# embeddings_queue

created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889190-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 7, "chroma:document": "8  SPE 107877 \na tendency for rapid screenout and difficulty placing high \nproppant concentration slurries. These observations suggest \nthat another mechanism may be responsible for the same \ndiagnostic derivative signature. The alternate mechanism is \ncalled \u201ctransverse fracture storage\u201d.  \nIn transverse fracture storag e a secondary fracture set is \nopened when the fluid pressure exceeds the critical fissure-\nopening pressure, just as in PD L. As the secondary fractures \ndilate they create a storage volume for fluid which is taken \nfrom the primary hydraulic fract ure. While the fracture storage \nvolume increases, leakoff can al so be accelerated so PDL and \nstorage are aspects of the same coupled mechanism of fissure dilation. The relative magnitude of the enhanced leakoff and \nstorage mechanisms determines whether the G-function \nderivatives show PDL or storage. Numerical modeling studies indicate that the storage mech anism can easily dominate even \nlarge PDL."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8891e0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 7, "chroma:document": "derivatives show PDL or storage. Numerical modeling studies indicate that the storage mech anism can easily dominate even \nlarge PDL. \nAt shut-in the secondary fractures will close before the \nprimary fracture because they ar e held open against a stress \nhigher than the minimum in-situ horizontal stress. As they close fluid will be expelled from the transverse storage volume \nback into the main fracture d ecreasing the normal rate of \npressure decline and, in effect , supporting the observed shut-in \npressure by re-injection of stor ed fluid. Accelerated leakoff \ncan still occur at the same time but if the storage and \nexpulsion mechanism exceeds the enhanced leakoff rate then \nthe only signature observed during falloff will be storage. In \nmany cases a period of linear, constant area, constant matrix \npermeability dominated leakoff will occur after the end of storage.  \n \nG-Function Analysis with Storage \nThe characteristic G-function derivative signature is a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889226-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 7, "chroma:document": "G-Function Analysis with Storage \nThe characteristic G-function derivative signature is a \n\u201cbelly\u201d below the straight line through the origin and tangent \nto the semilog derivative of p\nw vs. G at the point of fracture \nclosure. Figure 20 shows an example of slight to moderate \nstorage. In Figure 20 fracture closure, indicated by the same \ndeparture of the tangent line from the semilog derivative, \noccurs just after the end of the storage effect.  \n  \n5 10 15 20\nG(Time)750080008500900095001000010500\n0200400600800100012001400160018002000\n1\nP vs. G\nGdP/dG vs. G\ndP/dG vs. GFracture ClosurePressure\nDerivatives\n \nFigure 20: Storage G-function plot  \nSqrt(t) Analysis with Storage or Height Recession \nThe sqrt( t) plot (Figure 21) shows a clear indication of \nclosure based on both the first-derivative inflection point and \nthe semilog derivative curve. Pi cking closure in the case of \nstorage is not generally a problem. \n \n1/24/200702:00 04:00 06:00 08:00\n1/24/200710:00"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889280-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 7, "chroma:document": "the semilog derivative curve. Pi cking closure in the case of \nstorage is not generally a problem. \n \n1/24/200702:00 04:00 06:00 08:00\n1/24/200710:00\nTime750080008500900095001000010500\n0100200300400\n1Pressure\nDerivativesP vs. \u221at\nxdP/dxvs. \u221at\ndP/dxvs. \u221atFracture Closure\n \nFigure 21: Storage sqrt(t) plot \n \nThe storage model, whether cau sed by height recession or \ntransverse fractures, requires that a larger volume of fluid \nmust be leaked-off to reach fr acture closure than is expected \nfor a single planar constant-heigh t fracture. In either case the \ntime to reach fracture closure is delayed by the excess fluid \nvolume that must be lost. Any estimation of reservoir \npermeability will give an incorrect result if the uncorrected \nclosure time (either G c or time-to closure in minutes, tc) is \nused. The observed closure time must be corrected by \nmultiplying by the storage ratio, rp. The magnitude of rp can \nbe determined by taking the ratio of the area under the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8892d0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 7, "chroma:document": "multiplying by the storage ratio, rp. The magnitude of rp can \nbe determined by taking the ratio of the area under the \nG-function semilog derivative up to the closure time, divided \nby the area of the right-tria ngle formed by the tangent line \nthrough the origin at closure. For normal leakoff and PDL the \nvalue of r p is set to 1.0 even though the ratio of the areas will \nbe greater than 1 for the PDL case. It is possible that the \nclosure time for PDL leakoff is proportional to the composite \nsystem permeability including both the matrix and fractures. \nFor severe cases of storage rp can be as low as 0.5 or less.  \n \nLog-Log Pressure Derivative with Storage \nFigure 22 shows the log-log plot of pressure difference and \nsemilog derivative for the storage case. Prior to closure, and \nwhile transverse storage is dominant, the semilog derivative \napproaches a unit slope, with the pressure difference curve \nnearly parallel. In some cases the two curves lie together on a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889320-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 7, "chroma:document": "approaches a unit slope, with the pressure difference curve \nnearly parallel. In some cases the two curves lie together on a \nsingle unit-slope line. In this case the curves are separated \nslightly and the slope is not exactly 1.0. After closure the \nreservoir transient signature is defined as in the previously \npresented cases. All fracture stor age effects are eliminated and \nthe reservoir pseudolinear flow period is shown by a -1/2 \nslope with a pseudoradial flow period indicated by a -1 slope \nof the semi-log derivative.  \n Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/07RMTC/All-07RMTC/SPE-107877-MS/2786245/spe-107877-ms.pdf/1 by University of Houston, Mohamed Gabry on 12 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889370-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 8, "chroma:document": "SPE 107877  9 \n2 3 4 56789 2 3 4 56789 2 3 4 56789 2 3 4 560.1 1 10 100\nTime (0 = 9.416667)234567892345678923\n101001000\n (m = 0.5)  (m = -0.5)  BH ISIP = 10000 psi 1Delta-Pressure and Derivative\u2206P vs. \u2206t\n\u2206td\u2206P/d\u2206t vs. \u2206t\n \nFigure 22: Storage log-log plot \n \n \nConclusions \nThe use of pre-frac injection/falloff diagnostic tests has \nbecome commonplace. Many impor tant decisions regarding \nfracture treatment designs and expectations of post-frac production are based on the results of these tests. In too many cases individual diagnostic plots and analysis techniques are \nmisapplied, leading to incorrect interpretations. The analyses \npresented here lead to the following conclusions: \n \n1. With consistent application of all available pressure decline diagnostics, a single unambiguous determination of fracture closure time and pressure can be made.  \n2. A single, unique closure event can be identified on all diagnostic plots.  \n3. The conventional analysis of the sqrt( t) plot, using the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8893b6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 8, "chroma:document": "2. A single, unique closure event can be identified on all diagnostic plots.  \n3. The conventional analysis of the sqrt( t) plot, using the \ninflection point identified by the first derivative, gives incorrect indications of closure for cases of PDL and tip \nextension and should not be relied upon. \n4. A modified sqrt( t) analysis, using the semilog derivative, \nis equivalent to the G-function analysis and helps avoid incorrect closure picks in cases of PDL and tip extension. \n5. Flow regimes can be identified using the semilog pressure \nderivative on the log-log plot of \u2206p\nwf \u2212 \u2206t during the shut-\nin period following the fracture injection test. \n6. As in conventional transient test analysis, a pseudolinear \nflow period is identified by parallel \u00bd slope lines, \nseparated by 2x, on the log-log \u2206pwf \u2212 \u2206t plot up until \nfracture closure.  \n7. Bilinear flow can be identified by parallel \u00bc slope lines \nseparated by 4x on the log-log \u2206pwf \u2212 \u2206t plot prior to \nfracture closure."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889406-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 8, "chroma:document": "7. Bilinear flow can be identified by parallel \u00bc slope lines \nseparated by 4x on the log-log \u2206pwf \u2212 \u2206t plot prior to \nfracture closure. \n8. After closure the pseudolinear reservoir flow period is \nidentified by a -1/2 slope of the semilog derivative of the \npressure difference on the log-log \u2206pwf \u2212 \u2206t plot, and a \n\u22123/2 slope of the first derivative of the pressure difference \nwith shut-in time on the same plot. \n9. Pseudoradial flow is identified by a -1 slope of the \nsemilog derivative on the log-log plot. 10. When a stable pseudolinear flow period exists, the after-\nclosure Cartesian plot of the linear flow function can be \nused to estimate reservoir pressure. \n11. When a pseudoradial flow period exists, both the \nconventional Horner analysis  and after-closure radial-\nflow analysis can be used to determine reservoir \ntransmissibility and pore pressure. \n \nAcknowledgements \nThe authors would like to thank Kumar Ramurthy, \nHalliburton, Mike Conway, Stim-Lab, and Stuart Cox,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889456-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 8, "chroma:document": "Acknowledgements \nThe authors would like to thank Kumar Ramurthy, \nHalliburton, Mike Conway, Stim-Lab, and Stuart Cox, \nMarathon, for their discussion and contribution to the procedures described. Sincere thanks are also due to the many \noperators whose diligence in pre-frac testing has allowed these \ndiagnostic analysis procedures to be developed and tested. \n \nNomenclature \nAf = fracture area, L2, ft2 \nB = formation volume factor, L3/L3, RB/STB \nct = total compressibility, Lt2/m, psi-1 \nCac = after-closure storage, L4t2/m, bbl/psi \nCbl = bilinear flow constant, m/Lt5/4, psi\u0387hr3/4 \nCpl = pseudolinear flow constant, m/Lt3/2, psi\u0387hr1/2  \nCpr = pseudoradial flow constant, m/Lt, psi \u0387hr  \nCfbc = before-closure fracture storage, L4t2/m, bbl/psi \nFL = linear flow time function, dimensionless  \nFR = radial flow time function, dimensionless  \ng = loss-volume function, dimensionless  \nG = G-function, dimensionless  \nh = height, L, ft  \nk = permeability, L2, md"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8894a6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 8, "chroma:document": "g = loss-volume function, dimensionless  \nG = G-function, dimensionless  \nh = height, L, ft  \nk = permeability, L2, md  \nLf = fracture half-length, L, ft  \nmH = slope of data on Horner plot, m/Lt2, psia  \nmL = slope of data on pseudolinear flow graph, m/Lt2, psia  \nmR = slope of data on pseudoradial flow graph, m/Lt2, psia  \np = pressure, m/Lt2, psia  \npwf = fracture pressure measured at wellbore, m/Lt2, psia  \nq = flow rate, L3/t, bbl/D \nQt = total injection volume, L3, bbl \nrp = storage ratio, dimensionless \nSf = fracture stiffness, m/L2t2, psi/ft \nt = time, hr \nta = adjusted pseudotime, hr \n \n \nGreek \n\u03b2 = constant, dimensionless \n\u2206 = difference, dimensionless \n\u03c7 = constant, dimensionless \n\u00b5 = viscosity, m/Lt, cp \n\u03c6 = porosity, dimensionless \n \nSubscripts \na = adjusted \nc = closure \nD = dimensionless \ne = end of injection \nf = filtrate \np = pumping \n0 = end of injection  \nw = wellbore \nz = process zone"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8894f6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 8, "chroma:document": "c = closure \nD = dimensionless \ne = end of injection \nf = filtrate \np = pumping \n0 = end of injection  \nw = wellbore \nz = process zone \n \n Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/07RMTC/All-07RMTC/SPE-107877-MS/2786245/spe-107877-ms.pdf/1 by University of Houston, Mohamed Gabry on 12 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889546-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 9, "chroma:document": "10  SPE 107877 \nReferences \n \n1. Nolte, K. G.: \u201cDetermination of Fracture Parameters from \nFracturing Pressure Decline, pa per SPE 3841, presented at the \nAnnual Technical Conference a nd Exhibition, Las Vegas, NV, \nSept. 23-26, 1979. \n2. Castillo, J. L.: \u201cModified Fracture Pressure Decline Analysis \nIncluding Pressure-Dependent Leakoff,\u201d paper SPE 16417, \npresented at the SPE/DOE Low Permeability Reservoirs Joint \nSymposium, Denver, CO, May 18-19, 1987. \n3. Barree, R. D., and Mukherjee, H. : \u201cDetermination of Pressure \nDependent Leakoff and Its Effect  on Fracture Geometry,\u201d paper \nSPE 36424, presented at the 71st Technical Conference and \nExhibition, Denver, CO, Oct. 6-9, 1996. \n4. Barree, R.D.: \"Applications of Pre-Frac Injection/Falloff Tests in \nFissured Reservoirs\u2014Field Examples,\" paper SPE 39932 \npresented at the SPE Rocky Mountain Regional/Low-\nPermeability Reservoirs Sympos ium, Denver, Apr. 5-8, 1998."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88958c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 9, "chroma:document": "presented at the SPE Rocky Mountain Regional/Low-\nPermeability Reservoirs Sympos ium, Denver, Apr. 5-8, 1998. \n5. Talley, G. R., Swindell, T. M., Waters, G. A. and Nolte, K. G.: \u201cField Application of After- Closure Analysis of Fracture \nCalibration Tests,\u201d paper SPE 5 2220, presented at the 1999 SPE \nMid-Continent Operations Symposium, Oklahoma City, OK, \nMarch 28\u201331, 1999. \n6. Cinco-Ley, H., and Samaniego- V., F.: \u201cTransient Pressure \nAnalysis for Fractured Wells,\u201d JPT (September 1981) 1749. \n7. Settari, A.: \u201cCoupled Fracture  and Reservoir Modeling,\u201d \npresented at the Workshop on Three Dimensional and Advanced \nHydraulic Fracture Modeling, held  in conjunction with the Fourth \nNorth American Rock Mechanics Symposium, July 29, 2000, Seattle, WA. \n8. Craig, D. P. and Bl asingame, T. A.: \u201cApplication of a New \nFracture-Injection/Falloff Mode l Accounting for Propagating, \nDilated, and Closing Hydrau lic Fractures,\u201d paper SPE 1005778"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8895dc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 9, "chroma:document": "Fracture-Injection/Falloff Mode l Accounting for Propagating, \nDilated, and Closing Hydrau lic Fractures,\u201d paper SPE 1005778 \npresented at the SPE Gas Technology Symposium, Calgary, \nAlberta, Canada, May, 15-17, 2006. \n9.  Hagoort, J.: \"Waterflood-Induced Hydraulic Facturing,\" PhD \nThesis, Delft Technical University, 1981. \n10.  Koning, E.J.L. and Niko, H.: \"Fractured Water-Injection Wells: \nA Pressure Falloff Test for Dete rmining Fracture Dimensions,\" \npaper SPE 14458 presented at the 1985 Annual Technical Conference and Exhibition of the Society of Petroleum \nEngineers, Las Vegas, NV,  September, 22-25, 1985. \n11.  Cinco-Ley, H., Kuchuk, F., Ay oub, J., Samaniego-V, F., and \nAyestaran, L.: \"Analysis of Pr essure Tests Through the Use of \nInstantaneous Source Response Concepts,\" paper SPE 15476 presented at the 61\nst Annual Technical Conference and Exhibition \nof the Society of Petroleum Engineers, New Orleans, LA, \nOctober, 5-8, 1986."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88964a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 9, "chroma:document": "st Annual Technical Conference and Exhibition \nof the Society of Petroleum Engineers, New Orleans, LA, \nOctober, 5-8, 1986. \n  \nAppendix A - Definition of diagnostic functions \n \nThe G-Function \nThe G-function is a representati on of the elapsed time after \nshut-in normalized to the duration of fracture extension. \nCorrections are made for the superposition of variable leakoff times while the fracture is growing. The form of the \nG-function used in this paper assumes high fluid efficiency in \nlow-permeability formations. Under that assumption the surface area of the fracture is a ssumed to vary linearly with \ntime during fracture propagation. The dimensionless pumping \ntime used in the G-function is defined as: \n( )/Dp ptt t t\u2206= \u2212 . ..........................................................(A-l) The elapsed total time from the start of fracture initiation \n(not start of pumping) is t and the total pumping time (elapsed"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88969a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 9, "chroma:document": "(not start of pumping) is t and the total pumping time (elapsed \ntime from fracture initiation to shut-in) in consistent time units \nis tP. For the assumption of low leakoff the dimensionless time \n(\u2206tD) is used to compute an intermediate function: \n() ()[ ]5.1 5.1134\nD D D t t tg \u2206\u2212 \u2206+ = \u2206 . ............................ (A-2) \nThe G-function used in the diagnostic plots is derived from \nthe intermediate function as follows: \n() () 04\nDD Gt gt g\u03c0\u2206 =\u23a1\u2206 \u2212 \u23a4\u23a3 \u23a6, ....................................... (A-3) \nwhere g0 is the dimensionless loss-volume function at shut-in \n(t = tp or \u2206tD = 0). All derivatives are calculated using a central \ndifference function of pressure and G-function (normalized \nshut-in time). \n \nAfter-Closure Analysis and Flow Regime Identification \nAfter-closure pressure decline analysis requires the \nidentification of fully-developed reservoir pseudolinear and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8896ea-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 9, "chroma:document": "After-closure pressure decline analysis requires the \nidentification of fully-developed reservoir pseudolinear and \npseudoradial transient flow regimes. The flow regimes can be identified by characteristic slopes on a log-log plot of \nobserved falloff pressure minus reservoir pressure, ( p\nw(t) \u2212 pi), \nversus the square of the linear-flow time function (F L2) and the \nsemilog derivative, (X*dY/dX), of the pressure difference \ncurve.5 It is important to note that the guess of reservoir \npressure, pi, used in construction of the flow regime plot \nseverely impacts the slope and magnitude of the pressure \ndifference curve. The pressure derivative, because of the \ndifference function used to generate it, is not affected by the \ninitial guess of reservoir pressure.  \nThe linear-flow time function is defined by: \n()cc\nc L ttforttttF \u2265 =\u22121sin2,\u03c0. ......................... (A-4)  \nThe linear-flow function al so requires an accurate \ndetermination of the time requ ired after shut-in to reach"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88973a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 9, "chroma:document": "The linear-flow function al so requires an accurate \ndetermination of the time requ ired after shut-in to reach \nfracture closure, tc. In the pseudolinear flow period the slope \nof the derivative curve on the log-log plot should be \u00bd. For the \ncorrect estimate of reservoir pore pressure, the pressure \ndifference curve should also have a slope of \u00bd and should be \nexactly twice the magnitude of the derivative. If a stable \npseudolinear flow period is identified then a Cartesian plot of \nobserved pressure during the falloff, pw(t), versus F L should \nyield a straight line with intercept equal to the reservoir pore \npressure, pi, and with a slope of mL.  \n() (),wi L L cptp m F t t\u2212= . ............................................ (A-5)  \nIf a pseudoradial flow period exists, the slope of the \nderivative and correct pressure difference curves on the log-\nlog flow regime plot should both be 1.0 and the two curves"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88979e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 9, "chroma:document": "derivative and correct pressure difference curves on the log-\nlog flow regime plot should both be 1.0 and the two curves \nshould coincide. In the pseudoradial flow period, a Cartesian plot of pressure versus F\nR should also yield a straight line with \nintercept equal to pi and slope of mR.  \n Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/07RMTC/All-07RMTC/SPE-107877-MS/2786245/spe-107877-ms.pdf/1 by University of Houston, Mohamed Gabry on 12 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 10, "chroma:document": "SPE 107877  11 \n() (),wi R R cptp m F t t\u2212= ............................................. (A-6) \n \nIn these equations tc is the time to fracture closure with \ntime zero set as the beginning of fracture extension, pi is the \ninitial reservoir pressure, and mR is the Cartesian slope of the \n\u201ccorrect\u201d straight line. The radial-flow function (F R) is given \nby5 \n() 6.116, 1ln41,2\u2245 =\u239f\u239f\n\u23a0\u239e\n\u239c\u239c\n\u239d\u239b\n\u2212+ =\u03c0\u03c7\u03c7\ncc\nc RtttttF . ......... (A-7)  \nIn the properly identified ps eudoradial flow period the \nreservoir far-field transmissibility can be determined from the \nslope, fracture closure time, and volume injected during the \ntest. \n \n251,000t\nRcQ kh\nmt \u00b5= . ...................................................... (A-8)  \nIn Equation A-8 the permeability, k, is in md, net pay \nthickness, h, is in feet, far-field mobile fluid viscosity,  \u00b5, \uf020in \ncp, tc in minutes, and the volume injected during the test, Qt, is \nin bbls, and the slope, mR, is in psi.  \n \nHorner analysis"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 10, "chroma:document": "cp, tc in minutes, and the volume injected during the test, Qt, is \nin bbls, and the slope, mR, is in psi.  \n \nHorner analysis \nThe conventional Horner  analysis uses a Cartesian plot of \nobserved pressure versus Horner time, ( tp + \u2206t)/\u2206t, with all \ntimes in consistent units. The fracture propagation time is tp \nand the elapsed shut-in time is \u2206t. As shut-in time approaches \ninfinity the Horner time function approaches 1. A straight-line \nextrapolation of the Horner plot to the intercept at a Horner \ntime of 1.0 gives an estimate of reservoir pressure. The slope \nof the correct straight-line extrapolation, mH, can be used to \nestimate reservoir transmissibility: \n \n()\nHmq kh 14406.162=\u00b5.....................................................(A-9) \nThe flow rate in Equation A-9 is assumed to be in barrels"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88988e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 10, "chroma:document": "()\nHmq kh 14406.162=\u00b5.....................................................(A-9) \nThe flow rate in Equation A-9 is assumed to be in barrels \nper minute and is the average rate for the time the fracture was extending. In both Equations A-8 and A-9, the viscosity is the far-field mobile fluid viscosity. The propagation of the \ntransient in pseudoradial flow oc curs at a great distance from \nthe fracture and is not affected by the injected fluid viscosity. \nThe major problem with the Horner analysis is that the \nresults are only valid if the da ta used to extrapolate the \napparent straight line are actually in fully developed \npseudoradial flow. There is no way to determine the validity \nof the Horner analysis or to determine the flow regime within \nthe Horner plot itself. \n \nG-function permeability estimate \nAn empirical function to  approximate formation \npermeability has been derived from numerous numerical \nsimulations of fracture closure. The correlation is based on the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 10, "chroma:document": "permeability has been derived from numerous numerical \nsimulations of fracture closure. The correlation is based on the \nobserved G-function time at fracture closure: 1.960.0086 0.01\n0.038f z\ncp\ntp\nk\nGE rc\u00b5\n\u03c6=\n\u239b\u239e\n\u239c\u239f\u239d\u23a0. ...................................... (A-10) \nThe rate of fluid loss from the fracture before closure is \ndominated by the mobility of the injected fluid instead of the \nfar-field viscosity. The total mobility of the injected fluid during leakoff is dependent on the viscosity of the injected \nfluid at leakoff temperature and the relative permeability to the \nleakoff fluid. The reservoir fluid and its residual saturation in the invaded region will have some effect on the leakoff fluid \nmobility. As a general rule, an assumed injected fluid viscosity \nof 1.0 cp is used to incorp orate the effects of reservoir \ntemperature and relative permeability in the invaded zone. \n Note that the correlation gives permeability and not kh."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 10, "chroma:document": "temperature and relative permeability in the invaded zone. \n Note that the correlation gives permeability and not kh. \nThe time to closure is related to fracture volume versus created area so both the fracture height and length do not \nappear in the equation. The process zone stress, P\nz, is the net \nfracture extension pressure above closure pressure, pc, or \npz = pISIP \u2212 pc. The net extension pressure and Young\u2019s \nModulus provide a relationship between facture volume \n(width) and surface area during pumping. \nThe other parameters in Equation A-10 are defined, except \nthe storage ratio, rp. This parameter represents the amount of \nexcess fluid that must be leaked -off to reach fracture closure \nwhen the fracture geometry deviates from the normally \nassumed constant-height planar  fracture. The storage ratio, rp, \nis the ratio of the area under the G-function semilog derivative \nup until closure divided by the area of the triangle defined by"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88997e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 10, "chroma:document": "is the ratio of the area under the G-function semilog derivative \nup until closure divided by the area of the triangle defined by \nthe straight-line (normal leakoff) tangent to the semilog \nderivative at closure.  For nor mal matrix leakoff and PDL, rp \nis therefore 1.0. For the transverse storage and height \nrecession signature, rp is some value less than 1.0. The \nobserved G-function closure time (G c) is always delayed by \nthe excess fluid volume in th e fracture for either height \nrecession or transverse storage.  Likewise the apparent time to \nclosure used in the after-closur e analysis will be delayed and \nwill cause errors in the reservoir transmissibility estimate. The \nclosure time should be corrected by multiplying by rp for all \npermeability and transmissibility estimates.  \n \n \nAppendix B - Analytical Solutions and the Log-Log \nDiagnostic Graph \n \nLinear and Bilinear Flow Before-Closure \nHagoort9 developed a before-closure analytical solution"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 10, "chroma:document": "Diagnostic Graph \n \nLinear and Bilinear Flow Before-Closure \nHagoort9 developed a before-closure analytical solution \naccounting for both storage and lin ear formation flow. Koning \nand Niko10 write the solution as \n() ( )22\n12DtDf b c DDpt C ee r f c t wD\u03b2\u03c0\u03c0 \u03b2\u2206 \u239b\u239e=\u2206\u2212 \u2212 \u239c\u239f \u2206\u239d\u23a0, ................ (B-1) \nwhere \n( ) () ( )()141.2we we\nDptp t t khptwDqB\u00b5\u2212 +\u2206\u2206=, ..................................... (B-2) \n20.0002637\nD\ntfktt\ncL\u03c6\u00b5\u2206\u2206=, ............................................................ (B-3) Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/07RMTC/All-07RMTC/SPE-107877-MS/2786245/spe-107877-ms.pdf/1 by University of Houston, Mohamed Gabry on 12 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889a14-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 11, "chroma:document": "12  SPE 107877 \n2\nfbcDC\u03b2\u03c0=,  ..................................................................... (B-4) \nand \n225.615 0.8936\n2fbc fbc\nfbcD\ntf tfCC\nC\nch L ch L\u03c0\u03c6 \u03c6==. ............................................ (B-5) \nHere, Cfbc is the before-closure fracture storage constant, \nwhich is defined as8 \n2\n5.615f\nfbc\nfA\nCS=, ................................................................. (B-6) \nwhere Af  is the fracture area (one wing) and  Sf is the fracture \nstiffness. \nHagoort's solution predicts that the before-closure falloff is \na combination of fracture storag e and linear flow. As fracture \nstorage becomes small, CfbcD\u21920, linear flow will dominate the \nbefore-closure pressure falloff. In most \"hard rock\" \nenvironments, CfbcD is small, and for a fracture-\ninjection/falloff sequence with \u2206t >> te and long closure times,  \n() ( )we weptp t t t\u2212+ \u2206 \u221d , ...................................................... (B-7) \nwhere t = te + \u2206t and pw(te) is the instantaneous shut-in"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889a64-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 11, "chroma:document": "() ( )we weptp t t t\u2212+ \u2206 \u221d , ...................................................... (B-7) \nwhere t = te + \u2206t and pw(te) is the instantaneous shut-in \npressure. Define a fracture-pressure difference as \n() ( )w f we wep pt pt t \u2206= \u2212 + \u2206 , ................................................... (B-8) \nand a log-log graph of \u2206pwf vs. t will exhibit a \u00bd slope during \nlinear flow before closure. An  analytical before-closure \nbilinear flow solution accounti ng for fracture tip extension \nduring shut-in does not exist, but field data suggest that during \nbefore-closure bilinear flow \n14()wfp t \u2206\u221d \u2206 , .................................................................... (B-9) \nand a log-log graph of \u2206pwf vs. t will exhibit a \u00bc slope during \nbilinear flow before closure. \n \nPseudoradial, Pseudolinear, and Bilinear Flow After-\nClosure \nCraig & Blasingame8 developed an analytical solution for a \nfracture-injection/falloff sequ ence with a propagating and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889ab4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 11, "chroma:document": "Closure \nCraig & Blasingame8 developed an analytical solution for a \nfracture-injection/falloff sequ ence with a propagating and \nclosing hydraulic fracture, and they derived the \"complete\" \nafter-closure impulse solutions accounting for fracture storage. \nThe after-closure impulse solution for pseudoradial flow is written as  \n() 0141.2(24) 1(0) ( ) ()2ti we i\neQp C p p pt t p wsD ackh t t\u00b5+\u2212 +\u2206 \u2212 =+\u2206. ..... (B-10) \nFor after-closure pseudolinear flow, \n0141.2(24) 0.0002637 1()(0) ( ) 2t\nwe ii fQ\npt t ppC p p hL wsD ac\u03c0 \u239b\u239e+\u2206 \u2212 = \u239c\u239f+\u2212\u239d\u23a0\n121\nteckt t\u00b5\n\u03c6\u239b\u239e\u00d7\u239c\u239f+\u2206 \u239d\u23a0, ........................................... (B-11) \nand for after-closure bilinear flow, \n1434\n0141.2(24)(0.6125)(0.0002637)()()t\nwe i\ni ffQ\npt t ppp C kw ac\u00b5\u239b\u239e+\u2206 \u2212 = \u239c\u239f+\u2212\u239d\u23a0  14 3411\nteck t t\u00b5\u239b\u239e \u239b \u239e\u00d7\u239c\u239f \u239c \u239f+\u2206 \u239d\u23a0 \u239d \u23a0. ..................................... (B-12) \nFor convenience, define a constant pseudoradial flow term as \n() 0141.2(24)(0) ( )\n2ti prQp C p p C wsD ackh\u00b5+\u2212 =. ........................... (B-13)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889afa-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 11, "chroma:document": "() 0141.2(24)(0) ( )\n2ti prQp C p p C wsD ackh\u00b5+\u2212 =. ........................... (B-13) \nFor pseudolinear flow, a constant term is defined as \n12\n0141.2(24) 0.0002637 1\n(0) ( ) 2t\nplt i fQ\nCck pC p p hL wsD ac\u00b5 \u03c0\n\u03c6\u239b\u239e \u239b\u239e= \u239c\u239f \u239c\u239f+\u2212 \u239d\u23a0 \u239d\u23a0. (B-14) \nSimilarly, for bilinear flow a constant term is written as \n 14 1434\n01 141.2(24)(0.6125)(0.0002637)\n()t\nblt i ffQ\nCck pp C kw ac\u00b5\u00b5\u239b\u239e \u239b\u239e= \u239c\u239f \u239c\u239f+\u2212 \u239d\u23a0 \u239d\u23a0. .. (B-15) \nWith the new definition, and defining a reservoir-pressure \ndifference, \u2206pw = pw(t) \u2212 pi, the pseudoradial-flow impulse \nsolution can be written as \n1wp rpC t\u2212\u2206= .  ................................................................... (B-16) \nSimilarly, the linear-flow impulse solution can be written as \n1/2wp lpC t\u2212\u2206= , .................................................................. (B-17) \nand the bilinear-flow impulse solution can be written as \n3/4wb lpC t\u2212\u2206= . ................................................................... (B-18)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889b4a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 11, "chroma:document": "3/4wb lpC t\u2212\u2206= . ................................................................... (B-18) \nThe derivatives with respect to t are written for after-closure \npseudoradial flow as,  \n2\n()wprpCtt\u2212 \u2202\u2206\u2212=\u2202, ................................................................ (B-19) \nfor after-closure pseudolinear flow as, \n3/2\n() 2pl wC ptt\u2212 \u2202\u2206\u2212=\u2202, ............................................................. (B-20) \nand for after-closure bilinear flow as, \n7/4 3\n() 4wb lpCtt\u2212 \u2202\u2206\u2212=\u2202. ............................................................ (B-21) \nThe semilog derivatives and the impulse derivatives11 are \ncalculated by multiplying the after-closure derivatives by t and \nt2, respectively. Table B-1 show s the derivative terms for each \nafter-closure flow regime. \n \nLog-Log Diagnostic Graph \nBefore-closure linear or bilinear flow are identified by the \nrelationship between the fracture-pressure difference, \n\u2206pwf, and total time, t, but the after-closure flow regimes are"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 11, "chroma:document": "relationship between the fracture-pressure difference, \n\u2206pwf, and total time, t, but the after-closure flow regimes are \nidentified by the relationship be tween the reservoir-pressure \ndifference, \u2206pw, and t, which requires knowing the initial \nreservoir pressure, pi. However, by noting that \nwf wp p\ntt\u2202\u2206 \u2202\u2206=\u2212\u2202 \u2202, ................................................................ (B-22) \na log-log diagnostic graph can be prepared that is independent of initial reservoir pressure but can be used to identify before- \nand after-closure flow regimes. Table B-2 shows the \ncharacteristic slopes of each flow regime for log-log graphs of \n\u2206p\nwf vs. t, wfpt\u2202\u2206\u2202 vs. t, wf tp t\u2202\u2206 \u2202 vs. t, and Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/07RMTC/All-07RMTC/SPE-107877-MS/2786245/spe-107877-ms.pdf/1 by University of Houston, Mohamed Gabry on 12 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889bea-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 12, "chroma:document": "SPE 107877  13 \n2wf tp t\u2202\u2206 \u2202 vs. t .  \nIn gas reservoirs, log-log diagnostic graphs can be prepared by \nplotting \u2206pawf vs. ta, awf apt\u2202\u2206 \u2202 vs. ta, aa w fatp t\u2202\u2206 \u2202 vs. ta, \nand 2aa w f atp t\u2202\u2206 \u2202 vs. ta where adjusted pseudopressure is \ndefined as \n0pzp d ppap zi\u00b5\n\u00b5\u2320\n\u23ae\n\u23ae\u2321\u239b\u239e=\u239c\u239f\u239d\u23a0, ........................................................... (B-23) \nand adjusted pseudotime is defined as ()\n0tdttcat ict\u00b5\u00b5\u2320\n\u23ae\n\u23ae\n\u2321=. .............................................................. (B-24) \nSince adjusted pseudopressure is a function of initial \nreservoir pressure, and if initial reservoir pressure is unknown, \nit's often helpful to complete the analysis in terms of pressure \nand time to obtain a first estimate of initial reservoir pressure before refining the estimate using diagnostic and interpretive \ngraphs plotted in terms of adjusted pseudovariables. \n \n \n  \n \n \nTable B-1. After-closure impulse solutions and derivatives. \nFlow Regime Impulse Solution Derivative Semilog \nDerivative Impulse"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 12, "chroma:document": "Table B-1. After-closure impulse solutions and derivatives. \nFlow Regime Impulse Solution Derivative Semilog \nDerivative Impulse \nDerivative \nBilinear 3/4wb lpC t\u2212\u2206=  7/4 3\n4wb lpCtt\u2212 \u2202\u2206\u2212=\u2202 3/4 3\n4wb lpCttt\u2212 \u2202\u2206\u2212=\u2202 21 / 4 3\n4wb lpCttt\u2202\u2206\u2212=\u2202 \nPseudolinear 1/2wp lpC t\u2212\u2206=  3/2\n2pl wC ptt\u2212 \u2202\u2206\u2212=\u2202 1/2\n2pl wC pttt\u2212 \u2202\u2206\u2212=\u2202 21 / 2\n2pl wC pttt\u2202\u2206\u2212=\u2202 \nPseudoradial 1wp rpC t\u2212\u2206=  2 wprpCtt\u2212 \u2202\u2206\u2212=\u2202 1 wprptC tt\u2212 \u2202\u2206\u2212=\u2202 2 wprptCt\u2202\u2206\u2212=\u2202 \n \n \nTable B-2. Log-log graph characteristic slopes. \nBefore Closure After Closure Log-Log Graph \nBilinear Linear Bilinear Pseudolinear Pseudoradial \n vs. \n vs. wf\nawf apt\npt\u2206\n\u2206 1/4 1/2 \u23af \u23af \u23af \n vs. \n vs. wf\nawf a apt t\npt t\u2202\u2206 \u2202\n\u2202\u2206 \u2202 \u22123/4 \u22121/2 \u22127/4 \u22123/2 \u22122 \n vs. \n vs. wf\naa w fa atp t t\ntp t t\u2202\u2206 \u2202\n\u2202\u2206 \u2202 1/4 1/2 \u22123/4 \u22121/2 \u22121 \n2\n2 vs. \n vs. wf\naa w fa atp t t\ntp t t\u2202\u2206 \u2202\n\u2202\u2206 \u2202 5/4 3/2 1/4 1/2 0 \n  Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/07RMTC/All-07RMTC/SPE-107877-MS/2786245/spe-107877-ms.pdf/1 by University of Houston, Mohamed Gabry on 12 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889cb2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 0, "chroma:document": "CHAPTER 8\nFracture diagnostic testing\nAli Rezaei1, Mohamed Y. Soliman2and Birol Dindoruk2\n1Midstream Production Systems, Houston, TX, United States\n2Cullen College of Engineering, Petroleum Engineering, University of Houston, Houston, TX, United States\n8.1 Overview\nThis chapter summarizes several conventional and recent methods to analyze hydraulic\nfracture testing in vertical and horizontal wells. These tests are conducted for two pri-\nmary purposes: (1) to understand the reservoir properties such as minimum horizontal\nstress and permeability; (2) and to optimize the hydraulic fracturing parameters.\nFracture diagnostic techniques are critical preexecution steps toward optimum fracture\ndesign. Using these techniques, one can estimate key parameters such as the target\nzone stress regime, fracture confinement height, number of stages, treatment size,\nproppant type and amount, and optimum well direction.\n8.2 Testing types"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889d02-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 0, "chroma:document": "proppant type and amount, and optimum well direction.\n8.2 Testing types\nIn general, three different fracture diagnostics groups exist, namely direct far-field\ntechniques, direct near-wellbore techniques, and indirect fracture diagnostics ( Cipolla\n& Wright 2000 ). The direct far-field techniques are suited to give the big picture\nabout fracture growth and are conducted in a separate well. The two commonly used\ntechniques for this type of fracture diagnostics are tiltmeter fracture mapping and\nmicroseismic fracture mapping. On the contrary, the second group of fracture diagnos-\ntics techniques is implemented in the same well and gives information about near-\nwellbore fracture parameters such as height and width and proppant placement.\nFinally, the most commonly used fracture diagnostics group is indirect fracture diag-\nnostics. The techniques used in this group can provide estimates about fracture con-\nductivity, dimension, and stress. This group includes fracture modeling, pressure"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 0, "chroma:document": "ductivity, dimension, and stress. This group includes fracture modeling, pressure\ntransient testing, and production data analysis ( Cipolla & Wright 2000 ). The pressure\ntransient testing (sometimes accompanied by rate transient testing) includes step\nrate test, pump in-shut in, and pump in/flow back ( Soliman, Craig, Bartko, Rahim, &\nAdams, 2005 ). These tests are most widely used because of the abundance in the\nrecorded data. Pump-in shut-in tests may be referred to as MiniFrac, or diagnostic\nfracture injection test (DFIT). There are, however, some differences between the two\ntests. Mini-Frac tests were conducted using the fluid to be used in the main fracturing\n217Unconventional Shale Gas Development\nDOI: https://doi.org/10.1016/B978-0-323-90185-7.00016-9r2022 Elsevier Inc.\nAll rights reserved."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889da2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 1, "chroma:document": "treatment, except no proppant was added. The goal of the test was to find the leak-off\ncoefficient and efficiency of the treatment. The treatment design was consequently\nadjusted if necessary. DFIT, on the other ha nd, is conducted to determine reservoir and\nfracture properties. Other approaches such as data-based analysis and signal processing\ntechniques such as wavelet tra nsform have been developed to p erform fracture diagnostics\nanalysis in recent years. Moreover, other te chniques such as step-rates techniques have\nbeen developed. Those step rate techniques will be briefly discussed. However, the bulk\nof the chapter will be devoted to pump-in shut-in test technology.\n8.3 Step-rate test\nStep-rate test (SRT) is commonly used for estimating the pressure at which the hydrau-\nlic fracture starts to propagate (i.e., fracture propagation pressure or FPP). FPP is the\npressure at which a fracture will initiate in an unfractured well, or the existing fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889df2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 1, "chroma:document": "pressure at which a fracture will initiate in an unfractured well, or the existing fracture\nin a fractured well starts to propagate. The test is primarily used for identifying the\nmaximum safe injection pressure without fracturing the reservoir rock ( Singh, Agarwal,\n& Krase, 1987 ). Although the SRT has been practiced in the industry for many years,\nthe first publication on the subject seems to be by Felsenthal (1974) . There are two\ntypes of SRT, step-up and step-down tests. In the following, a review of the two types\nis discussed. Also, it has been reported by Savitski and Dudley (2011) that the step rate\ntest is not efficient in low permeability reservoirs for identifying the closure pressure.\n8.3.1 Step-up test\nThe step-up test is performed on a well with preexisting hydraulic fracture and is used\nto estimate the fracture opening pressure. Injection starts at a low rate that is not suffi-\ncient to reopen the existing fracture. The injection is increased in a stepwise fashion"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889e38-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 1, "chroma:document": "cient to reopen the existing fracture. The injection is increased in a stepwise fashion\nuntil the fracture opens. At each stage, the injection continues until the pressure stabi-\nlizes. It is expected that a smaller change in pressure occurs after the fracture reopens,\nresulting from the higher injectivity. Plotting the stabilized pressure versus rate yields the\npoint of change in slope, indicating the reopening pressure as illustrated in Fig. 8.1 .T h e\nfigure shows that as the fluid loss decreases (lower formation permeability), the difference\nbetween the before closure (BC) and after closure (AC) slopes get smaller, resulting in a\nharder fracture opening pressure identification. More discussions and field examples on\nthe step-up test may be found in Tan, McGowen, Lee, and Soliman (1988) .\n8.3.2 Step-down test\nIn contrary to the step up test, the step-down test is also performed by injection at\na high enough rate to propagate the fracture. As the injection rate is reduced, how-"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889e88-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 1, "chroma:document": "a high enough rate to propagate the fracture. As the injection rate is reduced, how-\never, it stays above the fracture opening pressure. Step down test was proposed by218 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889ed8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 2, "chroma:document": "Cleary et al. (1993) . The goal of the test is to estimate the friction- and perforation-\ndominated pressure during injection. It is hypothesized that the net pressure will be a\nfunction of the rate as expressed below. The exponent B is a strong indication of the\nstatus of the fracture, as given in Tables 8.1, 8.2, 8.3, 8.4 and 8.5 . Depending on the\nresults of the test, remedial action may be taken.\n\u0394pnet5A3qB\nlog\u0394pnet5logA1Blogq\nwhere\u0394Pnet,q, and Aand Bare net pressure, injection rate, and test constants,\nrespectively.\nHyden and Stegent (1996) presented field cases using the step-down test for find-\ning the near-wellbore restrictions.\nFigure 8.1 A typical pressure-rate cross plot of the step-up test. Courtesy Advantek.\nTable 8.1 Indication of potential problems associated with slope Bin the step-down test.\nSlope, B Potential problem\n0.25 single fracture exists\n0.5/C01.0 Presence of a tortuous path\n2.0 Insufficient perforation219 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889f28-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 3, "chroma:document": "8.4 Pump in/shut-in test\nThe most commonly used pump-in/shut-in test is the fracture injection test. Fracture\ninjection fall-off test, also known as DFIT and minifrac test, has been a standardmethod to identify various formation properties such as closure pressure ( BminimumTable 8.2 A summary of the results for field example 1 and its comparison with G-function.\nG-function EDP\nClosure time (min) 27.47 27.95\nClosure pressure (psi) 5822 5790Closure point (#) 93 101Sampling rate 1 second\nTotal number of data points B1:2310\n3\nTable 8.3 A summary of the results for field example 2 and its comparison with G-function.\nG-function EDP\nClosure time (s) 822 761\nClosure pressure (psi) 26,756 28,756Closure point (#) 98 37Sampling rate 1 sTotal number of data points B4:6310\n3\nTable 8.4 A summary of the results for field example 3 and its comparison with G-function.\nG-function EDP\nClosure time (min) 13.6 13.5"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889f6e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 3, "chroma:document": "3\nTable 8.4 A summary of the results for field example 3 and its comparison with G-function.\nG-function EDP\nClosure time (min) 13.6 13.5\nClosure pressure (psi) 2656 2702Closure point (#) 101 93Sampling rate 1 sTotal number of data points B10310\n3\nTable 8.5 A summary of the results for field example 4 and its comparison with G-function.\nG-function EDP\nOur analysis Closure time (min) 45 46\nClosure pressure (psi) 13,539 13,521Closure point (#) 2509 2600\nSampling rate 1 s\nTotal number of data points 370 310\n3220 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889fbe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 4, "chroma:document": "horizontal stress), formation permeability, and the leak-off type in the last 30 years.\nClosure pressure identification is critically important in this test because of two main\nreasons. First, it is typically considered as the minimum horizontal stress and affects\nthe subsequent hydraulic fracturing design as well as analysis of real-time fracture prop-\nagation. Second, closure pressure defines two separate classes of analysis, namely BC\nanalysis and AC analysis ( Soliman et al., 2005; Soliman, Miranda, & Wang, 2010 ).\nDFIT involves injecting water without proppant at a sufficient rate and pressure to\ncreate a fracture into a formation, followed by a shut-in period that may last for hours\nor even days depending on reservoir permeability. After starting the shut-in period,\nthe pressure will begin to fall-off due to the fracturing fluid leak-off that causes the\nfracture to close gradually, resulting from the far-field compressive stress. The closure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a00e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 4, "chroma:document": "fracture to close gradually, resulting from the far-field compressive stress. The closure\npressure may be determined by analyzing the decline of the recorded pressure during\nthe fall-off period.\nFig. 8.2 shows the recorded wellbore pressure during a typical minifrac test. Two\nperiods, BC (fracture dominated) and AC (reservoir dominated) are separated by a\nvertical red dashed line.\n8.4.1 Before closure analysis\nThe methods to analyze the recorded pressure fall-off data before the fracture closure\nmoment are referred to BC analysis. The main parameters that are estimated using\nthese techniques are closure pressure, leak-off coefficient, and instantaneous shut-in\npressure. The net pressure at the closure is typically considered as minimum horizontal\nstress. The most commonly used method in this category is the DFIT. Various models\nhave been proposed to analyze DFIT data and determine the fracture closure pressure."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a05e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 4, "chroma:document": "have been proposed to analyze DFIT data and determine the fracture closure pressure.\nFigure 8.2 A Schematic of the DFIT test. After Pokalai et al. (2016) .221 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a0ae-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 5, "chroma:document": "Nolte (1979) introduced this technology. Further modifications of this technology\nwere introduced by further authors (e.g., Barree & Mukherjee 1996 ;Craig &\nBlasingame 2006 ;Marongiu-Porcu, Ehlig-Economides, & Economides, 2011 ;\nMohamed, Azmy, Sayed, Marongiu-Porcu, & Economides, 2011 ;Soliman, 1986 ).\nHowever, there is a significant disagreement in the calculated closure pressure from\nthese models in many cases. The primary source of error in the methods used for ana-\nlyzing DFIT is their underlying assumptions. Therefore, analyzing DFIT data using a\ndifferent methodology independent of premises such as fracture geometry is essential.\n8.4.1.1 G-function technique\nThe first and most widely used method for analyzing BC pressure fall-off was initially\npresented in Nolte \u2019s pioneering work ( Nolte, 1979, 1986 ). The technique, also\nknown as G-function, expanded by Barree and Mukherjee (1996) , is a tool for deter-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a0f4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 5, "chroma:document": "known as G-function, expanded by Barree and Mukherjee (1996) , is a tool for deter-\nmining closure pressure, leak-off coefficient, and fluid efficiency. This technique \u2019s cen-\ntral assumptions are that the leak-off is not pressure-dependent and fracture stiffness is\nconstant while the fracture is closing. Several modifications to the Nolte G-function\ntechnique have been proposed since then by addressing some of the limitations in the\nassumptions ( Castillo, 1987; Barree, Barree, & Craig, 2007; Barree & Mukherjee 1996;\nMukherjee, Larkin, & Kordziel, 1991; Barree et al., 2015 ). The primary purpose of\nthese modifications was to make the method more applicable to the new cases that\nwere encountered.\nMcClure, Blyton, Jung, and Sharma (2014) and McClure, Jung, Cramer, and\nSharma (2016) proposed a technique called the fracture compliance method. In this\ntechnique, the central assumption is that the created fracture does not reach a state of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a162-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 5, "chroma:document": "technique, the central assumption is that the created fracture does not reach a state of\ncomplete closure. Instead, the fracture retains a finite aperture after asperities come\ninto contact and result in an infinite fracture conductivity. Although this assumption\nmay be valid in some cases where the aperture of the created fracture in ultra-tight\nformations stays at \u03bcdrange, it gives contradictory results to the widely used tangent\nmethods in cases where reservoir permeability is less than one \u03bcD. Also, for such short\nfractures that are generated in DFIT, minimum to no asperities mismatch is more\nprobable, which contradicts the model \u2019s assumptions. McClure et al. (2019) further\nextended their method and recommended steps to analyze DFIT data from low per-\nmeability formations ranging from tens of nDto tens of \u03bcD.Wang and Sharma\n(2017) presented a variable compliance method based on averaging the closure point \u2019s"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a252-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 5, "chroma:document": "(2017) presented a variable compliance method based on averaging the closure point \u2019s\nG-time. Similar to the technique presented by McClure et al. (2014) andWang and\nSharma (2017) concluded that the G-function method underestimates the closure stress.\nIn another model, Liu and Ehlig-Economides (2015) and Liu, Ehlig-Economides, and\nSun (2016 ) extended the model by Marongiu-Porcu, Retnanto, Economides, and Ehlig-\nEconomides (2014) to account for wellbore storage, tip extension, and pressure dependant\nleak-off, and multiple closures.222 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a2ca-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 6, "chroma:document": "The definition of G-function is given below:\nG\u0394tD\u00f0\u00de54\n\u03c0g\u0394tD\u00f0\u00de2g0 \u00f0\u00de\ng\u0394tD\u00f0\u00de54\n311\u0394tD \u00f0\u00de1:52\u0394t1:5\nD/C0/C1\n;for\u03b151\ng\u0394tD\u00f0\u00de511\u0394tD \u00f0\u00de sin2111\u0394tD \u00f0\u00de1:5/C0/C1\n1\u0394t0:5\nD;for\u03b150:5\n\u0394tD5t2ti\nti\ng054\n3;for\u03b151\ng05\u03c0\n2;for\u03b150:5\nIn the above equations, \u03b1is a constant that governs the power-law propagation of\nthe fracture:\nA\nAe5t\nte/C18/C19\u03b1\n\u03b151 and 0 :5 in the above equations refer to low and high leak-off regimes,\nrespectively. A typical G-function plot is shown in Fig. 8.3 . In the plot, a straight tan-\ngent line that passes through the origin is fitted on the Gdp\ndGversus Gline. The closure\npoint is picked where the tangent line deviates from the plot. In order to read the clo-\nsure pressure, one needs to connect the deviation point to the pressure line (red line\nin the figure) using a vertical line (dashed line in the figure).\n8.4.1.2 Log /C0log analysis\nAnother widely used technique for DFIT is known as the log /C0log method\n(Marongiu-Porcu et al., 2011, 2014; Mayerhofer & Economides 1997; Mohamed"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a374-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 6, "chroma:document": "Another widely used technique for DFIT is known as the log /C0log method\n(Marongiu-Porcu et al., 2011, 2014; Mayerhofer & Economides 1997; Mohamed\net al., 2011; Valk\u00f3 & Economides, 1995 ). In this method, the closure time is deter-\nmined using the log /C0log diagnostic plot, which is used conventionally to analyze tran-\nsient well tests and analyze fall-off data. A typical log /C0log analysis of the pressure fall-\noff data is shown in Fig. 8.4 . In the figure, the dashed curve (pink) is the semilog\nderivative with respect to shut-in time. The slope of the derivative plot before the clo-\nsure is an identification of the flow regime before fracture closure (1/2 here indicated223 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a3ec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 7, "chroma:document": "Figure 8.3 A normal leakoff G-function plot. ( Barree et al., 2007 )After Barree, R. D., Barree, V. L., &\nCraig, D. (2007). Holistic fracture diagnostics. In Rocky mountain oil & gas technology symposium .\nSociety of Petroleum Engineers.\nFigure 8.4 A typical log /C0log analysis of pressure fall-off data. After Barree, R. D., Barree, V. L., &\nCraig, D. (2007). Holistic fracture diagnostics. In Rocky mountain oil & gas technology symposium .\nSociety of Petroleum Engineers.224 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a464-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 8, "chroma:document": "linear flow from fracture). In this technique, the separation of the two parallel lines is\nan identification of the fracture closure.\n8.4.1.3 Square root time method\nIn this technique, the fracture closure pressure is identified by the first peak in the\npressure plotted versus the square root of time. Fig. 8.5 shows a typical square root\ntime plot. The primary curve in this plot should form a straight line during the frac-\nture closure (similar to G-Function analysis). Unlike the G-Function analysis, where\nthe deviation from the straight line was indicating the fracture closure, in this analysis,\nthe peak of the first derivative of the pressure versus sqrt( t) indicated the fracture clo-\nsure point (pink dashed line in the figure).\n8.4.1.4 Modified technique to determine abnormalities\nUnal et al. (2019c) proposed a signal processing approach for analyzing DFIT based on\nthe signal processing approach. In the proposed technique, the noise of the recorded"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a4d2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 8, "chroma:document": "the signal processing approach. In the proposed technique, the noise of the recorded\npressure using wavelet transform is analyzed. The advantage of this method is that it\ndoes not depend on any assumptions of the currently available models and only relies\non the recorded pressure.\nFigure 8.5 An example of a normal Square Root time plot. After Barree, R. D., Barree, V. L., & Craig,\nD. (2007). Holistic fracture diagnostics. In Rocky mountain oil & gas technology symposium . Society\nof Petroleum Engineers.225 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a54a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 9, "chroma:document": "Other techniques in this area include the one by Mohamed et al. (2011) and\nMarongiu-Porcu et al. (2011) , who suggested a global approach for a combined before\nand AC analysis. In these approaches, the authors used piece-wise functions. Using\nthese approach, the BC analysis can be written as:\np-\nwD512e2ted1tcD \u00f0\u00de s/C0/C1\n3q-\nD\nSK00:5OS/C2/C3\nFor the AC analysis, an enlarged equivalent wellbore radius was used. Also, the\nfluid flow in the reservoir was given as:\np-\nwD5K0\u00bdrwdOS/C138\nS1:5K1\u00f0rwD\ufb03\ufb03\ufb03\nSp\n\u00de\nThe above equation needs to be inverted numerically with the Stehfest (1970)\nalgorithm. The limitation of this technique is that it can only be used for high perme-\nability formations with short fracture.\n8.4.1.5 Transient before closure analysis\nTransient flow regimes can occur during fall off test. Cinco-Ley and Samaniego\n(1981) graphically presented the major flow regimes around a fractured well. Other\ntechniques than the conventional methods discussed above have also been developed"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a5b8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 9, "chroma:document": "techniques than the conventional methods discussed above have also been developed\nin recent years. In a similar way to the traditional G-function analysis, Siddiqui,\nSoliman, House, and Ibragimov (2016) developed a new analytical solution that could\nbe used to determine the closure pressure. In contrast to the conventional G-function\nmethod, which models the fluid leak-off into the formation based on Carter \u2019s equa-\ntion ( Howard & Fast 1957; Hubbert & Willis 1972 ), partial differential equations to\ndescribe the linear leak-off were used in the model. This method requires previous\nknowledge of fluid mobility and fracture compliance.\n8.4.2 After closure analysis\nAC analysis is referred to those analyses that are performed on the pressure fall of data\nafter the closure point (i.e., when the fracture faces are closed). The conventional well\ntest analysis can be applied with a high degree of accuracy (Soliman & Dusterhuft,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a630-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 9, "chroma:document": "test analysis can be applied with a high degree of accuracy (Soliman & Dusterhuft,\n2016). This is because that the created fracture during the pumping period of most of\nthe fracturing tests is small enough that ignoring it does not affect the results tremen-\ndously. However, there is one fundamental difference between the developed solu-\ntions of the traditional well testing approaches and AC analysis. The difference is that\nthe solutions of conventional well testing are derived from the constant volume, while\nthe solution of AC analysis are derived from impulse solution. In cases where the226 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a69e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 10, "chroma:document": "pressure fall-off is recorded long enough to reach radial flow, one can obtain reservoir\npressure and permeability using the AC analysis.\nSoliman et al. (2004, 2005) presented a technique for AC analysis to distinguish the\ndominant flow regime AC. The method could be used to analyze the data in each\nregion and determine the reservoir pressure and permeability. A summary of the tech-\nnique in the case of bilinear flow is given in the following (Soliman & Dusterhuft,\n2016):\n1.A log /C0log plot of logtinj\n\u0394t/C0/C1\nversus log/C0\nt@pf0\n@t/C1\nneeds to be plotted. Here tinj,\u0394t, and\npfoare injection time, time since shut-in, and bottom hole fall off pressure.\n2.The data will follow a straight line that indicates the flow regime.\n3.The intercept of the log tinj1\u0394t/C0/C1nversus ( pfo2pi\u00de, with n being the slope from\nthe previous step, on a cartesian plot indicates the reservoir pressure.\n4.Create a logarithmic plot oftinj\n\u0394t/C0/C1\nversus \u00f0pfo2pi\u00de."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a716-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 10, "chroma:document": "the previous step, on a cartesian plot indicates the reservoir pressure.\n4.Create a logarithmic plot oftinj\n\u0394t/C0/C1\nversus \u00f0pfo2pi\u00de.\n5.Assuming the bilinear flow, the intercept will be a function of permeability and\nreservoir conductivity.\nbr5264 :6V\nh\u03bc\u00f0\u00de0:75 1\n\u03c6ctk/C18/C190:251\nOkfwf !\nAlso, the end of bilinear flow is a function of both fracture conductivity and\npermeability as the following:\ntDebf54:55\nCfD22:5/C18/C1924\nCfD5kfw\nkLf\nCombining these equations by assuming that the fracture conductivity is low,\nthe formation permeability can be calculated as:\nk5264 :6V\nh3\u03bc\nbr1\n2:637tef/C0/C10:25\nThe fluid properties used in these equations are reservoir fluid properties.\n6.If the shut in time gets sufficiently large, the pseudo-radial flow will probably be\nobserved. For this regime to happen, the dimensionless time from the following\nequation should be greater than 1:\nt$3:7923103\u03c6\u03bcCtL2\nf\nkh\n7.A similar approach can be followed for the linear flow.227 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a78e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 11, "chroma:document": "8.5 Pump-in/flow-back test (micro-frac)\nThe conventional DFIT has several limitations. For example, one needs to wait so\nlong (days) for the closure to happen. Also, the test gives inaccurate results in the case\nof the temperature difference between the test fluid and rocks or when the reservoirs\nare naturally fractured. Pump-in flow-back test is designed to address some of the lim-\nitations of the conventional pump-in shut-in approaches. During the test, usually, less\nthan four barrels of fluids are injected into the well (Soliman & Dusterhoft, 2016). A\nfollow back starts at the end of the test (rather than the shut-in). During the test,\nthe flow back period is analyzed to find the closure pressure. A typical recorded pres-\nsure for the flow back test is shown in Fig. 8.6 . As can be seen, the pressure plot in\nthe flow back region is concave with two almost constant slopes before and after\npoints A and B. The slope of the curve above point A represents the stiffness of the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a806-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 11, "chroma:document": "points A and B. The slope of the curve above point A represents the stiffness of the\nsystem, and the slope below point C represents the stiffness of the fracture alone\n(Savitski & Dudley 2011 ). Note that the return rate is very low and should stay con-\nstant during the flow back period, as shown in Fig. 8.6B . Different interpretations\nhave been proposed for picking up the closure pressure at points A, B, or C in this\ntest (Nolte,1990; Plahn et al., 1997; Soliman & Daneshy, 1991 ).\nSavitski and Dudley (2011) showed that in low permeability formations, the con-\ntinuous flow back at a constant rate, as shown in Fig. 8.6A , does not result in an\ninterpretable trend. Hence, an incremental flow back test with pressure stabilization\nprotocol was suggested. In the suggested approach, instead of a continuous fluid flow,\nrequired by the conventional pump in flow back test, a small incremental volumetric\nflow back followed by the pressure stabilization is used. The pressure stabilization"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a874-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 11, "chroma:document": "flow back followed by the pressure stabilization is used. The pressure stabilization\nallows for the reaching an equilibrium condition between the wellbore and fracture\npressures. The advantage of this approach is that it removes the uncertainty about the\nFigure 8.6 Examples of recorded pressure during the pump-in flow-back test. (A) Schematic of the\npressure (B) a field case reported by Savitski and Dudley (2011) .228 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a8ec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 12, "chroma:document": "transient flow between the fracture and wellbore and results in a quasiequilibrium situ-\nation. An example of a field case from Savitski and Dudley (2011) using this approach\nis shown in Fig. 8.7 .\n8.6 New analysis technique\nSoliman and Kabir (2012) andSoliman and Gamadi (2012) revisited applications of\nsome of the mentioned techniques to unconventional and tight reservoirs, respectively.\nThey concluded that, in general, these methods are not practical for these reservoirs.\nTo address these limitations, new approaches have emerged in recent years. These\ntechniques are mainly based on the recorded data from the tests and have limited\nassumptions. They include signal processing approaches and data analysis approaches.\nIn the following, we review the signal processing approach in detail.\n8.6.1 Wavelet analysis\nSignal processing is a branch of electrical engineering that models and analyzes differ-\nent data types and their representations of physical events. Traditionally, signal proces-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88a98c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 12, "chroma:document": "ent data types and their representations of physical events. Traditionally, signal proces-\nsing involves using filters to separate the signal of interest or even remove the\nunwanted frequency. The main objective of signal processing is to extract relevant\ninformation from a signal by transforming it. Fourier and wavelet transforms\nFigure 8.7 The quasiequilibrium pump in flow back, suggested by Savitski and Dudley (2011) .229 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88aa04-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 13, "chroma:document": "are conventional techniques for signal analysis. Fourier transform is applied for\nstationary signals, signals whose properties do not evolve in time (e.g., sinewaves).\nFourier transform is not recommended for nonstationary signals because any abrupt\nchange in time would spread out the signal over the whole frequency domain ( Rioul\n& Vetterli, 1991 ). Also, the events cannot be located in time using the Fourier\ntransform.\nWavelet transform is of interest for the analysis of nonstationary signals. Wavelet is\na small wave that grows and decays primarily in a limited time period; on the contrary,\nFourier transform decomposes signal into sin waves, which keep on oscillating up and\ndown to infinity. The advantage of wavelet transform over Fourier transform in DFIT\nis the one can identify the events and their frequencies in time using this technique\n(Unal et al., 2019a, 2019b ). Wavelet is a function characterizing by the following\nproperties ( Percival & Walden, 2000 )"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88aa5e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 13, "chroma:document": "(Unal et al., 2019a, 2019b ). Wavelet is a function characterizing by the following\nproperties ( Percival & Walden, 2000 )\n\u0081The integral of real-valued function \u03c8is equal to zero:\n\u00f01N\n2N\u03c8u\u00f0\u00dedu50: \u00f08:1\u00de\n\u0081The square of \u03c8integrates to unity:\n\u00f01N\n2N\u03c82u\u00f0\u00dedu51: \u00f08:2\u00de\nBased on orthogonality, there are two types of wavelet transforms, continuous and\ndiscrete wavelet transform.\n1.Continuous Wavelet Transform (CWT): This transform can be used to obtain a simul-\ntaneous time-frequency analysis of a signal. CWT is best suited for time-frequency\nanalysis as these wavelets do not have negative frequency components. Examples\nof analytical wavelets are: Morse wavelet, Bump wavelet, and analytical Morlet\nwavelet. Continuous wavelet is now widely used in various disciplines, from x-ray\nimages in the medical field to well-logging in geophysics.\n2.Discrete Wavelet Transform (DWT): It is an essential tool needed for studying"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88aaae-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 13, "chroma:document": "images in the medical field to well-logging in geophysics.\n2.Discrete Wavelet Transform (DWT): It is an essential tool needed for studying\ntime series via wavelet by decomposing the signal into a mutually orthogonal set of\nwavelets. The critical usage for discrete wavelet analysis is de-noising and compres-\nsion of signals and images. DWT has numerous applications in science, engineer-\ning, mathematics, and computer science. For instance, DWT improved the analysis\nof dynamic fracture behavior in unconventional reservoirs. In reservoir engineer-\ning, DWT provided means of inferring inter-well connectivity in water flooding\noperations ( Unal et al., 2019c ).230 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88aafe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 14, "chroma:document": "The base scale in DWT is set to 2. Different scales can be obtained by raising the\nbase scale to integer values represented as follows\n2j\u00f0j51;2;3;4...\u00de\nThe translation occurs at integer multiples represented as\n2jm\u00f0m51;2;3;4...\u00de\nThe DWT analyzes the signal at different frequency bands with different resolutions\nby decomposing the signal into coarse approximation and detail information. As shown\ninFigure 8.8 , the original signal passes through a high pass filter D1and low pass filter\nA1. Half of the samples are eliminated after filtering according to Nyquist \u2019s rule, which\nstates that in order to reproduce a signal adequately, it should be periodically sampled\nat a rate, that is 2 X, the highest frequency has been recorded ( Cramer & Grenader,\n1959). Filtering a signal corresponds to the mathematical operation of convolution of\nthe signal with an impulse response of the filter. The convolution equation is given by\nxn\u00bd/C1383hn\u00bd/C1385XN\nk52Nxk\u00bd/C138:h\u00bdn2k/C138\u00f0 8:3\u00de"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ab4e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 14, "chroma:document": "the signal with an impulse response of the filter. The convolution equation is given by\nxn\u00bd/C1383hn\u00bd/C1385XN\nk52Nxk\u00bd/C138:h\u00bdn2k/C138\u00f0 8:3\u00de\nFigure 8.8 Discrete wavelet multilevel decomposition. The signal is separated to high pass (noise)\nand a low pass (approximation) at each level.231 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88aba8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 15, "chroma:document": "The low-pass filter halves the resolution but keeps the scale intact. The procedure\ncan mathematically be expressed as\nyn\u00bd/C1385XN\nk52Nhk\u00bd/C138:x\u00bd2n2k/C138\u00f0 8:4\u00de\nThe signal is then subsampled by two by discarding every other sample. This pro-\ncess continues one level of decomposition and mathematically can be expressed as\nyhighk\u00bd/C1385X\nnxn\u00bd/C138:g\u00bd2k2n/C138\u00f0 8:5\u00de\nylowk\u00bd/C1385X\nnxn\u00bd/C138:g\u00bd2k2n/C138\u00f0 8:6\u00de\nwhere yhighk\u00bd/C138andylowk\u00bd/C138are the outputs of the high-pass and low-pass filters, respec-\ntively. For the next level of decomposition, the low-pass sub-band A1is iteratively fil-\ntered by the same technique into narrower sub-bands AjandDj. With this technique,\nthe signal of interest can be captured with a few large magnitudes of discrete wavelet\ndecompositions ( Polikar, 2001 )(Fig. 8.8 ).\nIn DWT, the total energy of the signal is decomposed into components (i.e., dif-\nferent decomposition levels). Therefore DWT preserves the energy of the signal."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88abee-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 15, "chroma:document": "ferent decomposition levels). Therefore DWT preserves the energy of the signal.\nParseval \u2019s theorem relates the energy of the total signal to the energy of each compo-\nnent and its wavelet coefficients ( Burrus, Gopinath, & Guo, 1998 ). For a discrete sig-\nnal with the number of data points, the detail coefficients energy of the signal can be\ncalculated as follows:\nEd\ni5dijj2;i51;2;3;... ;l\nwhere51, 2, 3, ...,lis the wavelet decomposition level up to l.\n8.6.1.1 Field example 1\nFigure 8.9 shows the analysis of the MiniFrac by G-function of the first field\nexample case presented in this section ( Eltaleb et al., 2020 ). In this test, an average of\n16.8 bpm of treated water was injected into the formation for 15 minutes. Pressure\nfall-off was recorded after shut-in for 20 minutes, with a sampling rate of 1 seconds.\nNormal leak-off (i.e., fracture area is constant during shut-in) can be recognized from\nthe derivative shape. The closure can be identified evidently when G3dp/dGdeviates"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ac3e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 15, "chroma:document": "the derivative shape. The closure can be identified evidently when G3dp/dGdeviates\nfrom the straight-line, reporting a closure pressure of 5822 psi and closure time of\n27.8 minutes. The fracture closure occurred at the 93rd data point in the analysis data\nset (Fig. 8.9 ).232 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ac98-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 16, "chroma:document": "This example is analyzed using our proposed technique. Figure 8.10 shows the\nenergy distribution plot of the noise at the decomposition level D 5. Two different dis-\ntinct regions (A and B) can be identified based on the energy magnitude. It can be\nnoticed that the energy magnitude is declining, then leveling off, and remains constant\nat a minimum level until the end of the job. Note that there are almost six orders of\nmagnitude reduction in the energy of the noise until the minimum. We hypothesize\nthat after the closure point, the energy of the noise should be minimum and stay con-\nstant. Also, it can be inferred from the energy trend that there is a change in system\nproperties with respect to time. This change is attributed to the decrease in fracture\nvolume over time@V\n@t/C0/C1\n. The closure point is identified from the intersection between\nlines connecting the energy levels of regions A and B, as indicated by the dashed line"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88acde-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 16, "chroma:document": "lines connecting the energy levels of regions A and B, as indicated by the dashed line\ninFigure 8.10 . The intersection point is at the 101st data point, which corresponds to\nthe closure time of 27.95 minutes and closure pressure of 5790 psi ( Fig. 8.10 ).\nA comparison between the results by our proposed technique and G-function anal-\nysis is presented in Table 8.2 . As can be seen, according to our analysis, fracture\nclosure happens slightly after the closure point by G-function. The reason for this\nClosure time = 27.8 min\nClosure pressure = 5822 psi\nClosure G           = ~ 0.126\nClosure point (#)   = 93\nFigure 8.9 G-function plot of field example 1.\nData points #Signal Energy, BHPClosure time = 27.95 min & closure pressure of 5790 psi\nClosure point (#)   = 101AB\nFigure 8.10 Distribution of the noise energy at decomposition level 3 (D 3) for the field example 1\n(Eltaleb et al., 2020 ).233 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ad2e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 17, "chroma:document": "difference could be that the closure point by our technique is the complete closure of\nthe fracture, while the closure point by the G-function method is the start of the clos-\ning process.\n8.6.1.2 Field example 2\nFig. 8.11 shows the analysis of DFIT by G-function for this case. In this test, an aver-\nage of 0.28 bpm of water was injected into the formation for 12 minutes. Pressure\nfall-off was recorded after shut-in for B77 minutes, with a sampling rate of 1 second.\nAs can be seen in the figure, the closure pressure and closure time are estimated to be\n26756 psi and 822 seconds, respectively. The closure occurred at the 98th data point\nin the data set. This example is relatively straightforward to analyze using the\nG-function technique.\nThe figure below shows the energy distribution plot of decomposition level 3 (D 3).\nWe can notice that energy magnitude is declining, then leveling off to a minimum"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ad7e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 17, "chroma:document": "We can notice that energy magnitude is declining, then leveling off to a minimum\nlevel until the end of the test. The closure point is identified from the intersection of\nregions A and B, as indicated by the dashed line in Fig. 8.12 . The intersection point is\nat the 37th data point, which corresponds to the closure time of B14 minutes.\nThe summary of the results of the proposed methodology for field example 2 and\nits comparison with G-function analysis is presented in Table 8.3 . As can be seen,\nunlike field example 1, our method suggests an earlier fracture closure compared with\nthe G-function methods. The difference between the closure pressures of the two\nmethods is about 2000 psi. In this case, our method indicates the G-function underes-\ntimates the closure pressure. However, as shown in the field Case 1, this is not always\nthe case as many parameters affect the fracture closure.\nClosure time       = 822 \ns \nClosure pressure = 26,756 psi \nClosure G           = 0.27"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88adce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 17, "chroma:document": "the case as many parameters affect the fracture closure.\nClosure time       = 822 \ns \nClosure pressure = 26,756 psi \nClosure G           = 0.27 \nClosure point (#)   = 98 \nFigure 8.11 G-function plot of the field example 2 ( Eltaleb et al., 2020 ).234 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ae1e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 18, "chroma:document": "8.6.1.3 Field example 3\nFigs. 8.13 and 8.14 show the analysis of DFIT by G-function for the example. In this\nDFIT, fracture fluid was injected into the formation for 12 minutes. The Pressure fall-off\nwas recorded after shut-in for B165 minutes, with a sample rate of 1 second. Also, the\nwater hammer signature in the early portion of the derivative G3dp/dGis an indication\nof a tight formation. The slight increase of the derivative G3dp/dGafter the closure\nattributes to fracture growth after pump shut-in. The fracture closure pressure using the\nG-function method is estimated to be 2656 psi and closure time of 13.6 minutes.\nThe analysis of the same data set via the energy distribution plot is shown in\nFig. 8.15 . The closure pressure is explicitly identified when energy magnitude levels\noff from region A to region B. The closure point is identified from the intersection\nbetween regions A and B, as indicated by the dashed line in Fig. 8.15 . The\nClosure time = 761 s"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ae6e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 18, "chroma:document": "between regions A and B, as indicated by the dashed line in Fig. 8.15 . The\nClosure time = 761 s\nClosure point (#)   = 37B\nData points #Signal Energy, BHPA\nFigure 8.12 Distribution of the noise energy at decomposition level 3 (D 3) for the field example 2\n(Eltaleb et al., 2020 ).\nFigure 8.13 G-function plot of the field example 3 ( Eltaleb et al., 2020 ).235 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88aebe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 19, "chroma:document": "intersection point is at the 93rd data point, which corresponds to a closure pressure of\n2708 psi and a closure time of 13.5 minutes.\nThe results of both methods for this case are summarized in Table 8.4 . In this case,\nsimilar to field example 2, the fracture closure happens before the closure identified by\nthe G-function technique. The closure pressure using our technique, in this case, is\nfollowing the methods presented by McClure et al. (2014) andWang and Sharma\n(2017) in the sense that the closure happens earlier than the G-function. However,\none needs to compare the methods more closely for a better conclusion. Also, note\nthat the models presented by Maclure and Wang almost always pick the closure before\nthe G-function. However, as shown in example 1, this is not always the case with our\nmethod. Moreover, this method is not restricted to any assumption and solely depends\non the recorded data and its quality.\n8.6.1.4 Field example 4"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88af0e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 19, "chroma:document": "method. Moreover, this method is not restricted to any assumption and solely depends\non the recorded data and its quality.\n8.6.1.4 Field example 4\nFig. 8.16 shows an analysis of DFIT of the fourth field example that is analyzed in this\npaper. Water is injected with an average rate of 2.8 bbl/min for 3 minutes into a\nClosure pressure = 2702 psi & Closure time = 13.5 min\nClosure point (#) = 94 BA\nData points #Signal Energy, BHP\nFigure 8.15 A summary of the results for field example 3 and its comparison with G-function\n(Eltaleb at al., 2020 ).\nClosure time = 13.6 min\nClosure G            = 0.28\nClosure pressure = 2656 psi\nClosure point (#) = 101\nFigure 8.14 Zoomed G-function plot of the field example 3 ( Eltaleb et al., 2020 ).236 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88af5e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 20, "chroma:document": "formation that has 140 ft thickness, 9.7% porosity, and 0.58 mD permeability. The\npressure fall-off has been observed for 26 hours, with a sampling rate of 1 second.\nThe data, beyond 32 hours of shut-in time and corresponding to GB565, is ignored\nin the analysis because there is an observed pressure increase due to fluid heating\nup (Amini, Soliman, & House, 2015; Soliman, 1986 ). From G3dp/dGsignature\n(red line), a natural fracture system can be inferred. However, closure cannot be accu-\nrately identified since multiple straight line candidates can be plotted. The possible clo-\nsure points corresponding to closure pressures of 13,539, 13,068, and 12,815 psi. We\nwere given analysis for this case by an oil company, indicating the closure pressure as\n13,544 psi (first tangent line).\nThe analysis of this DFIT using the proposed technique yields more affirmative\nresults about the interpretation of the pressure data. The decomposition level (D 3) has"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88afae-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 20, "chroma:document": "results about the interpretation of the pressure data. The decomposition level (D 3) has\nbeen used in this example. As shown in Fig. 8.17 , two regions of energy levels are rec-\nognized as A and B as follows:\n\u0081Region A : The energy decline describes the closing of the hydraulic fracture. The\nintersection between regions A and B would be the minimum stress for hydraulic\nfractures (closure pressure 513,521 psi, closure time 546 minutes, and closure\npoint (#) 52600).\n\u0081Region B : The energy levels off as the pressure continue to decline but no further\nreduction in the noise, indicating no physical changes are happening in the system,\nand the hydraulic fracture is completely closed.\nA summary of results from our proposed methodology and G-function is presented\ninTable 8.5 . As can be seen, in this case, although multiple closures were possible on\ntheG3dp/dGplot, the wavelet technique showed an obvious minimum energy level\nT closure =45 min\nP closure   = 13,539  psi \nT closure =294 min"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88aff4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 20, "chroma:document": "theG3dp/dGplot, the wavelet technique showed an obvious minimum energy level\nT closure =45 min\nP closure   = 13,539  psi \nT closure =294 min\nP closure   = 13,068  psi \nT closure   = 713 min\nP closure   = 12,815  psi \nFigure 8.16 G-function plot of the field example 4 ( Eltaleb et al., 2020 ).237 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b044-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 21, "chroma:document": "that matched with the G-function analysis. This is an advantage of our proposed tech-\nnique as it does not limit it to a specific rock type and job parameter.\n8.6.2 Effect of natural fracture and temperature\nCurrent techniques for estimating the closure stress often contradict each other, reach-\ning up to 2000 psi difference in the identified closure stress. This discrepancy is due to\ntwo main reasons, (1) the underlying assumptions of these techniques, (2) ultra-tight\npermeability, natural fractures, and heat exchange.\nEltaleb, Rezaei, Soliman, and Dindoruk (2021) proposed a signal processing tech-\nnique for analyzing DFIT in geothermal reservoirs, where it showed several advantages\nover traditional methods in evaluating in-situ stresses. Because of the changing temper-\nature during the test, conventional techniques may yield inaccurate results. To show\nthe temperature effect on DFIT in geothermal reservoirs, two FORGE field cases are"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b094-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 21, "chroma:document": "the temperature effect on DFIT in geothermal reservoirs, two FORGE field cases are\nanalyzed using the conventional and modified G-function analyses and the proposed\nsignal processing technique.\n8.6.3 Utah FORGE example (effect of heat exchange)\nA series of injection tests were performed in 2019 to estimate in situ stresses and for-\nmation parameters. Nine different test cycles have been performed, including pump-\nin/flow back and pump-in/shut-in. For this section, we focused on the pump in\nshut-in only.\nIn this test, water was injected at the rate of 15 BPM into FORGE formation\nthrough a 3.5-inch diameter tubing in Well 58 /C032 in April 2019. Series of fracture\ninjection/shut-in tests and Injection/flow-back tests were performed, as shown in\nFig. 8.18 . In this study, the results from DFIT 1 and DFIT 2 are analyzed.\nBoth temperature and pressure data have been analyzed for the first and second\nDFITs using the developed methodology before considering the temperature and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b0e4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 21, "chroma:document": "DFITs using the developed methodology before considering the temperature and\ncompressibility effect. Also, the pressure was analyzed after applying the corrections\nto pressure. The energies of the noise in pressure and temperature were plotted\nData points #Signal Energy, BHPFracture closure pressure = 13,521                       psi & Closure time = 46\nminute\nClosure point (#) = 2600AB\nFigure 8.17 Distribution of the noise energy at decomposition level 3 (D 3) for the field example 4\n(Eltaleb et al., 2020 ).238 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b134-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 22, "chroma:document": "against time. Our methodology for interpretation of pressure energy for unconven-\ntional reservoirs shows a negative slope in the energy distribution plot that is indicative\nof energy change in the system attributed to fracture closure. However, in geothermal\nreservoirs, the expected change of injected fluid temperature has a significant impact\non the observed pressure signal. It, therefore, may lead to an ambiguous estimation of\nthe rock in-situ stresses. Consequently, it is essential to include the effect of the frac-\nturing fluid \u2019s temperature change in DFIT. As shown in Fig. 8.19 , during water injec-\ntion into the hot formation, heat convection dominated as the temperature decreases.\nThe temperature energy shows two distinctive regions, indicated by the yellow and\nblack lines in Fig. 8.19 . Contrary to the pressure energy, the recorded temperature\nnoise energy AC decays in a constant slope until the end of the test, which attributes"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b184-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 22, "chroma:document": "noise energy AC decays in a constant slope until the end of the test, which attributes\nto a decrease in the heat exchange rate as the system reaches equilibrium.\nDetailed analyses of the two DFITs in Fig. 8.19 are given in the following section.\n8.6.4 DFIT 1\nFig. 8.20 shows the G-function of the pressure analysis in DFIT 1. As can be seen, the\nclosure, in this case, is equal to B4200 psi, which is 200 psi lower than what was\nidentified from the wavelet analysis in Fig. 8.19 . The closure pressure using our tech-\nnique, in this case, is in accordance with the methods presented by McClure et al.\n(2014) andWang and Sharma (2017) in the sense that the closure happens earlier than\nthe G-function (i.e., G-function underestimates closure).\nFigure 8.18 The diagnostic test on Utah FORGE geothermal reservoir (granite) ( Eltaleb et al., 2021 ).239 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b1d4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 23, "chroma:document": "Figure 8.19 Energy distribution of the noise in the recorded pressure and temperature in the semi-\nlog plot ( Eltaleb et al., 2021 ).\nFigure 8.20 G-function analysis of DFIT 1 before applying the corrections ( Eltaleb et al., 2021 ).240 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b224-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 24, "chroma:document": "The energy distribution of the noise in the pressure and temperature data are plot-\nted in Fig. 8.21 . As can be seen, there are two drops in the level of noise in the pres-\nsure data. These drops correspond to 4400 psi and 3800 psi. After the second drop, the\nlevel of noise in the pressure data remains constant. However, the noise in the temper-\nature shows a different trend. The temperature curve shows only one sharp drop in\nthe noise and a continuous drop in the noise after that.\nWe think that the first drop in the pressure noise is the closure pressure, and the\nsecond drop might be due to the shearing of the natural fracture planes, as discussed\nbyNadimi et al. (2020) . The temperature plot confirms the closure because, BC, the\nmajority of the noise will be from the conduction and convection, with the former\nbecome dominant. However, after the fracture closure, the noise in the temperature\ndata will be from conduction and vanish as the system reaches equilibrium."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b274-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 24, "chroma:document": "data will be from conduction and vanish as the system reaches equilibrium.\nThe method that was developed by Soliman (1986) accounts for the fracturing fluid\ncompressibility and temperature. The technique works up until the closure moment.\nAccording to the method, the fracturing temperature and compressibility cause the\npressure fall-off to be higher than what it should be in reality. In this study, the thermal\nconductivity and fluid compressibility were assumed to be 300 310261/psi and\n50310261//C14F, respectively. Fig. 8.22 shows the corrected pressure for DFIT 1.\nFigure 8.21 Energy distribution of the noise in the pressure and temperature for DFIT 1 ( Eltaleb\net al., 2021 ).241 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b2c4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 25, "chroma:document": "Based on the corrected pressure, one may apply the conventional G-function\nagain. After applying the correction for temperature, the closure pressure would be\npicked at 3900 psi, which is 400 psi lower than the closure identified from the wavelet\nin DFIT 1. This shows that the conventional G-Function is not suited for ultra-tight\nand hot reservoirs ( Fig. 8.23 ).\nThe energy distribution of the noise in the corrected pressure is not plotted, but it\ncan be shown that the correction of the pressure will not affect the wavelet results.\nThis is an advantage of our technique over conventional analytical methods.\n8.6.5 DFIT 2\nIn this injection test cycle, 183 bbl was pumped into the formation. The pumping\nschedule started with pumping 8 at 3800 psi; then, the rate was increased to 15 bpm at\n5000 psi. The pump stopped and the pressure was allowed to fall off for B15 hours.\nThe conventional G-function analysis of DFIT 2 without considering the effect of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b314-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 25, "chroma:document": "The conventional G-function analysis of DFIT 2 without considering the effect of\nthe temperature and fracturing fluid \u2019s compressibility is shown in Fig. 8.24 . In this\ncase, the closure using G-function analysis is identified as 4300 psi.\nThe distribution of the noise energy in the recorded pressure and temperature\nis shown in Fig. 8.25 . As can be seen in this example, three levels of energy are\nFigure 8.22 Corrected pressure for compressibility and temperature for DFIT 1 ( Eltaleb et al., 2021 ).242 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b364-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 26, "chroma:document": "distinguished. The vertical line on the pressure plot shows where the closure pressure\nshould be picked from our proposed methodology. The closure, in this case, is equal to\n4350 psi, which is in accordance with the previous analysis on the FORGE. Also, we\nobserved a constant level of noise energy before the closure in the temperature noise.\nFigure 8.23 G-Function analysis of the corrected pressure of DFIT 1 ( Eltaleb et al., 2021 ).\nFigure 8.24 G-function analysis of DFIT 2 before applying the corrections ( Eltaleb et al., 2021 ).243 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b3b4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 27, "chroma:document": "Figure 8.25 Energy distribution of the noise in the pressure and temperature for DFIT 2 ( Eltaleb\net al., 2021 ).\nFigure 8.26 Corrected pressure for compressibility and temperature for DFIT 2 ( Eltaleb et al., 2021 ).244 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b40e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 28, "chroma:document": "This constant noise level is due to convection. After the closure point, the temperature\nnoise reduces gradually until the temperature stabilizes to the in-situ reservoir\ntemperature.\nThe correction of the pressure, accounting for the temperature and fluid compress-\nibility, is shown in Fig. 8.26 . As can be seen, the pressure difference can reach up to\n1000 psi that can result in erroneous conclusions.\nThe G-Function analysis of the corrected pressure is shown in Fig. 8.27 . As can\nbe seen, the G-function method again underestimates the closure. After applying the\ntemperature effect, its underestimation is more apparent.\n8.7 Summary\nIn this chapter, conventional and newly developed approaches for fracture diagnostics\nare reviewed. Fracture tests are typical pre- and posttreatment tools to estimate several\nreservoirs and design variables. Typically, in all of the tests, a small amount of fluid is\npumped into the reservoir, and a short fracture is created. The diagnostics can be cate-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b454-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 28, "chroma:document": "pumped into the reservoir, and a short fracture is created. The diagnostics can be cate-\ngorized into three main groups: direct far-field techniques, direct near-wellbore tech-\nniques, and indirect fracture diagnostics. In this chapter, we reviewed the indirect\nfracture diagnostics methods that are conducted on recorded response pressure and\nrate from the wellbore. Sometimes, a combination of several methods is good for hav-\ning a better understanding of the interesting parameters.\nFigure 8.27 G-Function analysis of the corrected pressure of DFIT 2 ( Eltaleb et al., 2021 ).245 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b4a4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 29, "chroma:document": "References\nAmini, K., Soliman, M. Y., & House, W. V. (2015). A three dimensional thermal model for hydraulic\nfracturing. Technical conference and exhibition. SPE-174858-MS; Society of Petroleum Engineers,\nHouston.\nBarree, R. D., Barree, V. L., & Craig, D. (2007). Holistic fracture diagnostics. Rocky mountain oil & gas\ntechnology symposium. Society of Petroleum Engineers.\nBarree, R. D., Miskimins, J., & Gilbert, J. (2015). Diagnostic fracture injection tests: Common mistakes,\nmisfires, and misdiagnoses. SPE Production & Operations ,30(02), 84 /C098.\nBarree, R. D., & Mukherjee, H. (1996). Determination of pressure dependent leakoff and its effect on\nfracture geometry. SPE annual technical conference and exhibition. Society of Petroleum Engineers.\nBurrus, C. S., Gopinath, R. A., & Guo, H. (1998). Introduction to wavelets and wavelet transforms: A primer\n(1st ed). Prentice Hall.\nCastillo, J. L. (1987). Modified fracture pressure decline analysis including pressure-dependent leak-off."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b4f4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 29, "chroma:document": "(1st ed). Prentice Hall.\nCastillo, J. L. (1987). Modified fracture pressure decline analysis including pressure-dependent leak-off.\nLow permeability reservoirs symposium. Society of Petroleum Engineers.\nCinco-Ley, H., & Samaniego, V. F. (1981). Transient pressure analysis for fractured wells. Journal of\nPetroleum Technology ,1766 .\nC i p o l l a ,C .L . ,&W r i g h t ,C .A .( 2 0 0 0 ) .S t a t e - o f - the-art in hydraulic fr acture diagnostics. Paper presented at the\nSPE Asia Pacific oil and gas conference and exhibition .A v a i l a b l ef r o m https://doi.org/10.2118/64434-MS ,\nBrisbane, Australia.\nCleary, M. P., Johnson, D. E., Kogsb\u00f8ll, H. H., Owens, K. A., Perry, K. F., De Pater, C. J., ... ...\nMauro, T. (1993). Field implementation of proppant slugs to avoid premature screen-out of hydraulic fractures\nwith adequate proppant concentration .Low permeability reservoirs symposium . Society of Petroleum\nEngineers."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b544-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 29, "chroma:document": "with adequate proppant concentration .Low permeability reservoirs symposium . Society of Petroleum\nEngineers.\nCraig, D. P., & Blasingame, T. A. (2006). Application of a new fracture-injection/fall-off model accounting for\npropagating, dilated, and closing hydraulic fractures .SPE gas technology symposium . Society of Petroleum\nEngineers.\nCramer, H., & Grenader, U. (1959). The Nyquist frequency is that frequency whose period is two sampling inter-\nvals.Probability and Statistics: The Harald Cramer Volume (p. 434) Almqvist & Wiksell.\nEltaleb, I., Rezaei, A., Siddiqui, F., Awad, M. M., Mansi, M., Dindoruk, B., & Soliman, M. Y. (2020).\nAnalysis of fracture injection tests using signal processing approach .Unconventional resources technology conference,\n20/C022 July 2020 (pp. 3994 /C04007). Unconventional Resources Technology Conference (URTeC).\nEltaleb, I., Rezaei, A., Soliman, M. Y., & Dindoruk, B. (2021). A signal processing approach for analysis"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b594-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 29, "chroma:document": "Eltaleb, I., Rezaei, A., Soliman, M. Y., & Dindoruk, B. (2021). A signal processing approach for analysis\nof fracture injection test in geothermal reservoirs: A case study on the Utah FORGE formation. SPE\nhydraulic fracturing technology conference and exhibition .\nFelsenthal, M. (1974). Step-rate tests determine safe injection pressures in floods. Oil Gas Journal (United\nStates) ,72(43).\nHoward, G. C., & Fast, C. R. (1957). Optimum fluid characteristics for fracture extension .Drilling and production\npractice . American Petroleum Institute.\nHubbert, M. K., & Willis, D. G. (1972). Mechanics of hydraulic fracturing. American Association of\nPetroleum Geologists ,18.\nHyden, Ron E., & Stegent, Neil A. (1996). Pump-in/shutdown tests key to finding near-welibore\nrestrictions. Paper presented at the Permian basin oil and gas recovery conference . Available from https://doi.\norg/10.2118/35194-MS , Midland, TX."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b5e4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 29, "chroma:document": "restrictions. Paper presented at the Permian basin oil and gas recovery conference . Available from https://doi.\norg/10.2118/35194-MS , Midland, TX.\nLiu, G., Ehlig-Economides, C., & Sun, J. (2016). Comprehensive global fracture calibration model .SPE Asia\nPacific hydraulic fracturing conference . Society of Petroleum Engineers.\nMarongiu-Porcu, M., Ehlig-Economides, C. A., & Economides, M. J. (2011). Global model for fracture fall-\noff analysis .North American unconventional gas conference and exhibition . Society of Petroleum Engineers.\nMarongiu-Porcu, M., Retnanto, A., Economides, M. J., & Ehlig-Economides, C. (2014). Comprehensive\nfracture calibration test design .SPE hydraulic fracturing technology conference . Society of Petroleum\nEngineers.\nMayerhofer, M. J., & Economides, M. J. (1997). Fracture-injection-test interpretation: Leakoff coefficient\nvs. permeability. SPE Production & Facilities ,12(04), 231 /C0236.246 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 30, "chroma:document": "McClure, M., Bammidi, V., Cipolla, C., Cramer, D., Martin, L., Savitski, A., ...Voller, K. (2019). A\ncollaborative study on DFIT interpretation: Integrating modeling, field data, and analytical techni-\nques. Paper presented at the SPE/AAPG/SEG unconventional resources technology conference,\nDenver, CO. Unconventional Resources Technology Conference (URTEC).\nMcClure, M. W., Blyton, C. A., Jung, H., & Sharma, M. M. (2014). The effect of changing fracture compli-\nance on pressure transient behavior during diagnostic fracture injection tests .SPE annual technical conference and\nexhibition . Society of Petroleum Engineers.\nMcClure, M. W., Jung, H., Cramer, D. D., & Sharma, M. M. (2016). The fracture-compliance method\nfor picking closure pressure from diagnostic fracture-injection tests (see associated supplementary dis-\ncussion/reply). SPE Journal ,21(04), 1 /C0321.\nMohamed, I. M., Azmy, R. M., Sayed, M. A. I., Marongiu-Porcu, M., & Economides, C. (2011)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b67a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 30, "chroma:document": "cussion/reply). SPE Journal ,21(04), 1 /C0321.\nMohamed, I. M., Azmy, R. M., Sayed, M. A. I., Marongiu-Porcu, M., & Economides, C. (2011).\nEvaluation of after-closure analysis techniques for tight and shale gas formations .SPE hydraulic fracturing technol-\nogy conference . Society of Petroleum Engineers.\nMohamed, Y. (2016). Soliman, Ph.D., P.E., NAI; Ron Dusterhoft. Fracturing Horizontal Wells (McGraw-Hill\nEducation: New York, Chicago, San Francisco, Athens, London, Madrid, Mexico City, Milan, New Delhi,\nSingapore, Sydney, Toronto . Available from https://www.accessengineeringlibrary.com/content/book/\n9781259585616 .\nMukherjee, H., Larkin, S., & Kordziel, W. (1991). Extension of fracture pressure decline curve analysis to fis-\nsured formations .Low permeability reservoirs symposium . Society of Petroleum Engineers.\nNadimi, S., Forbes, B., Moore, J., Podgorney, R., & McLennan, J. D. (2020). Utah FORGE:"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b6ca-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 30, "chroma:document": "Nadimi, S., Forbes, B., Moore, J., Podgorney, R., & McLennan, J. D. (2020). Utah FORGE:\nHydrogeothermal modeling of a granitic based discrete fracture network. Geothermics ,87, 101853.\nNolte, K. G. (1979). Determination of fracture parameters from fracturing pressure decline .SPE annual technical\nconference and exhibition . Society of Petroleum Engineers.\nNolte, K. G. (1986). A general analysis of fracturing pressure decline with application to three models.\nSPE Formation Evaluation ,1(06), 571 /C0583.\nNolte, K. G. (1991). Fracturing-pressure analysis for nonideal behavior. Journal of Petroleum Technology ,43\n(02), 210 /C0218.\nPan, H., Firoozabadi, A., & Fotland, P. (1997). SPE Production & Facilities .\nPercival, D. B., & Walden, A. T. (2000). Wavelet methods for time series analysis . Cambridge: Press\nSyndicate of The University of Cambridge.\nPokalai, K., Kulikowski, D., Johnson, R. L., Haghighi, M., & Cooke, D. (2016). Development of a new"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b71a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 30, "chroma:document": "Syndicate of The University of Cambridge.\nPokalai, K., Kulikowski, D., Johnson, R. L., Haghighi, M., & Cooke, D. (2016). Development of a new\napproach for hydraulic fracturing in tight sand with pre-existing natural fractures. The APPEA Journal ,\n56(1), 225 /C0238.\nPolikar, R. (2001). Multiresolution analysis: The discrete wavelet transform. Retrieved from The\nWavelet Tutorial: Available from http://users.rowan.edu/ Bpolikar/WTpreface.html .\nRioul, O., & Vetterli, M. (1991). Wavelet and signal processing. IEEE SP Magazine ,38.\nSavitski, Alexei A., & John, W. Dudley (2011). Revisiting Microfrac in-situ stress measurement via flow\nback \u2014A new protocol. Paper presented at the SPE annual technical conference and exhibition . Available\nfrom https://doi.org/10.2118/147248-MS , Denver, CO, USA, October.\nSiddiqui, F., Soliman, M. Y., House, W., & Ibragimov, A. (2016). A new analysis technique for inter-\npreting injection/shut-in tests. Hydraulic Fracturing Quarterly ."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b76a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 30, "chroma:document": "preting injection/shut-in tests. Hydraulic Fracturing Quarterly .\nSingh, P. K., Agarwal, R. G., & Krase, L. D. (1987). Systematic design and analysis of step-rate tests to\ndetermine formation parting pressure. Paper presented at the SPE annual technical conference and exhibition .\nAvailable from https://doi.org/10.2118/16798-MS , Dallas, TX, September.\nSoliman, M.Y. (1986). Technique for considering fluid compressibility and temperature changes in mini-frac analysis.\nPaper presented at the SPE annual technical conference and exhibition . SPE 15370. Society of Petroleum\nEngineers, New Orleans, LA.\nSoliman, M.Y., and A.A. Daneshy. Determination of Fracture Volume and Closure Pressure From\nPump-In/Flowback Tests. Paper presented at the Middle East Oil Show, Bahrain, November 1991.\nAvailable from https://doi.org/10.2118/21400-MS .\nSoliman, M. Y., & Gamadi, T. (2012). Testing tight gas and unconventional formations and determination of clo-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b7ba-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 30, "chroma:document": "Soliman, M. Y., & Gamadi, T. (2012). Testing tight gas and unconventional formations and determination of clo-\nsure pressure .SPE/EAGE European unconventional resources conference & exhibition-from potential to produc-\ntion. European Association of Geoscientists & Engineers.247 Fracture diagnostic testing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b80a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 31, "chroma:document": "Soliman, M. Y., & Kabir, C. S. (2012). Testing unconventional formations. Journal of Petroleum Science and\nEngineering ,92, 102 /C0109.\nSoliman, M. Y., Craig, D. P., Bartko, K. M., Rahim, Z., & Adams, D. M. (2005). Post-closure analysis to\ndetermine formation permeability, reservoir pressure, residual fracture properties .SPE Middle East oil and gas\nshow and conference . Society of Petroleum Engineers.\nSoliman, M. Y., Miranda, C., & Wang, H. M. (2010). Application of after-closure analysis to a dual-\nporosity formation, to CBM, and to a fractured horizontal well. SPE Production & Operations ,25(04),\n472/C0483.\nStehfest, H. (1970). Algorithm 368: Numerical inversion of Laplace transforms [D5]. Communications of the\nACM ,13(1), 47 /C049.\nTan, H. C., McGowen, J. M., Lee, W. S., & Soliman, M. Y. (1988). Field application of Minifrac analysis to\nimprove fracturing treatment design .California regional meeting (pp. 591 /C0612)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b85a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 31, "chroma:document": "improve fracturing treatment design .California regional meeting (pp. 591 /C0612).\nUnal, E., Siddiqui, F., Soliman, M. Y., & Dindoruk, B. (2019a). Wavelet analysis of DFIT data to identify\nfracture closure parameters .SPE hydraulic fracturing technology conference and exhibition . Society of Petroleum\nEngineers.\nUnal, E., Siddiqui, F., Rezaei, A., Eltaleb, I., Kabir, S., Soliman, M. Y., & Dindoruk, B. (2019b). Use of\nwavelet transform and signal processing techniques for inferring interwell connectivity in waterflooding operations .\nSPE annual technical conference and exhibition . Society of Petroleum Engineers.\nUnal, E., Rezaei, A., Siddiqui, F., Likrama, F., Soliman, M., & Dindoruk, B. (2019c). Improved understand-\ning of dynamic fracture behavior in unconventional horizontal wells using wavelet transformation .SPE annual\ntechnical conference and exhibition . Society of Petroleum Engineers.\nValk\u00f3, P., & Economides, M. J. (1995). Hydraulic fracture mechanics . United Kingdom: Wiley."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b8aa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 31, "chroma:document": "Valk\u00f3, P., & Economides, M. J. (1995). Hydraulic fracture mechanics . United Kingdom: Wiley.\nWang, H., & Sharma, M. M. (2017). New variable compliance method for estimating in-situ stress\nand leak-off from DFIT data. Paper presented at the SPE annual technical conference and exhibition , San\nAntonio, TX, USA, October.248 Unconventional Shale Gas Development"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b8fa-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "SPE\u0010 169539\u001006\nDiagnostic Fracture Injection Tests: Common Mistakes, Misfires, and \nMisdiagnoses \nR.D. Barree, J.L. Miskimins, and J.V. Gilbert, Barree & Associates \nCopyright 2014, Society of Petroleum Engineers \n \nThis paper was prepared for presentation at the SPE Western North American and Rocky Mountain Joint Regional Meeting held in Denver, Colorado, USA , 16\u201318 April 2014. \n \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 of the paper have not been \nreviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its \nofficers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohi bited. Permission to"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b94a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "reproduce in print is restricted to a n abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. \n \n \nAbstract \nOver the last twenty years, Diagnostic Fracture Injection Tests, or DFIT\u2019s, have evolved into commonly  used techniques that \ncan provide valuable information about the reservoir, as well as hydraulic fracture treatment parameters. Thousands are \npumped every year in both conventional and unconventional reservoirs. Unfortunately, many tests that are pumped provide \npoor or no results due to either problematic data acquisition or incorrect analysis of the acquired data. \nThis paper discusses common issues and mistakes made while acquiring DFIT data. Guidelines on how to avoid these \nerrors and secure the best possible data are provided including data resolution, pump rates, test duration, and fluid selection."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b99a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "errors and secure the best possible data are provided including data resolution, pump rates, test duration, and fluid selection. \nRules of thumb are provided to estimate the time required to reach fracture closure and establish stable reservoir transients for \nanalysis. \nThe last part of the paper addresses potential (and commonly observed) problems in the analysis of the DFIT. The se \nissues can be magnified in tight gas and shale reservoirs due the long data acquisition times and the subtle pressure transients \nthat can occur. Specific issues that are discussed include poor ISIP data from perforation restriction, loss of hydrostatic head, \ngas entry and the resulting phase segregation, the use of gelled fluids, and errors in after closure analysis. \n \n \nIntroduction \nDiagnostic fracture inject ion tests or DFIT\u2019s are small pump-in treatments performed to gather data to help design follow-up"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88b9ea-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "Introduction \nDiagnostic fracture inject ion tests or DFIT\u2019s are small pump-in treatments performed to gather data to help design follow-up \nhydraulic fracturing treatments, as well as to characterize the subject reservoir. DFIT\u2019s have their basis in co nventional mini-\nfrac treatments; however, they are subtly different and are intended to acquire significantly more data for fracture design and \nexecution and reservoir description. Conventional mini-frac treatments have historically been focused on acquiring very \nspecific treatment desig n parameters, such as fluid efficiencies and leakoff values, however, DFIT\u2019s are intended to expand \nthat role and acquire additional data such as reservoir pore pressure, detailed closure and fracture gradients, process zone \nstresses (PZS), transmissibility values which can be converted into reservoir permeability values, and leak-off mechanisms."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ba3a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "stresses (PZS), transmissibility values which can be converted into reservoir permeability values, and leak-off mechanisms. \nThe advent of unconventional reservoirs have added even more value to DFIT testing, as most of the information gained is \ncomparable to traditional pressure transient tests, which are impractical to run in tight sand and shale systems since the time \nto analyzable pseudo-radial flow can be months, if not years. \nA generic DFIT test is shown in Figure 1. The wellbore is first filled at low to moderate rate, until a positive surface \npressure response is observed. With low to moderate wellbore compressibility, the pressure should rise quickly until initial \nbreakdown occurs. Breakdown will either be indicated by a sharp drop in pressure as a new fracture initiates (as at point 1 in \nFigure 1), or a plateau in pressure as existing fractures are opened and extended. Once a breakdown event is observed, the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ba8a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "Figure 1), or a plateau in pressure as existing fractures are opened and extended. Once a breakdown event is observed, the \ninjection rate should be increased to the maximum rate allowed by available horsepower, or to 75% of the planned treatment \nrate of the main frac, whichever is achievable. A constant rate is then held for 3-5 minutes (step 2 in Figure 1) , after which a \nrapid step-down can be conducted. The step-down test is separate from the actual DFIT but is commonly run at the end of the \npump-in to determine perforation and ne ar-wellbore frictional pressure losses. The rate is then immediately reduced to zero, \nto obtain the instantaneous shut-in pressure (ISIP, shown as step 4) and the falloff pressure is monitored for as long as \npossible or as long as necessary to acquire the desired data. Even when high friction is not expected, the step-down is \nrecommended to make identification of ISIP easier. More specific details of how to pump DFIT tests and recommended"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88bada-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "recommended to make identification of ISIP easier. More specific details of how to pump DFIT tests and recommended \nacquisition procedures are discussed later in this paper. \n \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88bb2a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 1, "chroma:document": "2  SPE 169539  \n \n \nFigure 1:  Generic DFIT procedure. Initial breakdown is achieved at point 1; a constant  rate is held for 3 -5 minutes indicated by  point \n2; point 3 shows a rapid step -down; point 4 indicates ISIP; and point 5 shows falloff.  \n \n \nThis paper not intend ed to provide specific  instructions on the basics of how to  analyze  DFIT tests, as that information is \ndescribed in detail in other papers ( Barree, et al, 2009; Barree, 1998 ). Rather, as the title implies, it aims to aid in the \nacquisition  of useful and analyzable data , as well as  provide hints to common problems that occur either during the pumping \nof the test or during the analysis of the results . It is not uncommon to hear statements that disparage the test , however, most \nof the  problems  can be attributed to failed te sts that do not provide any useful data  because they we re pumped  or analyzed"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88bb7a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 1, "chroma:document": "of the  problems  can be attributed to failed te sts that do not provide any useful data  because they we re pumped  or analyzed  \nincorrectly . This is a valid concern \u2013 these tests cost additional time and money, and if they fail to provide usable  information \nvalue is lost or d estroyed . However, more often than not, it is the quality of the acquired data  and how the acquisition does \n(or does not) take place  that i s the root issue. I f appropriate steps are taken and quality data acquired, the tests are quite valid \nand correct int erpretation can shed light on what the reservoir is trying to  say. \nThis paper tries to address these acquisition issues, provide guidance on acquiring quality data, and discuss some common \nmistakes that happen during analysis procedures. If these steps are  addressed, the success rate of the treatments should \nincrease significantly.  Most of t he examples in this paper focus  on unconventional, tight hydrocarbon systems, however, all"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88bbca-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 1, "chroma:document": "increase significantly.  Most of t he examples in this paper focus  on unconventional, tight hydrocarbon systems, however, all \npoints are equally  applicable to conventional  reservoirs . \n \n \nRecommended Acquis ition Procedure  \nEvery time fluid is pumped into a formation, there is a risk of formation damage.  Therefore, fluid injections of any kind \nshould be minimized  and be conducted under controlled conditions. However, at the same time, enough fluid must be \ninjected under fracturing conditions  to adequately contact the reservoir and provide conditions under which the desi red \nparameters can be measured.  \nA DFIT is a fracture test, and must be conducted at a stable fracturing rate. I t does not take extremely h igh rates to initiate \nand propagate a fracture  in low to moderate permeability formations . In milli -Darcy range permeabilities, rates of 1 -2 BP M"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88bc1a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 1, "chroma:document": "and propagate a fracture  in low to moderate permeability formations . In milli -Darcy range permeabilities, rates of 1 -2 BP M \nare frequently high enough to exceed  fracturing pressure. Approximate  rates that cause fracture extension  in a giv en situation \ncan be calculated using radial Darcy\u2019s Law , as shown in Equation 1. To extend a fracture the injection rate must be high \nenough to generate a pressure differential  (\uf044psafe) greater than the net fracture extension pressure, FG*D -p. \nFor micro - and nano -Darcy systems, the necessary rates are even lower. Figure 2  shows a graph relating the generated \npressure for a variety of reservoir permeabilities. In an effort to pump enough fluid to adequately contact the reservoir, do so \nin a relatively short amount of time, and provide a safety factor, rates of 5 -6 BPM, or even slightly higher, 7-8 BPM, have \nproven to  be very successful in providing good results. This maximum rate is recommended to be held for 3 -5 minutes, as"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88bc6a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 1, "chroma:document": "proven to  be very successful in providing good results. This maximum rate is recommended to be held for 3 -5 minutes, as \nshown in Figure 1, which results i n ~600-1800 gallons of fluid being injected.  \n \n) (ln] )* [( 10 917.46\nmax,\nsrrp p D FGkh Xq\nwesafe\ni\n\uf02b\uf02d\uf044\uf02d\uf03d\uf02d\n\uf06d\uf062\n    (1) \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
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id: 6b88bcba-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 2, "chroma:document": "SPE 169539   3 \n \nWhere,  qi,max  =  injection rate in bbl/min  \nk  =  permeability of undamaged formation, md  \nh  =  net thickness, ft  \nFG  =  fracture gradient, psi/ft  \nD  =  depth, ft  \n\u0394psafe  =  safety margin, psi  \np  =  reservoir pressure, psi  \n\u03bc  =  viscosity of injected fluid, cp  \n\u03b2  =  formation volume factor  \nre  =  drainage radius, ft  \nrw  =  wellbore radius, ft  \ns  =  skin \n \n \n \n \nFigure 2 : Rate necessary to initiate a fracture at various reservoir permeabilities. Assumes a reservoir depth of 7000 ft, fracture \ngradient of 0.8 psi/ft,  normal hydrostatic pore gradient,  formation thickness  of 20 ft, and a water fluid system.  \n \nData resolution fo r the entire injection and falloff period is a critical co mponent. Common pumping gauge resolutions of \n5-10 psi are not adequate for DFIT acquisition , since the intent of the treatment is look for subtle variations in the derivative"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88bd1e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 2, "chroma:document": "5-10 psi are not adequate for DFIT acquisition , since the intent of the treatment is look for subtle variations in the derivative \nof the pressure versus time. Low resolution gauges can miss th ese data and render the test unusable . It is recommended to use \ngauges that have a resolution of at least 0.01 \u2013 0.10 psi, with a sampling rate of one measurement per second during the \npumping period  and through fract ure closure . This sampling rate can then be expanded during the falloff period after closure . \nDuring the post-closure falloff period, a sampling rate of up to one measurement every 30 seconds is adequate  and achievable \nwith appropriate gauge memory systems . \nTwo k ey parameter s in the analysis of a DFIT  is the time and volume of injection  (Barree, et al, 2009; Barree, 1998) , \ntherefore, the injection schedule  must be recording precisely. Ideally, it is measured digitally in conjunction with the pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88bd6e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 2, "chroma:document": "therefore, the injection schedule  must be recording precisely. Ideally, it is measured digitally in conjunction with the pressure \nduring the injection period, however, if this is not possible or is not done, extremely detailed notes must be kept that detail \nthe pumping start/stop times and any rate changes  and times of such made during the procedure . If the data are recorded in \ndetail, a rate schedule can then be recreated during analysis.  \nFluid selection for the treatment is a common question \u2013 what is the best option? In general, a Newtonian, non -wall \nbuilding fluid should be used. This is one area that differs significantly from traditional mini -fracs, which commonly inject \ngelled or other non -Newtonian fluid systems , specifically to measure fluid efficiency . For DFIT purposes, water, diesel, or \nsome other type of non -wall building fluid should be u sed. The reason for t his is demonstrated by Figures 3 -5. Figure 3"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88be5e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 2, "chroma:document": "some other type of non -wall building fluid should be u sed. The reason for t his is demonstrated by Figures 3 -5. Figure 3  \ndemonstrates t he conventional fluid loss model as a one -dimensional solution for linear transient flow with constant pressure \nboundary conditions. The f luid pressure at the fracture face is assumed constant with time and the far -field pore pressure is \nassumed to be constant. Initially the pressure gradient, and the associated leakoff rate, is very high. With time, the transient \nmoves further into the reservoir and the g radient (and rate) decr ease. This solution shows  rate decreasing linearly with the \nsquare -root of time.  \n0.0000010.000010.00010.0010.010.1110100\n0.0001 0.001 0.01 0.1 1 10 100 1000\nPermeability (md)Rate (BPM)Downloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88beb8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 3, "chroma:document": "4  SPE 169539  \nFigure 4  then shows leakoff  modeled as a combination of series flows. The figure roughly describes a high permeability \nfar-field reservoir zone, a near -fracture invaded zone,  and a thin wall filter -cake zone. In series flow , the total pressure drop \nthrough the system is the sum of the pressure drops through each zone. Using Darcy\u2019s Law  in linear fashion , each pressure \ndrop can be determined from the length and permeability of each zone. When even a thin film of very high flow resistance is \npresent, such as the filter -cake, the flow capacity of the least conductive region dominates the system. When this filter -cake is \ndeposited on a  fracture wall, as demonstrated in Figure 5 , most of the pressure drop is taken across the filter -cake during \nleakoff. The far -field pressure grad ient is much less than expected  when compu ted based on the leakoff rate, and t he after -"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88bf08-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 3, "chroma:document": "leakoff. The far -field pressure grad ient is much less than expected  when compu ted based on the leakoff rate, and t he after -\nclosure analysis yields an estimate of reservoir flow capacity , i.e. k h, that is much too high and is inconsistent with the \nobserved closure time.  \n \n \n \nFigure 3 : Conventional fluid loss model as a one -dimensional solution for linear transient flow with constant pressure boundary \nconditions . \n \n \n \n \nFigure 4 : Leakoff  modeled as a combination of series flows  for permeabilities of 100 md, 1 md, and 0.001 md.  \n \n \n \nFigure 5 : When a filter -cake is deposited on a fracture wall most of the pressure drop is taken across the filter -cake during leakoff  \nunlike that shown in Figure 3 which de monstrates the pressure drop in an undamaged system.  \n \nAs a last acquisition component , isolation of the wellhead after pumping ends is required in order to eliminate any"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88bf62-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 3, "chroma:document": "As a last acquisition component , isolation of the wellhead after pumping ends is required in order to eliminate any  \ninadvertent pressure transients that might be caused by mechanical or logistical issues. Since DFIT analysis uses derivatives, \nany large changes or \u201cbumps\u201d in press ure, can inadvertently alter, invalidate the test , or render it impossible to analyze . Any \npressure bleedoff that might occur during rig -down  can render the test useless. Likewise, if pressure measurements are being \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88bfb2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "SPE 169539   5 \nacquired using long-term gauges that will remain in place after the pumping equipment is removed, care must be taken during \nother r outine field operations that these  gauges are not disturbed in any way.  \n \n \nComm on Acquisition Issues  \nAs noted above, a DFIT consists of i nject ing water or other clean fluid above fra cture extension pressure, creating  a stable \nfracture geometry, shut ting down injection and watch ing the pressure decay to evaluate leakoff mechanism and find fracture \nclosure, and then evaluating  the after-closure pressure decline using appropriate reservoir transient solution s. If any of these \nsteps are compromised during acquisition of the data, the data c an be unusable. This section discusses common acquisition \nissue s. \nAs noted in the previous section and shown in Figures 3 -5, it should be stressed that a Newtonian, non -wall building fluid"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c00c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "issue s. \nAs noted in the previous section and shown in Figures 3 -5, it should be stressed that a Newtonian, non -wall building fluid \nmust be used  when pumping the treatment , if any reservoir propertie s are to be obtained from the analysis . Using gelled or \nother non -Newtonian fluids can disrupt the after -closure pressure gradient and ma sk the reservoir flow capacity. Another  \ncommon issue that is also a  holdover from old style mini -frac treatments is the use of multiple pump -ins. DFIT\u2019s should be \nconsidered  as \u201cone and done\u201d. If the treatment is not pumped correctly the first time, a second attempt is almost pointless, as \nthe reservoir conditions have now been altered by the first injection and , in low pe rmeability systems , the created pressure \ntransients will not have dissipated by the time the second attempt is usually made.  The assumptions required for valid"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c05c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "transients will not have dissipated by the time the second attempt is usually made.  The assumptions required for valid \nanalysis of a pulse test do not allow for superposition of multiple injections.  A second attempt can possibly be made if the \nfirst attempt was not too invasive, however, remember that the pressure transient may take days if not weeks to fully \ndissipate.  \nNot acquiring falloff data for a long enough period is also a com mon acquisition is sue. Specifically h ow long to plan on \nletting the falloff period be recorded for different reservoir types is disc ussed in following sections of this paper, however, it \nsuffices to say here that the time period will be longer than the pumping equipment wil l physically stay on location. \nTherefore, secondary gauges that remain after the pumping equipment is removed are generally required. A common issue"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c0b6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "Therefore, secondary gauges that remain after the pumping equipment is removed are generally required. A common issue \nwith these secondary, long -term gauges is that they are not opened to the wellhead when the treatment is pu mped. Since these \nsecondary gauge s are commonly calibrated to a slightly different level than the pump gauges, if the two data sets are \noverlapped there will often be a  difference in the readings . Since the analysis of DFIT\u2019s calls for pressure derivatives , any \ndifference in readings will show as a slope change and will provide false indications of reservoir conditions on the analysis . \nThe secondary long -term gauges must be opened to the wellhead during the pumping period also to eliminate this issue.  In \nany case, accurate calibration of all pressure gauges should be tested and assured.  \nAdditional field operational issues that can cause acquisition problems are frozen  or temperature -affected  wellheads and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c106-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "Additional field operational issues that can cause acquisition problems are frozen  or temperature -affected  wellheads and \noffset reservoir interruptions. Pre cautions should be  taken for wells in winter conditions to prevent freezing of the surface \ngauges. Even if the gauges don\u2019t fully freeze, temperature fluctuations can impact the pressure readings, therefore, insulati ng \nthe wellheads during the falloff periods is often helpf ul to prevent these pressure movements. Thermal fluid expansion or \ncontraction in the wellbore will affect bo th surface and down -hole gauges.  Some people assume that a down -hole gauge will \nbe in a constant temperature environment, and will therefore not be  affected. In a low compressibility fluid -filled wellbore the \ncoefficient of thermal expansion, coupled with density driven convection currents, will still cause a pressure change \nthroughout the wellbore volume ."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c156-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "throughout the wellbore volume . \nAgain, the behavior of pressure transients i s critical to that analysis of the treatment \u2013 if the pressure changes are caused \nby anything but the reservoir  and fracture response , the treatment can provide false readings. This is also the case if the \nreservoir itself is upset by any pressure changes such as pumping offset hydraulic fracturing treatments. A quiet environment \nin both the surface and downhole environments is needed for optimal data acquisition.  \nOne final acquisition precaution relates to the step -down portion of the test. It is strongly recommended to use a step -\ndown test versus a step -up test for t he reasons displayed in Figure 6. Figure 6  shows the treating pressure for increasing rates \n(overlapped by the pink line) and then the treating pressure for decreasing rates. The hysteresis in the curve is obvious and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c1b0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "(overlapped by the pink line) and then the treating pressure for decreasing rates. The hysteresis in the curve is obvious and \nindicates that during the initial rate increase period, the wellbore is still experiencing breakdown periods and changes in t he \noverall net pressure and fracture extension period.  In many cases, the number of perforations open to i njection changes with \neach increase in pump rate. The step -down period does a better job of measuring the frictional change information that is \ndesired rather than the complexity of friction and fracture extension components combined.  \n \n \nCommon Analysis Mis takes  \nIn addition to the acquisition issues previously mentioned , there are also several common analysis mistakes after the DFIT \ndata is acquired. The following sections discuss some of these more common errors and ways that they can be avoided (if \npossibl e). \n \nIncorrect ISIP Determination"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c200-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "possibl e). \n \nIncorrect ISIP Determination  \nAnalysis of a pressure falloff begins with determination of the instantaneous shut -in pressure (ISIP). This value is taken to \nrepresent the fracture extension pressure, when corrected to bottomhole conditions, and the frac ture extension gradient. The \ndifference between the ISIP and determined closure pressure is taken as the net pressure in the fracture, or as a measure of the Downloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c25a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 5, "chroma:document": "6  SPE 169539  \nresistance of the rock to facture extension, or process -zone stress  (PZS) . Since net pressure dete rmines fracture width, and to \na large degree height (due to the expectation that confining stress contrast controls containment) the accurate determination  of \nISIP is critical to any later analysis and fracture geometry modeling.  \n \n \nFigur e 6: A step -rate analysis chart showing increasing rate (step -up) measurements versus decreasing rate (step -down) \nmeasurements. Note the hysteresis exhibited between the two curves.  \n \n \nIn many cases the ISIP is not obvious, and does not occur immediately after shut-in. When a substantial near -well \npressure drop exists, either through poor perforation efficiency or, more commonly, high near -wellbore tortuosity, injection \nat the fracture entrance may not stop for some time after the surface injection stops. The am ount of continued injection after"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c2aa-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 5, "chroma:document": "at the fracture entrance may not stop for some time after the surface injection stops. The am ount of continued injection after \nshut-in, the amount of excess frictional pressure that must dissipate, and the time required for decompression of the wellbore \nfluids depends on the severity of the near -well restriction to flow and the compressibility of the wellbore volume.  \nFigure 7 shows a fairly extreme case with an apparent ISIP of about 3640 psi at surface. The pressure falls nearly 1800 psi \nin the first few minutes after shut -in, with an injection rate of only 4 bpm. This DFIT was conducted through perforations in \nthe toe of a cemented horizontal well. Inside diameter of the pipe was 4.0 inches and total depth of the well was \napproximately 15,000 feet. The wellbore was filled with fresh water for the test. Before any meaningful analysis can be done,  \nan ISIP must be selected somewhere between 3640 psi and 1750 psi. If a value significantly below the pressure at shut -in"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c2fa-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 5, "chroma:document": "an ISIP must be selected somewhere between 3640 psi and 1750 psi. If a value significantly below the pressure at shut -in \n(3640 psi) is used, the excess pressure drop must be explained.  \n \n \n \n \n \nFigure 7 : Rate and pressure chart for a test with extremely high entry friction . \n20002500300035004000450050005500\n0 5 10 15 20 25 30 35 40\nPump rate, bpmTreating Pressure, psi\nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c354-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 6, "chroma:document": "SPE 169539   7 \n \nTotal compressibility of the wellbore described can be estimated from the water compressibility (3.0e -6/psi) and wellbore \nvolume (233 bbl). Expansion of the pipe should also be considered. Using the thi n-walled cylinder equation (Eq. 2 ), the \nchange in volume of the wellbore can be estimated, where d is the pipe diameter, t is the wall thickness, p is the internal \npressure change, and E is the modulus of the steel (30.0e6 psi).  \n \nd\ntEpd\uf044\uf03d\n22\n     (2) \n \nWhere,  p  =  internal pressure  change, psi  \nd  =  pipe diameter, in  \nt  =  wall thickness, in  \nE = modulus of steel, psi  \n \nCombining the water and pipe compressibility, the pressure of the fluid in the wellbore will change by approximately \n1170 psi for every 1 bbl of volume change. This re lationship can be used with an estimate of pressure drop due to tortuosity, \nassuming a square -root of rate linear relation, to estimate the frictional pressure drop driven by fluid expansion, and the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c3a4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 6, "chroma:document": "assuming a square -root of rate linear relation, to estimate the frictional pressure drop driven by fluid expansion, and the \nexpansion rate after shut -down. With an injection rate o f 4 bpm at shut -in, a frictional pressure drop of 1940 psi result s from \na tortuosity factor of 970 psi/ \uf0d6(bpm). In the first second after shut -in, this rate decreases the wellbore volume by 0.0667 bbls, \ncausing the pressure to drop from 3640 to 3562 psi. As  the fluid continues to expand, the injection rate drops, and the inlet \nfrictional pressure decays. Figure 8  shows a plot of the pressure decay computed from this simple relation, compared to the \nobserved pressure decline in the test.  \n \n \n \nFigure 8 : Actual  (thin blue line)  and computed  (thick blue line)  pressure decay after shut -in, accounting for near -well tortuosity and \nwellbore decompression . \n \nThe thin blue line is the  measured surface pressure for the test and the heavy line is the computed wellbore pressure with"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c3fe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 6, "chroma:document": "The thin blue line is the  measured surface pressure for the test and the heavy line is the computed wellbore pressure with \nthe frictional pressure drop calculated from a constant tortuosity factor. The injection rate declines from 4 bpm at the inst ant \nof shut -in to 1.0 bpm after 2 5 seconds, and finally to less than 0.05 bpm after 200 seconds. Perforation pressure drop and \nother  factors are ignored in this analysis. The main point is that wellbore storage and decompression can drive injection after \nshut-in for a long time, in excess  of several minutes, and can account for large pressure drops. With large wellbore volumes, \ntypical of extended reach horizontal wells and larger pipe sizes, this effect becomes more pronounced. Any gas or more \ncompressible fluid in the wellbore will exten d the blow -down period even longer.  \nNow that the source and duration of the early pressure  decay is accounted for, what is the actual representative ISIP? One"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c44e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 6, "chroma:document": "Now that the source and duration of the early pressure  decay is accounted for, what is the actual representative ISIP? One \nmethod that can help is to extrapolate the pressure versus log of time curve, as shown in Figure 9, back to the point of shut -in. \nThis construction suggests that some effect of wellbore fluid expansion may be felt for as long as 18 minutes after shut -in, \nand gives an estimated effective ISIP of 1766 psi. This may be a lower -bound of ISIP, but is a goo d starting estimate.  \n \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c4a8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 7, "chroma:document": "8  SPE 169539  \n \n \nFigure 9 : Extrapolation of the pressure versus log time to approximate ISIP . \n \nThe validity of the ISIP estimate can often be verified by examination of the log -log plot of pressure change from the \nassumed ISIP after shut -in and th e semi -log derivative of the pressure difference curve versus shut -in time. This plot, shown \nin Figure 10 , should produce parallel lines of the pressure difference (blue Delta Pressure) and derivative (red) during the pre -\nclosure period. The magnitude of t he derivative should be the pressure difference multiplied by the slope of the derivative \ncurve. In the example, when the pressure difference curve is 300 psi at closure and the derivative is roughly 0.28 (the slope ) \ntimes that value. Note that any change to the estimated ISIP value will move the pressure difference curve but will have no \neffect on the derivative curve slope or position on the plot. When a stable linear derivative is apparent through the pre -closure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 7, "chroma:document": "effect on the derivative curve slope or position on the plot. When a stable linear derivative is apparent through the pre -closure \ndata, this method provides an effective f inal check, but is not always infallible.  \n \n \n \nFigure 10 : Log -log plot of pressure difference and derivative versus time . \n \nBasic Selection of Closure  \nBasic DFIT analysis should be covered in sufficient detail in SPE 107877 (2009), but some mistakes in the most basic \ninterpretation of the G -function diagnostic semi -log derivative continue to be made by many analysts. Figure 11 shows a \nDFIT with variable fracture compliance, or storage during closure, where the closure time and pressure have been mistakenly \ndiagnosed.  In the original  analysis the clo sure time and pressure were identified by the positions of the red lines, at a closure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c552-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 7, "chroma:document": "diagnosed.  In the original  analysis the clo sure time and pressure were identified by the positions of the red lines, at a closure \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c5a2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 8, "chroma:document": "SPE 169539   9 \ntime of G=14 and P=3960 psi. The correct closure time is G=32 and P=3640 psi. This discrepancy wi ll obviously affect any \ninterpr etation of closure stress for calibration of a geomechanical model or stress profile, and will impact estimates of \nformation flow capacity and post -frac production. The red arrows in Figure 11 indicate other incorrect closure events that are \noften selected  by mistake. The one correct closure event is shown by the blue arrow, after the end of the variable compliance \nand linear closure periods. The error in closure stress also leads to an error in the interpretation of fracture net extensio n \npressure. This af fects the predicted width of the fracture, and therefore directly impacts the computed fracture length, through \nconservation of injected volume. Predicted fracture height may also be affected, depending on the strength and stress of the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c5fc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 8, "chroma:document": "conservation of injected volume. Predicted fracture height may also be affected, depending on the strength and stress of the \nconfining layers. I n short, if the wrong analysis results are applied to the calibration of any fracture design model, the results \nwill be incorrect.  \n \n \nFigure 11: G -Function  derivative plot for variable compliance during closure, with incorrect closure picks.  \n \n \nEffect of Injection Time versus Pump Rate  \nAssuming a high enough injection rate is used so that the rock is dilated to its ultimate capacity, the width of the fracture  \nwill be determined by the net pressure generated, modulus of the rock, and some characteristic dim ension of the fracture. The \ntheoretical basis of the G -function analysis assumes that the fracture adheres to Perkins -Kern -Nordgren geometry \nassumptions (Nolte, 1979). While this assumption is not necessarily valid, it implies that the generated fracture h eight will be"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c64c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 8, "chroma:document": "assumptions (Nolte, 1979). While this assumption is not necessarily valid, it implies that the generated fracture h eight will be \nthe controlling dimension. This leads to a somewhat circular argument as net pressure, which is  proportional  to fracture \nwidth, and fracture compliance (H/E) are directly linked in this model. A confined height, for a constant modulus, means the \nnet pressure must be higher for a given frac width. A higher net pressure implies the ability to break through more barriers \nand possibly generate more fracture height, thus increasing compliance. The system should stabilize at an equilibrium \nfracture height, width, and net pressure for a given injection rate and fluid system.   \nFor a DFIT to be valid , an injection rate must be selected that will generate a net pressure and fracture geometry that is \nrepresentative of the main frac. In practical terms, that means that the highest possible injection rate for the test will le ad to"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c69c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 8, "chroma:document": "representative of the main frac. In practical terms, that means that the highest possible injection rate for the test will le ad to \nthe most representative r esults. Once a stable net pressure and fracture geometry is achieved, a higher injection rate will cause \nthe fracture to grow faster, but should not alter the width or height significantly. This assumption deviates from the classi cal \nPKN assumptions wherei n all net pressure is generated solely through frictional pressure gradient of the moving fluid. More \nrealistic analysis of DFIT results requires that there be some resistance to fracture propagation inherent in the rock. This has \nbeen referred to as \u201cproc ess zone stress,\u201d \u201cfracture toughness,\u201d \u201crock strength,\u201d and by other names, although each carries \ncertain different connotations regarding the mechanism of resistance to fracture growth. A very low injection rate will"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c6f6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 8, "chroma:document": "certain different connotations regarding the mechanism of resistance to fracture growth. A very low injection rate will \ndevelop less net pressure, therefore less fracture height and width, and will not strain the rock to its ultimate limit. This can \nresult in missing the evolution of secondary shear fractures  that can affect compliance, leakoff rate, and system permeability. \nThe original theoretical models ass umed the rock to be linearly elastic and homogeneous, with no consideration that shear \nfailure could exist.  \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c750-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 9, "chroma:document": "10  SPE 169539  \nAssuming a stable net pressure and fracture geometry are achieved, the fracture volume to surface area, or fracture width, \nwill remain constant for  any duration of injection. That implies that a fracture with height of 50 feet and length of 300 feet \nwill close in the same time as a fracture 50 feet tall and 600 feet in length , as long as leakoff flux per unit area is the same in \nboth cases . For this reason the time to closure is not a function of injected volume, and is insensitive to rate as long as a high \nenough rate is achieved to reach a stable failure and fracture propagation condition. In fact, time to closure is a function of \npumpi ng time and n ot volume injected.  \nThe theoretical calculation for time to closure depends on the integration of the leakoff rate through  each ele ment of the \nfracture face as it s being created, and during the closure process. For single -phase flow, with no damage to the face of the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c7a0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 9, "chroma:document": "fracture face as it s being created, and during the closure process. For single -phase flow, with no damage to the face of the \nfracture (such as a gel filtercake), the leakoff rate through each element of fracture face should decrease linearly with the  \nsquare -root of time since exposure of the face element.  For a slow injection rate each element of the face of the fra cture is \nexposed for a longer time, so the leakoff rate from the total fracture face will be much slower at shut -in than for the high rate \ninjection case.  \n \n \nFigure 1 2: Pressure transients established by low rate (A) and high rate (B) injection.  \n \nFigure 1 2 shows conceptually the radius of investigation of the leakoff pressure transients at three times for a low rate (A) \nand high rate (B) injection scenario. The center point  represents the wellbore or point of fracture initiation. The inner set of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c7fa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 9, "chroma:document": "and high rate (B) injection scenario. The center point  represents the wellbore or point of fracture initiation. The inner set of \npoints re present the fracture half-length  for some point near the middle of the injection period. In case A , the pressure \ntransient has penetrated a much larger distance into the formation , due to the longer injection time at low rate,  and the leakoff \nrate is much lower than in case B. In the case B example, the same fracture length is reached at a much shorter injection time \nso the pressure transient cannot travel as far from the fracture face, and leakoff rate is faster than in case A. The second set of \npoints rep resents the fracture position at the end of injection. In case A , the pressure transients along the length of the fracture \nhave travelled a greater distance into the formation, leakoff rate through each element of fracture surface is much lower"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c85e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 9, "chroma:document": "have travelled a greater distance into the formation, leakoff rate through each element of fracture surface is much lower \n(following the square -root of time function), and therefore time to reach closure is significantly longer than in case B. In the \nhigh rate case, the entire fracture length is established with a short time of exposure o f all elements of the fracture surface and \nleakof f rate through each element remains high.  \nFor the same injected fluid volume the fracture of case B may be slightly longer than the case A fracture, but the \ndifference is not linear with rate. In case B , the leakoff rate is higher throughout the injection  period but the fluid efficiency is \nalso higher. All this assumes a similar net pressure and fracture compliance in both cases A and B .  \nA second result of the impact of rate is apparent from Figure 12. In the low rate (case A) condition, the pressure tran sient"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88c994-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 9, "chroma:document": "A second result of the impact of rate is apparent from Figure 12. In the low rate (case A) condition, the pressure tran sient \nat closure, represented by the outer ellipse, has reached a nearly pseudo -radial flow case very quickly after closure. In case B \nthe transient remains in pseudo -linear flow for a very long time after closure. For this reason many people, generally th ose \nconcerned with application of classical pressure transient theory, recommend very low injection rates. This recommendation \nis based solely on the desire to establish a pseudo -radial flow period within a practical test duration. Unfortunately, in the re al \nworld where rocks are not isotropic, homogeneous, and linearly  elastic, with no  inherent resistance to fracture growth, the use \nof a very low injection rate makes the test essentially useless for fracture diagnostics. These tests seek to approach a matr ix"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ca3e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 9, "chroma:document": "of a very low injection rate makes the test essentially useless for fracture diagnostics. These tests seek to approach a matr ix \ninjection/falloff test and should not be considered  as valid diagnostic  fracture injection tests as the information critical to \nfracture design will all be compromised. Another failing of the low rate test is that the height of the zone contacted will r arely \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cac0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 10, "chroma:document": "SPE 169539   11 \n(in the real world that means effectively never) be the perforated p ay height. Therefore any permeability or even KH estimate \nwill probably not match post -frac production.  \n \nSize of Generated Fractures  \nMost people consider a short -duration fracture injection test to be too small to effectively evaluate enough reservoir \nvolume to be applicable for post -frac production . Figure 1 3 shows the estimated fracture  half that would be generated for a 30 \nfoot fracture height, with a fracture width of 0.1 inches, given 100% fluid efficiency. These may seem to be arbitrary input \nassumpt ions, but are reasonable for water injection in \u201ctypical\u201d rocks of 3 -4 million psi Young\u2019s Modulus with a net pressure \nof 1000 psi and very low system permeability. The estimated fracture length can be directly multiplied by fluid efficiency to  \ncorrect for  leakoff in higher permeability systems, and corrected by the ratio of created to assumed fracture height, if it is \nknown."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cb42-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 10, "chroma:document": "correct for  leakoff in higher permeability systems, and corrected by the ratio of created to assumed fracture height, if it is \nknown.  \n \n \n \nFigure 1 3: Fracture half -length created as a function of pumping time and rate . \n \nNote that for the recommended rate of 10 bpm, a pumping time of 5 minutes generates a fracture half -length of more than \n600 feet, when leakoff during the 5 -minute injection period is negligible. This is very likely the case in a shale or ultra -tight \nsand or carbonate reservoir s. Extending the pumping ti me to 10 minutes increases the created length to almost 1200 feet and \nincreases the time to closure by increasing the average exposure time of all fracture face elements. Clearly, in tight rocks,  \nthese are not \u201csmall\u201d fractures and the formation surface ar ea exposed is statistically significant. For the 5 -minute, 10 bpm \ninjection case , the surface are a of one of the four fracture wing faces exposed is 18,000 square feet."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cb9c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 10, "chroma:document": "injection case , the surface are a of one of the four fracture wing faces exposed is 18,000 square feet.  \n \nDesign of Test Duration  \nLonger pumping times allow more time for penetration of the i nduced pressure transient. Given a stable fracture \ngeometry, the time required to close the fracture by leaking off a fixed volume to surface -area ratio of fluid in the fracture can \nbe related to the system permeability. A good approximation for time t o closure is given in Equation 3 : \n \nkttp\nc3\uf03d\n     (3) \n \nWhere,  tc =  time to fracture closure, min  \ntp =  pumping time, min  \nk =  permeability of leakoff system, md  \n \nWhere t c is the time to reach fracture closure (minutes), t p is the pumping time (minutes), and k is the permeability of the \nleakoff system connected to the fracture face, including any secondary permeability enhancement due to induced shear fa ilure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cbf6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 10, "chroma:document": "leakoff system connected to the fracture face, including any secondary permeability enhancement due to induced shear fa ilure \nof the host rock. Figure 1 4 is a plot of the estimated closure tim e for pumping times of 2 to 20 minutes ove r a range of system \npermeabilities  from 100 nano -darcies (0.0001 md) to 1 md. For convenience the time scale has been converted to hours of \nshut-in.  \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cc50-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 11, "chroma:document": "12  SPE 169539  \n \n \n \nFigure 1 4: Approximate time to reach fracture closure for va rious pumping times . \n \nNote that for a 5 -minute injection period into a 0.1 md formation, fracture closure occurs in about 0.2 hours (12 minutes). \nIn these moderately high permeability formations, where this technique was first applied, extending the pumpin g time may \nnot be a serious concern. For this 0.1 md rock, a pump time of 20 minutes will still reach fracture closure in about one hour  of \nshut-in time. Note that for higher permeability formations closure can happen too quickly to be easily identified wh en other \nfactors such as wellbore friction and compressibility are considered.  \nAt 0.01 md, the 5 -minute pumping time requires 2 -3 hours to reach closure. For a 0.001 md formation, which is not \natypical for what are considered commercial tight silt or shal e reservoirs, closure can take up to 24 hours after a 5 -minute"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cca0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 11, "chroma:document": "atypical for what are considered commercial tight silt or shal e reservoirs, closure can take up to 24 hours after a 5 -minute \ninjection. If the system permeability is actually in the 100 -nano -darcy range, closure can take up to ten days following a 5 -\nminute injection. When system permeability is this low , the created fracture length will be large, and the pressure transient \nestablished at closure will remain in a pseudo -linear flow regime for a very long time.  \nOnce the fracture has closed, some time is required for a stable reservoir transient flow regime to be establ ished. On a log -\nlog plot of pressure change versus shut -in time, a safe and realistic lag time is \u00bd of a log cycle in time after closure. That \nroughly means that no data should be analyzed for any reservoir flow regime, including pseudo -linear flow, until three times \nthe closure time has elapsed. So, using the 0.01 md, 5 -minute injection case, allow 2 -3 hours for closure and 6 -9 hours after"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ccfa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 11, "chroma:document": "the closure time has elapsed. So, using the 0.01 md, 5 -minute injection case, allow 2 -3 hours for closure and 6 -9 hours after \nshut-in to the start of a valid reservoir flow regime. For the 0.001 md case, that is 24 hours to closure and 3 days o f shut -in \nfor any useful reservoir information.  \nA goo d example of the time lag required to reach a stable reservo ir transient  is shown in Figure 1 5. After some non -linear \nleakoff behavior (including some mechanical noise in the data), there is an obvious break in the semi -log derivative curve  at \nthe closure time of 52 minutes after shut -in.  The derivative continues to curve until the first indication of a valid reservoir \npseudo -linear flow transient, at about 185 minutes after shut -in. The derivative cont inues to steepen, and approaches a \nnegative unit slope that some may be tempted to analyze as a pseudo -radial reservoir flow regime. For the purposes of this"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cd4a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 11, "chroma:document": "negative unit slope that some may be tempted to analyze as a pseudo -radial reservoir flow regime. For the purposes of this \ndiscussion, the important consideration is that any reservoir transient must take time to develop.  Expecting a sharp break in \nthe derivative curve immediately after closure to represent a reservoir flow transient is simply not reasonable.  \n \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cda4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 12, "chroma:document": "SPE 169539   13 \n \n \nFigure 1 5: Log -log pressure change versus shut -in time plot showing closure and start of pseudo -linear flow.  \n \nIf we follow the assumptions for the PKN fracture geometry, and assume that linear transient flow governs fracture \nleakoff flow up until closure, then the time required for the induced pressure transient to establish a pseudo -radial flow \nregime can be comp uted from the definition of t Dxf. For pseudo -radial flow , a value of t Dxf = 1.0  (at least)  must be reached i n \nthe falloff period. Equation 4  gives the time, in hours, to reach pseudo -radial flow (t pr) as a function of reservoir storativity, \npermeability, and fracture length.  \n \nktxCtDxfft\npr0002637.02\uf066\uf06d\uf03d\n     (4) \n \nWhere,  tpr =  time to reach pseudo -radial flow, hours  \n\u03c6 =  porosity, fraction  \n\u03bc = fluid viscosity, cp  \nCt = total reservoir compressibility, 1/psi  \nxf = fracture half -length, ft  \nk =  permeability of leakoff system, md"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cdf4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 12, "chroma:document": "Ct = total reservoir compressibility, 1/psi  \nxf = fracture half -length, ft  \nk =  permeability of leakoff system, md  \n \n \nEquation 4  has been solved for t Dxf=1 for a gas reservoir case with viscosity of 0.02 cp, porosity of 8%, and total reservoir \ncompressibility of 3.0e -5/psi. The time, in days, require d to reach the fully developed pseudo -radial flow period, according to \nthese a ssumptions, is shown in Figure 1 6. Daltaban and Wall (1998) suggest that pseudo -radial flow may not be identified \nuntil t Dxf=2 for an infinite conductivity fracture, or t Dxf=3 fo r a uniform flux fracture.  The assumptions used in Figure 1 6 are, \ntherefore, somewhat optimistic.  \nConsider a moderate permeability DFIT in a 0.1 md systems with a pump time of 5 minutes at 10 bpm. The generated \nfracture will close in about 15 minutes and have a fluid efficiency of about 50%. According to Figure 13, the generated"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ce4e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 12, "chroma:document": "fracture will close in about 15 minutes and have a fluid efficiency of about 50%. According to Figure 13, the generated \nfracture half-length  would be approximately 300 feet, for a fracture height of 30 feet (the default assumed height in the plot). \nUsing the rule of thumb for start of after closure analysis, a pseudo -linear transient may develop in about 45 minutes after \nshut-in. If the created f racture is planar, constant height, and follows the assumptions for a homogeneous system permeability \nunder li near flow during closure, Figure 16 shows that a pseudo -radial flow regime should theoretically not be established \nuntil 2 -3 days after shut -in.  \n \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cea8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 13, "chroma:document": "14  SPE 169539  \n \n \nFigure 16: Time, in days, to theoretically reach pseudo-radial reservoir transient flow conditions for a gas reservoir for various \nsystem permeabilities. \n \nConducting the same analysis with a 0.001 md system permeability leads to a predicted closure time of 27 hours, start of \npseudo-linear flow after 83 hours, or 3.5 days, and start of pseudo-radial flow after about 1000 days of shut-in for a created \nfracture half-length of about 500 feet (83% efficiency). This implies that expecting pseudo-radial flow behavior in a DFIT in \nunconventional reservoirs is unreasonable. No combination of pump rate and pumping time will establish a stable fracture \ngeometry and result in stabilized pseudo-radial flow in a practical test duration with system permeability less than about 0.01 \nmd. Attempting to induce early onset of pseudo-radial flow by conducting the test at very low rate, or very short duration,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cef8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 13, "chroma:document": "md. Attempting to induce early onset of pseudo-radial flow by conducting the test at very low rate, or very short duration, \ncompromises the geometry of the fracture and the validity of any data associated with fracture extension criteria. If a test is to \nbe conducted as an injection/falloff test for reservoir properties, then it should not be confused as a diagnostic of fracture \nextension or closure conditions. Low rate, and small volume tests are then compromised by the inability to achieve \nbreakdown of many perforations or uniform injection over a predictable formation height. \nWhy do some DFITs appear to enter a pseudo-radial flow period, based on the negative unit slope of the semi-log \nderivative on the log-log pressure-time plot, or based on the after-closure flow regime analysis plot? The most plausible \nanswer is that fractures do not adhere to the simple planar geometry of a PKN fracture that is assumed in the derivation of the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cf48-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 13, "chroma:document": "answer is that fractures do not adhere to the simple planar geometry of a PKN fracture that is assumed in the derivation of the \nG-function equations and the conventional after-closure solution of the diffusivity equation. A more likely, or at least \nplausible, image of the fracture system created in an unconventional reservoir is shown in map view in Figure 1 \u001a.  \n \n \n \nFigure 1\u001a: Complex, non-planar, fracture system with coalescing transient pressure fields. \n \nIf a complex, non-planar fracture system develops during injection, leakoff will occur through each face of all fracture \nstrands. Even with high volumetric fluid efficiency, the primary fracture will be much shorter than predicted for a planar \nfracture, as shown in Figure 12, and normally assumed in theory. Time to closure, based on the G-function, will be"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cfa2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 13, "chroma:document": "fracture, as shown in Figure 12, and normally assumed in theory. Time to closure, based on the G-function, will be \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88cff2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 14, "chroma:document": "SPE 169539   15 \nproportional to the overall surface area to fracture volume ratio at shut -in, whether the fracture is planar  or not. For this \nreason, the permeability estimated from the G -function closure time, and given in Barree et al, 2009,  is a reliable estimate of \nthe permeability of the system contacted by the induced fracture(s). The leakoff rate will be affected slightl y by the \noverlapping of the transient pressure envelopes around each fracture, but time required to leak off the fluid volume in the \nfracture system should be related to net pressure and system flow capacity or permeability. Some crossflow between fracture  \nstands opening against different normal stresses should be expected. This can lead to the variable storage signature seen  in G-\nfunction derivative analysis. Low compliance in the fracture systems coupled with a large exposed surface area can also lead"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d07e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 14, "chroma:document": "function derivative analysis. Low compliance in the fracture systems coupled with a large exposed surface area can also lead \nto the pressure -dependent permeability signature. Since both of these phenomena are commonly observed, it is reasonable to \nassume that complex fracture systems in unconventional reservoirs are common.  \nAs shut -in time progresses the overlapping transient pres sure envelopes with coalesce into what appears to be a more \nradial flow geometry, illustrated by the outer ellipse in Figure 16. As this pressure transient dissipates in to the far -field it will \nappear as a radial flow signature on the diagnostic derivativ e plots. However, this radial flow pattern does not conform to the \nassumptions inherent in the after -closure pseudo -radial flow solution. This solution is based on the assumption of a single \nplanar fracture with a transient evolving from a linear flow patt ern along the face of a single created fracture, which"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d0ce-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 14, "chroma:document": "planar fracture with a transient evolving from a linear flow patt ern along the face of a single created fracture, which \ntransitions to a radial flow pattern over a dimensionless time proportional to the assumptions in Equation 4 and Figure 12. \nThe net result is that an apparent pseudo -radial flow regime develops much fa ster than would be the case for a single planar \nfracture of equivalent fluid efficiency. Any transmissibility derived from the apparent pseudo -radial flow time function may \nbe orders of magnitude too high to represent the actual flow capacity of the reserv oir system. The problem and errors in \ninterpretation are compounded when the radial flow or Horner analysis techniques are applied when a true pseudo -radial flow \npattern does not exist at all.  \n \nPhase Segregation and Gas Entry  \nDuring the falloff period , while the well is sitting undisturbed, gas entry from the formation can occur.  For the ideal case"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d128-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 14, "chroma:document": "During the falloff period , while the well is sitting undisturbed, gas entry from the formation can occur.  For the ideal case \nof a sealed wellbore under isothermal conditions, the volume of the gas bubble remains constant as it rises. With no mass \ntransfer from the gas to the wellbore fluid, the moles of gas in the bubble remains constant, therefore its pressure remains \nconstant as it rises. If a single gas bubble floats from the perfs to the surface under these conditions , the surface pressure wil l \nrise to the original bottomhole press ure and the pressure at the perf oration s will double. In reality, leakoff from the well is not \nidentically zero, the increased pressure generated by the rising bubble causes an increase in leakoff rate, the gas temperatu re \ndecreases somewhat during transit , and some gas may dissol ve in the wellbore fluid, therefore,  a very small gas bubble"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d178-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 14, "chroma:document": "decreases somewhat during transit , and some gas may dissol ve in the wellbore fluid, therefore,  a very small gas bubble \nentering at the perforations can cause a large pressure upset  as demonstrated in Figure 1 8. Figure 1 9 shows the effects of gas \nentry on an actual treatment.  \n \n \n \nFigure 1 8: Schematic showing a gas bubble that enters from the perforations can generate increased pressures at it rises to the \nsurface.  \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d1d2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 15, "chroma:document": "16  SPE 169539  \n \nFigure 1 9: The complete data set for a long -term injection test in an over -pressured formation is shown. The minimum pressure \nrecorded at surface was 743 psi after 2.5 hours of falloff. The pressure increases after that time until about 9 hours of fal loff.  For \npurposes of analysis, the end of the valid data occurs before the minimum pressure point at 2.5 hours. The later pressur e rise is \ncaused by entry of small gas bubbles at the perforations which rise in the wellbore fluid column.  \n \n \nLoss of Hydrostatic Head  \nThe loss of the hydrostatic head effectively terminates a DFIT test. Bottomhole gauges can and are installed to acquire data in \ncertain circumstances, however, these will not aid in extending the test if the hydrostatic column starts to fall. In these cases, \nthe bottomhole gauge will record  the weight of the fluid standing above the gauge. The fluid column is supported by a  partial"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d254-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 15, "chroma:document": "the bottomhole gauge will record  the weight of the fluid standing above the gauge. The fluid column is supported by a  partial \nvacuum between the fluid level in the well and the sealed wellhead. The rate of fluid level fall is then controlled more by t he \nrate of vaporization of the wellbore fluid than the reser voir transmissibility. Figure 20 shows a typical pressure resp onse for a \nbottomhole gauge in a well with falling fluid level.  \nThe data for the first few hours of falloff accurately represent the ISIP and initial leakoff rate and closure of the fractur e. \nThe remaining data, covering about a week of shut -in, shows almost no change in the pressure on the gauge because the fluid \nhead  above the gauge is nearly constant. Analysis of this part of the pressure falloff will give no  useful reservoir or  fracture \ninformation. Figure 2 1 shows the log -log plot for this falloff, and provides a useful clue for identifying the falling fluid level"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d2a4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 15, "chroma:document": "information. Figure 2 1 shows the log -log plot for this falloff, and provides a useful clue for identifying the falling fluid level \ncase. As the fluid level begins to drop, the pressure deriv ative (magenta line in Figure 2 1) exhibits a large negative slope. \nOnce the fluid level in the well stabilizes, and begins to drop at a rate controlled by vaporization of the fluid at the surf ace, \nthe derivative assumes a positive, nearly straight -line, slope of about \u00bd. During this period , the fluid at the surface of the \nstanding column is effectively boiling (fluid pressure equals vapor pressure), and the heat of phase transformation causes th e \nfluid temperature to drop. This increases fluid density, driving a convection cell which replaces the colder surface fluid with  \nwarmer fluid from below. The important point here, is that analysis of the pressure -time data in this case cannot provide \nuseful r eservoir or fracture data."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d2f4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 15, "chroma:document": "useful r eservoir or fracture data.  \n \n \nFigure 20: Bottomhole gauge response with falling fluid level, or surface pressure on vacuum.  \n3/22/200322:00\n3/23/200300:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00\n3/23/200318:00\nTime0100020003000400050006000A\n0.00.51.01.52.02.53.03.5B Wellhead Pressure (psi) Slurry Rate (bpm)A B\nCustomer: Job Date: Ticket #:\nWell Desc: UWI:GohWin v1.6.3\n18-Dec-06 15:35\nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d344-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 16, "chroma:document": "SPE 169539   17 \n \n \n \nFigure 2 1: Log -log derivative an d pressure difference for a bottomhole gauge  with falling fluid level.  \n \nThere are three practic al ways to avoid this problem: f irst, use a fluid of low enough density so that hydrostatic wellbore \nhead is less than reservoir pressure. That can be achieved in some cases by using oil (a surface gauge can then be used) if t he \nreservoir is not badly unde r-pressured. Second, use a bottomhole gauge and bottomhole shut-in or isolation tool (that work s). \nThe example in Figures 20 and 2 1 was run with a bottomhole shut -in tool and memory gauge, but the shut -in tool leaked. The \nthird methods is to vent the wellh ead when the surface pressure drops to zero. This will allow the fluid level to fall to a \npressure in equilibrium with the reservoir. Fracture closure will often occur before the wellhead pressure drops to zero, and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d39e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 16, "chroma:document": "pressure in equilibrium with the reservoir. Fracture closure will often occur before the wellhead pressure drops to zero, and  \nthe closure time and pressure will be wi thin acceptable accuracy. After closure there will be an extended transient period as \nthe fluid level seeks equilibrium. After that, the pressure decay to reservoir conditions  will be analyzable, but all reservoir \ntransients will be delayed. Corrections ca n be made for the added injection volume in the after -closure calculations.  \n \nCommon Mistakes in After -Closure Analysis  \nThe following example is one of many and shows some extremely common mistakes in DFIT after -closure analysis. The \nexample is not intende d to disparage any particular software or analyst and identifying information about the specific test has \nbeen hidden or removed whenever possible. The test data were acquired with a botto mhole gauge and the test was pumped"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d3ee-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 16, "chroma:document": "been hidden or removed whenever possible. The test data were acquired with a botto mhole gauge and the test was pumped \nthrough the toe perforations in a horizontal well. Figure 2 2 (a and b) show the G -function diagnostic derivatives for the test , \ncomputed in two different software packages. The result s are essentially the same, with closu re pressures of 22.463 and \n22.419 MPa , respectively. The semi -log derivative shows variable storage and a long after -closure transient period. This part \nof the analysis is consistent across almost all software. The slight  difference in the value of G at cl osure may be due to slight \ndifferences in the computed pumping time.  \n \n \n  \n(a)                                                                                                  (b)  \n \nFigure 2 2: G-function diagnostic derivative plots from different software anal ysis systems ."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d448-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 16, "chroma:document": "Figure 2 2: G-function diagnostic derivative plots from different software anal ysis systems . \n \nOnce ISIP and closure are identified, the net extension pressure can be computed from the difference. In this ca se, the \nISIP is slightly different due to wellbore expansion effects of short duration. The next step in the analysis is the log -log plot \nof pressure change from IS IP versus shut -in time. Figure 2 3 (a and b) show these plots from the two analysis packages.  \n \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d4a2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 17, "chroma:document": "18  SPE 169539  \n \n(a)                                                                                             (b) \n \nFigure 2 3: Log -log pressure  change versus time after shut -in, with semi -log derivative . \n \nAfter the end of the variable storage period, and for a very brief time prior to closure, the plot in Figure 2 3(a) shows a \npositive \u00bd slope derivative corresponding to a linear fracture leakoff mechanism. After closure the derivative falls on a \nnegative slope that is slightly shallower than -1/2. Through the entire test , the flow regime does not develop into an ideal \npseudo -linear flow regime, and certainly shows no evidence whatsoever of a pseud o-radial f low regime. The plot in Figure \n23(b) identifies the late time slope at -1/2 (shown in the green text box), which is an approximation.  \nThe next step in the analysis should be to extrapolate the after -closure pressure decline to estimate reservoir  pore pressure."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d4f2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 17, "chroma:document": "The next step in the analysis should be to extrapolate the after -closure pressure decline to estimate reservoir  pore pressure. \nSince the pseudo -linear flow regime is not fully developed, the extrapolation of the Cartesian linear flow plot will probably \ngive a pressure estimate that is slightly too high. Use of the Cartesian radial flow plot i s not warranted at all.  Figure 2 4(a) \nshows the construction and extrapolation of the Cartesian linear flow plot, with an extrapolation to a pore pressure of 17.5 5 \nMPa. Figure 2 4(b) shows the construction and extrapolation of the Cartesian radial flow plot that was presented in t he other \nanalysis. This extrapolation gives a reservoir pore pressure of 18.03 MPa.  \n \n \n \n(a)                                                                                                  (b) \n \nFigure 2 4: Pressure versus linear and radial time functions for linear extrapolation to reservoir pore pressure ."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d542-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 17, "chroma:document": "Figure 2 4: Pressure versus linear and radial time functions for linear extrapolation to reservoir pore pressure . \n \nIn this case , the difference in the estimated pressure is probably insignificant (about 3%), although in many cases the \nsame error in flow regime identification can lead to pressure errors of up to 30%. A m ore serious  error develops if the wrong \nflow regime, and wrong pore pressure are used in the Horner or radial -flow solution for reservoir transmissibility. The best \nway to assure that the after -closure flow regime is correctly identified is to use the Tall ey et al (1999) log -log flow regime \nplot. This plot displays the difference between calculated bottomhole pressure and static reservoir pressure (p* or p i) as a \nfunction of the square of the linear -flow time function. Entering the wrong pore pressure chang es the shape and position of \nthe pressure difference curve, but does not alter the shape and position of the derivative curve."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d592-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 17, "chroma:document": "the pressure difference curve, but does not alter the shape and position of the derivative curve.  \nFigure 2 5 (a and b) show the two after -closure flow regime plots for the same test data. Figure 2 5(a) shows the plot using \nthe po re pressure estimated from the linear flow extrapolation. The straight line connecting the beginning and end of the \nassumed linear flow period has the required slope of \u00bd. Clearly the derivative falls on a significantly lower sl ope, which is \nconsistent with the slope of the  semi -log derivative in Figure 2 4(a). The pressure difference curve is forced to fall on the \u00bd \nslope and be separated from the derivative by approximately 2x because of the selection of the pore pressure value derived \nfrom the extrapol ation of the Cart esian linear flow plot (Figure 2 4(a)). \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d5ec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 18, "chroma:document": "SPE 169539   19 \n \n \n \n(a)                                                                                          (b) \n \nFigure 2 5: Log -log of well pressure minus static reservoir pressure versus square of the linear flow time function . \n \nFigure 25 (b) shows the plot with the pore pressure picked from the Cartesian radial flow extrapolation. This value forces \nthe pressure difference curve to approach a -1 slope, and to fall on top of the derivative curve. Clearly, the deriva tive is not on \na -1 slope, and is still, in fact, of a slope less than -1/2. There appears to be a consistent trend in the industry to force a \npseudo -radial solution out of a DFIT analysis, even when the data clearly show that no such flow regime exists. T he final \nresults of this error in flow regime identification, and the forcing of an imposed incorrect analysis is most obvious in the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d63c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 18, "chroma:document": "results of this error in flow regime identification, and the forcing of an imposed incorrect analysis is most obvious in the \ncomputed reservoir transmissibility. Figure 25(b) indicates an estimate permeability of more than 0.1 md, which is consist ent \nwith a transmissibility of more than 0.8 md -m/cp. These results can be reproduced in the software used for the case (a) results \nwhen the same mistakes are made. The closure time of G=20, from Figure 21, is more consistent with a system permeability \nof less than 0.002 md and transmissibility of less than 0.014 md -m/cp.  \nApplying the other relations described in this paper to this example gives a clearer interpretation of a consistent result. \nThe average pump rate for the test was 0.6 m3/m (3.7 bpm) with a pump time of 9.5 minutes. Fluid efficiency estimated from \nclosure time is 90% with a transverse storage factor of 91%. Based on Figure 13, this should generate a fracture half-length"}


created_at: 2023-11-16 17:06:54
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id: 6b88d68c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 18, "chroma:document": "closure time is 90% with a transverse storage factor of 91%. Based on Figure 13, this should generate a fracture half-length  \nof about 100m (320 ft). The rule of thumb for closure from Figure 14, assuming a permeability of about 0.002 md, is 10 \nhours. Actual closure time was 688 minutes (11.4 hours). A valid linear flow reservoir transient may be expected after 30 \nhours, but a fully developed pseudo -linear flow regime never developed, even up to the  end of the test at 330 hours (13.8 \ndays). According to Figure 16, a pseudo -radial flow regime consistent with a single planar fracture should not be expected \nbefore 300 days. Clearly any results obtained from a forced radial flow analysis are not valid.  \nA final comment about the use of the Horner plot in after -closure analysis is warranted. The Horner plot is only valid, and \nshould only be relied upon, when a fully developed pseudo -radial flow regime is identified  in the data. The conditions"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d6dc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 18, "chroma:document": "should only be relied upon, when a fully developed pseudo -radial flow regime is identified  in the data. The conditions \ndescribed abo ve for the use of the Cartesian radial flow analysis must also be met for the Horner extrapolation to be valid. In \npractical terms, that means that extrapolation of an apparent straight line at the end of a Horner plot will almost always be  \nwrong. Both the  Cartesian radial flow analysis and Horner plots can be extrapolated to the pore pressure derived from a \npseudo -linear flow analysis (if the pseudo -linear flow regime exists) , to obtain a maximum upper bound of reservoir \ntransmissibility. Be aware that thi s estimate may be at least an order of magnitude too high.  \n \nConclusions  \nDFIT tests can provide a wide variety of data to aid in designing hydraulic fracturing treatments and characterizing the \nsubject reservoir. However, there are many factors associated with data collection and analysis that can result in poor or"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d736-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 18, "chroma:document": "subject reservoir. However, there are many factors associated with data collection and analysis that can result in poor or \nincorrect results. This paper attempts to describe  some of the common problems  and to help prevent some common errors  \noften observed in DFIT execution and analysis. These issues (and their possib le solutions) include:  \n \n\uf0b7 DFIT\u2019s should be pumped with a New tonian, non -wall building fluid;  \n\uf0b7 Multiple pump -ins must be avoided;  \n\uf0b7 The tests must be planned to allow for closure and  enough falloff time to enter linear flow at a minimum. This \ntime period may be several days, if not weeks, in low permeability systems;   \n\uf0b7 Use step -down  not step -up tests  to determine near wellbore and perforation friction;  \n\uf0b7 Correct ISIP determination  is cri tical to further analysis of the test. Wellbore compressibility and other factors \nmust be taken into consideration;"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d786-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 18, "chroma:document": "must be taken into consideration;  \n\uf0b7 The tests must b e of adequate duration and rate  (shortest practical duration at highest practical rate) ; \n\uf0b7 The possibility of p hase segregatio n and gas entry  must be considered;  \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d7e0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 19, "chroma:document": "20  SPE 169539  \n\uf0b7 Loss of hydrostatic head  will likely render the test useless , even with bottomhole gauges,  unless certain \nadditional steps are taken; and,  \n\uf0b7 Not al l tests result in pseudo -radial flow regimes , and, i n fact, reaching pseud o-radial conditions is more the \nexception to the ru le. There are numerous reasons for f alse indications of pseudo -radial. To avoid these, full \nintegration of the test results must be considered and the physics of the solution must be respected.  \n \nConsiderat ion of these points and the other s listed in this paper will lead to i mproved data acquisition and analysis , which \nin turn,  will lead to better tests, better results, and ultimately better predictions of production and reserve recovery.  \n \nReferences  \nBarree,  R.D. 1998. Applications of Pre -Frac Injection/Falloff Tests in Fissured Reservoirs \u2013 Field Examples. Paper SPE 39932 presented  at"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d830-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 19, "chroma:document": "Barree,  R.D. 1998. Applications of Pre -Frac Injection/Falloff Tests in Fissured Reservoirs \u2013 Field Examples. Paper SPE 39932 presented  at \nthe SPE Rocky Mountain Regional/Low -Permeability Reservoirs Symposium and Exhibition, Denver, CO, 5 -8 April.  \nBarree, R.D., Ba rree, V.L, and Craig, D.P. 2009. Holistic Fracture Diagnostics: Consistent Interpretation of Prefrac Injection Tests Using \nMultiple Analysis Methods SPE Prod & Oper 24(3): 396 -406. SPE 107877 -PA. DOI 10.2118/107877 -PA. \nDaltaban, T. S. and Wall, C. G. 1998. Fundamenta l and Applied Pressure Analysis, Imperial College Press,  p438 . \nTalley, G. R., Swindell, T. M., Waters, G. A. and Nolte, K. G. 1999. Field Application of After -Closure Analysis of Fracture Calibration \nTests. Paper SPE 52220 presented a t the SPE Mid -Continent Operations Symposium, Oklahoma City, OK, 28 -31 March.  \nNolte, K. G. 1979. Determination of Fracture Parameters from Fracturing Pressure Decline. Paper SPE 3841 presented at the Ann ual"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d8a8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 19, "chroma:document": "Nolte, K. G. 1979. Determination of Fracture Parameters from Fracturing Pressure Decline. Paper SPE 3841 presented at the Ann ual \nTechnical Conference and Exhibition, Las Vegas, NV, 23 -26 Sept. 23 -26. \n \n Downloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d8f8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 0, "chroma:document": "Transient Pressure Analysis \nfor Fractured Wells \nHeber Cinco-Ley, * SPE, Stanford U. \nFernando Samaniego-V., * SPE, Inst. Mexicano del Petr6leo \nSummary \nA new technique is presented for analyzing pressure \ntransient data for wells intercepted by a finite\u00ad\nconductivity vertical fracture. This method is based \non the bilinear flow theory, which considers transient \nlinear flow in both fracture and formation. It is \ndemonstrated that a graph of Pwf vs. tv. produces a \nstraight line whose slope is inversely proportional to \nhf(kfbf} Yz. New type curves are presented that \novercome the uniqueness problem exhibited by other \ntype curves. \nIntroduction \nA large amount of information concerning well test \nanalysis has appeared in the literature over the last \nthree decades. As a result of developments in this \narea, three monographs 1 ,2,3 and one book4 have \nbeen published covering different aspects of pressure \ntransient analysis. Ramey 5 also has presented a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d952-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 0, "chroma:document": "been published covering different aspects of pressure \ntransient analysis. Ramey 5 also has presented a \nreview on the state of the art. \nThe analysis of pressure data for fractured wells \nhas deserved special attention because of the number \nof wells that have been stimulated by hydraulic \nfracturing techniques. A summary of the work done \non flow toward fractured wells' was presented by \nRaghavan 6 in 1977. \nIt was recognized early that intercepting fractures \ncan strongly affect the transient flow behavior of a \nwell7-9 and that, consequently, the application of \nclassical methods 10-12 to the analysis of transient \npressure data in this situation may produce erroneous \nresults. Several methods 13-24 were proposed to solve \nthis problem. \nThese analysis techniques consider a well in\u00ad\ntersected by either an infinite-conductivity vertical \nfracture or a uniform-flux vertical fracture. Cinco\u00ad\nLey et al.25 demonstrated that the assumption of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d9a2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 0, "chroma:document": "fracture or a uniform-flux vertical fracture. Cinco\u00ad\nLey et al.25 demonstrated that the assumption of \ninfinite fracture conductivity is valid whenever \n*Now with Petr61eos Mexicanos and U. Nacional de Mexico. \n0149\u00b72136/8110009\u00b77490$00.25 \nCopyright 1981 Society of Petroleum Engineers of AIME \nSEPTEMBER 1981 the dimensionless fracture conductivity \n(kfbflkxf) ~300; all other cases; such as those \nrepresented by long or poorly conductive fractures, \nmust be analyzed by considering a finite-conductivity \nfracture model. \nExploitation of low-permeability gas reservoirs has \nrequired stimulation of wells by massive hydraulic \nfracturing (MHF) techniques. Vertical fractures of \nlarge horizontal extension are created as a result of \nthis operation; consequently, pressure drop along the \nfracture cannot be ne~lected. \nSeveral papers25-3 have been published on the \nbehavior of finite-conductivity vertical fractures. \nType-curve matching has been proposed as an"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88d9f2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 0, "chroma:document": "Several papers25-3 have been published on the \nbehavior of finite-conductivity vertical fractures. \nType-curve matching has been proposed as an \nanalysis method under these conditions; however, \nsome regions of the curves present a uniqueness \nproblem in the analysis. Barker and Ramey31 in\u00ad\ndicated that the use of published type curves becomes \npractical when a large span of pressure data is \navailable. \nThe purpose of this work is to present a new in\u00ad\nterpretation technique for early-time pressure data \nfor a well intercepted by a finite-conductivity vertical \nfracture, including the criteria to determine the end \nof wellbore storage effects. In addition, new type \ncurves are discussed to overcome the uniqueness \nproblem exhibited by previous curves at intermediate \nand large time values. \nTransient Pressure Behavior \nfor Fractured Wells \nConsider a vertically fractured well producing at a \nconstant flow rate, q, in an infinite, isotropic,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88da4c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 0, "chroma:document": "for Fractured Wells \nConsider a vertically fractured well producing at a \nconstant flow rate, q, in an infinite, isotropic, \nhomogeneous, horizontal reservoir that contains a \nslightly compressible fluid of constant com\u00ad\npressibility c, and viscosity p.. The porous medium \nhas a permeability k, porosity 1>, thickness h, and \ninitial pressure Pi' \nLet us assume that the well is intercepted by an \nundeformable, fully penetrating vertical fracture of \n1749 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88da9c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 1, "chroma:document": "TABLE 1 -SI PREFERRED UNITS, CUSTOMARY UNITS, \nAND UNIT CONVERSION CONSTANTS \nParameter \nor Variable \nk \nh \nqo \nqg \np. \nB \n<P \nCt \np \nm(p) \nt \nIMPERMEABLE \nBOUNDARIES USED IN THESE SYSTEMS \nSI Preferred Units \np'm2 \nm \nm3/d \nm3/d \nPa\u00b7s \nm3/m3 \nfraction \nPa-1 \nkPa \nkPa2/Pa\u00b7s \nhours \n1,842 \n1,293 \n3.6x 10-9 \n34.97 \n24.57 \n0.3918 \n0.275 \nK \nm3/Pa Customary Units \nmd \nft \nSTBID \nMscf/D \ncp \nRB/STB \nfraction \npsi-1 \npsi \npsi2/cp \nhours \n141.2 \n1,424 \n2.637 x 10-4 \n44.1 \n444.75 \n8.128 \n81.97 \noR \ncu ft/psi \nWELLBORE \nFRACTURE \nh \nFig. 1 -Finite\u00b7conductivity vertical fracture in an infinite\u00b7 \nslab reservoir. \n, CASE \nf:>wD \nA \nF B D E \n\"', I< \ntDXf \nFig. 2 -Low\u00b7log graph of typical cases for fractured wells. \n!750 half-length xf' width bf, permeability kf' porosity \nr/>f' and total compressibility Cft (Fig. 1). The \nproperties of both the reservoir and the fracture are \nindependent of pressure and the flow in the entire \nsystem obeys Darcy's law. In addition, it is con\u00ad"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88daec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 1, "chroma:document": "independent of pressure and the flow in the entire \nsystem obeys Darcy's law. In addition, it is con\u00ad\nvenient to assume that pressure gradients are small, \ngravity effects are negligible, and flow entering the \nwell bore comes only through the fracture. \nWith these assumptions, the unsteady-state flow in \nthe system can be described by the diffusivity \nequation.! For details on the boundary conditions \nand a semianalytical solution for this flow problem, \nsee Ref. 25. \nThe general solution for the well bore flowing \npressure P wf for oil is given by25 \nkh(Pi-Pwf) \n----!....-B~- =PWD(tDxf,'Y/fD,CfDf) ...... (1) aoq J), \nand, for gas, \nwhere \n{3kt \ntDxf = r/>J),ctx}' ......................\u2022 (3) \n'Y/fD=~' ..\u2022...................... (4) \nkr/>jCft \nand \nCfDf= ~r;~ ....................... (5) \nP wD represents the dimensionless pressure drop; it is \na function of dimensionless time, t Dx ' dimen\u00ad\nsionless fracture hydraulic diffusivity, 'Y/ib, and di\u00ad"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88db3c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 1, "chroma:document": "a function of dimensionless time, t Dx ' dimen\u00ad\nsionless fracture hydraulic diffusivity, 'Y/ib, and di\u00ad\nmensionless fracture storage capacity, CfDJ. ao' ag, \nand {3 are unit conversion constants (see Table 1). \nCinco-Ley et at.25 showed that for practical values \nof dimensionless time the pressure behavior depends \non two parameters only: the dimensionless time t Dx.r' \nand the dimensionless fracture conductivity \n(kfb f) D\u00b7 The former was defined in Eq. 3 and the \nlatter may be obtained from Eqs. 4 and 5. By \ndefinition, the dimensionless fracture conductivity is \nkb (kfbf) D = ~k , ..................... (6) xf \nand it appears to be related to CfDf and 'Y/fD as \nfollows. \n(kfbf)D=7rCfDf'Y/fD. . ................. (7) \nFig. 2 shows the general behavior of a well with a \nfinite-conductivity vertical fracture. There, we show \na log-log graph of dimensionless wellbore pressure, \nPwD' vs. dimensionless time, tDX[\" For the sake of \nsimplicity only two cases are presented. Case 1"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88db96-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 1, "chroma:document": "PwD' vs. dimensionless time, tDX[\" For the sake of \nsimplicity only two cases are presented. Case 1 \nrepresents the behavior of a low-conductivity \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88dbe6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 2, "chroma:document": "~L--=~c5well ) \\ \nFracture \n(0) \nFRACTURE LINEAR FLOW \nFracture -----_/ \n(c ) \nFORMATION LINEAR FL()\\~ (b) \nB I LIN EAR FLO W \n\\ / \nFracture , . \nI \nWell \n\\ ~ \nPSEUDO-RADIAL FLOW \nFig. 3 -Flow periods for a vertically fractured well. \nfracture (kfbf) D =0.1; Case 2 considers a highly \nconductive fracture, (kfbf) D = 500. These cases \nwere selected because they exhibit all the features of \nthe transient pressure behavior for a fractured well. \nAn analysis of Fig. 2 shows that the transient \nbehavior of a well with a finite-conductivity vertical \nfracture includes several flow periods. Initially, there \nis a/racture linear flow characterized by a half-slope \nstraight iine; after a transition flow period, the \nsystem mayor may not exhibit a bilinear flow period, \nindicated by a one-fourth-slope straight line. As time \nincreases, a formation linear flow period might \ndevelop. Eventually, in all cases, the system reaches a \npseudoradial flow period (see Fig. 3)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88dc36-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 2, "chroma:document": "increases, a formation linear flow period might \ndevelop. Eventually, in all cases, the system reaches a \npseudoradial flow period (see Fig. 3). \nPoints A, F, and L in Fig. 2 represent the end of \nthe fracture linear flow period (half-slope straight \nline). The bilinear flow period (one-quarter-slope \nstraight line) is defined by Segments B-C and G-H; \nthis behavior is not present when the fracture has a \nhigh storage capacity and a high conductivity (lower \ncurve in Case 2). \nThe formation linear flow period is shown by the \nhalf-slope straight line between Points I and J, and it \nis only exhibited by fractures of high conductivity, \n(k fb f) D ~ 300. Points D and K show the beginning \nof the pseudoradial flow period. \nWe present a detailed description of both the \nfractured linear flow and the bilinear flow. The \nformation linear flow and the pseudoradial flow have \nbeen discussed in the literature. 14,15,17,19,22,25 \nSEPTEMBER 1981 Fracture Linear Flow Period"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88dc86-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 2, "chroma:document": "been discussed in the literature. 14,15,17,19,22,25 \nSEPTEMBER 1981 Fracture Linear Flow Period \nThis behavior occurs at very small values of dimen\u00ad\nsionless time, and it is exhibited by all cases. During \nthis flow period, most of the fluid entering the well\u00ad\nbore comes from the expansion of the system within \nthe fracture and the flow is essentially linear, as \nshown in Fig. 3a. \nThe dimensionless pressure response at the \nwellbore is given by\u00b7 \nP D -2 ..j 1'('YIfDtD ............ (8) w -(kfbf) D -, 'Xf \nHence, for oil, \n_ _ 0ffoqB I p,t \nPwf-Pi b h ..,J k cJ> c ' ... ---. ---... (9) \nf f1ft \nand for gas, \n_ 0ffgqT I t m(pwf) -m(Pi) -b h ..,J k cJ> , \u2022\u2022\u2022\u2022\u2022 (10) \nj f jp,Ct \nwhere 0ffo and 0ffg are unit conversion constants. \nThese equations indicate that a log-log graph of \npressure vs. time yields a straight line whose slope is \nequal to one half. A graph of pressure or pseudo\u00ad\npressure vs. the square root of time also gives a \nstraight line whose slope depends on the fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88dcd6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 2, "chroma:document": "pressure vs. the square root of time also gives a \nstraight line whose slope depends on the fracture \ncharacteristics excluding the fracture half-length xf-\nThe fracture linear flow ends when \n\u00b7See Appendix A for derivation. \n1751 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88dd30-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 3, "chroma:document": "2 \nP wD ----End of Straight \nLine O.21T \nFig. 4 -PwD vs. tb~l for a well with a finite\u00b7conductivity \nvertical fracture. \n_ 0.01 (kfbf) b tDxf- 2 ...........\u2022..... (11) \n'YIfD \nUnfortunately, this flow period occurs at a time too \nearly to be of practical use. \nBilinear Flow Period \nTo the best of our knowledge, this is a new type of \nflow behavior that has not been considered in the \nliterature. It is called bilinear flow because two linear \nflows occur simultaneously. One flow is a linear \nincompressiblejlow withinthefracture and the other \nis a linear compressible flow in the formation, as \nshown in Fig. 3b. A bilinear flow exists, as shown in \nAppendix A, whenever most of the fluid entering the \nwell bore comes from the formation and fracture tip \neffects have not yet affected the well behavior. \nLet us now examine this behavior in a log-log \ngraph of PwD vs. tDx (Fig. 2). In Case 1 \n[ (kjb f) D = 0.1], the bili6ear flow exists between \nPomts Band C after a transition flow period"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88dd80-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 3, "chroma:document": "graph of PwD vs. tDx (Fig. 2). In Case 1 \n[ (kjb f) D = 0.1], the bili6ear flow exists between \nPomts Band C after a transition flow period \nrepresented by Segment A-B. The pressure behavior \nfor the bilinear jlow exhibits a straight line whose \nslope is equal to one fourth. The duration of this \nperiod depends on both (kfbf) D and CfPf. Case 2 \n[(kfbf) D = 500] mayor may not exhibit the bilinear \nflow period, as shown by the upper and lower curves. \nThe upper curve for Case 2 corresponds to a low \nvalue for CfDf and does exhibit bilinear flow over a \nshort perioo of time (Segment G-H); however, the \n1752 -4 10 \nFig. 5 -Dimensionless time for the end of the bilinear flow \nperiod vs. dimensionless fracture conductivity. \nlower curve corresponding to a high value of CfDf does not exhibit the bilinear flow behavior because \nfracture tip effects are felt before this flow regime is \nestablished (Segment L-I). \nThe dimensionless wellbore pressure for the \nbilinear flow period is given by*"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ddd0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 3, "chroma:document": "established (Segment L-I). \nThe dimensionless wellbore pressure for the \nbilinear flow period is given by* \n7r \\1.1 \nPwD = r(1.25)..)2(k\nfb\nf) D t DXf' ......... (12) \nor \n2.45 II. \nPwD = ..) (kfb\nf) D t DXj\" ................ (13) \nThis equation indicates that a graph of PwD vs. \n{j t Dx produces a straight line whose slope is \n2.451..) (kfb f) D, intercepting the origin. Fig. 4 \npresents that type of graph for different values of \n(kfbf)D\u00b7 . \nAn important feature of this graph is that after the \nbilinear flow period (straight-line portion), the curves \nfor (kfbf) D :51.6 are concave downward and the \ncurves for (kfbf) D > 1.6 are concave upward. \nThe end 0 the straight-line portion of the curves \ndepends on the fracture conductivity and may be \nexpressed by \n0.1 \n\u00b7See Appendix A for derivation. \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88de2a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 4, "chroma:document": "0. \n<J \no \nFig. 6 -Graph for analysis of pressure data of bilinear \nflow. \n. [ ] -1.53 tDebf=O.0205 (kfbf}D-1.5 \nfor 1.6$ (kfbf) D $3, ........... (l4b) \nand \nt _ [ 4.55 _ 2.5] -4 \nDebf--J (kfbf) D \nfor (kiJf) D $1.6 ............... (l4c) \nFig. 5 shows a graphical representation of these \nequations. \nBilinear Fiow Analysis \nBilinear flow is exhibited by finite-conductivity \nfractures with a small dimensionless storage capacity; \nCfDf. Any attempt to analyze pressure data observed \nover this flow period using conventional methods (p \nvs. Yt or p vs. log t) will produce erroneous results. \nWe present the appropriate analysis method based on \nthe bilinear flow theory. \nBasic Equations and Graphs \nFrom Eq. 13, the pressure drop for oil may be ex\u00ad\npressed as \nSEPTEMBER 1981 Q \n<l \nOl o -1 \nSlope = 1/4 \nLog t \nFig. 7 -Log\u00b7log graph of pressure data for bilinear flow. \nand, for gas, \nwhere t:.p is the pressure (pseudopressure) change for \na given test. Both 0bfo and 0bfg are unit conversion"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88de7a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 4, "chroma:document": "and, for gas, \nwhere t:.p is the pressure (pseudopressure) change for \na given test. Both 0bfo and 0bfg are unit conversion \nconstants and are given in Table 1. \nEqs. 15 and 16 indicate that the pressure change is \nboth inversely proportional to the square root of the \nfracture conductivity and directly proportional to the \nfourth root of time. \nAccording to Eqs. 15 and 16, a graph of t:.p vs. Vi \nproduces a straight line passing through the origin, \nwhose slope, m bf' for oil, is given by \nm -\u00b0bfoqBp, \nbf-h(kfbf} Y2(~p,Ctk} y. , ............ (17) \nand, for gas, \nm - \u00b0bfgqT \nbf-h(kfb\nf} 'I2(~p,ctk} y., .\u2022.......... (18) \nHence, the product h(kfbf} '12 can be estimated by \nusing the following equations. For oil, \nh (k b ) Y2 = \u00b0bfoqBp, (19) f f mbf(~p,Ctk} y., \u2022........... \nand, for gas, \n1753 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88def2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 5, "chroma:document": "[lP \no \nFig. 8 -Bilinear\u00b7flow graph for a fracture with a flow \nrestriction near the well bore. \nThese equations indicate that values of reservoir \nproperties must be available to estimate the group \nh (kfbf) Y2 \u2022 Note that this analysis technique tends to \ndecrease the effect of the error introduced when poor \ninformation on reservoir properties (i.e., k, cp, and \net) is used. \nAll comments on the concavity of the curve in Fig. \n4 are valid for the curve in Fig. 6. \nFrom Eqs. 13 and 14, if (kfbf) D ??3, the \ndimensionless pressure drop at the end of the bilinear \nflow period is given by \n1.38 \n(PwD}ebf=- (kfbf}D ................. (21) \nHence, the dimensionless fracture conductivity can \nbe estimated using the following equation. \n1.38 (kfbf) D=- ................. (22) \n(PwD}ebf \n(p wD ) ebf can be calculated using Eq. 1 or Eq. 2 and \n(1\u00a5J) ebf or &n (p) ebf obtained from the bilinear \nflow graph. \nFrom Eqs. 15 and 16, a graph of log 1\u00a5J vs. log t"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88df4c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 5, "chroma:document": "(1\u00a5J) ebf or &n (p) ebf obtained from the bilinear \nflow graph. \nFrom Eqs. 15 and 16, a graph of log 1\u00a5J vs. log t \nyields a quarter-slope straight line (Fig. 7) that can be \n. used as a diagnostic tool for bilinear flow detection. \nExtensions and Limitations \nThe region disturbed during bilinear flow includes \nonly the fracture and its vicinities because it occurs at \nearly time, even in partially penetrating fracture \nsystems. Thus, the equations and graphs discussed in \nthe previous section for bilinear flow can be extended \nto cases where the fracture does not penetrate the \n1754 llP \n,. /\" \\\\'.~ \n<#\\<1' \\.-\ns'-\n~\\.-O'\\ \n\\{c'r<!- ~ \n\",\\\\.-\\ ~ \nfvC,'\\ ~ \nI<!-\"'/\"\"''''-:~ \n\",.. \n\",.. PRESSURE BEHAVIOR WITH WELLBORE \n/\" /\" ?---- STORAGE EFFECTS \n4 \u00ab \nFig. 9 -Wellbore storage effect on the bilinear flow graph. \nentire thickness of the formation. This is possible \nsimply by using the fracture height, hf' instead ofthe \nformation thickness, h."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88df9c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 5, "chroma:document": "entire thickness of the formation. This is possible \nsimply by using the fracture height, hf' instead ofthe \nformation thickness, h. \nIn cases where a flow restriction (low conductivity, \nturbulent flow) exists within the fracture in the \nvicinity of the well bore, bilinear flow still occurs and \nthe pressure data analysis discussed cim be applied \n(see Fig. 8). An extra pressure drop, 1\u00a5Js' is created in \nthis case and the straight-line portion does not in\u00ad\ntercept the origin. These situations distort the \nstraight-line portion in the log-log graph. \nIf well bore storage affects the system, the bilinear \nflow pressure behavior may be masked, as shown in \nFig. 9, and data analysis becomes difficult (if not \nimpossible) with current interpretation methods. \nFlow Regime Identification \nand New Type Curves \nThe pressure behavior of a fractured well may exhibit \nseveral flow periods for practical values of time: \nbilinear flow, formation linear flow, and \npseudoradial flow."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88dfec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 5, "chroma:document": "several flow periods for practical values of time: \nbilinear flow, formation linear flow, and \npseudoradial flow. \nPressure data for each flow period should be \nanalyzed using a specific interpretation method (i.e., \nPw vs. Vi, Pw vs. Vi, and Pw vs. log t for bilinear, \nlinear, and pseudoradial flows, respectively). \nThe log-log graph has been used commonly as a \ndiagnostic tool to detect different flow regimes in a \ntransient pressure test. The use of type curves in the \nanalysis of pressure data for fractured wells \nrepresents a major step in that area. The first type \ncurves for fractured wells were presented by \nGringarten et. af.19 Cinco-Ley et af.25 showed that \nthe infinite-conductivity vertical fracture solution of \nGringarten and Ramey17 behaves like the solution \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e046-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 6, "chroma:document": "for a finite-conductivity vertical fracture of \n(k fb f ) D ~ 300; furthermore, they showed that the \numform-flux vertical fracture behaves as a variable\u00ad\nconductivity vertical fracture. The type-curve \nanalysis offers an advantage over the specific analysis \nmethods already mentioned because it can be applied \nto interpret at once pressure test data that correspond \nto different flow periods. In addition, the type-curve \nanalysis could indicate when the different graphical \ntechniques apply. \nExperience has shown that, in some cases, ap\u00ad\nplication of the type curves available for finite\u00ad\nconductivity vertical fractures does not yield unique \nresults. This is because the shape of pressure \nbehavior curves is similar for different values of \ndimensionless fracture conductivity over some \nregions of the type curves. A close inspection of Fig. \n2 indicates that the uniqueness problem can exist if \npressure data to be analyzed occur at either the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e096-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 6, "chroma:document": "2 indicates that the uniqueness problem can exist if \npressure data to be analyzed occur at either the \nbilinear flow period (one-fourth slope) or the \npseudoradial flow period. \nA convenient presentation of the type curve \npublished by Cinco-Ley et al., 25 Ramey et al., 31 and \nAgarwal et al.29 is given in Fig. 10. We show a graph \nof log [PwD(kfbf}vl vs. log [tDx (kfbf}~l.* The \nmain feature of this graph is that for all values of \n(k fb J ) D the behavior of both bilinear flow (quarter \nslope) and the formation linear flow (half slope) is \ngiven by a single curve. Note that there is a transition \nperiod between the bilinear and linear flows. The \ndashed line in this figure indicates the approximate \nstart of the pseudoradial flow period (semilog \nstraight line). Also shown are the end of the bilinear \nflow and the start of the formation linear flow; the \ntime for the end of the bilinear flow from Fig. lO \nagrees with the results presented in Fig. 5. The groups"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e0e6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 6, "chroma:document": "time for the end of the bilinear flow from Fig. lO \nagrees with the results presented in Fig. 5. The groups \nof variables used in Fig. lO were derived in Appendix \nB, where it is shown that, for some values of fracture \nconductivity, bilinear flow ends when fracture tip \neffects are felt at the wellbore. \nAlthough many curves are presented for \n(kfbf) D > 207r, the shape of these lines is essentially \nthe same. The only difference is the duration of the \nformation linear flow (half slope); that is, the higher \nthe fracture conductivity, the longer the linear flow \nperiod. \nThe beginning of the formation linear flow occurs \nat tDxf (kfbf) b::::: 102; that is, \n100 \nt Dblf == 2 \u2022 \u2022 \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022.\u2022\u2022\u2022\u2022\u2022.\u2022.\u2022\u2022\u2022 (23) \n(kfbf) D \nThe end of this flow period is given by19 \ntDelf==0.016 .......................... (24) \nHence, the fracture conductivity may be estimated as \nfollows: \nlO (kfbf}D== ~, ................... (25) \n'ItDblf \n\u2022 A large-scale copy of this graph may be obtained from the authors."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e140-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 6, "chroma:document": "follows: \nlO (kfbf}D== ~, ................... (25) \n'ItDblf \n\u2022 A large-scale copy of this graph may be obtained from the authors. \nSEPTEMBER 1981 slope=-} \n'~~~~-'~6~2~--~'070~--,O~2~--~,~~~-,~~~~~,o8 \n2 t DX\nf (kf bflD \nFig. 10 -Type curve for vertically fractured wells. \nor \n(kfbf}D==1.25XlO-2j telf ........... (26) \ntblf \nThese equations apply when (k fbf) D ~ 100. \nFig. lO can be used as a type curve to analyze \npressure data for a fractured well. Pressure data on a \ngraph of log tlp vs. log t is matched on a type curve to \ndetermine (tlp}M' [PwD(kfbf}DlM, (t}M' [tDx \n. (kfbf}blM' [(k/b/}DlM, (tebf}M' (tblj}M' anl~ \n(tbssl J M' From thiS mformation, we can estimate the \nfollowing. \nDimensionless Fracture Conductivity. \nFormation Permeability. For oil, \nko = _Q!o,,-q_B_J1._ [PwD' (kfbf) DlM \nh(tlp}M [(kfbf}vlM ....... (27) \nand, for gas, \nk -Q!gqT [PwD' (kfbf) DlM \ng-h[~(p}lM [(kfbf}vlM ..... (28) \nFracture Half-Length. \n... (29) \nFracture Conductivity. \nEnd of Bilinear Flow."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e190-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 6, "chroma:document": "k -Q!gqT [PwD' (kfbf) DlM \ng-h[~(p}lM [(kfbf}vlM ..... (28) \nFracture Half-Length. \n... (29) \nFracture Conductivity. \nEnd of Bilinear Flow. \nBeginning of Formation Linear Flow . \n1755 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e1e0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 7, "chroma:document": "End of Wellbore \nStorage Effects \nFig. 11 -Type curve for well bore storage under bilinear \nflow conditions. \n-:: 102 \n.D \n.x-\na \no.~ 0. \n<l \n01 \n0 \n---' \n'fA Log t ----Approximate start \nof Semi log Straight \nLine \n10-2 L----'--------'-_-'----'--_1-----'--------'-_-'-----L_L----'--------'-\n10-4 10-2 102 104 106 108 \n2 \nt DX\nf ( kf bflD \nFig. 12 -Type-curve matching for data in bilinear and \ntransitional flow. \nQ \n<l \nOJ o \n---' \nLog t \nFig. 13 -Pressure data for a half\u00b7slope straight line in a \n10g\u00b7log graph. \n1756 Beginning of Semilog Straight Line. \nThese results can be obtained if a large span of \npressure data is available. It should be kept in mind \nthat specific analysis graphs must be used for dif\u00ad\nferent flow regimes to obtain a better estimate of \nboth fracture and reservoir parameters. \nNow we discuss cases where all pressure data fall \non a very small portion of the type curve and a \ncomplete set of information may not be obtained."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e230-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 7, "chroma:document": "Now we discuss cases where all pressure data fall \non a very small portion of the type curve and a \ncomplete set of information may not be obtained. \nCase 1. Pressure data exhibit one-fourth slope on a \nlog-log graph (Fig. 7). According to the discussion \nin the previous section, these data correspond to the \nbilinear flow period and a unique match with Fig. 10 \ncannot be attained. The bilinear flow type of analysis \nis the only method available for this case to obtain \ninformation regarding the fracture characteristics \n(kfbf)\u00b7 \nA minimum value for fracture half-length, xf' can \nbe estimated from Eqs. 14a through 14c for tiie end \nof the bilinear flow; that is, for (kfbf) D ~ 3, we \nhave \n> 411O(3(k fbf)2tebf xf-\"<I c/>/l-ctk .. ............... (31) \nGenerally, wellbore storage affects a test at early \ntime; thus, it is expected to have pressure data \ndistorted by this effect, causing deviation from the \none-fourth slope characteristic of this flow period."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e280-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 7, "chroma:document": "distorted by this effect, causing deviation from the \none-fourth slope characteristic of this flow period. \nFig. 11 may be applied to analyze pressure data for \nthis case even if the duration of the test is not enough \nto reach the one-fourth slope portion. It is important \nto note that pressure behavior in Fig. 11 for both \nwellbore-storage-dominated and bilinear-flow \nportions is given by a single curve that completely \neliminates the uniqueness matching problem. The \ncorrelating parameters FI (PwD) and F2 (tDxl) used \nin this figure are derived in Appendix C and aefined \nin Fig. 11. \nThe end of well bore stora~e effects in Fig. 11 \noccurs when F 2 (t Dx f) \"\" 2 x 10 ; that yields \n17.25 3/ c4 tews :::::--\"<1 2 4 \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 (32) \n(3 (kfbf) h c/>ctk \nFrom observation of the results presented in Fig. 11, \nwe can see that the end of well bore storage effects \noccurs three log cycles after the end of the unit slope. \nThis criterion is useful to determine whether the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e2da-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 7, "chroma:document": "occurs three log cycles after the end of the unit slope. \nThis criterion is useful to determine whether the \nproper straight-line portion for bilinear flow analysis \nis chosen (see Fig. 9). If Fig. 11 is used as a type \ncurve, the following information may be obtained: \n[FI (PwD\u00bb)M' [F2(tDXf\u00bb)M' (i\u00a5J)M' and (t)M' \nHence, we can estimate the following. \nWeI/bore Storage Constant. For oil, \nC= 27rDto(3qB/l-(t)M [FI (PwD\u00bb)M , ...... (33) \n(i\u00a5J)M [F2(tDXf\u00bb)M \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e3b6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 8, "chroma:document": "1m.,....,.,\"\"\"\"\"\"\"\"\" \n~ +I+++t~ftHlttiH \n7 \n1++l+l~+l+~f!HlH-\n4 \nFig. 14 -Effective wellbore radius vs. dimensionless fracture conductivity for a vertical fracture. \nand, for gas, \nC= 2'1rcxg{3qT(t)M [FI (PwD)lM , ....... (34) \n[.::lm(p)lM [F2(tDXf)lM \nFracture Conductivity. For oil, \n_ 0.4 I ~ \\ cxoqBp,[FI (PwD) lM '13 \nkfbf- h2 ...j \u00a2ctk l (flp) M j' \n........................ (35) \nand, for gas, \nk b = 0.4 J ~ \\ cxgqI1FI (PwD)lM'I 3. \nf f h2 \u00a2ctk l [.::lm(p)lM j \n........................ (36) \nCase 2. Pressure data partially match the curve for \nthe transition period between bilinear and linear \nflows (Fig. 12). In this case, the remaining portion \nof the data may correspond to bilinear or linear flow \nand the type-curve match is unique because the \ntransition period has a characteristic shape. This \ncomment is valid for dimensionless fracture con\u00ad\nductivities, (kfbf) D ~57f. \nFrom the type-curve match of pressure data for \nthis case in Fig. 10, we obtain IPwD (kfbf) DlM'"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e438-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 8, "chroma:document": "ductivities, (kfbf) D ~57f. \nFrom the type-curve match of pressure data for \nthis case in Fig. 10, we obtain IPwD (kfbf) DlM' \n[tDxf (kfbf) blM, (M) M' and (flp) M' \nHence, for oil, \nSEPTEMBER 1981 and, for gas, \n(kfbf)_ cxgqT rpWD(kfbf)D]M' .(38) xf -h[.::lm(p)lM t \nFracture half-length and fracture conductivity. For \noil or gas, \n.... (39) \nand \nSince the formation permeability generally is \nknown from prefracture tests, the dimensionless \nfracture conductivity can be estimated by using \nresults from Eq. 37 or Eq. 38. Some of these results \nalso can be obtained from a specific analysis method \ncorresponding to the flow period exhibited by data \nother than the transition flow region (i.e., bilinear \nflow or linear formation flow, as discussed in the \nbilinear flow analysis section and in Ref. 14). \nIf all pressure data fall on the transition period of \nthe curve, type-curve matching (Fig. 10) is the only \nanalysis method available."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e4a6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 8, "chroma:document": "If all pressure data fall on the transition period of \nthe curve, type-curve matching (Fig. 10) is the only \nanalysis method available. \nCase 3. Pressure data exhibit a half-slope line on a \nlog-log graph. (Fig. 13). For this case there is no \nunique match with Fig. 10; however, the linear flow \n1757 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e500-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 9, "chroma:document": "P wD \nFig. 15 -Type curve for a finite-conductivity vertical \nfracture. \nanalysis presented by Clark 14 can be applied to \nobtain fracture half-length if formation permeability \nis known. In addition, a minimum value for the \ndimensionless fracture conductivity, (kfb J) D.' can \nbe estimated using Eq. 26. Note that tb/f In Fig. 13 \nrepresents a maximum value for the time of the \nbeginning of the linear flo~ period and t elf represents \na minimum value for the tIme of the end of the half \nslope. \nIf well bore storage effects are present at early \ntimes in a test for this case, the analysis can be made \nusing the type curve presented by Ramey and \nGringarten.21 \nCase 4. Pressure data partially match the curve jor \nthe pseudoradial flow period. If a large span of \npressure data is not available, a unique match would \nnot be obtained by using Fig. 10 because curves for different values of fracture conductivity are similarly \nshaped for the pseudoradial flow period. However,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 9, "chroma:document": "shaped for the pseudoradial flow period. However, \nthe transient pressure behavior shown in Fig. 10 can \nbe correlated to analyze these cases better. \nFor the pseudoradial flow period, a fractured well \nbehaves like an unfractured well with an effective \nwellbore radius being a function of dimensionless \nfracture conductivity, (kfbf) D. Fig. 14 presents a \ngraph of dimensionless effective wellbore radius, \nr~/xf' vs. dimensionless fracture conductivity, \n(kfbf) D. Notice that for large values of \n(k b f) D ( > 300), the dimensionless effective \nwefibore radius is 0.5, as mentioned by Prats et al. 8 \nIf the dimensionless time is defined by using r~ \ninstead of xf, a graph of Pwq vs. tDr~ t;>rovides a \nsingle curve for the pseudoradlal flow penod for all \nvalues of dimensionless fracture conductivity (see \nFig. 15). This curve provides an excellent tool for \ntype-curve analysis of pressure data partially falling \nin the pseudoradial flow period because the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 9, "chroma:document": "type-curve analysis of pressure data partially falling \nin the pseudoradial flow period because the \nremaining data must follow one of the curves for \ndifferent fracture conductivities. Fig. 14 must be \nused as an auxiliary curve to determine (kfbf) D \nwhen using Fig. 15. \nApplication of Fig. 15 to match pressure data \nprovides (PwD)M' (tDr )M' (tlp)M' (t)M' and \n[(kfbf) D]M. Hence, th~ following equations are \ngiven. \nReservoir Permeability. For oil, \nDloqBp. k= (PwD) M' ................ (41) h(tlp) M \n102r----------,----------~----------1I----------r_------~ \n.-\ntil a. \na. \nE \n<J o \n.D MdLCh Point \n[ot]M c 1 hour \n= 0.35 hour \nt '2 _ 5 hour ebf \n10~----------~----------~----------_t-------\nI \nI \nI \nI \n,-- ___ ~_O. \nI \nI o \nI 0 I - -,\u00ad\nI \nI \nBeginning of Senilog Straight Line 10. \nlo10-1~----~I--~~-----L---L._----i---~------~~~----~~ 3 2 1 101 107 '-_ .!.O-_ I 10-. I 10- _ 1 __ \n- - - - - - - - - - 2 1 102 /). t [hoursl \n10-2 10-1 t DXf (kf bflD 10"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 9, "chroma:document": "- - - - - - - - - - 2 1 102 /). t [hoursl \n10-2 10-1 t DXf (kf bflD 10 \nFig. 16 -Type-curve matching for Well A. \n1758 JOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e67c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 10, "chroma:document": "and, for gas, \n(XgqT k= (PwD) M. . ............ (42) \nh[~(p}lM \nEffective WeI/bore Radius. For oil or gas, \nr' =J (3k(t) M w cPJlCt (tDr ~) M\u00b7 ................. (43) \nBy using [(kfbj) DlM in Fig. 14, we obtain \n(r~/xj) Fig. 14; hence, \nr' Xj= [' j ..................... (44) \nr wlXj Fig. 14 \nThe pressure data falling in the pseudoradial flow \nperiod also must be analyzed using the semilog \nmethods to estimate k and r ~ . \nThe discussion in this section clearly indicates (as \nmentioned by Agarwal et af.29) that caution and \ndiligence should be exercised when applying the type\u00ad\ncurve matching technique. To perform the type of \nanalysis presented in the four cases, it is necessary to \nhave prefracture information. \nIt should be kept in mind that application of the \ntype-curve analysis method to pressure buildup tests \nis appropriate when the producing time is large. \nExamples of Application \nThree examples illustrate the application of several of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e6cc-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 10, "chroma:document": "is appropriate when the producing time is large. \nExamples of Application \nThree examples illustrate the application of several of \nthe methods and theory previously discussed. \nWell A \nA buildup test was conducted in this fractured well \nproducing in a low-permeability reservoir. Table 2 \npresents the information and results of the analysis \nfor this test. Fig. 16 shows a log-log graph of pressure \ndata. matching the type curve given in Fig. 10. Notice \nthat the first data points are influenced by well bore \nstorage and the rest of the data fall in both the \nbilinear and the transition flow periods. The match\u00ad\npoint results also are presented in Fig. 16. A \nminimum value for (k jb j ) D can be estimated from \nthe position of the last data point with respect to the \ntype curves; for this case, (kjbj}D min =511\". \nThe end of well bore storage occurs at ap\u00ad\nproximately 0.35 hour and the end of bilinear flow is \nat 2.5 hours. We also see that the formation linear"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 10, "chroma:document": "proximately 0.35 hour and the end of bilinear flow is \nat 2.5 hours. We also see that the formation linear \nflow period was not reached in this test. \nSince the test was not long enough to match a \ncurve for a specific value of (kjbj) D' this example \ncorresponds to Case 2 in the type-curve-analysis \nsection. \nUsing the pressure data match and Eq. 38, we \nobtain \nkjbj _ 1,424x7,350x690x6.5 \nXj - 118x109 \n=0.3978 md-ftlft. \nSEPTEMBER 1981 TABLE 2 -TEST INFORMATION AND ANALYSIS RESULTS \nFORWELLA \nReservoir Data \nProduction rate q, MscflD \nProducing time tp, hours \nFormation thickness h, ft \nPorosity cJ>, fraction \nPermeability k, md \nFormation temperature T, oR \nAverage gas viscosity 1-', cp \nTotal compressibility ct, psi-1 \nFlowing well bore pressure Pwl, psia \nAnalysis Results \nk,b\n\" md-ft \nx\" ft \n(k:~'). md-ftlft \n(klbl)D \n,;.., ft Type-Curve \nAnalysis \n148 \n373 \n0.3978 \n15.9 \n171.6 7,350 \n2,640 \n118 \n0.1 \n0.025 \n690 \n0.0252 \n0.129x 10-3 \n1,320 \nBilinear \nFlow Analysis \n154 \n368"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e76c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 10, "chroma:document": "Analysis \n148 \n373 \n0.3978 \n15.9 \n171.6 7,350 \n2,640 \n118 \n0.1 \n0.025 \n690 \n0.0252 \n0.129x 10-3 \n1,320 \nBilinear \nFlow Analysis \n154 \n368 \n0.4185 \n-16.71 \n-169.3 \nFrom the time-match information and Eq. 39, we can \ncalculate \nJ 2.637 x 10 4 x 1 \n. 0.1 x 0.025 x 1.29 x 10-4 x 0.025 x 3.69 x 10-2 \n=373 ft. \nNow, application of Eq. 40 yields \nWe also can estimate \n(kjbj}D= kjbf ..!.. \nXj k \n0.3978 \n= 0.025 = 15.9. \nFrom Fig. 14, r~/xj=0.46. \n:. r~=373x0.46=171.6ft. \nFi~. 17 shows the bilinear flow graph [~(p) vs. \nllt ~ 1 for this example. Based on the information \nprovided by Fig. 16, the correct straight line is \ndrawn. The slope of this line is 1.62 X 108 psi2/cp\u00ad\nhr ~, and at the end of bilinear flow \nllm(p}ebj=2.05x 108 psi2/cp-hr~. Notice that the \npressure curve after the end of the bilinear flow \nperiod is concave upward, indicating that \n(kjbj) D > 1.6."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e7c6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 10, "chroma:document": "pressure curve after the end of the bilinear flow \nperiod is concave upward, indicating that \n(kjbj) D > 1.6. \n1759 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 11, "chroma:document": "'\" 0. 10 ~ \nE \u2022 \n<J \no Cucve concave upwards ... (kfbf) D > 1.6 \n1~ V. IllI) (hour I \nFig. 17 -Bilinear flow graph for Well A. \nTABLE 3 -TEST INFORMATION AND ANALYSIS RESULTS \nFOR WEll B ' \nReservoir Data \nProduction rate q, MscflD \nProducing time tp, hours \nFormation thickness h, ft \nPorosity C/>, fraction \nPermeability k, md \nFormation temperature T, OR \nAverage gas viscosity p., cp \nTotal compressibility ct, psi-1 \nFlowing wellbore pressure Pwt, psia 1,675 \n1,800 \n85 \n0.11 \n0.0045 \n675 \n0.025 \n0.152x 10-3 \n1,250 \nAnalysis Results Type\u00b7Curve Bilinear \nAnalysis Flow Analysis \nktbt, md\u00b7ft \nXt, ft \n(k:~t), md.ftlft \n(ktbt)D \nr';\", ft \nFrom Eq. 20, 95.3 \n;;::692 \n::50.1377 \n::530.6 \n::5325 \n(kjbj) Yz = (444.75 X 7,350 X 690)/11.62 X 108 X 118 \n\u00b7(0.1 x 0.0252 x 1.29 x 10-4 xO.025)1~, \n:. (kjbj) = 154md-ft. \nUsing Eqs. 22 and 2, \n(k b ) D \"'\" 1.38 \nj j (0.025X1l8X2.05XI08) \n1,424 X 7,350 x 690 \n\"'\" 16.71. \n1760 109 \n0: u \nN~ \n'\" 0. \nCi 108 \nE \n<J Slope = 1/4 \nII t Ihours)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e866-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 11, "chroma:document": "(k b ) D \"'\" 1.38 \nj j (0.025X1l8X2.05XI08) \n1,424 X 7,350 x 690 \n\"'\" 16.71. \n1760 109 \n0: u \nN~ \n'\" 0. \nCi 108 \nE \n<J Slope = 1/4 \nII t Ihours) \nFig. 18 -Log\u00b7log graph of pressure data for Well B. \nHence, \n154 ---- \"'\" 368 ft. 0.025 x 16.71 \nFrom Fig. 14, r:V1xj = 0.46. \n:.r:V =368 x 0.46 = 169.3 ft. \nWe see that the results obtained by using both the \nbilinear flow and the type-curve methods are ap\u00ad\nproximately the same; this fact increases confidence \nin the analysis performed. \nWellB \nA buildup test was run after fracturing this gas well. \nInformation about the test and results of analysis are \npresented in Table 3. A log-log graph of pressure \ndata (Fig. 18) indicates that the test was completely \ndominated by bilinear flow (quarter slope), \ncorresponding this example to Case 1 in the type\u00ad\ncurve-analysis section. \nThe bilinear flow graph (Fig. 19) yields a straight \nline whose slope, m bj' can be used to calculate \n(kjbj) usingEq. 20:"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 11, "chroma:document": "curve-analysis section. \nThe bilinear flow graph (Fig. 19) yields a straight \nline whose slope, m bj' can be used to calculate \n(kjbj) usingEq. 20: \nor (kjbj) Yz = (444.75 x 1,675 x 675)/[0.92 x 108 \nx 85 x (0.11 x 0.025 x 1.52x 10-4 \nx 0.0045) ~], \nIf we assume that the last data point corresponds to \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 12, "chroma:document": "0. u \n\"''::' U) \n0. \nco 9 \nQ \nE \n<J 2 \n(.H) last = 18 hours \nmbf = 0.92 x 108 ~, \ncp hrV\" \n2 \n1;4 1/4 (lit) (hour ) \nFig. 19 -Bilinear flow graph for Well B. 3 \nthe end of the bilinear flow period and (k fb f) D ~ 3, \nthen from Eq. 31, \n~ lOx2.637xlO-4X(95.3)2 X18 \nxf ~ 0.11 x 0.025 x 1.52 x lO -4 x 0.0045 \n=692 ft, \nand \nk b 95.3 ~ !S --=0.1377 md-ft/ft. xf 692 \nFromEq.6, \n( kfbf) 95.3 \n(k fb f) D = kx f !S -0-.0-04-5-x-6-9-2 ' \nFrom Fig. 14, r~/xf!S0.47; hence, r~ !S0.47 X 692, \nr~ !S325 ft. \nWelle \nAfter a flowing time of 1,890 hours, a buildup test \nwas run on this fractured oil well. Information for \nthe test and analysis results are presented in Table 4. \nFig. 20 shows a log-log graph of the pressure data; \nfrom this graph we can see that neither a one-fourth \nslope nor a half slope is exhibited by the data. This \nfigure also shows that pressure data match the curve \nfor (kfbf) D = 27r given in Fig. 15 and the last six \npoints fall on the semilog straight line."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e960-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 12, "chroma:document": "for (kfbf) D = 27r given in Fig. 15 and the last six \npoints fall on the semilog straight line. \nFrom the pressure match obtained in Fig. 20 and \nEq. 41, we estimate \nk= 141.2 x 220 x 1.2 x 0.8 x 0.34 \n49x 100 \n=2.07md. \nSEPTEMBER 1981 101 r-----r---,---,---,---,-----, \nBeg~nning of Semllog \nStraight Llnc \n1031-- - -1-- -1--1-- - -\nI I I !>latch POl.nt \nI (tlp)1'-! = 100 psi \n(PWO)M '\" 0.34 ___ 1 ___ J._ \nI {6t)M = 1 hr \n1 (tDr~)M = 0.19 \n1 I ' \n10 '----- -L ___ 1 ____ 1 ___ ..J \n10-1 I 10 102 103 \nLIt (hours) \n10-2 L,-----'-:----'--,-----'--~---'7-----'-;;-----.J \n10-3 10-2 10-1 10 1 102 103 \nFig. 20 -Type\u00b7curve matching for Well C. \nTABLE 4 -TEST INFORMATION AND ANALYSIS RESULTS \nFORWELLC \nReservoir Data \nProduction rate q, STBID \nProducing time tp, hours \nFormation thickness h, ft \nPorosity </>, fraction \nViscosity /1-, cp \nTotal compressibility ct, psi-1 \nFormation volume factor 80, bbllSTB \nWell bore radius r w, ft \nFlowing well bore pressure Pw', pSia \nAnalysis Results \nk,md"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88e9b0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 12, "chroma:document": "Formation volume factor 80, bbllSTB \nWell bore radius r w, ft \nFlowing well bore pressure Pw', pSia \nAnalysis Results \nk,md \n(k,btlo \nx\" ft \nk,b\" md-ft \nr;', ft \nS Type-Curve \nAnalysis \n2.07 \n211\" \n88.7 \n1,156 \n36.89 \n-4.99 220 \n1,890 \n49 \n0.15 \n0.8 \n17.6x 10-6 \n1.2 \n0.25 \n1,704 \nSemi log \nAnalysis \n2.28 \n30.37 \n-4.8 \nUsing information from the time match in Eq. 43, \nr' _~ 2.637x 10 4 x2.07x 1 \nw-0.15xO.8xI7.6xlO 6xO.19 \n= 36.9 ft. \nFrom Fig. 14, r~/xf=0.415; hence, \n36.9 \nxf= 0.415 = 88.9 ft. \nThe skin factor is estimated by \nr 0.25 s=ln ~ =In-- = -4 99 \nr~ 36.9 .. \n1761 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 13, "chroma:document": "7.--------,-------,--------,---r----, \n6 \n5 \n2. 4 \n'\" ~ m = 307 psi/cycle \n-3 \nQ. \n<l \n2 \no \no \n10-1 00 \no 00 \n{l>p} : -47 psi // 1hr \n101 \nlit Ihours/ \nFig. 21 -Semi log graph for Well C. \nThe fracture conductivity is \nkjbj= {kjbj)nkXj \n=27rx 2.07 x 88.9= 1,156.2 md-ft. \nFig. 21 is a semilog graph for this example. The \ncorrect semilog straight line has a slope m = 307 \npsi/cycle and (ilp) Ihr = -47 psi. The formation \npermeability can be calculated as \nk = _16_2_._6_qB_fJ. \nmh \n162.6 x 220 x 1.2 x 0.8 = =2.28md. 307x49 \nThe skin factor is \nS=1.151[{Llp)lhr -log( k 2)+3.2275J \nm 1>fJ.ctrw \n[-47 = 1.151 -307 \n2.28 \n-log 0.15 xO.8 x 17.6x 10-6 x (0.25)2 \n+ 3.2275 J = -4.8. \nFinally, the effective wellbore radius is \nr~ =r we-s =0.25 e4.8 \n= 30.37 ft. \nThe results provided by both the type-curve \nanalysis and semilog analysis methods are in good \nagreement. From these examples it is demonstrated \nthat type-curve analysis, when applied properly,"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 13, "chroma:document": "agreement. From these examples it is demonstrated \nthat type-curve analysis, when applied properly, \nprovides an excellent diagnostic tool and a technique \nto estimate both reservoir and fracture parameters. \n1762 Conclusions \nBased on the material presented in this work, the \nfollowing remarks are pertinent. \n1. The transient flow behavior of a vertically \nfractured well may exhibit four flow periods: (a) \nfracture linear flow, (b) bilinear flow, (c) formation \nlinear flow, and (d) pseudoradial flow. Bilinear flow \nis a new type of flow that has not been considered \nbefore. \n2. A new technique is presented to analyze data in \nthe bilinear flow period. It is shown that, during this \nflow period, a graph of pwj[or m (Pwj)] vs. Vi yields \na straight line whose slope is inversely proportional \nto h j{kjbj) Yz. \n3. New type curves are now available for pressure \nanalysis of fractured wells. The uniqueness problem \nin the analysis is reduced considerably with the use of"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 13, "chroma:document": "analysis of fractured wells. The uniqueness problem \nin the analysis is reduced considerably with the use of \nthese type curves. \n4. Prefracture information about the reservoir is \nnecessary to estimate fracture parameters. \n5. The type-curve analysis method must be used \nsimultaneously with the specific analysis methods \n(Pwfvs. Vt,Pwjvs.1t, andpwjvs.log t) to produce \nreliable results. \nAcknowledgments \nPart of this work was develo,ped at Stanford U. and \nthe Inst. Mexicano del Petroleo. We are grateful to \nmany people, especially H.J. Ramey Jr. for his \nencouragement and helpful comments. \nNomenclature \nb j = fracture width \nB = formation volume factor \nc = compressibility \nC = well bore storage coefficient \nFI ,F2 = correlating parameters for well bore \nstorage \nh = formation thickness \nh j = fracture height \nk = permeability \nkjbj = fracture conductivity \n(k jb j) n = dimensionless fracture conductivity \nm = slope of semilog straight line, gas \npseudopressure"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 13, "chroma:document": "kjbj = fracture conductivity \n(k jb j) n = dimensionless fracture conductivity \nm = slope of semilog straight line, gas \npseudopressure \nmbj = slope of straight line for bilinear flow \nP = pressure \nq = well flow rate \nr w = wellbore radius \nr~ = effective well bore radius \ns = skin factor or Laplace space variable \nt = time \nilt = shut-in time \nT = reservoir temperature \nX,Y = space coordinates \nXj = fracture half-length \n(X,{3 = unit conversion constants \nr = gamma function \n'Y/ = hydraulic diffusivity \n1> = porosity \nfJ. = fluid viscosity \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "Subscripts \nb= beginning \nbf = bilinear flow \ng gas \nD= dimensionless \ne = end \nf= fracture, flowing \ni = initial \n/f= linear flow \n0 oil \nt total \nxf based on xf \nw wellbore \nReferences \n1. Matthews, C.S. and Russell, D.G.: Pressure Buildup and \nFlow Tests in Wells, Monograph Series, SPE, DaJlas (1967) 1. \n2. Ramey, H.J. Jr., Kumar, A., and Gulati, M.S.: Gas Well Test \nAnalysis Under Water-Drive Conditions, AGA, Arlington, \nVA (1973). \n3. Earlougher, R.C. Jr.: Advances in Well Test Analysis, \nMonograph Series, SPE, Dallas (1977) 5. \n4. Theory and Practice of Testing of Gas Wells, third edition, \nEnergy Resources Conservation Board, Calgary, Alta. (1975). \n5. Ramey, H.J. Jr.: \"Practical Use of Modern Well Test \nAnalysis,\" paper SPE 5878 presented at the SPE 46th Annual \nCalifornia Regional Meeting, Long Beach, April 8-9, 1976. \n6. Raghavan, R.: \"Pressure Behavior of Wells Intercepting \nFractures,\" Proc., Invitational Well-Testing Symposium, \nBerkeley, CA, Oct. 19-21, 1977."}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "6. Raghavan, R.: \"Pressure Behavior of Wells Intercepting \nFractures,\" Proc., Invitational Well-Testing Symposium, \nBerkeley, CA, Oct. 19-21, 1977. \n7. Dyes, A.B., Kemp, C.E., and Caudle, B.H.: \"Effect of \nFractures on Sweep-Out Patterns,\" Trans., AI ME (1958) 213, \n245. \n8. Prats, M., Hazebroek, P., and Stickler, W.R.: \"Effect of \nVertical Fractures on Reservoir Behavior -Compressible\u00ad\nFluid Case,\" Soc. Pet. Eng. J. (June 1962) 87-94; Trans., \nAIME,225. \n9. Scott, J.O.: \"The Effect of Vertical Fractures on Transient \nPressure Behavior of Wells,\" J. Pet. Tech. (Dec. 1963) 1365-\n1369; Trans., AIME, 228. \n10. Horner, D.R.: \"Pressure Build-Up in Wells,\" Proc., Third \nWorld Pet. Cong., The Hague (1951) Sec. 11,503-523. \nII. Miller, C.C., Dyes, A.V., and Hutchinson, C.A. Jr.: \n\"Estimation of Permeability and Reservoir Pressure from \nBottom-Hole Pressure Build-Up Characteristics,\" Trans., \nAIME (1950) 189, 91-104. \n12. Matthews, C.S., Brons, F., and Hazebroek, P.: \"A Method"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "Bottom-Hole Pressure Build-Up Characteristics,\" Trans., \nAIME (1950) 189, 91-104. \n12. Matthews, C.S., Brons, F., and Hazebroek, P.: \"A Method \nfor Determination of Average Pressure in a Bounded \nReservoir,\" Trans., AIME (1954) 201,182-191. \n13. RusseJl, D.G. and Truitt, N.E.: \"Transient Pressure Behavior \nin Vertically Fractured Reservoirs,\" J. Pet. Tech. (Oct. 1964) \n1159-1170; Trans., AIME, 231. \n14. Clark, K.K.: \"Transient Pressure Testing of Fractured Water \nInjection WeJls,\" J. Pet. Tech. (June 1968) 639-643; Trans., \nAIME,243. \n15. Millheim, K.K. and Cichowicz, L.: \"Testing and Analyzing \nLow-Permeability Fractured Gas WeJls,\" J. Pet. Tech. (Feb. \n1968) 193-198; Trans., AIME, 243. \n16. Raghavan, R., Cady, G.V., and Ramey, H.J. Jr.: \"Well-Test \nAnalysis for VerticaJly Fractured Wells,\" J. Pet. Tech. (Aug. \n1972) 1014-1020; Trans., AIME, 253. \n17. Gringarten, A.C. and Ramey, H.J. Jr.: \"Unsteady-State \nPressure Distributions Created by a WeJl With a Single In\u00ad"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "17. Gringarten, A.C. and Ramey, H.J. Jr.: \"Unsteady-State \nPressure Distributions Created by a WeJl With a Single In\u00ad\nfinite-Conductivity Vertical Fracture, Soc. Pet. Eng. J. (Aug. \n1974) 347-360; Trans., AIME, 257. \n18. Gringarten, A.C. and Ramey, H.J. Jr.: \"Unsteady-State \nPressure Distributions Created by a Well With a Single \nHorizontal Fracture, Partial Penetration or Restricted En\u00ad\ntry,\" Soc. Pet. Eng. J. (Aug. 1974) 413-426; Trans., AIME, \n257. \n19. Gringarten, A.C., Ramey, H.J. Jr., and Raghavan, R.: \n\"Applied Pressure Analysis for Fractured WeJls,\" J. Pet. \nTech. (July 1975) 887-892; Trans., AIME, 259. \nSEPTEMBER 1981 20. Wattenbarger, R.A. and Ramey, H.J. Jr.: \"Well Test In\u00ad\nterpretations of Vertically Fractured Gas WeJls,\" J. Pet. \nTech. (May 1969) 625-632; Trans., AIME, 246. \n21. Ramey, H.J. Jr. and Gringarten, A.C.: \"Effect of High\u00ad\nVolume Vertical Fractures on Geothermal Steam WeJl \nBehavior,\" Proc., Second United Nations Symposium on the"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "Volume Vertical Fractures on Geothermal Steam WeJl \nBehavior,\" Proc., Second United Nations Symposium on the \nUse and Development of Geothermal Energy, San Francisco, \nMay 20-29, 1975. \n22. Cinco, H., Ramey, H.J. Jr., and Miller, F.: \"Unsteady-State \nPressure Distribution Created by a Well With an Inclined \nFracture,\" paper SPE 5591 presented at the SPE 50th Annual \nTechnical Conference and Exhibition, Dallas, Sept. 30-0ct. 3, \n1975. \n23. Raghavan, R. and Hadinoto, N.: \"Analysis of Pressure Data \nfor Fractured Wells: The Constant-Pressure Outer Boun\u00ad\ndary,\" Soc. Pet. Eng. J. (April 1978) 139-150; Trans., AIME, \n265. \n24. Raghavan, R., Uraiet, A., and Thomas, G.W.: \"Vertical \nFracture Height: Effect on Transient Flow Behavior,\" Soc. \nPet. Eng. J. (Aug. 1978) 265-277. \n25. Cinco, H., Samaniego, F., and Domlnguez, N.: \"Transient \nPressure Behavior for a Well with a Finite-Conductivity \nVertical Fracture,\" Soc. Pet. Eng. J. (Aug. 1978) 253-264."}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "Pressure Behavior for a Well with a Finite-Conductivity \nVertical Fracture,\" Soc. Pet. Eng. J. (Aug. 1978) 253-264. \n26. Holditch, S.A. and Morse, R.A.: \"The Effects of Non-Darcy \nFlow on the Behavior of HydraulicaJly Fractured Wells,\" J. \nPet. Tech. (Oct. 1976) 1169-1178. \n27. Ramey, H.J. Jr., Barker, B., Arihara, N., Mao, M.L., and \nMarques, J.K.: \"Pressure Transient Testing of Hydraulically \nFractured Wells,\" paper presented at American Society \nTopical Meeting, Golden, CO, April 12-14, 1977. \n28. Cinco, H. and Samaniego, F.: \"Effect of Wellbore Storage \nand Damage on the Transient Pressure Behavior of Vertically \nFractured WeJls,\" paper SPE 6752 presented at the SPE 52nd \nAnnual Technical Conference and Exhibition, Denver, Oct. 9-\n12,1977. \n29. Agarwal, R.G., Carter, R.D., and Pollock, C.B.: \n\"Evaluation and Prediction of Performance of Low\u00ad\nPermeability Gas WeJls Stimulated by Massive Hydraulic \nFracturing,\" J. Pet. Tech. (March 1979) 362-372; Trans., \nAIME,267."}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "Permeability Gas WeJls Stimulated by Massive Hydraulic \nFracturing,\" J. Pet. Tech. (March 1979) 362-372; Trans., \nAIME,267. \n30. Barker, B.: \"Transient Flow to Finite-Conductivity Vertical \nFractures,\" PhD dissertation, Stanford U., Palo Alto, CA \n1977. \n31. Barker, B.J. and Ramey, H.J. Jr.: \"Transient Flow to Finite\u00ad\nConductivity Vertical Fractures,\" paper SPE 7489 presented \nat the SPE 53rd Annual Technical Conference and Exhibition, \nHouston, Oct. 1-3, 1978. \n32. Scott, J.O.: \"A New Method for Determining Flow \nCharacteristics of Fractured WeJls -Application to Gas WeJls \nin Tight Formations,\" paper 78-T-2, AGA 1978 Transmission \nConference, Montreal, T-279-186. \nAPPENDIX A \nShort-Time Transient Pressure \nBehavior for a Well With \na Finite-Conductivity Fracture \nDerivation of Solution \nLet us consider the system described in the text of this \npaper. A fractured well produces at a constant flow \nrate from an infinite reservoir. At small time values,"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "paper. A fractured well produces at a constant flow \nrate from an infinite reservoir. At small time values, \nthe pressure behavior of the system is not affected by \nthe tips of the fracture. In addition, the flow in the \nformation is essentially linear and perpendicular to \nthe fracture plane. The reservoir and the fracture \nmay be treated as two different homogeneous \nregions. 25 \nIf the flow within the fracture is assumed to be \nlinear, the pressure behavior can be described by \na2pfD \na 2 + xD 2 apD I \n(kfbf) D aYD YD=O \n1763 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 15, "chroma:document": "= _1_ ap[D .................. (A-I) \n7JjD atDXj \nfor O<xD < 00, tDxj >0. \nInitial Condition. \nPfD =0, tDXj=O, O:s;xD <00. . .......... (A-2) \nBoundary Conditions. \napfD I = - 7r , tDx >0, \naXD XD=O (kfbf)D f \n. . . . . . . . . . . . . . (A-3) \nand \nlim PfD =0, tDxj >0, ............... (A-4) \nXD-OO \nwhere, in oilfield units, \n_ kh[Pi-Pf] \nPjD -141.2 qBJ.I. \nand kh [Pi -p] \nP D = 141.2 qBJ.I. \nx xD=-' xf \nY YD=-\u00b7 xf \nThe variables not included above are defined in the \ntext. P and P f represent the formation pressure and \nthe fracture pressure, respectively, x is the flow \ndirection in the fracture, and Y is the formation flow \ndirection perpendicular to the fracture plane. \nThe transient flow in the formation may be \ndescribed by \na2p ap D_~\u00b7O<y <00\u00b7 ~-!:I ' D ' aYD utDxj \ntDxj>O. . ................... (A-5) \nInitial Condition. \nPD =0; O<YD <00; tDXj=O ............. (A-6) \nBoundary Conditions. \nPD IYD=O =PfD; tDXj>O, .............. (A-7) \nand \nlim PD =0; tDxj>O ................. (A-8)"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 15, "chroma:document": "Boundary Conditions. \nPD IYD=O =PfD; tDXj>O, .............. (A-7) \nand \nlim PD =0; tDxj>O ................. (A-8) \nYD-OO \n1764 The two partial differential equations are already \ncoupled by the boundary conditions. Application of \nthe Laplace transformation with respect to. time to \nEqs. A-I through A-8 and simplification yields \na2pfD 2 apD I + --\naXD2 (kfbf) D aYD Yd=O \ns _ \n= -PfD; O<xD < 00 ........... (A-9) \n7JjD \nBoundary Conditions . \napfD I = - 7r , \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 (A-lO) \naXD Xd=O (kfbf) D \nlim PjD =0, ..................... (A-ll) \nXD-OO \nand \na2pD \naYD2 =SPD; O<YD<oo ............ (A-12) \nBoundary Conditions. \nPD IYD=O =PfD' .................... (A-l3) \nlim PD=O' ..................... . (A-14) \nYD-OO \nwhere \nPjD (xD' s) =\u00a3tDXj [PjD (XD,IDXj)]' \nand \nPD (YD' s) = \u00a3tDXj [PD (YD' tDXj) ]. \nNow let us define \nPD (r,s) = \u00a3YD [PD (YD,s)]. \nApplication of the Laplace transformation, with \nrespect tOYD, to Eq. A-12 yields \n2 ~ I ap D I ~ (A 15) r PD-rPD YD=O--a-- =sPD\u00b7\u00b7\u00b7-\n'YD YD=O"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 15, "chroma:document": "Application of the Laplace transformation, with \nrespect tOYD, to Eq. A-12 yields \n2 ~ I ap D I ~ (A 15) r PD-rPD YD=O--a-- =sPD\u00b7\u00b7\u00b7-\n'YD YD=O \nBy solving for PD and considering Eq. A-l3, we \nobtain \n_ oPD I rPfD+ -a-\n~ 'YD YD=O (A 16) PD= 2 \u2022 ...\u2022.\u2022.\u2022.. -r -s \nThe inversion of this equation with respect to Y D \nyields \na-\nP D = P jD cosh (...;s Y D) + : D I \n'YD YD=O \n................. (A-17) \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 16, "chroma:document": "From Eqs. A-14 and A-17, we can write \napD I - -- = -PfDYs. . ............. (A-18) \naYD YD=O \nNext, substitution of Eq. A-18 into Eq. A-9 allows \nus to write a partial differential equation with only \none dependent variable: \na2pfD _ S 2Ys_ \n2 - -+ PfD\u00b7 ........ (A-19) \naXD 'YlfD (kfbf) D \nThe solution of Eq. A-19 with boundary conditions \ngiven by Eqs. A-tO and A-II can be expressed as \n[ [ S 2Ys] Yz 7rexp -xD -+ \n-_ 'YlfD (kfbf) D ] prD-\np S 2Ys Yz \n(kfbf}DS[-+ b ] \n'YlfD (kf f) D \n....................... (A-20) \nThe pressure at the wellbore PwD is calculated at \nxD =0; thus, \n7r \nPwD = S 2Ys Y2\u00b7\u00b7 (A-21) \n(kfbf}D s[-+ ] \n'YlfD (kfbf}D \nFinally, the Laplace inversion of Eq. A-21 with \nrespect to 1 DXf produces \nPwD= ~ rDXf \n(kfbf) D 0 \n....................... (A-22) \nUnfortunately, Eq. A-22 is too complex to analyze \nboth the short-and long-time behavior of the \nsolution. Eq. A-21 may be used for this purpose. \nShort-Time Behavior \nThe short-time approximation of the solution can be"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 16, "chroma:document": "solution. Eq. A-21 may be used for this purpose. \nShort-Time Behavior \nThe short-time approximation of the solution can be \nobtained from Eq. A-21 by taking the limit as the \nvariable S approaches infinity. Thus, \n--~ PwD-(k\nfb\nf}DS312 ................. (A-23) \nInversion of this formula produces Eq. 8. \nLong-Time Behavior \nWe can obtain the solution for large values of time by \ntaking the limit of Eq. A-21 as S approaches zero; \nhence, \n7r \nPwD =::. ..J2(k\nfb\nf) D s5/4\u00b7 ............. (A-24) \nInverting Eq. A-24 produces Eq. 12. This solution \nalso may be obtained by considering incompressible \nflow within the fracture. \nSEPTEMBER 1981 Total Formation Flow \nEqs. A-18 and A-20 can be used to calculate the \nfraction of the well flow rate that is being produced \nfrom the formation. The formula for this case ap\u00ad\npears to be \nq formation = 1 _ exp( 41 DXr 2 ) \nq 7r2CfDf \n( 2..JIDxr ) . erfc . . ........ (A-25) \n7rCfDf \nFor small values of 1 Dx' the amount of fluid"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 16, "chroma:document": "q formation = 1 _ exp( 41 DXr 2 ) \nq 7r2CfDf \n( 2..JIDxr ) . erfc . . ........ (A-25) \n7rCfDf \nFor small values of 1 Dx' the amount of fluid \ncoming from the formation {s negligible; however, at \nlarge values of 1 Dx' most of the produced fluid \ncomes from the formation. This illustrates the \nphysical behavior of the system. \nAPPENDIXB \nDerivation of Correlation Parameters \nfor Bilinear and Linear Flows \nIf we consider a fracture of length xf' Eq. A-4 \nbecomes \napfD I =0 ....................... (B-1) \naXD xD=1 \nUsing Eq. B-1 instead of Eq. A-4 and considering \nincompressible flow within the fracture, the Laplace \ntransformation solution for the problem stated in \nAppendix A is \npWD=(-7r+ E 27rexp[-2n \nn=O \n[~ (kfb~)D2 tJ )/(S(kl'tln \n.[~ (kfb~)D2 t) ............ (B-2) \nor \nPWD (kfbf)D3~( -<+ 00 E 27r eXPt -2n \nn=O \nHence, \n1 [ S ~] PWD(kfbf}D = (k\nfb\nf}D2! (k\nfb\nf}D2 ... (B-4) \nFrom Laplace inversion tables, \nPWD (kfbf) D =F[tDx/ (kfbf) D2]. . ..... (B-6)"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 16, "chroma:document": "n=O \nHence, \n1 [ S ~] PWD(kfbf}D = (k\nfb\nf}D2! (k\nfb\nf}D2 ... (B-4) \nFrom Laplace inversion tables, \nPWD (kfbf) D =F[tDx/ (kfbf) D2]. . ..... (B-6) \n1765 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f13a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 17, "chroma:document": "Hence, a graph of Pw (kfbf)D vs. tDx (kfbf)2 . ld . I D f Yle s a smg e curve. \nFor small values of dimensionless time, Eq. B-3 \nyields Eq. A-24, corresponding to bilinear flow. \nThe long-time approximation of Eq. B-3 yields \n7r P WD ~ 2s312 ' .\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 (B-7) \nwhich is the Laplace transform of the dimensionless \npressure for the formation linear flow. \nAPPENDIXC \nDerivation of Correlation Parameters \nfor Bilinear Flow with \nWellbore Storage Effects \nWhen well bore storage effects are considered in the \nflow problem defined in Appendix A, the boundary \ncondition at x D = 0 becomes \napfD I 7r (1-CDf apWD), . (C-l) \naXD xD=O (kfbf) D atDxf \nwhere \nC = C Df 27rA.c hx 2' ................... (C-2) \n'I' t f \nand C is the wellbore storage coefficient. \nIf flow within the fracture is considered in\u00ad\ncompressible and Eq. C-1 is taken instead of Eq. A-\n3, the solution for the wellbore pressure in the \nLaplace space is given by \n7r \nPwD = -V2(kfbf) D s5/4 + 7rCDfS2'"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f18a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 17, "chroma:document": "3, the solution for the wellbore pressure in the \nLaplace space is given by \n7r \nPwD = -V2(kfbf) D s5/4 + 7rCDfS2' \nwhich can be written as \n1766 ...... (C-3) 4/3 C 4/3 s 5/4 \n(kfbf) D - _ ~Y2[ Df ] \nC 5/3 PwD-7r (k b ) 2/3 Df f f D \nCD//3s ~ \n+7r[ (kfbf)D2/3] j\" .. (C-4) \nFrom properties of the Laplace transformation, \n-I _1 [t] L !(as) -~F ~ ................... (C-5) \nHence, Eq. C-4 can be written as \n(kfbf)D2I3 =F[ (kfbf)D2I3 t ] \n(CDf) 113 PwD (CDf) 4/3 DXf' \n................... (C-6) \nThis means that the bilinear flow solutions including \nwell bore storage are represented by a single curve \nwhen graphed in terms of \n(k b ) 213 (k b ) 2/3 \n--\"\"f'--Lf'I::;'~;--PWD vs. f f ~/3 tDx' Cw (Cw) f \nSI Metric Conversion Factors \ncp x 1.0* E-03 = Pa\u00b7s \nft x 3.048* E-Ol = m \npsi x 6.894 757 E + 00 = kPa \n\u00b7Conversion factor is exact. JPT \nOriginal manuscript received in Society of Petroleum Engineers office Aug. \n10, 1978. Paper accepted for publication June 4, 1979. Revised manuscript"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f1da-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-7490-pa.pdf", "page": 17, "chroma:document": "10, 1978. Paper accepted for publication June 4, 1979. Revised manuscript \nreceived July 6,1981. Paper (SPE 7490) first presented at the SPE 53rd Annual \nTechnical Conference and Exhibition, held in Houston, Oct. 1-3, 1978. \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f22a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 0, "chroma:document": "Citation: Gabry, M.A.; Eltaleb, I.;\nSoliman, M.Y.; Farouq-Ali, S.M. A\nNew Technique for Estimating Stress\nfrom Fracture Injection Tests Using\nContinuous Wavelet Transform.\nEnergies 2023 ,16, 764. https://\ndoi.org/10.3390/en16020764\nAcademic Editor: Maria Grazia\nDe Giorgi\nReceived: 2 December 2022\nRevised: 23 December 2022\nAccepted: 27 December 2022\nPublished: 9 January 2023\nCopyright: \u00a9 2023 by the authors.\nLicensee MDPI, Basel, Switzerland.\nThis article is an open access article\ndistributed under the terms and\nconditions of the Creative Commons\nAttribution (CC BY) license (https://\ncreativecommons.org/licenses/by/\n4.0/).\nenergies\nArticle\nA New Technique for Estimating Stress from Fracture Injection\nTests Using Continuous Wavelet Transform\u2020\nMohamed Adel Gabry *\n , Ibrahim Eltaleb\n , Mohamed Y. Soliman\n and Syed M. Farouq-Ali\nDepartment of Petroleum Engineering, The University of Houston, Houston, TX 77023, USA\n*Correspondence: magabry@cougarnet.uh.edu"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f284-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 0, "chroma:document": "Department of Petroleum Engineering, The University of Houston, Houston, TX 77023, USA\n*Correspondence: magabry@cougarnet.uh.edu\n\u2020 Society of Petroleum Engineers Technical Conference and Exhibition, Houston, TX, USA, 3\u20135 October 2022.\nAbstract: The diagnostic fracture injection test (DFIT) is widely used to obtain the fracture closure\npressure, reservoir permeability, and reservoir pressure. Conventional methods for analyzing DFIT\nare based on the assumption that a vertical well is drilled in ultra-low permeability reservoirs with\npotential multiple closures but fails to consider horizontal wells. There is still signi\ufb01cant debate about\nthe rigorousness and validity of these techniques due to the complexity of the hydraulic fracture\nopening and closure process and assumptions of conventional fracture detection methods. The\npaper introduces a new method for detecting fracture closure pressure using the continuous wavelet"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f2d4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 0, "chroma:document": "paper introduces a new method for detecting fracture closure pressure using the continuous wavelet\ntransform (CWT). The new method aims to decompose the pressure fall-off signal into multiple levels\nwith different frequencies using the CWT. This \u201cshort wavy\u201d function is stretched or compressed and\nplaced at many positions along the signal to be analyzed. The wavelet then convoluted the signal\nyielding a wavelet coef\ufb01cient value. The signal energy is observed during the fracture closure process\n(pressure fall-off) and the fracture closure event is identi\ufb01ed when the signal energy stabilizes to\na minimum level. A prede\ufb01ned simple commercial fracture simulation case with known fracture\nclosure, \ufb02ow regime modeling, and actual \ufb01eld cases was used to validate the new methodology.\nKeywords: continuous wavelet transform; diagnostic fracture injection test; hydraulic fracture;\nminimum horizontal stress; geothermal reservoirs\n1. Introduction\n1.1. Scope of Study"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f324-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 0, "chroma:document": "minimum horizontal stress; geothermal reservoirs\n1. Introduction\n1.1. Scope of Study\nEstimating the minimum horizontal stress is a critical part of building formation\ngeomechanical models, designing hydraulic fractures, designing drilling schedules, etc.\nHydraulic fracturing design and execution need to calibrate the mechanical Earth model\nwith a reliable method. This is performed to identify the formation stresses. Classical\nmethods for obtaining the minimum horizontal stress of the formation relies on the open-\nhole well logs (Eaton (1969) [ 1]; Blanton and Olson (1999) [ 2]). These methods can be\ncategorized into two main techniques. The \ufb01rst technique relies on compressional and\nshear sonic waves to estimate dynamic geo-mechanical properties. The second technique\nuses correlations to calculate the dynamic properties of the rock from conventional well-\nlogging parameters, then calculates the minimum horizontal stress [3]."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f3ce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 0, "chroma:document": "logging parameters, then calculates the minimum horizontal stress [3].\nThe actual in situ minimum principal stress of the formation is calculated by calibrating\nagainst the closure pressure from diagnostic pumping test [ 4]. That is performed by\npumping a small volume of non-wall building \ufb02uids to create a small fracture and then\nanalyze the pressure decline to know the pressure at which that fracture closes. That\nfracture closure pressure should be the average of the minimum principal stress for the\narea covered by the created fracture.\nAs no possible physical observation of the fracture propagation and closure in com-\nplicated subsurface formations, there are signi\ufb01cant debates surrounding the various\nmethodologies used to determine closure pressure. This is because of several reasons. The\nEnergies 2023 ,16, 764. https://doi.org/10.3390/en16020764 https://www.mdpi.com/journal/energies"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f450-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 1, "chroma:document": "Energies 2023 ,16, 764 2 of 29\n\ufb01rst reason is that the hydraulic fracture propagation and closure process are fairly compli-\ncated due to the formation stress state, the presence of natural fractures, heterogeneity, and\nthe anisotropy of the subsurface formations\u2019 properties. Conventional closure detection\nmethods have pre-set assumptions to simplify the state of the subsurface formation. Some\nof them may simplify the leak off to carter leak off, whilst other methods assume the\nconstant compliance or make certain assumptions regarding the \ufb02ow regimes or the state\nof injection. Many tests may deviate from the assumed pre-set conditions. The detected\nclosure be confused by the formation pressure response after the fracture closure. The\npressure change propagates in the formation and produces behavior that may be confused\nwith fracture closure detection.\nAlthough fracture closure is de\ufb01ned as the pressure at which a fracture closes, there"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f4c8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 1, "chroma:document": "with fracture closure detection.\nAlthough fracture closure is de\ufb01ned as the pressure at which a fracture closes, there\nis an attempt to detect the contact pressure when the two fracture faces \ufb01rst come into\ncontact with one another. Assuming that closure pressure does not really exist, there is an\naperture between fracture faces. Complications regarding how the fracture propagates and\ncloses cause the interpreted fracture closure pressure debatable. In most cases, the industry\nworkers try various methods to determine the range of closure pressure. To date, there is no\nglobal technique that can detect closure without pre-assumptions. Each of the conventional\nmethods detects the closure from a speci\ufb01c point of view with certain pre-assumptions.\nThis paper introduces an innovative method to \ufb01nd the closure pressure using the wavelet\ntransform technique as a general technique without any pre-assumptions. It uses an"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f540-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 1, "chroma:document": "transform technique as a general technique without any pre-assumptions. It uses an\nindependent mathematical microscope to \ufb01nd the fracture closure pressure in the pressure\nfall-off signal. The new technique is validated using different ways: using simulated\nsynthetic pressure data from a fracture simulator and using \ufb02ow regime modeling by\nreverse calculating a pressure decay signal assumed to be both before fracture closure and\nafter fracture closure \ufb02ow regimes. The main advantage of this technique is that there is no\nneed to know formation parameters in advance or have a pre-prescribed testing procedure.\nSince the beginning of the 1990s, the science and engineering applications of wavelet\ntransform have increased at a remarkable growth rate. Thousands of peer-reviewed journals\nare now interested in wavelet transform applications covering numerous disciplines such\nas \ufb02uids, medicine, and fractal geometry. However, its use in the oil and gas industry"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f5b8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 1, "chroma:document": "as \ufb02uids, medicine, and fractal geometry. However, its use in the oil and gas industry\nand geothermal energy has been limited to date. A lot of the data recorded in multiple\ndisciplines are considered as signals to be analyzed to understand the physics-based\nmodels covering the many applications. For example, Germ\u00e1n-Sall\u00f3 et al. (2018) [ 5]\nintroduced a method for crack detection in manufacturing systems using digital signal\nprocessing methods.\nSignal processing is widely used in the medical \ufb01eld to detect heart problems by\nanalyzing electrocardiography (ECG) signals. Research in the medical \ufb01eld deploys wavelet\ntransform to compare the ECG signals of a healthy heart to another ECG signal associated\nwith a diseased heart. The same methodology is adopted in the industrial application\nof signal processing to predict motor failure. For instance, the analysis of the vibration\nsignal of a motor can help detect bearing failure when the recorded signal is compared to a\nfunctional motor."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f644-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 1, "chroma:document": "signal of a motor can help detect bearing failure when the recorded signal is compared to a\nfunctional motor.\nWith the ongoing digitalization of the modern oil and gas industry and geothermal\nenergy industry, the same technique can be used in the analysis of hydraulic fracturing. In\nthis case, changes in pressure and rate over time are recorded during the fracture propa-\ngation stages, proppant placement, and fracture closure to determine what is happening\nthousands of feet below the Earth\u2019s surface during hydraulic fracturing treatment. The\nmost common methodology used by researchers for engineering wavelets applications is\nto try to \ufb01nd a correlation between the features detected from the signals and the actual\nphysical response of the system. The main problem with this methodology in hydraulic\nfracturing is the complexity of hydraulic fracturing propagation and closure due to fracture\nface roughness or natural fracture intensity and directions and a lot of other factors. This"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f6d0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 1, "chroma:document": "face roughness or natural fracture intensity and directions and a lot of other factors. This\nmay be complex not only because of the heterogeneity of the reservoir, but also because of\nthe interaction of the hydraulic fracture with natural fractures, \ufb01ssures, and other geologic"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f75c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 2, "chroma:document": "Energies 2023 ,16, 764 3 of 29\nfeatures. Thus, all the complicating factors should be removed from the system to \ufb01nd a\nsignal representing a closure event in a homogeneous reservoir with no geologic complexi-\nties. In order to understand the CWT behavior during fracture closure, a numerical fracture\nsimulator is used in this study.\nThe application of wavelet analysis in the oil industry was pioneered twenty years\nago by Soliman et al. (2003) [ 6] as an application for well-test analysis and fracturing. The\nwavelet transform technique is a data transform technique that convolves the pressure\nand/or temperature data using a short wavy signal called \u201cwavelet\u201d. This convolution can\nbe performed at discrete points in the discrete wavelet transform (DWT) or continuously\nusing the CWT. The wavelet transform provides a representation of the pressure signal\nby letting the translation and scales of the wavelets vary continuously. This enables the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f7b6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 2, "chroma:document": "by letting the translation and scales of the wavelets vary continuously. This enables the\nanalyst to \ufb01nd the details of the pressure data by observing the wavelet energy spectrum\nfor the monitored signal (pressure and/or temperature).\nAs the DWT is computationally cheaper, it was used as the \ufb01rst step to detect fracture\nclosure. The main disadvantage of using the DWT is its requirement of a uniform sampling\nrate and the detected closure pressure changes with an increasing level of decomposition.\nSoliman, Unal, Siddiqui, Rezaei, and Eltaleb (2019) [7,8] initiated a methodology to detect\nthe fracture closure pressure using the DWT. Determining the closure pressure in this\nmethodology is based on analyzing the detail levels to pick the time when the variance\nchanges. Eltaleb et al. (2020) [ 9] and Eltaleb et al. (2021) [ 10] improved the rigor of the\ntechnique using an energy density plot. The technique was compared to the G-function"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f810-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 2, "chroma:document": "technique using an energy density plot. The technique was compared to the G-function\ntechnique and showed good agreement. The DWT technique involves a multiresolution\nwavelet decomposition that breaks the (recorder pressure) signal into high pass (noise) and\nlow pass (approximation) components at various levels. The plot of energy distribution\nin time is constructed using the energy of the high pass component (noise) at different\ndecomposition levels. These plots provide means of capturing the physical changes in\nthe fracture system through pressure fall-off. They represented the noise energy in the\nrecorded pressure at different frequency levels. The closure pressure in this methodology\nwas determined based on changes in the noise energy of the recorded pressure and where\nit drops to a minimum stabilized level.\nThis paper introduces a closure detection technique similar to that introduced by\nEltaleb et al. (2021) [ 10], however, using the CWT. Using the CWT does not need a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f860-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 2, "chroma:document": "Eltaleb et al. (2021) [ 10], however, using the CWT. Using the CWT does not need a\nuniform sampling rate and captures all signal details. CWT can be used as a method for\ndetecting the fractal dimension which is one of the key features of complex wavelets that\nis sometimes referred to as a \u201cmathematical microscope\u201d to detect the features. Using\nCWT was recommended by Fatmir (2020) through personal communication. CWT can\nbe used as a \ufb01lter to detect the signal features. It has the \ufb02exibility to be used with or\nwithout a uniform sampling rate. Thus, it could be validated using any type of data. This\nnew method was applied to both the fracture simulator data and actual \ufb01eld data. The\nsynthetic data were produced using a commercially available fracture simulator developed\nby Barree (1983) [ 11] based on fracture propagation and closure simulation principles with\nprede\ufb01ned fracture closure. Azlinda et al. (2010) [ 12] showed good agreement between the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f8b0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 2, "chroma:document": "prede\ufb01ned fracture closure. Azlinda et al. (2010) [ 12] showed good agreement between the\nused fracture simulator with down-hole events in a stacked \ufb02uvial pay system. The CWT\ntechnique showed success with the actual real \ufb01eld data conducted on one of the oil and\ngas \ufb01elds and in another case in a geothermal reservoir.\n1.2. History of Closure Pressure Detection Techniques\nThe basic concept of classical methods of closure event detection from the pressure\ndecay of the diagnostic fracture injection test is combining the basic concepts of well\ntesting and hydraulic fracture analysis. After hydraulic fracturing was \ufb01rst introduced by\nClark (1949) [ 13], it was recognized that hydraulic fracturing could be used as a method\nto estimate the magnitude of minimum principal stress (Hubbert and Willis (1957) [ 14];\nGodbey and Hodges (1958) [ 15]; Kehle (1964) [ 16]; Haimson and Fairhurst (1967) [ 17];\nHickman and Zoback (1983) [ 18]). The main idea was to pump \ufb02uid at a pressure higher"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f90a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 3, "chroma:document": "Energies 2023 ,16, 764 4 of 29\nthan the fracturing pressure, to initiate a hydraulic fracture and propagate it through the\nformation. The minimum principal stress can be estimated from pressure measurements\nduring and after injection. Nolte (1979) [ 19] extended the applicability of fracturing tests\nby developing analytical techniques that can be used to estimate \ufb02uid leak-off parameters.\nThese techniques can be used to obtain the leak-off rate of complex \ufb02uids such as linear gel\nor cross-linked gel. These tests are typically called mini-frac tests (McLennan and Roegiers,\n(1982) [ 20]) or fracture calibration tests (Mayerhofer and Economides (1993) [ 21]). This is\nperformed to estimate the ef\ufb01ciency of the fracturing \ufb02uid after the interpretation of the\nminimum horizontal stress. One of the most widely used functions to obtain the closure\npressure is G-function (Nolte (1979) [ 19]). Several techniques have subsequently been"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f95a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 3, "chroma:document": "pressure is G-function (Nolte (1979) [ 19]). Several techniques have subsequently been\npublished as essential parts of the analysis, including those by Castillo (1987) [ 22] as well\nas Barree and Mukherjee (1996) [ 23]. Further modi\ufb01cations for the analysis were added,\nfor example, by Mayerhofer and Economides (1993) [ 21] and Mayerhofer et al. (1995) [ 24]\nshowed how to remove the \ufb01lter cake effect and its effect on the \ufb02uid leak-off factor from\nthe analysis. The recent development of the shale gas reservoirs came out with a new test\nthat uses the non-wall building \ufb02uid instead of the cross-linked gel or linear gel. It is called\nthe \u201cdiagnostic fracture injection test\u201d (DFIT). It is routinely performed in unconventional\nreservoirs due to the incapability to \ufb02ow the well to do a pressure transient analysis. The\nDFIT is used to obtain the best estimates for stress, permeability, and pore pressure (Craig\nand Brown (1999) [25]. The analysis of pressure decay data has two parts."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f9aa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 3, "chroma:document": "and Brown (1999) [25]. The analysis of pressure decay data has two parts.\nThe \ufb01rst part of the DFIT analysis is called \u201cPre-closure analysis methods\u201d which\nare usually based on techniques from Nolte (1979) [ 19] and Mayerhofer and Economides\n(1993) [ 21], Mayerhofer et al. (1995) [ 24], Barree and Mukherjee (1996) [ 23], and Barree\net al. (2009) [ 26]. These methods are used to estimate the closure pressure and calibrate\nthe minimum principal stress. The second part is called \u2018Post-closure\u2019 analysis methods\nwhich are usually based on techniques from conventional well testing (Gu et al. (1993) [ 27];\nSoliman et al. (2005) [ 28]; Craig and Blasingame (2006) [ 29]) or the \u2018linear \ufb02ow time\nfunction\u2019 technique developed by Nolte et al. (1997) [ 30]. Due the development of uncon-\nventional reservoirs, multiple DFIT interpretation techniques have recently been developed\nby Marongiu-Porcu et al. (2011; 2014) [ 31,32], Soliman and Kabir (2012) [ 33], Soliman and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88f9fa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 3, "chroma:document": "by Marongiu-Porcu et al. (2011; 2014) [ 31,32], Soliman and Kabir (2012) [ 33], Soliman and\nGamadi (2012) [ 33], Cramer and Nguyen (2013) [ 34], Padmakar (2013) [ 35], Wallace et al.\n(2014) [ 36], Meng et al. (2014) [ 37], Craig (2014) [ 38], Zanganeh et al. (2018) [ 39], and\nHawkes et al. (2018) [40].\nOne of the noticeable techniques is the compliance method that was recently intro-\nduced by McClure et al. (2014; 2016) [ 41,42] and Jung et al. (2016) [ 43]. This technique\nusually leads to an earlier and higher stress estimate in contrast to the commonly used\ntangent method (Barree et al. (2009) [ 26]) which is considered a modi\ufb01cations to Nolte\u2019s\n(1979) [ 19] technique. The technique introduced a new concept which is contact pressure\ninstead of closure pressure. McClure et al. (2016) [ 42] and Jung et al. (2016) [ 43] per-\nformed detailed DFIT simulations considering the effect of a residual aperture fracture"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fa54-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 3, "chroma:document": "formed detailed DFIT simulations considering the effect of a residual aperture fracture\nafter the contact between the fracture walls. Simulations indicate that, in low permeabil-\nity formations, the contacting of the fracture walls causes the magnitude of the pressure\nderivative to increase, resulting in a pressure signal that was previously interpreted as\nthe height recession or closure of transverse fractures (Barree et al. (2009) [ 26]. Wang\nand Sharma (2017) [ 44] reproduced these \ufb01ndings and proposed a modi\ufb01ed approach for\nestimating stress called the \u2018variable compliance method\u2019. Currently, there are two main\nclosure detection techniques that are used by the industry, the tangent method, and the\ncompliance method.\nThe initial technique of the G function introduced by Nolte (1979) [ 19] relied on several\nassumptions for the pumping and shut-in periods with some simpli\ufb01ed concepts of how a\nfracture propagates and closes. Nolte (1979) [ 19] provided the G time function to detect"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88faa4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 3, "chroma:document": "fracture propagates and closes. Nolte (1979) [ 19] provided the G time function to detect\nthe changes in the pressure during the shut-in period of the diagnostic pumping. The\nsecond derivative (GdP/dG) is used to detect the closure. The closure de\ufb01ned by this\ntechnique is the pressure at a time when the deviation from the straight line starting from"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fafe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 4, "chroma:document": "Energies 2023 ,16, 764 5 of 29\nzero in GdP/dG occurs. The detailed equations for the G time function were discussed\nby Nolte (1979) [ 19]. Castillo (1987) [ 22] added the condition that dP/dG should be with\nzero slopes at the same point. The tangent method was introduced to cope with the\ncomplicated fracture closure as a modi\ufb01cation for the Nolte (1979) [ 19] technique. The\ntangent method proposed four types of leak-off in the formation during the closure, normal\nleak-off, pressure-dependent leak-off, transverse storage leak-off or height recessions, and\ntip extension leak-off. It is taken from a plot of GdP/dG versus G. A straight line is\ndrawn from the origin to the tangent to the curve. The closure pressure is de\ufb01ned as the\npressure when the GdP/dG starts to deviate downward. The pressure at that point is\ntaken as the tangent method stress estimate. The tangent method was developed to match\nnumerical simulations by Barree and Mukherjee (1996) [ 23] and Barree et al. (2009) [ 26]."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fb9e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 4, "chroma:document": "numerical simulations by Barree and Mukherjee (1996) [ 23] and Barree et al. (2009) [ 26].\nTheir work introduced a G-function signature for each type of leak-off. Each type of leak-\noff can characterize speci\ufb01c reservoir properties such as the presence of natural fractures,\nthe presence of lower permeability streaks or weak barriers surrounding the pay zone.\nThe tangent method in many cases shows a monotonic increase which makes the closure\npressure too low to be identi\ufb01ed. The tangent method is affected by the formation response\nafter the fracture closure. It is normally associated with the square root of time and log\u2013log\nanalysis, as recommended by Baree et al. (2009) [ 26]. The pre-closure \ufb02ow regime and\npost-closure \ufb02ow regimes should be identi\ufb01ed to support the closure detected using the\ntangent method. The second derivative of pressure to the square root of time should show\na local peak at the closure. The relations between the log\u2013log, square root of time, and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fbee-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 4, "chroma:document": "a local peak at the closure. The relations between the log\u2013log, square root of time, and\ntangent method were discussed in detail by Baree et al. (2009) [ 26]. The log\u2013log technique\nand square root of time method can be combined as the \u201cHolistic Fracture Diagnostics\u201d as\ndescribed by Baree et al. (2007) [45].\nThe compliance method for estimating stress was developed from mathematical\nsolutions of the fracture closure process (McClure et al. (2016) [ 42]). As per the compliance\nmethod, the very early part of the shut-in is ignored as the pressure drops very rapidly.\nThis part of the transient is ignored because it is caused by the dissipation of near-wellbore\ntortuosity related to the initiation of a transverse hydraulic fracture from a horizontal\nwell. The straight section of the pressure versus G-time plot can be extrapolated back to\nthe y-intercept to estimate the pressure in the far-\ufb01eld fracture at shut-in (the so-called"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fc48-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 4, "chroma:document": "the y-intercept to estimate the pressure in the far-\ufb01eld fracture at shut-in (the so-called\neffective initial shut-in pressure). After the initial period, the pressure curve settles into\nan approximately straight line. The \u2018compliance method\u2019 of estimating stress identi\ufb01es\nthe contact pressure at the point where the derivative increased from the minimum and\nsubtracts 75 psi to account for a stress shadow from the residual aperture (McClure et al.\n(2019) [ 46]). The 75 psi adjustment is based on a numerical simulation that matches the\n\ufb01eld DFITs (McClure et al. (2019) [46]).\nWhen the fracture walls contact, the stiffness increases, and the storage coef\ufb01cient\ndrops as per Sneddon (1946) [ 47]. This causes the dP/dG to increase when the fracture walls\ncome into contact. McClure et al. (2016 [ 42], 2019 [ 46]) note that, because of the roughness\nof the fracture walls, the \ufb02uid pressure may be higher than the minimum principal stress"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fc98-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 4, "chroma:document": "of the fracture walls, the \ufb02uid pressure may be higher than the minimum principal stress\nwhen the walls come into contact. Thus, it is recommended to estimate the closure pressure\nas 75 psi lower than the contact pressure based on numerical simulations. The contact\npressure is estimated by plotting the magnitude of dP/dG and identifying the point where\nthis derivative reaches a minimum and begins to increase. This is the so-called \u2018compliance\u2019\nmethod stress estimate. It is noticeable that the \u2018compliance method\u2019 is close to the classical\nmethod by Nolte (1979) [ 19]. However, an upward de\ufb02ection in dP/dG is not always seen\nin the shut-in transients.\nIn a lot of cases, dP/dG continuously decreases during the shut-in. McClure et al.\n(2019) [ 46] discussed the possible causes of the lack of an upward de\ufb02ection. That may\nbe due to the excessive near-wellbore tortuosity as the fracture closes almost immediately"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fce8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 4, "chroma:document": "be due to the excessive near-wellbore tortuosity as the fracture closes almost immediately\nafter shut-in. The monotonic dP/dG might arise from the continued fracture propagation\nafter shut-in. One of the key assumptions of G-function is that the fracture does not\npropagate after shut-in. This makes the G-function not accurate in many cases. McClure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fd42-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 5, "chroma:document": "Energies 2023 ,16, 764 6 of 29\net al. (2019) [ 46] recommended interpreting tests with a monotonic dP/dG as indicating\n\u2018rapid closure\u2019 in vertical wells where the near wellbore tortuosity is usually minimal and\nsupplementing dP/dG plots with plots of \u2018relative stiffness\u2019 versus pressure. The relative\nstiffness is not a normalized value calculated to be proportional to the system stiffness.\nIn tests where near-wellbore tortuosity is possible, McClure et al. (2019 [ 46]; 2022 [ 48])\nrecommended declining to provide a stress estimate and labeling the stress uninterpretable.\nMcClure et al. (2022) [ 48] found that \ufb01fty-nine percent of cases showed a clear upward\nde\ufb02ection; twenty-\ufb01ve percent of cases showed an adequate upward de\ufb02ection; and sixteen\npercent of cases showed no indication of an upward de\ufb02ection (i.e., a monotonic decrease\nin dP/dG).\nFrom the previous discussions, closure detection is still open for research and needs"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fd92-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 5, "chroma:document": "in dP/dG).\nFrom the previous discussions, closure detection is still open for research and needs\nmore studies to understand the complications of fracture closure without pre-assumptions\nand fewer data requirements, which is the main advantage of wavelet transform techniques.\n2. Methodology\n2.1. Wavelet Transform\nWavelet transform is a mathematical transformation applied to signals to obtain\ninformation that is not readily available. This signal can be pressure or any parameter\nrecorded during \ufb01eld operations. In practice, most signals are in the time domain in their\nraw format and plotted as a time\u2013amplitude representation of the signal. As a result,\nthis is not always the best representation of the signal for most signal processing-related\napplications; hence, the most valuable features are usually hidden in the signal frequency.\nSeveral transformations may be used to analyze the acquired signals. Fourier trans-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fde2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 5, "chroma:document": "Several transformations may be used to analyze the acquired signals. Fourier trans-\nforms (FTs) are the most widely used signal processing technique that gives signal frequency\ninformation. However, it does not provide timely information on which those frequency\ncomponents exist. FT works best in the analysis of stationary signals whose time domain\nis periodic; then, the time domain signal can be converted into a combination of sine and\ncosine waves to in\ufb01nity duration (Rioul and Vetidsaerli (1991) [49]).\nOne modi\ufb01cation for the Fourier transform is the windowed Fourier transform (WFT).\nIt is a tool for extracting local-frequency information from the non-stationary signal. The\nsignal is divided into small stationary segments through window functions whose width\nmust equal the part of the signal where it is stationary. As discussed by Kaiser (1994) [ 50],\nWFT is prone to inaccurate results due to the aliasing of high- and low-frequency compo-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fe32-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 5, "chroma:document": "WFT is prone to inaccurate results due to the aliasing of high- and low-frequency compo-\nnents that do not fall within the window function proposed by the technique. Wavelet\ntransform (WT) has a dynamical frequency spectrum and can represent the signals in\nboth the time and frequency domains. Figure 1 summarizes the difference between each\nsignal representation. As the wavelets analysis has a high dynamical frequency and a high\nresolution in both frequency and time domains, it is preferred for signals with a wide range\nof dominant frequencies and time\u2013frequency localization independence.\nWavelet transform analysis uses small wavelike functions known as wavelets. Math-\nematically, it can be de\ufb01ned as the convolution of the signal with the wavelet function.\nFigure 2 shows a few of the most common wavelet types.\nWavelets can be manipulated through translation (i.e., moving the wavelets along\nthe time axis) and scale (i.e., stretching and squeezing the wavelet at a particular point in"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fe8c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 5, "chroma:document": "the time axis) and scale (i.e., stretching and squeezing the wavelet at a particular point in\ntime). The scale and translation of wavelets govern parameters (b) and (a), respectively, in\nEquation (1).\nT(a,b)=1\u221aa\u222b\u221e\n\u2212\u221ex(t)\u03c8\u2217(t\u2212b\na)\ndt (1)\nThe Equation (1) comprised both the signal x(t), which could represent the pressure,\ntemperature, or any time series data, as well as the ( \u03c8\u2217(t\u2212b)/a) mother wavelet function.\nThe wavelet transform works by superimposing the wavelet function on an arbitrary signal,\nas illustrated in Figure 3. Time segments A and B, where both the wavelet and original\nsignal agree (positive or negative), will result in a large positive transformation value of"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88fedc-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 6, "chroma:document": "Energies 2023 ,16, 764 7 of 29\nthe integral given by Equation (1). On the contrary, in regions C, D, and E, when the\nwavelet and the signal have opposite signs, the overall transformation results in a negative\ncontribution to T(a,b).\nFigure 1. Comparison between different signal representations.\nFigure 2. Shapes of different wavelet transform families.\nFigure 3. Mechanism of wavelet transform [51]."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ff2c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 7, "chroma:document": "Energies 2023 ,16, 764 8 of 29\nWhen using complex wavelets, the resulting coef\ufb01cient consists of both real and\nimaginary parts. Fourier transforms of complex wavelets are zero for negative frequencies.\nTherefore, we can separate the phase and frequency components within the signal using\ncomplex wavelets. For instance, taking Fourier to transform the Mexican hat wavelet\nand then performing an inverse Fourier transform after neglecting the zero components\nin the Fourier transform will create a complex wavelet. It produces a less oscillatory\ntransform than in the case of real wavelets because a complex wavelet only responds to\nthe non-negative frequencies of the particular real signal. Therefore, it outperforms real\nwavelets in detecting and tracking instantaneous frequencies (Guerrero, A.P ., and Paredes,\nG. E. (2018) [52]). Complex wavelet transform is used in our analysis, which is de\ufb01ned by\nEquation (2) where the \ufb01rst part is the normalization factor, the second part is the complex"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ff7c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 7, "chroma:document": "Equation (2) where the \ufb01rst part is the normalization factor, the second part is the complex\nsinusoid, and the \ufb01nal part is the Gaussian bell curve.\n\u03c8(t)=1\n\u03c01/4ei2\u03c0f0te\u2212t2/2(2)\nTo inspect the multi-scale dimensional characteristics of a signal using complex\nwavelets, the Wavelet Transform Modulus (WTM) can be calculated using Equation (3).\nT(a,b)=\u221a\n[Re(T(a,b))]+[Im(T(a,b))] (3)\nOne of the main features of the signals that can be observed and analyzed to identify\nthe system properties is the analysis of signal energy. For any signal, the total energy\ncontained in a signal, x(t), is de\ufb01ned as its integrated squared magnitude as in Equation (4)\nwith the condition that the signal must contain \ufb01nite energy.\nE=\u222b\u221e\n\u2212\u221e|x(t)|2dt (4)\nThe relative contribution of the signal energy contained at a speci\ufb01c scale (a) and\nlocation (b) is given by the two-dimensional wavelet energy density function:\nE(a,b)=|T(a,b)|2(5)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88ffd6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 7, "chroma:document": "location (b) is given by the two-dimensional wavelet energy density function:\nE(a,b)=|T(a,b)|2(5)\nThe plot E(a)versus time (different location parameters b values) at different dilation\nparameter values (scale) (a) can be plotted in a plot called a scalogram. From the scalogram,\nthe location and scale of dominant energetic features within the signal can be detected from\nthe scale-dependent wavelet energy spectrum of signal E(a)at a speci\ufb01c scale. A plot of\nE(a,b)as a function of time and frequency is known as a scalogram. Scalograms are usually\nplotted with a logarithm and a scale axis. For example, Figure 4 shows a scalogram for The\nNino3 SST monthly climate time data series analyzed using Morlet wavelets (Torrence and\nCompo (1998) [53]), as discussed by Addison, P .S. (2016) [51].\nThe features that are detected at small scales, the compressed wavelet, are the rapidly\nchanging details (\ufb01ne features) that cause high frequency in the signal while the features"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890030-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 7, "chroma:document": "changing details (\ufb01ne features) that cause high frequency in the signal while the features\nthat are detected at large scales (stretched wavelet) are the slowly changing details (coarse\nfeatures) that cause high frequency in the signal."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890080-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 8, "chroma:document": "Energies 2023 ,16, 764 9 of 29\nFigure 4. Example for the wavelet transform analysis of the monthly climate temperature (Nino3 SST)\ntime series data: ( a) The Ni\u00f1o3 SST time series data; and ( b) the local wavelet power spectrum using\nthe wavelet transform analysis of ( a) using the Morlet wavelet (Torrence and Compo (1998) [53]).\n2.2. CWT Fracture Closure Detection Technique\nIn this study, a new innovative technique to \ufb01nd a closure pressure using the CWT\ntechnique is introduced. The main idea behind estimating the minimum stress using the\ndiagnostic fracture injection test is to create a small fracture at a constant rate and then\nshut down the pumps and observe the pressure at which the fracture closes. The closure\npressure is the minimum average of the minimum stress for the area covered by the fracture\ncreated by the DFIT. The pressure during the shut-in and the observation period represents\nthe closure process of the formation. The main goal is to detect and magnify the pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8900d0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 8, "chroma:document": "the closure process of the formation. The main goal is to detect and magnify the pressure\nchanges that re\ufb02ect the fracture\u2019s closure event. The pressure signal during the shut-in\nperiod after DFIT is analyzed using the CWT technique with a complex Morlet wavelet to\nobtain the signal energy. The complete work\ufb02ow for the CWT closure detection technique\nis shown in Figure 5. The technique starts by getting the coef\ufb01cient of CWT using the\ncomplex Morlet wavelets at multiple scales (from zero up to a scale of 256) and then getting\nthe wavelet transform modulus (WTM) using Equation (3) as a scalogram. The scalogram\nof signal energy is plotted using a log scale. The scalogram can be averaged to the average\nof the log signal energy of all scales. Fracture closure as a dominant feature can be identi\ufb01ed\nby the average of all log signal energies at several wavelet scales. The average of the log of\nsignal energy can be plotted with time. The plot can be used to detect the closure event as"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89012a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 8, "chroma:document": "signal energy can be plotted with time. The plot can be used to detect the closure event as\nseen in Figure 5.\nFracture closure can be identi\ufb01ed with the two following features: the fracture closure\nstarts with a peak in the average of the log signal energy, which represents the fracture walls\ncoming into contact, then the drop in log signal energy level to a minimum stabilized level,\nwhich represents reaching the equilibrium state. The characteristics of fracture closure\ncan be seen in Figure 6. When the real \ufb01eld data are analyzed, high oscillatory signal\nenergy may be observed due to the noise of real \ufb01eld data. That may be due to several\nreasons, and the fracture faces are not smooth faces and the closure does not happen in\nsubsurface formation instantaneously, or there is noise in the pressure data, or due to that,\nthe equilibrium state is still disturbed with the DFIT."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89017a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 9, "chroma:document": "Energies 2023 ,16, 764 10 of 29\nFigure 5. Fracture closure detection work\ufb02ow using the CWT closure detection technique.\nFigure 6. Fracture closure pressure using CWT closure detection technique.\n2.3. Summary\nThe new CWT fracture closure detection technique can be conducted as the following\nsteps: The \ufb01rst step is to apply the CWT using a complex Morlet wavelet for the pressure\nsignal starting from the start of DFIT pumping to obtain the CWT coef\ufb01cient at different\nscales up to (a = 256) as per Equation (1) and then obtain the wavelet transform modulus\n(WTM) as per Equation (4) from the complex continuous wavelet coef\ufb01cient. This can\nbe followed by the calculation of signal energy using Equation (2). Considering fracture\nclosure is a dominant feature so it can be detected by averaging the log of signal energy\nvalues at each time point for different scales (up to scale (a) = 256). From the plotted signal"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8901f2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 9, "chroma:document": "values at each time point for different scales (up to scale (a) = 256). From the plotted signal\naverage log energy versus time, the start and the end of the fracture closure event can\nbe identi\ufb01ed with the following characteristics. The start of the fracture closure which\nrepresents the contact of two fracture faces can be recognized by a peak in average signal\nlog energy at the start of the fracture closure. The fracture closure can be identi\ufb01ed by the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89024c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 10, "chroma:document": "Energies 2023 ,16, 764 11 of 29\ndrop in signal average log energy level to a minimum stabilized level. The start of the\nminimum stabilized level characterizes the end of the fracture closure event.\n3. Results and Discussion\n3.1. Validation Using Fracture Simulation\nThe numerical simulations in this study were performed using the commercial pla-\nnar 3D fracture simulator introduced by Barree (1983). The simulator integrates a \ufb01nite\ndifference formulation for the \ufb02uid \ufb02ow calculation within the fracture with an integral\nequation for fracture width. Fluid pressure and fracture width solutions are sequentially\ncoupled based on the linear-elastic solution of the deformation for an in\ufb01nite half-space\nwith a concentrated load. This relies on Poiseuille\u2019s equation along with the continuity\ncondition. It uses a pressure-dependent leak-off model for the effect of natural fractures.\nThis simulation is solved using \ufb01nite differences with a regular grid. The shear-rate and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89029c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 10, "chroma:document": "This simulation is solved using \ufb01nite differences with a regular grid. The shear-rate and\ntime-dependent laboratory \ufb02uid test data are used to model the \ufb02uid rheology. Proppant\ntransport is coupled with \ufb02uid \ufb02ow and iteratively solved for proppant distribution in\nfractures. The simulator is widely used by the oil and gas industry and its fracture geometry\nis validated by downhole events in a stacked \ufb02uvial pay system as per Nur. Azlinda et al.\n(2010) [12].\nTo test the new CWT closure detection technique using fracture simulation, grids for\nthe synthetic model are created with ideal properties; the idealized reservoir model has\n25 ft. of the sand body between two shale barriers with a sharp stress contrast and constant\nvalues for reservoir characteristics and geo-mechanical parameters. High-stress contrast\nbetween the pay zone and the surrounding shale zones is assumed. It is assumed that\nthe reservoir is tight (the formation permeability is 5 micro Darcy) and a simulation run"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8902ec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 10, "chroma:document": "the reservoir is tight (the formation permeability is 5 micro Darcy) and a simulation run\nwas conducted with a \ufb02uid volume (10,000 gallons of KCL water) of diagnostic fracture\ninjection test with the typical pumping rate of 8 bbl/min followed by 700 min of leak-off.\nThis is a standard DFIT procedure that is followed by the oil/gas industry. The KCL\nwater is commonly used to prevent clay swelling and it is a non-wall building \ufb02uid with\nviscosity changes with temperatures. The concentration of KCL is dependent on the needed\nhydrostatic for the DFIT. The pumping rate is selected to be 8 bbl/min as the maximum\nof the range of the DFIT pumping rate (3\u20138 bbl/MIN). The geomechanical and reservoir\nproperties are shown in Figure 7. The perforation shot per foot is selected to be six shots per\nfoot. The DFIT pumping schedule is implemented in the fracture simulator as per Figure 8.\nThe simulation model showed fracture propagation followed by complete fracture closure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890346-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 10, "chroma:document": "The simulation model showed fracture propagation followed by complete fracture closure\nat 153 min when the average width is equal to zero, as shown in Figure 9. The complete\nclosure pressure is 5075 psi as per the fracture simulation."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890396-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 11, "chroma:document": "Energies 2023 ,16, 764 12 of 29\nFigure 7. The mechanical Earth model and reservoir properties for the fracture simulation model\nused to test the CWT closure detection technique.\nFigure 8. Synthetic model 1 pumping chart.\nFigure 9. Average width pro\ufb01le for synthetic model 1."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8903e6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 12, "chroma:document": "Energies 2023 ,16, 764 13 of 29\nThe pressure from the fracture stimulation was analyzed with CWT to obtain the\naverage energy over wavelet scales (up to scale (a) = 256). The average log signal energy\nwas plotted against the time to detect the fracture closure in Figure 10. The energy signal in\nFigure 10 showed a peak at a time of 149 min which happens at a bottom-hole pressure of\n5095 psi. That pressure represents the start of the closure. The complete closure is when\nthe signal average energy drops to a stabilized level. As shown in Figure 10, the CWT\ntechnique showed a closure pressure at 5075 psi.\nFigure 10. Fracture closure pressure detection using the CWT technique for synthetic model 1.\nTo understand how the average log signal energy responds to fracture closure, the\nchange in the average width pro\ufb01le created by the fracture simulator is plotted as a semi-\nlog scale against time to magnify the changes in width during the closure. That is to be"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890440-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 12, "chroma:document": "log scale against time to magnify the changes in width during the closure. That is to be\ncompared with the average log signal energy to understand how the CWT closure detection\ntechnique detected fracture closure. It can be noticed that the difference in the average\nwidth pro\ufb01le reached zero at the same time when the average log signal energy reached\nthe stabilized level, as seen in Figure 11.\nThe limitations of the conventional methods are the assumptions behind each method.\nFor example, the G-function, square root, time, and log\u2013log are based on well-testing con-\ncepts, built on a constant pumping rate and shut-in. Therefore, the variable-rate pumping\nschedule does not ideally \ufb01t the basic concepts of these methodologies. However, the\nintroduced CWT closure detection is a technique that does not rely on built-in assump-\ntions. It depends on the wavelet transform acting as a global mathematical microscope"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890490-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 12, "chroma:document": "tions. It depends on the wavelet transform acting as a global mathematical microscope\nto obtain the physical response of the signal. The closure detection technique was tested\nfor a variable pumping rate case. A pumping schedule with a variable pumping rate was\nsimulated using the same ideal homogeneous geomechanical parameters used in Figure 7.\nThe pumping rate started at 4 bbl/min and then increased to 8 bbl/min and \ufb01nally to\n10 bbl/min, as shown in Figure 12. The simulation model showed fracture propagation\nand then complete fracture closure at 184.5 min, where the average width is equal to zero\nas shown in Figure 13."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8904e0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 13, "chroma:document": "Energies 2023 ,16, 764 14 of 29\nFigure 11. Comparison between the change in average width pro\ufb01le and CWT closure detection\ntechnique plot.\nFigure 12. Synthetic model 2 pumping chart."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89053a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 14, "chroma:document": "Energies 2023 ,16, 764 15 of 29\nFigure 13. Average width pro\ufb01le for synthetic model 2.\nThe simulation for synthetic example 2 yielded the same closure pressure of 5075 psi\nbut at a time of 184.5 min. That is what was expected using as the pumping rate changed\nfrom the synthetic model 1. The pressure from the fracture stimulation was analyzed\nwith the CWT closure detection technique by plotting the average of the log signal energy\nagainst time. From Figure 14, it is clear that the signal energy showed a peak at 169 min,\nrepresenting the bottom hole pressure of 5095 psi, which represents the start of the closure\nprocess. The complete closure pressure is at the moment when the signal average energy\ndrops to a stabilized level at a time of 184.5 min (closure pressure = 5075 psi). As shown\nin Figure 14, the CWT analysis yielded a closure pressure at 5075, the fracture closure is\nthe same as in the \ufb01rst synthetic model since the geomechanical parameters are the same."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89058a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 14, "chroma:document": "the same as in the \ufb01rst synthetic model since the geomechanical parameters are the same.\nHowever, the closure time changed due to a change in the pumping rate and \ufb02uid volume.\nFigure 14. Signal average log energy using CWT for synthetic model 2.\n3.2. Validation Using Flow Regime Modeling\nTo further test the new technique with the complicated nature of the fracture closure, a\nnew approach was developed. This approach may be used to validate the CWT technique\nusing \ufb02ow regime modeling with a synthetic pressure decay signal that has no noise and\nrepresents the characteristic \ufb02ow regimes that happen before and after fracture closure. The\n\ufb02ow regime is identi\ufb01ed by the rate of change in pressure with time. A set of \ufb02ow regimes\nwere assumed to obtain a synthetic pressure leak-off signal that has a rate of change in\npressure representing those \ufb02ow regimes, then the wavelet transform technique was tested"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8905da-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 15, "chroma:document": "Energies 2023 ,16, 764 16 of 29\nto know how the CWT closure detection technique detects the closure. Various pre-closure\nand post-closure \ufb02ow regimes can be identi\ufb01ed on the log\u2013log \u2206t d\u2206p /d\u2206t versus \u2206t\nplot. Table 1 shows the \ufb02ow regimes that happen pre-closure and post-closure and their\ncorresponding slopes on the log\u2013log \u2206td\u2206p /d\u2206t versus \u2206t. The basic concept can be\nvisualized as given in Figure 15. Table 1 the \ufb02ow regimes that happen pre-closure and\npost-closure and their corresponding slopes on the log\u2013log \u2206t d\u2206p /d\u2206t versus \u2206t.\nTable 1. The \ufb02ow regimes that happen pre-closure and post-closure and their corresponding slopes\non the log\u2013log \u2206t d\u2206p /d\u2206t versus \u2206t.\nThe Slope of the log\u2013log \u2206t d\u2206p/d\u2206t vs.\u2206t Flow Regime\nHalf slope (1/2) Pre-closure Linear \ufb02ow regime\nQuarter slope (1/4) Pre-closure bilinear \ufb02ow regime\nNegative half-slope ( \u22121/2) Post-closure linear \ufb02ow regime\nNegative three-fourth slope ( \u22123/4) Post-closure bilinear \ufb02ow regime"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89062a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 15, "chroma:document": "Negative half-slope ( \u22121/2) Post-closure linear \ufb02ow regime\nNegative three-fourth slope ( \u22123/4) Post-closure bilinear \ufb02ow regime\nNegative unit slope ( \u22121) Post-closure pseudo radial \ufb02ow regime\nFigure 15. Transient \ufb02ow regimes before and after fracture closure.\nPre-closure and post-closure \ufb02ow regimes can be identi\ufb01ed using the semi-log pressure\nderivative on the log\u2013log plot of \u2206p vs.\u2206t during the shut-in period following the fracture\ninjection test. A pseudo linear \ufb02ow period is identi\ufb01ed by parallel (1/2) slope lines on the\nlog\u2013log \u2206p\u2206t and\u2206t d\u2206p/d\u2206t\u2206t plot up until fracture closure as seen in Figure 16a,b.\nBilinear \ufb02ow can be identi\ufb01ed by parallel (1/4) slope lines on log\u2013log \u2206pwf versus \u2206t and\n\u2206t d\u2206p/d\u2206t versus \u2206t prior to fracture closure as seen in Figure 16c.\nAfter closure, the pseudo linear formation \ufb02ow period is identi\ufb01ed by a ( \u22121/2) slope\nof the semi-log derivative of the pressure difference on the same plot, and pseudo radial"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890684-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 15, "chroma:document": "of the semi-log derivative of the pressure difference on the same plot, and pseudo radial\n\ufb02ow is identi\ufb01ed by a ( \u22121) slope of the semi-log derivative on the log\u2013log plot, as seen in\nFigure 16a,b. It is dif\ufb01cult to obtain all the \ufb02ow regimes in one real \ufb01eld case. Thus, the\nperfect fracture closure log\u2013log plot can be synthetically created assuming \ufb02ow regime\nslopes and then calculating the pressure decay signal as seen in Figure 17. The slopes that\nwere assumed are the slopes of the log\u2013log plot of \u2206t d\u2206p/d\u2206t vs.\u2206t for each period of\npressure decay signal are shown in Table 2."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8906d4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 16, "chroma:document": "Energies 2023 ,16, 764 17 of 29\nFigure 16. (a) Normal leak off log\u2013log plot; ( b) pressure-dependent leak off log\u2013log plot; and ( c) tip\nextension log\u2013log plot (Barree et al. (2009) [26]).\nTable 2. The slopes of the log\u2013log plot of \u2206t d\u2206P/d\u2206t vs.\u2206t for the reverse-calculated pressure\ndecay signal.\nStart, min. End, min.The Slopes of\nthe log\u2013log Plot\nof\u2206t d\u2206P/d\u2206t\nvs.\u2206tPressure at\nStart, psi.Pressure at\nEnd, psi.\n0 5 Pumping period Pumping period Pumping period\n5 15 0.3 12,000 11,692\n15 40 0.5 11,692 11,499\n40 50 0.25 11,499 11,445\n50 200 \u22120.5 11,445 11,216\n200 360 \u22121 11,216 11,168"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890724-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 17, "chroma:document": "Energies 2023 ,16, 764 18 of 29\nThe pressure decay signal and its corresponding \ufb02ow regimes are shown in Figure 17.\nThe synthetic pressure decay signal can be used to illustrate that the wavelet transform\ndetects the features within the signal itself and not only the noise associated with it. It can\nalso be used to investigate the response of each closure detection technique. The synthetic\npressure decay signal was analyzed using each technique as if it was real \ufb01eld data.\nFigure 17. Synthetic reverse-calculated pressure decay signal.\nThe application of the conventional technique, the tangent method (Barree et al.\n(2009) [ 26]), showed that dP/dG monotonically decreases so it can be either rapid closure\nor it is not valid to be analyzed using the compliance method (Mcclure et al. (2022) [ 48]).\nHowever, the effective shut-in pressure is 11,850 psi which is delayed from the pump\nshut-down time by a minute and a half. There is no rise in dP/dG. The tangent method"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890774-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 17, "chroma:document": "shut-down time by a minute and a half. There is no rise in dP/dG. The tangent method\nusing GdP/dG detected the closure pressure at 11,445 psi which represents the end of the\nlinear pre-closure \ufb02ow regime. The dP/dG and GdP/dG are shown in Figure 18. The\npre-closure bilinear \ufb02ow regime is ignored by the tangent method. The application of the\nCWT closure detection technique detected the closure at the same point of the change\nfrom the bilinear \ufb02ow regime to the after-fracture-closure linear \ufb02ow regime. It accurately\ndetected the transition period between pre-closure and post-closure, as can be seen in\nFigure 19. The fracture closure is usually identi\ufb01ed at the end of the pre-closure linear \ufb02ow,\nbut this is not accurate as the pre-closure bilinear \ufb02ow can be detected in several real \ufb01eld\ncases. However, that bilinear \ufb02ow period is very short and cannot be observed in many real\n\ufb01eld cases. CWT closure detection technique detected the transition between pre-closure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8907ce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 17, "chroma:document": "\ufb01eld cases. CWT closure detection technique detected the transition between pre-closure\nand post-closure with a clear peak. The change in \ufb02ow regime between the pre-closure\nand post-closure periods can also be identi\ufb01ed with smaller and smoother peaks. The\nclosure pressure detected using the CWT technique matches the most accurate de\ufb01nition of\ncomplete fracture closure.\nFigure 18. Tangent method (dP/dG and GdP/dG) for the synthetic reverse-calculated pressure\ndecay signal.\nThe large peak matches the closure process as seen in Figure 19. This is when the\nfracture closes and the \ufb02ow starts to follow a formation linear \ufb02ow regime. This includes\nthe period of bilinear \ufb02ow where the formation and fracture \ufb02ow together and each of them"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890846-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 18, "chroma:document": "Energies 2023 ,16, 764 19 of 29\nshows a linear \ufb02ow regime. The multiple peaks that are shown in the reverse-calculated\npressure decay signal are not shown in fracture simulation synthetic data as the fracture\nsimulation did not include the post-closure reservoir \ufb02ow regimes. It only simulates\nhydraulic fracture propagation and closure.\nFigure 19. Closure pressure detection using the CWT technique for the synthetic reverse-calculated\npressure decay signal.\n3.3. Application of CWT on Real Field Data\nThe main challenge for any technique is to be applied to real \ufb01eld data. We compared\nthe closure pressure of a real \ufb01eld DFIT case estimated using the CWT technique to the\nconventional methods such as the tangent method, log\u2013log, and square root of the time and\ncompliance methods. This was performed to determine how the CWT closure detection\ntechnique stands up against other techniques used in the industry. Thus, two real \ufb01eld"}


