# embeddings_queue

created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8810b2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 2, "chroma:document": "to negative change in aperture) with respect to effective normal\nstress, the negative of the derivative of aperture with respect to\neffective normal stress, or the derivative of aperture with respectto pressure [Chapter 12 from Jaeger et al. (2007)]. The fracture\nstiffness is equal to the reciprocal of the fracture compliance. The\nname \u201cfracture compliance method\u201d is chosen because the\nmethod is based on understanding how fracture compliance (and\nequivalently, stiffness) change because of fracture closure.At very early time, there is often a sharp drop in pressure\ncaused by the disappearance of friction in the wellbore and near-\nwellbore. This period should not be considered when picking clo-sure pressure. A linear period on the plot of Pvs.Gshould be\nvisible after the end of this initial period. When closure occurs in\nlow-permeability formations, increasing fracture stiffness causes\npressure to de\ufb02ect downward and G/C2dP/dGto de\ufb02ect upward, as"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88110c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 2, "chroma:document": "low-permeability formations, increasing fracture stiffness causes\npressure to de\ufb02ect downward and G/C2dP/dGto de\ufb02ect upward, as\ndiscussed in the Stiffness Contrast at Closure section. A detailedderivation of the equations describing this process are provided in\nAppendix A.\nIn high-permeability formations, closure reduces the leakoff\nrate, and closure can cause pressure to de\ufb02ect upward and G/C2dP/\ndGto de\ufb02ect downward (though continue increasing), as dis-\ncussed in Section 3.1.6. The G/C2dP/dGplot is useful for identify-\ning closure because it makes it easy to identify these de\ufb02ections.\nThe key difference between our work and most previous work\non this topic is that we consider the effect of residual aperture on\n\ufb02uid storage after mechanical closure. We use a 3D hydraulic-fracture simulator that rigorously solves the hydromechanically\ncoupled problem of fracture initiation and closure. When fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88115c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 2, "chroma:document": "coupled problem of fracture initiation and closure. When fracture\nwalls come into contact, the simulator switches to a nonlinearjoint-closure law on the basis of the work of Barton et al. (1985),\nwhich allows the fracture to remain hydraulically conductive\nand continue to store \ufb02uid after mechanical closure has occurred.\nSimilar approaches were used by other authors (Koning and\nNiko 1985; Plahn et al. 1997; van den Hoek 2002; Ribeiro andHorne 2013).\nThere is abundant evidence demonstrating that fractures retain\nstorativity and conductivity after the walls have come into contact\n(mechanical closure). Fractures retain aperture after mechanical\nclosure because of mismatch of asperities in the fracture walls.An extensive literature exists on the relationship between fracture\naperture, conductivity, \ufb02uid pressure, and stress (Gangi 1978;\nWitherspoon et al. 1980; Walsh 1981; Barton et al. 1985; Brown\nand Bruhn 1998; Pyrak-Nolte and Morris 2000). The \u20131/2 slope"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8811b6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 2, "chroma:document": "Witherspoon et al. 1980; Walsh 1981; Barton et al. 1985; Brown\nand Bruhn 1998; Pyrak-Nolte and Morris 2000). The \u20131/2 slope\npressure transients frequently observed in Bourdet plots of DFITdata indicate the presence of a post-closure in\ufb01nite conductivity\nfracture, demonstrating that the fracture has retained signi\ufb01cant\naperture after closure. In high-permeability formations, the \ufb02uidstorage and conductivity-retained post-closure quickly becomes\nnegligible. But in very-low permeability formations, leakoff into\nthe matrix is very slow, and an extremely narrow fracture aperture\ncan have a dominant effect on the pressure transient.\nThe dimensionless fracture conductivity (or equivalently,\ndimensionless fracture transmissivity) is de\ufb01ned as:\nC\nfD\u00bcT\nkLf; \u00f05\u00de\nwhere Tis the fracture transmissivity, kis the matrix permeability,\nandLfis the fracture half-length. A fracture will behave similar to\nan in\ufb01nite-conductivity fracture as long as Cfd>300. From the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881206-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 2, "chroma:document": "andLfis the fracture half-length. A fracture will behave similar to\nan in\ufb01nite-conductivity fracture as long as Cfd>300. From the\ncubic law (Witherspoon et al. 1980), the fracture transmissivity isde\ufb01ned as\nT\u00bce3\n12; \u00f06\u00de\nwhere eis the hydraulic aperture.\nFor a fracture with half-length of 50 m and a matrix permeabil-\nity of 10/C019m2(/C25100 nd), the fracture will be in\ufb01nitely conduc-\ntive as long as the fracture aperture is greater than 26 mm.\nMethods\nThe numerical simulations are performed with CFRAC (Complex\nFracturing ReseArch Code), which fully couples \ufb02uid \ufb02ow with\nthe stresses induced by fracture deformation in discrete-fracture\nnetworks (McClure and Horne 2013). All simulations described in\nthis paper assume a single planar fracture perpendicular to theminimum principal stress. The simulations are fully 3D, with the\nfractures discretized into square elements in the vertical and hori-\nzontal directions. Complete descriptions of CFRAC are provided.............................."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881260-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 2, "chroma:document": "zontal directions. Complete descriptions of CFRAC are provided..............................\n...................\n...............................\n................................J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1323 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###160007August 2016 SPE Journal 1323"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8812b0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 3, "chroma:document": "by McClure and Horne (2013) and McClure et al. (2015). Rele-\nvant details are summarized in this section.\nThe \ufb02uid is single phase, single component, constant compres-\nsibility ( cf), constant viscosity ( l), and has initial density of qinit.\nThe simulations are isothermal, and the effect of gravity is\nneglected. The simulations are initialized with homogeneous\nstress and \ufb02uid pressure.\nNonlinear relationships are used to relate pressure, stress, and\ndeformation to aperture. We de\ufb01ne a \u201cclosed\u201d fracture as a frac-\nture in which the \ufb02uid pressure is less than the normal stress and\nthe walls of the fracture are in contact. Roughness of the fracture\nwalls allows closed fractures to retain hydraulic and void aperture.\nWe de\ufb01ne an \u201copen\u201d fracture as a fracture where the \ufb02uid pres-sure has reached the normal stress and the walls are no longer\nin contact.\nThe aperture of closed-fracture elements is estimating with the\nfollowing joint-closure relation, which was written in this form by"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881300-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 3, "chroma:document": "in contact.\nThe aperture of closed-fracture elements is estimating with the\nfollowing joint-closure relation, which was written in this form by\nWillis-Richards et al. (1996), on the basis of the work of Bartonet al. (1985):\nE\u00bc\nE0\n1\u00fe9r0\nn=rn;ref; \u00f07\u00de\nwhere Eis the void aperture (\ufb02uid volume stored in the fracture\nper surface area), E0is the residual aperture (the aperture at effec-\ntive normal stress equal to zero), and rn,refis the 90% closure\nstress (i.e., the effective normal stress that reduces Eto 10% of\nE0). The fracture-effective normal stress, r0\nn, is equal to the nor-\nmal stress, rn,minus \ufb02uid pressure, P. In the simulations for this\nstudy, the void aperture and hydraulic aperture are assumed to\nbe equal.\nFor open elements, the aperture is de\ufb01ned as:\nE\u00bcE0\u00feEopen; \u00f08\u00de\nwhere Eopenis the mechanical separation between the fracture walls.\nA special algorithm is used to de\ufb01ne the value of E0for hy-\ndraulic fractures. When a hydraulic-fracture element \ufb01rst starts, it"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88135a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 3, "chroma:document": "A special algorithm is used to de\ufb01ne the value of E0for hy-\ndraulic fractures. When a hydraulic-fracture element \ufb01rst starts, it\nis given a very small aperture, 0.1 mm. But the residual aperture of\na fully open fracture should be on the order of ten or hundred of\nmicrons. To handle this issue, an algorithm is used that allows E0\nto increase as the fracture opens. The algorithm mimics the natu-\nral process of fracture-roughness development as the crack starts\nand opens. The algorithm sets E0of each element to be equal to\n90% of the maximum aperture reached by the element, allowingE\n0to increase, but never decrease. A maximum value for E0is\nspeci\ufb01ed, Ehf,max,resid .\nFluid leakoff is calculated, assuming that the reservoir is\nslightly compressible with compressibility of c/,initial porosity\nof/init, and contains the same \ufb02uid as the injection \ufb02uid. Leakoff\nis calculated with the semianalytical method of Vinsome and\nWesterveld (1980), which assumes 1D leakoff, but accounts for"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8813aa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 3, "chroma:document": "is calculated with the semianalytical method of Vinsome and\nWesterveld (1980), which assumes 1D leakoff, but accounts for\nchanging pressure in the fracture over time.\nPoroelastic-stress changes in the fracture caused by \ufb02ow in the\nmatrix are neglected. Also, poroelastic-pressure response in thematrix caused by fracture deformation is neglected. Poroelastic-\nstress effects on the fracture are not typically considered for DFIT\nanalysis (Nolte 1979; Barree and Mukherjee 1996). In a typical\nDFIT (very-low permeability), the region of pressure increase\naround the fracture is very narrow, and so the poroelastic effect ofstress on the fracture is slight (Perkins and Gonzalez 1985; Wal-\nlace et al. 2014).\nThe mechanical calculations are performed, assuming that the\nformation is mechanically homogeneous, isotropic, and linearly\nelastic. The calculations are performed with the boundary-element\nmethod of Okada (1992), which uses constant displacement, rec-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881404-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 3, "chroma:document": "elastic. The calculations are performed with the boundary-element\nmethod of Okada (1992), which uses constant displacement, rec-\ntangular elements in an elastic half-space. This method satis\ufb01es\nthe equations of quasistatic-stress equilibrium, Hooke\u2019s law,and compatibility, giving results that are convergent with\nmesh re\ufb01nement to exact analytical solutions (Babazadeh and\nMcClure 2015).For a mechanically open element, the condition is enforced\nthat (Crouch and Star\ufb01eld 1983)\nr\nr\nn/C0P\u00feDrn\u00bc0; \u00f09\u00de\nwhere rr\nnis the normal stress on the fracture caused by remote\nloading (calculated from the initial conditions) and Drnis the\nchange in normal stress caused by stress induced by the cumula-\ntive deformation of all the fracture elements in the system, as cal-\nculated from the Okada (1992) method.\nClosed elements experience small normal displacements in\nresponse to changes in effective normal stress (Eq. 7). The stress\nchanges caused by these aperture changes are included in the sim-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881454-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 3, "chroma:document": "response to changes in effective normal stress (Eq. 7). The stress\nchanges caused by these aperture changes are included in the sim-\nulations with the method described in Sections 2.2.3 and 2.2.4 of\nMcClure and Horne (2013).\nFracture initiation occurs at the wellbore when the \ufb02uid pres-\nsure reaches the minimum principal stress. Propagation is handled\nwith linear elastic-fracture mechanics. The stress-intensity factor\nat the crack tips (vertically and horizontally) is calculated numeri-\ncally, and propagation occurs when the stress-intensity factorreaches the fracture toughness.\nIn the simulations for this paper, the fracture height is assumed\nto be limited to no more than 7 m. The only exception is Simula-tion G1, in which there is no height con\ufb01nement and the fracture\npropagates radially.\nThe wellbore and near-wellbore pressure drop is modeled as\nproportional to the square of the \ufb02ow rate from the wellbore to\nthe formation,\nDP\nnw\u00bcCnwQ2; \u00f010\u00de"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8814ae-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 3, "chroma:document": "proportional to the square of the \ufb02ow rate from the wellbore to\nthe formation,\nDP\nnw\u00bcCnwQ2; \u00f010\u00de\nwhere Cnwis a constant and Qis the volumetric \ufb02ow rate from the\nwellbore to the formation. This term combines the effect of fric-\ntion in the wellbore, the perforations, and the near-wellbore\nregion. The perforation pressure drop is a function of the numberof \ufb02owing perforations, the perforation diameter, and the perfora-\ntion shape (Cramer 1987). Friction in the wellbore is related to\nwellbore diameter and the wellbore roughness (Moody 1944).\nTypically, the pressure drop associated with injection through\nwell tubulars and perforations during DFIT treatments is verysmall, especially when the injection rate is 2 bbl/min or less. The\nmost-important pressure drop is typically downstream of the per-\nforations: (1) along a tortuous \ufb02ow path from the perforations tothe primary fracture and/or (2) caused by the interaction of multi-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8814fe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 3, "chroma:document": "forations: (1) along a tortuous \ufb02ow path from the perforations tothe primary fracture and/or (2) caused by the interaction of multi-\nple (short) fractures of different orientations (longitudinal, multi-\nple transverse orientations, horizontal) which is set up as the\nresult of near-wellbore stress concentration (e.g., hoop stress).\nResults and Discussion\nIn the following sections, various simulation results are presented\nand discussed. In the Generic Simulations subsection, a series ofgeneric simulations are performed to investigate the effect of differ-\nent physical processes on pressure-transient behavior. In the Field\nDFIT #1 subsection, a simulation result is provided that matches\nField DFIT #1. Field DFIT #1 is a straight-forward, uncomplicated\ncase, and so an almost perfect match to the data is possible. In theGas Research Institute/Department of Energy (GRI/DOE) M-site\nTests subsection, data are provided from the GRI/DOE M-site \ufb01eld-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88154e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 3, "chroma:document": "Tests subsection, data are provided from the GRI/DOE M-site \ufb01eld-\ndemonstration project. At this site, hydraulic-fracture injectionswere performed in conjunction with downhole tiltmeter measure-\nments in an offset well that provide an independent estimate of the\nclosure pressure. Table 1 provides the settings used in all simula-\ntions. Table 2 provides settings that are varied between simulations.\nIn all \ufb01gures showing pressure-transient results, arrows indi-\ncate the identi\ufb01cation of closure from the tangent method (blue),\nthe fracture compliance method (orange), the Mohamed et al.\n(2011) method (green), and the Craig and Blasingame (2006)\nmethod (red).\nGeneric Simulations. In this section, a series of generic DFIT\nsimulations is presented. Superposition time, s,andG-time are........................\n.....................................................\n..........................J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1324 Total Pages: 19"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88159e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 3, "chroma:document": "..........................J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1324 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###1600071324 August 2016 SPE Journal"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881620-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 4, "chroma:document": "calculated as functions of time of shut-in, Dt,and the duration of\ninjection, te. Before the leakoff point, injected \ufb02uid is almost\nentirely stored in the wellbore, and leakoff into the formation isnegligible. To account for this, t\neis de\ufb01ned to be equal to the du-ration of injection after the leakoff point is reached, rather than\nthe entire duration of injection.\nSimple Baseline Simulations. Simulation G1 assumes radial-\nfracture geometry (no height containment) with no wellbore stor-\nage, very-small residual aperture, and fairly high fracture tough-ness. Simulation G2 is similar to Simulation G1, but the hydraulic\nfracture is assumed to be con\ufb01ned in height to 7 meters. Figs. 3 and\n4show the results from Simulations G1 and G2. For calculating t\ne,\nthe \u201cleakoff point\u201d in Simulations G1 and G2 occurs immediately at\nthe start of injection because there is not any wellbore storage.\nSimulations G1 and G2 have a very sharp (unrealistic) spike in"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881670-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 4, "chroma:document": "the start of injection because there is not any wellbore storage.\nSimulations G1 and G2 have a very sharp (unrealistic) spike in\nderivative when closure occurred. Closure clearly and unambigu-\nously occurs at a \ufb02uid pressure equal to 55.1 MPa, precisely the\nsame as the minimum principal stress assumed in the simulation.\nClosure can be identi\ufb01ed consistently in all four plots.\n(a) Stiffness Contrast at Closure. In Appendix A, a detailed\nderivation is provided for the equations governing a DFIT pres-sure transient. After shut-in and the period after shut-in when\n\ufb02ow-rate-dependent pressure gradients dissipate, it is shown thatTable 1 \u2014Simulation settings used in all simulations. Variables are\nde\ufb01ned in the Nomenclature section.\nTable 2 \u2014Simulation settings varied between simulations. Variables are de\ufb01ned in the Nomenclature section.\n60\n57\n5154\n48\n45\n42Pressure (solid) (MPa)\n0 20 40 60 80 100 12030\n25\n20\n15\n10\n5\n0\nG-time\n\u0394t (hours) \u0394t (hours)\u0394t (hours)\u0394P (solid), \u03c4*dP/d\u03c4 (dashed) (MPa)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8816c0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 4, "chroma:document": "5154\n48\n45\n42Pressure (solid) (MPa)\n0 20 40 60 80 100 12030\n25\n20\n15\n10\n5\n0\nG-time\n\u0394t (hours) \u0394t (hours)\u0394t (hours)\u0394P (solid), \u03c4*dP/d\u03c4 (dashed) (MPa)\nI (solid), \u0394t*dI/d\u0394t (dashed)\n(MPa-hr)\u0394P (solid), \u0394t*dP/d\u0394t ((dashed)\n(MPa)G*dP/dG (dashed) (MPa)\n10\u2013210\u20132\n100100\n102\n10\u20132100100100100\n102102103\n102105\n101101\n101\nFig. 3\u2014Results from Simulation G1. Upper left: G-function plot. Upper right: Bourdet plot with derivative with respect to time.\nLower left: Bourdet plot with derivative with respect to superposition time. Lower right: Bourdet plot with integrated pressure\n(zoomed in).J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1325 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###160007August 2016 SPE Journal 1325"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881710-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 5, "chroma:document": "dP\ndt\u00bc/C0qleakoff\ncfVwl\u00feA\nSf; \u00f011\u00de\nwhere cfis the compressibility of the \ufb02uid, Vwlis the volume of\nthe well, Ais the surface area of the fracture, qleakoff is the volu-\nmetric leakoff rate from the fracture, and Sfis the fracture stiff-\nness. Eq. 11 neglects the effect of the compressibility of the \ufb02uid\nin the fracture and the effect of the changing wellbore volume\nbecause both terms are of negligible magnitude in typical DFITapplications (Appendix A).\nFor a radial fracture, the stiffness of an open fracture (de\ufb01ned\nasS\nf,o) can be written as (Sneddon 1946)\nSf;r\u00bc3pGm\n8\u00f01/C0/C23\u00deRf; \u00f012\u00de\nwhere Gmis the shear modulus, /C23is Poisson\u2019s ratio, and Rfis the\nradius. For a fracture with length much longer than its height, the\nstiffness can be estimated with the Perkins-Kern-Nordgren (PKN)\nassumption of plane strain in vertical cross section (Sneddon1946; Perkins and Kern 1961; Nordgren 1972):\nS\nf;PKN\u00bc4Gm\np\u00f01/C0/C23\u00dehf; \u00f013\u00de\nwhere hfis the fracture height."}


created_at: 2023-11-16 17:06:54
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id: 6b88176a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 5, "chroma:document": "S\nf;PKN\u00bc4Gm\np\u00f01/C0/C23\u00dehf; \u00f013\u00de\nwhere hfis the fracture height.\nBefore closure, the leakoff rate scales with time according to\ntheG-function (Nolte 1979), and the denominator of Eq. 11 is\nconstant, which is why a plot of pressure vs. G-time forms a\nstraight line.\nIn Appendix A, the stiffness of a closed fracture is derived [in\nanalogy to the discussion in Chapter 12 from Jaeger et al. (2007)]:\ndr0\nn\ndE\u00bcSf;c\u00bcSf;o\u00feSf;cont; \u00f014\u00de\nwhere Sf,cis the stiffness of a closed fracture and Sf,contis the con-\ntribution to the stiffness from the contacting of the fracture walls.\nSf,contcan be calculated from a constitutive law that relates aper-\nture to effective normal stress (such as Eq. 7) by solving for effec-\ntive normal stress and then taking the derivative with respect\nto aperture:Sf;cont\u00bcrn;ref\n9E0\nE2\u00bcrn;ref\n9E01\u00fe9\u00f0rn/C0P\u00de\nrn;ref/C20/C212\n: \u00f015\u00de\nIn Simulation G1, the fracture is circular. The radius at shut-in"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8817c4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 5, "chroma:document": "to aperture:Sf;cont\u00bcrn;ref\n9E0\nE2\u00bcrn;ref\n9E01\u00fe9\u00f0rn/C0P\u00de\nrn;ref/C20/C212\n: \u00f015\u00de\nIn Simulation G1, the fracture is circular. The radius at shut-in\nis 21 m, but the fracture extends slightly after shut-in and reachesa \ufb01nal radius of 21.6 m. From Eq. 12, the preclosure stiffness is\n1.09 MPa/mm. From Eq. 13, the preclosure stiffness in Simulation\nG2 (which has fracture height of 7 m) is 3.64 MPa/mm.\nEq. 15 shows that two parameters, E\n0andrn;ref, affect the con-\ntact stiffness at the moment of closure. To avoid a sharp disconti-nuity in stiffness and the pressure derivative, the stiffness at\nmechanical closure cannot be much greater than the stiffness\nbefore closure. In Simulations G1 and G2, the value of E\n0at clo-\nsure is very small, causing Sf,contto be very large (5.7 /C2106MPa/\nmm when Pis equal to rn), which is why there is a very sharp\nchange in the pressure derivative with closure.\n(b) Comparison to Analytical Solutions. As summarized by"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881814-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 5, "chroma:document": "change in the pressure derivative with closure.\n(b) Comparison to Analytical Solutions. As summarized by\nMarongiu-Porcu et al. (2011), the pressure trend before closure\ncan be used to estimate the leakoff coef\ufb01cient and the fracture size\n(Nolte 1979; Shlyapobersky et al. 1988; Valko and Economides1999). The technique involves drawing a straight line through the\nplot of pressure vs. G-time during the preclosure period.\nIn Simulation G1, the slope of the line is \u20130.0166 MPa/ Gwith\nan intercept of 56.51 MPa, and the fracture has radial geometry.\nThis yields an estimate of fracture radius of 20.4. In the simula-tion, the actual radius at shut-in is 21 m, and a bit of additional\npropagation occurs so that the \ufb01nal radius is 21.6 m. With the \ufb01nal\nvalue of radius in the simulation, 21.6 m, the equations yield an\nestimate of leakoff coef\ufb01cient of 6.95 /C210\n/C07m/s. From Howard\nand Fast (1957), CL\u00bcDP\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03k/ct\nplr\n, where ctis total compressibil-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88186e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 5, "chroma:document": "estimate of leakoff coef\ufb01cient of 6.95 /C210\n/C07m/s. From Howard\nand Fast (1957), CL\u00bcDP\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03k/ct\nplr\n, where ctis total compressibil-\nity, the sum of the \ufb02uid compressibility and porosity compressi-\nbility. Assuming a value of DPequal to 56.51 \u2013 35 \u00bc21.51 MPa,\nthe true value of CLis 9.18 /C210/C07m/s, close to the estimated\nvalue, though somewhat larger. The modest discrepancy is per-\nhaps not surprising because the derivation of these G-function-\nbased methods relies on several assumptions, such as Carter\nleakoff and power-law growth of the fracture, that are not exactlysatis\ufb01ed in our more-general numerical calculations. With the true\nvalues of radius at shut-in (21 m) and leakoff coef\ufb01cient, the ana-\nlytical equation predicts an average fracture aperture of 1.12 mm,.........................\n........................\n.......................\n..........................\n60\n57\n5154\n48\n45\n42Pressure (solid) (MPa)\n0 20 40 60 80 100 12030\n25\n20\n15\n10\n5\n0\nG-time"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8818be-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 5, "chroma:document": ".......................\n..........................\n60\n57\n5154\n48\n45\n42Pressure (solid) (MPa)\n0 20 40 60 80 100 12030\n25\n20\n15\n10\n5\n0\nG-time\n\u0394t (hours) \u0394t (hours) \u0394t (hours) \u0394P (solid), \u03c4*dP/d\u03c4 (dashed) (MPa)\nI (solid), \u0394t*dI/d\u0394t (dashed)\n(MPa-hr)\u0394P (solid), \u0394t*dP/d\u0394t (dashed)\n(MPa)G*dP/dG (dashed) (MPa)\n10\u2013210\u20132\n100100\n102\n10\u20132100100100100\n102102103\n102105\n104\n102\n101101\n101\nFig. 4\u2014Results from Simulation G2. Upper left: G-function plot. Upper right: Bourdet plot with derivative with respect to time.\nLower left: Bourdet plot with derivative with respect to superposition time. Lower right: Bourdet plot with integrated pressure\n(zoomed in).J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1326 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###1600071326 August 2016 SPE Journal"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88190e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 6, "chroma:document": "compared to the actual value from the simulation value of\n1.11 mm. With the actual simulation values of average aperture\nand radius at shut-in, the analytical equation predicts ef\ufb01ciency\n(volume of \ufb02uid in the fracture divided by volume injected) at\nshut-in of 97%, the same as the actual ef\ufb01ciency at shut-in during\nthe simulation.\nIn Simulation G2, the slope of the line is -0.0496 MPa/ Gwith\nan intercept of 58.19 MPa. With the equations for a PKN fracture,\nthis yields an estimate of fracture half-length of 133.7 m. At shut-in, the actual fracture half-length is 108.6 m. The fracture propa-\ngates a bit further after shut-in, reaching 122.6 m. Withthe actual\nvalue of \ufb01nal fracture half-length, the analytical equation predicts\nleakoff coef\ufb01cient of 6.95 /C210/C07m/s. With actual values of half-\nlength at shut-in and leakoff coef\ufb01cient, the analytical expressionspredict average aperture of 1.02 mm, compared to the actual simu-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881968-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 6, "chroma:document": "length at shut-in and leakoff coef\ufb01cient, the analytical expressionspredict average aperture of 1.02 mm, compared to the actual simu-\nlation value of 1.01 mm. With the actual value of average aperture\nand fracture half-length at shut-in, the analytical expression pre-\ndicts ef\ufb01ciency at shut-in of 97%, the same as the actual ef\ufb01-\nciency at shut-in during the simulation.\nEffect of Increasing Residual Aperture. Simulation G3 is a\nPKN-like simulation (height con\ufb01ned to 7 m), identical to Simula-tion G2, except that the fracture is given a maximum residual\naperture of 500 mm. The results are shown in Fig. 5.\nA discontinuity in the derivative of pressure still occurs when\nclosure occurs, but it is much less pronounced than in Simulations\nG1 and G2. The 90% closure stress is 51 MPa, and so the stiffnessat closure caused by contact is 11.3 MPa/mm, a factor of 3 greater\nthan the stiffness of the fracture preclosure.\nAs indicated by the orange arrows, the fracture compliance"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8819b8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 6, "chroma:document": "than the stiffness of the fracture preclosure.\nAs indicated by the orange arrows, the fracture compliance\nmethod indicates closure at the upward deviation of the G/C2dP/dG\ncurve, at G-time of approximately 20 (2.4 hours) and a pressure\nequal to 57 MPa, or at G-time of 25.5 (3.8 hours) and a pressure\nequal to 56.6 MPa.\nAs indicated by the blue arrow, the tangent method indicates\nclosure from the G-function plot at G-time equal to approximately\n46, equivalent to approximately 12 hours. This yields an estimate\nof closure pressure equal to approximately 51.8 MPa. In the Bour-\ndet plot with superposition derivative, there appears to be a 1.5\nslope, followed by a disturbance in the derivative at around thetime of closure, followed by what appears to be a resumption of the\n1.5 slope until approximately 12 hours. Picking closure at the end\nof the second 1.5 slope (solid green arrow) yields a closure estimatesimilar to the tangent method, approximately 51.8 MPa. Picking"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881a12-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 6, "chroma:document": "of the second 1.5 slope (solid green arrow) yields a closure estimatesimilar to the tangent method, approximately 51.8 MPa. Picking\nclosure at the end of the \ufb01rst 1.5 slope (dashed green arrow) yields\na result similar to the fracture compliance method. In the Bourdet\nplot with integrated pressure, an upward de\ufb02ection of the deriva-\ntive plot can be seen as early as 1.7 hours after shut-in (red arrow),\nequivalent to G-time of 16.7, giving a closure pick of 57.2 MPa.\nFrom the simulation results, it is possible to identify when and\nhow mechanical closure occurs. Fig. 6 shows the distribution of\naperture and residual aperture in the fracture shortly after shut-in.The red lines represent the residual aperture, and the blue lines\nrepresent the total aperture. The upper part of the \ufb01gure shows the\naperture distribution along the fracture length, down the midpoint.\nThe lower part of the \ufb01gure shows the aperture distribution along\na vertical line running through the center of the fracture."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881a62-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 6, "chroma:document": "The lower part of the \ufb01gure shows the aperture distribution along\na vertical line running through the center of the fracture.\nFig. 7 shows the aperture distribution after 2.32 hours of shut-\nin. Here, one can see that although the fracture has not closed\nalong its length, a fracture-height recession process has begun to\noccur. The fracture has closed to the residual aperture along the\nupper and bottom 1.5 m of the fracture. The beginning of this frac-ture-height recession process is what causes the initial slight dis-\ncontinuity and increase in the derivative at G-time equal to\napproximately 20.\nThe height recession is not caused by stress layering in the for-\nmation (stress is homogeneous). Instead, height recession iscaused by the residual aperture. As predicted by the PKN approxi-\nmation, the aperture distribution in the vertical direction is ellipti-\ncal, tapering to zero at the edges (though this is imperfectlycaptured in the simulation because of mesh coarseness). The max-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881abc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 6, "chroma:document": "cal, tapering to zero at the edges (though this is imperfectlycaptured in the simulation because of mesh coarseness). The max-\nimum residual aperture is speci\ufb01ed to be a constant value,\n500mm. As the \ufb02uid pressure decreases, aperture gradually\ndecreases, maintaining an elliptical shape and continuing to taper\nto zero at the top and bottom. As aperture decreases, regions de-velop where the aperture has reached the residual aperture (me-\nchanical closure). These regions extend inward from the top and\nbottom of the fracture.\nFig. 8 shows that at approximately 4 hours, the aperture has\nreached the residual aperture everywhere along the fracture. Thisis complete mechanical closure and coincides with the sharp\nincrease in the derivative.\nEven though fracture-height recession occurs in this simula-\ntion (and occurs in all the simulations with non-negligible residual\naperture), there is no ambiguity between its effect on the pressure\n60\n54\n48"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881b0c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 6, "chroma:document": "tion (and occurs in all the simulations with non-negligible residual\naperture), there is no ambiguity between its effect on the pressure\n60\n54\n48\n42Pressure (solid) (MPa) \u0394P (solid), \u03c4*dP/d\u03c4 (dashed) (MPa)\n\u0394t (hours) \u0394t (hours)\u0394t (hours)I (solid), \u0394t*dI/d\u0394t (dashed)\n(MPa-hr)\n100100102\n102102\n102104103\n102101101\n101G-time0 20 40 60 80 100 12015\n10\n5\n0\n\u0394P (solid), \u0394t*dP/d\u0394t (dashed)\n(MPa)G*dP/dG (dashed) (MPa)100\n10010010010\u20131\n10\u2013210\u20132101\nFig. 5\u2014Results from Simulation G3. Upper left: G-function plot. Upper right: Bourdet plot with derivative with respect to time.\nLower left: Bourdet plot with derivative with respect to superposition time. Lower right: Bourdet plot with integrated pressure\n(zoomed in).J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1327 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###160007August 2016 SPE Journal 1327"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881b5c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 7, "chroma:document": "transient and the effect of closure on the pressure transient. Fig. 8\nshows that the fracture closes fully by G-time of 28, coinciding\nwith the time when G/C2dP/dGbegins to increase rapidly (Fig. 5).\nThe fracture-height recession occurring before complete closure(seen by comparison between Fig. 7 and Fig. 8) during the period\nof approximately 20 G-time to 28 G-time causes a visible upward\nde\ufb02ection of G/C2dP/dG, but this de\ufb02ection is slight compared to\nthe much-larger de\ufb02ection that occurs after complete closure.\nThe true value of the minimum principal stress is 55.1 MPa,\nbut the \ufb02uid pressure at the time of mechanical closure is slightly\nlarger, approximately 57 MPa. This occurs because there is stillsome stress shadow on the fracture at closure as a result of the re-\nsidual aperture. This stress shadow can be estimated by multiply-\ning the residual aperture (500 mm) by the fracture stiffness causedby elastic deformation of the formation, S\nf,o(calculated from Eq."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881bb6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 7, "chroma:document": "ing the residual aperture (500 mm) by the fracture stiffness causedby elastic deformation of the formation, S\nf,o(calculated from Eq.\n13). This yields an estimate of 1.82 MPa, close to the overesti-\nmate that is observed.\nAdding Wellbore Storage. In Simulation G3, several aspects\nof the simulation remain unrealistic. Wellbore storage isneglected, there is not near-wellbore pressure loss, and there is\nstill a rather sharp discontinuity in derivative with closure. In Sim-\nulation G4, these issues are resolved. Simulation G4 is similar toSimulation G3 but includes wellbore storage, wellbore/near-well-\nbore pressure drop, and uses a much lower value of r\nn;ref, 5 MPa,\nto prevent a sharp increase in derivative with closure. From these\nvalues, we can calculate Sf,contto be 1.1 MPa/mm at Pequal to rn\n(Eq. 15). This is less than the stiffness caused by the elastic com-\npliance of the surrounding formation, Sf,o(3.64 MPa/mm). Thus,\nTime since shut-in: 0.0013386 hr, G-time: 0.08962"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881c06-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 7, "chroma:document": "pliance of the surrounding formation, Sf,o(3.64 MPa/mm). Thus,\nTime since shut-in: 0.0013386 hr, G-time: 0.08962\nDistance (m)Distance (m)\n\u20133 \u20132 \u20131 0 1 2 3Aperture distribution in vertical cross section at the wellboreAperture at Crack Center (mm) Aperture Along Crack Center (mm)1.5\n1.51\n10.5\n0.50\n0\u2013150 \u2013100 \u201350 0 50 100 150\nFig. 6\u2014Distribution of aperture during Simulation G3 soon after shut-in. The upper \ufb01gure shows aperture along the length of the\nfracture, and the lower \ufb01gure shows aperture along a vertical cross section at the center of the crack.\nTime since shut-in: 2.3205 hr, G-time: 19.6252\nDistance (m)Distance (m)\n\u20133 \u20132 \u20131 0 1 2 3Aperture distribution in vertical cross section at the wellboreAperture at Crack Center (mm) Aperture Along Crack Center (mm)1.5\n1.51\n10.5\n0.50\n0\u2013150 \u2013100 \u201350 0 50 100 150\nFig. 7\u2014Distribution of aperture during Simulation G3 at 2.3205 hours after shut-in (19.6252 G-time). The upper \ufb01gure shows aper-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881c7e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 7, "chroma:document": "Fig. 7\u2014Distribution of aperture during Simulation G3 at 2.3205 hours after shut-in (19.6252 G-time). The upper \ufb01gure shows aper-\nture along the length of the fracture, and the lower \ufb01gure shows aperture along a vertical cross section at the center of the crack.J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1328 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###1600071328 August 2016 SPE Journal"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881d8c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 8, "chroma:document": "when mechanical closure occurs in Simulation G4, the stiffness\nincreases only fractionally, and a sharp discontinuity in pressure\nderivative does not occur.\nThe fracture forms after 36.6 seconds of injection, at a break-\ndown pressure of 61.15 MPa, before dropping down to a fracture-propagation pressure approximately 60 MPa. The fracture-propa-\ngation pressure is considerably higher than the ISIP because of\nthe wellbore and near-wellbore pressure drop (Fig. 9).\nThe pressure transient in this simulation appears realistic and\nis similar to the match to \ufb01eld data described in the Field DFIT #1subsection. The fracture-compliance method gives a closure pick\natG-time equal to 33, pressure of 56.7 MPa, and 4.3 hours after\nshut-in (orange arrow). The closure pick from the tangent methodis at G-time equal to 77, pressure of 52.75 MPa, and 22 hours af-\nter shut-in (blue arrow).\nThe method of Mohamed et al. (2011) gives a closure pick"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881df0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 8, "chroma:document": "ter shut-in (blue arrow).\nThe method of Mohamed et al. (2011) gives a closure pick\nsimilar to that of the tangent method (green arrow). The Bourdet\nplot with integrated pressure gives a rather ambiguous pick forclosure, with the \ufb01rst de\ufb02ection of the curve at 1 hour (15.1 G-\ntime; dashed red arrow), earlier than the interpretation from any\nother method. An in\ufb02ection is also apparent at approximately 20\nhours (73 G-time), close to the timing of the closure pick from the\ntangent method (solid red arrow).\nAs in Simulation G3, fracture-height recession occurs. How-\never, this causes only the very-slight concave upward behavior\nseen in the G/C2dP/dGcurve from approximately G-time equal to\nTime since shut-in: 4.4788 hr, G-time: 27.8749\nDistance (m)Distance (m)\n\u20133 \u20132 \u20131 0 1 2 3Aperture distribution in vertical cross section at the wellboreAperture at Crack Center (mm) Aperture Along Crack Center (mm)1.5\n1.51\n10.5\n0.50\n0\u2013150 \u2013100 \u201350 0 50 100 150"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 8, "chroma:document": "1.51\n10.5\n0.50\n0\u2013150 \u2013100 \u201350 0 50 100 150\nFig. 8\u2014Distribution of aperture during Simulation G3 at 4.4788 hours after shut-in (27.8749 G-time). The upper \ufb01gure shows aper-\nture along the length of the fracture, and the lower \ufb01gure shows aperture along a vertical cross section at the center of the crack.\n60\n54\n48\n42Pressure (solid) (MPa)\u0394P (solid), \u03c4*dP/d\u03c4 (dashed) (MPa)\n\u0394t (hours) \u0394t (hours) \u0394t (hours) I (solid), \u0394t*dI/d\u0394t (dashed)\n(MPa-hr)\n100100102\n102102\n102104\n101G-time0 20 40 60 80 100 12015\n10\n5\n0\n\u0394P (solid), \u0394t*dP/d\u0394t (dashed)\n(MPa)G*dP/dG (dashed) (MPa)100\n10010010010\u20132\n10\u2013210\u20132\nFig. 9\u2014Results from Simulation G4. Upper left: G-function plot. Upper right: Bourdet plot with derivative with respect to time.\nLower left: Bourdet plot with derivative with respect to superposition time. Lower right: Bourdet plot with integrated pressure\n(zoomed in).J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1329 Total Pages: 19"}


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-179725-PA-Fracture Compliance Method.pdf", "page": 8, "chroma:document": "(zoomed in).J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1329 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###160007August 2016 SPE Journal 1329"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881efe-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 9, "chroma:document": "20 to G-time equal to 38. There is no ambiguity between this\nmodest effect and the sharply increasing G/C2dP/dGcurve from 38\nG-time to 80 G-time, which is interpreted as fracture-height reces-\nsion by the tangent method. As we have shown here, the increas-\ningG/C2dP/dGcurve is caused solely by the increasing fracture\nstiffness after mechanical closure.\nReduction in the wellbore and near-wellbore pressure drop\ncauses the very rapid, brief period of pressure decrease immedi-ately after shut-in.\nFracture Tip-Extension. Simulation G5 is performed with a\nlower value of fracture toughness, 2 MPa /C1m1/2(instead of\n10 MPa /C1m1/2, used in Simulations G1-G4). Simulation G5 is oth-\nerwise identical to Simulation G4. With this lower value of frac-\nture toughness, a large amount of fracture tip-extension occurs\nafter shut-in. As in Simulation G4, the fracture forms after 36.6seconds of injection, at a breakdown pressure of 61.15 MPa,"}


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-179725-PA-Fracture Compliance Method.pdf", "page": 9, "chroma:document": "after shut-in. As in Simulation G4, the fracture forms after 36.6seconds of injection, at a breakdown pressure of 61.15 MPa,\nbefore dropping down to a fracture-propagation pressure approxi-\nmately 60 MPa (Fig. 10).\nThe fracture tip-extension is visible on the G-function plot. As\ndescribed by Nolte (1991) and Barree and Mukherjee (1996), tip-extension causes the G/C2dP/dGcurve to increase sharply and then\ncurve concave down. At shut-in, the fracture half-length is 110 m.\nHowever, after shut-in the fracture reaches a half-length of 204 m.\nFracture growth does not end until the fracture closes. The tip-\nextension accelerates closure because it increases surface area andleakoff. Also, as the fracture grows, the average aperture along\nthe fracture is forced to decrease to accommodate mass balance,\ncausing aperture to reach the residual aperture sooner.\nThe high fracture length from this simulation may seem unre-\nalistic for such a relatively modest volume of \ufb02uid pumped. Simu-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b881fb2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 9, "chroma:document": "The high fracture length from this simulation may seem unre-\nalistic for such a relatively modest volume of \ufb02uid pumped. Simu-\nlations (not shown in this paper) show that with multiple\npropagating-fracture strands, the transient looks similar, but the\noverall fracture length is proportionally decreased, according tothe number of fractures. Thus, the transient from a single fracture\nwith a half-length of 200 m will be similar to the transient from\nmultiple-fracture strands, each with length much less than 200 m.\nStress shadowing tends to cause only one or two fractures to prop-\nagate, but near-wellbore pressure drop has the opposite effect,encouraging propagation of a larger number of fractures.\nInvestigation of the simulation results indicates that closure\noccurs at G-time of approximately 3.9 (0.1 hour) and a pressureof 56.5 MPa. The fracture-compliance method indicates that clo-\nsure occurs at a G-time of 12.7 (0.7 hour) and a pressure of 55.5"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882016-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 9, "chroma:document": "sure occurs at a G-time of 12.7 (0.7 hour) and a pressure of 55.5\nMPa (orange arrow). The tangent method indicates that closure\noccurs at G-time of 32.6 (4.2 hours) and pressure of 52.35 MPa\n(blue arrow). The Bourdet plot with superposition-derivativemethod suggests that closure occurs at 3.2 hours (28.3 G-time)\nand a pressure of 53.3 MPa (green arrow). The integrated-pressure\nplot suggests that closure occurs at approximately 2.5 hours (24.7G-time) and a pressure of 54 MPa (red arrow).\nHigher Permeability. Simulation G6 is performed with a\npermeability of 10\n/C015m2(/C241 millidarcy), much higher than the\nother simulations. As in Simulations G4 and G5, the fracture\nforms after 36.6 seconds of injection, at a breakdown pressure\nof 61.15 MPa, before dropping down to a fracture-propagation\npressure approximately 60 MPa. The other simulations in thisstudy are performed with a 1D leakoff model. But this simulation\nis performed with a fully numerical treatment of \ufb02ow in the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8820a2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 9, "chroma:document": "is performed with a fully numerical treatment of \ufb02ow in the\nmatrix around the fracture, with the method described by\nMcClure (2014).\nFig. 11 shows that before mechanical closure, a straight line\ncan be seen on the G/C2dP/dGplot, as expected. When mechanical\nclosure occurs, at approximately 0.85 G-time (0.012 hours), the\nrate of pressure drop decreases (orange arrow). This behavior is\ndifferent from the previous cases, when closure causes the rate of\npressure drop to increase. The different behavior can be under-stood by considering Eq. 11, which shows that the rate of pressure\ndecrease is equal to the product of system stiffness (the reciprocal\nof total storage coef\ufb01cient, de\ufb01ned in Appendix A) and leakoffrate. In a very-low permeability formation, the fracture remains\nin\ufb01nitely conductive (dimensionless fracture conductivity greater\nthan 300) even after closure. But with higher permeability, the\ndimensionless fracture conductivity rapidly drops below 300 after"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8820fc-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 9, "chroma:document": "than 300) even after closure. But with higher permeability, the\ndimensionless fracture conductivity rapidly drops below 300 after\nclosure. As a result, the rate at which \ufb02uid can \ufb02ow from the well(where \ufb02uid is stored because of wellbore storage) into the frac-\nture is reduced by closure. If leakoff rate decreases enough to\ncounteract the effect of increasing stiffness, the rate of pressure\ndecline will decrease.\nIn addition, in cases of high leakoff, the fracture length is\nmuch shorter. Eq. 11 shows that with lower fracture area, closure\nhas a relatively smaller impact on the system stiffness, and well-\nbore storage has a relatively larger effect. Thus, closure has less\n60\n51\n42Pressure (solid) (MPa)\u0394P (solid), \u03c4*dP/d\u03c4 (dashed) (MPa)\n\u0394t (hours) \u0394t (hours) \u0394t (hours) I (solid), \u0394t*dI/d\u0394t (dashed)\n(MPa-hr)\n100100102\n102102\n102104\n101G-time0 20 40 60 80 100 12015\n10\n5\n0\n\u0394P (solid), \u0394t*dP/d\u0394t (dashed)\n(MPa)G*dP/dG (dashed) (MPa)100101\n10010010010\u20131\n10\u2013210\u20132"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882156-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 9, "chroma:document": "102102\n102104\n101G-time0 20 40 60 80 100 12015\n10\n5\n0\n\u0394P (solid), \u0394t*dP/d\u0394t (dashed)\n(MPa)G*dP/dG (dashed) (MPa)100101\n10010010010\u20131\n10\u2013210\u20132\nFig. 10\u2014Results from Simulation G5. Upper left: G-function plot. Upper right: Bourdet plot with derivative with respect to time.\nLower left: Bourdet plot with derivative with respect to superposition time. Lower right: Bourdet plot with integrated pressure\n(zoomed in).J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1330 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###1600071330 August 2016 SPE Journal"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8821b0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 10, "chroma:document": "effect on the overall stiffness, which lessens the tendency of clo-\nsure to increase the derivative.\nThe linear \ufb02ow period that corresponds to the straight line on\ntheG/C2dP/dGcurve can be seen from approximately 0.001 hour\nto approximately 0.01 hours on the Bourdet plot (upper right ofFig. 11). After the linear \ufb02ow period, the Bourdet derivative-plot\n\ufb02attens out to a slope of approximately zero (with some gradual\nincrease), corresponding to a radial \ufb02ow period (which begins\nrapidly because of the relatively high permeability and short frac-\nture), before \ufb01nally reaching an impulse radial \ufb02ow period with anegative one slope, starting at approximately 1.00 hour ( G-time of\n15). Comparison of the Bourdet plot with the G-function plot indi-\ncates that the G/C2dP/dGcurve continues increasing after closure,\nthough more slowly.\nIn the Bourdet plot with superposition derivative, the late-time\nimpulse radial appears as a \ufb02at line, as expected. The intermediate"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88220a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 10, "chroma:document": "In the Bourdet plot with superposition derivative, the late-time\nimpulse radial appears as a \ufb02at line, as expected. The intermediate\ntime, approximately radial, period shows a slope of 1.0, which is\nexpected because taking the derivative with respect to superposi-tion time increases the log-log slope by one at shut-in times much\ngreater than the period of injection (Section 1.2.2). Careful\ninspection of the Bourdet plot with respect to integrated pressure\nshows no indication of closure.\nAs in the previous cases, closure should be picked at the devia-\ntion from linearity of the G/C2dP/dGcurve (orange arrow). How-\never, in this relatively high-permeability case, the slope of the\nG/C2dP/dGcurve decreases after closure, rather than increasing.\nThe tangent method provides a closure pick at approximately 8\nG-time, at a pressure far below the minimum principal stress\n(blue line).\nField DFIT #1. In this subsection, we review Field DFIT #1."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882264-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 10, "chroma:document": "G-time, at a pressure far below the minimum principal stress\n(blue line).\nField DFIT #1. In this subsection, we review Field DFIT #1.\nThis DFIT was previously shown on the left side of Figs. 4 and 5\nfrom Cramer and Nguyen (2013). The simulation that we perform\nto match the data is called Simulation F1 in Table 2. The injection\nrate over time is shown in Fig. 1.\nThere are several reasons that this is a good example of a\nDFIT transient.\n\u2022Cement integrity is excellent, as evidenced by the cement-\nbond log, assuring adequate interzonal isolation throughout\nthe injection and falloff periods.\n\u2022The test interval is mechanically strong (low-clay content)\nand suf\ufb01ciently thick (7 m) for establishing a dominant verti-cal hydraulic fracture. These mechanical characteristics are\nindicated by openhole log signatures: neutron density, resis-\ntivity, and sonic log responses (Fig. 12).\n\u2022As shown in Fig. 12, the stress contrast to higher-stress\nbounding rock layers is suf\ufb01cient for containing a DFIT-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8822be-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 10, "chroma:document": "\u2022As shown in Fig. 12, the stress contrast to higher-stress\nbounding rock layers is suf\ufb01cient for containing a DFIT-\nscale fracture to the test interval.\n\u2022A conductive drilling-induced tensile fracture is exhibited\nin the center of the test interval by an openhole image log(Fig. 13). This pre-existing fracture facilitates noncomplex,\nplanar fracture initiation and propagation.\n\u2022The vertical orientation of the wellbore ensures that the axial\nstarter fracture will be in line with the plane normal to the\nminimum principal/horizontal stress, further reducing the\npotential for fracture complexity (Cramer and Nguyen\n2013).\n\u2022The pressure rollover event observed near the beginning of\ninjection and at a relatively low bottomhole pressure is a\nstrong indication that the preexisting fracture is reopened\nduring the DFIT (Fig. 1). Reopening of an existing fracture\nensures that the in\ufb02uence of wellbore hoop-stress zone is\nmitigated or eliminated."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882318-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 10, "chroma:document": "during the DFIT (Fig. 1). Reopening of an existing fracture\nensures that the in\ufb02uence of wellbore hoop-stress zone is\nmitigated or eliminated.\n\u2022The onset of the pressure rollover event, in which the pres-\nsure plot departs from the wellbore-storage trend line (at\n55.3 MPa), is, in effect, the fracture-reopening pressure.\nThis fracture-reopening pressure should be slightly above\nthe fracture-closure pressure.\n\u2022There is a water-hammer event at the end of injection, con-\n\ufb01rming that an excellent connection existed between the\nwellbore and primary, far-\ufb01eld fracture. This is assurancethat there was no distortion of the shut-in pressure response\ncaused by near-wellbore fracture complexity or tortuosity.\n\u2022Borehole breakout analysis of adjacent intervals indicates\nthe existence of a large difference between minimum and\nmaximum horizontal stresses. Consequently, the probabilityof a primary hydraulic fracture interacting with and reopen-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882368-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 10, "chroma:document": "maximum horizontal stresses. Consequently, the probabilityof a primary hydraulic fracture interacting with and reopen-\ning crossed natural fractures is very-low; transverse fracture\nstorage is extremely unlikely.\n\u2022Permeability in the tested interval is very low, in the range\nof 50 to 150 nd. Consequently, dimensionless fracture con-ductivity should be very high following mechanical-fracture\nclosure, resulting in a stable \ufb02uid leakoff rate during closure.\nThus, the change in fracture compliance/stiffness caused by\n60\n40Pressure (solid) (MPa)\u0394P (solid), \u03c4*dP/d\u03c4 (dashed) (MPa)\n\u0394t (hours) \u0394t (hours) \u0394t (hours) I (solid), \u0394t*dI/d\u0394t (dashed)\n(MPa-hr)102G-time0 246 8 10 125\n0\n\u0394P (solid), \u0394t*dP/d\u0394t (dashed)\n(MPa)G*dP/dG (dashed) (MPa)\n100100100100\n105\n100100\n10\u2013310\u2013110\u2013210\u2013210\u2013210\u20132\nFig. 11\u2014Results from Simulation G6. Upper left: G-function plot. Upper right: Bourdet plot with derivative with respect to time."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8823c2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 10, "chroma:document": "Fig. 11\u2014Results from Simulation G6. Upper left: G-function plot. Upper right: Bourdet plot with derivative with respect to time.\nLower left: Bourdet plot with derivative with respect to superposition time. Lower right: Bourdet plot with integrated pressure.J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1331 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###160007August 2016 SPE Journal 1331"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88244e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 11, "chroma:document": "fracture closure should dominate the pressure falloff\nresponse when fracture closure occurs.\nThe simulation very closely matches the \ufb01eld data. The simu-\nlation match is accomplished with a minimum principal stress\nequal to 54.3 MPa. This compares well with the fracture-reopen-\ning pressure of 55.3 MPa, which is derived in analyzing Fig. 2.\nThe corresponding net pressure at the ISIP (57.1 MPa) is equal to\n2.8 MPa, which is a reasonable value with the small-injection vol-ume and compatible with simulations performed with commercial\nhydraulic-fracture models.Fig. 2 shows there is a very-brief period of rapid-pressure drop\nat the start, as wellbore friction and near-wellbore friction\ndecrease. Subsequently, the G/C2dP/dGcurve appears to be contin-\nuously concave upward during the shut-in period. However, a\nclose examination of the data indicates that it forms a relatively\ufb02at straight line until approximately G-time of 7 (0.48 hours),"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8824a8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 11, "chroma:document": "close examination of the data indicates that it forms a relatively\ufb02at straight line until approximately G-time of 7 (0.48 hours),\nwhen it begins to increase sharply. Thus, according to fracture-\ncompliance method, the closure estimate is at G-time of 7, for a\npressure of 55.2 MPa (orange arrow). Plots of aperture vs. posi-\ntion from the simulation results (similar to those shown in theTVD\nm\n3025.0\n3030.03035.03040.0\n3045.0\nHCGR GAPI0 200 100\nHSGR GAPI0 200 100AT90 \u03a9.m0.10 100\nAT30 \u03a9.m\nAT10 \u03a9.mPDMC dec0.30 \u20130.10 0.1000\nTNPH_LIM V/V0.30 \u20130.10 0.1000DTCO US/F50.00 150 100\nDTSM_SL US/F\nDTSM_FA US/FCorr_Stress MPa40.00            65.00 52.50\nLog_Stress MPa40.00               65.00 52.50Dyn_PR unitless0.15              0.30 0.22\nStatic_E GPa20.00                50.00 35.00\nFig. 12\u2014Openhole log data for Field DFIT #1.\nConductive Fracture\nPerforations: 3035\u20133040 m\nFracture noted from 3037 to 3039 m\nFrom Lane/CoP303930383037"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882502-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 11, "chroma:document": "Conductive Fracture\nPerforations: 3035\u20133040 m\nFracture noted from 3037 to 3039 m\nFrom Lane/CoP303930383037\nFig. 13\u2014Wellbore imaging log for Field DFIT #1.J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1332 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###1600071332 August 2016 SPE Journal"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88255c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 12, "chroma:document": "Effect of Increasing Residual Aperture subsection) con\ufb01rm that\nclosure occurs at G-time of 7 in the simulation. Fracture closure\noccurs at a pressure approximately 0.9 MPa greater than rhmin\nbecause of the stress shadow caused by the residual aperture.\nThe tangent method yields an estimate of closure pressure\napproximately G-time of 36 (approximately 9.4 hours), which is\nat a pressure approximately 49.3 MPa. The net pressure corre-sponding to this estimate is 7.8 MPa, which is unrealistically high\nwith the small injection volume because it implies exceptionally\nhigh fracture toughness. The Mohamed et al. (2011) method picksclosure at approximately 8 hours ( G-time of 33.2), for a pressure\nof approximately 50 MPa. There is a slight deviation in the Bour-\ndet plot with integrated pressure curve at approximately 4 hours\n(G-time of 23) and at pressure of 52.5 MPa.\nThe GRI/DOE M-Site Tests. The GRI/DOE M-Site project\ninvolved a series of hydraulic-fracturing injections into two inter-"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 12, "chroma:document": "The GRI/DOE M-Site Tests. The GRI/DOE M-Site project\ninvolved a series of hydraulic-fracturing injections into two inter-\nvals - the \u201cB-sand\u201d and the \u201cC-sand\u201d. In this section, we consider\nthe tests in the B-sand. The B-sand consists of a complexsequence of sandstone, mudstone, siltstone, and shale. The site\nwas unusually well-instrumented, involving a microseismic arrayand downhole tiltmeters in an offset well (Branagan et al. 1996).\nThe tiltmeters provide an independent estimate of the mini-\nmum principal stress. In the B-sand, seven different injection tests\nwere performed, some involving clear water, others involving\ngelled or cross-linked \ufb02uid, and one involving proppant. Pump-in\ufb02uid volume during these tests ranges from 3.0 to 95 m\n3(19 to\n600 bbl). Pressure measurements are available for an extended\ntime after shut-in for two of the tests: the initial breakdown injec-tion, which involved 3.0 m3(19 bbl) of crosslinked gel pumped at"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882610-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 12, "chroma:document": "time after shut-in for two of the tests: the initial breakdown injec-tion, which involved 3.0 m3(19 bbl) of crosslinked gel pumped at\n13.25 L/s (5 bbl/min), and injection 6B, which involved 63.6 m3\n(400 bbl) of linear gel pumped at 58.3 L/s (22 bbl/min). The ma-trix permeability is approximately 0.1 md ( /C2510/C016m2), signi\ufb01-\ncantly higher than Field DFIT #1 (see the Field DFIT #1subsection).\nFig. 14 shows the result from the initial breakdown injection\ntest. Breakdown of the formation occurred 2.7 minutes before\nshut-in at 30.77 MPa before dropping to a fracture-propagation\npressure of approximately 27 MPa.\nThe 6B injection shut-in transient is unusual (showing no clear\nindication of closure at any pressure), was the sixth injection into\nthe interval, and used a much larger volume than is typically used\nin a DFIT. Therefore, the results from that test are not presented.\nTheG-function plot shows a period of fracture tip-extension at"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88266a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 12, "chroma:document": "in a DFIT. Therefore, the results from that test are not presented.\nTheG-function plot shows a period of fracture tip-extension at\nearly-time, which terminates at G-time /C241. Afterward, the G/C2dP/\ndGcurve \ufb02attens out before beginning to increase sharply after\napproximately G-time of 3.5 (0.16 hours; indicated by orange\narrow). According to the fracture-compliance method, this\nincrease in the G/C2dP/dGcurve represents closure, and so the\nminimum principal stress should be picked from the pressure cor-\nresponding to G-time of 3.5, which is 24.3 MPa.\nThe tangent method and the Mohamed et al. (2011) method\nyield a closure pick at approximately 0.85 hours of shut-in ( G-\ntime of 9.5), corresponding to a pressure of 22.75 MPa (blue and\ngreen arrows). In the Bourdet with integrated pressure plot, there\nis no apparent de\ufb02ection indicating closure.\nFig. 15 shows the normalized tiltmeter response plotted\nagainst wellbore pressure during injection 2B, the test immedi-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8826c4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 12, "chroma:document": "Fig. 15 shows the normalized tiltmeter response plotted\nagainst wellbore pressure during injection 2B, the test immedi-\nately after the breakdown test shown in Fig. 14. A smoothed ver-\nsion of this \ufb01gure is shown in Fig. 9A-4 of Economides and Nolte\n30\n25\n20Pressure (solid) (MPa) \u0394P (solid), \u03c4*dP/d\u03c4 (dashed) (MPa)\n\u0394t (hours) \u0394t (hours)\u0394t (hours)I (solid), \u0394t*dI/d\u0394t (dashed)\n(MPa-hr)G-time0 246 8 100\n\u0394P (solid), \u0394t*dP/d\u0394t (dashed)\n(MPa)G*dP/dG (dashed) (MPa)\n101101\n100100100100\n10\u2013110\u2013110\u20131\n10\u2013310\u20133\n10\u20132100100\n10\u2013110\u20131\n10\u2013310\u2013210\u2013210\u20132\nFig. 14\u2014Field data from the M-site, B-sand breakdown injection. Upper left: G-function plot. Upper right: Bourdet plot with deriva-\ntive with respect to time. Lower left: Bourdet plot with derivative with respect to superposition time. Lower right: Bourdet plot withintegrated pressure.\n1\n0.9\n0.8\n0.7\n0.6\n0.5\n0.4\n0.3\n0.2\n0.1\n0\n20 22 26\nPressure (MPa)4628\n4558\n4487\n44184348\n4274Normalized Tilt\nFig. 15\u2014Normalized tiltmeter data from Injection 2B from the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88271e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 12, "chroma:document": "0.5\n0.4\n0.3\n0.2\n0.1\n0\n20 22 26\nPressure (MPa)4628\n4558\n4487\n44184348\n4274Normalized Tilt\nFig. 15\u2014Normalized tiltmeter data from Injection 2B from the\nGRI/DOE M-site. Data courtesy of Norm Warpinski.J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1333 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###160007August 2016 SPE Journal 1333"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882778-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 13, "chroma:document": "(2000). Each tiltmeter response is normalized by dividing by the\nmaximum tilt measured at that instrument during the test. The tilt-\nmeters demonstrate that the fracture began opening at approxi-mately 23.9 MPa, very close to the closure pressure estimated by\nthe fracture-compliance method from the shut-in transient after\nthe breakdown injection (which immediately preceded the 2B\ninjection). At 23.9 MPa, the derivative of tilt with respect to pres-\nsure becomes much greater, indicating an abrupt drop in fracturestiffness at that pressure corresponding to reopening.\nFig. 15 shows only the data during injection, not shut-in. The\nshut-in tiltmeter response is much smoother and shows a more-\ngradual relationship between tilt and wellbore pressure. This dif-\nference is caused by the contribution to the tiltmeter responsefrom the poroelastic effect of the \ufb02uid leaked off into the forma-\ntion. During injection, the amount of leakoff is relatively minimal,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8827d2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 13, "chroma:document": "tion. During injection, the amount of leakoff is relatively minimal,\nwhich is why the tiltmeter response during injection (reopening)\nis more appropriate for estimating the minimum principal stress.\nBranagan et al. (1996) report substantial residual deformation\n(20% of the maximum de\ufb02ection) many weeks after the \ufb01rst four\ninjections into the B-sand, which they interpret as suggesting that\nthe fractures retained signi\ufb01cant residual aperture after closure.\nNonuniqueness in Simulation Results. The simulation matches\nto the \ufb01eld data are subject to nonuniqueness. Lower shear modu-\nlus, higher fracture toughness, and greater fracture height (or ra-\ndial geometry) all result in lower fracture surface area, which can\nbe compensated by using a higher permeability or lower \ufb02uid vis-\ncosity. The selection of \ufb02uid viscosity is complicated because inmost cases clear water is being injected into a gas- or oil-saturated\nformation. Leakoff will be affected by multiphase effects, and the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88282c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 13, "chroma:document": "formation. Leakoff will be affected by multiphase effects, and the\ninjection \ufb02uid has a different viscosity and compressibility than\nthe reservoir \ufb02uid. In the simulations in this paper, we have not\nmade an attempt to choose a realistic viscosity and have merelyset the \ufb02uid viscosity to 1 cp. Adjustments to viscosity require\nproportional adjustments to the permeability to achieve a simula-\ntion match.\nBecause of this nonuniqueness, many of the values used in the\nsimulation matches should not necessarily be interpreted as beingactual estimates for those parameters in the formation. However,\nthere are certain features of the transients that allow unique esti-\nmation of formation parameters. For example, the wellbore-stor-age coef\ufb01cient can be estimated with high con\ufb01dence from the\nslope of a plot of pressure vs. volume injected before the leakoff\npoint or breakdown pressure. Additional data sources can be used\nto constrain parameters. For example, the shear moduli can be"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882886-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 13, "chroma:document": "point or breakdown pressure. Additional data sources can be used\nto constrain parameters. For example, the shear moduli can be\nestimated from core or geophysical logs.\nRegardless of these uncertainties, the estimates for closure\npressure that are based on the simulations matches are always\nunique. In every case, closure causes the G/C2dP/dGcurve to\nde\ufb02ect upward (except the high-permeability case, when it\nde\ufb02ected downward). Therefore, the location of the de\ufb02ection intheG/C2dP/dGcurve can be taken as a unique estimate for the clo-\nsure pressure. Because the residual aperture creates a stress\nshadow, the closure-pressure estimate could be up to 1 to 2 MPa\ngreater than the actual value of r\nhmin(depending on the magni-\ntude of the residual aperture and the geometry of the fracture),which creates some uncertainty (see the Effect of Increasing Re-\nsidual Aperture subsection).\nThe net pressures implied by the tangent method of G-function"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8828d6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 13, "chroma:document": "sidual Aperture subsection).\nThe net pressures implied by the tangent method of G-function\ninterpretation and the Mohamed et al. (2011) method are much\nhigher than the values derived from our proposed method. For\nexample, for Field DFIT #1, the net pressure at the ISIP is 2.8\nMPa according to the pick from the fracture-compliance method,\nand 7.8 MPa according to the pick from the tangent method.Matching these very-high net pressures requires very-high values\nof fracture toughness or poorly constrained adjustments for a\n\ufb02uid-lag zone or inelastic deformation ahead of the crack tip (Jef-\nfrey 1989; Yew and Liu 1993; Mack and Warpinski 2000). This is\nnot inconceivable, but in the context of the results from this study,the more-likely explanation is that net pressure is overestimated\nbecause of the method of DFIT interpretation. The lower net pres-\nsures implied by the fracture-compliance method are consistentwith values of fracture toughness derived from laboratory\nmeasurements."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882944-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 13, "chroma:document": "sures implied by the fracture-compliance method are consistentwith values of fracture toughness derived from laboratory\nmeasurements.\nConclusions\n1. Using a hydraulic-fracturing simulator that includes the effect\nof residual-fracture aperture, simulations of DFITs can be per-\nformed that closely match \ufb01eld data, including the preclosure,\nclosure, and post-closure periods.\n2. The results suggest that the tangent method for identifying clo-\nsure from G-function plots (Barree and Mukherjee 1996; Bar-\nree et al. 2007) tends to underestimate the minimum principal\nstress in low-permeability formations because it neglects the\neffect of changing residual fracture aperture after closure.\n3. The method proposed by Mohamed et al. (2011) for picking\nclosure from a Bourdet plot with superposition time derivativetends to give results similar to the tangent method, underesti-\nmating closure pressure in low-permeability intervals.\n4. The method of Craig and Blasingame (2006) for identifying"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882994-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 13, "chroma:document": "mating closure pressure in low-permeability intervals.\n4. The method of Craig and Blasingame (2006) for identifying\nclosure from a Bourdet plot with integrated pressure is based\non picking closure from a change in storage and thus identi\ufb01esthe correct closure pressure in some cases. However, the\nde\ufb02ection on the plot is often ambiguous or impossible to\nidentify.\n5. Closure can best be picked by identifying the departure from\nlinearity on the plot of pressure vs. G-time or the square root of\ntime (after the very-early time period after shut-in when dissi-\npating wellbore and near-wellbore friction causes the pressure\nto drop rapidly). Identi\ufb01cation of this departure from linearitycan be assisted by the G/C2dP/dGcurve. In low-permeability\nformations, the G/C2dP/dGcurve should de\ufb02ect upward at clo-\nsure. We refer to this method as the \u201cfracture compliance\nmethod\u201d for picking closure.\n6. In high-permeability cases, the G/C2dP/dGcurve may de\ufb02ect"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8829ee-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 13, "chroma:document": "sure. We refer to this method as the \u201cfracture compliance\nmethod\u201d for picking closure.\n6. In high-permeability cases, the G/C2dP/dGcurve may de\ufb02ect\ndownward (with pressure de\ufb02ecting upward) when closure\noccurs because closure can signi\ufb01cantly reduce the rate of\nleakoff.\n7. The residual fracture aperture upon closure can cause a stress\nshadow of up to 1 to 2 MPa. As a result, the closure pressurecan be as much as 1 to 2 MPa above the value of the minimum\nprincipal stress.\n8. In a fracture-injection test from the GRI/DOE M-site project,\nthe closure pick can be independently estimated from down-\nhole tiltmeters and is consistent with the pick from the frac-ture-compliance method presented in this paper.\nNomenclature\nA\u00bcfracture area, m\n2\ncf\u00bc\ufb02uid compressibility, MPa/C01\nc/\u00bcporosity compressibility, MPa/C01\nCac\u00bcafter-closure storage coef\ufb01cient, m3/MPa\nCfD\u00bcdimensionless fracture conductivity, unitless\nCL\u00bcCarter leakoff model leakoff coef\ufb01cient, m3/(m2/C1s)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882a48-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 13, "chroma:document": "CfD\u00bcdimensionless fracture conductivity, unitless\nCL\u00bcCarter leakoff model leakoff coef\ufb01cient, m3/(m2/C1s)\nCnw\u00bcconstant for wellbore and near-wellbore pressure\ndrop, MPa/(m3/s)2\nCw\u00bcwellbore-storage coef\ufb01cient, m3/MPa\nCt\u00bctotal storage coef\ufb01cient for fracture and wellbore\nsystem, m3/MPa\ne\u00bchydraulic aperture, related to the transmissivity by\nthe cubic law, m\nE\u00bcvoid aperture, volume of \ufb02uid stored per fracture\nsurface area, m\nE0\u00bcresidual fracture aperture, m\nEhf,max,resid \u00bcmaximum residual aperture, m\nEopen\u00bcmechanical fracture opening, m\ng\u00bcdimensionless variable used in de\ufb01ning G,de\ufb01ned\nin Eq. 2, unitless\nG\u00bcG-time, de\ufb01ned in Eq. 1, unitless\nGm\u00bcshear modulus, MPa\nhf\u00bcfracture height, m\nI\u00bcintegrated pressure, MPa /C1s\nk\u00bcpermeability, m2J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1334 Total Pages: 19\nID:jaganm Time: 18:39 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###1600071334 August 2016 SPE Journal"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882aa2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 14, "chroma:document": "KIc\u00bcfracture toughness, MPa /C1m1/2\nLf\u00bcfracture half-length, m\nm\u00bcmass of \ufb02uid in the wellbore and fracture, kg\nP\u00bc\ufb02uid pressure, MPa\nP0\u00bcreference pressure used to calculate \ufb02uid density,\nMPa\nPinit\u00bcinitial \ufb02uid pressure, MPa\nqinj\u00bcvolumetric surface-injection rate, m3/s\nqm,inj\u00bcsurface mass injection rate, kg/s\nqleakoff \u00bctotal volumetric leakoff rate across entire fracture,\nm3/s\nqm,leakoff \u00bctotal-mass leakoff rate across entire fracture, kg/s\nQ\u00bcvolumetric \ufb02ow rate, m3/s\nRf\u00bcfracture radius, m\nSf\u00bcfracture stiffness, MPa/m\nSf,c\u00bcstiffness of a closed fracture, MPa/m\nSf,cont \u00bccontribution to stiffness of a closed fracture from\ncontact stress, MPa/m\nSf,o\u00bcstiffness of open fracture, or equivalently, contribu-\ntion to stiffness of a closed fracture from the defor-\nmation of the surrounding formation, MPa/m\nSf,PKN\u00bcstiffness of an open PKN fracture, MPa/m\nSf,r\u00bcstiffness of an open radial fracture, MPa/m\nt\u00bctime, seconds\nte\u00bcduration of injection, seconds\nT\u00bctransmissivity, m3"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882b1a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 14, "chroma:document": "Sf,r\u00bcstiffness of an open radial fracture, MPa/m\nt\u00bctime, seconds\nte\u00bcduration of injection, seconds\nT\u00bctransmissivity, m3\nVfr\u00bcvolume of \ufb02uid in fracture, m3\nVwl\u00bcvolume of \ufb02uid in wellbore, m3\na\u00bcpower-law exponent for fracture growth used in the\nG-time derivation, unitless\nDP\u00bcchange in pressure since the start of the transient,\nMPa\nDPnw\u00bcwellbore and near-wellbore pressure drop, MPa\nDt\u00bctime from start of transient, seconds\nDtD\u00bcdimensionless time from start of transient, unitless\nDrn\u00bcdeformation-induced change in normal stress, MPa\nl\u00bc\ufb02uid viscosity, MPa /C1s\n/C23\u00bcPoisson\u2019s ratio, unitless\nq\u00bc\ufb02uid density, kg/m3\nq0\u00bc\ufb02uid density at the reference pressure, kg/m3\nqfr\u00bcaverage density of \ufb02uid in fracture, kg/m3\nqinit\u00bcinitial \ufb02uid density, kg/m3\nqinj\u00bcdensity of injected \ufb02uid, kg/m3\nqleakoff \u00bcaverage density of \ufb02uid leaking off from the frac-\nture, kg/m3\nqwl\u00bcaverage density of \ufb02uid in wellbore, kg/m3\nrhmin\u00bcminimum principal stress, MPa\nr0\nn\u00bceffective normal stress, MPa\nrn\u00bcnormal stress, MPa\nrr"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882b74-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 14, "chroma:document": "qwl\u00bcaverage density of \ufb02uid in wellbore, kg/m3\nrhmin\u00bcminimum principal stress, MPa\nr0\nn\u00bceffective normal stress, MPa\nrn\u00bcnormal stress, MPa\nrr\nn\u00bcremote-loading normal stress, MPa\nrn,ref\u00bcreference normal stress, MPa\n/init\u00bcinitial porosity, unitless\n/\u00bcporosity, unitless\ns\u00bcsuperposition time, unitless\nAcknowledgments\nThe \ufb01nancial support provided by the Fracturing and Sand Con-\ntrol JIP at the University of Texas at Austin is gratefully acknowl-\nedged. The authors would like to thank Norm Warpinski for\nsupplying data from the GRI/DOE M-site project used in the pa-per and Priscila Ribeiro and Bertrand Rohmer for their useful\ncomments. Thank you to our friends and colleagues who encour-\naged us in pursuing this research.\nReferences\nBabazadeh, M. and McClure, M. 2015. Coupling Fluid Flow and Geome-\nchanics in a Three-Dimensional Discrete Fracture Network Simulator.\nPaper presented at the 49th US Rock Mechanics/Geomechanics Sym-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b882bd8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 14, "chroma:document": "chanics in a Three-Dimensional Discrete Fracture Network Simulator.\nPaper presented at the 49th US Rock Mechanics/Geomechanics Sym-\nposium, San Francisco, 28 June\u20131 July.Barree, R. D. and Mukherjee, H. 1996. Determination of Pressure Depend-\nent Leakoff and Its Effect on Fracture Geometry. Paper presented atthe 71st Annual Technical Conference and Exhibition, Denver, 6\u20139\nOctober. SPE-36424-MS. http://dx.doi.org/10.2118/36424-MS.\nBarree, R. D. 1998. Applications of Pre-Frac Injection/Falloff Tests in Fis-\nsured Reservoirs\u2014Field Examples. Paper presented at the SPE Rocky\nMountain Regional/Low Permeability Reservoirs Symposium, Denver,\n5\u20138 April. SPE-39932-MS. http://dx.doi.org/10.2118/39932-MS.\nBarree, R. D., Barree, V. L., and Craig, D. P. 2007. Holistic Fracture Diag-\nnostics. Paper presented at the SPE Rocky Mountain Oil and Gas\nTechnology Symposium, Denver, 16\u201318 April. SPE-107877-MS.http://dx.doi.org/10.2118/107877-MS."}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 14, "chroma:document": "Technology Symposium, Denver, 16\u201318 April. SPE-107877-MS.http://dx.doi.org/10.2118/107877-MS.\nBarree, R. D., Miskimins, J. L., and Gilbert, J. V. 2014. Diagnostic Frac-\nture Injection Tests: Common Mistakes, Mis\ufb01res, and Misdiagnoses.\nSPE Prod & Oper 30(2): 84\u201398. SPE-169539-PA. http://dx.doi.org/\n10.2118/169539-PA.\nBarton, N., Bandis, S., and Bakhtar, K. 1985. Strength, Deformation and\nConductivity Coupling of Rock Joints. International Journal of Rock\nMechanics and Mining Sciences & Geomechanics Abstracts 22(3):\n121\u2013140. http://dx.doi.org/10.1016/0148-9062(85)93227-9.\nBourdet, D., Ayoub, J. A., and Pirard, Y. M. 1989. Use of Pressure Deriva-\ntive in Well-Test Interpretation. SPE Form Eval 4(2): 293\u2013302. SPE-\n12777-PA. http://dx.doi.org/10.2118/12777-PA.\nBranagan, P. T., Warpinski, N. R., Engler, B. et al. 1996. Measuring the\nHydraulic Fracture-Induced Deformation of Reservoir and Adjacent\nRocks Employing a Deeply Buried Inclinometer Array: Gri/Doe"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 14, "chroma:document": "Hydraulic Fracture-Induced Deformation of Reservoir and Adjacent\nRocks Employing a Deeply Buried Inclinometer Array: Gri/Doe\nMulti-Site Project. Paper presented at the SPE Annual Technical Con-ference and Exhibition, Denver, 6\u20139 October. SPE-36451-MS. http://\ndx.doi.org/10.2118/36451-MS.\nBrown, S. R. and Bruhn, R. L. 1998. Fluid Permeability of Deformable\nFracture Networks. J. Geophysical Research 103(B2): 2489\u20132500.\nhttp://dx.doi.org/10.1029/97JB03113.\nCastillo, J. L. 1987. Modi\ufb01ed Fracture Pressure Decline Analysis Includ-\ning Pressure-Dependent Leakoff. Paper presented at the SPE/DOE\nLow Permeability Reservoir Symposium, Denver, 18\u201319 May. SPE-\n16417-MS. http://dx.doi.org/10.2118/16417-MS.\nCraig, D. P. and Blasingame, T. A. 2006. Application of a New Fracture-\nInjection/Falloff Model Accounting for Propagating, Dilated, andClosing Hydraulic Fractures. Paper presented at the SPE Gas Technol-\nogy Symposium, Calgary, 15\u201317 May. SPE-100578-MS. http://\ndx.doi.org/10.2118/100578-MS."}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 14, "chroma:document": "ogy Symposium, Calgary, 15\u201317 May. SPE-100578-MS. http://\ndx.doi.org/10.2118/100578-MS.\nCraig, D. P. 2014. New Type Curve Analysis Removes Limitations of Con-\nventional After-Closure Analysis of D\ufb01t Data. Paper presented at the SPEUnconventional Resources Conference-USA, The Woodlands, Texas,\n1\u20133 April. SPE-168988-MS. http://dx.doi.org/10.2118/168988-MS.\nCramer, D. D. 1987. The Application of Limited-Entry Techniques in\nMassive Hydraulic Fracturing Treatments. Paper presented at the SPE\nProduction Operations Symposium, Oklahoma City, Oklahoma, 8\u201310\nMarch. SPE-16189-MS. http://dx.doi.org/10.2118/16189-MS.\nCramer, D. D. and Nguyen, D. H. 2013. Diagnostic Fracture Injection\nTesting Tactics in Unconventional Reservoirs. Paper presented at the\nSPE Hydraulic Fracturing Technology Conference, The Woodlands,Texas, 4\u20136 February. SPE-163863-MS. http://dx.doi.org/10.2118/\n163863-MS.\nCrouch, S. L. and Star\ufb01eld, A. M. 1983. Boundary Element Methods in"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 14, "chroma:document": "163863-MS.\nCrouch, S. L. and Star\ufb01eld, A. M. 1983. Boundary Element Methods in\nSolid Mechanics: With Applications in Rock Mechanics and Geologi-\ncal Engineering . London: Allen & Unwin.\nEconomides, M. J. and Nolte, K. G. (eds.) 2000. Reservoir Stimulation ,\nthird edition. New York, New York: John Wiley.\nGangi, A. F. 1978. Variation of Whole and Fractured Porous Rock Perme-\nability With Con\ufb01ning Pressure. International J. Rock Mechanics and\nMining Sciences 15: 249\u2013257. http://dx.doi.org/10.1016/0148-\n9062(78)90957-9.\nGodbey, J. K. and Hodges, H. D. 1958. Pressure Measurements During\nFormation Fracturing Operations. In Petroleum Transactions , AIME,\nVol. 213, 65\u201369. SPE-889-G. Richardson, Texas: Society of Petroleum\nEngineers.\nHaimson, B. and Fairhurst, C. 1967. Initiation and Extension of Hydraulic\nFractures in Rocks. SPE J .7(3): 310\u2013318. SPE-1710-PA. http://\ndx.doi.org/10.2118/1710-PA.J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1335 Total Pages: 19"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 15, "chroma:document": "Horne, R. N. 1995. Modern Well Test Analysis: A Computer-Aided\nApproach , second edition. Palo Alto, California: Petroway, Inc.\nHoward, G. and Fast, C. R. 1957. Optimum Fluid Characteristics for Frac-\nture Extension. Drilling and Production Practice 24:261\u2013270. API-\n57-261. New York: American Petroleum Institute.\nHubbert, M. K. and Willis, D. G. 1957. Mechanics of Hydraulic Fracturing.\nInPetroleum Transactions , AIME, Vol. 210, 153\u2013168. SPE-686-G.\nRichardson, Texas: Society of Petroleum Engineers.\nJ a e g e r ,J .C . ,C o o k ,N .G .W . ,a n dZ i m m e r m a n ,R . .2 0 0 7 . Fundamentals of Rock\nMechanics , fourth edition. Malden, Massachusetts: Blackwell Publications.\nJeffrey, R. G. 1989. The Combined Effect of Fluid Lag and Fracture\nToughness on Hydraulic Fracture Propagation. Paper presented at the\nLow Permeability Reservoirs Symposium, Denver, 6\u20138 March. SPE-\n18957-MS. http://dx.doi.org/10.2118/18957-MS.\nKoning, E. J. L. and Niko, H. 1985. Fractured Water-Injection Wells: A"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 15, "chroma:document": "18957-MS. http://dx.doi.org/10.2118/18957-MS.\nKoning, E. J. L. and Niko, H. 1985. Fractured Water-Injection Wells: A\nPressure Falloff Test for Determining Fracture Dimensions. Paper pre-sented at the SPE Annual Technical Conference and Exhibition, Las\nVegas, Nevada, 22\u201325 September. SPE-14458-MS. http://dx.doi.org/\n10.2118/14458-MS.\nMack, M. G. and Warpinski, N. R. 2000. Mechanics of Hydraulic Fractur-\ning. In Reservoir Stimulation , ed. M. J. Economides and K. G. Nolte,\nChap. 6.1\u20136.48. New York, New York: John Wiley & Sons.\nMarongiu-Porcu, M., Ehlig-Economides, C. A., and Economides, M. J.\n2011. Global Model for Fracture Falloff Analysis. Paper presented at\nthe SPE North American Unconventional Gas Conference and Exhibi-tion, The Woodlands, Texas, 14\u201316 June. SPE-144028-MS. http://\ndx.doi.org/10.2118/144028-MS.\nMarongiu-Porcu, M., Retnanto, A., Economides, M. J. et al. 2014. Compre-\nhensive Fracture Calibration Test Design. Paper presented at the SPE"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 15, "chroma:document": "Marongiu-Porcu, M., Retnanto, A., Economides, M. J. et al. 2014. Compre-\nhensive Fracture Calibration Test Design. Paper presented at the SPE\nHydraulic Fracturing Technology Conference, The Woodlands, Texas,\n4\u20136 February. SPE-168634-MS. http://dx.doi.org/10.2118/168634-MS.\nMcClure, M. W. and Horne, R. N. 2013. Discrete Fracture Network Mod-\neling of Hydraulic Stimulation: Coupling Flow and Geomechanics .\nSpringerBriefs in EarthSciences, Springer.\nMcClure, M. W. 2014. The Potential Effect of Network Complexity on\nRecovery of Injected Fluid Following Hydraulic Fracturing. Paper pre-\nsented at the SPE Unconventional Resources Conference-USA, The\nWoodlands, Texas, 1\u20133 April. SPE-168991-MS. http://dx.doi.org/10.2118/168991-MS.\nMcClure, M. W., Christopher, A. J., Blyton, H. J. et al. 2014. The Effect of\nChanging Fracture Compliance on Pressure Transient Behavior During\nDiagnostic Fracture Injection Tests. Paper presented at the SPE Annual"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 15, "chroma:document": "Changing Fracture Compliance on Pressure Transient Behavior During\nDiagnostic Fracture Injection Tests. Paper presented at the SPE Annual\nTechnical Conference and Exhibition, Amsterdam, 27\u201329 October.\nSPE-170956-MS. http://dx.doi.org/10.2118/170956-MS.\nMcClure, M. W., Babazadeh, M., Shiozawa, S. et al. 2015. Fully Coupled\nHydromechanical Simulation of Hydraulic Fracturing in Three-Dimen-\nsional Discrete Fracture Networks. Paper presented at the SPE Hydrau-lic Fracturing Technology Conference, The Woodlands, Texas, 3\u20135\nFebruary. SPE-173354-MS. http://dx.doi.org/10.2118/173354-MS.\nMeng, C., Wei, L., and Yuan, R. 2014. Coupled Fluid Flow and Geome-\nchanics Modeling for DFIT Analysis in Unconventional Gas Develop-\nment. Paper presented at the International Petroleum Technology\nConference, Kuala Lumpur, 10\u201312 December. IPTC-18159-MS.\nhttp://dx.doi.org/10.2523/IPTC-18159-MS.\nMohamed, I. M., Nasralla, R. A., Sayed, M. A. et al. 2011. Evaluation of"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 15, "chroma:document": "http://dx.doi.org/10.2523/IPTC-18159-MS.\nMohamed, I. M., Nasralla, R. A., Sayed, M. A. et al. 2011. Evaluation of\nafter-Closure Analysis Techniques for Tight and Shale Gas Forma-tions. Paper presented at the SPE Hydraulic Fracturing Technology\nConference, The Woodlands, Texas, 24\u201326 January. SPE-140136-MS.\nhttp://dx.doi.org/10.2118/140136-MS.\nMoody, L. F. 1944. Friction Factors for Pipe Flow. Trans. of the ASME 66\n(8): 671\u2013684.\nNolte, K. 1979. Determination of Fracture Parameters From Fracturing\nPressure Decline. Paper presented at the SPE Annual Technical Con-\nference and Exhibition, Las Vegas, Nevada, 23\u201326 September. SPE-\n8341-MS. http://dx.doi.org/10.2118/8341-MS.\nNolte, K. G. and Smith, M. B. 1981. Interpretation of Fracturing Pressures.\nJ Pet Technol 33(9): 1767\u20131775. SPE-8297-PA. http://dx.doi.org/\n10.2118/8297-PA.\nNolte, K. G. 1991. Fracturing-Pressure Analysis for Nonideal Behavior. J\nPet Technol 43(2): 210\u2013218. SPE-20704-PA. http://dx.doi.org/"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 15, "chroma:document": "Nolte, K. G. 1991. Fracturing-Pressure Analysis for Nonideal Behavior. J\nPet Technol 43(2): 210\u2013218. SPE-20704-PA. http://dx.doi.org/\n10.2118/20704-PA.Nolte, K. G., Mack, M. G., and Lie, W. L. 1993. A Systematic Method for\nApplying Fracturing Pressure Decline: Part I. Paper presented at theSPE Rocky Mountain Regional/Low Permeability Reservoirs Sympo-\nsium, Denver, 26\u201328 April. SPE-25845-MS. http://dx.doi.org/10.2118/\n25845-MS.\nNordgren, R. P. 1972. Propagation of a Vertical Hydraulic Fracture. SPE\nJ.12(4): 306\u2013314. SPE-3009-PA. http://dx.doi.org/10.2118/3009-PA.\nOkada, Y. 1992. Internal Deformation Due to Shear and Tensile Faults in\na Half-Space. Bull. of the Seismological Society of America 82(2):\n1018\u20131040.\nPerkins, T. K. and Kern, L. R. 1961. Widths of Hydraulic Fractures. J Pet\nTechnol 13(9): 937\u2013949. SPE-89-PA. http://dx.doi.org/10.2118/89-\nPA.\nPerkins, T. K. and Gonzalez, J. A. 1985. The Effect of Thermoelastic\nStresses on Injection Well Fracturing. SPE J. 25(1): 78\u201388. SPE-"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 15, "chroma:document": "PA.\nPerkins, T. K. and Gonzalez, J. A. 1985. The Effect of Thermoelastic\nStresses on Injection Well Fracturing. SPE J. 25(1): 78\u201388. SPE-\n11332-PA. http://dx.doi.org/10.2118/11332-PA.\nPlahn, S. V., Nolte, K. G., Thompson, L. G. et al. 1997. A Quantitative\nInvestigation of the Fracture Pump-in/Flowback Test. SPE Prod & Fac\n12(1): 20\u201327. SPE-30504-PA. http://dx.doi.org/10.2118/30504-PA.\nPyrak-Nolte, L. J. and Morris, J. P. 2000. Single Fractures Under Normal\nStress: The Relation Between Fracture Speci\ufb01c Stiffness and Fluid\nFlow. International J. Rock Mechanics and Mining Sciences 37:\n245\u2013262. http://dx.doi.org/10.1016/S1365-1609(99)00104-5.\nRaaen, A. M., Skomedal, E., Kjorholt, H. et al. 2001. Stress Determination\nFrom Hydrualic Fracturing Tests: The System Stiffness Approach.International J. for Rock Mechanics and Mining Sciences 38(4):\n529\u2013541. http://dx.doi.org/10.1016/S1365-1609(01)00020-X.\nRibeiro, P. and Horne, R. 2013. Pressure and Temperature Transient Anal-"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 15, "chroma:document": "529\u2013541. http://dx.doi.org/10.1016/S1365-1609(01)00020-X.\nRibeiro, P. and Horne, R. 2013. Pressure and Temperature Transient Anal-\nysis: Hydraulic Fractured Well Application. Paper presented at the\nSPE Annual Technical Conference and Exhibition, New Orleans, 30\nSeptember\u20132 October. SPE-166222-MS. http://dx.doi.org/10.2118/\n166222-MS.\nShlyapobersky, J. W., Walhaug, W. W. Shef\ufb01eld, R. E. et al. 1988. Field\nDetermination of Fracturing Parameters for Overpressure CalibratedDesign of Hydraulic Fracturing. Paper presented at the SPE Annual\nTechnical Conference and Exhibition, Houston, 2\u20135 October. SPE-\n18195-MS. http://dx.doi.org/10.2118/18195-MS.\nSneddon, I. N. 1946. The Distribution of Stress in the Neighborhood of a\nCrack in an Elastic Solid. Proc., Royal Society of London Series A 187\n(1009): 229\u2013260. http://dx.doi.org/10.1098/rspa.1946.0077.\nSoliman, M. Y. and Gamadi, T. 2012. Testing Tight Gas and Unconven-\ntional Formations and Determination of Closure Pressure. Paper pre-"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 15, "chroma:document": "Soliman, M. Y. and Gamadi, T. 2012. Testing Tight Gas and Unconven-\ntional Formations and Determination of Closure Pressure. Paper pre-\nsented at the SPE/EAGE European Unconventional Resources\nConference and Exhibition, Vienna, Austria, 20\u201322 March. SPE-\n150948-MS. http://dx.doi.org/10.2118/150948-MS.\nSoliman, M. Y. and Kabir, C. S. 2012. Testing Unconventional Forma-\ntions. J. Petroleum Science and Technology 92\u201393: 102\u2013109. http://\ndx.doi.org/10.1016/j.petrol.2012.04.027.\nValko, P. P. and Economides, M. J. 1999. Fluid-Leakoff Delineation in\nHigh-Permeability Fracturing. SPE Prod & Fac 14(2): 117\u2013130. SPE-\n56135-PA. http://dx.doi.org/10.2118/56135-PA.\nvan den Hoek, P. J. 2002. Pressure Transient Analysis in Fractured Pro-\nduced Water Injection Wells. Paper presented at the SPE Asia Paci\ufb01cOil and Gas Conference and Exhibition, Melbourne, Australia, 8\u201310\nOctober. SPE-77946-MS. http://dx.doi.org/10.2118/77946-MS.\nVinsome, P. K. and Westerveld, J. 1980. A Simple Method for Predicting"}


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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-179725-PA-Fracture Compliance Method.pdf", "page": 15, "chroma:document": "October. SPE-77946-MS. http://dx.doi.org/10.2118/77946-MS.\nVinsome, P. K. and Westerveld, J. 1980. A Simple Method for Predicting\nCap and Base Rock Heat Loses in Thermal Reservoir Simulators. J\nCan Pet Technol 19(3): 87\u201390. SPE-80-03-04-PA. http://dx.doi.org/\n10.2118/80-03-04.\nWallace, J., Kabir, C. S., and Cipolla, C. L. 2014. Multiphysics Investiga-\ntion of Diagnostic Fracture Injection Tests in Unconventional Reser-\nvoirs. Paper presented at the SPE Hydraulic Fracturing TechnologyConference, The Woodlands, Texas, 4\u20136 February. SPE-168620-MS.\nhttp://dx.doi.org/10.2118/168620-MS.\nWalsh, J. B. 1981. Effect of Pore Pressure and Con\ufb01ning Pressure on Frac-\nture Permeability. International J. of Rock Mechanics and Mining Sci-\nences 18:429\u2013435. http://dx.doi.org/10.1016/0148-9062(81)90006-1.\nWillis-Richards, J., Watanabe, K., and Takahashi, H. 1996. Progress To-\nward a Stochastic Rock Mechanics Model of Engineered Geothermal\nSystems. J. Geophysical Research 101 (B8): 17481\u201317496. http://"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 15, "chroma:document": "ward a Stochastic Rock Mechanics Model of Engineered Geothermal\nSystems. J. Geophysical Research 101 (B8): 17481\u201317496. http://\ndx.doi.org/10.1029/96JB00882.J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1336 Total Pages: 19\nID:jaganm Time: 18:40 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###1600071336 August 2016 SPE Journal"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 16, "chroma:document": "Witherspoon, P. A., Wang, J. S. Y., Iwa i, K. et al. 1980. Validity of Cubic Law\nfor Fluid Flow in a Deformable Rock Fracture. Water Resources Research\n16(6): 1016\u20131024. http://dx.doi.org/10.1029/WR016i006p01016.\nYew, C. H. and Liu, G. H. 1993. The Fracture Tip and Critical Stress In-\ntensity Factor of a Hydraulically Induced Fracture. SPE Prod & Fac 8\n(3): 171\u2013177. SPE-22875-PA. http://dx.doi.org/10.2118/22875-PA.\nZoback, M. D. 2007. Reservoir Geomechanics . Cambridge: Cambridge\nUniversity Press.\nAppendix A: Derivation of the Equations\nGoverning Pressure-Transient BehaviorDuring a DFIT\nHere, we derive the equations governing pressure-transient behav-\nior during a DFIT.\nWe describe the entire fracture and wellbore system with a\n\u201clumped parameter model,\u201d in which we assume thatdP\ndtis uni-\nform throughout the entire system. This approach is isothermal\nand implicitly neglects pressure gradient caused by \ufb02ow in thewell, perforation, near-wellbore region, and along the fracture."}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 16, "chroma:document": "and implicitly neglects pressure gradient caused by \ufb02ow in thewell, perforation, near-wellbore region, and along the fracture.\nConsidering these effects would not fundamentally change the\nconclusions drawn from the analysis. Related approaches are used\nby Raaen et al. (2001) and Craig and Blasingame (2006), though\nthe derivation we provide here has important differences.\nThe pressure derivative with time can be decomposed with the\nchain rule as\ndP\ndt\u00bcdP\ndmdm\ndt; \u00f0A-1\u00de\nwhere mis the total mass of \ufb02uid in the wellbore and in the frac-\nture and Pis the pressure that is either measured at the bottom of\nthe well or calculated from surface-pressure measurements.dm\ndtis\nequal to the surface mass-injection rate, qm,inj, minus the rate at\nwhich \ufb02uid mass \ufb02ows out of the well and fracture into the ma-\ntrix,qm,leakoff . We can expand these terms by saying that\ndm\ndt\u00bcqm;inj/C0qm;leakoff \u00bcqinjqinj/C0qleakoff qleakoff ; \u00f0A-2\u00de\nwhere qinjis the volumetric surface injection rate, qinjis the den-"}


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-179725-PA-Fracture Compliance Method.pdf", "page": 16, "chroma:document": "dm\ndt\u00bcqm;inj/C0qm;leakoff \u00bcqinjqinj/C0qleakoff qleakoff ; \u00f0A-2\u00de\nwhere qinjis the volumetric surface injection rate, qinjis the den-\nsity of the \ufb02uid injected, qleakoff is the volumetric rate of leakoff\ninto the matrix, and qleakoff is the average density of the \ufb02uid leak-\ning off into the matrix.dP\ndmcan be expanded by starting with\nthe de\ufb01nition\nm\u00bcqwlVwl\u00feqfrVfr; \u00f0A-3\u00de\nwhere qwlis the average density of the \ufb02uid in the wellbore, Vwlis\nthe volume of the wellbore, qfris the average density of the \ufb02uid\nin the fracture, and Vfris the volume of the fracture.\nTo simplify further, we assume that the \ufb02uid is slightly com-\npressible and has constant compressibility, cf. In this case, we\ncan write\nq\u00bcq0exp\u00bd\u00f0P/C0P0\u00decf/C138; \u00f0A-4\u00de\nwhere P0is a reference pressure and q0is the density of the \ufb02uid\nat that pressure. Taking the Taylor-series expansion and discard-\ning higher-order terms provides the approximation\nq\u00bcq0\u00bd1\u00fecf\u00f0P/C0P0\u00de/C138: \u00f0A-5\u00de\nWe can take the derivative of this linearized equation with"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88340c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 16, "chroma:document": "ing higher-order terms provides the approximation\nq\u00bcq0\u00bd1\u00fecf\u00f0P/C0P0\u00de/C138: \u00f0A-5\u00de\nWe can take the derivative of this linearized equation with\nrespect to pressure and determine that\ndq\ndP\u00bcq0cf: \u00f0A-6\u00de\nNow, we take the derivative of Eq. A-3 with respect to\npressure:dm\ndP\u00bcdqwl\ndPVwl\u00feqwldVwl\ndP\u00fedqfr\ndPVfr\u00feqfrdVfr\ndP: \u00f0A-7\u00de\nCombining Eqs. A-1, A-2, and A-7, we arrive at\ndP\ndt\u00bcqinjqinj/C0qleakoff qleakoff\ndqwl\ndPVwl\u00feqwldVwl\ndP\u00fedqfr\ndPVfr\u00feqfrdVfr\ndP: \u00f0A-8\u00de\nEq. A-8 can be simpli\ufb01ed by relying on the assumption that\nthe \ufb02uid is slightly compressible. If we assume that qinj,qleakoff ,\nqwl, and qfrare all approximately equal (for isothermal fresh\nwater, they would be within a few percentages), and these quanti-\nties are also equal to the q0value used to calculate the derivatives\nof \ufb02uid density with respect to pressure in the wellbore and the\nfracture, then we can cancel them out of the numerator and the de-nominator of Eq. A-8 and arrive at\ndP\ndt\u00bcqinj/C0qleakoff\ncfVwl\u00fedVwl\ndP\u00fecfVfr\u00fedVfr"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883466-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 16, "chroma:document": "fracture, then we can cancel them out of the numerator and the de-nominator of Eq. A-8 and arrive at\ndP\ndt\u00bcqinj/C0qleakoff\ncfVwl\u00fedVwl\ndP\u00fecfVfr\u00fedVfr\ndP\u00bcqinj/C0qleakoff\nCt;\n/C1/C1/C1/C1/C1/C1/C1/C1/C1/C1/C1/C1/C1/C1/C1/C1/C1/C1/C1 \u00f0 A-9\u00de\nwhere Ctis the total storage coef\ufb01cient of the entire system. The\nde\ufb01nition of total-storage coef\ufb01cient used in Eq. A-9 is more gen-\neral than the expressions used by Raaen et al. (2001) and by Craig\nand Blasingame (2006).\nCraig and Blasingame (2006) de\ufb01ne the after-closure storage\ncoef\ufb01cient as (with slightly different variable de\ufb01nitions)\nCac\u00bccfVwl\u00fecfVfr; \u00f0A-10 \u00de\nwhere Vfris assumed constant. Comparing this expression with\nEq. A-9, we can see that Craig and Blasingame (2006) implicitly\nassume that qwldVwl\ndPandqfrdVfr\ndPare zero. The former term, the\nchanging wellbore volume, is routinely assumed negligible. How-\never, the latter term, for the changing fracture volume after clo-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8834c0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 16, "chroma:document": "changing wellbore volume, is routinely assumed negligible. How-\never, the latter term, for the changing fracture volume after clo-\nsure, is large, as shown next. Craig and Blasingame (2006) permitthat the \ufb02uid in the wellbore and fracture may have different com-\npressibility, whereas we assume that their compressibility is the\nsame. The distinction should have a negligible effect in a DFIT,where clear water is injected.\nRaaen et al. (2001) use an approach similar to that shown in\nEq. A-9. However, they assume that \u201cwhen the fracture is closed,\nthere are three main contributions to the system stiffness: from\nthe compliance of the wellbore \ufb02uid, from the deformation of thecasing and top-side tubes, and from the deformation of the open-\nhole below the casing shoe.\u201d Therefore, they implicitly assume\nthat the\ndqfr\ndPVfrandqfrdVfr\ndPterms in Eq. A-9 are zero.\nWith the assumptions we describe, Eq. A-9 applies during all"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88351a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 16, "chroma:document": "that the\ndqfr\ndPVfrandqfrdVfr\ndPterms in Eq. A-9 are zero.\nWith the assumptions we describe, Eq. A-9 applies during all\nphases of a fracturing test: during injection, the before-closureshut-in period, during closure, and the after-closure shut-in period.\nIn reality, during injection, pressure gradient caused by \ufb02ow\nthrough the well, perforations, near-wellbore region, and fracture\ncausedP\ndtto vary spatially throughout the system, but after the\nearly shut-in period, these pressure gradients should be minimal.\nThe total storage coef\ufb01cient has four parts: compressibility of\n\ufb02uid in the wellbore, changes in the wellbore volume, compressi-\nbility of the \ufb02uid in the fracture, and changes in fracture volume.Conventionally, changes in wellbore volume are assumed negligi-\nble relative to c\nfVwland thedVwl\ndPterm is neglected (Horne 1995).\ndVfr\ndPcan be written asA\nSf, where Ais the surface area of the\nfracture and Sfis the fracture stiffness, the derivative of effective"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883574-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 16, "chroma:document": "dVfr\ndPcan be written asA\nSf, where Ais the surface area of the\nfracture and Sfis the fracture stiffness, the derivative of effective\nnormal stress with respect to aperture (Jaeger et al. 2007).dVfr\ndP\ndepends on fracture geometry and mechanical characteristics of\nthe formation. In practice, the fracture geometry is usually not...........................\n....\n......................\n.....................\n.....................\n.................................\n.....\n. ......................J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1337 Total Pages: 19\nID:jaganm Time: 18:40 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###160007August 2016 SPE Journal 1337"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8835ce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 17, "chroma:document": "well-constrained. Two limiting cases for fracture geometry are\ncircular and PKN (Perkins and Kern 1961; Nordgren 1972). If\nthere is no fracture-height restraint caused by layering, then thefracture will be approximately circular (though not completely cir-\ncular because the trends in stress with depth will cause it to prefer-\nentially propagate upward). If the fracture is con\ufb01ned between\nhigher stress intervals, then the fracture length will be much\ngreater than its height, and stiffness can be approximated from a2D plane-strain solution, the key assumption of the PKN model.\nFor a radial fracture, the stiffness of the fracture (when open),\nS\nf,o, can be written as (Sneddon 1946):\nSf;r\u00bc3pGm\n8\u00f01/C0/C23\u00deRf; \u00f0A-11 \u00de\nwhere Gmis the shear modulus, /C23is Poisson\u2019s ratio, and Rfis the\nradius. For a fracture with length much longer than its height, the\nstiffness can be estimated as (Sneddon 1946; Perkins and Kern\n1961; Nordgren 1972):\nSf;PKN\u00bc4Gm\np\u00f01/C0/C23\u00dehf: \u00f0A-12 \u00de\nThe magnitudes of theA"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88361e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 17, "chroma:document": "stiffness can be estimated as (Sneddon 1946; Perkins and Kern\n1961; Nordgren 1972):\nSf;PKN\u00bc4Gm\np\u00f01/C0/C23\u00dehf: \u00f0A-12 \u00de\nThe magnitudes of theA\nSf,cfVwl, and cfVfrterms can be\nroughly assessed (for example, in the fracture simulation shown\nin the Effect of Increasing Residual Aperture subsection). The\n\ufb01nal fracture length is approximately 250 m, with a height of 7 m,\nfor a surface area of 1750 m2. Fig. 6 shows that the average frac-\nture aperture is roughly 1 mm, which means that Vfris roughly\n1.75 m3andcfVfris roughly (with the value of water compressi-\nbility given in Table 1) 0.0008 m3/MPa. Vwldepends on wellbore\nlength and diameter. A typical value is approximately 100 m3, and\nsocfVfrcan be estimated as 0.0458 m3/MPa. The fracture shown\nin Fig. 6 has length much greater than height, 7 m. Therefore, its\npreclosure stiffness can be assessed from Eq. A-12 and is equal to\n3.638 MPa/mm. TheA\nSfterm is equal to 0.48 m3/MPa. This analy-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883678-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 17, "chroma:document": "preclosure stiffness can be assessed from Eq. A-12 and is equal to\n3.638 MPa/mm. TheA\nSfterm is equal to 0.48 m3/MPa. This analy-\nsis indicates that the dominant effect in the total-storage coef\ufb01-\ncient is likely to be the fracture stiffness, the wellbore storage has\nminor but nonnegligible effect, and the compressibility of the\nwater in the fracture is negligible.\nAfter shut-in, the pressure derivative can be written as (assum-\ning constant wellbore volume and that the cfVfrterm is negligible)\ndP\ndt\u00bc/C0qleakoff\ncfVwl\u00feA\nSf: \u00f0A-13 \u00de\nIf the fracture continues propagating after closure, Amay\nchange signi\ufb01cantly and Sfmay change (depending on the geome-\ntry). If the fracture is no longer propagating, Sfwill be constant\nbefore fracture closure, but will change when the fracture closes.\nUsing the Carter model to calculate leakoff rate yields a value\nofqleakoff that scales with the inverse of the square root of time"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8836d2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 17, "chroma:document": "Using the Carter model to calculate leakoff rate yields a value\nofqleakoff that scales with the inverse of the square root of time\n(Howard and Fast 1957). This is why plots of pressure vs. thesquare root of time during shut-in yield a straight line. If leakoff\nrate scales with time according to the G-function introduced by\nNolte (1979), then a plot of pressure vs. G-time will yield a\nstraight line. The straight line will only occur if the denominator\nin Eq. A-13 is constant, which is why closure causes a deviationfrom the straight line. Closure also decreases the fracture trans-\nmissivity. If this causes the fracture to no longer be effectively in-\n\ufb01nite conductivity, then, pressure gradients can develop along the\nfracture, and this can cause the lumped parameter approach used\nin this section to no longer be applicable.\nTo understand the pressure trend after closure, it is necessary\nto investigate how stiffness is affected by closure. The stiffness\nafter closure, S"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88372c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 17, "chroma:document": "To understand the pressure trend after closure, it is necessary\nto investigate how stiffness is affected by closure. The stiffness\nafter closure, S\nf,c, includes the effect of the elastic response of the\nformation (as shown in Eqs. A-11 and A-12), but also includes a\ncontribution from the contacting fracture walls (Section 12.3 fromJaeger et al. 2007).As a simplifying assumption, we assume that both the stress\nand aperture are constant along the fracture. This is not strictly\ncorrect, but is suf\ufb01ciently accurate for providing a conceptual ex-planation. Under this simplifying assumption, we can write\nr\n0\nn\u00bcrr\nn\u00feESf;o/C0P: \u00f0A-14 \u00de\nBecause the initial aperture of a hydraulic fracture is zero\n(because it does not initially exist), backstress is created by its\nentire aperture, E.\nTo \ufb01nd the fracture stiffness, Eq. A-14 can be solved for Pand\ndifferentiated with respect to E:\nSf;c\u00bcdE\ndP/C18/C19/C01\n\u00bcdP\ndE\u00bcSf;o/C0dr0\ndE\u00bcSf;o/C0dE\ndr0n/C18/C19/C01\n\u00bcSf;o\u00fedE\ndP/C18/C19/C01"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883786-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 17, "chroma:document": "differentiated with respect to E:\nSf;c\u00bcdE\ndP/C18/C19/C01\n\u00bcdP\ndE\u00bcSf;o/C0dr0\ndE\u00bcSf;o/C0dE\ndr0n/C18/C19/C01\n\u00bcSf;o\u00fedE\ndP/C18/C19/C01\n\u00bcSf;o\u00feSf;cont;/C1/C1/C1/C1/C1/C1/C1/C1/C1 \u00f0 A-15 \u00de\nwhere Sf,contis the contribution to the stiffness from the contact\nstress. Sf,contcan be calculated from any constitutive equation that\nspeci\ufb01es Eas a function of effective normal stress. For example,\nEq. 12 yields\nSf;cont\u00bc/C0dE\ndr0\nn/C18/C19/C01\n\u00bc9E0\nrn;ref1\u00fe9r0\nn\nrn;ref/C18/C19/C02\"#/C01\n\u00bcrn;ref\n9E0\nE2: \u00f0A-16 \u00de\nThus, with Eq. 12, the stiffness of a closed fracture is\nSf;c\u00bcSf;o\u00fern;ref\n9E0\nE2: \u00f0A-17 \u00de\nThe value of Sf,contincreases as the fracture closes. At closure\nSclosure\nf;cont\u00bcrn;ref\n9E0: \u00f0A-18 \u00de\nReferring to the simulation described in the Effect of Increas-\ning Residual Aperture subsection, we can calculate Sclosure\nf;cont to be\n11.333 MPa/mm (for a total Sfof 14.971 MPa/mm), signi\ufb01cantly\ngreater than the value of Sf,oof 3.638 MPa/mm. Closure causes a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8837e0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 17, "chroma:document": "f;cont to be\n11.333 MPa/mm (for a total Sfof 14.971 MPa/mm), signi\ufb01cantly\ngreater than the value of Sf,oof 3.638 MPa/mm. Closure causes a\nsharp increase in Sffrom Sf,otoSf,c, which (from Eq. A-13) causes\nan increase in the pressure derivative. The derivative increasesvery sharply because stiffness increases so much with closure,\nincreasing by roughly a factor of 4, and continuing to increase fur-\nther as aperture drops further below E\n0. In the Adding Wellbore\nStorage subsection, a simulation is shown with a smaller value of\nrn;ref, 5 MPa instead of 51 MPa, and so Sclosure\nf;contis 1.111 MPa/mm\n(for a total Sfof 4.749 MPa/mm), causing only a modest increase\ncompared to the stiffness before closure. As a result, the deriva-\ntive increases less abruptly.\nMark McClure is the founder and chief executive officer of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88383a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 17, "chroma:document": "tive increases less abruptly.\nMark McClure is the founder and chief executive officer of\nMcClure Geomechanics and is a consulting professor at Stan-ford University. He was an assistant professor in the Departmentof Petroleum and Geosystems Engineering at the University of\nTexas at Austin from 2013 to 2015. McClure\u2019s research focuses\non modeling and characterization of hydraulic fracturing,induced seismicity, and enhanced geothermal systems. Hewas honored with the 2015 SPE Regional Completions Optimi-\nzation and Technology Award from the Southwest North Amer-\nican Region, Outstanding Service as a Technical Editor for SPE\nReservoir Evaluation & Engineering in 2014, the Hank Ramey\nAward for Outstanding Research and Service to the Depart-\nment from the Department of Energy Resources Engineering at\nStanford University in 2012, and Best Paper in Geophysics from\nthe Society of Exploration Geophysicists (SEG) in 2011. McClureholds a BS degree in chemical engineering, an MS degree in"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883894-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 17, "chroma:document": "the Society of Exploration Geophysicists (SEG) in 2011. McClureholds a BS degree in chemical engineering, an MS degree in\npetroleum engineering, and a PhD degree in energy-resources\nengineering, all from Stanford University.\nHojung Jung is a PhD degree student at the University of Texas\nat Austin. Her research interests include experiments and.......................\n.....................\n.............................................\n........................\n.....................\n.........................J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1338 Total Pages: 19\nID:jaganm Time: 18:40 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###1600071338 August 2016 SPE Journal"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8838ee-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 18, "chroma:document": "simulations of geomechanical problems in the context of hy-\ndraulic fracturing and carbon dioxide storage. Jung holds an\nMS degree in petroleum engineering from the University ofTexas at Austin and a BS degree (cum laude) in energy-resour-ces engineering from Seoul National University, South Korea.\nShe is a member of SPE.\nDave Cramer is a senior engineering fellow on the ConocoPhil-\nlips Global Completions Engineering staff in Houston and spe-\ncializes in hydraulic-fracturing applications. He has published\n48 technical papers and holds two US patents. Cramer is aregistered professional engineer in Colorado. Industry recogni-tions include the Henry Mattson Technical Achievement\nAward by the SPE Denver Chapter in 1993 and the SPE Interna-\ntional Completions Optimization and Technologies Award in2011. Cramer was an SPE Distinguished Lecturer during2003\u20132004 and the SPE Region Director for the US and Canada"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883948-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 18, "chroma:document": "Rocky Mountain Region from 2004 to 2007.Mukul M. Sharma is a professor and holds the \u201cTex\u201d Moncrief\nChair in the Department of Petroleum and Geosystems Engineer-\ning at the University of Texas at Austin, where he has been for thepast 30 years. He served as chair of the Department from 2001 to2005. Sharma\u2019s current research interests include improved oil re-\ncovery, injection-water management, hydraulic fracturing, for-\nmation damage, and petrophysics. He has published more than350 journal articles and conference proceedings and holds 15patents. Sharma has a bachelor of technology degree in chemi-\ncal engineering from the Indian Institute of Technology and MS\nand PhD degrees in chemical and petroleum engineering,respectively, from the University of Southern California. Amonghis many awards, he is the recipient of the 2009 Anthony Lucas\nGold Medal, the 2004 SPE Faculty Distinguished Achievement"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-PA-Fracture Compliance Method.pdf", "page": 18, "chroma:document": "Gold Medal, the 2004 SPE Faculty Distinguished Achievement\nAward, the 2002 SPE Lester C. Uren Award, and the 1998 SPE For-mation Evaluation Award. Sharma served as an SPE DistinguishedLecturer in 2002, has served on the editorial boards of many jour-\nnals, and has taught and consulted for industry worldwide.J179725 DOI: 10.2118/179725-PA Date: 2-August-16 Stage: Page: 1339 Total Pages: 19\nID:jaganm Time: 18:40 I Path: S:/J###/Vol00000/160007/Comp/APPFile/SA-J###160007August 2016 SPE Journal 1339"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 0, "chroma:document": "Discussion of The\nFracture-Compliance Method for\nPicking Closure Pressure From\nDiagnostic Fracture-Injection Tests\nMatteo Marongiu Porcu, Schlumberger; Christine Ehlig-Economides, University of Houston;\nand Robert D. Barree, Barree & Associates\nWe would like to open this discussion on SPE-179725-PA\n(McClure et al. 2016) directly from its title. The \u201cfracture-compli-\nance method\u201d does not allow determination of the closure pres-\nsure associated with minimum principal in-situ stress. What\nMcClure et al. refer to as \u201cclosure pressure\u201d is in fact the manifes-\ntation of known physical phenomena that are generally addressed\nas nonlinear leakoff, departing from Carter\u2019s ideal leakoff\n(Howard and Fast 1957), which all occur at higher to much higher\npressures than the minimum principal in-situ stress.\nMcClure et al. do cite the essential published work that\naddresses these nonlinear-leakoff phenomena, but they do so with\na very dismissive tone. Barree and Miskimins (2016) de\ufb01ned"}


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-179725-DISC Fracture Compliance Discussions.pdf", "page": 0, "chroma:document": "addresses these nonlinear-leakoff phenomena, but they do so with\na very dismissive tone. Barree and Miskimins (2016) de\ufb01ned\nthese as \u201caccelerated leakoff\u201d and \u201cdelayed leakoff,\u201d and pro-\nvided a very clear description of all physical causes of these pres-sure-falloff behaviors.\nIn particular, Barree and Miskimins (2016) dedicated a consid-\nerable effort to describing features of diagnostic fracture-injection\ntests (DFITs) in multistage/multicluster hydraulically fractured\nhorizontal wells in naturally fractured/laminated shale formationsthat are not expected in vertical-well DFITs. In such settings, it is\nhighly unrealistic to expect ideal planar biwing propagation of\ninduced hydraulic fractures. Instead, it is possible to have highlynonideal con\ufb01gurations, including sublongitudinal coalescence of\ndiscrete cracks along the wellbore, strong near-wellbore tortuosity,\nand hydraulic-fracture complexity (Weng et al. 2011) because of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883ace-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 0, "chroma:document": "discrete cracks along the wellbore, strong near-wellbore tortuosity,\nand hydraulic-fracture complexity (Weng et al. 2011) because of\nthe severe interaction with near-wellbore stresses possibly altered\nby drilling, pre-existing natural fractures, joints, and genericplanes of weakness. These nonideal fracture features (near-well-\nbore and far-\ufb01eld) are arbitrarily oriented, and, at the moment of\ninjection shut-in, are held open against a higher stress than the\nminimal principal stress. Consequently, they will be the \ufb01rst ones\nto gradually close during the pressure falloff, and, during theirown closure process, they will keep transmitting their higher pres-\nsure to the primary fracture (orthogonal to the minimum principal\nin-situ stress), causing the slower or delayed leakoff behavior\nsymptomatic of the upward concavity in a Cartesian ( G-function)\nplot of the GdP/dGderivative function vs. the G-time function.\nThus, application of the \u201cfracture-compliance method\u201d might"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883b28-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 0, "chroma:document": "plot of the GdP/dGderivative function vs. the G-time function.\nThus, application of the \u201cfracture-compliance method\u201d might\nlead to identi\ufb01cation of a closure event ascribable to the nonideal\ncon\ufb01gurations described above, but not to a \ufb01nal primary-fractureclosure that would re\ufb02ect the minimum principal in-situ stress.\nThe authors confuse this point in their Conclusions 2 through\n4 by claiming that the picks by other cited analysis methods\nunderestimate minimum stress, while stating in their Conclusion 7\nthat the closure pressure (picked from their method) can be asmuch as 1 to 2 MPa (145 to 290 psi) greater than the minimum-\nprincipal-stress value. The other analysis methods cited in Con-\nclusions 2 through 4 will all pick the same closure event, correctly\nassociated to the minimum principal in-situ stress.\nThe numerical model used by the authors to present the variable"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883b8c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 0, "chroma:document": "associated to the minimum principal in-situ stress.\nThe numerical model used by the authors to present the variable\ncompliance simulations exposes signi\ufb01cant limitations, the \ufb01rst ofwhich is that the model is incapable of handling such features as\nnormal leakoff behavior; faster or accelerated leakoff scenariossuch as pressure-dependent leakoff that produce downward con-\ncavities in the GdP/dGderivative function; and multiple closure\nscenarios consistent with multiple straight-line portions that appearin DFIT data illustrated in Mohamed et al. (2011) and others.\nA second model limitation, which is really a serious model\n\ufb02aw, is shown by obvious discontinuities occurring immediately\nafter what the authors pick as the closure pressure. The authors\nacknowledge that such discontinuities are not seen in DFIT\nresponses. They attempt to avoid the model discontinuity by mod-eling a fracture with a residual aperture exceeding 0.5 mm at the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883be6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 0, "chroma:document": "responses. They attempt to avoid the model discontinuity by mod-eling a fracture with a residual aperture exceeding 0.5 mm at the\nclosure pressure claimed to correspond to the minimum principal\nstress. Few if any analysts would envision such a fracture width\nas closed. Even so, to completely remove the model discontinuity,\nthey add wellbore-storage and tip-extension model features. Onlywith all this (including residual fracture aperture at minimum\nprincipal stress exceeding 0.5 mm) do they produce simulations\nremotely similar to typical DFIT data.\nFrom our experience from falloff-test analyses performed on\nEagle Ford, Wolfcamp, Haynesville, Fayetteville, Marcellus, andHorn River shale wells, the real closure events indicating the min-\nimum principal in-situ stresses systematically occur at equivalent\nstress gradients 0.05 to 0.1 psi/ft lower than the gradients associ-ated with nonideal-con\ufb01gurations events (described above) that\none would pick using the \u201cfracture-compliance method.\u201d"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883c36-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 0, "chroma:document": "one would pick using the \u201cfracture-compliance method.\u201d\nFor instance, the extra 0.05 psi/ft (and often higher) in the mini-\nmum principal in-situ-stress gradient that we systematically obtain\nwhen we attempt to pick closure events using the \u201cfracture-com-pliance method\u201d in a vast number of Eagle Ford and Wolfcamp\ncalibration tests is impossible to reconcile within state-of-the-art\nmechanical Earth models [refer to, among others, the example of\nmechanical Earth models built and used in Berard et al. (2015) and\nMarongiu Porcu et al. (2016)] that were built using anisotropicacoustic borehole measurements calibrated with actual core-\nderived mechanical properties and pore pressures either deter-\nmined from after-closure analysis or measured with MDT tools.\nReferences\nBarree, R. D. and Miskimins, J. L. 2016. Physical Explanation of Non-\nLinear Derivatives in Diagnostic Fracture Injection Test Analysis. Pa-\nper presented at the SPE Hydraulic Fracturing Technology Confer-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883c90-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 0, "chroma:document": "Linear Derivatives in Diagnostic Fracture Injection Test Analysis. Pa-\nper presented at the SPE Hydraulic Fracturing Technology Confer-\nence, The Woodlands, Texas, 9\u201311 February. SPE-179134-MS.\nhttps://doi.org/10.2118/179134-MS.\nBerard, T., Desroches, J., Yang, Y. et al. 2015. High-Resolution 3D Struc-\ntural Geomechanics Modeling for Hydraulic Fracturing. Paper pre-\nsented at the SPE Hydraulic Fracturing Technology Conference, The\nWoodlands, Texas, 3\u20135 February. SPE-173362-MS. https://doi.org/10.2118/173362-MS.\nHoward, G. C. and Fast, C. R. 1957. Optimum Fluid Characteristics for\nFracture Extension. Drilling and Production Practices, New York, 1\nJanuary, API-57-261, 261-270 (Appendix by Carter, E. D.). American\nPetroleum Institute.\nMarongiu Porcu, M., Lee, D., Shan, D. et al. 2016. Advanced Modeling of\nInterwell-Fracturing Interference: An Eagle Ford Shale-Oil Study.\nSPE J. 21(5): 1567\u20131582. SPE-174902-PA. https://doi.org/10.2118/\n174902-PA."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883cea-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 0, "chroma:document": "Interwell-Fracturing Interference: An Eagle Ford Shale-Oil Study.\nSPE J. 21(5): 1567\u20131582. SPE-174902-PA. https://doi.org/10.2118/\n174902-PA.\nCopyright VC2017 Society of Petroleum EngineersJ179725 DOI: 10.2118/179725-PA Date: 11-May-17 Stage: Page: 1 Total Pages: 3\nID:jaganm Time: 19:06 I Path: S:/J###/Vol00000/170027/Comp/APPFile/SA-J###1700272017 SPE Journal 1"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883d44-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 1, "chroma:document": "McClure, M. W., Jung, H., Cramer, D. D. et al. 2016. The Fracture-Com-\npliance Method for Picking Closure Pressure From Diagnostic Frac-ture-Injection Tests. SPE J. 21(4): 1321\u20131339. SPE-179725-PA.\nhttps://doi.org/10.2118/179725-PA.\nMohamed, I. M., Nasralla, R. A., Sayed, M. A. et al. 2011. Evaluation of\nAfter-Closure Analysis Techniques for Tight and Shale Gas Forma-\ntions. Paper presented at the SPE Hydraulic Fracturing TechnologyConference, The Woodlands, Texas, 24\u201326 January. SPE-140136-MS.\nhttps://doi.org/10.2118/140136-MS.\nWeng, X., Kresse, O., Cohen, C. -E. et al. 2011. Modeling of Hydraulic-\nFracture-Network Propagation in a Naturally Fractured Formation.\nSPE Prod & Oper 26(4): 368\u2013380. SPE-140253-PA. https://doi.org/\n10.2118/140253-PA.J179725 DOI: 10.2118/179725-PA Date: 11-May-17 Stage: Page: 2 Total Pages: 3\nID:jaganm Time: 19:06 I Path: S:/J###/Vol00000/170027/Comp/APPFile/SA-J###1700272 2017 SPE Journal"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883d9e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 2, "chroma:document": "Reply to the Discussion of The\nFracture-Compliance Method for\nPicking Closure Pressure From\nDiagnostic Fracture-Injection Tests\nMark McClure, McClure Geomechanics; Hojung Jung and Mukul Sharma, University of Texas at Austin;\nand Dave Cramer, ConocoPhillips\nMcClure et al. (2016) provides a mathematically consistent\ndescription of an ideal diagnostic fracture-injection test (DFIT)\npressure transient. We set out the governing and constitutive\nequations of the coupled \ufb02uid-\ufb02ow and fracture-mechanics prob-lem, use realistic input parameters, and solve the equations. The\nresult is a close match to a real DFIT pressure transient. Our work\nis the \ufb01rst to provide a single continuous calculation that realisti-\ncally describes an entire DFIT pressure transient\u2014before, during,\nand after closure. Previous investigators have focused on onlyparts of the transient and/or have interpolated between before-clo-\nsure and after-closure solutions without providing a mathematical"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883df8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 2, "chroma:document": "sure and after-closure solutions without providing a mathematical\ndescription of the closure process itself.\nThe appendix in McClure et al. (2016) derives equations\ndemonstrating that the effect of closure on the pressure derivative\ndepends on the relative effect on system compliance (which\ndecreases as the asperities in the fracture come into contact) and\non the leakoff rate from wellbore/fracture storage (which is\nrelated to the dimensionless fracture conductivity as closure\noccurs). If the compliance effect dominates, then the pressure\ndecreases more rapidly in response to closure. If the fracture con-\nductivity effect dominates, the pressure decreases less rapidly in\nresponse to closure. These principles should form the basis\nfor DFIT interpretation, whether or not more-complicated (and\ndif\ufb01cult to validate) \u201cnonideal\u201d processes are believed to be tak-\ning place.\nA key aspect of our model (and difference from most prior"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883e52-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 2, "chroma:document": "dif\ufb01cult to validate) \u201cnonideal\u201d processes are believed to be tak-\ning place.\nA key aspect of our model (and difference from most prior\nwork) is that we allow the fracture to have residual aperture after\nthe aperities come into contact. Is this reasonable? The strongest\nproof is that linear \ufb02ow regimes are routinely observed after clo-\nsure in DFITs. Linear \ufb02ow regimes require an in\ufb01nite conductiv-\nity fracture. In McClure et al. (2016), we provide a brief\ncalculation showing that residual aperture of only tens of microns\nis suf\ufb01cient for a fracture to maintain in\ufb01nite conductivity in a\nformation with very low permeability. There is a large scienti\ufb01c\nliterature demonstrating the ability of mechanically closed frac-tures to store and conduct \ufb02uid. We used a fracture closure law\nand input values based on this literature.\nIn their discussion, Marongiu Porcu et al. state that our paper\ndoes not address the wide range of \u201cnonideal\u201d processes that are"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883eac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 2, "chroma:document": "In their discussion, Marongiu Porcu et al. state that our paper\ndoes not address the wide range of \u201cnonideal\u201d processes that are\npossible during DFITs. In a follow-up paper (Jung et al. 2016),we performed simulations of a variety of nonideal processes,\nincluding near-wellbore tortuosity and opening of transverse frac-\ntures. These results add signi\ufb01cant new insight, but none of them\ncontradict the basic \ufb01ndings of McClure et al. (2016). The simula-\ntions demonstrate that near-wellbore tortuosity causes a rapiddrop in pressure at the start of the shut-in period, before the tran-\nsient settles into a \u201cnormal\u201d preclosure trend (Jung et al. 2016,\nFig. 17). This causes an early peak in G/C2dP/dGbefore the main\nclosure [as noted in McClure et al. (2016) and by Barree and\nMiskimins (2016)]. Jung et al. (2016) showed that mechanical\nopening/closing of transverse fractures away from the well is\nunlikely to occur unless there is very low stress anisotropy. If it"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883f06-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 2, "chroma:document": "opening/closing of transverse fractures away from the well is\nunlikely to occur unless there is very low stress anisotropy. If it\ndoes occur, the transverse fractures will close early in the tran-sient. This \ufb01nding contradicts the conventional DFIT interpreta-\ntion that \u201cclosure of transverse fractures\u201d causes G/C2dP/dG to\ncurve upward later in the transient (Barree and Miskimins 2016).\nHowever, review of the literature indicates that this conventional\ninterpretation is based on heuristic arguments, not a rigorous\nmathematical solution to the equations governing the problem.\nMarongiu P\norcu et al. note in their discussion that we did not\nconsider nonideal leakoff processes and cite discussion from\nBarree and Miskimins (2016). Barree and Miskimins (2016) state\nthat they will not \u201cdwell on derivative calculation methods and\ntheoretical elastic model derivations\u201d and instead \u201cpresent some\nreal physical mechanisms.\u201d They provide a list of nonideal proc-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883f60-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 2, "chroma:document": "theoretical elastic model derivations\u201d and instead \u201cpresent some\nreal physical mechanisms.\u201d They provide a list of nonideal proc-\nesses that could hypothetically occur during a DFIT. Merely pro-\nviding a list of alternative hypotheses does not refute our analysis;\nthey do not provide mathematical analysis or validating data.\nMarongiu P et al. also state in their discussion that our\nnumerical model is incapable of handling pressure-dependent\nleakoff or multiple closures. The model can handle all these proc-\nesses, as addressed in the follow-up paper Jung et al. (2016).\nMarongiu Porcu et al. note that some of our simulations had a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b883fb0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 2, "chroma:document": "esses, as addressed in the follow-up paper Jung et al. (2016).\nMarongiu Porcu et al. note that some of our simulations had a\ndiscontinuity in the pressure derivative at closure. As stated in thepaper, those simulations intentionally used unrealistic input pa-rameters and were included for sensitivity analysis and to demon-strate the effect of compliance on the pressure trend; they were notintended to be realistic. We also provided simulations that appearvery realistic and do not have discontinuity in the pressure deriva-tive, including one simulation that closely matches \ufb01eld data.\nFinally, Marongiu Porcu et al. state that our closure picks can-\nnot be reconciled with \u201cstate-of-the-art mechanical Earth models\u201dand cite two papers. We reviewed those papers and did not identify\nany discussion that refuted our results.\nA convincing theory of DFIT transients should lay out the gov-\nerning and constitutive equations of \ufb02uid \ufb02ow and fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88400a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 2, "chroma:document": "A convincing theory of DFIT transients should lay out the gov-\nerning and constitutive equations of \ufb02uid \ufb02ow and fracture\nmechanics, solve them, and provide a match to \ufb01eld data with a\nsingle, continuous calculation (before, during, and after closure).\nOur work is the \ufb01rst to have demonstrated this. We stand by our\nconclusions.\nReferences\nBarree, R. D. and Miskimins, J. L. 2016. Physical Explanation of Non-\nLinear Derivatives in Diagnostic Fracture Injection Test Analysis.\nPaper presented at the SPE Hydraulic Fracturing Technology Con-\nference, The Woodlands, Texas, 9\u201311 February. SPE-179134-MS.\nhttps://doi.org/10.2118/179134-MS.\nJung, H., Sharma, M. M., Cramer, D. D. et al. 2016. Re-examining Inter-\npretations of Non-Ideal Behavior During Diagnostic Fracture InjectionTests. Journal of Petroleum Science and Engineering 145: 114\u2013136.\nhttps://doi.org/10.1016/j.petrol.2016.03.016.\nMcClure, M. W., Jung, H., Cramer, D. D. et al. 2016. The Fracture-Com-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88408c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-179725-DISC Fracture Compliance Discussions.pdf", "page": 2, "chroma:document": "https://doi.org/10.1016/j.petrol.2016.03.016.\nMcClure, M. W., Jung, H., Cramer, D. D. et al. 2016. The Fracture-Com-\npliance Method for Picking Closure Pressure From Diagnostic Frac-\nture-Injection Tests. SPE J. 21(4): 1321\u20131339. SPE-179725-PA.\nhttps://doi.org/10.2118/179725-PA.J179725 DOI: 10.2118/179725-PA Date: 11-May-17 Stage: Page: 3 Total Pages: 3\nID:jaganm Time: 19:06 I Path: S:/J###/Vol00000/170027/Comp/APPFile/SA-J###1700272017 SPE Journal 3orcu"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8840e6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 0, "chroma:document": "The Spurious Deflection on Log-Log\nSuperposition-Time Derivative Plots\nof Diagnostic Fracture-Injection Tests\nMark McClure, McClure Geomechanics\nSummary\nLog-log superposition-time derivative plots are used to identify \ufb02ow regimes in well tests with variable rate. The use of superposition\ntime adjusts for the effect of the prior rate history, and (under some conditions) shows what the transient would have looked like if the\ntest had been performed at a constant rate. In this report, I show that if these plots are used to interpret shut-in transients from diagnostic\nfracture-injection tests (DFITs), the superposition-time derivative has an upward de\ufb02ection that does not represent actual reservoir or\ntransient behavior. I review mathematical properties of the superposition-time derivative. I derive equations for the pressure transient ina simpli\ufb01ed model DFIT in which closure does not occur. I show that the onset of late-time impulse \ufb02ow is controlled by injection vol-"}


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-186098-PA Superious Deflection.pdf", "page": 0, "chroma:document": "ume and formation, wellbore, and fracture properties, not the duration of injection (as implied by the de\ufb01nition of superposition time).\nLog-log superposition-time derivative plots of DFITs exhibit a slope of 3/2 at intermediate time. However, pressure change never scales\nwith a 3/2 power of time. One form of the G-function super\ufb01cially resembles a superposition-time function constructed by summing\nconstant-rate solutions with 3/2 power scaling. However, this is not a mathematically or physically valid interpretation. The 3/2 powerarises from a spatial integration of the Carter leakoff solution. There is not a mathematical, physical, or practical justi\ufb01cation for plot-\nting DFIT pressure-time data in a way that creates a 3/2 slope. I conclude by providing a \ufb01eld example and practical recommendations\nfor DFIT interpretation.\nIntroduction\nThe log-log derivative plot is widely used in well-test analysis. The slope of the derivative curve, d p/d[ln( t)], is used to diagnose"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 0, "chroma:document": "Introduction\nThe log-log derivative plot is widely used in well-test analysis. The slope of the derivative curve, d p/d[ln( t)], is used to diagnose\n\ufb02ow regimes\u2013it is more precise to call d p/d[ln( t)] the semilog derivative, but it is common convention in well-test analysis to call\nit simply the \u201cderivative curve.\u201d In tests that involve varying rate, such as buildup tests and falloff tests, the derivative is oftencalculated with respect to an effective time function, sometimes called superposition time. In in\ufb01nite-acting radial \ufb02ow, the superposi-\ntion-time derivative curve shows what the transient would have looked like if the test had been performed at a constant rate (Ehlig-\nEconomides 1988).\nIn recent years, log-log derivative plots have been used for the interpretation of DFITs. In a DFIT, 1\u2013100 bbl of water is injected for\nseveral minutes, creating a small hydraulic fracture. The term \u201cDFIT\u201d speci\ufb01cally refers to a fracturing test performed in a low-perme-"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 0, "chroma:document": "several minutes, creating a small hydraulic fracture. The term \u201cDFIT\u201d speci\ufb01cally refers to a fracturing test performed in a low-perme-\nability formation in a completed well. After shut-in, the transient is monitored to estimate the fracture-closure pressure, formation per-\nmeability, formation pressure, and other properties.\nThe calculation of formation properties requires the identi\ufb01cation of \ufb02ow regimes, which is assisted by log-log derivative plots.\nPractitioners often interpret DFITs with log-log plots with derivative taken with respect to superposition time (Mohamed et al. 2011;\nMarongiu-Porcu et al. 2011; Soliman and Kabir 2012; Bachman et al. 2012; Hawkes et al. 2013; Wallace et al. 2016; Ibrahim and\nPieprzica 2016; Liu et al. 2016). However, unlike in a conventional well test, the superposition-time derivative curve does not show\nwhat the transient would have looked like if the test had been performed at a constant rate. The early-time transient is controlled by the"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 0, "chroma:document": "what the transient would have looked like if the test had been performed at a constant rate. The early-time transient is controlled by the\ninterplay of fracture compliance and leakoff in a way that has no analogy to a conventional well test. The late-time transient is similarto an impulse (or slug) test, in which a volume of \ufb02uid is instantaneously placed into the well, causing an immediate pressure response\nand then a decay back to the formation pressure (Craig and Blasingame 2006). The onset of the impulse \ufb02ow regime causes a downward\nde\ufb02ection in the derivative curve.\nAs shown in the Properties of the Superposition-Time Derivative section, taking the derivative with respect to superposition time,\ninstead of shut-in time, causes an upward de\ufb02ection on the log-log plot at the point when shut-in time is equal to injection time. This isa mathematical property of how the derivative is calculated. In a conventional well test; the de\ufb02ection adjusts for the effect of the prior"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 0, "chroma:document": "rate history because it occurs at approximately the same time as the transition to impulse \ufb02ow. In a DFIT transient, there is no relation-\nship between the timing of the superposition-time derivative de\ufb02ection and the onset of impulse \ufb02ow. In the Simpli\ufb01ed Model Problem\nsection, I show that the timing of the transition to late-time impulse behavior is controlled by injection volume and the formation, well-\nbore, and fracture properties, and is unrelated to injection time. To be precise, the timing of the onset of impulse \ufb02ow actually has aweak (but nonzero) relationship with injection time, but this is a minor effect that does not need to be examined in this report. van den\nHoek (2016) also discusses issues with interpreting DFITs with superposition-time derivative plots.\nAs discussed in the Properties of Nolte\u2019s G-Function section, the superposition-time derivative de\ufb02ection occurs at the same time as"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8843b6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 0, "chroma:document": "As discussed in the Properties of Nolte\u2019s G-Function section, the superposition-time derivative de\ufb02ection occurs at the same time as\na transition from a one slope to a 1/2 slope in an ideal DFIT shut-in transient. However, the superposition-time derivative de\ufb02ection\nadds unity to the slope, whereas the ideal transient behavior experiences a decrease in slope of 1/2, not unity. In any case, it would not\nassist the interpretation to calculate the derivative in a way that masks the \u201cideal\u201d transition from unit slope to 1/2 slope. In actual \ufb01eld\ndata, the ideal early-time slope of unity is not typically observed.\nIn the Properties of Nolte\u2019s G-Function section, I review the properties of Nolte\u2019s G-function, which describes the scaling of pres-\nsure with time in an idealized DFIT shut-in transient. One form of the G-function contains terms with 3/2 powers of time and super\ufb01-"}


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-186098-PA Superious Deflection.pdf", "page": 0, "chroma:document": "sure with time in an idealized DFIT shut-in transient. One form of the G-function contains terms with 3/2 powers of time and super\ufb01-\ncially resembles conventional well-test analysis solutions constructed by applying time superposition. However, I show that the 3/2\npower terms arise from a spatial integration of Carter\u2019s leakoff equation, not from using time superposition to sum constant-rate\nsolutions.\nCopyright VC2017 Society of Petroleum Engineers\nOriginal SPE manuscript received for review 5 November 2016. Revised manuscript received for review 1 March 2017. Paper (SPE 186098) peer approved 15 March 2017.REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1045 Total Pages: 11\nID:jaganm Time: 13:19 I Path: //chenas03/cenpro/ApplicationFiles/Journals/SA/SPE/REE#/Vol00000/170018/Comp/APPFile/SA-REE#170018November 2017 SPE Reservoir Evaluation & Engineering 1045"}


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-186098-PA Superious Deflection.pdf", "page": 1, "chroma:document": "In the Practical Implications section, I provide practical recommendations for interpreting DFIT transients. In the Field Example\nsection, I provide a \ufb01eld example. I conclude that there is no physical, mathematical, or practical reason to plot DFIT transients in a\nway that implies 3/2 power scaling of pressure with time.\nProperties of the Superposition-Time Derivative\nSuperposition time can be de\ufb01ned in a variety of ways. For interpretation of DFITs, it is common to de\ufb01ne superposition time as\n(Mohamed et al. 2011; Marongiu-Porcu et al. 2011; Liu et al. 2016)\ns\u00bcte\u00feDt\nDt; \u00f01\u00de\nwhere teis duration of injection and Dtis the time elapsed since the end of injection. This de\ufb01nition of superposition time is identical to\nthe de\ufb01nition of Horner time. A related parameter, Agarwal time, is de\ufb01ned as (Agarwal 1980)\nta\u00bcteDt\nte\u00feDt\u00bc1\n1\nte\u00fe1\nDt\u00bcte\ns: \u00f02\u00de\nThe \ufb01nal equality in Eq. 2 shows that there is a simple relationship between Agarwal time and superposition time (or Horner time)."}


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-186098-PA Superious Deflection.pdf", "page": 1, "chroma:document": "te\u00fe1\nDt\u00bcte\ns: \u00f02\u00de\nThe \ufb01nal equality in Eq. 2 shows that there is a simple relationship between Agarwal time and superposition time (or Horner time).\nAgarwal time is equal to one-half the harmonic average of teandDt. Agarwal time has the property that it is approximately equal to Dt\nwhenDt/C28teand approximately equal to tewhenDt/C29te.I fDtis much larger than te,taking the derivative with respect to Agarwal\ntime is equivalent to adding unity to the slope of the d P/d[ln(Dt)] curve on the log-log plot. This is true because\ntadp\ndta\u00bctadp\ndDtdDt\ndta\u00bctadp\ndDt1\nt2\na1\nta/C01\nte/C18/C192\u00bctadp\ndDtDt2\nt2\na\u00bcDt2\ntadP\ndDt/C25Dt2\ntedp\ndDt; \u00f03\u00de\nwhere the \ufb01nal step is taken because taasymptotically approaches teforDt>>te. Therefore, for Dt>>te,\nd log tadp\ndta/C18/C19/C20/C21\nd\u00bdlog\u00f0Dt\u00de/C138/C25d logDt2\ntedp\ndDt/C18/C19/C20/C21\nd\u00bdlog\u00f0Dt\u00de/C138\u00bcd log Dtdp\ndDt/C18/C19/C20/C21\nd\u00bdlog\u00f0Dt\u00de/C138\u00fe1: \u00f04\u00de"}


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-186098-PA Superious Deflection.pdf", "page": 1, "chroma:document": "dta/C18/C19/C20/C21\nd\u00bdlog\u00f0Dt\u00de/C138/C25d logDt2\ntedp\ndDt/C18/C19/C20/C21\nd\u00bdlog\u00f0Dt\u00de/C138\u00bcd log Dtdp\ndDt/C18/C19/C20/C21\nd\u00bdlog\u00f0Dt\u00de/C138\u00fe1: \u00f04\u00de\nOn a log-log plot, the derivative curve with derivative taken with respect to Agarwal time is the same as the derivative curve with\nderivative taken with respect to superposition time because teis a constant and (from Eq. 2)\ndp\nd\u00bdlog\u00f0ta\u00de/C138\u00bc/C0dp\nd\u00bdlog\u00f0s\u00de/C138: \u00f05\u00de\nThe change in sign does not affect the log-log plot because the derivative is commonly plotted as positive on the log-log plot.\nFig. 1 shows a log-log plot of the function DP\u00bc\ufb03\ufb03tp,along with derivatives taken with respect to time and superposition time.\nSuperposition time is calculated assuming teis equal to 0.0833 hours (5 minutes), which is a typical injection duration for a DFIT.\nWhen time is approximately equal to te,the superposition semilog derivative curves upward to a slope of 3/2; the pressure plot and 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-186098-PA Superious Deflection.pdf", "page": 1, "chroma:document": "When time is approximately equal to te,the superposition semilog derivative curves upward to a slope of 3/2; the pressure plot and the\nderivative with respect to time continue with a slope of 1/2..............................................................................\n..................................................................\n...................................\n..........................................\n.....................................................................\n1\u00d710\u20133\n1\u00d710\u201341\u00d710\u201331\u00d710\u201321\u00d710\u20131\nHours\u0394P (blue), d \u0394P/d(ln( t)) (orange), d \u0394P/d(ln( \u03c4)) (grey)\n1\u00d71001\u00d71011\u00d71021\u00d710\u201321\u00d710\u201311\u00d71001\u00d71011\u00d71021\u00d71031\u00d7104\nFig. 1\u2014Log-log diagnostic plot showing the function DP5\ufb03\ufb03 \ufb03\ntp\n, along with derivative taken with respect to time and superposition\ntime. The superposition-time derivative curves upward when time teis approximately equal to 0.0833 hours.REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1046 Total Pages: 11"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 1, "chroma:document": "ID:jaganm Time: 13:19 I Path: //chenas03/cenpro/ApplicationFiles/Journals/SA/SPE/REE#/Vol00000/170018/Comp/APPFile/SA-REE#1700181046 November 2017 SPE Reservoir Evaluation & Engineering"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 2, "chroma:document": "Simplified Model Problem\nProblem Definition. I analyze an idealized DFIT model problem with the following assumptions:\n1. A single fracture forms.\n2. The fracture forms effectively instantaneously before the start of the shut-in transient.\n3. The volume of \ufb02uid stored in the fracture is linearly proportional to the difference between formation pressure and fracture\npressure.\n4. The fracture is effectively in\ufb01nite-conductivity so that pressure gradient caused by \ufb02ow along the fracture can be neglected.5. Thermal effects can be neglected.\n6. Leakoff is linear away from the fracture, and can be modeled assuming single-phase, single-component \ufb02ow.\n7. The fracture-surface area is constant during shut-in.\nEven though these assumptions are simpli\ufb01ed relative to actual DFITs, they are suf\ufb01cient to analyze the properties of the superposi-\ntion-time derivative and to investigate certain aspects of real DFIT transients."}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 2, "chroma:document": "tion-time derivative and to investigate certain aspects of real DFIT transients.\nAssumption 3 neglects the effect of fracture closure. In reality, when the fracture mechanically closes (asperities in contact), the\nstorage coef\ufb01cient changes because fracture compliance becomes controlled by a nonlinear joint-closure process related to the rough-\nness and stiffness of fracture asperities (Barton et al. 1985; McClure et al. 2016).\nAssumptions 4 and 7 are idealizations, but they are reasonable approximations of real DFIT transients in very-low-permeability for-\nmations, suitable for the purposes of this analysis. Fractures are in\ufb01nite-conductivity as long as they have dimensionless fracture con-\nductivity greater than 300. In nanodarcy permeability, fractures retain dimensionless conductivity greater than 300 even if they have\nvery small aperture. This is supported by the consistent observation of post-closure linear \ufb02ow in \ufb01eld data sets (linear \ufb02ow requires an"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 2, "chroma:document": "very small aperture. This is supported by the consistent observation of post-closure linear \ufb02ow in \ufb01eld data sets (linear \ufb02ow requires an\nin\ufb01nite-conductivity fracture). The fracture may cease to be in\ufb01nite-conductivity after closure in formations that are not very low per-meability, or late in the transient when the effective normal stress on the fracture becomes high because of pressure decline. Also, there\nmay be fracture-tip extension immediately after shut-in.\nAnalytical Solution of the Model Problem. From Assumption 2, we assume the fracture forms instantaneously. At the start of the\ntransient, the fracture contains a volume of \ufb02uid equal to C\nt\u00f0Pf;init/C0Pinit\u00de, where Pinitis the initial formation pressure, Pf,initis the initial\npressure in the fracture, and Ctis a total storage coef\ufb01cient equal to\nCt\u00bcCw\u00feA\nSf; \u00f06\u00de\nwhere Cwis the wellbore-storage coef\ufb01cient and Sfis the fracture stiffness. The compressibility of the \ufb02uid in the fracture has a very"}


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-186098-PA Superious Deflection.pdf", "page": 2, "chroma:document": "Sf; \u00f06\u00de\nwhere Cwis the wellbore-storage coef\ufb01cient and Sfis the fracture stiffness. The compressibility of the \ufb02uid in the fracture has a very\nsmall contribution that is neglected in Eq. 6 for simplicity.\nBefore the fracture pressure has changed signi\ufb01cantly, the rate of \ufb02uid \ufb02ow out of the fracture into the matrix can be described\napproximately as 1D \ufb02ow from a constant-pressure boundary condition (equivalent to Carter leakoff). The cumulative \ufb02ow of \ufb02uid\nfrom the fracture into the matrix is therefore (Howard and Fast 1957)\nVLs\u00bc4A\ufb03\ufb03\ufb03\ufb03\ufb03\nDtp\n\u00f0pf;init/C0pinit\u00de\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\n/ctk\npls\n; \u00f07\u00de\nwhere VLsis cumulative volume of \ufb02uid leaked off during shut-in, Dtis shut-in time, pf,initis the initial pressure in the fracture, pinitis\nthe initial formation pressure, /is the formation porosity, ctis the formation total compressibility, kis the formation permeability, and\nlis the \ufb02uid viscosity. Note that Eq. 7 is valid only because the fracture is assumed to form instantaneously."}


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-186098-PA Superious Deflection.pdf", "page": 2, "chroma:document": "lis the \ufb02uid viscosity. Note that Eq. 7 is valid only because the fracture is assumed to form instantaneously.\nEqs. 6 and 7 can be combined to write the overall material balance on the system:\nCt\u00f0p/C0pinit\u00de\u00bcCt\u00f0pf;init/C0pinit\u00de/C04A\ufb03\ufb03\ufb03\ufb03\ufb03\nDtp\n\u00f0pf;init/C0pinit\u00de\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\nkct/\npls\n; \u00f08\u00de\nwhere pis the \ufb02uid pressure in the fracture at time Dt:\nIf we de\ufb01ne dimensionless time as\ntD\u00bc16A\nCt/C18/C192kct/\nplDt; \u00f09\u00de\nand we de\ufb01ne dimensionless pressure as\npD\u00bcp/C0pinit\npf;init/C0pinit; \u00f010\u00de\nthen we can write the material-balance equation as a simple expression giving the evolution of pressure with respect to time,\npDE\u00bc1/C0\ufb03\ufb03\ufb03\ufb03 \ufb03tDp: \u00f011\u00de\nEq. 8 can also be written as,\nCt\u00f0p/C0pf;init\u00de\u00bc/C0 VLs: \u00f012\u00de\nEq. 12 shows that if Ctis constant, then the change in pressure during shut-in is proportional to the cumulative leakoff volume dur-\ning shut-in. If the fracture forms instantaneously, then VLsscales with\ufb03\ufb03\ufb03\ufb03\ufb03\nDtp\n, as shown in Eq. 11. As discussed in the Properties of Nolte\u2019s"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 2, "chroma:document": "ing shut-in. If the fracture forms instantaneously, then VLsscales with\ufb03\ufb03\ufb03\ufb03\ufb03\nDtp\n, as shown in Eq. 11. As discussed in the Properties of Nolte\u2019s\nG-Function section, Nolte\u2019s G-function is based on a generalization of Eq. 11 that accounts for the leakoff that occurs as the fracture\npropagates during injection. If fracture-propagation time is considered, then VLsscales with the G-function during shut-in. This is why\nplots of pressure vs. Gare (ideally) linear before closure and can be used to infer leakoff coef\ufb01cient if Ctis assumed to be known (Nolte...........................................................................\n.............................................................\n..........................................\n......................................................................\n........................................................................\n.........................................................................."}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 2, "chroma:document": "........................................................................\n..........................................................................\n.....................................................................REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1047 Total Pages: 11\nID:jaganm Time: 13:19 I Path: //chenas03/cenpro/ApplicationFiles/Journals/SA/SPE/REE#/Vol00000/170018/Comp/APPFile/SA-REE#170018November 2017 SPE Reservoir Evaluation & Engineering 1047"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 3, "chroma:document": "1979; Nolte and Smith 1981). When closure occurs, this affects both the leakoff rate and Ct, which causes pressure to deviate from line-\narity. Whether pressure begins to increase more rapidly or less rapidly after closure depends on the relative effect of closure on leakoff\nrate and the Ct(discussed in the Appendix of McClure et al. 2016). A variety of other \u201cnonideal\u201d processes may affect the pressure\ntrend during a real DFIT transient.\nThe square-root-of-time behavior in Eq. 11 is not the same as the well-test solution for linear \ufb02ow (Gringarten et al. 1974). The\nGringarten et al. (1974) linear-\ufb02ow solution is derived for constant-rate injection and neglects wellbore/fracture storage. Eq. 11 is\nderived on the basis of constant-pressure leakoff from a high-storage wellbore/fracture system. The square root of time appears in both"}


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-186098-PA Superious Deflection.pdf", "page": 3, "chroma:document": "derived on the basis of constant-pressure leakoff from a high-storage wellbore/fracture system. The square root of time appears in both\nsolutions because diffusivity has units of length squared per time, and so square-root-of time scaling is frequently present in mathemati-cal relationships involving the diffusivity equation (such as the expression for radius of investigation).\nAfter a period of time, the pressure in the fracture drops suf\ufb01ciently so that leakoff is no longer well-approximated by Carter leakoff,\nwhich assumes constant pressure in the fracture (Howard and Fast 1957). The late-time pressure transient can be found by taking the\ndimensionless time derivative of the nondimensionalized solution for constant-rate injection (Houze et al. 1988; Ayoub et al. 1988; Gu\net al. 1993). The solution for constant-rate injection into an in\ufb01nite-conductivity fracture, neglecting the \ufb02uid storage of the wellbore, is(Gringarten et al. 1974)\np\u00bcp\ninit\u00feq\nA\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03l\npkct/r\ufb03\ufb03\ufb03\ufb03\ufb03\nDtp\n; \u00f013\u00de"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884b18-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 3, "chroma:document": "p\u00bcp\ninit\u00feq\nA\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03l\npkct/r\ufb03\ufb03\ufb03\ufb03\ufb03\nDtp\n; \u00f013\u00de\nwhere qis the volumetric injection rate. Taking the derivative of the nondimensionalized form of this equation, we can \ufb01nd the solution\nfor the injection of a volume of \ufb02uid Vsluginto the system:\np\u00bcpinit\u00feVslug\n2A\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03l\npkct/r1\ufb03\ufb03\ufb03\ufb03\ufb03\nDtp : \u00f014\u00de\nFor our problem,\nVslug\u00bcCt\u00f0pf;init/C0pinit\u00de: \u00f015\u00de\nTherefore,\np\u00bcpinit\u00feCt\n2A\u00f0pf;init/C0pinit\u00de\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\n1\npkct/s\n1\ufb03\ufb03\ufb03\ufb03\ufb03\nDtp : \u00f016\u00de\nWith the same dimensionless variables as before, Eq. 16 can be written as\npDL\u00bc2\np1\ufb03\ufb03\ufb03\ufb03 \ufb03tDp : \u00f017\u00de\nEq. 11 describes the early-time behavior of the transient, and Eq. 17 describes the late-time behavior of the transient. There is not a\nsimple expression to describe the evolution of pressure during the transition between these two limiting cases. However, we can \ufb01nd asimple estimate for the time at which the transition occurs.\nEnforcing equality of the derivatives at the transition time,\ndpDE\ndtd\u00bcdpDL\ndtdfortD\u00bctD;trans; \u00f018\u00de\nresults in the expression\ntD;trans\u00bc2"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884b7c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 3, "chroma:document": "Enforcing equality of the derivatives at the transition time,\ndpDE\ndtd\u00bcdpDL\ndtdfortD\u00bctD;trans; \u00f018\u00de\nresults in the expression\ntD;trans\u00bc2\np; \u00f019\u00de\nwhich in dimensional form is\nDttrans\u00bc1\n8Ct\nA/C18/C192l\nkct/: \u00f020\u00de\nThe transition to impulse \ufb02ow marks the peak in the d p/d[ln(Dt)] curve, which occurs at the same time as the peak in the d P/\nd[ln( G)] curve and the transition from 3/2 slope to 1/2 slope on the log-log plot of d p/d[ln( s)]. This provides a physical interpretation\nfor the peak in the d p/d[ln( G)] curve in G-function plots: the onset of impulse \ufb02ow. This occurs as the leakoff rate deviates from Carter\nleakoff (which is derived from the assumption that pressure in the fracture is constant). In real transients, Ctchanges strongly when the\nfracture closes, and so Eq. 20 cannot be applied directly. However, Eq. 20 demonstrates that the onset of the peak in d p/d[ln( G)] is con-\ntrolled by the interplay of formation and fracture properties in causing the onset of impulse \ufb02ow."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884be0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 3, "chroma:document": "trolled by the interplay of formation and fracture properties in causing the onset of impulse \ufb02ow.\nNumerical Solution to the Model Problem. To con\ufb01rm the results in the Analytical Solution of the Model Problem section, I solve\nthe model problem with a numerical simulator. The simulator calculates leakoff rate from the fracture by solving the diffusivity equa-tion with a 1D \ufb01nite-difference grid with logarithmically spaced elements. On one side of the model, a special \u201cfracture\u201d element is\nplaced with \ufb02uid-storage coef\ufb01cient equal to C\nt. The fracture element is initialized at an elevated pressure pf,init, and the matrix elements\nare initialized with pressure pinit. Away from the fracture element, the grid is suf\ufb01ciently large that it is effectively in\ufb01nite for the dura-\ntion of the simulation.\nFig. 2 shows a log-log diagnostic plot of pressure and the derivative taken with respect to shut-in time. The numerical solution is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884c3a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 3, "chroma:document": "Fig. 2 shows a log-log diagnostic plot of pressure and the derivative taken with respect to shut-in time. The numerical solution is\nshown with solid lines, and the two approximate analytical solutions (Eqs. 11 and 17) are shown with dashed lines. The comparison\nshows that the analytical results are very accurate at early and late time. The transition between the two solutions occurs at approxi-\nmately when the derivatives of the two analytical solutions are equal, consistent with Eq. 19...................................................................\n................................................................\n...................................................................\n.......................................................\n...........................................................................\n.............................................................\n............................................................................"}


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-186098-PA Superious Deflection.pdf", "page": 3, "chroma:document": ".............................................................\n............................................................................\n...................................................................REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1048 Total Pages: 11\nID:jaganm Time: 13:19 I Path: //chenas03/cenpro/ApplicationFiles/Journals/SA/SPE/REE#/Vol00000/170018/Comp/APPFile/SA-REE#1700181048 November 2017 SPE Reservoir Evaluation & Engineering"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884cf8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 4, "chroma:document": "Fig. 3 shows the numerical solution to the model problem with derivative taken with respect to shut-in time and superposition time.\nAs discussed previously, the model problem neglects the effect of fracture closure and assumes that the fracture formed instantaneously\nduring injection. To calculate superposition time, it is necessary to de\ufb01ne a value for te. In Fig. 1, superposition time is calculated\nassuming teis equal to 0.0833 hours, or 5 minutes, which is a typical injection duration in a DFIT. The superposition-time plot curves\nupward when Dtis equal to te. The derivative with respect to time continues with a slope of 1/2 (indicating square-root-of-time scaling)\nuntil the onset of impulse \ufb02ow at approximately 15 hours. The onset of impulse \ufb02ow causes a transition from a 1/2 slope to a \u20131/2 slope\non the actual-time derivative curve and a 3/2 slope to a 1/2 slope on the superposition-time derivative curve. The superposition-time de-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884d52-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 4, "chroma:document": "on the actual-time derivative curve and a 3/2 slope to a 1/2 slope on the superposition-time derivative curve. The superposition-time de-\nrivative plot does not quite reach a full slope of 3/2 because the pressure trend begins deviating downward from pure square-root-of-\ntime scaling as it approaches the onset of impulse \ufb02ow.\nProperties of Nolte\u2019s G-Function\nIn this section, I review properties of Nolte\u2019s G-function (Nolte 1979; Nolte and Smith 1981; Castillo 1987; Gulrajani and Nolte 2000)\nto show that there is not a physical or mathematical justi\ufb01cation for plotting it in a way that implies 3/2 power scaling with respect\nto time.\nThe G-function is de\ufb01ned so that it is proportional to the cumulative leakoff volume during shut-in, given certain simplifying\nassumptions: (a) the leakoff rate at a given location along the fracture is described by Carter leakoff (leakoff rate is proportional to the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884dac-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 4, "chroma:document": "assumptions: (a) the leakoff rate at a given location along the fracture is described by Carter leakoff (leakoff rate is proportional to the\ninverse of the square root of leakoff duration); (b) during injection, the fracture length is equal to the duration of injection to the powera; and (c) the fracture immediately stops propagating after shut-in.\nIf the fracture is assumed to grow linearly with time during injection ( a\u00bc1), then Nolte (1979) showed that the G-function\nscales as\nG\u00f0a\u00bc1\u00de/ 1\u00feDt\nte/C18/C191:5\n/C0Dt\nte/C18/C191:5\n/C01: \u00f021\u00de .........................................................\n\u0394P (blue), d \u0394P/d(ln( t)) (orange),\nd\u0394P/d(ln( \u03c4)) (grey)\n1\u00d710\u201321\u00d710\u201311\u00d71001\u00d71011\u00d71021\u00d71031\u00d71041\u00d7105\n1\u00d710\u201341\u00d710\u201331\u00d710\u201321\u00d710\u20131\nHours1\u00d71001\u00d71011\u00d71021\u00d71031\u00d7104\nFig. 3\u2014Log-log diagnostic plot showing the numerical solution to the model problem described in the Simpli\ufb01ed Model Problem"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884e06-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 4, "chroma:document": "Fig. 3\u2014Log-log diagnostic plot showing the numerical solution to the model problem described in the Simpli\ufb01ed Model Problem\nsection. The model problem is based on the simplifying assumption that the fracture does not mechanically close. The plot showschange in pressure (blue) and the derivative curves with derivative taken with respect to shut-in time (orange) and superpositiontime (gray).\n\u0394P (blue), d \u0394P/d(ln( t)) (orange),\nd\u0394P/d(ln( \u03c4)) (grey)\n1\u00d710\u201321\u00d710\u201311\u00d71001\u00d71011\u00d71021\u00d7103\n1\u00d710\u201341\u00d710\u201331\u00d710\u201321\u00d710\u20131\nHours1\u00d71001\u00d71011\u00d71021\u00d71031\u00d7104\nFig. 2\u2014Log-log diagnostic plot with derivative taken with respect to time showing the numerical solution to the model problem\n(blue lines) and the early-time and late-time analytical solutions to the model problem (green lines). The solid lines show change in\npressure, and the dashed lines show the derivative curves.REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1049 Total Pages: 11"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884e6a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 4, "chroma:document": "pressure, and the dashed lines show the derivative curves.REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1049 Total Pages: 11\nID:jaganm Time: 13:19 I Path: //chenas03/cenpro/ApplicationFiles/Journals/SA/SPE/REE#/Vol00000/170018/Comp/APPFile/SA-REE#170018November 2017 SPE Reservoir Evaluation & Engineering 1049"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884ec4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 5, "chroma:document": "Even though Eq. 21 contains terms with a 3/2 power, it never scales according to a 3/2 power. At early time, Eq. 21 scales linearly\nwithDt;and at late time, it scales with the square root of Dt:Derivations of these properties are provided in Appendix A, and they are\nshown graphically in Fig. 4.\nNolte (1979) also de\ufb01ned a function gthat is proportional to the total volume of \ufb02uid leakoff from the start of injection (rather than\ntotal leakoff volume after shut-in). As shown by Eq. 12, pressure after shut-in scales with leakoff volume during shut-in, not total leak-off volume (Gulrajani and Nolte 2000). Nolte (1979) derived the G-function by subtracting gat shut-in from gat a point in time after\nshut-in.\nIn Eq. 21, the transition between linear and square-root scaling occurs at Dt\u00bct\ne:This is the same time at which the spurious de\ufb02ec-\ntion occurs in the superposition-time derivative plot (Eq. 2). It might be argued that the de\ufb02ection in the superposition-time plot adjusts"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884f1e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 5, "chroma:document": "tion occurs in the superposition-time derivative plot (Eq. 2). It might be argued that the de\ufb02ection in the superposition-time plot adjusts\nfor this downward bend in the G-function that occurs near the same time (though it is unclear why this would assist in an analysis).\nHowever, taking the derivative with respect to superposition time adds unity to the slope of the curve, whereas the transition in Eq. 21\ncauses the slope of the line to reduce by 1/2, not unity. In real DFIT transients, various complex processes cause deviation from ideality\nin the minutes after shut-in. As a result, the early-time unit slope predicted by Eq. 21 is not typically observed.\nFig. 4 shows G\u00f0a\u00bc1\u00de(Eq. 21) and the derivative curves taken with respect to time and superposition time (for teis equal to 0.0833\nhours). All three curves show a slope of unity at early time, indicating linear scaling. At approximately 0.0833 hours, the G-function"}


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-186098-PA Superious Deflection.pdf", "page": 5, "chroma:document": "hours). All three curves show a slope of unity at early time, indicating linear scaling. At approximately 0.0833 hours, the G-function\ncurve bends toward a slope of 1/2. The derivative curve with respect to time also bends to a slope of 1/2. The superposition-time deriva-\ntive curve bends upward to a slope of 3/2.\nIf the fracture is assumed to grow according to the square root of time ( a\u00bc0:5), then the G-function scales (Nolte 1979) as\nG\u00f0a\u00bc0:5\u00de/ 1\u00feDt\nte/C18/C19\narcsin 1 \u00feDt\nte/C18/C19/C00:5\"#\n\u00feDt\nte/C18/C190:5\n/C0p\n2: \u00f022\u00de\nIn this form of the G-function, there are not terms with a 3/2 power. G\u00f0a\u00bc0:5\u00dehas the same asymptotic scaling as G\u00f0a\u00bc1:0\u00de: lin-\near at early-time and square root of Dtat late time.\nEqs. 21 and 22 scale linearly with time at early time because shut-in does not cause a discontinuous change in leakoff rate. By de\ufb01ni-\ntion, continuous functions have a constant derivative when evaluated over a suf\ufb01ciently short interval. This implies that leakoff rate is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b884fdc-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 5, "chroma:document": "tion, continuous functions have a constant derivative when evaluated over a suf\ufb01ciently short interval. This implies that leakoff rate is\napproximately constant at early time after shut-in. Eq. 12 shows that if leakoff rate is constant, then pressure change will be linear with\nshut-in time.\nEqs. 21 and 22 scale with the square root of time at late time because the difference in leakoff duration at each point along the frac-\nture becomes negligible. As a result, the leakoff rate asymptotically becomes the same everywhere along the fracture. This is analogousto St. Venant\u2019s principle of mechanical loading, which states that complex applied loads are asymptotically equivalent to point loading\nat suf\ufb01cient distance.\nEq. 21 appears super\ufb01cially similar to superposition-time solutions constructed by addition of constant-rate solutions. However, it is\nnot mathematically or physically valid to interpret Eq. 21 in this way. For example, the linear-\ufb02ow buildup-test transient can be con-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885036-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 5, "chroma:document": "not mathematically or physically valid to interpret Eq. 21 in this way. For example, the linear-\ufb02ow buildup-test transient can be con-\nstructed from superposition by use of the Gringarten et al. (1974) constant-rate solution and scales as\nDP/1\u00feDt\nte/C18/C190:5\n/C0Dt\nte/C18/C190:5\n: \u00f023\u00de\nEq. 23 is a speci\ufb01c case of the more general method of performing a time-convolution integral of a constant-rate analytical solution\nmultiplied by the derivative of \ufb02ow rate with respect to time. Implicit in the construction of Eq. 23 is the requirement that the constant-.........................................\n................................................................\n\u0394P (blue), d \u0394P/d(ln( t)) (orange), d \u0394P/d(ln( \u03c4)) (grey)\n1\u00d710\u20132\n1\u00d710\u201331\u00d710\u201311\u00d71001\u00d71011\u00d71021\u00d71031\u00d71041\u00d7105\n1\u00d710\u201341\u00d710\u201331\u00d710\u201321\u00d710\u20131\nHours1\u00d71001\u00d71011\u00d7102\nFig. 4\u2014Log-log diagnostic plot showing G(a51) (blue) and the derivative curve taken with respect to time (orange) and superposi-"}


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-186098-PA Superious Deflection.pdf", "page": 5, "chroma:document": "Hours1\u00d71001\u00d71011\u00d7102\nFig. 4\u2014Log-log diagnostic plot showing G(a51) (blue) and the derivative curve taken with respect to time (orange) and superposi-\ntion time (gray).REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1050 Total Pages: 11\nID:jaganm Time: 13:19 I Path: //chenas03/cenpro/ApplicationFiles/Journals/SA/SPE/REE#/Vol00000/170018/Comp/APPFile/SA-REE#1700181050 November 2017 SPE Reservoir Evaluation & Engineering"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885112-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 6, "chroma:document": "rate solution is not itself changing over time. For example, the line source in the Gringarten et al. (1974) solution is \ufb01xed in size, shape,\nand location. All conventional well-test solutions (in\ufb01nite-acting radial \ufb02ow, bilinear, and others) assume that the source does not\nchange geometry over time. In contrast, in the hydraulic-fracturing problem, the fracture grows during the injection period prior.\nvan den Hoek (2002) and Sections 3.2.3 and 4.2.2 from Koning (1987) analyze the propagation of a hydraulic fracture with very\nlong injection time and very high leakoff. Under these conditions, the fracture-propagation rate is slow, and the injection rate is approx-\nimately equal to the leakoff rate. Under these conditions, they \ufb01nd that it is a reasonable approximation to use time-convolution inte-\ngrals of the constant-rate analytical solution to analyze fracture propagation. This is valid because they restrict their analysis to consider"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 6, "chroma:document": "grals of the constant-rate analytical solution to analyze fracture propagation. This is valid because they restrict their analysis to consider\nonly a very-high-leakoff, slow-propagation scenario. DFITs are the opposite: very low leakoff, rapid propagation, and short injectiontime. In a DFIT, until Dtis much greater than t\ne,the changing fracture geometry during injection cannot be neglected.\nAccording to the assumptions underlying G\u00f0a\u00bc1:0\u00de, the leakoff duration at each point along the fracture (the duration of time since\nthe fracture formed at that location) is equal to Dt\u00fex\nv, where vis the fracture-propagation velocity (assumed constant during injection\nbecause a\u00bc1) and xis position along the fracture (where the tip of the fracture is located at xequal to 0 and the center is at xequal to\na). Using Carter leakoff, the cumulative leakoff volume (including \ufb02uid leaked off during injection) is equal to\nVL\u00f0Dt\u00de\u00bc8h\u00f0pf;init/C0pinit\u00de\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\n/ctk\npls\u00f0a\n0\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\nDt\u00fex\nvr\ndx/\u00f0a"}


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-186098-PA Superious Deflection.pdf", "page": 6, "chroma:document": "VL\u00f0Dt\u00de\u00bc8h\u00f0pf;init/C0pinit\u00de\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\n/ctk\npls\u00f0a\n0\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\nDt\u00fex\nvr\ndx/\u00f0a\n0\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\ufb03\nDt\u00fex\nvr\ndx/1\u00feDt\nte/C18/C191:5\n/C0Dt\nte/C18/C191:5\n; \u00f024\u00de\nwhere his the fracture height and teis equal toa\nv. Eq. 24 is proportional to the g-function for total leakoff volume (for a\u00bc1:0). The cu-\nmulative leakoff volume during the shut-in period is equal to VLminus the cumulative leakoff volume at shut-in ( Dt\u00bc0\u00de, which recov-\nersG\u00f0a\u00bc1\u00de:\nVLs\u00f0Dt\u00de\u00bcVL\u00f0Dt\u00de/C0VL\u00f00\u00de/ 1\u00feDt\nte/C18/C191:5\n/C0Dt\nte/C18/C191:5\n/C01: \u00f025\u00de\nThe origin of the 3/2 power in G\u00f0a\u00bc1\u00de(Eq. 21) is a spatial integration of the Carter leakoff solution over the length of the fracture.\nIt is not derived in a way that is analogous to Eq. 23, and Eq. 21 cannot be interpreted as being constructed from the sum of constant-rate analytical solutions.\nPractical Implications\nLog-log superposition-time derivative plots can be used to diagnose \ufb02ow regimes in DFIT transients, but the interpreter must be aware"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885248-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 6, "chroma:document": "Log-log superposition-time derivative plots can be used to diagnose \ufb02ow regimes in DFIT transients, but the interpreter must be aware\nthat the use of superposition time causes the plot to curve upward when Dtis equal to t\ne. The G-function experiences a downward bend\nat the same time, but the downward bend is a decrease in slope of 1/2, and the superposition-time bend causes an increase in slope of\nunity. The interpreter must understand the complex relationship between the slope of the curve and the scaling of pressure with time,and must be aware that there is no physical signi\ufb01cance to the 3/2 slope on the plot.\nTo avoid confusion, I recommend interpreting DFIT transients from the basic pressure-transient interpretation plot\u2014the log-log plot\nwith derivative taken with respect to actual-time. To assist the identi\ufb01cation of closure and other preclosure trends, plots of pressure\nandG/C2dG/dPvs.Gcan be used."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8852de-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 6, "chroma:document": "andG/C2dG/dPvs.Gcan be used.\nWhen the derivative is taken with respect to shut-in time in a log-log plot, there is a simple mathematical interpretation of the slope\nof the derivative curve. If the pressure change scales with respect to t\nb, then the slope of the derivative curve on a log-log plot is equal\ntob. If the pressure change scales with respect to logarithmic time, then the slope is zero. In contrast, if the derivative is taken with\nrespect to superposition time, then after the spurious de\ufb02ection, the superposition-time derivative curve has a slope of b\u00fe1. Before the\nonset of impulse \ufb02ow, the slope of b\u00fe1 does not have a physical interpretation. In conventional (nonfracturing) buildup/falloff transi-\nents, the onset of impulse \ufb02ow occurs at approximately the same time as the de\ufb02ection, which is why the superposition derivativemethod can be used to show what the transient \u201cwould have been\u201d if it was a constant-rate test. But in DFIT transients, the de\ufb02ection"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88540a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 6, "chroma:document": "occurs much earlier than the onset of impulse \ufb02ow, and the superposition-time derivative curve does not have the same interpretation.\nInterpreters are tempted to identify a change in \ufb02ow regime at the spurious de\ufb02ection. If the de\ufb02ection occurs in a part of the tran-\nsient where the derivative is curving because of an actual pressure-transient response, the real response is distorted by the overprint of\nthe spurious de\ufb02ection and will be more dif\ufb01cult to interpret.\nLate-time impulse \ufb02ow regimes can be identi\ufb01ed easily on derivative plots, regardless of whether the derivative is taken with respect\nto shut-in time or superposition time. The late-time impulse solution is the derivative of the constant-rate solution (Houze et al. 1988).\nIf pressure change in a constant-rate solution scales with respect to t\nbor the logarithm of time, then, for the impulse solution, the slope"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885c34-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 6, "chroma:document": "If pressure change in a constant-rate solution scales with respect to t\nbor the logarithm of time, then, for the impulse solution, the slope\nof the derivative curve (taken with respect to shut-in time) is the slope of the constant-rate solution minus unity. For example, impulse\nradial \ufb02ow has a slope of /C01, and impulse linear has a slope of /C01/2.\nField Example\nFig. 5 shows a log-log diagnostic plot for the \ufb01eld data set described by McClure et al. (2016). The data are from a DFIT in a vertical\nwell in a formation with strong stress contrast between layers (causing fracture-height con\ufb01nement), high stress anisotropy (precluding\nthe possibility of \u201copening transverse fractures\u201d), drilling-induced axial tensile fractures visible in an image log perpendicular to the min-\nimum principal stress (indicating that fractures will not be forced to rotate into the far-\ufb01eld orientation as they propagate away from the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885cac-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 6, "chroma:document": "imum principal stress (indicating that fractures will not be forced to rotate into the far-\ufb01eld orientation as they propagate away from the\nwellbore), and very low permeability (approximately 100 nd). The injection volume was 11.5 bbl. These conditions are as close as practi-cally possible to being an \u201cideal\u201d DFIT in very tight rock. Nevertheless, there is strong deviation from the ideal G-function response.\nTypically, the transient would be interpreted in conjunction with a plot of G/C2dP/dGvs.G. However, for simplicity, I provide only the\nlog-log diagnostic plot. Fig. 2 from McClure et al. (2016) provides a G-function plot of these data. For calculating superposition time, the\nvalue of t\neis determined by dividing the total injection volume by the \ufb01nal injection rate and is equal to 0.0383 hours (138 seconds).\nThe \ufb01rst 0.01 hours (36 seconds) is dominated by water hammer in the wellbore, causing sharp pressure oscillations. The superposi-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885d10-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 6, "chroma:document": "The \ufb01rst 0.01 hours (36 seconds) is dominated by water hammer in the wellbore, causing sharp pressure oscillations. The superposi-\ntion-time derivative curve de\ufb02ects upward at approximately te(0.0383) hours of shut-in. As discussed in the Properties of the Superpo-\nsition-Time Derivative section, the upward curve of the superposition-time derivative curve is a consequence of how the derivative is\ncalculated and should not be interpreted as representing a reservoir process. The actual-time derivative curve is nearly \ufb02at from 0.01 to.......................\n.............................................REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1051 Total Pages: 11\nID:jaganm Time: 13:19 I Path: //chenas03/cenpro/ApplicationFiles/Journals/SA/SPE/REE#/Vol00000/170018/Comp/APPFile/SA-REE#170018November 2017 SPE Reservoir Evaluation & Engineering 1051"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885d6a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 7, "chroma:document": "0.1 hours. The early-time slope of unity predicted by the G-function is not apparent. A variety of processes, with con\ufb02icting effects,\nmay be occurring during the early-time transient: reheating of the \ufb02uid in the wellbore caused by conduction from the surrounding for-\nmation, fracture-tip extension (continued propagation after shut-in), and many other possible effects. Because of the variety of complexprocesses that may be occurring in the early minutes of shut-in, it is dif\ufb01cult to draw conclusions from this part of the transient. The\nnearly \ufb02at actual-time derivative from 0.01 to 0.1 hours should not be interpreted as representing radial \ufb02ow.\nThe actual-time derivative curve gently curves upward to a slope of 1/2, centered at approximately 1.0 hours. However, it subse-\nquently curves up to a slope approaching unity, indicating that the pressure is decreasing signi\ufb01cantly faster than square-root-of-time"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885dd8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 7, "chroma:document": "quently curves up to a slope approaching unity, indicating that the pressure is decreasing signi\ufb01cantly faster than square-root-of-time\nscaling. The superposition-time plot curves upward in tandem, approaching a slope of two. In the superposition-time plot, it would be\ndif\ufb01cult to identify that the slope has deviated from 3/2 slope without the help of the dashed yellow guide line. It is visually easier to\ndistinguish between a slope of 1/2 and unity than a slope of 3/2 and two.\nA curving-upward pressure derivative, indicating pressure scaling more rapid than square root of time, has been the subject of dis-\ncussion in the literature. On a G-function plot, this phenomenon manifests as curving upward G/C2dP/dG. Barree and Miskimins (2016)\ncall this behavior \u201cdelayed leakoff\u201d and hypothesize that it could be caused by wellbore effects, near-wellbore fracture complexity, clo-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885e3c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 7, "chroma:document": "call this behavior \u201cdelayed leakoff\u201d and hypothesize that it could be caused by wellbore effects, near-wellbore fracture complexity, clo-\nsure of transverse fractures, or poroelastic effects. McClure et al. (2016) provide a different explanation that is based on analytical and\nnumerical calculations that provide a match to the \ufb01eld data shown in Fig. 5. Their explanation is that fracture compliance decreases(stiffness increases) as the fracture walls come into contact, accelerating the rate of pressure decline. Eventually, the leakoff rate devi-\nates suf\ufb01ciently from Carter leakoff that the rate of pressure decline decelerates, causing the onset of impulse \ufb02ow.\nConventionally, fracture closure is picked from G-function plots by drawing a tangent to the G/C2dP/dGcurve from the origin\n(Barree and Miskimins 2016). This has the effect of picking closure very close to the peak in G/C2dP/dG. The peak in G/C2dP/dGoccurs"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885e96-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 7, "chroma:document": "(Barree and Miskimins 2016). This has the effect of picking closure very close to the peak in G/C2dP/dG. The peak in G/C2dP/dGoccurs\nat exactly the same time as the peak in the derivative plot and at the same time as the transition from 3/2 to 1/2 slope on the superposi-tion-time derivative plot. Consequently, picking closure at the start of the 1/2 slope on a superposition-time derivative plot is equivalent\nto the tangent method of picking closure from a G/C2dP/dGcurve. The Simpli\ufb01ed Model Problem section demonstrates that this transi-\ntion occurs at the onset of impulse \ufb02ow. Thus, the conventional closure pick is equivalent to picking closure at the onset of impulse\ufb02ow. In contrast, McClure et al. (2016) suggest picking closure earlier, at the deviation from square-root-of-time scaling. In Fig. 5, the\ntwo different methods provide substantially different closure picks, either at approximately 0.5\u20131.5 hours or at approximately 10 hours."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885efa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 7, "chroma:document": "two different methods provide substantially different closure picks, either at approximately 0.5\u20131.5 hours or at approximately 10 hours.\nIf the transient does not curve upward past square-root-of-time scaling, the methods described by McClure et al. (2016) and Barree\nand Miskimins (2016) yield similar closure picks. McClure et al. (2016) explain that if permeability is not very low, closure can reduce\ndimensionless fracture conductivity suf\ufb01ciently that closure causes a decrease in leakoff rate (as \ufb02uid continues to \ufb02ow into the fracturebecause of wellbore storage) and weakening of the hydraulic connection between the fracture and the wellbore. The decrease in leakoff\nrate can overwhelm the effect of closure on compliance, resulting in a decrease in the rate of leakoff when closure occurs, causing\nDt/C2dP/dDtandG/C2dP/dGto curve downward and peak, rather than curve upward."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885f5e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 7, "chroma:document": "Dt/C2dP/dDtandG/C2dP/dGto curve downward and peak, rather than curve upward.\nIn real DFITs, there is often a period of rapid pressure drop at the start of the transient (e.g., Fig. 3 from Liu et al. 2016). Fracture-tip\nextension could explain this phenomenon, but sometimes the pressure drop occurs over thousands of psi. It is unlikely that tip-extensioncould explain such large pressure changes. An alternative explanation is that fractures start at the wellbore with orientation different\nfrom their far-\ufb01eld orientation and then are forced to rotate as they propagate away from the well. After shut-in, pressure drops as \ufb02uid\n\ufb02ows out of the misoriented fractures near the wellbore (which require high pressure to remain open during injection) into the far-\ufb01eld\nfracture (which remains open at a lower pressure). Figs. 13 and 17 from Jung et al. (2016) show numerical simulations of this process.\nConclusions"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b885fc2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 7, "chroma:document": "fracture (which remains open at a lower pressure). Figs. 13 and 17 from Jung et al. (2016) show numerical simulations of this process.\nConclusions\nThe following conclusions are drawn regarding the use of superposition-time derivative plots for DFIT shut-in transients:\n\u2022Superposition-time derivative plots of DFIT data commonly exhibit a 3/2 slope. This slope does not re\ufb02ect the actual scaling of pres-\nsure with time and does not have a physical or theoretical interpretation. For the particular case of constant propagation velocity, the\nG-function contains terms with a 3/2 power, but these terms arise from an integration of the Carter leakoff solution along the length\nof the fracture, and are not analogous to buildup/falloff solutions constructed from superposition of constant-rate solutions.\n1\u00d710\u20133 1\u00d710\u20132 1\u00d710\u20131\nHours1\u00d7100 1\u00d7101 1\u00d7102 1\u00d7103\u0394P (blue), d \u0394P/d(ln( t)) (orange),\nd\u0394P/d(ln( \u03c4)) (grey)\n1\u00d71011\u00d71021\u00d71031\u00d71041\u00d71051\u00d71061\u00d7107"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88601c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 7, "chroma:document": "1\u00d710\u20133 1\u00d710\u20132 1\u00d710\u20131\nHours1\u00d7100 1\u00d7101 1\u00d7102 1\u00d7103\u0394P (blue), d \u0394P/d(ln( t)) (orange),\nd\u0394P/d(ln( \u03c4)) (grey)\n1\u00d71011\u00d71021\u00d71031\u00d71041\u00d71051\u00d71061\u00d7107\nFig. 5\u2014Log-log diagnostic plot showing the \ufb01eld data set described by McClure et al. (2016). The plot shows change in pressure\n(blue), and the derivative curve taken with respect to time (orange) and superposition time (gray). The dashed yellow lines are pro-vided for reference to show slopes of 1/2 and 3/2.REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1052 Total Pages: 11\nID:jaganm Time: 13:19 I Path: //chenas03/cenpro/ApplicationFiles/Journals/SA/SPE/REE#/Vol00000/170018/Comp/APPFile/SA-REE#1700181052 November 2017 SPE Reservoir Evaluation & Engineering"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886080-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 8, "chroma:document": "\u2022The superposition-time derivative plot de\ufb02ects upward, adding unity to the slope, when shut-in time is equal to injection time. The ideal\nG-function response transitions from a slope of unity to a slope of 1/2 (decrease of 1/2) at approximately the same time as the de\ufb02ection.\n\u2022The transition from 3/2 to 1/2 slope on a superposition-time plot (equivalent to the transition from 1/2 to \u20131/2 slope if the derivative\nis taken with respect to time) indicates the onset of impulse \ufb02ow. This occurs even in an idealized model problem in which closure\ndoes not occur. Closure and the onset of impulse \ufb02ow are related, but they should not be regarded as the same thing, and they do not\nnecessarily occur at the same time.\n\u2022The slope of log-log plots with the derivative taken with respect to actual shut-in time has a simple and intuitive relationship with the\npressure transient. Although superposition-time derivative curves are useful for conventional buildup/falloff tests, they complicate"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8860e4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 8, "chroma:document": "pressure transient. Although superposition-time derivative curves are useful for conventional buildup/falloff tests, they complicate\nthe interpretation of DFIT transients and do not aid in the interpretation.\n\u2022I recommend interpreting DFIT transients with log-log diagnostic plots with the derivative taken with respect to actual shut-in time\nand plots of pressure and G/C2dG/dPvs.G.\nNomenclature\na\u00bcfracture half-length, m\nA\u00bcfracture area, m2\nct\u00bcformation total compressibility, MPa\u20131\nCt\u00bctotal-storage coef\ufb01cient, m3/MPa\nCw\u00bcwellbore-storage coef\ufb01cient, m3/MPa\ng\u00bcg-time function (dimensionless \ufb02uid-loss volume function), dimensionless\nG\u00bcG-time function (dimensionless \ufb02uid-loss time function), dimensionless\nh\u00bcfracture height, m\nk\u00bcformation permeability, m2\np\u00bcpressure, MPa\npD\u00bcdimensionless pressure, dimensionless\npDE\u00bcsolution for early-time dimensionless pressure, dimensionless\npDL\u00bcsolution for late-time dimensionless pressure, dimensionless\npf,init\u00bc\ufb01nal fracture pressure, MPa"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886148-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 8, "chroma:document": "pDL\u00bcsolution for late-time dimensionless pressure, dimensionless\npf,init\u00bc\ufb01nal fracture pressure, MPa\npinit\u00bcinitial pressure, MPa\nq\u00bcvolumetric injection rate, m3/s\nSf\u00bcfracture stiffness, MPa/m\nt\u00bctime, seconds\nta\u00bcAgarwal time, dimensionless\ntD\u00bcdimensionless time, dimensionless\ntD,trans\u00bctime at the transition between early-time and late-time transient, seconds\nte\u00bcduration of injection, seconds\nv\u00bcfracture-propagation velocity, m/s\nVf\u00bcvolume of \ufb02uid in the fracture, m3\nVL\u00bctotal cumulative leakoff volume from the start of injection, m3\nVLs\u00bctotal cumulative leakoff volume from shut-in, m3\nVslug\u00bctotal injection volume, m3\nx\u00bcdistance from the location of the \ufb01nal fracture tip, m\na\u00bcfracture power-law growth exponent, dimensionless\nb\u00bcexponent, dimensionless\nDp\u00bcchange in pressure since the start of shut-in, seconds\nDt\u00bctime elapsed since the start of shut-in, seconds\n/\u00bcformation porosity, dimensionless\nl\u00bc\ufb02uid viscosity, MPa /C1s\ns\u00bcsuperposition time (identical to Horner time), dimensionless"}


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-186098-PA Superious Deflection.pdf", "page": 8, "chroma:document": "/\u00bcformation porosity, dimensionless\nl\u00bc\ufb02uid viscosity, MPa /C1s\ns\u00bcsuperposition time (identical to Horner time), dimensionless\nAcknowledgments\nGratitude is expressed to Roland Horne for informally reviewing this manuscript, and the journal editor and two anonymous reviewers\ndeserve thanks for their thoughtful comments. Dave Cramer and ConocoPhillips deserve appreciation for providing permission to repro-\nduce the \ufb01eld data shown in Fig. 5.\nReferences\nAgarwal, R. G. 1980. A New Method to Account for Producing Time Effects When Drawdown Type Curves Are Used to Analyze Pressure Buildup and\nOther Test Data. Presented at the SPE Annual Technical Conference and Exhibition, Dallas, 21\u201324 September. SPE-9289-MS. https://doi.org/\n10.2118/9289-MS.\nAyoub, J. A., Bourdet, D. P., and Chauvel, Y. L. 1988. Impulse Testing. SPE Form Eval 3(3): 534\u2013546. SPE-15911-PA. https://doi.org/10.2118/15911-\nPA."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886210-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 8, "chroma:document": "Ayoub, J. A., Bourdet, D. P., and Chauvel, Y. L. 1988. Impulse Testing. SPE Form Eval 3(3): 534\u2013546. SPE-15911-PA. https://doi.org/10.2118/15911-\nPA.\nBachman, R. C., Walters, D. A., Hawkes, R. A. et al. 2012. Reappraisal of the G Time Concept in Mini-Frac Analysis. Presented at the SPE Annual\nTechnical Conference and Exhibition, San Antonio, Texas, USA, 8\u201310 October. SPE-160169-MS. https://doi.org/10.2118/160169-MS.\nBarree, R. D. and Miskimins, J. L. 2016. Physical Explanation of Non-Linear Derivatives in Diagnostic Fracture Injection Test Analysis. Presented a t\nthe SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, USA, 9\u201311 February. SPE-179134-MS. https://doi.org/10.2118/\n179134-MS.\nBarton, N., Bandis, S., and Bakhtar, K. 1985. Strength, Deformation, and Conductivity Coupling of Rock Joints. International Journal of Rock Mechan-\nics and Mining Sciences & Geomechanics Abstracts 22(3): 121\u2013140. https://doi.org/10.1016/0148-9062(85)93227-9."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88626a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 8, "chroma:document": "ics and Mining Sciences & Geomechanics Abstracts 22(3): 121\u2013140. https://doi.org/10.1016/0148-9062(85)93227-9.\nCastillo, J. L. 1987. Modi\ufb01ed Fracture Pressure Decline Analysis Including Pressure-Dependent Leakoff. Presented at the SPE/DOE Low-Permeabilit y\nReservoir Symposium, Denver, 18\u201319 May. SPE-16417-MS. https://doi.org/10.2118/16417-MS.REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1053 Total Pages: 11\nID:jaganm Time: 13:19 I Path: //chenas03/cenpro/ApplicationFiles/Journals/SA/SPE/REE#/Vol00000/170018/Comp/APPFile/SA-REE#170018November 2017 SPE Reservoir Evaluation & Engineering 1053"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8862d8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 9, "chroma:document": "Craig, D. P. and Blasingame, T. A. 2006. Application of a New Fracture-Injection/Falloff Model Accounting for Propagating, Dilated, and Closing Hy-\ndraulic Fractures. Paper presented at the SPE Gas Technology Symposium, Calgary, 15\u201317 May. SPE-100578-MS. https://doi.org/10.2118/100578-MS.\nEhlig-Economides, C. 1988. Use of the Pressure Derivative for Diagnosing Pressure-Transient Behavior. J Pet Technol 40(10): 1280\u20131282. SPE-18594-\nPA. https://doi.org/10.2118/18594-PA.\nGringarten, A. C., Ramey, H. J., and Raghavan, R. 1974. Unsteady-State Pressure Distributions Created by a Well With a Single In\ufb01nite Conductivity\nVertical Fracture. SPE J. 14(4): 347\u2013360. SPE-4051-PA. https://doi.org/10.2118/4051-PA.\nGu, H., Elbel, J. L., Nolte, K. G. et al. 1993. Formation Permeability Determination Using Impulse-Fracture Injection. Presented at the Production O pera-\ntions Symposium, Oklahoma City, Oklahoma, USA, 21\u201323 March. SPE-25425-MS. https://doi.org/10.2118/25425-MS."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886332-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 9, "chroma:document": "tions Symposium, Oklahoma City, Oklahoma, USA, 21\u201323 March. SPE-25425-MS. https://doi.org/10.2118/25425-MS.\nGulrajani, S. N. and Nolte, K. G. 2000. Appendix: Background for Hydraulic Fracturing Pressure Analysis Techniques. In Reservoir Stimulation , ed. M.\nJ. Economides and K. G. Nolte, Chichester, England: John Wiley.\nHawkes, R. V., Anderson, I., Bachman, R. C. et al. 2013. Interpretation of Closure Stress in the Montney Shale Using PTA Based Techniques. Presented\nat the SPE Hydraulic Fracturing Technology Conference, The Woodlands, Texas, USA, 4\u20136 February. SPE-163825-MS. https://doi.org/10.2118/\n163825-MS.\nHouze, O. P., Horne, R. N., and Ramey, H. J. 1988. Pressure-Transient Response of an In\ufb01nite Conductivity Vertical Fracture in a Reservoir With Dou-\nble-Porosity Behavior. SPE Form Eval 3(3): 510\u2013518. SPE-12778-PA. https://doi.org/10.2118/12778-PA."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886396-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 9, "chroma:document": "ble-Porosity Behavior. SPE Form Eval 3(3): 510\u2013518. SPE-12778-PA. https://doi.org/10.2118/12778-PA.\nHoward, G. and Fast, C. R. 1957. Optimum Fluid Characteristics for Fracture Extension. Drilling and Production Practice 24:261\u2013270. API-57-261.\nIbrahim, M. and Pieprzica, C. 2016. Appraising Unconventional Play From Mini-Frac Test Analysis, Actual Field Case. Presented at the SPE Annual\nTechnical Conference and Exhibition, Dubai, 26\u201328 September. SPE-181465-MS. https://doi.org/10.2118/181465-MS.\nJung, H., Sharma, M. M., Cramer, D. D. et al. 2016. Re-examining Interpretations of Non-Ideal Behavior During Diagnostic Fracture Injection Tests.\nJournal of Petroleum Science and Engineering 145: 114\u2013136. https://doi.org/10.1016/j.petrol.2016.03.016.\nKoning, E. J. L. 1987. Water\ufb02ooding Under Fracturing Conditions. PhD thesis, Delft University of Technology."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8863f0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 9, "chroma:document": "Koning, E. J. L. 1987. Water\ufb02ooding Under Fracturing Conditions. PhD thesis, Delft University of Technology.\nLiu, G., Ehlig-Economides, C., and Sun, J. 2016. Comprehensive Global Fracture Calibration Model. Presented at the SPE Asia Paci\ufb01c Hydraulic Frac-\nturing Conference, Beijing, 24\u201326 August. SPE-181856-MS. https://doi.org/10.2118/181856-MS.\nMarongiu-Porcu, M., Ehlig-Economides, C. A., and Economides, M. J. 2011. Global Model for Fracture Falloff Analysis. Presented at the SPE North\nAmerican Unconventional Gas Conference and Exhibition, The Woodlands, Texas, USA, 14\u201316 June. SPE-144028-MS. https://doi.org/10.2118/\n144028-MS.\nMcClure, M. W., Jung, H., Cramer, D. D. et al. 2016. The Fracture Compliance Method for Picking Closure Pressure From Diagnostic Fracture Injection\nTests. SPE J. 21(4): 1321\u20131339. SPE-179725-PA. https://doi.org/10.2118/179725-PA."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886454-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 9, "chroma:document": "Tests. SPE J. 21(4): 1321\u20131339. SPE-179725-PA. https://doi.org/10.2118/179725-PA.\nMohamed, I. M., Nasralla, R. A., Sayed, M. A. et al. 2011. Evaluation of After-Closure Analysis Techniques for Tight and Shale Gas Formations. Pre-\nsented at the SPE Hydraulic Fracturing Technology Conference. The Woodlands, Texas, USA, 24\u201326 January. SPE-140136-MS. https://doi.org/\n10.2118/140136-MS.\nNolte, K. 1979. Determination of Fracture Parameters From Fracturing Pressure Decline. Presented at the SPE Annual Technical Conference and Exhibi -\ntion, Las Vegas, Nevada, USA, 23\u201326 September. SPE-8341-MS. https://doi.org/10.2118/8341-MS.\nNolte, K. G. and Smith, M. B. 1981. Interpretation of Fracturing Pressures. J Pet Technol 33(9): 1767\u20131775. SPE-8297-PA. https://doi.org/10.2118/\n8297-PA.\nSoliman, M. Y. and Kabir, C. S. 2012. Testing Unconventional Formations. Journal of Petroleum Science and Engineering 92\u201393: 102\u2013109. https://\ndoi.org/10.1016/j.petrol.2012.04.027."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8864b8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 9, "chroma:document": "doi.org/10.1016/j.petrol.2012.04.027.\nvan den Hoek, P. J. 2002. Pressure Transient Analysis in Fractured Produced Water Injection Wells. Presented at the SPE Asia Paci\ufb01c Oil and Gas Con-\nference and Exhibition, Melbourne, Australia, 8\u201310 October. SPE-77946-MS. https://doi.org/10.2118/77946-MS.\nvan den Hoek, P. 2016. A Simple Uni\ufb01ed Pressure Transient Analysis Method for Fractured Water\ufb02ood Injectors and Minifracs in Hydraulic Fracture\nStimulation. Presented at the SPE Annual Technical Conference and Exhibition, Dubai, 26\u201328 September. SPE-181593-MS. https://doi.org/10.2118/\n181593-MS.\nWallace, J., Kabir, C. S., and Cipolla, C. 2016. Probing Diagnostic Fracture Injection Tests in Conventional Reservoirs. Journal of Petroleum Science &\nEngineering 143: 245\u2013257. https://doi.org/10.1016/j.petrol.2016.01.039.\nAppendix A\nHere, I derive equations for the asymptotic behavior of G\u00f0a\u00bc1\u00defor small Dtand large Dt:G\u00f0a\u00bc1\u00deis de\ufb01ned in Eq. 21. To calculate"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886512-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 9, "chroma:document": "Appendix A\nHere, I derive equations for the asymptotic behavior of G\u00f0a\u00bc1\u00defor small Dtand large Dt:G\u00f0a\u00bc1\u00deis de\ufb01ned in Eq. 21. To calculate\nthe behavior at small Dt;take the Taylor-series expansion of the 1 \u00feDt\nte/C18/C191:5\nterm centered at Dt\u00bc0:\nG\u00f0a\u00bc1;Dt!0\u00de//C0Dt\nte/C18/C191:5\n/C01\u00fe1\u00fe0\nte/C18/C191:5\n\u00fe1:5\nte1\u00fe0\nte/C18/C190:5\nDt\u00fe0:75\nt2\ne1\u00fe0\nte/C18/C19/C00:5\nDt2\u00fe\u2026 \u00f0A-1\u00de\nThe two constant terms cancel out. The lowest-order term in Eq. A-1 (the term that decreases most slowly as Dtapproaches zero) is\nlinear with Dt:Therefore,\nlimDt!0G\u00f0a\u00bc1\u00de/1:5Dt\nte: \u00f0A-2\u00de\nTo calculate the behavior at large Dt;note that\nlimDt!1Dt\nte\u00fe1/C18/C191:5\n/C0Dt\nte/C18/C191:5\n\u00bclimDt!1Dt\nte\u00fe1/C18/C191:5\n/C0Dt\nte/C18/C191:5\n1\u00bclimD!0Dt\nte\u00feD/C18/C191:5\n/C0Dt\nte/C18/C191:5\nD\u00bc1:5\ufb03\ufb03\ufb03\ufb03\ufb03\nDt\ntes\n: \u00f0A-3\u00de\nThe second equality is true because 1.0 becomes in\ufb01nitesimally small relative toDt\nteasDtapproaches in\ufb01nity. The third equality is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886576-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 9, "chroma:document": "Dt\ntes\n: \u00f0A-3\u00de\nThe second equality is true because 1.0 becomes in\ufb01nitesimally small relative toDt\nteasDtapproaches in\ufb01nity. The third equality is\ntrue from the de\ufb01nition of a derivative and the power rule of differentiation. Finally, as Dtapproaches in\ufb01nity, the \u201c\u20131\u201d term in Eq. 21\nbecomes negligibly small; therefore,................\n................................................................\n.......REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1054 Total Pages: 11\nID:jaganm Time: 13:19 I Path: //chenas03/cenpro/ApplicationFiles/Journals/SA/SPE/REE#/Vol00000/170018/Comp/APPFile/SA-REE#1700181054 November 2017 SPE Reservoir Evaluation & Engineering"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8865da-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 10, "chroma:document": "limDt!1G\u00f0a\u00bc1\u00de/1:5\ufb03\ufb03\ufb03\ufb03\ufb03\nDt\ntes\n: \u00f0A-4\u00de\nMark McClure is the founder and chief executive officer of McClure Geomechanics and is a consulting professor at Stanford Uni-\nversity. He was an assistant professor in the Department of Petroleum and Geosystems Engineering at the University of Texas atAustin from 2013 to 2015. McClure\u2019s research focuses on modeling and characterization of hydraulic fracturing, induced seismic-\nity, and enhanced geothermal systems. He was honored with the SPE Regional Completions Optimization and Technology\nAward from the Southwest North American Region in 2015 and an Outstanding Service as a Technical Editor award for SPE Res-\nervoir Evaluation & Engineering in 2014, the Hank Ramey Award for Outstanding Research and Service to the Department from\nthe Department of Energy Resources Engineering at Stanford University in 2012, and the Best Paper in Geophysics award from"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886634-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-186098-PA Superious Deflection.pdf", "page": 10, "chroma:document": "the Department of Energy Resources Engineering at Stanford University in 2012, and the Best Paper in Geophysics award from\nthe Society of Exploration Geophysicists in 2011. McClure holds a BS degree in chemical engineering, an MS degree in petroleum\nengineering, and a PhD degree in energy-resources engineering, all from Stanford University................................................................REE186098 DOI: 10.2118/186098-PA Date: 26-October-17 Stage: Page: 1055 Total Pages: 11\nID:jaganm Time: 13:19 I Path: //chenas03/cenpro/ApplicationFiles/Journals/SA/SPE/REE#/Vol00000/170018/Comp/APPFile/SA-REE#170018November 2017 SPE Reservoir Evaluation & Engineering 1055"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886698-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 0, "chroma:document": "396 August 2009 SPE Production & OperationsHolistic Fracture Diagnostics: Consistent \nInterpretation of Prefrac Injection Tests \nUsing Multiple Analysis Methods\nR.D. Barree,  SPE, and V .L. Barree,  Barree & Associates LLC; and D.P . Craig,  SPE, Halliburton\nCopyright \u00a9 2009 Society of Petroleum Engineers\nThis paper (SPE 107877) was accepted for presentation at the 2007 SPE Rocky Mountain \nOil & Gas Technology Symposium, Denver, 16 \u201318 April, and revised for publication. Original manuscript received for review 12 February 2007. Revised manuscript received for review 2 April 2008. Paper peer approved 4 April 2008.Summary\nSince the introduction of the G-function derivative analysis, prefrac"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8866fc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 0, "chroma:document": "Since the introduction of the G-function derivative analysis, prefrac \ndiagnostic injection tests have become a valuable and commonly used technique. Unfortunately, the technique is frequently misapplied or misinterpreted, leading to confusion and misdiagnosis of fracturing parameters. This paper presents a consistent method of analysis of the G-function, its derivatives, and its relationship to other diagnostic techniques including square-root(time) and log( /H9004p\nwf)-log( /H9004t) plots \nand their appropriate diagnostic derivatives.\nFour field test examples are given for the most common diag-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886760-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 0, "chroma:document": "wf)-log( /H9004t) plots \nand their appropriate diagnostic derivatives.\nFour field test examples are given for the most common diag-\nnostic curve signatures. These show how multiple analysis methods can be applied to consistently interpret closure pressure and time, as well as pre- and post-closure flow regimes and reservoir proper-ties from the test data. The cases include normal constant-area and constant permeability leakoff, pressure dependent fissure leakoff, fracture tip extension, and variable fracture storage. In some cases conventionally accepted analysis methods, such as the Sqrt(time) plot, can lead to misleading interpretations. A single consistent approach to analysis is described for each case. The example cases can be used to build a foundation for consistent and less ambiguous analysis of any complex fracture injection/falloff test.\nIntroduction\nPrefrac diagnostic injection test analysis provides critical input data"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8867ba-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 0, "chroma:document": "Introduction\nPrefrac diagnostic injection test analysis provides critical input data \nfor fracture design models, and reservoir characterization data used to predict post-fracture production. An accurate post-stimulation production forecast is necessary for economic optimization of the fracture treatment design. Reliable results require an accurate and consistent interpretation of the test data. In many cases closure is mistakenly identified through misapplication of one or more analy-sis techniques. In general, a single unique closure event will satisfy all diagnostic plots or methods. All available analysis methods should be used in concert to arrive at a consistent interpretation of fracture closure.\nRelationship of the pre-closure analysis to after-closure analysis"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88681e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 0, "chroma:document": "Relationship of the pre-closure analysis to after-closure analysis \nresults must also be consistent. To correctly perform the after-closure analysis the transient flow regime must be correctly identified. Flow regime identification has been a consistent problem in many analyses. There remains no consensus regarding methods to identify reservoir transient flow regimes after fracture closure. The method presented here is not universally accepted but appears to fit the gen-erally assumed model for leakoff used in most fracture simulators.\nFour examples are presented to show the application of mul-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886878-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 0, "chroma:document": "Four examples are presented to show the application of mul-\ntiple diagnostic analysis methods. The first illustrates the expected behavior of normal fracture closure dominated by matrix leakoff with a constant fracture surface area after shut-in. The second example shows pressure dependent leakoff (PDL) in a reser-voir with pressure-variable permeability or flow capacity, usually caused by natural or induced secondary fractures or fissures. The third example shows fracture tip extension after shut-in. These cases generally show definable fracture closure. The fourth example shows what has been commonly identified as fracture height recession during closure, but which can also indicate vari-\nable storage in a transverse fracture system.\nFor each example the analysis will be demonstrated using the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8868dc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 0, "chroma:document": "able storage in a transverse fracture system.\nFor each example the analysis will be demonstrated using the \nG-function and its diagnostic derivatives, the sqrt(time) and its derivatives, and the log-log plot of pressure change after shut-in and its derivatives (Nolte 1979; Castillo 1987; Barree and Mukherjee 1996; Barree 1998). When appropriate, the after-closure analy-sis is presented for each case, as is an empirical correlation for permeability from the identified G-function closure time (Talley et al. 1999). A critical part of the analysis is the realization that there is a common event indicating closure that should be consis-tently identified by all diagnostic methods. To reach a conclusion all analyses must give consistent results. \nThe goal of this paper is to provide a method for consistent"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886936-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 0, "chroma:document": "The goal of this paper is to provide a method for consistent \nidentification of after-closure flow regimes, an unambiguous frac-ture closure time and stress, and a reasonable engineering estimate of reservoir flow capacity from the pressure falloff data, without requiring assumptions such as a known reservoir pressure. Other methods, based on sound transient test theory, require pressure dif-ference curves based on the observed bottomhole pressure during falloff minus the \u201cknown\u201d reservoir pressure (Talley et al. 1999; Craig and Blasingame 2006). While these methods are technically correct they can lead to confusing results at times, especially in low permeability reservoirs when pore pressure is difficult to determine accurately prior to stimulation.\nThis is not a transient test analysis paper but is intended to"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88699a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 0, "chroma:document": "This is not a transient test analysis paper but is intended to \npresent a practical approach to analysis of real, and frequently marginal-quality, prefracture field test data. The techniques applied are based on some transient test theory. Some of the results pre-sented here are still under debate and development. The methods shown have been tested and, we believe, proven in the analysis of hundreds of tests. Application of these methods provides consis-tent analysis that helps to avoid misinterpretation of falloff data and gives the most useful information available from diagnostic injection tests.\nStep-rate injection tests and their analysis are not included in the \nscope of this paper. Determination of the pressure-dependent leakoff coefficient is also not described here, because it has been previ-ously reported (Barree and Mukherjee 1996; Barree 1998). Only the analysis of pressure decline following shut-in of a fracture-rate injection test is considered."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8869f4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 0, "chroma:document": "Transient Flow Regimes During and After \nFracture Closure\nSeveral transient flow regimes may occur during a falloff test after \ninjection at fracture rate. The major flow regimes are graphically illustrated in the classic paper by Cinco-Ley and Samaniego (1981). \nImmediately after shut-in the pressure gradient along the length"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886a58-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 0, "chroma:document": "Immediately after shut-in the pressure gradient along the length \nof the fracture dissipates in a short-duration linear flow period. In a long fracture in low permeability rock the initial fracture linear flow can be followed by a bi-linear flow period with the linear flow transient persisting in the fracture while reservoir linear flow occurs simultaneously. After the fracture transient dissipates, the reservoir linear flow period can continue for some time, depend-ing on the permeability of the reservoir and the volume of fluid stored in the fracture and subsequently leaked off during closure. After closure the pressure transient established around the fracture propagates into the reservoir and transitions into elliptical, then"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886abc-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 1, "chroma:document": "August 2009 SPE Production & Operations 397pseudoradial flow. Each of these flow regimes has a characteristic \nappearance on various diagnostic plots.\nFluid leakoff from a propagating fracture is normally modeled \nassuming one-dimensional linear flow perpendicular to the fracture face. Settari (2000) has pointed out that in some cases of moder-ate reservoir permeability the linear flow regime may not occur, even during fracture extension and early leakoff. During fracture extension and shut-in, the transient may already be in transition to elliptical or pseudoradial flow. In this case analyses based on an assumed pseudolinear flow regime will give incorrect results. In all cases an understanding of the flow regime and its relation to the fracture geometry is critical to arriving at a consistent interpretation of the fracture falloff test.\nDiagnostic Derivative Examples\nFor each analysis technique various curves are used to help define"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886b20-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 1, "chroma:document": "Diagnostic Derivative Examples\nFor each analysis technique various curves are used to help define \nclosure, leakoff mechanisms, and after-closure flow regimes. On each plot the curves are labeled as the primary (y vs. x), the first derivative ( /H11128y//H11128x), and the semilog derivative ( /H11128y//H11128(lnx) or \nx/H11128y//H11128x). For convenience the primary curve is plotted on the left \ny-axis and all derivatives are plotted on the right y-axis for all Cartesian plots. For the log-log plot all curves are shown on the same y-axis.\nFor pre-closure analysis, and consistent identification of frac-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886b7a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 1, "chroma:document": "For pre-closure analysis, and consistent identification of frac-\nture closure, three techniques are illustrated for each example: G-function, Square-root of shut-in time, and log-log plot of pres-sure change with shut-in time. All these analyses begin at shut-in. The instantaneous shut-in pressure (ISIP) is taken as the incipient fracture extension pressure for all cases. When there is significant wellbore afterflow (fluid expansion or continued low-rate injec-tion), or severe near-well pressure drop, the ISIP can be difficult to interpret accurately and may be too high to represent actual fracture extension pressure. In all the examples in the paper the pressures have been offset to an approximate ISIP of 10,000 psi to remove any relation to the original field test data. The follow-ing sections detail the data and analysis for the four major leakoff type examples.\nNormal Leakoff Behavior.  Normal leakoff is observed when the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886bde-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 1, "chroma:document": "Normal Leakoff Behavior.  Normal leakoff is observed when the \ncomposite reservoir system permeability is constant. The reservoir may exhibit only matrix permeability or have a secondary natural fracture or \ufb01  ssure overprint in which the \ufb02  ow capacity of the \nsecondary fracture system does not change with pore pressure or net stress. After shut-in the fracture is assumed to stop propagat-ing and the fracture surface area open to leakoff remains constant during closure.\nNormal Leakoff G-Function. As noted in previous papers, \nthe expected signature of the G-function semilog derivative is a straight-line through the origin (zero G-function and zero deriva-tive) (Barree 1998). In all cases the correct straight line tangent to the semilog derivative of the pressure vs. G-function curve must pass through the origin. Fracture closure is identified by the departure of the semi-log derivative of pressure with respect to \nG-function (G /H11128p"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886c42-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 1, "chroma:document": "G-function (G /H11128p\nw//H11128G) from the straight line through the origin. \nDuring normal leakoff, with constant fracture surface area and constant permeability, the first derivative ( /H11128p\nw//H11128G) should also be \nconstant (Castillo 1987). The primary pw vs. G curve should follow \na straight line (Nolte 1979). The example in Fig. 1  shows some \nslight deviation from the perfect constant leakoff but is a good example of the expected curve shapes with a clear indication of closure at G\nc = 2.31. The closure event is marked by the dashed \nvertical line [1].\nNormal Leakoff Sqrt(t) Analysis . The sqrt( t) plot has fre-\nquently been misinterpreted when picking fracture closure, even for the simplest cases. The primary p\nw vs. sqrt( t) curve should form"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886ca6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 1, "chroma:document": "quently been misinterpreted when picking fracture closure, even for the simplest cases. The primary p\nw vs. sqrt( t) curve should form \na straight line during fracture closure, as with the G-function plot. Some users suggest that the closure is identified by the departure of the data from the straight line trend, similar to the way the G-function closure is picked. This is incorrect and leads to a later closure and lower apparent closure pressure. The correct indication of closure is the inflection point on the p\nw vs. sqrt( t) plot. \nThe best way to find the inflection point is to plot the first \nderivative of pw vs. sqrt( t) and find the point of maximum ampli-\ntude of the derivative. Many fracture-pressure analysis software packages plot the inverse of the actual first derivative and show the inflection point as the minimum of the derivative. The plot in Fig. 2,  shows that the slope of the pressure curve starts low, then"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886d00-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 1, "chroma:document": "increases and reaches a maximum rate of decline at the inflection point, then decreases again after closure. The first derivative curve in Fig. 2 is plotted with the proper sign. The dashed vertical line [1] is the G-function closure pick that is synchronized in time and pressure with the sqrt( t) plot. Clearly the consistent closure lies \nat the inflection point and not at the point of departure from the straight line tangent to the pressure curve.\nThe semilog derivative of the pressure curve is also shown on \nthe sqrt( t) plot. This curve is equivalent to the semilog derivative of \nthe G-function for most low-perm cases. The closure pick falls at the departure from the straight line through the origin on the semi-log derivative of the P vs. sqrt( t) curve. A single closure point must \nsatisfy the requirement on both the G-function and sqrt( t) plots.\nNormal Leakoff Log-Log Pressure Derivative. The log-log"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886ddc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 1, "chroma:document": "satisfy the requirement on both the G-function and sqrt( t) plots.\nNormal Leakoff Log-Log Pressure Derivative. The log-log \nplot of pressure change from ISIP vs. shut-in time for the normal leakoff example is shown in Fig. 3.  The heavy curve is the pres-\nsure difference and the dashed curve is its semilog derivative with respect to shut-in time. The vertical dashed line is the unique closure pick from the G-function and sqrt( t) plot. It is common for \nthe pressure difference and derivative curves to be parallel immedi-ately before closure. The slope of these parallel lines is diagnostic of the flow regime established during leakoff before closure. In many cases a near-perfect \u00bd slope is observed, strongly suggesting linear flow from the fracture. In this example the slope is greater than \u00bd suggesting possible linear flow coupled with changing fracture/wellbore storage (See Appendix B). The separation of the \n0 5 10 15 20 25\nG (Time)750080008500900095001000010500"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886e7c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 1, "chroma:document": "0 5 10 15 20 25\nG (Time)750080008500900095001000010500\n0200400600800100012001400160018002000\n1\nP vs. G\nGdP/dG vs. G\ndP/dG vs. GFracture ClosurePressure\nDerivatives\nFig. 1\u2014Normal leakoff G-function plot.1/24/200704:00 08:00 12:00\n1/24/200716:00\nTime750080008500900095001000010500\n01002003004005006007008009001000\n1Pressure\nDerivativesP vs. \u221at\n\u221atdP/d\u221at vs. \u221at\ndP/d\u221at vs. \u221atFracture Closure\nFig. 2\u2014Normal leakoff sqrt( t) plot."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886ed6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 2, "chroma:document": "398 August 2009 SPE Production & Operationstwo parallel lines always marks fracture closure and is the final \nconfirmation of a consistent closure identification.\nAfter closure the semilog derivative curve will show a slope \nof \u22121/2 in a fully developed reservoir pseudolinear flow regime and a slope of \u22121 in fully developed pseudoradial flow. In the example the derivative slope is \u22121 indicating that reservoir pseu-doradial flow was observed. The late-time data shows a drop in the derivative probably caused by wellbore effects such as gas entry and phase segregation. The use of the semilog derivative of the log-log plot for after-closure flow regime identification, as well as closure confirmation, is a powerful new addition to fracture pressure decline diagnostics.\nAfter-Closure Analysis for Normal Leakoff Example. The \nTalley-Nolte After-Closure Analysis (ACA) flow regime identi-fication plot for the normal leakoff example is shown as Fig. 4"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886f30-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 2, "chroma:document": "Talley-Nolte After-Closure Analysis (ACA) flow regime identi-fication plot for the normal leakoff example is shown as Fig. 4  \n(Talley et al. 1999). The heavy solid line is the observed bottomhole pressure during the falloff minus the initial reservoir pressure. The slope of the semi-log derivative of the pressure difference function (dashed line) is 1.0 during the identified pseudoradial flow period. If a linear-flow period existed in this data set a derivative slope of \u00bd would exist. It is critical to remember that the slope of the pressure difference curve on this plot is determined solely by the guess of reservoir pressure used to construct the plot. The slope of the deriva-tive is not affected by the input reservoir pressure value.\nIf a pseudoradial flow regime is identified, then the Cartesian \nRadial Flow plot (Fig. 5)  can be used to determine reservoir \nfar-field transmissibility, kh/\n/H9262. The viscosity used is the far-field"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b886f94-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 2, "chroma:document": "Radial Flow plot (Fig. 5)  can be used to determine reservoir \nfar-field transmissibility, kh/\n/H9262. The viscosity used is the far-field \nmobile fluid viscosity and h is the estimated net pay height. For the \nanalysis of the example data kh//H9262 = 299 md-ft/cp. For gas viscosity at reservoir temperature, kh = 7.9 md-ft. For the assumed net pay, \nthe effective reservoir permeability is 0.097 md. \nHorner Analysis for Normal Leakoff Example. If a pseudo-\nradial flow period is identified, then a conventional Horner plot can also be used to determine reservoir transmissibility. In Fig. 6 \nthe Horner slope through the radial flow data is 14411 psi. Using an average pump rate of 18.4 bpm, kh/\n/H9262 = 298 md-ft/cp. For the \nassumed gas viscosity kh = 7.9 md-ft. Using the same assumed \nnet gives k = 0.097 md. This result is consistent with the ACA \nresults. \nG-Function Permeability Estimate. An empirical correlation"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88705c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 2, "chroma:document": "net gives k = 0.097 md. This result is consistent with the ACA \nresults. \nG-Function Permeability Estimate. An empirical correlation \nhas also been developed to estimate formation permeability from the G-function closure time when after-closure data is not avail-able. The correlation is described in detail in the Appendix. Fig. 7 \nshows the G-function correlation permeability estimate for the observed closure time and other input parameters. The perme-ability estimate of 0.097 md is consistent with the Horner and ACA results. \nPressure-Dependent Leakoff.  Pressure dependent leakoff (PDL) \noccurs when the \ufb02  uid loss rate changes with pore pressure or net \neffective stress in the rock surrounding the fracture. PDL is not caused by the normal change in transient pressure gradient during leakoff. This is part of the normal leakoff mode and is handled by the one-dimensional linear \ufb02  ow solution of the diffusivity"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8870ac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 2, "chroma:document": "equation used to model fracture leakoff in a constant permeability system. The pressure dependence referred to here is a change in the transmissibility of the reservoir \ufb01  ssure or fracture system that \ndominates the \ufb02  uid loss rate. PDL is only apparent when there 2 3 4 5 6789 2 3 4 5 6789 2 3 4 5 67890.001 0.01 0.1 1\nSquare Linear Flow (FL^2)234567892345678923456789\n10100100010000\n (m = 1) Delta-Pressure and Derivative\u0394P vs. FL2\nFL2d\u0394P/dFL2vs. FL2\u0394P= (pw\u2013pr)\nStart of Radial Flow\nFig. 4\u2014Normal leakoff ACA log plot.\n2 3 1\nHorner Time72507500775080008250850087509000925095009750\n (m = 14411) \n  (Reservoir = 7476)  1Pressure\nFig. 6\u2014Normal leakoff Horner Plot. \n0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8\nRadial Flow Time Function72007400760078008000820084008600880090009200\n (m = 4814.2) Results\nReservoir Pressure  = 7475.68 psi\nTransmissibility, kh/\u03bc = 298.94991 md*ft\nkh = 7.94014 md*ft\nPermeability, k = 0.0968 md\nStart of Pseudo Radial Time = 2.15 hours 1Pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8870fc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 2, "chroma:document": "Transmissibility, kh/\u03bc = 298.94991 md*ft\nkh = 7.94014 md*ft\nPermeability, k = 0.0968 md\nStart of Pseudo Radial Time = 2.15 hours 1Pressure\nFig. 5\u2014Normal leakoff ACA radial flow plot.2 3 456789 2 3 456789 2 3 456789 2 3 456789\n0.1 1 10 100 1000\nTime (0 = 8.15)2345678923456789234\n101001000\n (m = \u20131)  (m = 0.632)  BH ISIP = 9998 psi 1Delta-Pressure and Derivative\u0394P vs. \u0394t\n\u0394td\u0394P/d\u0394tv s .  \u0394t\nFracture ClosureRadial Flow\nFig. 3\u2014Normal leakoff log-log plot."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887156-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 3, "chroma:document": "August 2009 SPE Production & Operations 399is substantial stress dependent permeability in a composite dual-\npermeability reservoir.\nG-Function for Pressure-Dependent Leakoff.  Fig. 8 shows \nthe G-function behavior expected for PDL. The primary pw vs. \nG curve is concave upward and curved while PDL persists. The semilog derivative exhibits the characteristic \u201chump\u201d above the straight line extrapolated to the derivative origin. The end of PDL and the critical fissure opening pressure corresponds to the end of the \u201chump\u201d and the beginning of the straight line representing matrix dominated leakoff. Fracture closure is still shown by the departure of the semilog derivative from the straight line through the origin. \nSqrt(t) Analysis for PDL. Interpretation of the sqrt(t) plot in \nPDL cases has often led to incorrect closure picks. Fig. 9 shows an \nexpanded view of the sqrt( t) plot for the example with the curves"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8871a6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 3, "chroma:document": "PDL cases has often led to incorrect closure picks. Fig. 9 shows an \nexpanded view of the sqrt( t) plot for the example with the curves \nscaled for better visibility. Note that the semilog derivative is nearly identical in shape and information content to the G-function semilog derivative. It clearly shows the PDL \u201chump\u201d and closure, which has been synchronized to the G-function result. \nIncorrect closure picks on the sqrt( t) plot will not occur if the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887200-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 3, "chroma:document": "Incorrect closure picks on the sqrt( t) plot will not occur if the \nsemilog derivative is used. Problems arise when the first deriva-tive is used exclusively to pick closure. In PDL cases the obvious derivative maximum, or most prominent inflection point, is caused by the changing leakoff associated with PDL and does not indicate fracture closure. The false closure indication is shown on the plot. Many fracture diagnostic tests have been badly misdiagnosed because the early and incorrect closure was picked because of dependence on only the sqrt( t) plot. This example clearly illustrates why all available diagnostic plots must be used in concert to arrive \nat a single consistent closure event. \nLog-Log Pressure Derivative for PDL Example. Fig. 10 shows"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887250-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 3, "chroma:document": "at a single consistent closure event. \nLog-Log Pressure Derivative for PDL Example. Fig. 10 shows \nthe log-log plot for the PDL example. The normal matrix leakoff period, following the end of PDL, appears as a perfect \u00bd slope of the semilog derivative with a parallel pressure difference curve exactly 2-times the magnitude of the derivative. The parallel trend ends at the identified closure time and pressure difference. In this example a well-defined \u2212\u00bd slope, or reservoir pseudolinear flow period, is \nshown shortly after closure. The later data approach a slope of \u22121, \nwhich indicates pseudoradial flow has been established. \nAfter-Closure Analysis for PDL Example. The ACA log-log \nplot (Fig. 11)  shows both the reservoir linear and radial flow peri-\nods in their expected locations. \nFigs. 12 and 13  show the ACA Cartesian plots for the linear and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8872aa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 3, "chroma:document": "ods in their expected locations. \nFigs. 12 and 13  show the ACA Cartesian plots for the linear and \nradial flow analyses. Both give consistent estimates of reservoir pore pressure. The pseudoradial flow analysis gives a transmissibil-ity of 37.2 md-ft/cp and estimated permeability of 0.047 md. \nHorner Analysis for PDL Example. For an average pump rate \nof 6.7 bpm the Horner plot gives kh/\n/H9262 = 35.72 md-ft/cp. The Horner \nestimated permeability is 0.046 md compared to 0.047 md from the ACA Radial Flow analysis. Pore pressure estimated from the Horner plot is also consistent with both the linear and radial analyses because a well-developed pseudoradial flow period does exist in this case. The vertical dotted line in Fig. 14  shows the start of pseudora-\ndial flow. If a pseudoradial flow period does not exist, extrapolation of an apparent straight-line on the Horner plot can give extremely \ninaccurate estimates of pressure and flow capacity. 0.0010.010.1110100"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8872fa-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 3, "chroma:document": "inaccurate estimates of pressure and flow capacity. 0.0010.010.1110100\n0              2              4               6              8             10            12            14             16            18            20\nGcData Input\nrp 1\n\u03c6 0.09 V/V\nct 7.50E-05 psi\u20131\nE3 . 5 M p s i\n\u03bc 1c p\nGc 2.44\nPz 966.0 psiEstimated Permeability = 0.0974 mdPermeability, md\nFig. 7\u2014Normal leakoff permeability estimate.\n2 3 456789 2 3 456789 2 3 456789 2 3 4567890.1 1 10 100 1000\nTime (0 = 9.133333)23456789234567892\n101001000\n (m = 0.5) \n(m = \u20131) (m = \u20130.5)  BH ISIP = 10000 psi 1Pressure Difference and Derivative\u0394P vs. \u0394t\n\u0394td\u0394P/d\u0394tv s .  \u0394tFracture ClosureLinear Flow\nRadial Flow\nFig. 10\u2014PDL log-log plot. \n0 2 4 6 8 10 12 14 16 18 20\nG (Time)8250850087509000925095009750100001025010500\n01002003004005006007008009001000\n21\nP vs. G\nGdP/dG vs. G\ndP/dG vs. GFracture ClosurePressure\nDerivatives\nFig. 8\u2014PDL G-function plot.\n1/24/200700:20 00:40 01:00 01:20 01:40\n1/24/200702:00"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887354-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 3, "chroma:document": "GdP/dG vs. G\ndP/dG vs. GFracture ClosurePressure\nDerivatives\nFig. 8\u2014PDL G-function plot.\n1/24/200700:20 00:40 01:00 01:20 01:40\n1/24/200702:00\nTime825085008750900092509500975010000102 50\n0100200300400500\n1False ClosurePressure\nDerivativesP vs. \u221at\n\u221atdP/d\u221at vs. \u221at\ndP/d\u221at vs. \u221atFracture Closure\nFig. 9\u2014PDL Sqrt plot."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8873a4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 4, "chroma:document": "400 August 2009 SPE Production & OperationsG-Function Permeability Estimate for PDL Example. The \nG-function permeability correlation for the PDL example is shown in Fig. 15. It also gives a consistent permeability of 0.045 md. The \nimpact of the accelerated leakoff during PDL gives an estimate of the composite reservoir effective permeability. Note that the injected fluid viscosity is used for the permeability estimate based on closure time. Fracture Tip Extension.  In very low permeability reservoirs \nthe decline in wellbore pressure observed after shut-in may be caused by the dissipation of the pressure transient established in the fracture during pumping. The near-well pressure decreases as the fracture closes, which results in a decrease of fracture width at the well. The closing of the fracture volumetrically displaces \ufb02 uid to the tip of the fracture, causing continued extension of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8873f4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 4, "chroma:document": "the fracture length. Much of the pressure decline is therefore not related to leakoff but to the dissipation of the linear transient along the fracture length. \nG-Function Analysis for Tip Extension. During fracture tip \nextension the G-function derivatives fail to develop any straight-line trends. The primary P vs. G curve is concave upward, as is the first derivative. The semilog derivative starts with a large posi-tive slope, and the slope continues to decrease with shut-in time, giving a concave-down curvature (Barree and Mukherjee 1996; Barree 1998). Fig. 16  shows a typical case of fracture tip exten-\nsion with minimal leakoff. This is another case that is frequently misdiagnosed. \nSqrt(t) Analysis With Fracture Tip Extension. Many times the \nfirst break in the semilog derivative curve has been misinterpreted as a closure event. The mistake is often compounded by the use of the sqrt( t) plot.  Fig. 17  shows the sqrt( t) plot for the same data."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88744e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 4, "chroma:document": "The first derivative shows a large maximum very shortly after shut-in. This is often mistaken for closure. The semilog deriva-tive on the sqrt( t) plot helps to avoid this mistaken closure pick, \nand shows the same continuously increasing trend as seen on the G-function semilog derivative plot. In low permeability systems it is generally safe to assume that as long as the semilog derivative is still rising, the fracture has not yet closed. This is not true in 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0\nLinear Flow Time Function8000820084008600880090009200\n (m = 1438.5) \nResults\nReservoir Pressure = 8056.66 psi\nStart of Pseudo Linear Time = 15.9End of Pseudo Linear Time = 54.391 2PressureStart Linear Flow End Linear Flow\nFig. 12\u2014PDL ACA linear flow plot.2 3 4 5 6789 2 3 4 5 6789 2 3 4 5 67890.001 0.01 0.1 1\nSquare Linear Flow (FL^2)234567892345678923456789\n10100100010000\n (m = 1) \n (m = 0.5) \n1 2 3Delta-Pressure and Derivative\u0394P vs. FL2\nFL2d\u0394P/dFL2vs. FL2\u0394P=(pw\u2013pr)\nStart Linear Flow"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88749e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 4, "chroma:document": "10100100010000\n (m = 1) \n (m = 0.5) \n1 2 3Delta-Pressure and Derivative\u0394P vs. FL2\nFL2d\u0394P/dFL2vs. FL2\u0394P=(pw\u2013pr)\nStart Linear Flow\nEnd Linear Flow\nStart Radial Flow\nFig. 11\u2014PDL ACA log plot.\n0.0 0.1 0.2 0.3 0.4 0.5 0.6\nRadial Flow Time Function8000820084008600880090009200\n (m = 11373) Results\nReservoir Pressure = 8068.81 psi\nTransmissibility, kh/\u03bc = 37.21984 m\nkh = 0.93764 md*ft\nPermeability, k = 0.0469 md\nStart of Pseudo Radial Time = 11.2 6 1Pressure\nFig. 13\u2014PDL ACA radial flow plot.1Horner Time8000810082008300840085008600870088008900\n (m = 43920) \n  (Reservoir = 8064)  1Pressure\nFig. 14\u2014PDL Horner plot.\n0.0010.010.1110100\n0              2              4              6               8             10            12            14             16            18            20\nGcData Input\nrp 1\n\u03c6 0.08 V/V\nct 6.00E-05 psi\u20131\nE5 M p s i\n\u03bc 1c p\nGc 2.9\nPz 841.0 psiEstimated Permeability = 0.0453 mdPermeability, md\nFig. 15\u2014PDL permeability estimate."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8874f8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 5, "chroma:document": "August 2009 SPE Production & Operations 401very high permeability reservoirs and should always be checked \nusing the log-log pressure difference plot. \nLog-Log Pressure Derivative Analysis With Tip Extension. \nThe log-log plot of pressure change after shut-in is particularly useful for diagnosing fracture tip extension. Fig. 18  shows the \npressure difference and pressure derivative (semilog) for the tip extension example. \nIn Fig. 18, the pressure derivative departs from the early unit-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88757a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 5, "chroma:document": "In Fig. 18, the pressure derivative departs from the early unit-\nslope (storage) and establishes a \u00bc slope during fracture tip exten-sion. The pressure difference curve falls on a parallel \u00bc slope line separated by 4-times the magnitude of the derivative. The \u00bc slope signature is diagnostic of bilinear flow representing a continued dissipation of the linear pressure transient along the fracture length (extension and concomitant fluid flow) and some linear flow driv-ing minimal leakoff. For tip extension to occur the leakoff rate to the formation must be low. As long as the parallel \u00bc slope trend continues, the fracture has not closed and is still in the process of extending. Closure cannot be determined and no after-closure analysis can be conducted.\nHeight Recession or Transverse Storage.  There are two differ-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8875d4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 5, "chroma:document": "Height Recession or Transverse Storage.  There are two differ-\nent mechanisms that can generate a similar diagnostic derivative signature during fracture closure. Both are caused by an excess stored volume of \ufb02  uid in the fracture at shut-in relative to the \nexpected surface area of the fracture for a planar, constant-height geometry model. \nTraditionally this signature has been called \u201cfracture height \nrecession\u201d. The usual model assumes that leakoff occurs only through a thin permeable bed and that the fracture extends in height to cover impermeable strata with no leakoff. At shut-in there is a large volume of fluid stored in the fracture and the leakoff rate relative to the stored volume is small, hence the rate of pressure decline is likewise small. As the fracture empties, the rate of leakoff"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887624-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 5, "chroma:document": "relative to the remaining stored fluid accelerates and the pressure declines more rapidly. If the fracture height changes during leakoff, the fracture compliance may also decrease, adding to the rate of pressure loss.\nHowever, the same signature is observed in many cases where \nfracture height growth out of zone is not observed by tracers, inclinometer, or micro-seismic mapping. Some of these cases show treating behavior similar to PDL cases, with a tendency for rapid screenout and difficulty placing high proppant concentration slur-ries. These observations suggest that another mechanism may be responsible for the same diagnostic derivative signature. The alter-nate mechanism is called \u201ctransverse fracture storage\u201d. \nIn transverse fracture storage a secondary fracture set is opened"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887674-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 5, "chroma:document": "In transverse fracture storage a secondary fracture set is opened \nwhen the fluid pressure exceeds the critical fissure-opening pres-sure, just as in PDL. As the secondary fractures dilate they create a storage volume for fluid which is taken from the primary hydraulic fracture. While the fracture storage volume increases, leakoff can also be accelerated so PDL and storage are aspects of the same coupled mechanism of fissure dilation. The relative magnitude of the enhanced leakoff and storage mechanisms determines whether the G-function derivatives show PDL or storage. Numerical model-ing studies indicate that the storage mechanism can easily domi-nate even large PDL.\nAt shut-in the secondary fractures will close before the primary"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8876ce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 5, "chroma:document": "At shut-in the secondary fractures will close before the primary \nfracture because they are held open against a stress higher than the minimum in-situ horizontal stress. As they close fluid will be expelled from the transverse storage volume back into the main fracture decreasing the normal rate of pressure decline and, in effect, supporting the observed shut-in pressure by re-injection of stored fluid. Accelerated leakoff can still occur at the same time but if the storage and expulsion mechanism exceeds the enhanced leakoff rate then the only signature observed during falloff will be storage. In many cases a period of linear, constant area, constant matrix perme-ability dominated leakoff will occur after the end of storage. \nG-Function Analysis With Storage. The characteristic G-function \nderivative signature is a \u201cbelly\u201d below the straight line through the origin and tangent to the semilog derivative of p\nw vs. G at the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887728-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 5, "chroma:document": "derivative signature is a \u201cbelly\u201d below the straight line through the origin and tangent to the semilog derivative of p\nw vs. G at the \npoint of fracture closure. Fig. 19  shows an example of slight to \nmoderate storage. In Fig. 19, fracture closure, indicated by the same departure of the tangent line from the semilog derivative, occurs just after the end of the storage effect. \nSqrt(t) Analysis With Storage or Height Recession. The sqrt( t) \nplot (Fig. 20)  shows a clear indication of closure based on both the \nfirst-derivative inflection point and the semilog derivative curve. Picking closure in the case of storage is not generally a problem.\nThe storage model, whether caused by height recession or"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887778-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 5, "chroma:document": "The storage model, whether caused by height recession or \ntransverse fractures, requires that a larger volume of fluid must be leaked-off to reach fracture closure than is expected for a single planar constant-height fracture. In either case the time to reach fracture closure is delayed by the excess fluid volume that must be lost. Any estimation of reservoir permeability will give an incorrect result if the uncorrected closure time (either G\nc or time-to closure 0 5 10 15 20 25 30\nG (Time)840086008800900092009400960098001000010200\n0255075100125150\n1\nP vs. G\nGdP/dG vs. G\ndP/dG vs. GPressure\nDerivatives\nFig. 16\u2014Tip extension G-function plot.1/25/200704:00 08:00 12:00 16:00\n1/25/200720:00\nTime840086008800900092009400960098001000010200\n0102030405060708090100\n1Incorrect ClosurePressure\nDerivativesP vs. \u221at xdP/dxvs. \u221atdP/dxvs. \u221at\nFig. 17\u2014Tip extension sqrt( t) plot.\n2 3 4 56789 2 3 4 56789 2 3 4 56789 21 10 100 1000\nTime (0 = 33.7)23456789234567892345\n101001000"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8877d2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 5, "chroma:document": "Fig. 17\u2014Tip extension sqrt( t) plot.\n2 3 4 56789 2 3 4 56789 2 3 4 56789 21 10 100 1000\nTime (0 = 33.7)23456789234567892345\n101001000\n (m = 0.25)  BH ISIP = 10000 psi 1Delta-Pressure and Derivative\u0394P vs. \u0394t\n\u0394td\u0394P/d\u0394tv s .  \u0394t\nFig. 18\u2014Tip extension log-log plot."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88782c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 6, "chroma:document": "402 August 2009 SPE Production & Operationsin minutes, tc) is used. The observed closure time must be corrected \nby multiplying by the storage ratio, rp. The magnitude of rp can \nbe determined by taking the ratio of the area under the G-function semilog derivative up to the closure time, divided by the area of the right-triangle formed by the tangent line through the origin at closure. For normal leakoff and PDL the value of r\np is set to 1.0 \neven though the ratio of the areas will be greater than 1 for the PDL case. It is possible that the closure time for PDL leakoff is proportional to the composite system permeability including both the matrix and fractures. For severe cases of storage r\np can be as \nlow as 0.5 or less. \nLog-Log Pressure Derivative With Storage. Fig. 21  shows"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88787c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 6, "chroma:document": "p can be as \nlow as 0.5 or less. \nLog-Log Pressure Derivative With Storage. Fig. 21  shows \nthe log-log plot of pressure difference and semilog derivative for the storage case. Prior to closure, and while transverse storage is dominant, the semilog derivative approaches a unit slope, with the pressure difference curve nearly parallel. In some cases the two curves lie together on a single unit-slope line. In this case the curves are separated slightly and the slope is not exactly 1.0. After closure the reservoir transient signature is defined as in the previ-ously presented cases. All fracture storage effects are eliminated and the reservoir pseudolinear flow period is shown by a \u22121/2 slope with a pseudoradial flow period indicated by a \u22121 slope of the semi-log derivative. \nConclusions\nThe use of prefrac injection/falloff diagnostic tests has become"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8878d6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 6, "chroma:document": "Conclusions\nThe use of prefrac injection/falloff diagnostic tests has become \ncommonplace. Many important decisions regarding fracture treat-ment 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 misapplied, leading to incorrect \ninterpretations. The analyses presented here lead to the following conclusions: 1.  With consistent application of all available pressure decline \ndiagnostics, a single unambiguous determination of fracture closure time and pressure can be made. \n 2.  A single, unique closure event can be identified on all diag-\nnostic plots. \n 3.  The conventional analysis of the sqrt( t) plot, using the inflec-\ntion point identified by the first derivative, gives incorrect indications of closure for cases of PDL and tip extension and should not be relied upon.\n 4.  A modified sqrt( t) analysis, using the semilog derivative, is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887926-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 6, "chroma:document": "4.  A modified sqrt( t) analysis, using the semilog derivative, is \nequivalent to the G-function analysis and helps avoid incorrect closure picks in cases of PDL and tip extension.\n 5.  Flow regimes can be identified using the semilog pressure \nderivative on the log-log plot of /H9004p\nwf \u2212 /H9004t during the shut-in \nperiod following the fracture injection test.\n 6.  As in conventional transient test analysis, a pseudolinear flow \nperiod is identified by parallel \u00bd slope lines, separated by 2x, on the log-log /H9004p\nwf \u2212 /H9004t plot up until fracture closure. \n 7.  Bilinear flow can be identified by parallel \u00bc slope lines \nseparated by 4x on the log-log /H9004pwf \u2212 /H9004t plot prior to fracture \nclosure.\n 8.  After closure the pseudolinear reservoir flow period is identi-\nfied by a \u22121/2 slope of the semilog derivative of the pressure difference on the log-log /H9004p\nwf \u2212 /H9004t plot, and a \u22123/2 slope of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887980-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 6, "chroma:document": "fied by a \u22121/2 slope of the semilog derivative of the pressure difference on the log-log /H9004p\nwf \u2212 /H9004t plot, and a \u22123/2 slope of \nthe first derivative of the pressure difference with shut-in time on the same plot.\n 9.  Pseudoradial flow is identified by a \u22121 slope of the semilog \nderivative on the log-log plot.\n10.  When a stable pseudolinear flow period exists, the after-clo-\nsure Cartesian plot of the linear flow function can be used to estimate reservoir pressure.\n11.  When a pseudoradial flow period exists, both the conventional \nHorner analysis and after-closure radial-flow analysis can be used to determine reservoir transmissibility and pore pressure.\nNomenclature\n A\nf = fracture area, L2, ft2\n B = formation volume factor, L3/L3, RB/STB\n ct = total compressibility, Lt2/m, psi\u22121\n Cac = after-closure storage, L4t2/m, bbl/psi\n Cbl = bilinear \ufb02  ow constant, m/Lt5/4, psi\u00b7hr3/4\n Cfbc = before-closure fracture storage, L4t2/m, bbl/psi"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8879d0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 6, "chroma:document": "Cbl = bilinear \ufb02  ow constant, m/Lt5/4, psi\u00b7hr3/4\n Cfbc = before-closure fracture storage, L4t2/m, bbl/psi\n Cpl = pseudolinear \ufb02  ow constant, m/Lt3/2, psi\u00b7hr1/2 \n Cpr = pseudoradial \ufb02  ow constant, m/Lt, psi\u00b7hr \n FL = linear \ufb02  ow time function, dimensionless \n FR = radial \ufb02  ow time function, dimensionless 5 10 15 20\nG (Time)750080008500900095001000010500\n0200400600800100012001400160018002000\n1\nP vs. G\nGdP/dG vs. G\ndP/dG vs. GFracture ClosurePressure\nDerivatives\nFig. 19\u2014Storage G-function plot.1/24/200702:00 04:00 06:00 08:00\n1/24/200710:00\nTime750080008500900095001000010500\n0100200300400\n1Pressure\nDerivativesP vs. \u221at\nxdP/dxvs. \u221at\ndP/dxvs. \u221atFracture Closure\nFig. 20\u2014Storage sqrt( t) plot.\n2 3 456789 2 3 456789 2 3 456789 2 3 4560.1 1 10 100\nTime (0 = 9.416667)234567892345678923\n101001000\n (m = 0.5)  (m = \u20130.5)  BH ISIP = 10000 psi 1Delta-Pressure and Derivative\u0394P vs. \u0394t\n\u0394td\u0394P/d\u0394tv s .  \u0394t\nFig. 21\u2014Storage log-log plot."}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 7, "chroma:document": "August 2009 SPE Production & Operations 403 g = loss-volume function, dimensionless \n G = G-function, dimensionless \n h = height, L, ft \n k = permeability, L2, md \n Lf = fracture half-length, L, ft \n mH = slope of data on Horner plot, m/Lt2, psia\n mL = slope of data on pseudolinear \ufb02  ow graph, m/Lt2, psia\n mR = slope of data on pseudoradial \ufb02  ow graph, m/Lt2, psia\n p = pressure, m/Lt2, psia\n pwf = fracture pressure measured at wellbore, m/Lt2, psia\n q = \ufb02 ow rate, L3/t, bbl/D\n Qt = total injection volume, L3, bbl\n rp = storage ratio, dimensionless\n Sf = fracture stiffness, m/L2t2, psi/ft\n t = time, hr\n ta = adjusted pseudotime, hr\n /H9252 = constant, dimensionless\n /H9004 = difference, dimensionless\n /H9262 = viscosity, m/Lt, cp\n /H9278 = porosity, dimensionless\n /H9273 = constant, dimensionless\nSubscripts\n a = adjusted\n c = closure\n D = dimensionless\n e = end of injection\n f = \ufb01 ltrate\n p = pumping\n w = wellbore\n z = process zone\n 0 = end of injection\nAcknowledgments"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887ab6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 7, "chroma:document": "D = dimensionless\n e = end of injection\n f = \ufb01 ltrate\n p = pumping\n w = wellbore\n z = process zone\n 0 = end of injection\nAcknowledgments\nThe authors would like to thank Kumar Ramurthy, Halliburton, \nMike Conway, Stim-Lab, and Stuart Cox, Marathon, for their discussion and contribution to the procedures described. Sincere thanks are also due to the many operators whose diligence in prefrac testing has allowed these diagnostic analysis procedures to be developed and tested.\nReferences\nBarree, R.D. 1998. Applications of Pre-Frac Injection/Falloff Tests in \nFissured Reservoirs\u2014Field Examples. Paper SPE 39932 presented at the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium, Denver, 5\u20138 April. DOI: 10.2118/39932-MS.\nBarree, R.D. and Mukherjee, H. 1996. Determination of Pressure Depen-\ndent Leakoff and its Effect on Fracture Geometry. Paper SPE 36424 presented at the SPE Annual Technical Conference and Exhibition, Denver, 6\u20139 October. DOI: 10.2118/36424-MS."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887ba6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 7, "chroma:document": "Castillo, J.L. 1987. Modified Fracture Pressure Decline Analysis Includ-\ning Pressure-Dependent Leakoff. Paper SPE 16417 presented at the Low-Permeability Reservoirs Symposium, Denver, 18\u201319 May. DOI: 10.2118/16417-MS.\nCinco-Ley, H. and Samaniego-V ., F. 1981. Transient Pressure Analysis for \nFractured Wells. J. Pet Tech  33 (9): 1749\u20131766. SPE-7490-PA. DOI: \n10.2118/7490-PA.\nCinco-Ley, H., Kuchuk, F., Ayoub, J., Samaniego-V ., F., and Ayestaran, \nL. 1986. Analysis of Pressure Tests Through the Use of Instantaneous Source Response Concepts. Paper SPE 15476 presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 5\u20138 Octo-ber. DOI: 10.2118/15476-MS.\nCraig, D.P. and Blasingame, T.A. 2006. Application of a New Fracture-\nInjection/Falloff Model Accounting for Propagating, Dilated, and Closing Hydraulic Fractures. Paper SPE 100578 presented at the SPE Gas Technology Symposium, Calgary, 15\u201317 May. DOI: 10.2118/ 100578-MS."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887c0a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 7, "chroma:document": "Hagoort, J. 1981. Waterflood-induced hydraulic fracturing. PhD thesis, \nDelft Technical University, Delft, The Netherlands.Koning, E.J.L. and Niko, H. 1985. Fractured Water-Injection Wells: A \nPressure Falloff Test for Determining Fracture Dimensions. Paper SPE 14458 presented at the SPE Annual Technical Conference and Exhibi-tion, Las Vegas, Nevada, USA, 22\u201325 September. DOI: 10.2118/14458-MS.\nNolte, K.G. 1979. Determination of Fracture Parameters from Fractur-\ning Pressure Decline. Paper SPE 8341 presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, USA, 23\u201326 September. DOI: 10.2118/8341-MS.\nSettari, A. 2000. Coupled Fracture and Reservoir Modeling. Presented at \nthe Workshop on Three Dimensional and Advanced Hydraulic Frac-ture Modeling, Fourth North American Rock Mechanics Symposium, Seattle, Washington, USA, 29 July.\nTalley, G.R., Swindell, T.M., Waters, G.A., and Nolte, K.G. 1999. Field"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887c64-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 7, "chroma:document": "Talley, G.R., Swindell, T.M., Waters, G.A., and Nolte, K.G. 1999. Field \nApplication of After-Closure Analysis of Fracture Calibration Tests. Paper SPE 52220 presented at the SPE Mid-Continent Operations Symposium, Oklahoma City, Oklahoma, USA, 28\u201331 March. DOI: 10.2118/52220-MS.\nAppendix A\u2014Definition of Diagnostic \nFunctions\nThe G-Function.  The G-function is a representation of the elapsed \ntime after shut-in normalized to the duration of fracture extension. Corrections are made for the superposition of variable leakoff times while the fracture is growing. The form of the G-function used in this paper assumes high \ufb02  uid ef\ufb01  ciency in low-permeability \nformations. Under that assumption the surface area of the fracture is assumed to vary linearly with time during fracture propaga-tion. The dimensionless pumping time used in the G-function is de\ufb01 ned as:\n/H9004tt t t\nDp p=\u2212()/.   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-l)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887cf0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 7, "chroma:document": "/H9004tt t t\nDp p=\u2212()/.   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (A-l)\nThe elapsed total time from the start of fracture initiation (not \nstart of pumping) is t and the total pumping time (elapsed time from fracture initiation to shut-in) in consistent time units is t\nP. For \nthe assumption of low leakoff the dimensionless time ( /H9004tD) is used \nto compute an intermediate function:\ngt t tDD D/H9004/H9004 /H9004() =+() \u2212 \u23a1\u23a3\u23a4\u23a64\n3115 15 . ..   . . . . . . . . . . . . . . . . . .(A-2)\nThe G-function used in the diagnostic plots is derived from the \nintermediate function as follows:\nGt gt gDD/H9004/H9004() = () \u2212 \u23a1\u23a3\u23a4\u23a64\n0/H9266,  . . . . . . . . . . . . . . . . . . . . . . .(A-3)\nwhere g0 is the dimensionless loss-volume function at shut-in ( t = tp \nor /H9004tD = 0). All derivatives are calculated using a central difference \nfunction of pressure and G-function (normalized shut-in time).\nAfter-Closure Analysis and Flow Regime Identi\ufb01  cation.  After-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887d4a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 7, "chroma:document": "function of pressure and G-function (normalized shut-in time).\nAfter-Closure Analysis and Flow Regime Identi\ufb01  cation.  After-\nclosure pressure decline analysis requires the identi\ufb01  cation of fully-\ndeveloped reservoir pseudolinear and pseudoradial transient \ufb02  ow \nregimes. The \ufb02  ow regimes can be identi\ufb01  ed by characteristic slopes \non a log-log plot of observed falloff pressure minus reservoir pressure, (p\nw(t) \u2212 pi), vs. the square of the linear-\ufb02  ow time function ( FL2) and \nthe semilog derivative, (X*dY/dX), of the pressure difference curve Talley et al.). It is important to note that the guess of reservoir pressure, p\ni, used in construction of the \ufb02  ow regime plot severely impacts the \nslope and magnitude of the pressure difference curve. The pressure derivative, because of the difference function used to generate it, is not affected by the initial guess of reservoir pressure. \nThe linear-flow time function is defined by:\nFt tt\ntfor t tLcc\nc ,s i n() =\u2265\u2212 21"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887d9a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 7, "chroma:document": "The linear-flow time function is defined by:\nFt tt\ntfor t tLcc\nc ,s i n() =\u2265\u2212 21\n/H9266.  .  . . . . . . . . . . . . . . . . .(A-4)\nThe linear-flow function also requires an accurate determina-\ntion of the time required after shut-in to reach fracture closure, tc."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887dea-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 8, "chroma:document": "404 August 2009 SPE Production & OperationsIn the pseudolinear flow period the slope of the derivative curve \non the log-log plot should be \u00bd. For the correct estimate of reser-voir pore pressure, the pressure difference curve should also have a slope of \u00bd and should be exactly twice the magnitude of the derivative. If a stable pseudolinear flow period is identified then a Cartesian plot of observed pressure during the falloff, p\nw(t), vs. \nFL should yield a straight line with intercept equal to the reservoir \npore pressure, pi, and with a slope of mL. \npt p m Ft twi L L c()\u2212= (),.   . . . . . . . . . . . . . . . . . . . . . . . . .(A-5)\nIf a pseudoradial flow period exists, the slope of the derivative \nand correct pressure difference curves on the log-log flow regime plot should both be 1.0 and the two curves should coincide. In the pseudoradial flow period, a Cartesian plot of pressure vs. F\nR should \nalso yield a straight line with intercept equal to pi and slope of mR."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887e44-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 8, "chroma:document": "R should \nalso yield a straight line with intercept equal to pi and slope of mR. \npt p m Ft twi R R c()\u2212= (),.   . . . . . . . . . . . . . . . . . . . . . . . . .(A-6)\nIn these equations, tc is the time to fracture closure with time \nzero set as the beginning of fracture extension, pi is the initial reser-\nvoir pressure, and mR is the Cartesian slope of the \u201ccorrect\u201d straight \nline. The radial-flow function ( FR) is given by (Talley et al.)\nFt tt\nttRcc\nc,l n , .() =+\u2212\u239b\n\u239d\u239c\u239e\n\u23a0\u239f=\u22451\n4116162/H9273/H9273/H9266.  . . . . . . . . . . .(A-7)\nIn the properly identified pseudoradial flow period the reservoir \nfar-field transmissibility can be determined from the slope, fracture closure time, and volume injected during the test.\nkh Q\nmtt\nRc /H9262=251 000, .  . . . . . . . . . . . . . . . . . . . . . . . . . . . . .(A-8)\nIn Eq. A-8, the permeability, k, is in md, net pay thickness, h, \nis in feet, far-field mobile fluid viscosity,  /H9262, in cp, tc in minutes,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887e94-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 8, "chroma:document": "In Eq. A-8, the permeability, k, is in md, net pay thickness, h, \nis in feet, far-field mobile fluid viscosity,  /H9262, in cp, tc in minutes, \nand the volume injected during the test, Qt, is in bbls, and the \nslope, mR, is in psi. \nHorner Analysis.  The conventional Horner analysis uses a Cartesian \nplot of observed pressure vs. Horner time, ( tp + /H9004t)//H9004t, with all times \nin consistent units. The fracture propagation time is tp and the elapsed \nshut-in time is /H9004t. As shut-in time approaches in\ufb01  nity the Horner \ntime function approaches 1. A straight-line extrapolation of the Horner plot to the intercept at a Horner time of 1.0 gives an estimate of reservoir pressure. The slope of the correct straight-line extrapola-tion, m\nH, can be used to estimate reservoir transmissibility:\nkh q\nmH /H9262=() 162 6 1440..   . . . . . . . . . . . . . . . . . . . . . . . . . . . .(A-9)\nThe flow rate in Eq. A-9 is assumed to be in barrels per minute"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887eee-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 8, "chroma:document": "The flow rate in Eq. A-9 is assumed to be in barrels per minute \nand is the average rate for the time the fracture was extending. In both Eqs. A-8 and A-9, the viscosity is the far-field mobile fluid viscosity. The propagation of the transient in pseudoradial flow occurs at a great distance from the fracture and is not affected by the injected fluid viscosity.\nThe major problem with the Horner analysis is that the results \nare only valid if the data used to extrapolate the apparent straight line are actually in fully developed pseudoradial flow. There is no way to determine the validity of the Horner analysis or to determine the flow regime within the Horner plot itself.\nG-Function Permeability Estimate.  An empirical function to \napproximate formation permeability has been derived from numer-ous numerical simulations of fracture closure. The correlation is based on the observed G-function time at fracture closure:\nkp\ncGE rfz\ntcp=\n\u239b\n\u239d\u239c\u239e\n\u23a0\u239f0 0086 0 01\n0 03819 6..\n../H9262"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887f3e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 8, "chroma:document": "kp\ncGE rfz\ntcp=\n\u239b\n\u239d\u239c\u239e\n\u23a0\u239f0 0086 0 01\n0 03819 6..\n../H9262\n/H9278.   . . . . . . . . . . . . . . . . . . . . . .(A-10)The rate of fluid loss from the fracture before closure is dominated \nby the mobility of the injected fluid instead of the far-field viscosity. The total mobility of the injected fluid during leakoff is dependent on the viscosity of the injected fluid at leakoff temperature and the relative permeability to the leakoff fluid. The reservoir fluid and its residual saturation in the invaded region will have some effect on the leakoff fluid mobility. As a general rule, an assumed injected fluid viscosity of 1.0 cp is used to incorporate the effects of reservoir temperature and relative permeability in the invaded zone.\nNote that the correlation gives permeability and not kh. The \ntime to closure is related to fracture volume vs. created area so both the fracture height and length do not appear in the equation. The process zone stress, P"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887f8e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 8, "chroma:document": "z, is the net fracture extension pressure \nabove closure pressure, pc, or pz = pISIP \u2212 pc. The net extension pres-\nsure and Young\u2019s Modulus provide a relationship between facture volume (width) and surface area during pumping.\nThe other parameters in Eq. A-10 are defined, except the stor-\nage ratio, r\np. This parameter represents the amount of excess fluid \nthat must be leaked-off to reach fracture closure when the fracture geometry deviates from the normally assumed constant-height pla-nar fracture. The storage ratio, r\np, is the ratio of the area under the \nG-function semilog derivative up until closure divided by the area of the triangle defined by the straight-line (normal leakoff) tangent to the semilog derivative at closure. For normal matrix leakoff and PDL, r\np is therefore 1.0. For the transverse storage and height recession \nsignature, rp is some value less than 1.0. The observed G-function \nclosure time ( Gc) is always delayed by the excess fluid volume in the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b887fe8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 8, "chroma:document": "signature, rp is some value less than 1.0. The observed G-function \nclosure time ( Gc) is always delayed by the excess fluid volume in the \nfracture for either height recession or transverse storage. Likewise the apparent time to closure used in the after-closure analysis will be delayed and will cause errors in the reservoir transmissibility estimate. The closure time should be corrected by multiplying by r\np \nfor all permeability and transmissibility estimates. \nAppendix B\u2014Analytical Solutions and the \nLog-Log Diagnostic Graph\nLinear and Bilinear Flow Before Closure.  Hagoort (1981) developed \na before-closure analytical solution accounting for both storage and linear formation \ufb02  ow. Koning and Niko (1985) write the solution as\npwDtC ee r f c tDf b c Dt\nDD =\u2212\u239b\n\u239d\u239c\u239e\n\u23a0\u239f \u2212 () () /H9266/H9266/H9252/H9252/H9004 /H9004/H9004\n212\n2, \n . . . . . . . . . . . . . . . . . . . . . . (B-1)\nwhere\npwDtkhpt pt t\nqBDwe we()() ( )\n./H9004/H9004=\u2212+ ()\n141 2 /H9262,   . . . . . . . . . . . . . . (B-2)"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888038-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 8, "chroma:document": "where\npwDtkhpt pt t\nqBDwe we()() ( )\n./H9004/H9004=\u2212+ ()\n141 2 /H9262,   . . . . . . . . . . . . . . (B-2)\n/H9004/H9004tkt\ncLD\ntf=0 0002637\n2.\n/H9278/H9262,  . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-3)\n/H9252/H9266=2\nCfbcD,  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-4)\nand\nCC\nch LC\nch LfbcDfbc\ntffbc\ntf==5 615\n20 8936\n22..\n/H9266/H9278 /H9278.  . . . . . . . . . . . . . . . . . . . (B-5)\nHere, Cfbc is the before-closure fracture storage constant, which is \ndefined as (Craig and Blasingame 2006)\nCA\nSfbcf\nf=2\n5 615.,   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-6)\nwhere Af is the fracture area (one wing), and  Sf is the fracture \nstiffness."}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888088-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 9, "chroma:document": "August 2009 SPE Production & Operations 405Hagoort\u2019s solution predicts that the before-closure falloff is a \ncombination of fracture storage and linear flow. As fracture storage becomes small, C\nfbcD\u21920, linear flow will dominate the before-\nclosure pressure falloff. In most \"hard rock\" environments, CfbcD \nis small, and for a fracture-injection/falloff sequence with /H9004t >> te \nand long closure times, \npt pt t twe we() ( )\u2212+ \u221d /H9004 ,  . . . . . . . . . . . . . . . . . . . . . . . . . (B-7)\nwhere t = te + /H9004t, and pw(te) is the instantaneous shut-in pressure. \nDefine a fracture-pressure difference as\n/H9004/H9004pp t p ttw f we we=\u2212 + () ( ) ,  . . . . . . . . . . . . . . . . . . . . . . . (B-8)\nand a log-log graph of /H9004pwf vs. t will exhibit a \u00bd slope during \nlinear flow before closure. An analytical before-closure bilinear flow solution accounting for fracture tip extension during shut-in does not exist, but field data suggest that during before-closure bilinear flow"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 9, "chroma:document": "/H9004/H9004ptwf\u221d()14,  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-9)\nand a log-log graph of /H9004pwf vs. t will exhibit a \u00bc slope during \nbilinear flow before closure.\nPseudoradial, Pseudolinear, and Bilinear Flow After Closure.  \nCraig and Blasingame (2006) developed an analytical solution for a fracture-injection/falloff sequence with a propagating and closing hydraulic fracture, and they derived the \u201ccomplete\u201d after-closure impulse solutions accounting for fracture storage. The after-closure impulse solution for pseudoradial \ufb02  ow is written as \npt t pkhQpwsDCacpwe it ().( )() ( +\u2212 = +\u2212 /H9004141 2 24\n200/H9262pp\ntti\ne) . ( )+1\n/H9004\n . . . . . . . . . . . . . . . . . . . . . (B-10)\nFor after-closure pseudolinear flow,\npt t p\nhLQ\npwwe i\nft()\n.( ) .+\u2212\n=+/H9004\n141 2 24 0 0002637\n21 /H9266\nssDCacppi () ( )00\u2212\u239b\n\u239d\u239c\u239e\n\u23a0\u239f\n\u00d7+\u239b\n\u239d\u239c\u239e\n\u23a0\u239f/H9262\n/H9278ckt tte112\n/H9004,   . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-11)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888150-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 9, "chroma:document": "21 /H9266\nssDCacppi () ( )00\u2212\u239b\n\u239d\u239c\u239e\n\u23a0\u239f\n\u00d7+\u239b\n\u239d\u239c\u239e\n\u23a0\u239f/H9262\n/H9278ckt tte112\n/H9004,   . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-11)\nand for after-closure bilinear flow,\npt t pwe i()\n.( ) (. ) (. )+\u2212\n=/H9004\n141 2 24 0 6125 0 000263714\nkkwQ\npp Cac fft\ni +\u2212\u239b\n\u239d\u239c\u239e\n\u23a0\u239f()034/H9262\n\u00d7\u239b\n\u239d\u239c\u239e\n\u23a0\u239f+\u239b\n\u239d\u239c\u239e\n\u23a0\u239f1114 34\n/H9262ck t tte /H9004.   . . . . . . . . . . . . . . . . . . . . . . . (B-12)For convenience, define a constant pseudoradial flow term as\nCkhQpwsDCacppprti = +\u2212()141 2 24\n200.( )() ( )/H9262.   . . . . . (B-13)\nFor pseudolinear flow, a constant term is defined as\nC\nhLQ\npwsDCacpl\nft=+141 2 24 0 0002637\n21\n0.( ) .\n() (/H9266\nppp ck i t 012\n\u2212\u239b\n\u239d\u239c\u239e\n\u23a0\u239f\u239b\n\u239d\u239c\u239e\n\u23a0\u239f )./H9262\n/H9278\n . . . . . . . . . . . . . . . . . . . . . (B-14)\nSimilarly, for bilinear flow a constant term is written as\nC\nkwQ\nbl\nfft=+141 2 24 0 6125 0 000263714.( ) (. ) (. )\n(ppp Cacck i t 034141\n\u2212\u239b\n\u239d\u239c\u239e\n\u23a0\u239f\u239b\n\u239d\u239c\u239e\n\u23a0\u239f ). /H9262/H9262\n . . . . . . . . . . . . . . . . . . . . . (B-15)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8881aa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 9, "chroma:document": "(ppp Cacck i t 034141\n\u2212\u239b\n\u239d\u239c\u239e\n\u23a0\u239f\u239b\n\u239d\u239c\u239e\n\u23a0\u239f ). /H9262/H9262\n . . . . . . . . . . . . . . . . . . . . . (B-15)\nWith the new definition, and defining a reservoir-pressure differ-\nence, /H9004pw = pw(t) \u2212 pi, the pseudoradial-flow impulse solution can \nbe written as\n/H9004pC twp r=\u22121.   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-16)\nSimilarly, the linear-flow impulse solution can be written as\n/H9004pC twp l=\u221212/,   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-17)\nand the bilinear-flow impulse solution can be written as\n/H9004pC twb l=\u221234/.   . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-18)\nThe derivatives with respect to t are written for after-closure \npseudoradial flow as, \n\u2212\u2202\n\u2202=\u2212 /H9004p\ntCtw\npr()2,  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-19)\nfor after-closure pseudolinear flow as,\n\u2212\u2202\n\u2202=\u2212 /H9004p\ntCtw pl\n()/\n232,  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-20)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88822c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 9, "chroma:document": "for after-closure pseudolinear flow as,\n\u2212\u2202\n\u2202=\u2212 /H9004p\ntCtw pl\n()/\n232,  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-20)\nand for after-closure bilinear flow as,\n\u2212\u2202\n\u2202=\u2212 /H9004p\ntCtwb l\n()/ 3\n474.  . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-21)\nThe semilog derivatives and the impulse derivatives (Cinco-Ley \net al. 1986) are calculated by multiplying the after-closure deriva-tives by t and t\n2, respectively. Table B-1  shows the derivative terms \nfor each after-closure flow regime.\nLog-Log Diagnostic Graph.  Before-closure linear or bilinear \ufb02  ow \nare identi\ufb01  ed by the relationship between the fracture-pressure \nTABLE B-1\u2014AFTER-CLOSURE IMPULSE SOLUTIONS AND DERIVATIVES  \nFlow Regime  Impulse Solution  Derivative  Semilog Derivative  Impulse Derivative  \nBilinear     \nPseudolinear     \nPseudoradial"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888290-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 10, "chroma:document": "406 August 2009 SPE Production & Operationsdifference, /H9004pwf, and total time, t, but the after-closure \ufb02  ow regimes \nare identi\ufb01  ed by the relationship between the reservoir-pressure \ndifference, /H9004pw, and t, which requires knowing the initial reservoir \npressure, pi. However, by noting that\n\u2202\n\u2202=\u2212\u2202\n\u2202/H9004 /H9004 p\ntp\ntwf w,  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-22)\na log-log diagnostic graph can be prepared that is independent of \ninitial reservoir pressure but can be used to identify before- and \nafter-closure flow regimes. Table B-2  shows the characteristic \nslopes of each flow regime for log-log graphs of /H9004pwf vs. t, \u2202\u2202/H9004ptwf/ \nvs. t, tp twf\u2202\u2202/H9004 / vs. t, and tptwf2\u2202\u2202/H9004 / vs. t. \nIn gas reservoirs, log-log diagnostic graphs can be prepared \nby plotting /H9004pawf vs. ta, \u2202\u2202/H9004ptawf a/ vs. ta, tp taa w f a\u2202\u2202/H9004 / vs. ta, and \ntp taa w f a2\u2202\u2202/H9004 / vs. ta where adjusted pseudopressure is defined as\npaz\npipdp\nzp\n=\u239b\n\u239d\u239c\u239e\n\u23a0\u239f\u2320"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8882ea-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 10, "chroma:document": "tp taa w f a2\u2202\u2202/H9004 / vs. ta where adjusted pseudopressure is defined as\npaz\npipdp\nzp\n=\u239b\n\u239d\u239c\u239e\n\u23a0\u239f\u2320\n\u2321\u23ae\n\u23ae/H9262\n/H92620,  . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-23)\nand adjusted pseudotime is defined as\ntactidt\nctt\n=\u2320\n\u2321\u23ae\n\u23ae\u23ae()/H9262/H92620.  . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (B-24)\nBecause adjusted pseudopressure is a function of initial reser-\nvoir pressure, and if initial reservoir pressure is unknown, it\u2019s often helpful to complete the analysis in terms of pressure and time to obtain a first estimate of initial reservoir pressure before refining TABLE B-2\u2014LOG-LOG GRAPH CHARACTERISTIC SLOPES \nBefore Closure  After Closure  \nLog-Log Graph  Bilinear  Linear  Bilinear  Pseudolinear  Pseudoradial  \n 1/4 1/2 \u2013 \u2013 \u2013 \n \u20133/4 \u20131/2 \u20137/4 \u20133/2 \u20132 \n 1/4 1/2 \u20133/4 \u20131/2 \u20131 \n 5/4 3/2 1/4 1/2 0 \nthe estimate using diagnostic and interpretive graphs plotted in \nterms of adjusted pseudovariables.\nRobert D. Barree  is president and principal investigator of Barree"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88833a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 10, "chroma:document": "terms of adjusted pseudovariables.\nRobert D. Barree  is president and principal investigator of Barree \n& Associates, a consulting firm specializing in stimulation and well performance optimization. He has been involved in the development of hydraulic fracture technology since 1980 and is the primary author of the fully 3D hydraulic fracture simulator GOHFER. Barree is also the author of more than 50 technical publications and has served as SPE Distinguished Lecturer on the topic of new philosophies in hydraulic fracturing. He holds a BS degree in petroleum engineering from the Pennsylvania State University and PhD degree from Colorado School of Mines. Valencia Barree  is a partner at Barree & Associates LLC,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8883c6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 10, "chroma:document": "primarily working in well-test analysis and software development for the Stim Lab Proppant Consortium (including Predict-K) and GOHFER. Previously, she has focused on software development for core test analysis and instrumentation under the company name Custom Scientific Tools. Developed software includes tools for the acquisition and analysis of relative permeability and capillary pressure data, as well as many other customized testing procedures. She holds a BS degree in mineral engineering mathematics from the Colorado School of Mines. David P . Craig  currently writes a technical blog at www."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888420-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE-107877-PA Barree Method .pdf", "page": 10, "chroma:document": "refrac.net and is researching complex-fracture propagation models for Halliburton. In 2000, Craig was awarded the Henry Matson Technical Service Award from the Denver Section of SPE in \u201crecognition of significant contributions in engineering design and diagnostics of hydraulic fractures,\u201d and in 2006 he received the Award of Excellence for Outstanding Research from the Harold Vance Department of Petroleum Engineering at Texas A&M University. He holds a BS degree from Texas Tech University and MS and PhD degrees from Texas A&M University, all in petroleum engineering."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8884e8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 0, "chroma:document": "Copyright 2007, Society of Petroleum Engineers \n This paper was prepared for presentation at the 2007 SPE Rocky Mountain Oil & Gas Technology Symposium held in Denver, Colorado, U.S.A., 16\u201318 April 2007.  This 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, as \npresented, have not been reviewed by the Society of Petroleum Engineers and are subject to \ncorrection by the author(s). The material, as presented, does not necessarily reflect any"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888538-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 0, "chroma:document": "correction by the author(s). The material, as presented, does not necessarily reflect any \nposition of the Society of Petroleum Engineers, its officers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paper for commercial purposes without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than  300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O. Box 833836, Richardson, Texas 75083-3836 U.S.A., fax 01-972-952-9435. \n \nAbstract \nSince the introduction of the G-function derivative analysis, \npre-frac diagnostic injection tests have become a valuable and \ncommonly used technique. Unfo rtunately, the technique is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888588-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 0, "chroma:document": "pre-frac diagnostic injection tests have become a valuable and \ncommonly used technique. Unfo rtunately, the technique is \nfrequently misapplied or misinterpreted leading to confusion \nand misdiagnosis of fracturing parameters. This paper presents \na consistent method of analysis of the G-function, its derivatives, and its relationship to other diagnostic techniques \nincluding square-root(time) and log( \u2206p\nwf)-log( \u2206t) plots and \ntheir appropriate diagnostic de rivatives. Actual field test \nexamples are given for the most common diagnostic curve \nsignatures. \n  \nIntroduction \nPre-frac diagnostic injection te st analysis provides critical \ninput data for fracture design models, and reservoir \ncharacterization data used to pr edict post-fracture production. \nAn accurate post-stimulation prod uction forecast is necessary  \nfor economic optimization of th e fracture treatment design."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8885ce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 0, "chroma:document": "An accurate post-stimulation prod uction forecast is necessary  \nfor economic optimization of th e fracture treatment design. \nReliable results require an accurate and consistent interpretation of the test data. In many cases closure is \nmistakenly identified through misapplication of one or more \nanalysis techniques. In general, a single unique closure event \nwill satisfy all diagnostic pl ots or methods. All available \nanalysis methods should be used in concert to arrive at a consistent interpretation of fracture closure.  \nRelationship of the pre-closur e analysis to after-closure \nanalysis results must also be consistent. To correctly perform \nthe after-closure analysis the tr ansient flow regime must be \ncorrectly identified. Flow regime identification has been a \nconsistent problem in many analyses. There remains no \nconsensus regarding methods to identify reservoir transient flow regimes after fracture closure. The method presented here"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88861e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 0, "chroma:document": "consensus regarding methods to identify reservoir transient flow regimes after fracture closure. The method presented here \nis not universally accepted but appears to fit the generally assumed model for leakoff used in most fracture simulators. Four examples are presented to show the application of \nmultiple diagnostic analysis methods. The first illustrates the \nexpected behavior of normal fracture closure dominated by matrix leakoff with a constant fracture surface area after shut-\nin. The second example shows pressure dependent leakoff \n(PDL) in a reservoir with pressure-variable permeability or flow capacity, usually caused by natural or induced secondary \nfractures or fissures. The third example shows fracture tip \nextension after shut-in. These cases generally show definable fracture closure. The fourth example shows what has been \ncommonly identified as fractur e height recession during \nclosure, but which can also indicate variable storage in a \ntransverse fracture system."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888678-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 0, "chroma:document": "commonly identified as fractur e height recession during \nclosure, but which can also indicate variable storage in a \ntransverse fracture system. \nFor each example the analysis will be demonstrated using \nthe G-function and its diagnostic derivatives, the sqrt(time) and its derivatives, and the log-log plot of pressure change \nafter shut-in and its derivatives.\n1-4 When appropriate, the after-\nclosure analysis is presented for each case, as is an empirical \ncorrelation for permeability from the identified G-function \nclosure time.5 A critical part of the analysis is the realization \nthat there is a common event indi cating closure that should be \nconsistently identified by all diagnostic methods. To reach a conclusion all analyses must give consistent results.  \nThe goal of this paper is to provide a method for consistent \nidentification of after-closure flow regimes, an unambiguous"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8886be-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 0, "chroma:document": "The goal of this paper is to provide a method for consistent \nidentification of after-closure flow regimes, an unambiguous \nfracture closure time and stress, and a reasonable engineering estimate of reservoir flow capacity from the pressure falloff \ndata, without requiring assumptions such as a known reservoir \npressure. Other methods, based on sound transient test theory, require pressure difference curves based on the observed \nbottomhole pressure during falloff minus the \u201cknown\u201d \nreservoir pressure.\n5,8 While these methods are technically \ncorrect they can lead to confusin g results at times, especially \nin low permeability reservoirs when pore pressure is difficult \nto determine accurately prior to stimulation. \nThis is not a transient test analysis paper but is intended to \npresent a practical approach to analysis of real, and frequently marginal-quality, pre-fracture field test data. The techniques \napplied are based on some transient test theory. Some of the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88870e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 0, "chroma:document": "applied are based on some transient test theory. Some of the \nresults presented here are still under debate and development. The methods shown have been tested and, we believe, proven \nin the analysis of hundreds of  tests. Application of these \nmethods provides consistent analysis that helps to avoid \nmisinterpretation of falloff data, and give the most useful \ninformation available from diagnostic injection tests. \nStep-rate injection tests and th eir analysis are not included \nin the scope of this paper. Determination of the pressure-\ndependent leakoff coefficient is also not described here, as it \n \nSPE 107877 \nHolistic Fracture Diagnostics \nR.D. Barree, SPE, and V.L. Barree, Barree & A ssocs. LLC, and D.P. Craig, SPE, Halliburton 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: 6b88875e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 1, "chroma:document": "2  SPE 107877 \nhas been previously reported.3,4 Only the analysis of pressure \ndecline following shut-in of a fracture-rate injection test is \nconsidered. \n \nTransient Flow Regimes During and After Fracture \nClosure \nSeveral transient flow regimes may occur during a falloff test \nafter injection at fracture rate . The major flow regimes are \ngraphically illustrated in the classic paper by Cinco-Ley and \nSamaniego.6  \nImmediately after shut-in the pressure gradient along the \nlength of the fracture dissipates in a short-duration linear flow \nperiod. In a long fracture in low permeability rock the initial \nfracture linear flow can be follow ed by a bi-linear flow period \nwith the linear flow transient persisting in the fracture while \nreservoir linear flow occurs simu ltaneously.  After the fracture \ntransient dissipates the reservoir linear flow period can \ncontinue for some time, depending on the permeability of the reservoir and the volume of fluid stored in the fracture and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8887ae-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 1, "chroma:document": "continue for some time, depending on the permeability of the reservoir and the volume of fluid stored in the fracture and \nsubsequently leaked off duri ng closure. After closure the \npressure transient established around the fracture propagates \ninto the reservoir and transitions into elliptical, then \npseudoradial flow. Each of these flow regimes has a characteristic appearance on various diagnostic plots. \nFluid leakoff from a propagating fracture is normally \nmodeled assuming one-dimensional linear flow perpendicular to the fracture face. Settari has pointed out that in some cases \nof moderate reservoir permeability the linear flow regime may not occur, even during fracture extension and early leakoff.\n7 \nDuring fracture extension and shut-in the transient may \nalready be in transition to elliptical or pseudoradial flow.  In \nthis case analyses based on an  assumed pseudolinear flow \nregime will give incorrect results. In all cases an"}


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": 1, "chroma:document": "this case analyses based on an  assumed pseudolinear flow \nregime will give incorrect results. In all cases an \nunderstanding of the flow regime and its relation to the \nfracture geometry is critical to arriving at a consistent interpretation of the fracture falloff test. \n \nDiagnostic Derivative Examples \nFor each analysis technique various curves are used to help \ndefine closure, leakoff mechan isms, and after-closure flow \nregimes. On each plot the curves  are labeled as the primary (y \nvs. x), the first derivative ( \u2202y/\u2202x), and the semilog derivative \n(\u2202y/\u2202(lnx) or x \u2202y/\u2202x). For convenience th e primary curve is \nplotted on the left y-axis and all derivatives are plotted on the \nright y-axis for all Cartesian plots. For the log-log plot all \ncurves are shown on the same y-axis. \nFor pre-closure analysis, and consistent identification of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88884e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 1, "chroma:document": "curves are shown on the same y-axis. \nFor pre-closure analysis, and consistent identification of \nfracture closure, three techniques are illustrated for each example: G-function, Square-root of shut-in time, and log-log plot of pressure change with shut-in time. All these analyses \nbegin at shut-in. The instantaneous shut-in pressure (ISIP) is taken as the incipient fracture ex tension pressure for all cases. \nWhen there is significant wellbore afterflow (fluid expansion \nor continued low-rate injection), or severe near-well pressure \ndrop, the ISIP can be difficult to interpret accurately and may \nbe too high to represent actual fracture extension pressure. In \nall the examples in the paper the pressures have been offset to \nan approximate ISIP of 10,000 psi to remove any relation to the original field test data. The following sections detail the \ndata and analysis for the four  major leakoff type examples.  \nNormal Leakoff Behavior"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88889e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 1, "chroma:document": "data and analysis for the four  major leakoff type examples.  \nNormal Leakoff Behavior \nNormal leakoff is observed when the composite reservoir \nsystem permeability is constant. The reservoir may exhibit \nonly matrix permeability or have a secondary natural fracture \nor fissure overprint in which the flow capacity of the secondary fracture system does not change with pore pressure \nor net stress. After shut-in the fracture is assumed to stop propagating and the fracture su rface area open to leakoff \nremains constant during closure. \n \nNormal Leakoff G-Function \nAs noted in previous papers, the expected signature of the \nG-function semilog derivative is a straight-line through the \norigin (zero G-function and zero derivative).\n4 In all cases the \ncorrect straight line tangent to the semilog derivative of the \npressure vs. G-function curve must pass through the origin. \nFracture closure is identified by  the departure of the semi-log"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8888ee-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 1, "chroma:document": "pressure vs. G-function curve must pass through the origin. \nFracture closure is identified by  the departure of the semi-log \nderivative of pressure with respect to G-function (G \u2202pw/\u2202G) \nfrom the straight line through the origin. During normal \nleakoff, with constant fractu re surface area and constant \npermeability, the first derivative ( \u2202pw/\u2202G) should also be \nconstant.2 The primary pw vs. G curve should follow a straight \nline.1 The example in Figure 1 shows some slight deviation \nfrom the perfect constant leakoff but is a good example of the expected curve shapes with a clear indication of closure at \nG\nc=2.31. The closure event is marked by the dashed vertical \nline [1]. \n \n0 5 10 15 20 25\nG(Time)750080008500900095001000010500\n0200400600800100012001400160018002000\n1\nP vs. G\nGdP/dG vs. G\ndP/dG vs. GFracture ClosurePressure\nDerivatives\n \nFigure 1: Normal leakoff G-function plot \n \nNormal Leakoff Sqrt(t) Analysis \nThe sqrt( t) plot has frequently been misinterpreted when"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88893e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 1, "chroma:document": "Derivatives\n \nFigure 1: Normal leakoff G-function plot \n \nNormal Leakoff Sqrt(t) Analysis \nThe sqrt( t) plot has frequently been misinterpreted when \npicking fracture closure, even  for the simplest cases. The \nprimary pw vs. sqrt( t) curve should form a straight line during \nfracture closure, as with th e G-function plot. Some users \nsuggest that the closure is identified by the departure of the \ndata from the straight line trend, similar to the way the G-\nfunction closure is picked. This is incorrect and leads to a later \nclosure and lower apparent closure pressure. The correct indication of closure is the inflection point on the p\nw vs. sqrt( t) \nplot.  \nThe best way to find the inflection point is to plot the first \nderivative of pw vs. sqrt( t) and find the point of maximum 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: 6b88898e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 2, "chroma:document": "SPE 107877  3 \namplitude of the derivative. Many fracture-pressure analysis \nsoftware packages plot the inverse of the actual first derivative \nand show the inflection point as the minimum of the \nderivative. The plot in Figure 2, shows that the slope of the \npressure curve starts low, then increases and reaches a \nmaximum rate of decline at the inflection point, then decreases \nagain after closure. The first derivative curve in Figure 2 is \nplotted with the proper sign. The dashed vertical line [1] is the \nG-function closure pick that is synchronized in time and pressure with the sqrt( t) plot. Clearly the consistent closure \nlies at the inflection point and not at the point of departure from the straight line tangent to the pressure curve.  \nThe semilog derivative of the pressure curve is also shown \non the sqrt( t) plot. This curve is equivalent to the semilog \nderivative of the G-function for most low-perm cases. The closure pick falls at the departure from the straight line"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8889de-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 2, "chroma:document": "derivative of the G-function for most low-perm cases. The closure pick falls at the departure from the straight line \nthrough the origin on the semilog derivative of the P vs. sqrt( t) \ncurve. A single closure point mu st satisfy the requirement on \nboth the G-function and sqrt( t) plots. \n \n1/24/200704:00 08:00 12:00\n1/24/200716:00\nTime750080008500900095001000010500\n01002003004005006007008009001000\n1Pressure\nDerivativesP vs. \u221at\n\u221atdP/d\u221atv s .  \u221at\ndP/d\u221atv s .  \u221atFracture Closure\n \nFigure 2: Normal leakoff sqrt(t) plot \n \nNormal Leakoff Log-Log Pressure Derivative \nThe log-log plot of pressure change from ISIP versus shut-\nin time for the normal leakoff example is shown in Figure 3. \nThe heavy curve is the pressu re difference and the dashed \ncurve is its semilog derivative with respect to shut-in time. \nThe vertical dashed line is the unique closure pick from the G-\nfunction and sqrt( t) plot. It is common for the pressure \ndifference and derivative curves to be parallel immediately"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888a4c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 2, "chroma:document": "function and sqrt( t) plot. It is common for the pressure \ndifference and derivative curves to be parallel immediately \nbefore closure. The slope of these parallel lines is diagnostic \nof the flow regime established during leakoff before closure. \nIn many cases a near-perfect \u00bd slope is observed, strongly \nsuggesting linear flow from the fracture. In this example the \nslope is greater than \u00bd sugges ting possible linear flow coupled \nwith changing fracture/wellbor e storage (See Appendix B). \nThe separation of the two parallel lines always marks fracture \nclosure and is the final confirmation of a consistent closure \nidentification. \n 2 3 456789 2 3 456789 2 3 456789 2 3 4567890.1 1 10 100 1000\nTime (0 = 8.15)2345678923456789234\n101001000\n (m = -1)  (m = 0.632)  BH ISIP = 9998 psi 1Delta-Pressure and Derivative\u2206P vs. \u2206t\n\u2206td\u2206P/d\u2206t vs. \u2206t\nFracture ClosureRadial Flow\n \nFigure 3: Normal leakoff log-log plot \n \nAfter closure the semilog derivative curve will show a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888a9c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 2, "chroma:document": "\u2206td\u2206P/d\u2206t vs. \u2206t\nFracture ClosureRadial Flow\n \nFigure 3: Normal leakoff log-log plot \n \nAfter closure the semilog derivative curve will show a \nslope of -1/2 in a fully developed reservoir pseudolinear flow \nregime and a slope of -1 in fully developed pseudoradial flow.  \nIn the example the derivative slope is -1 indicating that \nreservoir pseudoradial flow was observed. The late-time data shows a drop in the derivative probably caused by wellbore \neffects such as gas entry and phase segregation. The use of the \nsemilog derivative of the log-log plot for after-closure flow regime identification, as well as closure confirmation, is a \npowerful new addition to fracture  pressure decline diagnostics. \n \nAfter-Closure Analysis for Normal Leakoff Example \nThe Talley-Nolte After-Closure Analysis (ACA) flow \nregime identification plot for the normal leakoff example is \nshown as Figure 4.\n5  The heavy solid line is the observed \nbottomhole pressure during the falloff minus the initial"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888aec-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 2, "chroma:document": "shown as Figure 4.\n5  The heavy solid line is the observed \nbottomhole pressure during the falloff minus the initial \nreservoir pressure. The slope of the semi-log derivative of the \npressure difference function (dashed line) is 1.0 during the \nidentified pseudoradial flow period. If a linear-flow period \nexisted in this data set a derivative slope of \u00bd would exist. It is \ncritical to remember that the sl ope of the pressure difference \ncurve on this plot is determined solely by the guess of \nreservoir pressure used to construct the plot. The slope of the \nderivative is not affected by the input reservoir pressure value. \n \n2 3 4 5 6 789 2 3 4 5 6 789 2 3 4 5 6 7890.001 0.01 0.1 1\nSquare Linear Flow (FL^2)234567892345678923456789\n10100100010000\n (m = 1) Delta-Pressure and Derivative\u2206P vs. FL2\nFL2d\u2206P/dFL2vs. FL2\u2206P=(pw-pr)\nStart of Radial Flow"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888b3c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 2, "chroma:document": "10100100010000\n (m = 1) Delta-Pressure and Derivative\u2206P vs. FL2\nFL2d\u2206P/dFL2vs. FL2\u2206P=(pw-pr)\nStart of Radial Flow\n \nFigure 4: Normal leakoff ACA log plot 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: 6b888b8c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 3, "chroma:document": "4  SPE 107877 \n \nIf a pseudoradial flow regime is identified, then the \nCartesian Radial Flow plot (Figure 5) can be used to \ndetermine reservoir far- field transmissibility, kh/\u00b5. The \nviscosity used is the far-field mobile fluid viscosity and h is \nthe estimated net pay height. For the analysis of the example \ndata kh/\u00b5 = 299 md-ft/cp. For gas viscosity at reservoir \ntemperature, kh=7.9 md-ft. For the assumed net pay, the \neffective reservoir permeability is 0.097 md.  \n \n \n0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8\nRadial Flow Time Function72007400760078008000820084008600880090009200\n (m = 4814.2) Results\nReservoir Pressure  = 7475.68 psi\nTransmissibility, kh/\u00b5 = 298.94991 md*f t\nkh = 7.94014 md*ft\nPermeability, k = 0.0968 md\nStart of Pseudo Radial Time = 2.15 hours 1Pressure\n \nFigure 5: Normal leakoff ACA radial flow plot \n \n \nHorner Analysis for Normal Leakoff Example \nIf a pseudoradial flow period is identified, then a \nconventional Horner plot can also be used to determine"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888bdc-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 3, "chroma:document": "If a pseudoradial flow period is identified, then a \nconventional Horner plot can also be used to determine \nreservoir transmissibility. In Figure 6 the Horner slope through \nthe radial flow data is 14411 psi. Using an average pump rate \nof 18.4 bpm, kh/\u00b5 = 298 md-ft/cp. For the assumed gas \nviscosity  kh=7.9 md-ft. Using the same assumed net gives \nk=0.097 md. This result is consistent with the ACA results.  \n \n \n2 31\nHorner Time72507500775080008250850087509000925095009750\n (m = 14411) \n  (Reservoir = 7476)  1Pressure\n \nFigure 6: Normal leakoff Horner Plot \n  \nG-Function Permeability Estimate \nAn empirical correlation has also been developed to \nestimate formation permeability from the G-function closure \ntime when after-closure data is not available. The correlation \nis described in detail in the Appendix. Figure 7 shows the G-function correlation permeability estimate for the observed \nclosure time and other input parameters. The permeability"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888c22-84a2-11ee-9ca1-0242ac1c000c
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metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 3, "chroma:document": "closure time and other input parameters. The permeability \nestimate of 0.097 md is consistent with the Horner and ACA results.   \n0.0010.010.1110100\n0 2 4 6 8 1 01 21 41 61 82 0\nGcData Input\nrp 1\n\u03c6 0.09 V/V\nct 7.50E-05 psi-1\nE3 . 5 M p s i\n\u00b5 1c p\nGc 2.44\nPz 966.0 psiEstimated Permeability = 0.0974 mdPermeability, md\n \nFigure 7: Normal leakoff permeability estimate \n \nPressure Dependent Leakoff \nPressure dependent leakoff (PDL) occurs when the fluid loss \nrate changes with pore pressure or net effective stress in the \nrock surrounding the fracture.  PDL is not caused by the \nnormal change in transient pressure gradient during leakoff. \nThis is part of the normal leakoff mode and is handled by the \none-dimensional linear flow solution of the diffusivity \nequation used to model fracture leakoff in a constant permeability system. The pressure dependence referred to here \nis a change in the transmissibility of the reservoir fissure or"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888c72-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 3, "chroma:document": "is a change in the transmissibility of the reservoir fissure or \nfracture system that dominates the fluid loss rate. PDL is only \napparent when there is substantial stress dependent \npermeability in a composite dual-permeability reservoir. \n \nG-Function for Pressure-Dependent Leakoff \nFigure 9 shows the G-function behavior expected for PDL. \nThe primary p\nw vs. G curve is concave upward and curved \nwhile PDL persists. The semilog derivative exhibits the \ncharacteristic \u201chump\u201d above the st raight line extrapolated to \nthe derivative origin. The end of PDL and the critical fissure \nopening pressure corresponds to the end of the \u201chump\u201d and \nthe beginning of the straight line representing matrix dominated leakoff. Fracture closure is still shown by the \ndeparture of the semilog derivative from the straight line \nthrough the origin."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888cc2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 3, "chroma:document": "departure of the semilog derivative from the straight line \nthrough the origin.  \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: 6b888d12-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 4, "chroma:document": "SPE 107877  5 \n0 2 4 6 8 10 12 14 16 18 20\nG(Time)8250850087509000925095009750100001025010500\n01002003004005006007008009001000\n21\nP vs. G\nGdP/dG vs. G\ndP/dG vs. GFracture ClosurePressure\nDerivatives\n \nFigure 9: PDL G-function plot \n \n \nSqrt(t) Analysis for PDL \nInterpretation of the sqrt( t) plot in PDL cases has often led \nto incorrect closure picks. Figu re 10 shows an expanded view \nof the sqrt( t) plot for the example with the curves scaled for \nbetter visibility. Note that the semilog derivative is nearly \nidentical in shape and informa tion content to the G-function \nsemilog derivative. It clearly shows the PDL \u201chump\u201d and \nclosure, which has been synchronized to the G-function result.  \nIncorrect closure picks on the sqrt( t) plot will not occur if \nthe semilog derivative is used. Problems arise when the first \nderivative is used exclusively to  pick closure. In PDL cases \nthe obvious derivative maximum, or most prominent inflection"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888d6c-84a2-11ee-9ca1-0242ac1c000c
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metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 4, "chroma:document": "derivative is used exclusively to  pick closure. In PDL cases \nthe obvious derivative maximum, or most prominent inflection \npoint, is caused by the changing leakoff associated with PDL \nand does not indicate fracture closure. The false closure \nindication is shown on the plot. Many fracture diagnostic tests \nhave been badly misdiagnosed because the early and incorrect \nclosure was picked because of dependence on only the sqrt( t) \nplot. This example clearly illustrates why all available \ndiagnostic plots must be used in concert to arrive at a single \nconsistent closure event.  \n \n1/24/200700:20 00:40 01:00 01:20 01:40\n1/24/200702:00\nTime82508500875090009250950097501000010250\n0100200300400500\n1False ClosurePressure\nDerivativesP vs. \u221at\n\u221atdP/d\u221at vs. \u221at\ndP/d\u221at vs. \u221atFracture Closure\n \nFigure 10: PDL Sqrt plot \n \n Log-Log Pressure Derivative for PDL Example \nFigure 11 shows the log-log plot for the PDL example. The \nnormal matrix leakoff period, following the end of PDL,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888dbc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 4, "chroma:document": "Figure 11 shows the log-log plot for the PDL example. The \nnormal matrix leakoff period, following the end of PDL, \nappears as a perfect \u00bd slope of the semilog derivative with a \nparallel pressure difference curve exactly 2-times the \nmagnitude of the derivative. The parallel trend ends at the identified closure time and pressure difference. In this \nexample a well-defined \u2212\u00bd slope, or reservoir pseudolinear \nflow period, is shown shortly after closure. The later data approach a slope of \u22121, which indicates pseudoradial flow has \nbeen established.  \n \n2 3 456789 2 3 456789 2 3 456789 2 3 4567890.1 1 10 100 1000\nTime (0 = 9.133333)23456789234567892\n101001000\n (m = 0.5) \n(m = -1) (m = -0.5)  BH ISIP = 10000 psi 1Pressure Difference and Derivative\u2206P vs. \u2206t\n\u2206td\u2206P/d\u2206tv s .  \u2206tFracture closureLinear Flow\nRadial Flow\n \nFigure 11: PDL log-log plot \n \nAfter-Closure Analysis for PDL Example \nThe ACA log-log plot (Figure 12) shows both the reservoir"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888e0c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 4, "chroma:document": "Radial Flow\n \nFigure 11: PDL log-log plot \n \nAfter-Closure Analysis for PDL Example \nThe ACA log-log plot (Figure 12) shows both the reservoir \nlinear and radial flow periods in their expected locations.  \n \n2 3 4 5 6789 2 3 4 5 6789 2 3 4 5 67890.001 0.01 0.1 1\nSquare Linear Flow (FL^2)234567892345678923456789\n10100100010000\n (m = 1) \n (m = 0.5) \n1 2 3Delta-Pressure and Derivative\u2206P vs. FL2\nFL2d\u2206P/dFL2vs. FL2\u2206P=(pw-pr)\nStart Linear Flow\nEnd Linear Flow\nStart Radial Flow\n \nFigure 12: PDL ACA log plot \n \nFigures 13 and 14 show the ACA Cartesian plots for the \nlinear and radial flow analyses. Both give consistent estimates \nof reservoir pore pressure. Th e pseudoradial flow analysis \ngives a transmissibility of 37.2 md-ft/cp and estimated \npermeability of 0.047 md.  \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
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id: 6b888e5c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 5, "chroma:document": "6  SPE 107877 \n0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0\nLinear Flow Time Function8000820084008600880090009200\n (m = 1438.5) \nResults\nReservoir Pressure = 8056.66 psi\nStart of Pseudo Linear Time = 15. 9\nEnd of Pseudo Linear Time = 54.3 9 1 2PressureStart Linear Flow End Linear Flow\n \nFigure 13: PDL ACA linear flow plot \n \n0.0 0.1 0.2 0.3 0.4 0.5 0.6\nRadial Flow Time Function8000820084008600880090009200\n (m = 11373) Results\nReservoir Pressure = 8068.81 psi\nTransmissibility, kh/\u00b5 = 37.21984 m\nkh = 0.93764 md*ft\nPermeability, k = 0.0469 md\nStart of Pseudo Radial Time = 11.2 6 1Pressure\n \nFigure 14: PDL ACA radial flow plot \n \nHorner Analysis for PDL Example \nFor an average pump rate of 6.7 bpm the Horner plot gives \nkh/\u00b5=35.72 md-ft/cp. The Horner estimated permeability is \n0.046 md compared to 0.047 md from the ACA Radial Flow \nanalysis. Pore pressure estimated from the Horner plot is also"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888ea2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 5, "chroma:document": "0.046 md compared to 0.047 md from the ACA Radial Flow \nanalysis. Pore pressure estimated from the Horner plot is also \nconsistent with both the linear and radial analyses because a well-developed pseudoradial flow period does exist in this \ncase. The vertical dotted line in  Figure 15 shows the start of \npseudoradial flow. If a pseudoradial flow period does not \nexist, extrapolation of an apparent straight-line on the Horner \nplot can give extremely inaccura te estimates of pressure and \nflow capacity.  1\nHorner Time8000810082008300840085008600870088008900\n (m = 43920) \n  (Reservoir = 8064)  1Pressure\n \nFigure 15: PDL Horner plot \n \n \nG-Function Permeability Estimate for PDL Example \nThe G-function permeability correlation for the PDL \nexample is shown in figure 16. It also gives a consistent \npermeability of 0.045 md. The impact of the accelerated \nleakoff during PDL gives an estimate of the composite \nreservoir effective permeability. Note that the injected fluid"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888ef2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 5, "chroma:document": "leakoff during PDL gives an estimate of the composite \nreservoir effective permeability. Note that the injected fluid \nviscosity is used for the permeability estimate based on \nclosure time.  \n \n0.0010.010.1110100\n0 2 4 6 8 1 01 21 41 61 82 0\nGcData Input\nrp 1\n\u03c6 0.08 V/V\nct 6.00E-05 psi-1\nE5 M p s i\n\u00b5 1c p\nGc 2.9\nPz 841.0 psiEstimated Permeability = 0.0453 mdPermeability, md\n \nFigure 16: PDL permeability estimate \n  \nFracture Tip Extension \nIn very low permeability reservoirs the decline in wellbore \npressure observed after shut-in may be caused by the \ndissipation of the pressure transient established in the fracture \nduring pumping. The near-well pressure decreases as the \nfracture closes, which results in a decrease of fracture width at \nthe well. The closing of the fracture volumetrically displaces \nfluid to the tip of the fracture, causing continued extension of the fracture length. Much of the pressure decline is therefore"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888f42-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 5, "chroma:document": "fluid to the tip of the fracture, causing continued extension of the fracture length. Much of the pressure decline is therefore \nnot related to leakoff but to the dissipation of the linear transient along the fracture length.  \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: 6b888f92-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 6, "chroma:document": "SPE 107877  7 \nG-Function Analysis for Tip Extension \nDuring fracture tip extension the G-function derivatives \nfail to develop any straight-line trends. The primary P vs. G \ncurve is concave upward, as is the first derivative. The \nsemilog derivative starts with a large positive slope and the \nslope continues to decrease w ith shut-in time, giving a \nconcave-down curvature.3,4 Figure 17 shows a typical case of \nfracture tip extension with minimal leakoff. This is another \ncase that is frequently misdiagnosed.  \n \n0 5 10 15 20 25 30\nG(Time)840086008800900092009400960098001000010200\n0255075100125150\n1\nP vs. G\nGdP/dG vs. G\ndP/dG vs. GPressure\nDerivatives\n \nFigure 17: Tip extension G-function plot \n \nSqrt(t) Analysis with Fracture Tip Extension \nMany times the first break in the semilog derivative curve \nhas been misinterpreted as a closure event. The mistake is \noften compounded by the use of the sqrt( t) plot. Figure 18 \nshows the sqrt( t) plot for the same data. The first derivative"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b888fe2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 6, "chroma:document": "often compounded by the use of the sqrt( t) plot. Figure 18 \nshows the sqrt( t) plot for the same data. The first derivative \nshows a large maximum very shortly after shut-in. This is \noften mistaken for closure. The semilog derivative on the \nsqrt(t) plot helps to avoid this mistaken closure pick, and \nshows the same continuously increasing trend as seen on the \nG-function semilog derivative plot. In low permeability \nsystems it is generally safe to assume that as long as the semilog derivative is still rising, the fracture has not yet \nclosed. This is not true in ve ry high permeability reservoirs \nand should always be checked using the log-log pressure difference plot.  \n \n1/25/200704:00 08:00 12:00 16:00\n1/25/200720:00\nTime840086008800900092009400960098001000010200\n0102030405060708090100\n1Incorrect ClosurePressure\nDerivativesP vs. \u221at xdP/dxvs. \u221atdP/dxvs. \u221at\n \nFigure 18: Tip extension sqrt(t) plot \n Log-Log Pressure Derivative Analysis with Tip Extension"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b88905a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 6, "chroma:document": "DerivativesP vs. \u221at xdP/dxvs. \u221atdP/dxvs. \u221at\n \nFigure 18: Tip extension sqrt(t) plot \n Log-Log Pressure Derivative Analysis with Tip Extension \nThe log-log plot of pressure change after shut-in is \nparticularly useful for diagnosing fracture tip extension. \nFigure 19 shows the pressure difference and pressure \nderivative (semilog) for the tip extension example.  \n \n2 3 4 5 6789 2 3 4 5 6789 2 3 4 5 6789 21 10 100 1000\nTime (0 = 33.7)23456789234567892345\n101001000\n (m = 0.25)  BH ISIP = 10000 psi 1Delta-Pressure and Derivative\u2206P vs. \u2206t\n\u2206td\u2206P/d\u2206t vs. \u2206t\n \nFigure 19: Tip extension log-log plot \n \nIn Figure 19 the pressure derivative departs from the early \nunit-slope (storage) and establishes a \u00bc slope during fracture \ntip extension. The pressure difference curve falls on a parallel \n\u00bc slope line separated by 4-times the magnitude of the \nderivative. The \u00bc slope signature is diagnostic of bilinear flow \nrepresenting a continued dissipation of the linear pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8890a0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 6, "chroma:document": "derivative. The \u00bc slope signature is diagnostic of bilinear flow \nrepresenting a continued dissipation of the linear pressure \ntransient along the fracture length (extension and concomitant \nfluid flow) and some linear flow driving minimal leakoff. For tip extension to occur the leakoff rate to the formation must be \nlow. As long as the parallel \u00bc slope trend continues, the \nfracture has not closed and is still in the process of extending. Closure cannot be determined and no after-closure analysis \ncan be conducted. \n \nHeight Recession or Transverse Storage \nThere are two different mechanisms that can generate a \nsimilar diagnostic derivative signature during fracture closure. \nBoth are caused by an excess st ored volume of fluid in the \nfracture at shut-in relative to the expected surface area of the \nfracture for a planar, constant -height geometry model.  \nTraditionally this signature has been called \u201cfracture height \nrecession\u201d. The usual model assu mes that leakoff occurs only"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8890f0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 6, "chroma:document": "Traditionally this signature has been called \u201cfracture height \nrecession\u201d. The usual model assu mes that leakoff occurs only \nthrough a thin permeable bed and that the fracture extends in height to cover impermeable strata with no leakoff. At shut-in \nthere is a large volume of flui d stored in the fracture and the \nleakoff rate relative to the stored volume is small, hence the \nrate of pressure decline is likewise small. As the fracture \nempties, the rate of leakoff relative to the remaining stored \nfluid accelerates and the pressure declines more rapidly. If the \nfracture height changes duri ng leakoff, the fracture \ncompliance may also decrease, addi ng to the rate of pressure \nloss. \nHowever, the same signature is observed in many cases \nwhere fracture height growth out of zone is not observed by \ntracers, inclinometer, or micr o-seismic mapping. Some of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b889140-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-107877-ms.pdf", "page": 6, "chroma:document": "where fracture height growth out of zone is not observed by \ntracers, inclinometer, or micr o-seismic mapping. Some of \nthese cases show treating behavior similar to PDL cases, with 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"}


