Xf \u221ak  and\nAf\u221akMust have at least achieved\nlinear flowEstimates are heavily dependent on assumptions\nof net pay. RTA estimates for Af\u221ak\nwere significantly higher, ~300x.\nDiscussion\nClarity of the \"compliance\" closure response\nFigure 14  shows the fraction of tests with strong, adequate, weak, and no \"compliance\" method indication\nof closure on the dP/dG plot.\nFigure 14\u2014Fraction of tests with strong (yellow), adequate (grey),\nweak (orange) and no (red) compliance indication of closure.\nClosure pressure from the compliance method and tangent method"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 11, "chroma:document": "Closure pressure from the compliance method and tangent method\nFigure 15  shows a comparison of the dP/dG and G*dP/dG plots from a Montney DFIT.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 12, "chroma:document": "SPE-215017-MS 13\nFigure 15\u2014dP/dG as a function of G-time (left) and G*dP/dG as a function of G-time\n(right) plots from Montney DFITs (Source: Discussion of the Paper SPE-187038-MS)\nThe methods yield similar results as far as closure pressure is concerned. compliance closure pressure is\n~8% higher for this dataset. Table 3 displays a comparison between compliance closure pressure (McClure\net al 2019 ) vs. the holistic closure pressure.\nTable 3\u2014Summary of closure pressure values\nCompliance Closure\nPressure (kPa)Holistic Closure\nPressure (kPa)Delta Closure\nPressure (Xx)Delta Closure\nPressure (kPa)\nWell 1 n/a 49898\nWell 2 40,742 38721 1.1x 2021\nWell 3 43,600 39441 1.1x 4159\nWell 4 n/a 48658\nWell 5 n/a 37136\nWell 6 53,908 50979 1.1x 2929\nWell 7 45000 40154 1.1x 4846\nWell 8 40000 38306 1.0x 1694\nWell 9 n/a 46274\nWell 10 n/a 40993\nWell 11 25500 22849 1.1x 2651\nWell 12 n/a 48941\nWell 13 n/a 42201\nWell 14 n/a 50861\nWell 15 n/a 46387\nWell 16 n/a 32003\nWell 17 n/a 62545\nWell 18 n/a 43727\nWell 19 n/a 36657"}


created_at: 2023-11-17 19:17:23
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 12, "chroma:document": "Well 17 n/a 62545\nWell 18 n/a 43727\nWell 19 n/a 36657\nWell 20 n/a 48642\nWell 21 n/a 44425\nWell 22 n/a 39274\nWell 23 n/a 49202\nWell 24 n/a 32177Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 13, "chroma:document": "14 SPE-215017-MS\nCompliance Closure\nPressure (kPa)Holistic Closure\nPressure (kPa)Delta Closure\nPressure (Xx)Delta Closure\nPressure (kPa)\nWell 25 42000 39822 1.1x 2178\nWell 26 n/a 40033\nWell 27 48000 42779 1.1x 5221\nWell 28 n/a 41951\nWell 29 n/a 41981\nWell 30 n 39572\nWell 31 41000 37289 1.1x 3711\nWell 32 43000 40722 1.1x 2278\nWell 33 n/a 50727\nWell 34 n/a 31641\nWell 35 n/a 45609\nWell 36 n/a 48477\nWell 37 52000 49933 1.0x 2067\nWell 38 n/a 50366\nWell 39 n/a 37965\nWell 40 n/a 35101\nWell 41 n/a 58321\nWell 42 n/a 45132\nWell 43 n/a 40327\nWell 44 n/a 46743\nWell 45 n/a 40408\nWell 46 n/a 43833\nWell 47 n/a 41213\nWell 48 52811 48611 1.1x 4200\nWell 49 41000 37157 1.1x 3843\nWell 50 50,000 49563 1.0x 437\nWell 51 n/a 53873\nWell 52 47000 43747 1.1x 3253\nWell 53 46250 44040 1.1x 2210\nWell 54 45500 43341 1.0x 2159\nWell 55 44000 39140 1.1x 4860\nWell 56 43000 40475 1.1x 2525\nWell 57 59500 53083 1.1x 6417\nWell 58 44500 38359 1.2x 6141\nWell 59 n/a 55895\nWell 60 42000 38344 1.1x 3656\nWell 61 47000 43332 1.1x 3668"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 13, "chroma:document": "Well 60 42000 38344 1.1x 3656\nWell 61 47000 43332 1.1x 3668\nWell 62 42000 37941 1.1x 4059\nWell 63 37500 36070 1.0x 1430\nWell 64 41000 37720 1.1x 3280Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae46f5a-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 14, "chroma:document": "SPE-215017-MS 15\nCompliance Closure\nPressure (kPa)Holistic Closure\nPressure (kPa)Delta Closure\nPressure (Xx)Delta Closure\nPressure (kPa)\nWell 65 50020 45652 1.1x 4368\nWell 66 39000 37827 1.0x 1173\nWell 67 46000 42301 1.1x 3699\nWell 68 40000 36382 1.1x 3618\nWell 69 44000 40475 1.1x 3525\nWell 70 44000 40934 1.1x 3066\nWell 71 45000 41406 1.1x 3594\nWell 72 41500 39774 1.0x 1726\nWell 73 44000 39551 1.1x 4449\nWell 74 44500 39371 1.1x 5129\nWell 75 47000 42233 1.1x 4767\nWell 76 46000 41633 1.1x 4367\nWell 77 47000 43466 1.1x 3534\nWell 78 43500 39560 1.1x 3940\nWell 79 46000 42845 1.1x 3155\nWell 80 42500 38906 1.1x 3594\nAverage 44,472 42,667 1.08x 3,419\nEstimating Permeability and Pore Pressure \u2013 Nolte and Soliman/Craig\nNolte ACA Derivative.   Figure 16  represents the log-log diagnostic plot for well 2 used to confirm fracture\nclosure and identify the flow regimes developed after closure.\nFigure 16\u2014Well 2 - Log-log derivative (diagnostic) plot \u2013 Nolte radial flow"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 14, "chroma:document": "Nolte ACA Linear Flow.   If impulse linear flow is identified in the derivative plot, the fluid loss coefficients,\nCR and CT, can also be estimated.\nThe equations 1 , 2, 3 and 4 governing impulse linear flow are defined as:Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 15, "chroma:document": "16 SPE-215017-MS\n(1)\n(2)\n(3)\nFigure 17  represents the Well 2 fall-off data using Nolte's linear time function.\nFigure 17\u2014Well 2 - Fall-off data using minifrac linear time function for Nolte\nNolte ACA Radial Flow.   The equations 4 , 5, 6 and 7 governing impulse radial flow are defined as:\n(4)\n(5)\n(6)\n(7)\nFigure 18  represents the Well 3 fall-off data using Nolte's radial time function.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 16, "chroma:document": "SPE-215017-MS 17\nFigure 18\u2014Well 3 - Fall-off data using minifrac radial time function for Nolte\nSoliman/Craig ACA Derivative.   Figure 19  represents the log-log diagnostic plot for well 3 used to confirm\nfracture closure and identify the flow regimes developed after closure.\nFigure 19\u2014Well 3 - Log-log Derivative (diagnostic) plot \u2013 Soliman/Craig Analysis radial flow\nSoliman/Craig ACA Radial Flow.   The equations 8 , 9, 10 and 11 governing radial flow are defined as:\n(8)\n(9)\n(10)\n(11)Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 17, "chroma:document": "18 SPE-215017-MS\nFigure 20  represents the Well 3 fall-off data using Soliman/Craig's radial time function. When radial flow\nis achieved after closure, this plot yields a constant slope. By fitting a straight line through the radial flow\ntrend, the analysis yields a kh of 0.0353 md.m and k = 1.26E-03md using net pay h = 28.1m.\nFigure 20\u2014Well 3 \u2013 Soliman/Craig analysis minifrac radial flow\nTable 4  summarizes the results of the 80 field cases.\nTable 4\u2014Summary of the permeability values for Nolte and Soliman/Craig After Closure Analysis for radial flow and key findings\nNolte Permeability\nRadial Flow\n(mD)Soliman/Craig\nPermeability Radial\nFlow (mD)Key Findings\nWell 1 3.96E-04 3.69E-04\nWell 2 7.67E-05 1.89E-04\nWell 3 7.30E-04 7.40E-04\nWell 4 4.65E-03 3.72E-03\nWell 5 4.30E-02 Radial flow not\nachieved (Soliman/Craig)\nWell 6 1.80E-04 1.90E-04\nWell 7 1.00E-02 9.10E-05\nWell 11 3.80E+00 3.24E+00\nWell 12 5.97E-03 6.00E-03\nWell 14 1.41E-02 1.29E-02\nWell 15 1.66E-03 1.60E-03\nWell 16 8.07E-02 2.84E-02"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 17, "chroma:document": "Well 15 1.66E-03 1.60E-03\nWell 16 8.07E-02 2.84E-02\nWell 20 3.10E-03 3.16-03\nWell 23 6.20E-03 2.00E-03\nWell 24 4.39E-02 4.36E-02\nWell 25 2.46E-04 2.46E-04\nWell 26 1.40E-04 1.60E-04\nWell 29 3.15E-04 3.04E-04\nWell 30 4.23E-03 Radial flow not\nachievedDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 18, "chroma:document": "SPE-215017-MS 19\nNolte Permeability\nRadial Flow\n(mD)Soliman/Craig\nPermeability Radial\nFlow (mD)Key Findings\n(Soliman/Craig)\nWell 33 1.00E-07 9.70E-08\nWell 34 1.58E-02 1.60E-02\nWell 35 1.50E-01 4.00E-02\nWell 36 3.98E-03 2.30E-03\nWell 37 8.45E+00 5.69E+00\nWell 38 1.03E-02 3.00E-03\nWell 39 3.20E-04 3.30E-04\nWell 41 2.50E-02 Radial flow not\nachieved\n(Soliman/Craig)\nWell 42 1.60E-03 1.60E-03\nWell 43 3.10E-01 3.08E-01\nWell 44 3.70E-03 3.80E-03\nWell 46 3.10E-04 3.10E-04\nWell 48 2.30E-02 2.24E-02\nWell 50 1.02E-03 Radial flow not\nachieved\n(Nolte)\nWell 62 2.40E-03 2.30E-03\nWell 65 1.20E-03 9.90E-04\nWell 80 3.96E-04 3.69E-04\nThe stacked chart in Figure 21  was used to display the relationship of part to whole over Nolte vs Soliman/\nCraig categories.\nFigure 21\u2014Stacked area chart for Nolte vs. Soliman/Craig permeability estimates using radial flow.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 19, "chroma:document": "20 SPE-215017-MS\nThe scatter chart in Figure 22  was used to compare Nolte and Soliman/Craig sets of permeability values\nfor radial flow. It shows the one-to-one relationship between both sets of values.\nFigure 22\u2014Scatter Chart for Nolte vs. Soliman/Craig permeability estimates using radial flow.\nThe histogram in Figure 23  shows the frequency of occurrence of values within both data sets, Nolte,\nand Soliman/Craig. Ranges of values are grouped into bins.\nFigure 23\u2014Histogram for Nolte vs. Soliman/Craig permeability estimates using radial flow.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47360-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 20, "chroma:document": "SPE-215017-MS 21\nA comparison of pore pressure estimated using Nolte and Soliman/Craig is shown in Table 5.\nTable 5\u2014Summary of the pore pressure for Nolte and Soliman/Craig ACA for radial and linear flow.\nNolte ACA Pore\nPressure Radial\nFlow (kPa)Nolte ACA Pore\nPressure Linear\nFlow (kPa)Soliman/Craig ACA\nPore Pressure Radial\nFlow (kPa)Soliman/Craig ACA\nPore Pressure Linear\nFlow (kPa)\nWell 1 28,013 26,000 28,058 26,560\nWell 2 31,187 30,562 31,700 30,467\nWell 3 29,735 29,188 29,781 29,287\nWell 4 40,377 39,912\nWell 5 29,120 29,210\nWell 6 43,432 41,413 42,350 41,182\nWell 7 31,105 31,101\nWell 8 24,639 23,193\nWell 11 17,014 15,059 16,895 13,749\nWell 12 37,390 36,302 37,397 35,362\nWell 14 41,783 40,870\nWell 15 39,140 39,133 35,699\nWell 16 31,830 31,799 31,674\nWell 17 82,400 79,110\nWell 18 30,397 30,400\nWell 19 27,448 27,370\nWell 20 36,971 35,796 37,022 35,228\nWell 21 31,085 31,102\nWell 22 29,108 28,689\nWell 23 41,763 41,758 41,257\nWell 24 25,981 25,985\nWell 25 26,870 26,871\nWell 26 28,784 28,385 28,844 28,361"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae473ec-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 20, "chroma:document": "Well 25 26,870 26,871\nWell 26 28,784 28,385 28,844 28,361\nWell 27 31,126 31,117\nWell 28 26,359\nWell 29 31,789 31,780\nWell 30 29,287 25,429\nWell 31 26,249 26,242\nWell 32 30,940 30,937\nWell 33 43,429 43,436\nWell 34 25,428 25,438\nWell 35 34,831 34,287 34,416 34,241\nWell 36 41,675 38,289 40,729 35,101\nWell 37 42,424 41,407 42,117 41,159\nWell 38 46,953 44,777 44,217 38,430\nWell 39 28,342 28,077 28,361 28,036Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47464-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 21, "chroma:document": "22 SPE-215017-MS\nNolte ACA Pore\nPressure Radial\nFlow (kPa)Nolte ACA Pore\nPressure Linear\nFlow (kPa)Soliman/Craig ACA\nPore Pressure Radial\nFlow (kPa)Soliman/Craig ACA\nPore Pressure Linear\nFlow (kPa)\nWell 40 24,911 22,801 24,866 22,676\nWell 41 43,230\nWell 42 37,073 37,116 30,547\nWell 43 27,083 25,622 27,084 25,924\nWell 44 37,914 37,058 37,920 27,154\nWell 46 31,267 31,262\nWell 47 29,967\nWell 48 38,105 36,533 38,072 37,830\nWell 49 27,647\nWell 50 32,097 32,142 33,210\nWell 51 44,104 43,188\nWell 52 27,197\nWell 53 27,741 27,711\nWell 54 30,607\nWell 55 30,273\nWell 56 29,024\nWell 57 39,255 37,361\nWell 58 25,492\nWell 59 24,103\nWell 60 29,127 29,106\nWell 61 32,655 32,593\nWell 62 28,748 28,740\nWell 63 26,154 23,335 26,162 23,276\nWell 64 28,904 28,896\nWell 65 38,074 35,506 37,819 34,912\nWell 66 25,348 25,385\nWell 67 29,848\nWell 68 29,482 29,454\nWell 69 29,024\nWell 70 25,001 24,986\nWell 71 27,632 27,564\nWell 72 28,010 27,998\nWell 73 28,908\nWell 74 26,322 26,286\nWell 76 27,551 27,559\nWell 77 28,927\nWell 78 30,112 30,087"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae474e6-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 21, "chroma:document": "Well 76 27,551 27,559\nWell 77 28,927\nWell 78 30,112 30,087\nWell 79 28,700 28,693\nWell 80 24,518 24,504Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47568-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 22, "chroma:document": "SPE-215017-MS 23\nThe clustered column chart in Figure 24 shows slightly higher estimates for radial flow vs. linear flow\nfor Nolte and Soliman/Craig methods.\nFigure 24\u2014Clustered column chart for Nolte vs. Soliman/Craig pressure estimates for linear and radial flow.\nNet pressure from the compliance method and tangent method\nThe \u2018compliance net pressure\u2019 is calculated as the \u2018effective ISIP\u2019 minus the estimate for compliance\nclosure pressure for the compliance closure the \u2018holistic net pressure\" is calculated as the \u2018ISIP\u2019 minus the\nestimate for holistic closure pressure. It is an estimate for the pressure driving crack propagation through\nthe formation \u2013 the amount that pressure exceeds closure pressure.\nThe holistic net pressures are on average about ~10x higher (~17,000 kPa higher). This comparison uses\nthe ~44% of the tests for which the compliance method closure pick was assessed as being \"strong\" or\n\"adequate\". Table 6  shows a summary of the net pressure values for Compliance and Holistic methods."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae475ea-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 22, "chroma:document": "Table 6\u2014Summary of Net Pressures using Holistic and Compliance with inputs.\nHolistic\nISIP (kPa)Compliance\n(Effective)\nISIP (kPa)Holistic Closure\nPressure (kPa)Compliance\nClosure\nPressure (kPa)Holistic Net\nPressure (kPa)Compliance Net\nPressure (kPa)\nWell 1 66,234 n/a 49,898 n/a 16,336 n/a\nWell 2 67,916 45,500 38,721 40,742 29,195 4,758\nWell 3 63,444 45,000 39,441 43,600 24,003 1,400\nWell 4 55,564 n/a 48,658 n/a 6,906 n/a\nWell 5 46,328 n/a 37,136 9,192 0\nWell 6 64,666 56,000 50,979 53,908 13,687 2,092\nWell 7 76,254 46,000 40,154 45,000 36,100 1,000\nWell 8 47,087 42,500 38,306 40,000 8,781 2,500\nWell 9 52,431 n/a 46,274 n/a 6,157 n/a\nWell 10 67,785 45,000 40,993 n/a 26,792 n/a\nWell 11 26,751 26,500 22,849 25,500 3,902 1,000Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4766c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 23, "chroma:document": "24 SPE-215017-MS\nHolistic\nISIP (kPa)Compliance\n(Effective)\nISIP (kPa)Holistic Closure\nPressure (kPa)Compliance\nClosure\nPressure (kPa)Holistic Net\nPressure (kPa)Compliance Net\nPressure (kPa)\nWell 12 56,048 54,000 48,941 n/a 7,107 n/a\nWell 13 45,975 n/a 42,201 n/a 3,774 n/a\nWell 14 72,438 59,000 50,861 n/a 21,577 n/a\nWell 15 53,541 50,000 46,387 n/a 7,154 n/a\nWell 16 32,385 32,325 32,003 n/a 382 n/a\nWell 17 101,279 n/a 62,545 n/a 38,734 0\nWell 18 68,256 50,000 43,727 n/a 24,529 n/a\nWell 19 81,662 43,500 36,657 n/a 45,005 n/a\nWell 20 55,261 52,500 48,642 n/a 6,619 n/a\nWell 21 56,144 48,000 44,425 n/a 11,719 n/a\nWell 22 42,903 n/a 39,274 n/a 3,629 n/a\nWell 23 58,341 55,000 49,202 n/a 9,139 n/a\nWell 24 37,224 n/a 32,177 n/a 5,047 n/a\nWell 25 76,049 44,000 39,822 42,000 36,227 2,000\nWell 26 45,008 44,000 40,033 n/a 4,975 n/a\nWell 27 72,672 49,000 42,779 48,000 29,893 1,000\nWell 28 73,982 n/a 41,951 n/a 32,031\nWell 29 68,290 45,750 41,981 n/a 26,309 n/a\nWell 30 63,821 n/a 39,572 n/a 24,249 0"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae476f8-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 23, "chroma:document": "Well 30 63,821 n/a 39,572 n/a 24,249 0\nWell 31 51,506 41,750 37,289 41,000 14,217 750\nWell 32 77,376 46,000 40,722 43,000 36,654 3,000\nWell 33 66,448 n/a 50,727 n/a 14,217 n/a\nWell 34 42,298 n/a 31,641 n/a 10,657 n/a\nWell 35 68,408 54,500 45,609 n/a 16,740 n/a\nWell 36 59,604 55,750 48,477 n/a 11,127 n/a\nWell 37 55,169 54,500 49,933 52,000 5,236 2,500\nWell 38 54,820 54,500 50,366 n/a 4,454 n/a\nWell 39 68,227 47,500 37,965 n/a 30,262 n/a\nWell 40 42,880 39,500 35,101 n/a 7,779 n/a\nWell 41 62,933 n/a 58,321 n/a 4,612 n/a\nWell 42 52,207 51,000 45,132 n/a 7,075 n/a\nWell 43 48,682 n/a 40,327 n/a 8,355 n/a\nWell 44 54,807 54,000 46,743 n/a 8,064 n/a\nWell 45 47,548 45,500 40,408 n/a 7,140 n/a\nWell 46 67,523 n/a 43,833 n/a 23,690 n/a\nWell 47 53,237 n/a 41,213 n/a 12,024 n/a\nWell 48 53,638 54,000 48,611 52,811 5,027 1,189\nWell 49 77,084 44,000 37,157 41,000 39,927 3,000"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47770-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 23, "chroma:document": "Well 49 77,084 44,000 37,157 41,000 39,927 3,000\nWell 50 52,700 52,500 49,563 48,500 3,137 4,000Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae477f2-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 24, "chroma:document": "SPE-215017-MS 25\nHolistic\nISIP (kPa)Compliance\n(Effective)\nISIP (kPa)Holistic Closure\nPressure (kPa)Compliance\nClosure\nPressure (kPa)Holistic Net\nPressure (kPa)Compliance Net\nPressure (kPa)\nWell 51 90,441 n/a 53,873 n/a 36,568 0\nWell 52 71,593 48,250 43,747 47,000 27,846 1,250\nWell 53 68,659 48,000 44,040 46,250 24,619 1,750\nWell 54 77,548 49,500 43,341 45,500 34,207 4,000\nWell 55 62,712 47,500 39,140 44,000 23,572 3,500\nWell 56 70,992 44,250 40,475 43,000 30,517 1,250\nWell 57 63,140 61,000 53,083 59,500 10,057 1,500\nWell 58 57,153 46,000 38,359 44,500 18,794 1,500\nWell 59 63,170 n/a 55,895 n/a 7,275 0\nWell 60 67,694 43,500 38,344 42,000 29,350 1,500\nWell 61 72,766 48,000 43,332 47,000 29,434 1,000\nWell 62 65,552 43,000 37,941 42,000 27,611 1,000\nWell 63 41,622 40,000 36,070 37,500 5,552 2,500\nWell 64 79,428 44,000 37,720 41,000 41,708 3,000\nWell 65 51,418 48,000 45,652 50,020 5,766 -2,020\nWell 66 72,990 47,250 37,827 39,000 35,163 8,250\nWell 67 60,842 47,750 42,301 46,000 18,541 1,750"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47874-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 24, "chroma:document": "Well 67 60,842 47,750 42,301 46,000 18,541 1,750\nWell 68 60,527 41,000 36,382 40,000 24,145 1,000\nWell 69 70,992 44,500 40,475 44,000 30,517 500\nWell 70 76,096 48,000 40,934 44,000 35,162 4,000\nWell 71 71,998 46,000 41,406 45,000 30,592 1,000\nWell 72 69,560 44,500 39,774 41,500 29,786 3,000\nWell 73 72,033 44,500 39,551 44,000 32,482 500\nWell 74 78,979 45,000 39,371 44,500 39,608 500\nWell 75 60,774 48,000 42,233 47,000 18,541 1,000\nWell 76 70,560 47,000 41,633 46,000 28,927 1,000\nWell 77 75,124 47,250 43,466 47,000 31,658 250\nWell 78 71,225 47,500 39,560 43,500 31,665 4,000\nWell 79 57,788 47,000 42,845 46,000 14,943 1,000\nWell 80 53,923 43,000 38,906 42,500 15,017 500\nAverage 18,939 1,908\nIn hydraulic fracturing, higher net fracture pressures can have several implications:\n1.Enhanced fracture growth: high net fracture pressures help create and extend fractures in the target\nformation, allowing for greater contact with the reservoir and improved flow of oil and gas."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47cde-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 24, "chroma:document": "2.Increased production rates: by generating larger and longer fractures, high net fracture pressures can\nenhance the productivity of a well, leading to increased production rates of oil and gas.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47d6a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 25, "chroma:document": "26 SPE-215017-MS\n3.Reservoir connectivity: high net fracture pressures can help establish better connectivity between the\nwellbore and the reservoir, enabling the extraction of hydrocarbons from a larger area within the\nformation.\n4.Risk of fracture propagation: while high net fracture pressures can be advantageous, they also carry\nthe risk of unintended fracture propagation.\n5.Hydraulic fracturing fluid requirements: achieving high net fracture pressures may require larger\nvolumes of hydraulic fracturing fluid, which can pose logistical challenges, increase costs and\npotentially impact water availability in some regions.\nRate Transient Analysis\nRate Transient Analysis was conducted to make a comparison on values of Af\u221a k estimates using DFIT\nACA methodologies. The periods analyzed for RTA ranged from 1 day up to 75 days of production and\npressure data. Figure 25  shows a typical production and pressure profile for the wells analyzed."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47dec-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 25, "chroma:document": "Figure 25\u2014Well 36 \u2013 Typical production and pressure profile used for rate transient analysis.\nSoliman/Craig ACA Linear Flow.   The equations 12, 13, 14 and 15 governing linear flow are defined as:\n(12)\n(13)\n(14)\n(15)\nFigure 26  shows minifrac linear flow plot for Soliman/Craig.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47e6e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 26, "chroma:document": "SPE-215017-MS 27\nFigure 26\u2014Well 3 - Soliman / Craig Analysis \u2013 Linear Flow\nTable 7  shows a summary of the Soliman -Craig estimates of Xf\u221ak, Af\u221ak and RTA estimates of Af\u221ak\n(linear flow). Wells with no or insufficient data are shown as non/available (n/a).\nTable 7\u2014Summary of the Soliman -Craig estimates of Xf\u221ak, Af\u221ak and RTA estimates of Af\u221ak (linear flow)\nSoliman / Craig\nLinear Flow\nXf \u221a k  (m*\u221amd)Assumed h\nNet Pay (m)Soliman / Craig Linear\nFlow Af\u221ak\n(m2 \u221amd)RTA Linear Flow\nAf\u221ak\n(m2 \u221amd)\nWell 1 0.03 45 1.35 7,595\nWell 6 0.06 15 0.9 788\nWell 9 9.64 45 434 n/a\nWell 12 0.39 15 5.85 13,753\nWell 15 0.05 10 0.5 41,668\nWell 16 2.87 15 43.05 3,970\nWell 20 0.21 15 3.15 4,805\nWell 21 0.34 20 6.80 n/a\nWell 26 0.05 15 0.75 1,163\nWell 35 5.68 20 113.6 769\nWell 36 0.14 15 2.1 5,748\nWell 37 70.87 20 1417 n/a\nWell 38 0.17 20 3.4 31,278\nWell 39 0.11 15 1.65 687\nWell 40 0.2 20 4 2,842\nWell 42 0.07 39 2.73 10,705\nWell 43 7.55 20 151 n/a\nWell 44 0.11 53 5.83 n/a\nWell 46 0.07 40 2.8 4,428\nWell 48 1.16 15 17.4 3,748"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47efa-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 26, "chroma:document": "Well 46 0.07 40 2.8 4,428\nWell 48 1.16 15 17.4 3,748\nWell 50 0.12 20 2.4 n/aDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47f72-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 27, "chroma:document": "28 SPE-215017-MS\nSoliman / Craig\nLinear Flow\nXf \u221a k  (m*\u221amd)Assumed h\nNet Pay (m)Soliman / Craig Linear\nFlow Af\u221ak\n(m2 \u221amd)RTA Linear Flow\nAf\u221ak\n(m2 \u221amd)\nWell 65 0.18 17 3.06 6,224\nConclusions\nThis study reviews results from 80 DFITs from different operators in the Canadian Unconventional Montney\nshale play. The key findings are as follows:\na.A \u2018compliance method\u2019 closure/stress estimate is not apparent in the significant majority of DFITs in\nthe Canadian Montney formation.\nb.The compliance method and tangent method provide similar closure pressures. The compliance\nclosure pressure was ~8% higher than the tangent closure pressure on average. To estimate the\nminimum principal stress, a subtraction of a pressure constant from the compliance closure pressure\nis suggested by McClure et al. 2019 .\nc.The clarity of the \u2018compliance method\u2019 closure response varies in the Montney.\nd.The net pressure estimated based on tangent closure and \u2018ISIP\u2019 are ~10x higher on average than that"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae47ff4-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 27, "chroma:document": "estimated based on compliance closure and \u2018effective ISIP\u2019.\ne.7 cases were identified as normal leak-off (NL). 56 cases were identified as transverse fracture storage/\nfracture height recession (TFS/FHR). 9 cases out of 80 cases were identified as pressure dependent\n(PDL). 2 cases were identified as fracture tip extension (FTE). 6 cases were not clearly identified. As\nexpected, McClure closure was not found in PDL signatures.\nf.Nolte and Soliman-Craig ACA permeability estimates were of similar order of magnitude for linear\nor radial flow, respectively.\ng.Nolte and Soliman-Craig ACA pore pressure estimates for linear and/or radial flow were of similar\norder of magnitude for linear or radial flow, respectively. Pore pressure estimates for linear flow were\nslightly lower than for radial flow.\nh.As far as RTA implications, Xf\u221ak  and Af\u221ak  estimates from ACA methodologies are heavily dependent\non the assumption on whether the net pay has been partially or fully accessed. When Af\u221a k estimates"}


created_at: 2023-11-17 19:17:23
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id: 9ae48062-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 27, "chroma:document": "from DFIT were compared with RTA estimates, the latter values were ~7,000x higher.\ni.The AER does not make recommendations or approve one single analysis method over another. The\nanalysis of the various methods demonstrates the range of possible outcomes and illustrates unique\nproperties of the Montney reservoir and can be used to optimize development.\nj.The ability to independently calculate reservoir pressure across the unconventional play allows better\nunderstanding the pressure variances of the Montney and enables more accurate resource estimation\nof the play to be performed and reported. Without DFIT data, resource evaluation has been historically\nmore difficult.\nNomenclature\nAf= fracture area, L2, m2\nct= total compressibility, Lt2/m, kPa\u22121\nCT= total fluid loss coefficient, L/t\u00bd, m/min1/2\nFL1= Nolte linear flow time function, dimensionless\nFR1= Nolte radial flow time function, dimensionless\nG= G-function, dimensionless\nh= net pay, L, m"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 27, "chroma:document": "G= G-function, dimensionless\nh= net pay, L, m\nk= permeability, L2, mdDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48166-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 28, "chroma:document": "SPE-215017-MS 29\nXf= fracture half-length, L, m\np= pressure, m/Lt2, kPa\npfo = fracture pressure measured at wellbore, m/Lt2, kPa\nq= flow rate, L3/t, m3/D\nQt= total injection volume, L3, m3\nt= time, hr\ntp= producing time, hr\nV= injection  volume, m3\n\u03c0= constant, dimensionless\n\u0394= difference, dimensionless\n\u00b5= viscosity, m/Lt, cp\n\u03a6= porosity, dimensionless\nSubscripts\na= adjusted\nc= closure\nD= dimensionless\ni= initial\nf= fracture\np= producing\nt= total\nw= wellbore\nReferences\nAlberta Energy Regulator Directive 040: Pressure and Deliverability Testing Oil and Gas Wells  https://www.aer.ca/\nregulating-development/rules-and-directives/directives/directive-040\nAlberta Energy Regulator Report ST98: Alberta Energy Outlook, https://www.aer.ca/providing-information/data-and-\nreports/statistical-reports/st98\nBarree, R.D. , H. Mukherjee . 1996 . Determination of pressure dependent leak-off and its effect on fracture geometry . Paper"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae481e8-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 28, "chroma:document": "SPE 36424 presented at the SPE Annual Technical Conference and Exhibition, Denver, CO, doi: 10.21118/36424-MS\nBarree, R.D. 1998 . Applications of Pre-Frac Injection/Falloff Tests in Fissured Reservoirs\u2014Field Examples. Paper SPE\n39932 presented at the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium, Denver, 5\u20138 April.\nDOI: 10.2118/39932-MS .\nBarree, R.D. , V .L. Barree  and D.P. Craig. 2007 . Holistic fracture diagnostics, Paper SPE 107877 presented at the SPE\nRocky Mountain Oil & Gas Technology Simposium, Denver, CO, doi: 10.2118/107877-MS\nBarree, R. D., V . L. Barree, and D.P. Craig . 2009 . \"Holistic fracture diagnostics: consistent interpretation of prefrac\ninjection tests using multiple analysis methods\". SPE Production & Operations 24 ( 3): 396\u2013406.\nBazan, Lucas W.  and Bruce R. Meyer . 2015 . \"Fracture complexity: analysis methodology and signature pressure behavior\nof hydraulic fracture propagation from horizontal wellbores \". SPE 176919. Paper presented at the SPE Asia Pacific"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4826a-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 28, "chroma:document": "Unconventional Resources Conference and Exhibition, Brisbane, Australia.\nCastillo, J. L. 1987 . Modified fracture pressure decline analysis including pressure-dependent leak-off. SPE 16417. Paper\npresented at the SPE/DOE Low Permeability Reservoir Symposium, Denver, CO.\nCraig, D. P. , R. D. Barree, N.R. Warpinski , and T.A. Blasingame. 2017 . Fracture closure stress: Reexamining field and\nlaboratory experiments of fracture closure using modern interpretation methodologies. SPE 187038. Paper presented\nat the SPE Annual Technical Conference and Exhibition, San Antonio, TX\nMcClure, Mark W., Christopher A. J. Blyton, Hojung Jung, and Mukul M. Sharma. 2014 . \"The Effect of Changing Fracture\nCompliance on Pressure Transient Behavior During Diagnostic Fracture Injection Tests\". SPE 170956. Paper presented\nat the SPE Annual Technical Conference and Exhibition, Amsterdam, The Netherlands.\nMcClure, Mark W., Hojung Jung, Dave D. Cramer , and Mukul M. Sharma. 2016 . \"The fracture compliance method"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae482e2-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 28, "chroma:document": "for picking closure pressure from diagnostic fracture injection tests\". SPE Journal 21 (4): 1321 \u20131339 , doi:\n10.2118/179725-PA .Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae483b4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 29, "chroma:document": "30 SPE-215017-MS\nMcClure, Mark . 2017 . \"The spurious deflection on log-log superposition-time derivative plots of diagnostic fracture-\ninjection tests \". SPE Reservoir Evaluation & Engineering  20 (4), doi: 10.2118/186098-PA.\nMcClure, Mark , Vidya Bammidi, Craig Cipolla, Dave Cramer, Lucas Martin , Alexei A. Savitski , Dave Sobernheim, and\nKate V oller . 2019 . \"A collaborative study on DFIT interpretation: integrating modeling, field data, and analytical\ntechniques \". URTeC 2019-123. Paper presented at the Unconventional Resources Technology Conference Denver, CO.\nMcClure, Mark . 2019 . Discussion of the Paper SPE-187038-MS: \"Fracture Closure Stress: Reexamining Field and\nLaboratory Experiments of Fracture Closure Using Modern Interpretation Methodologies.\" arXiv:1904.07126.\nMcClure, Mark . 2020 . \"Theoretical and Empirical Problems with the Holistic Permeability Correlation for\nDFIT Interpretation. ResFrac Blog Post.\" https://www.resfrac.com/blog/theoretical-and-empirical-problems-holistic-"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48440-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 29, "chroma:document": "permeability-correlation-DFIT-interpretation.\nNational Energy Board, British Oil and Gas Commission, Alberta Energy Regulator and British Columbia Ministry of\nNatural Gas Development. November 2013 . \"The Ultimate Potential for Unconventional Petroleum of the Montney\nFormation in Alberta and British Columbia \".\nNolte, K. G., \" Determination of Fracture Parameters from Fracturing Pressure Decline\", Paper SPE 8341, Presented at\ntheAnnual Technical Conference and Exhibition, Las Vegas, NV , Sept. 23-26, 1979.\nNolte, K.G. , Maniere, J.L. , and Owens, K.A., \" After-Closure Analysis of Fracture Calibration Tests,\" Paper SPE 38676,\nPresented at the1997 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5-8 October 1997.\nNolte, K. G., \" Background for After-Closure Analysis of Fracture Calibration Tests \", Paper SPE 39407, Unsolicited\ncompanion paper to SPE 38676 July 1997.\nSoliman, M.Y . , Craig D. , Barko, K., Rahim Z. , Ansah J. , and Adams D., \" New Method for Determination of Formation"}


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topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae484c2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-215017-ms.pdf", "page": 29, "chroma:document": "Permeability, Reservoir Pressure, and Fracture Properties from a Minifrac Test \", Paper ARMA/USRMS 05-658, 2005\nS&P Global \u2013 Minifrac (DFIT) Analysis for Unconventional Reservoir Course NotesDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48544-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 0, "chroma:document": "URTeC: 123 \n \nA Collaborative Study on DFIT Interpretation: Integrating Modeling, \nField Data, and Analytical Techniques  \nMark McClure*1, Vidya Bammidi2, Craig Cipolla3, Dave Cramer4, Lucas Martin5, Alexei A \nSavitski6, Dave Sobernheim2, and Kate Voller7; 1. ResFrac Corporation , 2. Keane \nGroup , 3. Hess Corporation , 4. ConocoPhillips  Company , 5. Formerly with Apache \nCorporation, now with Marathon Oil Corporation , 6. Shell  International Exploration and \nProduction Inc. , 7. Range Resources Corporation  \n \nCopyright 201 9, Unconventional Resources Technology Conference (URT eC) DOI 10.15530 /urtec -2019-123 \nThis paper was prepared for presentation at the Unconventional  Resources Tech nology Conference held in Denver , Colorado , USA, \n22-24 July 201 9. \nThe URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract \nsubmitted by the author(s).  The contents of this paper have not been rev iewed by URTeC and URTeC does not warrant the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae485c6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 0, "chroma:document": "accuracy, reliability, or timeliness of any information herein.  All information is the responsibility of, and, is subject to  corrections by \nthe author(s). Any person or entity that relies on any information obt ained from this paper does so at their own risk.  The information \nherein does not necessarily reflect any position of URTeC. Any reproduction, distribution, or storage of any part of this paper by \nanyone other than the author without the written consent of URTeC is prohibited.   \n \nAbstract  \nThis paper summarizes findings from a one -year study sponsored by seven operators and service companies \nto investigate interpretation of diagnostic fracture injection tests (DFIT\u2019s). The study combined \ncomputational modelin g, a diverse collection of field data, and operator experience. DFIT simulations were \nperformed with a three -dimensional hydraulic fracturing, wellbore, and reservoir simulator that describes"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48648-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 0, "chroma:document": "fracture propagation, contacting of the fracture walls, and mult iphase flow. Interpretation procedures were \napplied to estimate stress, permeability, and pressure from the synthetic data. The interpretations were \ncompared to the simulation input parameters to evaluate accuracy. Based on the results, new techniques \nwere  developed, existing techniques were refined, and an overall interpretation protocol was developed. \nThe techniques were applied to interpret over thirty field DFIT\u2019s drawn from shale plays across the US and \nCanada, and the methods were evaluated in the con text of operator experience. The results are applicable \nto fracturing tests in formations with permeability ranging from nanodarcies to 10s of microdarcies. The \nminimum principal stress is estimated by identifying the \u2018contact pressure\u2019 when the fracture w alls come \ninto contact, causing fracture compliance and system storage coefficient to decrease. After the walls come"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae486d4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 0, "chroma:document": "into contact, the pressure transient is controlled by the interplay of changing fracture compliance, deviation \nfrom Carter leakoff, and mul tiphase flow. The contact pressure is slightly greater than the minimum \nprincipal stress. It can be identified from either a plot of dP/dG or a relative stiffness plot. Permeability is \nestimated  using the G -function method, a newly developed h -function met hod that accounts for deviation \nfrom Carter leakoff, and impulse linear flow. These  three methods, which are based on linear flow \ngeometry,  require an estimate of fracture area . We derive equations for estimating area using mass balance \nequations, accounti ng for wellbore storage and fluid leakoff. The results from field data  show that  impulse \nlinear permeability estimates are usually 2 -5 times lower than estimates derived from the G -function and \nh-function methods, apparently indicating a difference between  effective permeability during leakoff and"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4874c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 0, "chroma:document": "permeability during flow of reservoir  fluid through the formation . Impulse radial flow regime may be used \nfor estimating permeability, but  should be used with caution.  Simulation results indicate that a variety of  \nprocesses can cause an apparent radial trend that is not actually radial flow. Simulations and field data \nindicate that \u2018false radial\u2019 is very common  in gas reservoirs and, if applied, leads to a large overestimate of \npermeability. Production history matc hing using overestimated permeability will underestimate fracture \nlength, potentially resulting in suboptimal choices for well and cluster spacing.  \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae487d8-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 1, "chroma:document": "URTeC 123   2 \n1. Introduction  \n1.1 Background  \nDiagnostic fracture injection tests (DFIT\u2019s) involve water injection at a rate and pressure sufficient to create \na dominant hydraulic fracture, followed by a shut -in period lasting days, weeks, or even months. The trend \nin pressure after shut -in is analyze d to estimate stress, permeability, and/or pore pressure. Compared with \nother types of fracture injection tests, DFIT\u2019s typically involve a longer shut -in, are performed after drilling \nis complete, are usually performed in low permeability rock, and have a  greater emphasis on estimating \nreservoir properties, such as permeability and pore pressure.  \nThe magnitude of the minimum principal stress, permeability, and pore pressure are key parameters in \nreservoir engineering, hydraulic fracturing, and drilling. K nowledge of the stress state is used during drilling \n(wellbore stability and mitigation of lost circulation), exploration (fault seal analysis and prediction of"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4885a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 1, "chroma:document": "critically stressed fractures), and hydraulic fracturing (predicting injection pressure, estima ting height \ngrowth, selecting proppant, and inferring net pressure) (Zoback, 2007; Economides and Nolte, 2000; Smith \nand Montgomery, 2015). Permeability estimates are used during optimization of hydraulic fracture design, \nwell spacing, and cluster spacing.  Pore pressure estimates are used to delineate the extent of drainage, which \nhelps with optimization of well spacing.  \nPermeability is difficult to measure in unconventional formations. Permeability from core may not be \ndirectly applicable in reservoir eng ineering calculations because in -situ flow can be strongly influenced by \npre-existing planes of weakness that are not sampled in the core. In addition, core measurement may be \nimpacted by changes in the rock as it is removed from the subsurface. Rate -trans ient analysis (RTA) yields \nan estimate of fracture surface area times  the square root of permeability ( \ud835\udc34\u221a\ud835\udc58), but cannot estimate these"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae488dc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 1, "chroma:document": "parameters separately. On the other hand, DFIT\u2019s provide the opportunity to derive a unique, in -situ \nestimate of permeab ility. The DFIT provides a permeability estimate that is the area -weighted average of \nthe permeability across the fracture surface area. It is an estimate of the effective permeability to the mobile \nreservoir phase (absolute permeability times relative per meability).  \nThis paper summarizes findings from a one -year study sponsored by seven operators and service \ncompanies. The purpose of the study was to evaluate the accuracy of existing DFIT interpretation \ntechniques, develop new techniques if needed, and ass emble an overall interpretation procedure. The study \nintegrated unique simulation capability, field data, and operator expertise. The interpretation procedure can \nbe performed entirely in an Excel spreadsheet.  \nThe body of the paper presents a step -by-step worked example, commentary on the most important findings,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4895e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 1, "chroma:document": "and additional field examples. The appendix provides detailed mathematical derivations explaining the \nmethods applied in the paper  \nThe study focused primarily on DFIT\u2019s performed in formations with  permeability on the order of \nnanodarcies to 10s of microdarcies. With higher permeability, transients behave qualitatively differently, \nand many of the techniques in this paper cannot be applied (discussed in Section 4.1).  \n1.2 Literature review  \nDFIT inte rpretation combines concepts from well test analysis and hydraulic fracture analysis. \nConventional well testing involves production or injection of fluid at pressure below the fracture gradient. \nPressure data is analyzed to infer permeability, skin, and ot her parameters (Theis, 1935; Horne, 1995; \nKamal et al., 2009; Stewart, 2011; Spivey and Lee, 2013). DFIT\u2019s involve similar physics, but with \nimportant differences. In conventional well tests, fractures are static. In DFIT\u2019s, fractures are dynamic \u2013"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae489e0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 1, "chroma:document": "changin g in size, compliance, and conductivity. As a result, c oncepts from conventional well test analysis \nare not always directly applicable to DFIT analysis .  \nHydraulic fracturing was first described in a publication by Clark (1949). In subsequent decades, it w as \nrecognized that hydraulic fracturing could be used as a method to estimate the magnitude of the minimum Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48a62-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "URTeC 123   3 \nprincipal stress (Hubbert and Willis, 1957; Godbey and Hodges, 1958; Kehle, 1964; Haimson and Fairhurst, \n1967; Hickman and Zoback, 1983). If fluid is  injected at pressure greater than the minimum principal stress, \na hydraulic fracture will form and propagate through the formation. As a result, the minimum principal \nstress can be estimated from pressure measurements during and after injection (Economide s and Nolte, \n2000; Zoback, 2007; Smith and Montgomery, 2015). The uniaxial stress/strain equations can be used for \nengineering purposes to help predict stress differences between layers (Eaton, 1969; Blanton and Olson, \n1999), but fracture injection tests a re needed for calibration and to ensure accuracy.  \nNolte (1979) extended the applicability of fracturing tests by developing analytical techniques that can be \nused to estimate fluid leakoff parameters. These techniques can assess leakoff even when using com plex"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48aee-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "fluids that develop filtercake. These tests are typically called minifrac tests (McLennan and Roegiers, 1982) \nor fracture calibration tests (Mayerhofer and Economides, 1993). The G -function developed by Nolte \n(1979) became a routine part of data plott ing and interpretation (Castillo, 1987; Barree and Mukherjee, \n1996). Mayerhofer and Economides (1993) and Mayerhofer et al. (1995) showed how to disentangle the \neffects of filtercake and formation permeability on leakoff.  \nConventional well testing is infe asible in very tight formations because of the difficulty of sustaining \nsufficiently low rates of production or injection. The \u201cdiagnostic fracture injection test\u201d (DFIT) emerged to \ncombine the benefits of a well test and a fracturing test \u2013 providing esti mates for stress, permeability, and \npore pressure (Craig and Brown, 1999). \u2018Preclosure\u2019 analysis methods are usually based on techniques from \nNolte (1979) and Mayerhofer and Economides (1993) and Mayerhofer et al. (1995). Barree and Mukherjee"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48b70-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "(1996) and Ba rree et al. (2009) developed techniques for qualitative interpretation and for estimating the \nclosure pressure and minimum principal stress. Impulse analysis is based on the use of impulse solutions \nfrom conventional well testing (Gu et al., 1993; Soliman et al., 2005; Craig and Blasingame, 2006) or the \n\u2018linear flow time function\u2019 technique developed by Nolte et al. (1997). Examples of DFIT interpretation \nare provided in recent papers by Marongiu -Porcu et al. (2011; 2014), Soliman and Kabir (2012), Soliman \nand Gamadi (2012), Cramer and Nguyen (2013), Padmakar (2013), Wallace et al. (2014), Meng et al. \n(2014), Craig (2014), Zanganeh et al. (2018), and Hawkes et al. (2018).  \nMcClure et al. (2014; 2016) and Jung et al. (2016) proposed the compliance method of e stimating stress \nfrom a DFIT ( Section 3.1.2 ). The compliance method leads to an earlier, higher stress estimate than the \ncommonly used tangent method (Barree et al., 2009). McClure et al. (2016) and Jung et al. (2016) performed"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48bf2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "detailed DFIT simulations co nsidering the effect of residual aperture fracture after the fracture walls \ncontact. Simulations indicate that in low permeability formations, the contacting of the fracture walls causes \nthe magnitude of the  pressure derivative to increase, resulting in a pressure signal often interpreted as height \nrecession or closure of transverse fractures (Barree et al., 2009). Wang and Sharma (2017) reproduced these \nfindings and proposed a modified approach for estimating stress called the \u2018variable compliance method.\u2019  \n1.3 Defining a new term \u2013 the \u2018contact pressure\u2019  \nThe term \u2018closure pressure\u2019 is used widely in the literature but is rarely given a precise definition. A review \nof the literature shows that a variety of assumptions are made about \u2018closure pressure ,\u2019 and these \nassumptions  are often problematic and inconsistent. Most authors assume that the closure pressure is equal"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48c74-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "to the magnitude of the minimum principal stress (issues with this definition are discussed in Section A.2). \nCraig and Blasingame (2006) as sume that the compliance (or compressibility) of a \u2018closed\u2019 fracture is \nnegligible (issues with this definition are discussed in Section A.2). The classical calculation of efficiency \nfrom the G -time to closure (Equation 5) is derived assuming that there is  zero fluid remaining in the fracture \nat \u2018closure\u2019 (issues with this assumption are discussed in Section A.12). McClure et al. (2016) define closure \nas being the point in time when the fracture walls first come into contact, decreasing the overall complian ce \nof the system (issues with this definition are discussed in Section 3.1.9). Nolte et al. (1997) derive the \u2018linear \nflow time function\u2019 assuming that Carter leakoff occurs until closure, at which point leakoff rate drops to"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48cf6-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "zero (issues with this definit ion are discussed in Section A.11).  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48d78-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 3, "chroma:document": "URTeC 123   4 \nIn Section A.2, we show that there is not any specific response in the pressure transient (or any other \nmeasurement) when fluid pressure is exactly equal to the minimum principal stress, Shmin. Instead, Shmin \ncan be esti mated from its proximity to a process that does create a signature in the pressure transient \u2013 the \ncontacting of the fracture walls, which causes a measurable increase in the system stiffness (or decrease in \ncompliance). We define the pressure at this poin t in time as the \u2018contact pressure.\u2019 It is equivalent to the \n\u2018closure pressure\u2019 defined by McClure et al. (2016). However, because the definition of \u2018closure pressure\u2019 \nis itself a point of confusion, we prefer to use the term \u2018contact pressure.\u2019  \n1.4 Study approach  \nIn our study, we performed a comprehensive reassessment of the entire DFIT analysis procedure \u2013 \nestimating stress, permeability, and pore pressure. Based on the results, we developed a detailed, step -by-\nstep interpretation procedure."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48dfa-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 3, "chroma:document": "step interpretation procedure.  \nFirst, a lar ge number of DFIT simulations were performed under a variety of conditions. The simulations \nwere performed with a three -dimensional hydraulic fracturing, wellbore, and reservoir simulator that \nrigorously handles fracture propagation, contacting of the frac ture walls, and multiphase flow (McClure \nand Kang, 2018). Conventionally, DFIT simulations and/or analytical approaches have isolated parts of the \nproblem and solved them separately. The fully integrated approach used in this study captures the \ninteraction s between processes, which have a material impact on system behavior.  \nDifferent analysis procedures were applied to analyze the simulations results, and the interpretations were \ncompared with the (known) simulation input parameters to assess accuracy. Base d on the results, a set of \nDFIT interpretation guidelines were developed (summarized in Section 2.2). The guidelines incorporate \nboth pre -existing methods and newly developed techniques."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48e7c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 3, "chroma:document": "both pre -existing methods and newly developed techniques.  \nThe interpretation guidelines were applied to analyze a dataset of f ield DFIT\u2019s contributed by operators. \nThe results were compared with operator experience and expertise to assess performance. Due to limits on \npaper length, only a small set of the simulations and the field results are shared in this paper.  \nThis paper doe s not address many operational aspects of performing DFIT\u2019s. Cramer and Nguyen (2013) \nreview practical guidelines for DFIT execution.  \n2. Method s \n2.1 Numerical simulator  \nNumerical simulations were performed using ResFrac, a three -dimensional hydraulic fracturing, reservoir, \nand wellbore simulator. The problem formulation  is briefly summarized in this section, and a detailed \ntechnical description is provided by McClure and Kang (2018). ResFrac has a unique combination of \nphysics that enables seamless description of the entire DFIT process, from the beginning of injection to"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48f08-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 3, "chroma:document": "late-time impulse flow. The wellbore is meshed from the surface as a series of line -segments. The frac ture \nis meshed with rectangles, and the reservoir is meshed with cuboids.  \nThe unsteady -state mass balance equation is solved in every element at every timestep. Multiphase flow is \ndescribed with the black oil model or the compositional model. Fracture wal ls come out of contact when \nfluid pressure exceeds normal stress. Then, the amount of mechanical opening in each element is calculated \nto enforce that the fluid pressure is equal to the normal stress on the element, including stress shadow effects \nfrom all  other mechanically open elements. The stress interaction is calculated with the 3D displacement \ndiscontinuity method of Shou et al.  (1997), an approach that provides mesh convergent solutions identical \nto classical continuum mechanics solutions, such as f rom Sneddon (1946). The opening of every fracture"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae48f8a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 3, "chroma:document": "element affects the stress on every other element, requiring the solution of a large, coupled system of \nequations in every timestep.  \nWhen the fluid pressure drops sufficiently, the fracture walls come into  contact. After the walls contact, the \nelements retain aperture and the ability to conduct fluid. The aperture is calculated using the Willis -Richards Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 4, "chroma:document": "URTeC 123   5 \net al. (1996) version of the Barton et al. (1985) relations. Th is joint closure law implicitly handles th e \ncontacting of the asperities in the fracture walls (Barton et al., 1985; Willis -Richards et al., 1996):  \n\ud835\udc4a=\ud835\udc4a0\n1+9(\ud835\udf0e\ud835\udc5b\u2212\ud835\udc43)\n\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53.            (1) \nThe W0 parameter (Equation  1) corresponds to the average fracture aperture at the contact press ure \u2013 the \npressure when asperities begin to contact, the fracture stiffens, and normal stress is transferred across the \nfracture by solid -solid contact. Conductivity is calculated with the cubic law (Witherspoon et al., 1980).  \nEven as the average fracture  aperture remains above zero, it is implicit to Equation 1  that the fracture walls \nare in contact across a fraction of the fracture area, at a scale below the resolution of the model (Barton et \nal., 1985). Some numerical modeling approaches explicitly repr esent individual asperities (Vogler et al.,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4908e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 4, "chroma:document": "2018). However, this approach is computationally expensive and infeasible for field -scale modeling.  \nWhen a new fracture element is created in the model, it is given a very low initial aperture, 1 micron. The \naperture when the walls contact, W0, cannot initially exceed this initial aperture, and so as the crack opens, \nW0 must increase along with aperture to reach a more physically realistic value. W0 is increased at the end \nof each timestep to be equal to a certai n fraction of the total aperture, up to a user -specified limit, W0,max. \nThis corresponds to a progressive process of crack formation \u2013 roughness developing as the crack \ntransitions from \u2018not -yet-formed\u2019 to \u2018fully formed.\u2019 In reality, this process is controlled by the rock fabric \n(Suarez -Rivera et al., 2013; Gale et al., 2018) , is probably scale -dependent (Delaney et al., 1986; Scholz, \n2010), and might depend on operational parameters such as injection rate. After the walls have come into"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49110-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 4, "chroma:document": "contact, aperture has decreased by 90% once effective normal stress reaches \ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53. \nThe wellbore model solves the momentum balance equation in each element (in addition to the mass balance \nequations) and includes hydrostatic head, friction, momentum accumulation, and pressure gradient. Flow \nbetween well elements and fracture elements inclu des the effect of pressure drop due to both perforation \n(scaling with the square of flow rate) and near -wellbore pressure drop (Equation 22). \nPoroelastic st ress changes are rarely considered in DFIT analysis and were not included in the simulations \nperformed for this study. In low permeability formations, the region of pressure increase around the fracture \nwill be very narrow. As a result, the poroelastic inc rease on fracture normal stress will be small (Perkins \nand Gonzalez, 1985). Nevertheless, it cannot be assumed that poroelastic stresses will never  have a \nsignificant impact, and this would be an interesting topic for further study."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4919c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 4, "chroma:document": "2.2 Interpretation proc edure  \nAn interpretation procedure was developed based on simulation results, analytical derivations, and \napplication to field data. The procedure is:  \n(1) Inspect a plot of pressure versus time to pick the start of injection and the shut -in time. The pressu re \nplot should be used  to pick shut -in because injection rate data is  often unavailable or not synchronized with \nthe pressure data.  \n(2) Smooth the shut -in pressure  transient by resampling along pressure increments (Horne, 1995). A 30 psi \nincrement usually yields good results.  \n(3) Construct plots of the shut -in data: dP/dG versus G (Section A.3) and a log -log plot of dP and t*dP/dt \n(using actual shut -in time, not superposition time; McClure, 2017). Depending on the interpretation, plots \nof pressure versus t^ -1 and t^( -1/2) may also be used. According to the interpreter\u2019s preference, other plots \ncan be constructed (G*dP/dG, a log -log plot with the primary derivative dP/dt, linear -flow time function,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4921e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 4, "chroma:document": "etc.).  \n(4) Estimate the wellbore storage coefficient from a p lot of cumulative volume injected versus pressure \nprior to breakdown.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae492a0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 5, "chroma:document": "URTeC 123   6 \n(5) Identify the point of minimum dP/dG prior to the contact pressure and extrapolate back to G -time equal \nto zero to estimate the effective ISIP (Section 3.1.1). Calculate the \u2018effecti ve pressure\u2019 curve, defined as \nbeing equal to measured pressure after the minimum dP/dG and equal to the linear extrapolation of pressure \nprior to dP/dG ( Section 3.1 .1). Section 4.1 discusses interpretation of tests with monotonically decreasing \ndP/dG.  \n(6) Construct an afterflow plot to assess near -wellbore pressure drop (Sections 3.1.4 and A.7).  \n(7) From the log -log plot, identify impulse linear or radial flow regimes from a -1/2 or -1 slope. Be cautious \nabout identification of these flow -regime trends (Section 3.1 .5). Do not use the log -log plot for \ninterpretation prior to the late -time impulse period  (ie, prior to  the peak in t*dP/dt) . \n(8) Depending on the diagnosis of impulse flow, estimate pore pressure from plots of pressure versus either"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49322-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 5, "chroma:document": "t^-1 or t^ (-1/2) (Sections 3.1.6 and A.6). If an unambiguous diagnosis of impulse flow is not possible, \nconsider reducing injection volume to accelerate  the onset of  impulse flow in subsequent tests. It is possible \nto perform an extrapolation of the t^( -1/2) or t^( -1) plot, even in the absence of a clear straight line. This \nstrategy should be used with caution because it can be significantly inaccurate.  Section A.13 outlines an \nalternative technique that can be used with short -duration transients.  \n(9) Calculate the  h-function (Section A.8) and construct a plot of h -function versus G -function and a relative \nstiffness plot (Sections 3.1.2 and A.9).  \n(10) Using the dP/dG  curve and the relative stiffness plot, identify the contact pressure and estimate the \nmagnitude of the minimum principal stress ( Section 3.1 .2). Section 4.1 discusses interpretation of tests \nwhere the contact pressure cannot be identified."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae493ae-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 5, "chroma:document": "where the contact pressure cannot be identified.  \n(11) Estimate p ermeability ( Section 3.1 .7) using the G -function method (Section A.10.i), the h -function \nmethod (Section A.10.ii), and (if applicable) impulse linear or radial (Sections A.10.iii and A.10.iv). \nCompare the results and check for consistency. Keep in mind tha t impulse linear estimates are usually 2 -5 \ntimes lower than estimates from the other methods. The impulse linear estimate is probably the most \napplicable for predictions of production, and so a downward adjustment may be warranted if an impulse \nlinear perm eability estimate is not available.  \n(12) Optionally, create a plot of estimated aperture versus effective normal stress (Sections 3.1.9 and A.14).  \nIn advance of a test, it is often useful to estimate the duration of shut -in needed to reach impulse flow. Th is \ncould be done by performing a numerical simulation with code such as ResFrac (McClure and Kang, 2018)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49430-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 5, "chroma:document": "or by performing a simplified DFIT simulation using the equations in Section A.13. DFIT simu lations may \nbe performed after the interpretation as a qual ity control to confirm that the simulation result is consistent \nwith the actual data.  \n3. Results  \n3.1 Example interpretation  \nThe interpretation procedure is demonstrated in the following example using a DFIT performed in a gas \nwell in the  Utica/Point Pleasa nt. Mathematical background is provided in the appendix. It may be useful to \nrefer to the appendix while reading this section.  \n3.1.1 Initial interpretation with the G -function plot  \nFigure 1 shows a plot of pressure and dP/dG versus G -time. For convenience, dP/dG is plotted as positive, \neven though it is actually negative (because pressure is decreasing over time).  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae494b2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 6, "chroma:document": "URTeC 123   7 \n \nFigure 1: dP/dG and pressure vers us G-time for the Utica DFIT.  \nIdeally, dP/dG should be constant as long as the fracture walls are out of contact (Nolte, 1979; Castillo, \n1987; Section A.3). However, this is not usually observed in field DFIT\u2019s, especially if performed in a \nhorizontal wel l. \nAt early time, the pressure derivative is elevated by near -wellbore pressure drop. The near -wellbore \npressure drop is caused by flow through a tortuous path through the cement sheath and axial (longitudinal) \nfractures in the near -wellbore region (Wright , 2000; Weijers et al., 2002; Economides and Martin, 2008; \nBazan and Meyer, 2015; Cramer et al., 2019). Because of this pressure drop, the pressure in the primary \nfracture away from the well is lower than the pressure measured in the wellbore ( Figure 2). Some authors \ndistinguish between \u2018near -field\u2019 and \u2018mid -field\u2019 pressure drop, but in this paper, we lump these processes"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49534-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 6, "chroma:document": "together and refer to them as simply \u2018near -wellbore  pressure drop.\u2019  \nIn Figure 1, the literal ISIP is around 11,500 psi. The effective ISIP, 8330 psi, is estimated by identifying \nthe point of minimum dP/dG and extrapolatin g the pressure versus G -time curve back to zero from this \npoint. The effective ISIP is an estimate for the pressure in the far -field fracture at shut -in. This is the pressure \nactually present in the fracture that is opening and propagating the crack.  \nFigure 2 illustrates the difference between literal ISIP and effective ISIP. A fracture is shown initiating \nlongitudinally along the well. Away from the well, a transverse fracture forms, resulting in a  complex, \ntortuous fracture geometry that causes a substantial pressure drop that takes at least several  minutes to \ndissipate. Figures 13 and 17 from Jung et al. (2016) show numerical simulations of this process.  \n \nFigure 2: Schema tic of near -wellbore pressure drop between the wellbore and the far -field fracture."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49610-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 6, "chroma:document": "As the fracture walls come into contact, the magnitude of the pressure derivative begins to increase as the \nfracture compliance and system storage coefficient decrease beca use of the contact stress (McClure et al., \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49692-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "URTeC 123   8 \n2016; Section A.2). The point of minimum dP/dG is closest to the \u2018true\u2019 dP/dG in the far -field fracture \nbecause it is least disturbed by near -wellbore pressure drop and the contacting of the fracture walls.  \nThe \u2018 effective pressure\u2019 is defined as being equal to measured pressure after the point of minimum dP/dG, \nand equal to the linear extrapolation of pressure back to G -time equal to zero prior to the point of minimum \ndP/dG  (Figure 1). Effective pressure is an estimate for the pressure that is actually in the fracture. As shown \nin Figure 2, the pr essure measured in the well is higher than the \u2018effective pressure\u2019 because of the pressure \ndrop that occurs between the well and the far -field fracture.  \nConventionally, a period of rapid pressure drop after shut -in has been called \u2018tip -extension\u2019 or \u2018pres sure-\ndependent leakoff\u2019 (PDL). It has been believed to be caused by accelerated leakoff or pressure gradient"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4970a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "along the fracture or at the tip (Barree et al., 2009; Liu et al., 2016). However, it has also been recognized \nthat near -wellbore fracture tortuosi ty is responsible for the huge pressure drops observed after shut -in \n(Bazan and Meyer, 2015; McClure et al., 2016; Barree and Misk imins, 2016). The distinction is that in the \n\u2018near -wellbore pressure drop\u2019 interpretation, the pressure in the fracture is muc h lower than the literal ISIP \n(the bottomhole pressure very shortly after shut -in), but in a \u2018tip -extension\u2019 or \u2018PDL\u2019 interpretation, the \npressure in the fracture is close to the  literal ISIP.  \nAs pressure drops after shut -in, a few barrels of water will b e released from wellbore storage and cause a \nlimited amount of tip -extension. If pressure -dependent leakoff is taking place, it will be impossible to \nobserve because of the huge pressure changes caused by the dissipation of near -wellbore pressure drop."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4978c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "Therefore, while PDL and tip -extension may occur, \u2018near -wellbore pressure drop\u2019 is the dominant physical \nprocess in most DFIT\u2019s and should be considered the primary interpretation.  \nIn vertical wells, the pressure drop after shut -in is usually  (though not always)  less pronounced than in \nhorizontal wells (Section 3.3). This is consistent with the interpretation that near -wellbore pressure drop is \nthe primary cause of the large pressure drops observed after shut -in, and this process is related to  fracture \ntortuosity due to fracture reorientation.  \n3.1.2 Estimating the minimum principal stress  \nAs described by McClure et al. (2016) and in Section A.2, the fracture compliance begins to decrease after \nthe fracture walls come into contact. The decreasin g fracture compliance causes the pressure to drop more \nrapidly ( the magnitude of dP/dG increases). McClure et al. (2016) recommend picking the contact pressure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4980e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "from a G*dP/dG plot.  However, there is not always a  unique feature on  the G *dP/dG plot that lends itself \nto identifying the contact pressure . It is better  to pick the contact pressure from a plot of dP/dG. The contact \npressure occurs when dP/dG begins to increase from its minimum value. A rule of thumb is to pick the \ncontact pressure w hen there has been a 10% increase from the minimum. When constructing a dP/dG plot, \nthe y -axis scale should be chosen so that the minimum and maximum dP/dG can be clearly observed. Large \nearly time dP/dG values do not need to be visible on the plot and can  go up off the scale. They are related \nto dissipative processes unrelated to fracture contact ( Section 3.1.1 ). \nAs explained in Section A.2, the contact pressure is slightly above the minimum principal stress. In \nsimulations that match field pressure data, we have found that subtracting approximately 75 psi from the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4989a-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "contact pressure is a good rule -of-thumb for providing a good estimate of Shmin. However, this is a source \nof uncertainty and is an inherent limitation to stress estimation from fracturing data. As discussed in Section \nA.2, there is not any response in the pressure transient when pressure is actually equal to Shmin. It is known \nthat the contact pressure is close to Shmin (and slightly larger), and so stress can be estimated by identifying \nthe cont act pressure and then making a small downward adjustment to reach Shmin.  \nThe G -function is derived assuming Carter leakoff, which is strictly valid only if fluid pressure in the \nfracture is constant over time. As pressure decreases during shut -in, deviati on from Carter leakoff occurs, \ncausing leakoff to occur more slowly than anticipated by the G -function. This overprints a tendency for \ndP/dG to decrease. Ultimately, decreasing leakoff rate is the reason that dP/dG decreases asymptotically to"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4991c-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "zero at late time.   Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4999e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 8, "chroma:document": "URTeC 123   9 \nFracture contact causes dP/dG to increase, and deviation from Carter leakoff causes dP/dG to decrease. If \nfracture contact occurs simultaneously with deviation from Carter leakoff, the effects could offset and mask \nthe effect of contact on the tran sient. The problem becomes more significant when effective ISIP minus \nShmin (net pressure) is a substantial fraction of effective ISIP minus pore pressure. The practical \nconsequence is that contact causes a stronger dP/dG response in formations where Shmin  and pore pressure \nare relatively further apart.  \nIn an extreme case, Craig et al. (2017) attempted to estimate stress using a G -function plot of pressure from \nlaboratory experiment in which ISIP was double the magnitude of the minimum principal stress  (and near-\nwellbore pressure drop was negligible) . Because net pressure was so large relative to ISIP minus pore \npressure, by the time that pressure reached the minimum principal stress, the overprint of deviation from"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49a20-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 8, "chroma:document": "Carter leakoff was very strong, and a G -function interpretation of the data was not meaningful.  \nTo solve this problem, a relative stiffness plot can be used to identify the contact pressure, even in cases \nwhere there is substantial deviation from Carter leakoff (Wang and Sharma, 2018; Section A.9 ). The plot \ncan be constructed solely from the pressure data and an estimate of pore pressure. The plot shows relative \nchanges in system stiffness (or storage coefficient) and rigorously accounts for the impact of pressure \nchange in the fracture on leakoff  rate.  \nFigure 3 shows that in the example dataset, there is a distinct increase in relative stiffness at around 8100 \npsi. This corresponds to the point in the G -function  plot when dP/dG begins to increase from the minimum.  \nThe Shmin estimate is 8100 \u2013 75 = 8025 psi.  \n \nFigure 3: Relative stiffness plot of the Utica DFIT.  \n3.1.3 Difference with conventional interpretation"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49a98-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 8, "chroma:document": "3.1.3 Difference with conventional interpretation  \nConventionally, Shmin has be en estimated from plots of G*dP/dG versus G -time, by drawing a line from \nthe origin to the tangent to G*dP/dG (Barree et al., 2009). This technique does not have theoretical or \nmathematical justification and yields an inaccurate stress estimate when applie d to numerical simulations \nthat realistically capture nonlinear evolving fracture stiffness after contact (McClure et al., 2014; 2016). \nCraig et al. (2017) claim to use field and laboratory data to validate the tangent method. McClure (2019) \ndescribes tech nical and methodological problems with this study.  \nThe tangent to G*dP/dG tends to occur very close to the peak in G*dP/dG. It can be shown mathematically \nthat the peak in G*dP/dG occurs at the same time as the peak in t*dP/dt. The peak in t*dP/dt has a ph ysical \nmeaning \u2013 it corresponds to the transition from Carter leakoff to late -time impulse flow (McClure, 2017)."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49b24-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 8, "chroma:document": "The timing of the transition is strongly affected by the formation fluid pressure (McClure, 2017). We \nperformed sensitivity analysis simulation s varying pore pressure and holding Shmin constant. The \nsimulations showed that as pore pressure was decreased, the tangent method estimate of Shmin decreased \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49ba6-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 9, "chroma:document": "URTeC 123   10 \n(even though Shmin was being held constant in the simulations).  The implication is that the tange nt method \nunderestimates Shmin more significantly in formations with greater difference between Shmin and pore \npressure.  \nFor the DFIT shown in Figure 1, the tangent meth od (applied to a plot of G*dP/dG) yields a stress estimate \nof 7633 psi, about 400 psi lower than the estimate presented in Section 3.1 .2. The implied net pressure from \nthe tangent method is nearly triple, implying a much shorter, wider fracture.  \nThe phenomenon of increasing dP/dG during shut -in (causing a concave up trend on a plot of G*dP/dG) \nhas conventionally been ascribed to \u2018fracture height recession\u2019 or \u2018closure of transverse fractures\u2019 (Barree \net al., 2009). Jung et al. (2016) performed det ailed simulations of these processes. The simulations showed \nthat these processes have a second -order effect and cause, at most, minor uncertainty in the stress estimate."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49c28-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 9, "chroma:document": "The bulk of the increase in dP/dG occurs after the fracture walls have come into cont act across the entire \nfracture area.  \nSome investigators have recently speculated that the contact pressure might be interpreted as the \u2018start of \nclosure\u2019 and the tangent method  pick might be interpreted as the \u2018end of closure.\u2019 This interpretation is not \nsupported by our modeling results. Simulations show that the great majority of increase in system stiffness \nand dP/dG occurs after contact has occurred along the entire fracture area , and this occurs at a pressure \nsubstantially higher than the tangent pick.  This was observed in simulations performed by McClure et al. \n(2016) and was also observed in the simulations performed for this study.  \n3.1.4 Afterflow plot  \nUsing the estimate of effective ISIP, it is possible to construct an afterflow plot showing the re lationship \nbetween flow rate from the well after shut -in and the pressure difference between the well and the far -field \nfracture (Section A.7)."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49caa-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 9, "chroma:document": "fracture (Section A.7).  \nFigure 4 shows the afterfl ow plot for the Utica DFIT. The relationship is well -described by a square root \ncurve, consistent with relations proposed in the literature (Equation 22; Wri ght, 2000). In Figure 4, data \nfrom the first 15 seconds after shut -in is not shown because it is complicated by water hammer and \nperforation pressure drop. From visual ins pection of Figure 4, the near -wellbore coefficient (Equation 22) \nis appr oximately 1600 psi/bpm^(1/2). Square root scaling of afterflow was observed in the great majority \nof the field DFIT\u2019s reviewed in this study.  \nSometimes, DFIT\u2019s are performed with a rate step -down at the end of injection. This is not necessary \nbecause an a fterflow plot can be used to extract information regarding the near -wellbore pressure drop \nwithout performing a step -down.  \nThe near -wellbore pressure drop observed in a DFIT is typically much larger than in field -scale fracturing"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49d2c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 9, "chroma:document": "treatments because the to rtuous path is scoured out by proppant, acid spearhead, and fracture development \nfrom progressive injection (Cramer et al., 2019).  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49dae-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 10, "chroma:document": "URTeC 123   11 \n \nFigure 4: Afterflow plots for the Utica DFIT.  \n3.1.5 Diagnosing impulse transients  \nFigure 5 shows a log -log plot of the data. The t*dP/dt curve has the useful property that if \u0394\ud835\udc43\u221d\ud835\udc61\ud835\udefc, then \nthe slope of the curve is equal to \ud835\udefc (Bourdet et al., 1983). The derivative is taken with respect to actual \nshut-in time. Sometimes, log -log derivative plots are calculated with superposition time, rather than actual \nshut-in time ( Marongiu -Porcu et al., 2011, 2014; Liu et al., 2016) . This technique is useful for conventional \nwell tests, but is unnecessary for interpretation of DFIT\u2019s (McClure, 2017).  \nIn a DFIT, the log -log plot should only be used to interpret the late -time transient behavior that occurs after \nthe hump in t*dP /dt (which occurs at 2000 min in Figure 5). The log -log plot should not be used to interpret \nthe transient prior to the hump in t*dP/dt. For example, the derivative curve  in Figure 5 is approximately"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49e30-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 10, "chroma:document": "flat from about 20 to 200 minutes In a conventional well test, this trend would be interpreted as being radial \nflow. However, the physics of a  DFIT are different from a conventional well test, and radial flow from 20 \nto 200 min is not the correct interpretation.  \n \nFigure 5: Log -log plot for a Utica DFIT. Derivative is taken with respect to actual shut -in time.  \nThe transient following the hump in t*dP/dt can be described mathematically as an \u2018impulse\u2019 test in which \na volume of fluid is instantaneously injected and then the fluid spreads out and pressure asymptotically \nreturns to the initial pressure (Gu et al., 1993;  Craig and Blasingame, 2006; McClure, 2017). Impulse linear \nbehavior scales with t^( -1/2) (a -1/2 slope on the log -log plot), and impulse radial scales with t^ -1 (a -1 \nslope on the log -log plot).  \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49eb2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 11, "chroma:document": "URTeC 123   12 \nFigure 5 shows that soon after the peak in t*dP/dt, the transient rolls over into a -1 slope. It is tempting to \nidentify this trend as impulse radial flow. However, our simulation results suggest that this apparent radial \nsignatur e should be interpreted as \u2018false radial\u2019 \u2013 a transient that exhibits t^ -1 scaling, but which is not \nactually radial flow. We observed this phenomenon in every simulation that we performed of a DFIT in a \ngas reservoir. The anomalously rapid pressure drop a pparently arises from interaction between several \neffects: viscosity contrast between the injection fluid and the gas in the formation, evolving fracture \nstiffness after contact, and the transition from  Carter leakoff to impulse flow. In examination of fie ld data \nfrom gas DFIT \u2019s in the Utica, Marcellus, and Montney, a rolling over from the peak t*dP/dt into an \napproximately -1 slope (without an intervening -1/2 slope) was observed  in the majority of cases ."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae49f34-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 11, "chroma:document": "Simulations predict  that if shut -in is performed l ong enough, the transient settles into a -1/2 slope after the \n-1 slope. This was observed in one of the DFIT\u2019s reviewed in this study, which had an unusually long shut -\nin after the peak in t*dP/dG. The -1 slope represents a period of transition from the hu mp in t*dP/dt to an \neventual -1/2 slope that indicates linear flow. Because of the low viscosity of the reservoir fluid, the location \nof the -1/2 slope on the log -log plot tends to be significantly lower than the hump in t*dP/dt. Therefore, the \ncurve tempo rarily steepens as it transitions from the peak t*dP/dt to the late -time impulse trend .  \nGenuine impulse radial is most likely to be seen in smaller volume tests (<15 bbl) and if permeability \ndivided by viscosity is  greater than 1 microdarcy/cp.  \nIn DFIT s imulations performed in water saturated or oil saturated formations, the baseline behavior  was for"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a010-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 11, "chroma:document": "the transient to roll over into a -1/2 slope, as expected for linear flow. However, sensitivity analysis \nsimulations suggest that a variety of non -ideal proc esses may cause anomalous late-time behavior. In \nsimulations performed with multiple closely spaced fractures, pressure interference between the fractures \ncaused a variety of different trends after the hump in t*dP/dt, including a false radial trend. Simul ations \nsuggest that dual porosity behavior in the surrounding reservoir (either pseudosteady state or transient) may \ncause a false radial signature. In real data, a variety of unusual behaviors can be seen in late -time data. We \ndo not attempt to interpret these signatures because of there is not enough information to differentiate \nbetween different possible interpretations. Because of these issues, impulse permeability estimates should \nbe compared with the results from the h -function and G -function methods,  and if there is large discrepancy,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a09c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 11, "chroma:document": "the results should be regarded with lower confidence. Performing multiple DFIT \u2019s in the same formation \nin different wells is a good way to test for consistency and identify anomalous results.   \nZanganeh et al. (2018) also  performed simulations suggesting the possibility of false radial flow after the \npeak in t*dP/dt. However, their simulations did not consider multiphase effects or multiple fracture strands. \nOur findings are different because under the basic conditions of one fracture strand and single phase flow, \nwe did not observe false radial. The cause of the discrepancy is unclear, but may be  related to how they \nmodeled fracture compliance evolution as the fracture closed.  \nFinally, interpreters should keep in mind that  poroelastic responses caused by injection or production \nactivity in offset wells can occur at substantial distances, causing abrupt and anomalous responses. These \nresponses are most likely to affect  late-time transients  because they  have the greatest dura tion and are"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a11e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 11, "chroma:document": "sensitive to  small pressure changes . \n3.1.6 Pore pressure estimation   \nThe pore pressure can be estimated by linearly extrapolating the pressure trend during impulse flow to \nreciprocal time (or reciprocal square root time) of zero (Section A.6). Extrapolation of the pressure trend in \nFigure 6 yields a pressure estimate of 6825 psi. As discussed in Section 3.1 .5, the straight line in Figure 6 \nis not actually r adial flow. If the transient had extended for much longer, the derivative curve would have \nlikely straightened into a linear signature (resulting in a more rapid decrease in pressure than if the trend \nhad continued along a t^ -1 scaling). Th erefore , pore pr essure is  probably  modestly lower than 6825 psi.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a196-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 12, "chroma:document": "URTeC 123   13 \n \nFigure 6: Pressure versus reciprocal time for a Utica DFIT.  \n3.1.7 Permeability estimation from linear flow transients  \nPermeability can be estimated using three linear -flow techniq ues (G -function, h -function, and impulse \nlinear) and from impulse radial -flow. In the example transient, impulse linear is not apparent and so cannot \nbe used.  \nThe G -function method calculates leakoff coefficient from dP/dG, and permeability is calculated f rom \nleakoff coefficient (Nolte, 1979; Valko and Economides, 1999; Section A.10.i). However, in the example \ndataset, dP/dG is constantly changing ( Figure 1). Which value o f dP/dG should be used? As discussed in \nSection 3.1 .1, the minimum dP/dG is the point least disturbed by either near -wellbore pressure drop or \ncontacting of the fracture walls. Therefore, this is the point that is most representative of the true value of \ndP/dG in the fracture, and it should be used to estimate leakoff coefficient."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a218-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 12, "chroma:document": "The calculation requires an assumption of either radial or PKN geometry. In most cases, we recommend \nthe radial assumption. The PKN assumption can be used if there is strong evid ence of height confinement \nin the layer. In many cases, the diameter calculated from the DFIT interpretation assuming radial geometry \nis less than or close to the \u2018height\u2019 that is under consideration for a PKN interpretation. In this case, the \nradial inter pretation is the preferred choice.  \nTo minimize uncertainty caused by unknown fracture geometry, it is preferable to perform DFIT\u2019s with \nrelatively low injection volume (5 -20 bbl). With larger injection volume, the fracture will be larger and \nmore likely t o hit stress barriers that limit height (or worse, low stress layers that capture the fracture). \nBecause these stress contrasts complicate the interpretation and may be difficult to predict, lower injection \nvolume reduces uncertainty. Also, with lower volu me, the onset of impulse flow occurs sooner, improving"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a290-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 12, "chroma:document": "the pore pressure estimate and increasing the probability that it will be possible to derive an impulse -flow \npermeability estimate.  \nConversely, Craig and Jackson (2017) recommend pumping DFIT\u2019s with mo re than 100 bbl. They argue \nthat a large fracture is needed to sample a sufficiently large volume of rock. To address concerns regarding \nheterogeneity, we recommend performing multiple DFIT\u2019s in different wells in the same interval and \nchecking for consist ency. In the field dataset reviewed in this study, the tests were generally performed \nwith 5 -40 bbl of injection, and we observed good consistency in permeability estimates between \nneighboring wells. This result supports the position that fractures created  by 5-40 bbl of injection are large \nenough to sample a representative volume of rock.  \nIn Section A.10.i, we derive equations that can be used to estimate leakoff coefficient from dP/dG. \nCommonly, the G -function leakoff calculation is performed using the eq uations derived by Valko and"}


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topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a312-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 12, "chroma:document": "Economides (1999). However, these equations neglect the impact of wellbore storage, which is \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a394-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 13, "chroma:document": "URTeC 123   14 \nnonnegligible in most DFIT\u2019s. The calculation requires estimation of the fracture size and requires an \nestimate of Shmin. Commonly, eq uations provided by Valko and Economides (1999) are used to estimate \nfracture size. However, these equations are only valid in the case of zero leakoff and zero wellbore storage. \nIf wellbore storage coefficient and leakoff coefficient are set to zero in th e equations in Section A.10.i, they \nsimplify to the relations from Valko and Economides (1999).  \nIn the analysis of the Utica DFIT, a PKN geometry is assumed with height of 110 ft. If the analysis is \nrepeated with a radial assumption, the diameter is estima ted to be 180 ft, and the permeability estimates are \nabout 30% lower.  \nWhen applied to the Utica dataset, the G -function estimate for leakoff coefficient is 9.2e -5 ft/min^(1/2). \nThe leakoff coefficient can be converted to permeability from the definition of  leakoff coefficient for"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a416-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 13, "chroma:document": "\u2018reservoir dominated flow\u2019 (Equation 19). This assumes that the impact of the filtrate zone is zero. The \nconvers ion to permeability uses the viscosity and compressibility of the mobile fluid phase in the reservoir, \nnot the viscosity and compressibility of the injection fluid. We implicitly neglect any other potential \nmultiphase flow effects, such as capillary pressu re, and neglect the possibility of pressure dependent \npermeability. Below, we discuss comparison of impulse linear permeability estimates with G -function \npermeability estimates to assess the impact of these additional processes. The G -function permeability  \nestimate is 27 nd.  \nNext, permeability can be estimated from the h -function method (Section A.10.ii). The h -function integrates \nthe effective pressure response using a time -convolution integral of the Carter leakoff solution, accounting \nfor the change in pressure over time. Fracture surface area is estimated using a mass balance equation"}


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topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a498-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 13, "chroma:document": "accounting for wellbore storage and fluid leakoff.  \nThe h -function method is related to the method of Mayerhofer et al. (1995). One difference is that \nMayerhofer et al. (19 95) use a convolution integral of the constant rate solution, and then estimate leakoff \nrate, whereas the h -function directly integrates the constant pressure solution. The method of Mayerhofer \net al. (1995) requires an estimate of fracture area. As with t he G -function method, the equations from Valko \nand Economides (1999) are sometimes used to estimate area with the method of Mayerhofer et al. (1995). \nBut as described above, this technique neglects wellbore storage and leakoff. The h -function method is als o \nrelated to the technique described by Wang and Sharma (2018).  \nSometimes, fracture size is estimated with the Mayerhofer method by using an equation for predicting the \ntime to impulse linear flow (Equation 3 from Craig et al., 2002). This equation is borr owed from"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a51a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 13, "chroma:document": "conventional well test analysis. While it is valid in the context for which it was originally developed \n(Section 6.10.1 from Lee and Wattenbarger, 1996), the physics of a DFIT are very different, and there is \nnot a theoretical justification for a pplying it to predict the timing of impulse linear flow in a DFIT. \nSimulation results indicate that it is often inaccurate. It not even directionally accurate in predicting the \nonset of impulse linear flow. For example, increasing Young\u2019s modulus causes a larger fracture, more \nsurface area, earlier fracture contact, and earlier impulse linear flow (because contact accelerates the onset \nof impulse linear, as discussed by McClure, 2017). Yet, the relation from Craig et al. (2002) predicts that \nwith more fract ure surface area, impulse linear flow will happen later.  \nIf the method of Mayerhofer  et al. (1999) is applied with an accurate estimate of fracture size, then it is \nexpected to yield an accurate estimation of permeability."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a592-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 13, "chroma:document": "expected to yield an accurate estimation of permeability.  \nWhen applied to the transient  in Figure 1, the h -function permeability estimate is 14 nd. Similar to the G -\nfunction permeability estimate above, this estimate neglects any potential multiphase flow effects.  \nImpulse linear is not presen t in Figure 1. However, if it were present, permeability could be estimated from \ndP/d(t^( -1/2)), using the standard impulse flow solutions (Section A.10.iii). As with the other linear \nmethods, surface area can be estimated from a mass balance relation (Section A.10.iii). Unlike the G -\nfunction and h -function methods, the impulse linear permeability estimate is unaffected by multiphase \nleakoff effects or the potential for pre ssure dependent permeability. It is controlled by the pressure transient Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a614-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 14, "chroma:document": "URTeC 123   15 \nin the reservoir away from the filtrate zone. Therefore, this estimate, if available, may be considered more \nrepresentative of reservoir flow behavior and more applicable to reservoir  engineering calculations of \nproduction.  \nIn our field dataset, impulse linear was present in a substantial percentage of tests. In these tests, we \nobserved that the impulse linear permeability estimate was usually 2 -5 times smaller than the G -function \nand h-function estimates. Because of this observation, in cases when an impulse linear estimate is not \navailable, it may be advisable to reduce the permeability estimate from the G -function or h -function \nmethods by 3-fold when used in rate -transient or reserv oir engineering calculations.  \nBarree et al. (2015a) propose that permeability can be related to  the time to closure ( as estimated from the \ntangent method), without considering the effect of injection volume, fluid viscosity, Young\u2019s modulus,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a696-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 14, "chroma:document": "fluid compress ibility, or any other parameters. Simulations and comparison with field data indicate that this \nmethod is often severely inaccurate. We performed sensitivity analysis simulations in which we held \npermeability constant, but varied parameters such as viscosi ty (difference between gas and oil), modulus, \nand injection volume. The time to \u2018closure\u2019  (as picked by the tangent method)  varied widely, resulting in \ngreatly different permeability estimates from the method of Barree et al. (2015a), even though the \nperme ability was the same in all simulations.  \nIn the Utica DFIT , using the tangent method of picking closure, the time to closure is 1960 min. The \ninjection duration is 9.7 min. Therefore, the equation proposed by Barree et al. (2015a) implies that \npermeability  is equal to 1. 6 microdarcy. This estimate is almost 100 times too high.  \n3.1.8 Permeability estimation from radial flow"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a718-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 14, "chroma:document": "3.1.8 Permeability estimation from radial flow  \nAs discussed in Section 3.1 .5, we believe that the late -time transient in Figure 5 is false radial caused by \ninteraction of evolving fracture stiffness after contact with multiphase flow effects. However, for \ncomparison, we can use it to estimate permeability. The permeability -height product (kh) is estim ated using \nthe impulse radial solution (Section A.10.iv). Permeability is estimated by dividing kh by the estimate for \nheight. If PKN geometry is assumed, then height is known. If radial geometry is assumed, we use the mass \nbalance approach to estimate dia meter, and set height equal to diameter.  \nThe radial permeability estimate from the example dataset is 734 nd. This estimate is roughly 50x greater \nthan the estimates from the G -function and h -function methods. The overestimate  is consistent with \nexpectati on from simulation  results  and comparison with field data, as discussed in Section 3.1 .5."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a790-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 14, "chroma:document": "In this case, the operator had already evaluated, and discarded, the radial permeability estimate. The \noperator\u2019s diagnostics and analysis (performed prior to this DF IT study) suggested that the permeability is \nin the range of 10 -20 nd, similar to the values calculated in Section 3.1 .7 (Cipolla et al., 2018).  \nWe observed a false radial signature in the majority of  field DFIT \u2019s that we reviewed from a gas reservoir, \ninvolving tests in the Montney, Marcellus, and Utica. False radial was also observed in every DFIT \nsimulation we performed of a gas reservoir. In these  cases, using the false radial yielded a large overestimate \nof permeability.  \n3.1.9 Estimating average aperture versus effective stress  \nUsing the technique in Section A.14, it is possible to derive a n approximate  plot of average aperture versus"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a812-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 14, "chroma:document": "effective stress. Figure 7 shows the inferred relationship for the Utica DFIT.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a89e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 15, "chroma:document": "URTeC 123   16 \n \nFigure 7: Approximate  average aperture versus Shmin minus pressure for the Utica DFIT.  \nFigure 7 indicates that the contact pressure (when the system begins to stiffen) occurs when inferred \naperture is around 2 mm. This is typical of the field data reviewed in this study: the aperture at the contact \npressure was usually inferred to be in th e range of 0.5 \u2013 3 mm.  \nIt is an important finding that the system begins to stiffen at an aperture on the order of millimeters. This \nfinding is consistent with the finding from Branagan et al. (1996) that the residual tilt at late -time was 20% \nof the maxi mum observed tilt, experimental results from (Suarez -Rivera et al., 2013) showing macroscopic \ncomplexity in hydraulic fracture geometry, and DFIT analyses from Wang and Sharma (2018).  \nMcClure et al. (2016) defined \u2018fracture closure\u2019 as being equivalent to  what we are now calling the \u2018contact"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a920-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 15, "chroma:document": "pressure\u2019 \u2013 the pressure at which the walls begin to contact and the system stiffens. The problem with the \ndefinition from McClure et al. (2016) is that it may seem counterintuitive to define \u2018closure\u2019 as occurring \nat a point when the average fracture aperture is still substantial.  \n3.2 Comparison with simulation  \nA numerical simulation was performed based on the parameters inferred from the data ( Figure 8). The \nsimulation is performed with permeability of 14 nd, Shmin equal to 7975 psi, pore pressure equal to 6900 \npsi, and near -wellbore pressure drop coefficient of 1500 psi/bpm^(1/2). The simulations appear very similar \nto the actual da ta (Figure 1 and Figure 5). The log -log plot indicates a bend into a -1 slope after t he hump \nin t*dP/dt. The simulation shows a -1/2 slope after the -1 slope. This is not visible in the data, but the actual \ntest terminated prior to 10^4 minutes, and the -1/2 slope in the simulation does not develop until after 10^4 \nminutes."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4a9a2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 15, "chroma:document": "minutes.  \nIn order to improve the match to data, it was necessary to vary the W0 and \ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53 parameters from the Willis -\nRichards et al. (1995) equation for fracture aperture after contact (Equation 1). This was necessary because \nthe shape of the aperture versus effective stress curve has a significant effect on the shape of the transient \nin the period after contact and prior to impulse flow. Permeability, pore pressure, and Shmin were not varied \nto match the data \u2013 the parameters were taken directly from the inte rpretation performed prior to running \nthe simulation.  \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4aa24-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 16, "chroma:document": "URTeC 123   17 \n \n \nFigure 8: DFIT simulation based on the Utica DFIT.  \n3.3 Other field examples  \nFigure 9 shows results from a DFIT performed in an oil well in the Wolfcamp shale (WHP is plotted without \nadjustment to BHP). Approximately 3000 psi of near -wellbore pressure drop dissipates in the first 30 \nminutes after shut -in. The dP/dG plot shows good indication o f contact, and the log -log plot shows a -1/2 \nslope after the hump in t*dP/dt. Using a radial fracture geometry, the G -function method yields a \npermeability estimate of 289 nd; the h -function method yields an estimate of 401 nd, and the impulse linear \ntrend  yields an estimate of 162 nd.   \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4ab3c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 17, "chroma:document": "URTeC 123   18 \n \nFigure 9: G-function and log -log plots for a DFIT performed in the Wolfcamp B. The G -function plot shows measured WHP.  \nDFIT\u2019s were performed in all five wells in this pad. All five were landed in the Wolfcamp B. They all show  \nthousands of psi of near -wellbore pressure drop and ha ve good indication of contact, as indicated from \ndP/dG increasing from a minimum. The estimates  of Shmin are all within 150 psi of each other. The G -\nfunction permeability estimates are: 168 nd, 212 nd, 289 nd, 188 nd, and 638 nd. The h -function \npermeability estimates are: 204 nd, 137 nd, 401 nd, 142 nd, and 619 nd. Three of the DFIT\u2019s show an \nindica tion of impulse linear. The impulse linear permeability estimates are 64 nd, 162 nd, and 44 nd. None \nof the DFIT\u2019s shown an indication of impulse radial.  \nFigure 10 shows a  dP/dG plot from a field DFIT in a vertical well the Lower Eagle Ford. As expected from"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4abbe-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 17, "chroma:document": "a vertical well (in a non -thrust faulting regime), the near -wellbore tortuosity pressure drop is minimal. The \nestimate for Shmin is 12,076 psi. Assuming radial geometry , the G -function method permeability estimates \nis 171 nd, and the h -function method estimate is 126 nd.  \n \nFigure 10: dP/dG  and pressure versus G -time for a DFIT in a vertical well in the Lower Eagle Ford.  \n4. Discussion  \n4.1 Tests without a clear pick for contact pressure  \nThe clarity of the pick for contact pressure can be assessed from the separation between the minimum and \nmaximum dP/dG. If there is not good separation, a clear pick may also be possible if an inflection can be \nidentified from the relative stiffness plot. Nevertheless, in some tests, a clear pick is not possible. Figure 11 \nshows an example of a test with monotonically decreasing dP/dG and a smoothly, gradually increasing \nrelative stiffness."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4ac36-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 17, "chroma:document": "relative stiffness.  \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4acb8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 18, "chroma:document": "URTeC 123   19 \n \nFigure 11: G-function plot and relative stiffness plot for a  DFIT performed in the Middle Bakken (in Figure 11a, blue is pressure and red is \ndP/dG). It is not possible to identify the contact pressure or estimate Shmin.  \nBy performing simulations under a variety of conditions, we identified processes that can cause \nmonotonically decreasing dP/dG:  \n1. If a significant volume of fluid has been pumped into the formation prior to the DFIT, such that the \nDFIT involves reinjection into a pre -existing, previously -created hydraulic fracture.  \n2. If injection occurs directly into a h ighly conductive natural fracture.  \n3. If the hydraulic fracture intersects a highly conductive natural or pre-existing hydraulic fracture.  \n4. If the matrix permeability divided by formation fluid viscosity is sufficiently high (> 0.01-0.1 \nmd/cp).  \n5. If near -wellbore  pressure drop is very severe, masking the pressure transient in the far -field \nfracture."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4ad3a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 18, "chroma:document": "fracture.  \nFor the first four scenarios listed above, dP/dG is monotonic because the fracture walls contact almost \ninstantly after shut -in (or perhaps, never fully separated) . If injection reopens a pre -existing hydraulic or \nnatural fracture, there is not any  \u2018toughness\u2019 that must be overcome  in order to propagate the effective \u2018tip\u2019 \nof reopening. As a result, the fracture opens just enough to conduct flow. After shut -in, the wall s contact \nvery rapidly, and fluid continues to flow outward into the rest of the pre -existing fracture. In scenario #3, \nthe fracture walls contact rapidly because fluid flows out into the pre -existing fracture. In scenario #4, the \nfracture walls contact ra pidly because growth is limited by leakoff, rather than resistance to propagation at \nthe tip. In scenario #5, the pinch -point caused by near -wellbore pressure drop is so severe that the real \npressure transient in the hydraulic fracture is not observed."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4adbc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 18, "chroma:document": "pressure transient in the hydraulic fracture is not observed.  \nIf the test in Figure 11 was in a vertical well, it might be justifiable to assume  that there is not any near -\nwellbore tortuosity , and the ISIP could be taken as an estimate for Shmin (because of the 'rapid contact\u2019 \ninterpretations #1 -#4). But because this test is in a horizontal well, it is unclear whether to interpret that the \nfracture walls have rapidly contacted or to interpret that near-wellbore pressure drop is obscuring the true \ntransient (or a combination of both). Because of these uncertainties, a test in a horizontal well without cl ear \nevidence of a contact pressure cannot be confidently interpreted. In either vertical or horizontal wells, it \nwill be impossible to estimate fracture area and permeability because the net pressure cannot be estimated. \nIt might be possible to estimate pe rmeability from impulse radial flow. If impulse  linear or radial  flow is \nreached, it will be possible to estimate pore pressure."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4ae3e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 18, "chroma:document": "reached, it will be possible to estimate pore pressure.  \n4.2 Impact of the permeability estimate  \nRate-transient analysis (RTA) of production data in shale typically indicates linear fl ow. By matching the \nlinear flow equation to the production data, it is possible to derive an estimate for \ud835\udc34\u221a\ud835\udc58. However, without \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4aec0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 19, "chroma:document": "URTeC 123   20 \nan independent estimate for permeability, the RTA match is nonunique. With a DFIT permeability estimate, \nit is possible to uniq uely estimate effective fracture area from the \ud835\udc34\u221a\ud835\udc58 value taken from the RTA.  \nIn the Utica dataset, the false/invalid radial flow evaluation and the method from Barree et al. (2015a) yield \na 50-100-fold overestimate of permeability. Holding \ud835\udc34\u221a\ud835\udc58 constant, this implies that the effective fracture \narea (or if height is assumed, effect ive fracture length) will be underestimated by a factor of 7 -10.  \nThe analysis provided by Barree et al. (2015b) may be an example of the consequences of overestimated \npermeability in a gas reservoir. They analyze a gas shale well with DFIT -derived permeab ility and an RTA \nmatch to production data. They estimate the effective fracture length to be just 35 ft. Th is estimate  seems  \nimplausibly low . \nTo test the impact on net -present value, we history matched ResFrac simulations to the Utica well"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4af42-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 19, "chroma:document": "production data,  using either 1 microdarcy or 20 nd as the permeability estimate. Then, we performed a \nseries of simulations with different cluster and well spacing and performed simple economic calculation s \nof net-present value. The high and low permeability models yielded different optimal designs. Applying \nthe optimal design from the \u2018high permeability\u2019 model to the \u2018low permeability\u2019 model resulted in large \nreduction in net present value. The details of this comparison will be shown in a separate, standalone  paper. \nThe analysis shows that improved accuracy from the DFIT permeability estimate can improve fracture \ndesign and well placement and significantly increase return on investment.  \n5. Conclusions  \nBy integrating detailed nume rical simulations, field data, operator experience, and mathematical analysis, \nwe developed a step -by-step procedure for estimating stress, permeability, and pore pressure from DFIT\u2019s \nin low permeability formations."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4afc4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 19, "chroma:document": "in low permeability formations.  \n\u2012 Near -wellbore pressure drop typically c auses 1000s of psi of pressure drop at early time in DFIT\u2019s \nin horizontal wells. If this occurs, then f or tens of minutes after shut -in, pressure measured in the \nwell is much higher than the pressure in the far -field hydraulic fracture. The effective ISIP (an \nestimate for the pressure in the fracture at shut -in) can be estimated from a G -function plot.  \n\u2012 Analogous to the g -function, the h -function is proportional to the cumulative volume of fluid leaked \noff from the fracture since the start of injection. Unl ike the g -function, the h -function accounts for \ndeviation from Carter leakoff as the pressure in the fracture decreases. The h -function is useful in \nmathematical derivations used for permeability estimation and for the construction of a relative \nstiffness plot. \n\u2012 The G -function and h -function methods can be used to estimate permeability from the data prior to"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b046-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 19, "chroma:document": "impulse flow. We derive mass balance equations for jointly inferring permeability and fracture size. \nUnlike equations commonly used in the literature  (Valko and Economides, 1999) , these equations \nconsider wellbore storage and leakoff.  \n\u2012 Impulse linear flow can be used to estimate permeability as long as fracture area can be estimated. \nSimilar to the G -function and h -function methods, permeability can be jo intly estimated with area \nusing a mass balance equation.  \n\u2012 Simulations show that a variety of processes can cause the appearance of impulse radial, even in \nsituations where flow is not actually radial. This problem is especially severe in gas shale, where \nfalse radial is common in both simulation results and in real data. Analysis based on false radial \nflow typically leads to a 10 -100x overestimate of permeability. Genuine radial is most likely to \noccur in low volume DFIT \u2019s and in formations with permeabilit y divided by viscosity greater than \n1 microdarcy/cp."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b0c8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 19, "chroma:document": "1 microdarcy/cp.  \n\u2012 The G -function and h -function permeability estimates are usually similar. The G -function method \nis more sensitive to error  due to  elevated dP/dG from near -wellbore pressure drop. With field data, \nimpulse  linear permeability estimates are usually 2 -5 times lower than the G -function and h -function \nmethods. The G -function and h -function estimates may be impacted by multiphase effects or by Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b14a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 20, "chroma:document": "URTeC 123   21 \npressure dependent permeability. Therefore, the impulse linear flow p ermeability estimate is \ntypically preferred for reservoir engineering calculations. If impulse linear flow is not available, the \nG-function or h -function methods may be adjusted downward by about 3-fold. There is moderate \nuncertainty in the permeability es timates, and modelers should have reasonable freedom to modify \npermeability  if needed to match production data.  \n\u2012 The magnitude of the minimum principal stress can be estimated by identifying the \u2018contact \npressure\u2019 which is the pressure at which the fracture  walls come into contact and the system begins \nto stiffen. The minimum principal stress can be estimated to be approximately 75 psi below the \ncontact pressure. This is effectively the \u2018compliance method\u2019 of picking \u2018fracture closure\u2019 (McClure \net al., 2016) . However, we have defined the new term \u2018contact pressure\u2019 to avoid confusion with a"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b1cc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 20, "chroma:document": "variety of other definitions of \u2018closure.\u2019 Rather than using a plot of G*dP/dG (as recommended by \nMcClure et al., 2016), we recommend identifying the contact pressure from  a plot of dP/dG or from \na relative stiffness plot.  \n\u2012 It is possible to approximately infer the relationship between aperture and effective stress. Field data \nshows that the average fracture aperture is between 0.5 -3 mm at the contact pressure, and continues  \nto be substantial when the fluid pressure is equal to the minimum principal stress. This is evidently \nthe manifestation of the roughness of in -situ hydraulic fractures.  \n\u2012 DFIT permeability estimates have direct implication for fracture design and can significantly impact \neconomic returns.  \n \nAcknowledgements  \nWe gratefully acknowledge the financial support of ConocoPhillips  Company , Hess Corporation, Shell  \nInternational Exploration and Production Inc. , Equinor, Keane Group, Range Resources Corporation, an d"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b24e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 20, "chroma:document": "Apache Corporation.  We also want to recognize the important contributions of the study participants who \nare not listed as coauthors.  \n \nReferences  \nAyoub, J. A., D. P. Bourdet, Y. L. Chauvel. 1988. Impulse testing. SPE Formation Evaluation 3 (3): 534 -\n546, d oi: 10.2118/15911 -PA. \nBarree, R. D., H. Mukherjee. 1996. Determination of pressure dependent leakoff and its effect on fracture \ngeometry. SPE 36424. Paper presented at the 71st Annual Technical Conference and Exhibition, Denver, \nCO. \nBarree, R. D., V. L. Ba rree, and D. P. Craig. 2009. Holistic fracture diagnostics: Consistent interpretation \nof prefrac injection tests using multiple analysis methods. SPE 107877. Paper presented at the SPE Rocky \nMountain Oil & Gas Technology Symposium, Denver, CO.  \nBarree, R. D ., J. L. Miskimins, and J. V. Gilbert. 2015 a. Diagnostic fracture injection tests: common \nmistakes, misfires, and misdiagnoses. SPE Production & Operations 30 (2): 84-98, doi: 10.2118/169539 -\nPA."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b2d0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 20, "chroma:document": "PA. \nBarree, R. D., S. A. Cox, J. L. Miskimins, J. V. Gilbert, and  M. W. Conway. 2015b. Economic optimization \nof horizontal -well completions in unconventional reservoirs. SPE Production & Operations 3 (4): 293 -311, \ndoi: 10.2118/168612 -PA. \nBarree, R. D. and J. L. Miskimins. 2016. Physical explanations of non-linear derivatives in diagnostic \nfracture injection test analysis. SPE 179134 -MS. Paper presented at the SPE Hydraulic Fracturing \nTechnology Conference, The Woodlands, TX.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b348-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 21, "chroma:document": "URTeC 123   22 \nBarton, N., S. Bandis, K. Bakhtar. 1985. Strength, deformation and conductivity coupling of rock joints. \nInternational Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts  22 (3): 121 -140, \ndoi: 10.1016/0148 -9062(85)93227 -9. \nBazan, Lucas W. and Bruce R. Meyer. 2015. Fracture complexity: analysis methodology and signat ure \npressure behavior of hydraulic fracture propagation from horizontal wellbores. SPE 176919. Paper \npresented at the SPE Asia Pacific Unconventional Resources Conference and Exhibition, Brisbane, \nAustralia.  \nBird, R. Byron, Warren E. Stewart, Edwin N. Ligh tfoot. 2006. Transport Phenomena, 2nd edition, John \nWiley & Sons, Inc.  \nBlanton, T. L. and J. E. Olson. 1999. Stress magnitudes from logs: Effects of Tectonic Strains and \nTemperature. SPE Reservoir Evaluation and Engineering 2 (1), 62 -68, doi: 10.2118/54653 -PA. \nBourdet, D., T. M. Whittle, and A. A. Douglas. 1983. A new set of type curves simplifies well test analysis. \nWorld Oil: 95 -106."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b3ca-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 21, "chroma:document": "World Oil: 95 -106. \nBranagan, P. T., N. R. Warpinski, B. Enger, and R. Wilmer. 1996. Measuring the hydraulic fracture -induced \ndeformation of reservoirs and adjacent rocks employing a deeply buried inclinometer arra y: GRI/DOE \nmulti-site project. SPE 36451. Paper presented at the SPE Annual Technical Conference and Exhibition, \nDenver, CO.  \nCarslaw, H. S., and J. C. Jaeger. 1959. Conduction of Heat in Solids. 2nd ed. Oxford University Press, Great \nBritain.  \nCastillo, J. L. 1987. Modified fracture pressure decline analysis including pressure -dependent leakoff. SPE \n16417. Paper presented at the SPE/DOE Low Permeability Reservoir Symposium, Denver, CO.  \nCipolla, Craig, Constance Gilbert, Aviral Sharma, and John LeBas. 2018. C ase history of completion \noptimization in the Utica. SPE 189838 -MS. Paper presented at the SPE Hydraulic Fracturing Technology \nConference and Exhibition, The Woodlands, TX.  \nClark, J. B. 1949. A hydraulic process for increasing the productivity of wells. Jo urnal of Petroleum"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b44c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 21, "chroma:document": "Technology 1 (1): 1 -8. \nCraig, David P., Ted D. Brown. 1999. Estimating pore pressure and permeability in massively stacked \nlenticular reservoirs using diagnostic fracture -injection tests. SPE 56600. Paper presented at the SPE \nAnnual Tech nical Conference and Exhibition, Houston, TX.  \nCraig, David P., Mike J. Eberhard, Chad E. Odegard, and Muthukumarappan Ramurthy. 2002. \nPermeability, pore pressure, and leakoff -type distributions in Rocky Mountain Basins. SPE 75717. Paper \npresented at the SP E Gas Technology Symposium, Calgary, Alberta, Canada.  \nCraig, David P. 2014. New type curve analysis removes limitations of conventional after -closure analysis \nof DFIT data. SPE 168988 -MS. Paper presented at the SPE Unconventional Resources Conference, The \nWoodlands, TX.  \nCraig, D. P. and T. A. Blasingame. 2006. Application of a new fracture -injection/falloff model accounting \nfor propagating, dilated, and closing hydraulic fractures. SPE 100578. Paper presented at the SPE Gas"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b4ce-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 21, "chroma:document": "Technology Symposium, Calgary, Al berta.  \nCraig, D. P., R. D. Barree, N. R. Warpinski, and T. A. Blasingame. 2017. Fracture closure stress: \nReexamining field and laboratory experiments of fracture closure using modern interpretation \nmethodologies. SPE 187038. Paper presented at the SPE Annu al Technical Conference and Exhibition, San \nAntonio, TX.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b55a-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 22, "chroma:document": "URTeC 123   23 \nCraig, David and Robert Jackson. 2017. Calculating the volume of reservoir investigated during a fracture -\ninjection/falloff test DFIT. SPE 184820. Paper presented at the SPE Hydraulic Fracturing Tech nology \nConference and Exhibition, The Woodlands, TX.  \nCramer, D. D. and D. H. Nguyen. 2013. Diagnostic fracture injection testing tactics in unconventional \nreservoirs. SPE 163863 . Paper presented at the SPE Hydraulic Fracturing Technology Conference, \nWoodla nds, TX.  \nCramer, D., Friehauf, K., Roberts, G., Whittaker, J. 2019. Integrating DAS, Treatment Pressure Analysis \nand Video -based Perforation Imaging to Evaluate Limited Entry Treatment Effectiveness. SPE 194334. \nPaper presented at the SPE Hydraulic Fractur ing Technology Conference, Woodlands, TX.  \nCrouch, S. L. and A. M. Starfield. 1983. Boundary Element Methods in Solid Mechanics . George Allen & \nUnwin (Publishers), Ltd.  \nDelaney, Paul T., David D. Pollard, Joseph I. Ziony, and Edwin H. McKee. 1986. Field rel ations between"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b5dc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 22, "chroma:document": "dikes and joints: emplacement processes and paleostress analysis. Journal of Geophysical Research, 91 \n(B5): 4920 -4938, doi: 10.1029/JB091iB05p04920 . \nEaton, Ben A. 1969. Fracture gradient prediction and its application in oilfield operations.  Journal of \nPetroleum Technology 21 (10): 1353 -1360, doi: 10.2118/2163 -PA \nEconomides, Michael J. and Kenneth G. Nolte, eds. 2000. Reservoir Stimulation. Wiley.  \nEconomides, Michael and Tony Martin. 2008. Modern Fracturing \u2013 Enhancing Natural Gas Production.  \nEnergy Tribune Publishing.  \nEhlig -Economides, Christine A. and Michael J. Economides. 2000. Chapter 2: Formation characterization: \nWell and reservoir testing. In Reservoir Stimulation, eds, Michael J. Economides and Kenneth G. Nolte, \nWiley.  \nGale, Julia F. W., Sara J. Elliott, and Stephen E. Laubach. 2018. Hydraulic fractures in core from stimulated \nreservoirs: core fracture description of HFTS slant core, Midland Basin, West Texas. Paper presented at the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b686-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 22, "chroma:document": "Unconventional Resources Technology Conference, Houst on, TX.  \nGodbey, J. K., H. D. Hodges. 1958. Pressure measurements during formation fracturing operations. \nPetroleum Transactions, AIME 213: 65 -69 \nGringarten, Alain C., Henry J. Ramey, R. Raghavan. 1974. Unsteady -state pressure distributions created \nby a wel l with a single infinite conductivity vertical fracture. SPE Journal 14 (4): 347 -360, doi: \n10.2118/4051 -PA. \nGu, H., J. L. Elbel, K. G. Nolte, A. H. D. Cheng, Y. Abousleiman. 1993. Formation permeability \ndetermination using impulse -fracture injection. SPE  25425. Paper presented at the Production Operations \nSymposium, Oklahoma City, OK.  \nGulrajani, Sunil N. and K. G. Nolte. 2000. Chapter 9: Fracture Evaluation using Pressure Diagnostics . In \nReservoir Stimulation, eds, Michael J. Economides and Kenneth G. Nolte, Wiley.  \nHaimson, Bezalel, Charles Fairhurst. 1967. Initiation and extension of hydraulic fractures in rocks. Society"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b708-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 22, "chroma:document": "of Petroleum Engineers Journal 7 (3), doi: 10.2118/1710 -PA. \nHawkes, R. V., R. Bachman, K. Nicholson, D. D. Cramer, and S. T. Chipperfield. 2018. Good tests cost \nmoney, bad tests cost more \u2013 a critical review of DFIT analysis gone wrong. SPE 191458. Paper presented \nat the SPE International Hydraulic Fracturing Technology Conference and Exhibition, Muscat, Oman.  \nHickman, Stephe n H., Mark D. Zoback. 1983. The interpretation of hydraulic fracturing pressure -time data \nfor in -situ stress determination. In Hydraulic Fracturing Measurements, ed. M. D. Zoback and B. C. \nHaimson, 44 -54. Washington D.C., National Academy Press.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b78a-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 23, "chroma:document": "URTeC 123   24 \nHorne, Rol and N. 1995. Modern Well Test Analysis: A Computer -Aided Approach, 2nd edition. Palo Alto, \nCA, Petroway, Inc.  \nHouze, Olivier P., Roland N. Horne, Henry J. Ramey. 1988. Pressure -transient response of an infinite \nconductivity vertical fracture in a reservoir  with double -porosity behavior. SPE Formation Evaluation 3 \n(3): 510 -518, doi: 10.2118/12778 -PA. \nHoward, George C. and C. R. Fast. 1957. Optimum fluid characteristics for fracture extension. Paper \npresented at the Spring Meeting of the Mid -Continental Distr ict, Division of Production, Tulsa, OK.  \nHubbert, M. K., D. G.  Willis. 1957. Mechanics of hydraulic fracturing. Journal of Petroleum Technology \n9 (6): 153 -168. \nJung, H., M. M. Sharma, D. D. Cramer, S. Oakes, and M. W. McClure. 2016. Re -examining interpreta tions \nof non -ideal behavior during diagnostic fracture injection tests. Journal of Petroleum Science and \nEngineering 145: 114 -136, doi: 10.1016/j.petrol.2016.03.016."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b816-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 23, "chroma:document": "Engineering 145: 114 -136, doi: 10.1016/j.petrol.2016.03.016.  \nKamal, Medhat M., ed. 2009. Transient Well Testing, Vol. Monograph Series Vol. 23, Society  of Petroleum \nEngineers.  \nKehle, Ralph O. 1964. The determination of tectonic stresses through analysis of hydraulic well fracturing. \nJournal of Geophysical Research 69 (2): 259 -273, doi: 10.1029/JZ069i002p00259.  \nLee, J. and R. Wattenbarger. 1996. Gas Reser voir Engineering. Society of Petroleum Engineers.  \nLiu, Guoqing, Christine Ehlig -Economides, and Jianlei Sun. 2016. Comprehensive Global Fracture \nCalibration Model. SPE 181856. Paper presented at the SPE Asia Pacific Hydraulic Fracturing Conference, \nBeijing , China.  \nMarongiu -Porcu, Matteo, Christine A. Ehlig -Economides, and Michael John Economides. 2011. Global \nmodel for fracture falloff analysis. SPE  144028. Paper presented at the SPE North American \nUnconventional Gas Conference and Exhibition, The Woodlands , TX."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b898-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 23, "chroma:document": "Marongiu -Porcu, Matteo, Albertus Retnanto, Michael J. Economides, Christine Ehlig -Economides. 2014. \nComprehensive fracture calibration test design. SPE 168634 . Paper  presented at the SPE Hydraulic \nFracturing Technology Conference, The Woodlands, TX.  \nMayerhofer, M. J. and M. J. Economides. 1993. Permeability estimation from fracture calibration \ntreatments. SPE 26039. Paper presented at the SPE Western Regional Meeting, Anchorage, AK.  \nMayerhofer, M. J., C. A. Ehlig -Economides, and M. J. Economides. 1995 . Pressure -transient analysis of \nfracture -calibration tests. SPE 26527. Journal of Petroleum Technology 47 (3): 231 -236. \nMcLennan, J. D., J. -C. Roegiers. 1982. How instantaneous are instantaneous shut -in pressures? SPE 11064. \nPaper presented at the 57th An nual Fall Technical Conference and Exhibition of the Society of Petroleum \nEngineers of AIME, New Orleans, LA.  \nMcClure, M. W. 2012. Modeling and characterization of hydraulic stimulation and induced seismicity in"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b91a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 23, "chroma:document": "geothermal and shale gas reservoirs. PhD The sis, Stanford University, Stanford, California.  \nMcClure, Mark W., Christopher A. J. Blyton, Hojung Jung, and Mukul M. Sharma. 2014. The Effect of \nChanging Fracture Compliance on Pressure Transient Behavior During Diagnostic Fracture Injection Tests . \nSPE 17 0956. Paper presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, The \nNetherlands.  \nMcClure, Mark W., Hojung Jung, Dave D. Cramer, and Mukul M. Sharma. 2016. The fracture compliance \nmethod for picking closure pressure from diagnostic f racture injection tests. SPE Journal 21 (4): 1321 -1339, \ndoi: 10.2118/179725 -PA. Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4b99c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 24, "chroma:document": "URTeC 123   25 \nMcClure, Mark. 2017. The spurious deflection on log -log superposition -time derivative plots of diagnostic \nfracture -injection tests. SPE Reservoir Evaluation & Engineering 20 (4 ), doi: 10.2118/186098 -PA. \nMcClure, Mark. 2019. Discussion of the Paper \u201cSPE -187038 -MS: Fracture Closure Stress: Reexamining \nField and Laboratory Experiments of Fracture Closure Using Modern Interpretation Methodologies .\u201d \narXiv:1904.07126  \nMcClure, Mark and Charles Kang. 2018. ResFrac Technical Writeup. arXiv:1804.02092 . \nMeng, Chunfang, Lingli Wei, Roger Yuan. 2014. Coupled fluid flow and geomechanics modeling for DFIT \nanalysis in unconventional gas development. Paper presented at the Intern ational Petroleum Technology \nConference, Kuala Lumpur, Malaysia, doi: 10.2523/18159 -MS. \nMukherjee, H. 1991. Extension of fracture pressure decline curve analysis to fissured formations. SPE \n21872. Paper presented at the Rocky Mountain Regional Meeting and Low-Permeability Reservoir \nSymposium, Denver, CO."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4ba1e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 24, "chroma:document": "Symposium, Denver, CO.  \nNolte, Kenneth. 1979. Determination of fracture parameters from fracturing pressure decline. SPE 8341. \nPaper presented at the Annual Fall Technical Conference and Exhibition of the Society of Petroleum \nEngi neers, Las Vegas, NV.  \nNolte, K. G., J. L. Maniere, and K. A. Owens. 1997. After -closure analysis of fracture calibration tests. SPE \n38676. Paper presented at the 1997 Annual Technology Conference and Exhibition of the Society of \nPetroleum Engineers, San Antonio, TX.  \nPadmakar, A.  S. 2013. Geomechanics coupled reservoir flow simulation for diagnostic fracture injection \ntest design and interpretation in shale reservoirs. SPE 166201 . Paper  presented at the SPE Annual Technical \nConference and Ex hibition, New Orleans, LA.  \nPerkins, T. K., and J. A. Gonzalez. 1985. The effect of thermoelastic stresses on injection well fracturing \n25(1): 78 -88, doi:  10.2118/11332 -PA. \nRaaen, A. M., E. Skomedal, H. Kjorholt, P. Markestad, D. Okland. 2001. Stress determ ination from"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4ba96-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 24, "chroma:document": "hydraulic  fracturing tests: the system stiffness approach. International Journal for Rock Mechanics and \nMining Sciences  38 (4): 529 -541, doi: 10.1016/S1365 -1609(01)00020 -X. \nScholz, Christopher H. 2010. A note on the scaling relations for openi ng mode fractures in rock. Journal of \nStructural Geology 32, doi:  10.1016/j.jsg.2010.09.007 . \nShou, Keh -Jian, Eduard Siebrits, Steven L. Crouch. 1997. A higher order displacement discontinuity \nmethod for three -dimensional elastostatic problems. Internationa l Journal of Rock Mechanics and Mining \nSciences 34 (2): 317 -322, doi: 10.1016/S0148 -9062(96)00052 -6. \nSmith, Michael Berry  and Carl T. Montgomery. 2015. Hydraulic Fracturing . CRC Press.  \nSneddon, I. N. 1946. The distribution of stress in the neighborhood of a crack in an elastic solid. Proceedings \nof the Royal Society of London Series A 187 (1009): 229 -260, doi: 10.1098/rspa.1946.0077  \nSoliman, M. Y.  and Talal Gamadi. 2012. Testing tight ga s and unconventional formations and"}


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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 24, "chroma:document": "determination of closure pressure. SPE 150948 . Paper  presented at the SPE/EAGE European \nUnconventional Resources Conference and Exhibition, Vienna, Austria.  \nSoliman, M. Y., C.S. Kabir. 2012. Testing unconventional format ions. Journal of Petroleum Science and \nTechnology 92-93: 102 -109, doi: 10.1016/j.petrol.2012.04.027.  \nSpivey, John P. and W. John Lee. 2013. Applied Well Test Interpretation. SPE Textbook Series, volume \n13. \nStewart, George. 2011. Well Test Design and Analys is. PennWell Corp.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 25, "chroma:document": "URTeC 123   26 \nSuarez -Rivera, Roberto, Jeff Burghardt, Sergei Stanchits, Eric Edelman, and Aniket Surdi. 2013. The effect \nof rock fabric on fracture complexity for improving completion design and well performance. Paper \npresented at the International P etroleum Technology Conference, Beijing, China.  \nTheis, Charles V. 1935. The relationship between the lowering of the Piezometric surface and the rate and \nduration of discharge of a well using ground -water storage. Eos, Transactions, American Geophysical \nUnion 16 (2): 519 -524, doi: 10.1029/TR016i002p00519.  \nValko, P. P. and M. J. Economides. 1999. Fluid -leakoff delineation in high -permeability fracturing. SPE \nProduction & Facilities 14 (2), doi: 10.2118/56135 -PA. \nVogler, D., R. R. Settgast, C. Annavarapu, C. Madonna, P. Bayer, and F. Amann. 2018. Experiments and \nsimulations of fully hydro -mechanically coupled response of rough fracture exposed to high -pressure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4bc12-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 25, "chroma:document": "injection. Journal of Geophysical Research: Solid Earth 123: 1186 -1200, doi: 10.1002/2017JB015057 .  \nWallace, J., C.  S. Kabir, C. L. Cipolla. 2014. Multiphysics investigation of diagnostic fracture injection \ntests in unconventional reservoirs. SPE 168620 . Paper  presented at the SPE Hydraulic Fracturing \nTechnology Conference, The Woodlands, TX.  \nWang, HanYi and Mukul M. Sharma. 2017. New variable compliance method for estimating in -situ stress \nand leak -off from DFIT data. SPE 187348. Paper presented at the SPE Annual Technical Conference and \nExhibition, San Antonio, TX.  \nWang, HanYi and Mukul M. Sharma. 2018. Estimating unpropped fracture conductivity and compliance \nfrom diagnostic fracture injection tests. SPE 189844. Paper presented at the SPE Hydraulic Fracturing \nTechnology Conference & Exhibition, The Woodlands, TX.  \nWarpinski, Norman R. 1991. Hydraulic frac turing in tight, fissured media. Journal of Petroleum \nTechnology, 43 (2), doi:  10.2118/20154 -PA."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4bc94-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 25, "chroma:document": "Technology, 43 (2), doi:  10.2118/20154 -PA. \nWeijers, L., L. G. Griffin, H. Sugiyama, T. Shimamoto, S. Takada, K. K. Chong, J. M. Terracina, and C. \nA. Wright. 2002. The first successful fracture treatment  campaign conducted in Japan: Stimulation \nchallenges in a deep, naturally fractured volcanic rock. SPE  77678. Paper presented at the Annual Technical \nConference and Exhibition, San Antonio, TX.  \nWillis -Richards, J., K. Watanabe, H. Takahashi. 1996. Progress toward a stochastic rock mechanics model \nof engineered geothermal systems. Journal of Geophysical Research  101 (B8): 17481 -17496, doi: \n10.1029/96JB00882.  \nWitherspoon, P. A., J. S. Y. Wang, K. I wai, J. E. Gale. 1980. Validity of cubic law for fluid flow in a \ndeformable rock fracture. Water Resources Research 16 (6): 1016 -1024, doi: 10.1029/WR016i006p01016.  \nWright, Chris. 2000. Section 9E: Rate step -down test analysis \u2013 a diagnostic for fracture e ntry. In Reservoir \nStimulation, eds, Michael J. Economides and Kenneth G. Nolte, Wiley."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 25, "chroma:document": "Yew, Ching H. and Xiaowei Weng. 2015. Mechanics of Hydraulic Fracturing. Gulf Professional \nPublishing.  \nZanganeh, Behnam, Christopher R. Clarkson, Jack R. Jones. 2019. R einterpretation of flow patterns during \nDFITs based on dynamic fracture geometry, leakoff and afterflow. SPE 189840. Paper presented at the SPE \nHydraulic Fracturing Technology Conference, The Woodlands, TX.  \nZhang, Junjing, Anton Kamenov, D. Zhu, A.D. Hill.  2013. Laboratory measurement of hydraulic fracture \nconductivities in the Barnett Shale . SPE 163839 . Paper  presented at the SPE Hydraulic Fracturing \nTechnology Conference, The Woodlands, TX.  \nZoback, Mark. 2007. Reservoir Geomechanics. Cambridge University Press.  \n  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4bd8e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 26, "chroma:document": "URTeC 123   27 \nList of variables  \nA: fracture surface area; does not count both sides of the fracture \u2013 ie, defined so that a fracture with sides \nof length 1 ft has area of 1  ft^2 (ft^2; m^2)  \ncfl: compressibility of the fluid in the fracture (psi^ -1; MPa^ -1) \n\ud835\udc36\ud835\udc53: fracture conductivity (md -ft; m^3)  \n\ud835\udc36\ud835\udc53\ud835\udc37: dimensionless fracture conductivity  \nCL: leakoff coefficient (ft/min^0.5; m/s^0.5)  \nCnw: near -wellbore pressure drop coefficient (psi/(bpm)^.5; MPa/(m^3/s)^.5)  \nCt: total system storage coefficient (bbl/psi; m^3/MPa)  \nct: total formation compressibility (psi^ -1; MPa^ -1) \nCw: wellbore storage coefficient (bbl/psi; m^3/MPa)  \nE\u2019: Plane strain Young\u2019s modulus  \nFL: linear flow time function (dimensionless)  \nG: G-function (dimensionless)  \nGc: G-funct ion at closure (dimensionless)  \ng: g-function (dimensionless)  \ng0: g-function at shut -in (dimensionless)  \nH: H-function (psi -min^.5; MPa -s^.5)  \nh: h-function (psi -min^.5; MPa -s^.5); or formation height (ft; m)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4be06-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 26, "chroma:document": "hf: fracture height (ft; m)  \nk: permeability (md; m ^2) \nLf: fracture length (ft; m)  \nm: mass of fluid in the wellbore/fracture system (lbs; kg)  \nP: fluid pressure (psi; MPa)  \nP0: effective fluid pressure at shut -in (estimate for effective ISIP) (psi; MPa)  \nPeff: effective fluid pressure (estimate for fluid pres sure in the fracture) (psi; MPa)  \n\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53: effective ISIP (psi; MPa)  \nPres: reservoir fluid pressure (psi; MPa)  \nPw,init: fluid pressure at the beginning of injection (psi; MPa)  \nQ: volumetric flow rate (bpm; m^3/s)  \nRf: fracture radius (ft; m)  \nrw: wellbore radius (ft; m)  \ns: skin factor (unitless)  \nSf,c: stiffness of a closed crack (psi/ft; MPa/m)  \nSf,o: stiffness of an open crack (psi/ft; MPa/m)  \nSrel: relative stiffness (min^ -.5; s^ -.5) \nSt: total system stiffness (psi/bbl; MPa/m^3)  \nt: time (various un its; s)  \nte: duration of injection (min; s)  \nV: volume of the wellbore/fracture system (bbl; m^3)  \nVf: volume of fluid in the fracture (bbl; m^3)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 26, "chroma:document": "Vf: volume of fluid in the fracture (bbl; m^3)  \nVinj: volume of fluid injected (bbl; m^3)  \nVL: volume of fluid leaked off from the fracture since the start of inj ection (bbl; m^3)  \n\ud835\udc49\ud835\udc3f\ud835\udc60: volume of fluid leaked off from the fracture since shut -in (bbl; m^3)  \nVslug: volume of fluid injected as part of a slug test (bbl; m^3)  \nW: fracture aperture (inches; m)  \nW0: fracture aperture when the walls come into contact (inches; m)  \nW0,max: numerical parameter; maximum allowed value of W0 in an element (inches; m)  \n\ud835\udefd: near -wellbore pressure drop exponent (unitless)  \n\u0394\ud835\udc43\ud835\udc5b\ud835\udc64: pressure drop due to near -wellbore pressure drop (psi; MPa)  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4bf14-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 27, "chroma:document": "URTeC 123   28 \n\u0394\ud835\udc61: shut -in duration (min; s)  \n\u0394\ud835\udc61\ud835\udc5d\ud835\udc52\ud835\udc4e\ud835\udc58: shut -in duration at the peak value of G*dP/dG (min; s)  \n\u0394\ud835\udf0e\ud835\udc5b,\ud835\udc4f\ud835\udc4e\ud835\udc50\ud835\udc58: additional normal stress on the fracture due to opening (psi; MPa)  \n\ud835\udf02: fracturing efficiency (dimensionless)  \n\ud835\udf07: fluid viscosity (cp; MPa -s) \n\ud835\udf0e\ud835\udc5b: normal stress (psi; MPa)  \n\ud835\udf0e\ud835\udc5b,\ud835\udc50: contact stress (psi; MPa)  \n\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53: effective normal stress at which the aperture has decreased 90% from W0 (psi; MPa)  \n\ud835\udf0f: integration variable for time (min; s)  \n\ud835\udf19: porosity (unitless)  \n \nA. Appendix   \nThis appendix reviews the physics of a DFIT pr essure transient and provides mathematical derivation of \ninterpretation techniques. All equations are provided in consistent ( SI) units.  \nA.1 Decomposing the pressure derivative  \nFrom the chain rule, the derivative of pressure with respect to time can be wri tten as: \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61=\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc5a\ud835\udc51\ud835\udc5a\n\ud835\udc51\ud835\udc61,           (2) \nwhere P is pressure, m is mass of fluid in the wellbore/fracture system, and t is time. Starting from Equation"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4bfd2-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 27, "chroma:document": "2, McClure et al. (2016) showed that for a slightly compressible fluid:  \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61=1\n\ud835\udc36\ud835\udc61\ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc61,           (3) \nwhere dV\ndt is the leakoff rate  and Ct is the system storage coefficient (the volume of fluid released from the \nsystem per increment of pressure) . Equation 3 provides a framework for understanding DFIT pressure \ntransients. Changes in slope are caused by changes in either system storage coefficient or leakoff.  \nEquation  2 assumes that a single value of press ure can be used for the entire fracture. This implicitly \nassumes that the fracture is effectively infinite conductivity and neglects perforation and near -wellbore \npressure drop.  The effect of finite fracture conductivity is discussed in Section A.5.  \nA.2 Sy stem storage and contact  \nMcClure et al. (2016) show ed that the system stiffness ( and its reciprocal,  system storage) can be written \nas: \n\ud835\udc46\ud835\udc61=1\n\ud835\udc36\ud835\udc61= 1\n\ud835\udc36\ud835\udc64+\ud835\udc34\n\ud835\udc46\ud835\udc53+\ud835\udc49\ud835\udc53\ud835\udc50\ud835\udc53\ud835\udc59.          (4)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c072-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 27, "chroma:document": "as: \n\ud835\udc46\ud835\udc61=1\n\ud835\udc36\ud835\udc61= 1\n\ud835\udc36\ud835\udc64+\ud835\udc34\n\ud835\udc46\ud835\udc53+\ud835\udc49\ud835\udc53\ud835\udc50\ud835\udc53\ud835\udc59.          (4) \nwhere Cw is the wellbore storage coefficient, A is the area of the fracture, Sf is the fracture stiffness  (equal \nto the reciprocal of the derivative of average fracture aperture with respect to pressure) , Vf is the volume of \nthe fracture, and cfl is the compressib ility of the fluid in the fracture. Equation 4 is valid during injection, \nand after shut -in: before, during, and after contact . Raaen et al. (2001) performed a si milar decomposition \nof system stiffness for application to pumpin/flowback tests.  \nThe wellbore storage coefficient has two components \u2013 the compressibility of the fluid in the well and the \ncompressibility of the wellbore volume itself. Wellbore storage coe fficient can be estimated directly from \nthe injection data. At the beginning of injection, prior to breakdown or fracture opening, a plot of pressure \nversus cumulative injection volume forms a straight line. The slope is equal to the wellbore storage"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c0ea-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 27, "chroma:document": "coeff icient.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c16c-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 28, "chroma:document": "URTeC 123   29 \nIn these derivations, v olumes and areas  are written  in terms of the full fracture volume and area, not the \nvolume and area of one-wing  of the fracture. Authors  sometimes  define terms using one-wing  of the \nfracture. We prefer not to follow this convention because  fractures can propagate radially, with complex \ngeometry, or asymmetrically, and so in the general case it is not always meaningful to refer to  \u2018one-wing\u2019 \nof a fracture . Also, sometimes authors define \u2018area\u2019 by counting both sides  of the fracture. This is not the \nconvention used in this paper. We define area according to the convention that a square fracture with length \nand height of 1 ft has an area of 1 ft2.  \nWe define the \u2018contact pressure\u2019  as being the pressure at which the fracture wa lls come back into contact  \nand the system begins to stiffen.  Prior to contact , the fracture stiffness can be written from an analytical"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c1ee-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 28, "chroma:document": "solution based on the geometry of the fracture and the mechanical properties of the rock. The two common \ngeometry assump tions are radial and PKN. PKN fracture geometry applies to a fracture that has length \nmuch greater than height.  \nIf the fracture is radial, the stiffness is ( Table 2 -2 from Ehlig -Economides and Economides, 2000 ): \n\ud835\udc46\ud835\udc53,\ud835\udc5c(\ud835\udc5f\ud835\udc4e\ud835\udc51\ud835\udc56\ud835\udc4e\ud835\udc59 )=3\ud835\udf0b\ud835\udc38\u2032\n16\ud835\udc45\ud835\udc53,          (5) \nwhere Sf,o is the stiffness of an open crack, E\u2019 is the plane strain Young\u2019s modulus, and Rf is the radius.  If \nthe fracture has PKN geometry, the stiffness is written as:  \n\ud835\udc46\ud835\udc53,\ud835\udc5c(\ud835\udc43\ud835\udc3e\ud835\udc41 )=2\ud835\udc38\u2032\n\ud835\udf0b\u210e\ud835\udc53,          (6) \nwhere hf is the assumed fracture height.  Once contact  occurs, the fracture begins to stiffen because of contact \nstress created by the contacting fracture walls. The total stiffness can be written as (McClure et al., 2016):  \n\ud835\udc46\ud835\udc53=\ud835\udc46\ud835\udc53,\ud835\udc5c+\ud835\udc46\ud835\udc53,\ud835\udc50,          (7) \nwhere Sf,c is the additional stiffness due to contact. The contact stiffness is equal to:  \n\ud835\udc46\ud835\udc53,\ud835\udc50=1\n\ud835\udc51\ud835\udc4a\n\ud835\udc51\ud835\udc43,           (8)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c270-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 28, "chroma:document": "\ud835\udc46\ud835\udc53,\ud835\udc50=1\n\ud835\udc51\ud835\udc4a\n\ud835\udc51\ud835\udc43,           (8) \nwhere W is the fracture aperture  (calculated as a function of effective normal stress) . Sometimes,  authors \ndifferentiate between fracture void aperture  and hydraulic aperture  (McClure, 2012),  but in this work, they \nare assumed to be equal.  \nPrior to contact, Sf,c is equal to zero. After contact, t he parameter Sf,c begins to increase  and asymptotically  \napproaches infinity as effective normal stress approaches infinity.  Sf,c can be calculated from an empirical \nrelation between aperture and effective normal stress.  \nThe resulting relation for contact stiffness is:  \n\ud835\udc46\ud835\udc53,\ud835\udc50=\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53\n9\ud835\udc4a0 (1+9(\ud835\udf0e\ud835\udc5b\u2212\ud835\udc43)\n\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53)2\n.         (9) \nEquation 9 indicates that \ud835\udc46\ud835\udc53,\ud835\udc50 is nonzero at the moment of contact, which implies a discontinuous jump in \nstiffness at t he point of contact. It is unclear whether this is realistic . In future work, it would be worthwhile \nto explore alternatives to Equation 1 that allow a smooth increase from contact stiffness from zero as contact \noccurs."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c2f2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 28, "chroma:document": "occurs.  \nEven after \u2018contact\u2019 has occurred a cross the entire fracture, the walls of the fracture are not literally touching \neverywhere along the fracture. Instead, asperities cause solid -to-solid contact across only a fraction of the \nfracture area. As effective stress increases, the percentage of ar ea with solid -to-solid contact increases. This \nprocess is implicit to  Equation 1. The equation to be used to capture average fracture aperture without \nperforming detailed modeling at the scale of individual asperities. As an example of the alternative \napproach, Vogler et al. (2018) performed small -scale modeling that captures individual asperities.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
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id: 9ae4c374-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 29, "chroma:document": "URTeC 123   30 \nPrior to contact , force balance requires that fracture effective normal stress is equal to zero  (Crouch and \nStarfield, 1983) . After contact , the effective normal stress becomes compressive  and equal to the contact \nstress created by the contacting of the fracture walls. Contact stress can be calculated by solving for effective \nnormal stress in a constitutive equation. Using Equation 1, contact stress is:  \n\ud835\udf0e\ud835\udc5b\u2212\ud835\udc43=\ud835\udf0e\ud835\udc5b,\ud835\udc50=\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53  \n9 (\ud835\udc4a0\n\ud835\udc4a\u22121).        (10) \nBecause of fracture roughness, the fracture aperture is not zero at contact. This residual aperture creates a \nbackstress so that the  normal stress is slightly above Shmin when  the walls come into contact. Th e \nbackstress can be calculated as:  \n\u0394\ud835\udf0e\ud835\udc5b,\ud835\udc4f\ud835\udc4e\ud835\udc50\ud835\udc58 =\ud835\udc4a\ud835\udc46\ud835\udc53,\ud835\udc5c.          (11) \nThe fluid pressure is equal to Shmin when the backstress is equ al to the contact stress:  \n\ud835\udc4a\ud835\udc46\ud835\udc53,\ud835\udc5c=\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53  \n9 (\ud835\udc4a0\n\ud835\udc4a\u22121).         (12) \nThere is a discrete  change in the physics at the point when the walls come into contact  \u2013 the contact stress"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c3f6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 29, "chroma:document": "begins to increase from zero. However, t here is no meaningful change in the physics or discernable signal \nin the transient when pressure is equal to  Shmin. Because  there is not a signal in the data when pressure \nreaches Shmin, the difference between contact pressure  and Shmin  is a source of uncertainty  when \nestimating Shmin . \nCraig and Blasingame (200 6) and Craig et al. (2017) define the total storage in a piece -wise fashion \u2013 \nneglecting different parts of the storage at different points during the test. In their definition, th e \ud835\udc34\n\ud835\udc46\ud835\udc53 term is \nnegligible after \u2018closure, \u2019 implying that Sf is infinite. This assumption does not appear to be well -founded. \nWith realistic values in Equation 4, the \ud835\udc34\n\ud835\udc46\ud835\udc53 term is not negligible until pressure is hundreds or thousands of \npsi below Shmin.  \nA.3 G -function analysis  \nThe G -function (also called G -time) is a monotonic transformation of \u0394\ud835\udc61 (shut-in time ). Nolte (1979)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c46e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 29, "chroma:document": "derived the G -function (also call ed G-time) such that, under reasonable assumptions, the cumulative leakoff \nafter shut -in is linearly proportional to G -time. A related function, the g -function, is derived to be linearly \nproportional to the cumulative leakoff from the start of injection (C astillo, 1987; Gulrajani and Nolte, 2000) : \n\ud835\udc49\ud835\udc3f(\u0394\ud835\udc61)=2\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\ud835\udc61\ud835\udc52\ud835\udc54(\u0394\ud835\udc61).          (13) \nThe G -function is defined as:  \n\ud835\udc3a(\u0394\ud835\udc61)=4\n\ud835\udf0b(\ud835\udc54(\u0394\ud835\udc61)\u2212\ud835\udc54(\u0394\ud835\udc61=0)).        (14) \nThe cumulative leakoff after shut -in is defined as:  \n\ud835\udc49\ud835\udc3f\ud835\udc60(\u0394\ud835\udc61)=2\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\ud835\udc61\ud835\udc52(\ud835\udc54(\u0394\ud835\udc61)\u2212\ud835\udc54(0))=\ud835\udf0b\n2\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\ud835\udc61\ud835\udc52\ud835\udc3a(\u0394\ud835\udc61).      (15) \nThe exact form of the G and g functions depend on assumptions about fracture growth. However, there is \nlittle practical difference between the different forms of the g and G -functions. For example, within \nreasonable ranges, the cumulative leakoff at shut -in can be bounded with \ud835\udc540=\ud835\udc54(\u0394\ud835\udc61=0) is a number in \nthe narrow range between 4/3 and \ud835\udf0b\n2 (Equation 30 of the appendix from Gulrajani and Nolte, 2001). The \nmost common form of the g -function is:  \n\ud835\udc54(\u0394\ud835\udc61)=4"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c4e6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 29, "chroma:document": "most common form of the g -function is:  \n\ud835\udc54(\u0394\ud835\udc61)=4\n3[(1+\u0394t\nte)1.5\n\u2212(\u0394t\nte)1.5\n].        (16) Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c568-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 30, "chroma:document": "URTeC 123   31 \nBecause cumulative leakoff after shut -in is proportional to G -time, the derivative of cumulative leakoff \nwith respect to G -time is equal to a constant. In the ideal case, f racture stiffness is constant prior to contact , \nand so the total system storage (and  stiffness) are also constant prior to contact.  Therefore, from Equation  \n3, a plot of pressure versus G -time should form a straight line  (Castillo, 1987) : \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc3a=1\n\ud835\udc36\ud835\udc61\ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc3a=\ud835\udc50\ud835\udc5c\ud835\udc5b\ud835\udc60\ud835\udc61\ud835\udc4e\ud835\udc5b\ud835\udc61 .          (17) \nIf fracture geometry and mechanical properties of the rock are known, then Equation 17 can be solved for \nthe leakoff coefficient  (Nolte, 1979; Castillo, 1987; Gulrajani and Nolte, 2000) .  \nIf the fracture formed instantaneously during injection, then the G -function would be equivalent  the square \nroot of time . The square root s caling aris es because the G -function assumes  Carter leakoff. The G-function \nis not exactly equal to the square root of time because accounts for the progressive growth of the fracture"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c5ea-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 30, "chroma:document": "during injection. As a result, t he duration of leakoff is a function of position along the fracture area. \nEquation 24 from  McClure (2017) provide s a succinct derivation of the G -function for the special case that \nthe fracture grows linearly with respect to time during injection.  \nA.4 Deviation from Carter leakoff  \nThe G -function  is derived based on the assumption of Carter leakoff (Nolte, 1979; Howard and Fast, 1957 ). \nFor the simple case with no filtrate zone or filtercake, Carter leakoff can be derived as the solution the 1D \ndiffusivity equation with a Dirichlet  (constant pressure)  boundary condition  (Bird et al., 2007) : \n\ud835\udc49\ud835\udc3f\ud835\udc60=4\ud835\udc34\u221a\u0394\ud835\udc61(\ud835\udc43\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\ud835\udf19\ud835\udc50\ud835\udc61\ud835\udc58\n\ud835\udf0b\ud835\udf07=4\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\u0394\ud835\udc61.       (18) \nThe leakoff coefficient is defined from Equation 18 as: \n\ud835\udc36\ud835\udc3f=(\ud835\udc43\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\ud835\udf19\ud835\udc50\ud835\udc61\ud835\udc58\n\ud835\udf0b\ud835\udf07.          (19) \nThe leakoff coefficient can be generalized to include the effect of filtrate invasion and filtercake formation. \nFiltercake does not form during a DFIT becaus e the injection is performed with water. Filtrate invasion is"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4c66c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 30, "chroma:document": "minor in DFIT\u2019s because of the low permeability and relatively large fracture surface area.  \nThe G-function assumption of Carter leakoff  is violated during a DFIT because pressure decreases over  \ntime (Castillo, 1987). As long as the change in the fracture pressure is relatively small relative to the \ndifference between ISIP (initial shut -in pressure) and the formation fluid pressure, then the leakoff rate is \nreasonably described by Carter leakoff.  But e ventually, the fluid pressure drops sufficiently far that there is \nsignificant deviation from Carter leakoff (Castillo, 1987) . The leakoff rate reduces relative to the rate that \nwould have occurred if Carter leakoff had continued. Because  \ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc3a is constant during  Carter leakoff , the \ndeviation causes  \ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc3a to decrease  (because leakoff occurs more slowly than if Carter leakoff had continued),  \nand so the derivative of pressure with respect to G -time begins to decrease.  This causes dP/dG  to decrease"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4ca9a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 30, "chroma:document": "and G*dP/dG to bend downward. The peaking of G*dP/dG and t*dP/dt occurs during the progressive \ntransition from Carter leakoff  to late -time impulse behavior (McClure, 2017).  \nA.5 The effect of closure  \nEquation  3 provides a conceptual framework f or understanding the effect contact between the fracture \nwalls. When the fracture walls come into contact, stiffness begins to increase (Equation 7). Increasing \nstiffness c auses dP/dG to increase. Based on this insight, contact can be identified as occurring when dP/dG \nbegins to increase (McClure et al., 2016).  \nEquation  3 depends on the assumption that pressure in the fracture can be described with a single parameter, \nP. This is valid if the fracture is approximately infinite conductivity. The dimensionless fracture \nconductivity is defined as:  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


