# embeddings_queue

created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897de4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 28, "chroma:document": "injection tests using multiple analysis methods\". SPE Production & Operations 24 ( 3): 396\u2013406.\nBazan, Lucas W.  and Bruce R. Meyer . 2015 . \"Fracture complexity: analysis methodology and signature pressure behavior\nof hydraulic fracture propagation from horizontal wellbores \". SPE 176919. Paper presented at the SPE Asia Pacific\nUnconventional Resources Conference and Exhibition, Brisbane, Australia.\nCastillo, J. L. 1987 . Modified fracture pressure decline analysis including pressure-dependent leak-off. SPE 16417. Paper\npresented at the SPE/DOE Low Permeability Reservoir Symposium, Denver, CO.\nCraig, D. P. , R. D. Barree, N.R. Warpinski , and T.A. Blasingame. 2017 . Fracture closure stress: Reexamining field and\nlaboratory experiments of fracture closure using modern interpretation methodologies. SPE 187038. Paper presented\nat the SPE Annual Technical Conference and Exhibition, San Antonio, TX"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897e34-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 28, "chroma:document": "at the SPE Annual Technical Conference and Exhibition, San Antonio, TX\nMcClure, Mark W., Christopher A. J. Blyton, Hojung Jung, and Mukul M. Sharma. 2014 . \"The Effect of Changing Fracture\nCompliance on Pressure Transient Behavior During Diagnostic Fracture Injection Tests\". SPE 170956. Paper presented\nat the SPE Annual Technical Conference and Exhibition, Amsterdam, The Netherlands.\nMcClure, Mark W., Hojung Jung, Dave D. Cramer , and Mukul M. Sharma. 2016 . \"The fracture compliance method\nfor picking closure pressure from diagnostic fracture injection tests\". SPE Journal 21 (4): 1321 \u20131339 , doi:\n10.2118/179725-PA .Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897e84-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 29, "chroma:document": "30 SPE-215017-MS\nMcClure, Mark . 2017 . \"The spurious deflection on log-log superposition-time derivative plots of diagnostic fracture-\ninjection tests \". SPE Reservoir Evaluation & Engineering  20 (4), doi: 10.2118/186098-PA.\nMcClure, Mark , Vidya Bammidi, Craig Cipolla, Dave Cramer, Lucas Martin , Alexei A. Savitski , Dave Sobernheim, and\nKate V oller . 2019 . \"A collaborative study on DFIT interpretation: integrating modeling, field data, and analytical\ntechniques \". URTeC 2019-123. Paper presented at the Unconventional Resources Technology Conference Denver, CO.\nMcClure, Mark . 2019 . Discussion of the Paper SPE-187038-MS: \"Fracture Closure Stress: Reexamining Field and\nLaboratory Experiments of Fracture Closure Using Modern Interpretation Methodologies.\" arXiv:1904.07126.\nMcClure, Mark . 2020 . \"Theoretical and Empirical Problems with the Holistic Permeability Correlation for"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897eca-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 29, "chroma:document": "McClure, Mark . 2020 . \"Theoretical and Empirical Problems with the Holistic Permeability Correlation for\nDFIT Interpretation. ResFrac Blog Post.\" https://www.resfrac.com/blog/theoretical-and-empirical-problems-holistic-\npermeability-correlation-DFIT-interpretation.\nNational Energy Board, British Oil and Gas Commission, Alberta Energy Regulator and British Columbia Ministry of\nNatural Gas Development. November 2013 . \"The Ultimate Potential for Unconventional Petroleum of the Montney\nFormation in Alberta and British Columbia \".\nNolte, K. G., \" Determination of Fracture Parameters from Fracturing Pressure Decline\", Paper SPE 8341, Presented at\ntheAnnual Technical Conference and Exhibition, Las Vegas, NV , Sept. 23-26, 1979.\nNolte, K.G. , Maniere, J.L. , and Owens, K.A., \" After-Closure Analysis of Fracture Calibration Tests,\" Paper SPE 38676,\nPresented at the1997 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5-8 October 1997."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897f1a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 29, "chroma:document": "Presented at the1997 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 5-8 October 1997.\nNolte, K. G., \" Background for After-Closure Analysis of Fracture Calibration Tests \", Paper SPE 39407, Unsolicited\ncompanion paper to SPE 38676 July 1997.\nSoliman, M.Y . , Craig D. , Barko, K., Rahim Z. , Ansah J. , and Adams D., \" New Method for Determination of Formation\nPermeability, Reservoir Pressure, and Fracture Properties from a Minifrac Test \", Paper ARMA/USRMS 05-658, 2005\nS&P Global \u2013 Minifrac (DFIT) Analysis for Unconventional Reservoir Course NotesDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897f6a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 0, "chroma:document": "URTeC: 123 \n \nA Collaborative Study on DFIT Interpretation: Integrating Modeling, \nField Data, and Analytical Techniques  \nMark McClure*1, Vidya Bammidi2, Craig Cipolla3, Dave Cramer4, Lucas Martin5, Alexei A \nSavitski6, Dave Sobernheim2, and Kate Voller7; 1. ResFrac Corporation , 2. Keane \nGroup , 3. Hess Corporation , 4. ConocoPhillips  Company , 5. Formerly with Apache \nCorporation, now with Marathon Oil Corporation , 6. Shell  International Exploration and \nProduction Inc. , 7. Range Resources Corporation  \n \nCopyright 201 9, Unconventional Resources Technology Conference (URT eC) DOI 10.15530 /urtec -2019-123 \nThis paper was prepared for presentation at the Unconventional  Resources Tech nology Conference held in Denver , Colorado , USA, \n22-24 July 201 9. \nThe URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897fba-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 0, "chroma:document": "22-24 July 201 9. \nThe URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract \nsubmitted by the author(s).  The contents of this paper have not been rev iewed by URTeC and URTeC does not warrant the \naccuracy, reliability, or timeliness of any information herein.  All information is the responsibility of, and, is subject to  corrections by \nthe author(s). Any person or entity that relies on any information obt ained from this paper does so at their own risk.  The information \nherein does not necessarily reflect any position of URTeC. Any reproduction, distribution, or storage of any part of this paper by \nanyone other than the author without the written consent of URTeC is prohibited.   \n \nAbstract  \nThis paper summarizes findings from a one -year study sponsored by seven operators and service companies \nto investigate interpretation of diagnostic fracture injection tests (DFIT\u2019s). The study combined"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898000-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 0, "chroma:document": "to investigate interpretation of diagnostic fracture injection tests (DFIT\u2019s). The study combined \ncomputational modelin g, a diverse collection of field data, and operator experience. DFIT simulations were \nperformed with a three -dimensional hydraulic fracturing, wellbore, and reservoir simulator that describes \nfracture propagation, contacting of the fracture walls, and mult iphase flow. Interpretation procedures were \napplied to estimate stress, permeability, and pressure from the synthetic data. The interpretations were \ncompared to the simulation input parameters to evaluate accuracy. Based on the results, new techniques \nwere  developed, existing techniques were refined, and an overall interpretation protocol was developed. \nThe techniques were applied to interpret over thirty field DFIT\u2019s drawn from shale plays across the US and \nCanada, and the methods were evaluated in the con text of operator experience. The results are applicable"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898050-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 0, "chroma:document": "Canada, and the methods were evaluated in the con text of operator experience. The results are applicable \nto fracturing tests in formations with permeability ranging from nanodarcies to 10s of microdarcies. The \nminimum principal stress is estimated by identifying the \u2018contact pressure\u2019 when the fracture w alls come \ninto contact, causing fracture compliance and system storage coefficient to decrease. After the walls come \ninto contact, the pressure transient is controlled by the interplay of changing fracture compliance, deviation \nfrom Carter leakoff, and mul tiphase flow. The contact pressure is slightly greater than the minimum \nprincipal stress. It can be identified from either a plot of dP/dG or a relative stiffness plot. Permeability is \nestimated  using the G -function method, a newly developed h -function met hod that accounts for deviation \nfrom Carter leakoff, and impulse linear flow. These  three methods, which are based on linear flow"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8980a0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 0, "chroma:document": "from Carter leakoff, and impulse linear flow. These  three methods, which are based on linear flow \ngeometry,  require an estimate of fracture area . We derive equations for estimating area using mass balance \nequations, accounti ng for wellbore storage and fluid leakoff. The results from field data  show that  impulse \nlinear permeability estimates are usually 2 -5 times lower than estimates derived from the G -function and \nh-function methods, apparently indicating a difference between  effective permeability during leakoff and \npermeability during flow of reservoir  fluid through the formation . Impulse radial flow regime may be used \nfor estimating permeability, but  should be used with caution.  Simulation results indicate that a variety of  \nprocesses can cause an apparent radial trend that is not actually radial flow. Simulations and field data \nindicate that \u2018false radial\u2019 is very common  in gas reservoirs and, if applied, leads to a large overestimate of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8980e6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 0, "chroma:document": "indicate that \u2018false radial\u2019 is very common  in gas reservoirs and, if applied, leads to a large overestimate of \npermeability. Production history matc hing using overestimated permeability will underestimate fracture \nlength, potentially resulting in suboptimal choices for well and cluster spacing.  \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898136-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 1, "chroma:document": "URTeC 123   2 \n1. Introduction  \n1.1 Background  \nDiagnostic fracture injection tests (DFIT\u2019s) involve water injection at a rate and pressure sufficient to create \na dominant hydraulic fracture, followed by a shut -in period lasting days, weeks, or even months. The trend \nin pressure after shut -in is analyze d to estimate stress, permeability, and/or pore pressure. Compared with \nother types of fracture injection tests, DFIT\u2019s typically involve a longer shut -in, are performed after drilling \nis complete, are usually performed in low permeability rock, and have a  greater emphasis on estimating \nreservoir properties, such as permeability and pore pressure.  \nThe magnitude of the minimum principal stress, permeability, and pore pressure are key parameters in \nreservoir engineering, hydraulic fracturing, and drilling. K nowledge of the stress state is used during drilling \n(wellbore stability and mitigation of lost circulation), exploration (fault seal analysis and prediction of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898186-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 1, "chroma:document": "(wellbore stability and mitigation of lost circulation), exploration (fault seal analysis and prediction of \ncritically stressed fractures), and hydraulic fracturing (predicting injection pressure, estima ting height \ngrowth, selecting proppant, and inferring net pressure) (Zoback, 2007; Economides and Nolte, 2000; Smith \nand Montgomery, 2015). Permeability estimates are used during optimization of hydraulic fracture design, \nwell spacing, and cluster spacing.  Pore pressure estimates are used to delineate the extent of drainage, which \nhelps with optimization of well spacing.  \nPermeability is difficult to measure in unconventional formations. Permeability from core may not be \ndirectly applicable in reservoir eng ineering calculations because in -situ flow can be strongly influenced by \npre-existing planes of weakness that are not sampled in the core. In addition, core measurement may be"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8981d6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 1, "chroma:document": "pre-existing planes of weakness that are not sampled in the core. In addition, core measurement may be \nimpacted by changes in the rock as it is removed from the subsurface. Rate -trans ient analysis (RTA) yields \nan estimate of fracture surface area times  the square root of permeability ( \ud835\udc34\u221a\ud835\udc58), but cannot estimate these \nparameters separately. On the other hand, DFIT\u2019s provide the opportunity to derive a unique, in -situ \nestimate of permeab ility. The DFIT provides a permeability estimate that is the area -weighted average of \nthe permeability across the fracture surface area. It is an estimate of the effective permeability to the mobile \nreservoir phase (absolute permeability times relative per meability).  \nThis paper summarizes findings from a one -year study sponsored by seven operators and service \ncompanies. The purpose of the study was to evaluate the accuracy of existing DFIT interpretation"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89821c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 1, "chroma:document": "companies. The purpose of the study was to evaluate the accuracy of existing DFIT interpretation \ntechniques, develop new techniques if needed, and ass emble an overall interpretation procedure. The study \nintegrated unique simulation capability, field data, and operator expertise. The interpretation procedure can \nbe performed entirely in an Excel spreadsheet.  \nThe body of the paper presents a step -by-step worked example, commentary on the most important findings, \nand additional field examples. The appendix provides detailed mathematical derivations explaining the \nmethods applied in the paper  \nThe study focused primarily on DFIT\u2019s performed in formations with  permeability on the order of \nnanodarcies to 10s of microdarcies. With higher permeability, transients behave qualitatively differently, \nand many of the techniques in this paper cannot be applied (discussed in Section 4.1).  \n1.2 Literature review"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89826c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 1, "chroma:document": "and many of the techniques in this paper cannot be applied (discussed in Section 4.1).  \n1.2 Literature review  \nDFIT inte rpretation combines concepts from well test analysis and hydraulic fracture analysis. \nConventional well testing involves production or injection of fluid at pressure below the fracture gradient. \nPressure data is analyzed to infer permeability, skin, and ot her parameters (Theis, 1935; Horne, 1995; \nKamal et al., 2009; Stewart, 2011; Spivey and Lee, 2013). DFIT\u2019s involve similar physics, but with \nimportant differences. In conventional well tests, fractures are static. In DFIT\u2019s, fractures are dynamic \u2013 \nchangin g in size, compliance, and conductivity. As a result, c oncepts from conventional well test analysis \nare not always directly applicable to DFIT analysis .  \nHydraulic fracturing was first described in a publication by Clark (1949). In subsequent decades, it w as"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8982bc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 1, "chroma:document": "Hydraulic fracturing was first described in a publication by Clark (1949). In subsequent decades, it w as \nrecognized that hydraulic fracturing could be used as a method to estimate the magnitude of the minimum Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898334-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "URTeC 123   3 \nprincipal stress (Hubbert and Willis, 1957; Godbey and Hodges, 1958; Kehle, 1964; Haimson and Fairhurst, \n1967; Hickman and Zoback, 1983). If fluid is  injected at pressure greater than the minimum principal stress, \na hydraulic fracture will form and propagate through the formation. As a result, the minimum principal \nstress can be estimated from pressure measurements during and after injection (Economide s and Nolte, \n2000; Zoback, 2007; Smith and Montgomery, 2015). The uniaxial stress/strain equations can be used for \nengineering purposes to help predict stress differences between layers (Eaton, 1969; Blanton and Olson, \n1999), but fracture injection tests a re needed for calibration and to ensure accuracy.  \nNolte (1979) extended the applicability of fracturing tests by developing analytical techniques that can be \nused to estimate fluid leakoff parameters. These techniques can assess leakoff even when using com plex"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898384-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "used to estimate fluid leakoff parameters. These techniques can assess leakoff even when using com plex \nfluids that develop filtercake. These tests are typically called minifrac tests (McLennan and Roegiers, 1982) \nor fracture calibration tests (Mayerhofer and Economides, 1993). The G -function developed by Nolte \n(1979) became a routine part of data plott ing and interpretation (Castillo, 1987; Barree and Mukherjee, \n1996). Mayerhofer and Economides (1993) and Mayerhofer et al. (1995) showed how to disentangle the \neffects of filtercake and formation permeability on leakoff.  \nConventional well testing is infe asible in very tight formations because of the difficulty of sustaining \nsufficiently low rates of production or injection. The \u201cdiagnostic fracture injection test\u201d (DFIT) emerged to \ncombine the benefits of a well test and a fracturing test \u2013 providing esti mates for stress, permeability, and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8983ca-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "combine the benefits of a well test and a fracturing test \u2013 providing esti mates for stress, permeability, and \npore pressure (Craig and Brown, 1999). \u2018Preclosure\u2019 analysis methods are usually based on techniques from \nNolte (1979) and Mayerhofer and Economides (1993) and Mayerhofer et al. (1995). Barree and Mukherjee \n(1996) and Ba rree et al. (2009) developed techniques for qualitative interpretation and for estimating the \nclosure pressure and minimum principal stress. Impulse analysis is based on the use of impulse solutions \nfrom conventional well testing (Gu et al., 1993; Soliman et al., 2005; Craig and Blasingame, 2006) or the \n\u2018linear flow time function\u2019 technique developed by Nolte et al. (1997). Examples of DFIT interpretation \nare provided in recent papers by Marongiu -Porcu et al. (2011; 2014), Soliman and Kabir (2012), Soliman \nand Gamadi (2012), Cramer and Nguyen (2013), Padmakar (2013), Wallace et al. (2014), Meng et al."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89841a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "and Gamadi (2012), Cramer and Nguyen (2013), Padmakar (2013), Wallace et al. (2014), Meng et al. \n(2014), Craig (2014), Zanganeh et al. (2018), and Hawkes et al. (2018).  \nMcClure et al. (2014; 2016) and Jung et al. (2016) proposed the compliance method of e stimating stress \nfrom a DFIT ( Section 3.1.2 ). The compliance method leads to an earlier, higher stress estimate than the \ncommonly used tangent method (Barree et al., 2009). McClure et al. (2016) and Jung et al. (2016) performed \ndetailed DFIT simulations co nsidering the effect of residual aperture fracture after the fracture walls \ncontact. Simulations indicate that in low permeability formations, the contacting of the fracture walls causes \nthe magnitude of the  pressure derivative to increase, resulting in a pressure signal often interpreted as height \nrecession or closure of transverse fractures (Barree et al., 2009). Wang and Sharma (2017) reproduced these"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89846a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "recession or closure of transverse fractures (Barree et al., 2009). Wang and Sharma (2017) reproduced these \nfindings and proposed a modified approach for estimating stress called the \u2018variable compliance method.\u2019  \n1.3 Defining a new term \u2013 the \u2018contact pressure\u2019  \nThe term \u2018closure pressure\u2019 is used widely in the literature but is rarely given a precise definition. A review \nof the literature shows that a variety of assumptions are made about \u2018closure pressure ,\u2019 and these \nassumptions  are often problematic and inconsistent. Most authors assume that the closure pressure is equal \nto the magnitude of the minimum principal stress (issues with this definition are discussed in Section A.2). \nCraig and Blasingame (2006) as sume that the compliance (or compressibility) of a \u2018closed\u2019 fracture is \nnegligible (issues with this definition are discussed in Section A.2). The classical calculation of efficiency"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8984ba-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 2, "chroma:document": "negligible (issues with this definition are discussed in Section A.2). The classical calculation of efficiency \nfrom the G -time to closure (Equation 5) is derived assuming that there is  zero fluid remaining in the fracture \nat \u2018closure\u2019 (issues with this assumption are discussed in Section A.12). McClure et al. (2016) define closure \nas being the point in time when the fracture walls first come into contact, decreasing the overall complian ce \nof the system (issues with this definition are discussed in Section 3.1.9). Nolte et al. (1997) derive the \u2018linear \nflow time function\u2019 assuming that Carter leakoff occurs until closure, at which point leakoff rate drops to \nzero (issues with this definit ion are discussed in Section A.11).  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898500-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 3, "chroma:document": "URTeC 123   4 \nIn Section A.2, we show that there is not any specific response in the pressure transient (or any other \nmeasurement) when fluid pressure is exactly equal to the minimum principal stress, Shmin. Instead, Shmin \ncan be esti mated from its proximity to a process that does create a signature in the pressure transient \u2013 the \ncontacting of the fracture walls, which causes a measurable increase in the system stiffness (or decrease in \ncompliance). We define the pressure at this poin t in time as the \u2018contact pressure.\u2019 It is equivalent to the \n\u2018closure pressure\u2019 defined by McClure et al. (2016). However, because the definition of \u2018closure pressure\u2019 \nis itself a point of confusion, we prefer to use the term \u2018contact pressure.\u2019  \n1.4 Study approach  \nIn our study, we performed a comprehensive reassessment of the entire DFIT analysis procedure \u2013 \nestimating stress, permeability, and pore pressure. Based on the results, we developed a detailed, step -by-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898550-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 3, "chroma:document": "estimating stress, permeability, and pore pressure. Based on the results, we developed a detailed, step -by-\nstep interpretation procedure.  \nFirst, a lar ge number of DFIT simulations were performed under a variety of conditions. The simulations \nwere performed with a three -dimensional hydraulic fracturing, wellbore, and reservoir simulator that \nrigorously handles fracture propagation, contacting of the frac ture walls, and multiphase flow (McClure \nand Kang, 2018). Conventionally, DFIT simulations and/or analytical approaches have isolated parts of the \nproblem and solved them separately. The fully integrated approach used in this study captures the \ninteraction s between processes, which have a material impact on system behavior.  \nDifferent analysis procedures were applied to analyze the simulations results, and the interpretations were \ncompared with the (known) simulation input parameters to assess accuracy. Base d on the results, a set of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8985a0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 3, "chroma:document": "compared with the (known) simulation input parameters to assess accuracy. Base d on the results, a set of \nDFIT interpretation guidelines were developed (summarized in Section 2.2). The guidelines incorporate \nboth pre -existing methods and newly developed techniques.  \nThe interpretation guidelines were applied to analyze a dataset of f ield DFIT\u2019s contributed by operators. \nThe results were compared with operator experience and expertise to assess performance. Due to limits on \npaper length, only a small set of the simulations and the field results are shared in this paper.  \nThis paper doe s not address many operational aspects of performing DFIT\u2019s. Cramer and Nguyen (2013) \nreview practical guidelines for DFIT execution.  \n2. Method s \n2.1 Numerical simulator  \nNumerical simulations were performed using ResFrac, a three -dimensional hydraulic fracturing, reservoir, \nand wellbore simulator. The problem formulation  is briefly summarized in this section, and a detailed"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8985f0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 3, "chroma:document": "and wellbore simulator. The problem formulation  is briefly summarized in this section, and a detailed \ntechnical description is provided by McClure and Kang (2018). ResFrac has a unique combination of \nphysics that enables seamless description of the entire DFIT process, from the beginning of injection to \nlate-time impulse flow. The wellbore is meshed from the surface as a series of line -segments. The frac ture \nis meshed with rectangles, and the reservoir is meshed with cuboids.  \nThe unsteady -state mass balance equation is solved in every element at every timestep. Multiphase flow is \ndescribed with the black oil model or the compositional model. Fracture wal ls come out of contact when \nfluid pressure exceeds normal stress. Then, the amount of mechanical opening in each element is calculated \nto enforce that the fluid pressure is equal to the normal stress on the element, including stress shadow effects"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898640-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 3, "chroma:document": "to enforce that the fluid pressure is equal to the normal stress on the element, including stress shadow effects \nfrom all  other mechanically open elements. The stress interaction is calculated with the 3D displacement \ndiscontinuity method of Shou et al.  (1997), an approach that provides mesh convergent solutions identical \nto classical continuum mechanics solutions, such as f rom Sneddon (1946). The opening of every fracture \nelement affects the stress on every other element, requiring the solution of a large, coupled system of \nequations in every timestep.  \nWhen the fluid pressure drops sufficiently, the fracture walls come into  contact. After the walls contact, the \nelements retain aperture and the ability to conduct fluid. The aperture is calculated using the Willis -Richards Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898690-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 4, "chroma:document": "URTeC 123   5 \net al. (1996) version of the Barton et al. (1985) relations. Th is joint closure law implicitly handles th e \ncontacting of the asperities in the fracture walls (Barton et al., 1985; Willis -Richards et al., 1996):  \n\ud835\udc4a=\ud835\udc4a0\n1+9(\ud835\udf0e\ud835\udc5b\u2212\ud835\udc43)\n\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53.            (1) \nThe W0 parameter (Equation  1) corresponds to the average fracture aperture at the contact press ure \u2013 the \npressure when asperities begin to contact, the fracture stiffens, and normal stress is transferred across the \nfracture by solid -solid contact. Conductivity is calculated with the cubic law (Witherspoon et al., 1980).  \nEven as the average fracture  aperture remains above zero, it is implicit to Equation 1  that the fracture walls \nare in contact across a fraction of the fracture area, at a scale below the resolution of the model (Barton et \nal., 1985). Some numerical modeling approaches explicitly repr esent individual asperities (Vogler et al.,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8986e0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 4, "chroma:document": "al., 1985). Some numerical modeling approaches explicitly repr esent individual asperities (Vogler et al., \n2018). However, this approach is computationally expensive and infeasible for field -scale modeling.  \nWhen a new fracture element is created in the model, it is given a very low initial aperture, 1 micron. The \naperture when the walls contact, W0, cannot initially exceed this initial aperture, and so as the crack opens, \nW0 must increase along with aperture to reach a more physically realistic value. W0 is increased at the end \nof each timestep to be equal to a certai n fraction of the total aperture, up to a user -specified limit, W0,max. \nThis corresponds to a progressive process of crack formation \u2013 roughness developing as the crack \ntransitions from \u2018not -yet-formed\u2019 to \u2018fully formed.\u2019 In reality, this process is controlled by the rock fabric \n(Suarez -Rivera et al., 2013; Gale et al., 2018) , is probably scale -dependent (Delaney et al., 1986; Scholz,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898730-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 4, "chroma:document": "(Suarez -Rivera et al., 2013; Gale et al., 2018) , is probably scale -dependent (Delaney et al., 1986; Scholz, \n2010), and might depend on operational parameters such as injection rate. After the walls have come into \ncontact, aperture has decreased by 90% once effective normal stress reaches \ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53. \nThe wellbore model solves the momentum balance equation in each element (in addition to the mass balance \nequations) and includes hydrostatic head, friction, momentum accumulation, and pressure gradient. Flow \nbetween well elements and fracture elements inclu des the effect of pressure drop due to both perforation \n(scaling with the square of flow rate) and near -wellbore pressure drop (Equation 22). \nPoroelastic st ress changes are rarely considered in DFIT analysis and were not included in the simulations \nperformed for this study. In low permeability formations, the region of pressure increase around the fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898780-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 4, "chroma:document": "performed for this study. In low permeability formations, the region of pressure increase around the fracture \nwill be very narrow. As a result, the poroelastic inc rease on fracture normal stress will be small (Perkins \nand Gonzalez, 1985). Nevertheless, it cannot be assumed that poroelastic stresses will never  have a \nsignificant impact, and this would be an interesting topic for further study.  \n2.2 Interpretation proc edure  \nAn interpretation procedure was developed based on simulation results, analytical derivations, and \napplication to field data. The procedure is:  \n(1) Inspect a plot of pressure versus time to pick the start of injection and the shut -in time. The pressu re \nplot should be used  to pick shut -in because injection rate data is  often unavailable or not synchronized with \nthe pressure data.  \n(2) Smooth the shut -in pressure  transient by resampling along pressure increments (Horne, 1995). A 30 psi \nincrement usually yields good results."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8987d0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 4, "chroma:document": "(2) Smooth the shut -in pressure  transient by resampling along pressure increments (Horne, 1995). A 30 psi \nincrement usually yields good results.  \n(3) Construct plots of the shut -in data: dP/dG versus G (Section A.3) and a log -log plot of dP and t*dP/dt \n(using actual shut -in time, not superposition time; McClure, 2017). Depending on the interpretation, plots \nof pressure versus t^ -1 and t^( -1/2) may also be used. According to the interpreter\u2019s preference, other plots \ncan be constructed (G*dP/dG, a log -log plot with the primary derivative dP/dt, linear -flow time function, \netc.).  \n(4) Estimate the wellbore storage coefficient from a p lot of cumulative volume injected versus pressure \nprior to breakdown.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898820-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 5, "chroma:document": "URTeC 123   6 \n(5) Identify the point of minimum dP/dG prior to the contact pressure and extrapolate back to G -time equal \nto zero to estimate the effective ISIP (Section 3.1.1). Calculate the \u2018effecti ve pressure\u2019 curve, defined as \nbeing equal to measured pressure after the minimum dP/dG and equal to the linear extrapolation of pressure \nprior to dP/dG ( Section 3.1 .1). Section 4.1 discusses interpretation of tests with monotonically decreasing \ndP/dG.  \n(6) Construct an afterflow plot to assess near -wellbore pressure drop (Sections 3.1.4 and A.7).  \n(7) From the log -log plot, identify impulse linear or radial flow regimes from a -1/2 or -1 slope. Be cautious \nabout identification of these flow -regime trends (Section 3.1 .5). Do not use the log -log plot for \ninterpretation prior to the late -time impulse period  (ie, prior to  the peak in t*dP/dt) . \n(8) Depending on the diagnosis of impulse flow, estimate pore pressure from plots of pressure versus either"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898870-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 5, "chroma:document": "(8) Depending on the diagnosis of impulse flow, estimate pore pressure from plots of pressure versus either \nt^-1 or t^ (-1/2) (Sections 3.1.6 and A.6). If an unambiguous diagnosis of impulse flow is not possible, \nconsider reducing injection volume to accelerate  the onset of  impulse flow in subsequent tests. It is possible \nto perform an extrapolation of the t^( -1/2) or t^( -1) plot, even in the absence of a clear straight line. This \nstrategy should be used with caution because it can be significantly inaccurate.  Section A.13 outlines an \nalternative technique that can be used with short -duration transients.  \n(9) Calculate the  h-function (Section A.8) and construct a plot of h -function versus G -function and a relative \nstiffness plot (Sections 3.1.2 and A.9).  \n(10) Using the dP/dG  curve and the relative stiffness plot, identify the contact pressure and estimate the \nmagnitude of the minimum principal stress ( Section 3.1 .2). Section 4.1 discusses interpretation of tests"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8988b6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 5, "chroma:document": "magnitude of the minimum principal stress ( Section 3.1 .2). Section 4.1 discusses interpretation of tests \nwhere the contact pressure cannot be identified.  \n(11) Estimate p ermeability ( Section 3.1 .7) using the G -function method (Section A.10.i), the h -function \nmethod (Section A.10.ii), and (if applicable) impulse linear or radial (Sections A.10.iii and A.10.iv). \nCompare the results and check for consistency. Keep in mind tha t impulse linear estimates are usually 2 -5 \ntimes lower than estimates from the other methods. The impulse linear estimate is probably the most \napplicable for predictions of production, and so a downward adjustment may be warranted if an impulse \nlinear perm eability estimate is not available.  \n(12) Optionally, create a plot of estimated aperture versus effective normal stress (Sections 3.1.9 and A.14).  \nIn advance of a test, it is often useful to estimate the duration of shut -in needed to reach impulse flow. Th is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898906-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 5, "chroma:document": "In advance of a test, it is often useful to estimate the duration of shut -in needed to reach impulse flow. Th is \ncould be done by performing a numerical simulation with code such as ResFrac (McClure and Kang, 2018) \nor by performing a simplified DFIT simulation using the equations in Section A.13. DFIT simu lations may \nbe performed after the interpretation as a qual ity control to confirm that the simulation result is consistent \nwith the actual data.  \n3. Results  \n3.1 Example interpretation  \nThe interpretation procedure is demonstrated in the following example using a DFIT performed in a gas \nwell in the  Utica/Point Pleasa nt. Mathematical background is provided in the appendix. It may be useful to \nrefer to the appendix while reading this section.  \n3.1.1 Initial interpretation with the G -function plot  \nFigure 1 shows a plot of pressure and dP/dG versus G -time. For convenience, dP/dG is plotted as positive,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898956-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 5, "chroma:document": "Figure 1 shows a plot of pressure and dP/dG versus G -time. For convenience, dP/dG is plotted as positive, \neven though it is actually negative (because pressure is decreasing over time).  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8989a6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 6, "chroma:document": "URTeC 123   7 \n \nFigure 1: dP/dG and pressure vers us G-time for the Utica DFIT.  \nIdeally, dP/dG should be constant as long as the fracture walls are out of contact (Nolte, 1979; Castillo, \n1987; Section A.3). However, this is not usually observed in field DFIT\u2019s, especially if performed in a \nhorizontal wel l. \nAt early time, the pressure derivative is elevated by near -wellbore pressure drop. The near -wellbore \npressure drop is caused by flow through a tortuous path through the cement sheath and axial (longitudinal) \nfractures in the near -wellbore region (Wright , 2000; Weijers et al., 2002; Economides and Martin, 2008; \nBazan and Meyer, 2015; Cramer et al., 2019). Because of this pressure drop, the pressure in the primary \nfracture away from the well is lower than the pressure measured in the wellbore ( Figure 2). Some authors \ndistinguish between \u2018near -field\u2019 and \u2018mid -field\u2019 pressure drop, but in this paper, we lump these processes"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8989f6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 6, "chroma:document": "distinguish between \u2018near -field\u2019 and \u2018mid -field\u2019 pressure drop, but in this paper, we lump these processes \ntogether and refer to them as simply \u2018near -wellbore  pressure drop.\u2019  \nIn Figure 1, the literal ISIP is around 11,500 psi. The effective ISIP, 8330 psi, is estimated by identifying \nthe point of minimum dP/dG and extrapolatin g the pressure versus G -time curve back to zero from this \npoint. The effective ISIP is an estimate for the pressure in the far -field fracture at shut -in. This is the pressure \nactually present in the fracture that is opening and propagating the crack.  \nFigure 2 illustrates the difference between literal ISIP and effective ISIP. A fracture is shown initiating \nlongitudinally along the well. Away from the well, a transverse fracture forms, resulting in a  complex, \ntortuous fracture geometry that causes a substantial pressure drop that takes at least several  minutes to"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898a3c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 6, "chroma:document": "tortuous fracture geometry that causes a substantial pressure drop that takes at least several  minutes to \ndissipate. Figures 13 and 17 from Jung et al. (2016) show numerical simulations of this process.  \n \nFigure 2: Schema tic of near -wellbore pressure drop between the wellbore and the far -field fracture.  \nAs the fracture walls come into contact, the magnitude of the pressure derivative begins to increase as the \nfracture compliance and system storage coefficient decrease beca use of the contact stress (McClure et al., \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898a8c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "URTeC 123   8 \n2016; Section A.2). The point of minimum dP/dG is closest to the \u2018true\u2019 dP/dG in the far -field fracture \nbecause it is least disturbed by near -wellbore pressure drop and the contacting of the fracture walls.  \nThe \u2018 effective pressure\u2019 is defined as being equal to measured pressure after the point of minimum dP/dG, \nand equal to the linear extrapolation of pressure back to G -time equal to zero prior to the point of minimum \ndP/dG  (Figure 1). Effective pressure is an estimate for the pressure that is actually in the fracture. As shown \nin Figure 2, the pr essure measured in the well is higher than the \u2018effective pressure\u2019 because of the pressure \ndrop that occurs between the well and the far -field fracture.  \nConventionally, a period of rapid pressure drop after shut -in has been called \u2018tip -extension\u2019 or \u2018pres sure-\ndependent leakoff\u2019 (PDL). It has been believed to be caused by accelerated leakoff or pressure gradient"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898adc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "dependent leakoff\u2019 (PDL). It has been believed to be caused by accelerated leakoff or pressure gradient \nalong the fracture or at the tip (Barree et al., 2009; Liu et al., 2016). However, it has also been recognized \nthat near -wellbore fracture tortuosi ty is responsible for the huge pressure drops observed after shut -in \n(Bazan and Meyer, 2015; McClure et al., 2016; Barree and Misk imins, 2016). The distinction is that in the \n\u2018near -wellbore pressure drop\u2019 interpretation, the pressure in the fracture is muc h lower than the literal ISIP \n(the bottomhole pressure very shortly after shut -in), but in a \u2018tip -extension\u2019 or \u2018PDL\u2019 interpretation, the \npressure in the fracture is close to the  literal ISIP.  \nAs pressure drops after shut -in, a few barrels of water will b e released from wellbore storage and cause a \nlimited amount of tip -extension. If pressure -dependent leakoff is taking place, it will be impossible to"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898b2c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "limited amount of tip -extension. If pressure -dependent leakoff is taking place, it will be impossible to \nobserve because of the huge pressure changes caused by the dissipation of near -wellbore pressure drop. \nTherefore, while PDL and tip -extension may occur, \u2018near -wellbore pressure drop\u2019 is the dominant physical \nprocess in most DFIT\u2019s and should be considered the primary interpretation.  \nIn vertical wells, the pressure drop after shut -in is usually  (though not always)  less pronounced than in \nhorizontal wells (Section 3.3). This is consistent with the interpretation that near -wellbore pressure drop is \nthe primary cause of the large pressure drops observed after shut -in, and this process is related to  fracture \ntortuosity due to fracture reorientation.  \n3.1.2 Estimating the minimum principal stress  \nAs described by McClure et al. (2016) and in Section A.2, the fracture compliance begins to decrease after"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898b72-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "As described by McClure et al. (2016) and in Section A.2, the fracture compliance begins to decrease after \nthe fracture walls come into contact. The decreasin g fracture compliance causes the pressure to drop more \nrapidly ( the magnitude of dP/dG increases). McClure et al. (2016) recommend picking the contact pressure \nfrom a G*dP/dG plot.  However, there is not always a  unique feature on  the G *dP/dG plot that lends itself \nto identifying the contact pressure . It is better  to pick the contact pressure from a plot of dP/dG. The contact \npressure occurs when dP/dG begins to increase from its minimum value. A rule of thumb is to pick the \ncontact pressure w hen there has been a 10% increase from the minimum. When constructing a dP/dG plot, \nthe y -axis scale should be chosen so that the minimum and maximum dP/dG can be clearly observed. Large \nearly time dP/dG values do not need to be visible on the plot and can  go up off the scale. They are related"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898c08-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "early time dP/dG values do not need to be visible on the plot and can  go up off the scale. They are related \nto dissipative processes unrelated to fracture contact ( Section 3.1.1 ). \nAs explained in Section A.2, the contact pressure is slightly above the minimum principal stress. In \nsimulations that match field pressure data, we have found that subtracting approximately 75 psi from the \ncontact pressure is a good rule -of-thumb for providing a good estimate of Shmin. However, this is a source \nof uncertainty and is an inherent limitation to stress estimation from fracturing data. As discussed in Section \nA.2, there is not any response in the pressure transient when pressure is actually equal to Shmin. It is known \nthat the contact pressure is close to Shmin (and slightly larger), and so stress can be estimated by identifying \nthe cont act pressure and then making a small downward adjustment to reach Shmin."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898c58-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 7, "chroma:document": "the cont act pressure and then making a small downward adjustment to reach Shmin.  \nThe G -function is derived assuming Carter leakoff, which is strictly valid only if fluid pressure in the \nfracture is constant over time. As pressure decreases during shut -in, deviati on from Carter leakoff occurs, \ncausing leakoff to occur more slowly than anticipated by the G -function. This overprints a tendency for \ndP/dG to decrease. Ultimately, decreasing leakoff rate is the reason that dP/dG decreases asymptotically to \nzero at late time.   Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898c9e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 8, "chroma:document": "URTeC 123   9 \nFracture contact causes dP/dG to increase, and deviation from Carter leakoff causes dP/dG to decrease. If \nfracture contact occurs simultaneously with deviation from Carter leakoff, the effects could offset and mask \nthe effect of contact on the tran sient. The problem becomes more significant when effective ISIP minus \nShmin (net pressure) is a substantial fraction of effective ISIP minus pore pressure. The practical \nconsequence is that contact causes a stronger dP/dG response in formations where Shmin  and pore pressure \nare relatively further apart.  \nIn an extreme case, Craig et al. (2017) attempted to estimate stress using a G -function plot of pressure from \nlaboratory experiment in which ISIP was double the magnitude of the minimum principal stress  (and near-\nwellbore pressure drop was negligible) . Because net pressure was so large relative to ISIP minus pore"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898cee-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 8, "chroma:document": "wellbore pressure drop was negligible) . Because net pressure was so large relative to ISIP minus pore \npressure, by the time that pressure reached the minimum principal stress, the overprint of deviation from \nCarter leakoff was very strong, and a G -function interpretation of the data was not meaningful.  \nTo solve this problem, a relative stiffness plot can be used to identify the contact pressure, even in cases \nwhere there is substantial deviation from Carter leakoff (Wang and Sharma, 2018; Section A.9 ). The plot \ncan be constructed solely from the pressure data and an estimate of pore pressure. The plot shows relative \nchanges in system stiffness (or storage coefficient) and rigorously accounts for the impact of pressure \nchange in the fracture on leakoff  rate.  \nFigure 3 shows that in the example dataset, there is a distinct increase in relative stiffness at around 8100"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898d3e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 8, "chroma:document": "Figure 3 shows that in the example dataset, there is a distinct increase in relative stiffness at around 8100 \npsi. This corresponds to the point in the G -function  plot when dP/dG begins to increase from the minimum.  \nThe Shmin estimate is 8100 \u2013 75 = 8025 psi.  \n \nFigure 3: Relative stiffness plot of the Utica DFIT.  \n3.1.3 Difference with conventional interpretation  \nConventionally, Shmin has be en estimated from plots of G*dP/dG versus G -time, by drawing a line from \nthe origin to the tangent to G*dP/dG (Barree et al., 2009). This technique does not have theoretical or \nmathematical justification and yields an inaccurate stress estimate when applie d to numerical simulations \nthat realistically capture nonlinear evolving fracture stiffness after contact (McClure et al., 2014; 2016). \nCraig et al. (2017) claim to use field and laboratory data to validate the tangent method. McClure (2019) \ndescribes tech nical and methodological problems with this study."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898d8e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 8, "chroma:document": "describes tech nical and methodological problems with this study.  \nThe tangent to G*dP/dG tends to occur very close to the peak in G*dP/dG. It can be shown mathematically \nthat the peak in G*dP/dG occurs at the same time as the peak in t*dP/dt. The peak in t*dP/dt has a ph ysical \nmeaning \u2013 it corresponds to the transition from Carter leakoff to late -time impulse flow (McClure, 2017). \nThe timing of the transition is strongly affected by the formation fluid pressure (McClure, 2017). We \nperformed sensitivity analysis simulation s varying pore pressure and holding Shmin constant. The \nsimulations showed that as pore pressure was decreased, the tangent method estimate of Shmin decreased \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898dd4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 9, "chroma:document": "URTeC 123   10 \n(even though Shmin was being held constant in the simulations).  The implication is that the tange nt method \nunderestimates Shmin more significantly in formations with greater difference between Shmin and pore \npressure.  \nFor the DFIT shown in Figure 1, the tangent meth od (applied to a plot of G*dP/dG) yields a stress estimate \nof 7633 psi, about 400 psi lower than the estimate presented in Section 3.1 .2. The implied net pressure from \nthe tangent method is nearly triple, implying a much shorter, wider fracture.  \nThe phenomenon of increasing dP/dG during shut -in (causing a concave up trend on a plot of G*dP/dG) \nhas conventionally been ascribed to \u2018fracture height recession\u2019 or \u2018closure of transverse fractures\u2019 (Barree \net al., 2009). Jung et al. (2016) performed det ailed simulations of these processes. The simulations showed \nthat these processes have a second -order effect and cause, at most, minor uncertainty in the stress estimate."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898e24-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 9, "chroma:document": "that these processes have a second -order effect and cause, at most, minor uncertainty in the stress estimate. \nThe bulk of the increase in dP/dG occurs after the fracture walls have come into cont act across the entire \nfracture area.  \nSome investigators have recently speculated that the contact pressure might be interpreted as the \u2018start of \nclosure\u2019 and the tangent method  pick might be interpreted as the \u2018end of closure.\u2019 This interpretation is not \nsupported by our modeling results. Simulations show that the great majority of increase in system stiffness \nand dP/dG occurs after contact has occurred along the entire fracture area , and this occurs at a pressure \nsubstantially higher than the tangent pick.  This was observed in simulations performed by McClure et al. \n(2016) and was also observed in the simulations performed for this study.  \n3.1.4 Afterflow plot  \nUsing the estimate of effective ISIP, it is possible to construct an afterflow plot showing the re lationship"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898e74-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 9, "chroma:document": "3.1.4 Afterflow plot  \nUsing the estimate of effective ISIP, it is possible to construct an afterflow plot showing the re lationship \nbetween flow rate from the well after shut -in and the pressure difference between the well and the far -field \nfracture (Section A.7).  \nFigure 4 shows the afterfl ow plot for the Utica DFIT. The relationship is well -described by a square root \ncurve, consistent with relations proposed in the literature (Equation 22; Wri ght, 2000). In Figure 4, data \nfrom the first 15 seconds after shut -in is not shown because it is complicated by water hammer and \nperforation pressure drop. From visual ins pection of Figure 4, the near -wellbore coefficient (Equation 22) \nis appr oximately 1600 psi/bpm^(1/2). Square root scaling of afterflow was observed in the great majority \nof the field DFIT\u2019s reviewed in this study.  \nSometimes, DFIT\u2019s are performed with a rate step -down at the end of injection. This is not necessary"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898ec4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 9, "chroma:document": "of the field DFIT\u2019s reviewed in this study.  \nSometimes, DFIT\u2019s are performed with a rate step -down at the end of injection. This is not necessary \nbecause an a fterflow plot can be used to extract information regarding the near -wellbore pressure drop \nwithout performing a step -down.  \nThe near -wellbore pressure drop observed in a DFIT is typically much larger than in field -scale fracturing \ntreatments because the to rtuous path is scoured out by proppant, acid spearhead, and fracture development \nfrom progressive injection (Cramer et al., 2019).  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898f14-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 10, "chroma:document": "URTeC 123   11 \n \nFigure 4: Afterflow plots for the Utica DFIT.  \n3.1.5 Diagnosing impulse transients  \nFigure 5 shows a log -log plot of the data. The t*dP/dt curve has the useful property that if \u0394\ud835\udc43\u221d\ud835\udc61\ud835\udefc, then \nthe slope of the curve is equal to \ud835\udefc (Bourdet et al., 1983). The derivative is taken with respect to actual \nshut-in time. Sometimes, log -log derivative plots are calculated with superposition time, rather than actual \nshut-in time ( Marongiu -Porcu et al., 2011, 2014; Liu et al., 2016) . This technique is useful for conventional \nwell tests, but is unnecessary for interpretation of DFIT\u2019s (McClure, 2017).  \nIn a DFIT, the log -log plot should only be used to interpret the late -time transient behavior that occurs after \nthe hump in t*dP /dt (which occurs at 2000 min in Figure 5). The log -log plot should not be used to interpret \nthe transient prior to the hump in t*dP/dt. For example, the derivative curve  in Figure 5 is approximately"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898f64-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 10, "chroma:document": "the transient prior to the hump in t*dP/dt. For example, the derivative curve  in Figure 5 is approximately \nflat from about 20 to 200 minutes In a conventional well test, this trend would be interpreted as being radial \nflow. However, the physics of a  DFIT are different from a conventional well test, and radial flow from 20 \nto 200 min is not the correct interpretation.  \n \nFigure 5: Log -log plot for a Utica DFIT. Derivative is taken with respect to actual shut -in time.  \nThe transient following the hump in t*dP/dt can be described mathematically as an \u2018impulse\u2019 test in which \na volume of fluid is instantaneously injected and then the fluid spreads out and pressure asymptotically \nreturns to the initial pressure (Gu et al., 1993;  Craig and Blasingame, 2006; McClure, 2017). Impulse linear \nbehavior scales with t^( -1/2) (a -1/2 slope on the log -log plot), and impulse radial scales with t^ -1 (a -1 \nslope on the log -log plot)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898faa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 10, "chroma:document": "behavior scales with t^( -1/2) (a -1/2 slope on the log -log plot), and impulse radial scales with t^ -1 (a -1 \nslope on the log -log plot).  \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b898ffa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 11, "chroma:document": "URTeC 123   12 \nFigure 5 shows that soon after the peak in t*dP/dt, the transient rolls over into a -1 slope. It is tempting to \nidentify this trend as impulse radial flow. However, our simulation results suggest that this apparent radial \nsignatur e should be interpreted as \u2018false radial\u2019 \u2013 a transient that exhibits t^ -1 scaling, but which is not \nactually radial flow. We observed this phenomenon in every simulation that we performed of a DFIT in a \ngas reservoir. The anomalously rapid pressure drop a pparently arises from interaction between several \neffects: viscosity contrast between the injection fluid and the gas in the formation, evolving fracture \nstiffness after contact, and the transition from  Carter leakoff to impulse flow. In examination of fie ld data \nfrom gas DFIT \u2019s in the Utica, Marcellus, and Montney, a rolling over from the peak t*dP/dt into an \napproximately -1 slope (without an intervening -1/2 slope) was observed  in the majority of cases ."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89904a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 11, "chroma:document": "approximately -1 slope (without an intervening -1/2 slope) was observed  in the majority of cases .  \nSimulations predict  that if shut -in is performed l ong enough, the transient settles into a -1/2 slope after the \n-1 slope. This was observed in one of the DFIT\u2019s reviewed in this study, which had an unusually long shut -\nin after the peak in t*dP/dG. The -1 slope represents a period of transition from the hu mp in t*dP/dt to an \neventual -1/2 slope that indicates linear flow. Because of the low viscosity of the reservoir fluid, the location \nof the -1/2 slope on the log -log plot tends to be significantly lower than the hump in t*dP/dt. Therefore, the \ncurve tempo rarily steepens as it transitions from the peak t*dP/dt to the late -time impulse trend .  \nGenuine impulse radial is most likely to be seen in smaller volume tests (<15 bbl) and if permeability \ndivided by viscosity is  greater than 1 microdarcy/cp."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89909a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 11, "chroma:document": "divided by viscosity is  greater than 1 microdarcy/cp.  \nIn DFIT s imulations performed in water saturated or oil saturated formations, the baseline behavior  was for \nthe transient to roll over into a -1/2 slope, as expected for linear flow. However, sensitivity analysis \nsimulations suggest that a variety of non -ideal proc esses may cause anomalous late-time behavior. In \nsimulations performed with multiple closely spaced fractures, pressure interference between the fractures \ncaused a variety of different trends after the hump in t*dP/dt, including a false radial trend. Simul ations \nsuggest that dual porosity behavior in the surrounding reservoir (either pseudosteady state or transient) may \ncause a false radial signature. In real data, a variety of unusual behaviors can be seen in late -time data. We \ndo not attempt to interpret these signatures because of there is not enough information to differentiate"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8990ea-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 11, "chroma:document": "do not attempt to interpret these signatures because of there is not enough information to differentiate \nbetween different possible interpretations. Because of these issues, impulse permeability estimates should \nbe compared with the results from the h -function and G -function methods,  and if there is large discrepancy, \nthe results should be regarded with lower confidence. Performing multiple DFIT \u2019s in the same formation \nin different wells is a good way to test for consistency and identify anomalous results.   \nZanganeh et al. (2018) also  performed simulations suggesting the possibility of false radial flow after the \npeak in t*dP/dt. However, their simulations did not consider multiphase effects or multiple fracture strands. \nOur findings are different because under the basic conditions of one fracture strand and single phase flow, \nwe did not observe false radial. The cause of the discrepancy is unclear, but may be  related to how they"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899130-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 11, "chroma:document": "we did not observe false radial. The cause of the discrepancy is unclear, but may be  related to how they \nmodeled fracture compliance evolution as the fracture closed.  \nFinally, interpreters should keep in mind that  poroelastic responses caused by injection or production \nactivity in offset wells can occur at substantial distances, causing abrupt and anomalous responses. These \nresponses are most likely to affect  late-time transients  because they  have the greatest dura tion and are \nsensitive to  small pressure changes . \n3.1.6 Pore pressure estimation   \nThe pore pressure can be estimated by linearly extrapolating the pressure trend during impulse flow to \nreciprocal time (or reciprocal square root time) of zero (Section A.6). Extrapolation of the pressure trend in \nFigure 6 yields a pressure estimate of 6825 psi. As discussed in Section 3.1 .5, the straight line in Figure 6"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899180-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 11, "chroma:document": "Figure 6 yields a pressure estimate of 6825 psi. As discussed in Section 3.1 .5, the straight line in Figure 6 \nis not actually r adial flow. If the transient had extended for much longer, the derivative curve would have \nlikely straightened into a linear signature (resulting in a more rapid decrease in pressure than if the trend \nhad continued along a t^ -1 scaling). Th erefore , pore pr essure is  probably  modestly lower than 6825 psi.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8991d0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 12, "chroma:document": "URTeC 123   13 \n \nFigure 6: Pressure versus reciprocal time for a Utica DFIT.  \n3.1.7 Permeability estimation from linear flow transients  \nPermeability can be estimated using three linear -flow techniq ues (G -function, h -function, and impulse \nlinear) and from impulse radial -flow. In the example transient, impulse linear is not apparent and so cannot \nbe used.  \nThe G -function method calculates leakoff coefficient from dP/dG, and permeability is calculated f rom \nleakoff coefficient (Nolte, 1979; Valko and Economides, 1999; Section A.10.i). However, in the example \ndataset, dP/dG is constantly changing ( Figure 1). Which value o f dP/dG should be used? As discussed in \nSection 3.1 .1, the minimum dP/dG is the point least disturbed by either near -wellbore pressure drop or \ncontacting of the fracture walls. Therefore, this is the point that is most representative of the true value of \ndP/dG in the fracture, and it should be used to estimate leakoff coefficient."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899220-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 12, "chroma:document": "dP/dG in the fracture, and it should be used to estimate leakoff coefficient.  \nThe calculation requires an assumption of either radial or PKN geometry. In most cases, we recommend \nthe radial assumption. The PKN assumption can be used if there is strong evid ence of height confinement \nin the layer. In many cases, the diameter calculated from the DFIT interpretation assuming radial geometry \nis less than or close to the \u2018height\u2019 that is under consideration for a PKN interpretation. In this case, the \nradial inter pretation is the preferred choice.  \nTo minimize uncertainty caused by unknown fracture geometry, it is preferable to perform DFIT\u2019s with \nrelatively low injection volume (5 -20 bbl). With larger injection volume, the fracture will be larger and \nmore likely t o hit stress barriers that limit height (or worse, low stress layers that capture the fracture). \nBecause these stress contrasts complicate the interpretation and may be difficult to predict, lower injection"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899270-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 12, "chroma:document": "Because these stress contrasts complicate the interpretation and may be difficult to predict, lower injection \nvolume reduces uncertainty. Also, with lower volu me, the onset of impulse flow occurs sooner, improving \nthe pore pressure estimate and increasing the probability that it will be possible to derive an impulse -flow \npermeability estimate.  \nConversely, Craig and Jackson (2017) recommend pumping DFIT\u2019s with mo re than 100 bbl. They argue \nthat a large fracture is needed to sample a sufficiently large volume of rock. To address concerns regarding \nheterogeneity, we recommend performing multiple DFIT\u2019s in different wells in the same interval and \nchecking for consist ency. In the field dataset reviewed in this study, the tests were generally performed \nwith 5 -40 bbl of injection, and we observed good consistency in permeability estimates between \nneighboring wells. This result supports the position that fractures created  by 5-40 bbl of injection are large"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8992c0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 12, "chroma:document": "neighboring wells. This result supports the position that fractures created  by 5-40 bbl of injection are large \nenough to sample a representative volume of rock.  \nIn Section A.10.i, we derive equations that can be used to estimate leakoff coefficient from dP/dG. \nCommonly, the G -function leakoff calculation is performed using the eq uations derived by Valko and \nEconomides (1999). However, these equations neglect the impact of wellbore storage, which is \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899310-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 13, "chroma:document": "URTeC 123   14 \nnonnegligible in most DFIT\u2019s. The calculation requires estimation of the fracture size and requires an \nestimate of Shmin. Commonly, eq uations provided by Valko and Economides (1999) are used to estimate \nfracture size. However, these equations are only valid in the case of zero leakoff and zero wellbore storage. \nIf wellbore storage coefficient and leakoff coefficient are set to zero in th e equations in Section A.10.i, they \nsimplify to the relations from Valko and Economides (1999).  \nIn the analysis of the Utica DFIT, a PKN geometry is assumed with height of 110 ft. If the analysis is \nrepeated with a radial assumption, the diameter is estima ted to be 180 ft, and the permeability estimates are \nabout 30% lower.  \nWhen applied to the Utica dataset, the G -function estimate for leakoff coefficient is 9.2e -5 ft/min^(1/2). \nThe leakoff coefficient can be converted to permeability from the definition of  leakoff coefficient for"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89937e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 13, "chroma:document": "The leakoff coefficient can be converted to permeability from the definition of  leakoff coefficient for \n\u2018reservoir dominated flow\u2019 (Equation 19). This assumes that the impact of the filtrate zone is zero. The \nconvers ion to permeability uses the viscosity and compressibility of the mobile fluid phase in the reservoir, \nnot the viscosity and compressibility of the injection fluid. We implicitly neglect any other potential \nmultiphase flow effects, such as capillary pressu re, and neglect the possibility of pressure dependent \npermeability. Below, we discuss comparison of impulse linear permeability estimates with G -function \npermeability estimates to assess the impact of these additional processes. The G -function permeability  \nestimate is 27 nd.  \nNext, permeability can be estimated from the h -function method (Section A.10.ii). The h -function integrates \nthe effective pressure response using a time -convolution integral of the Carter leakoff solution, accounting"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8993ce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 13, "chroma:document": "the effective pressure response using a time -convolution integral of the Carter leakoff solution, accounting \nfor the change in pressure over time. Fracture surface area is estimated using a mass balance equation \naccounting for wellbore storage and fluid leakoff.  \nThe h -function method is related to the method of Mayerhofer et al. (1995). One difference is that \nMayerhofer et al. (19 95) use a convolution integral of the constant rate solution, and then estimate leakoff \nrate, whereas the h -function directly integrates the constant pressure solution. The method of Mayerhofer \net al. (1995) requires an estimate of fracture area. As with t he G -function method, the equations from Valko \nand Economides (1999) are sometimes used to estimate area with the method of Mayerhofer et al. (1995). \nBut as described above, this technique neglects wellbore storage and leakoff. The h -function method is als o \nrelated to the technique described by Wang and Sharma (2018)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89941e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 13, "chroma:document": "related to the technique described by Wang and Sharma (2018).  \nSometimes, fracture size is estimated with the Mayerhofer method by using an equation for predicting the \ntime to impulse linear flow (Equation 3 from Craig et al., 2002). This equation is borr owed from \nconventional well test analysis. While it is valid in the context for which it was originally developed \n(Section 6.10.1 from Lee and Wattenbarger, 1996), the physics of a DFIT are very different, and there is \nnot a theoretical justification for a pplying it to predict the timing of impulse linear flow in a DFIT. \nSimulation results indicate that it is often inaccurate. It not even directionally accurate in predicting the \nonset of impulse linear flow. For example, increasing Young\u2019s modulus causes a larger fracture, more \nsurface area, earlier fracture contact, and earlier impulse linear flow (because contact accelerates the onset"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89946e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 13, "chroma:document": "surface area, earlier fracture contact, and earlier impulse linear flow (because contact accelerates the onset \nof impulse linear, as discussed by McClure, 2017). Yet, the relation from Craig et al. (2002) predicts that \nwith more fract ure surface area, impulse linear flow will happen later.  \nIf the method of Mayerhofer  et al. (1999) is applied with an accurate estimate of fracture size, then it is \nexpected to yield an accurate estimation of permeability.  \nWhen applied to the transient  in Figure 1, the h -function permeability estimate is 14 nd. Similar to the G -\nfunction permeability estimate above, this estimate neglects any potential multiphase flow effects.  \nImpulse linear is not presen t in Figure 1. However, if it were present, permeability could be estimated from \ndP/d(t^( -1/2)), using the standard impulse flow solutions (Section A.10.iii). As with the other linear \nmethods, surface area can be estimated from a mass balance relation (Section A.10.iii). Unlike the G -"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8994be-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 13, "chroma:document": "methods, surface area can be estimated from a mass balance relation (Section A.10.iii). Unlike the G -\nfunction and h -function methods, the impulse linear permeability estimate is unaffected by multiphase \nleakoff effects or the potential for pre ssure dependent permeability. It is controlled by the pressure transient Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899504-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 14, "chroma:document": "URTeC 123   15 \nin the reservoir away from the filtrate zone. Therefore, this estimate, if available, may be considered more \nrepresentative of reservoir flow behavior and more applicable to reservoir  engineering calculations of \nproduction.  \nIn our field dataset, impulse linear was present in a substantial percentage of tests. In these tests, we \nobserved that the impulse linear permeability estimate was usually 2 -5 times smaller than the G -function \nand h-function estimates. Because of this observation, in cases when an impulse linear estimate is not \navailable, it may be advisable to reduce the permeability estimate from the G -function or h -function \nmethods by 3-fold when used in rate -transient or reserv oir engineering calculations.  \nBarree et al. (2015a) propose that permeability can be related to  the time to closure ( as estimated from the \ntangent method), without considering the effect of injection volume, fluid viscosity, Young\u2019s modulus,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899554-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 14, "chroma:document": "tangent method), without considering the effect of injection volume, fluid viscosity, Young\u2019s modulus, \nfluid compress ibility, or any other parameters. Simulations and comparison with field data indicate that this \nmethod is often severely inaccurate. We performed sensitivity analysis simulations in which we held \npermeability constant, but varied parameters such as viscosi ty (difference between gas and oil), modulus, \nand injection volume. The time to \u2018closure\u2019  (as picked by the tangent method)  varied widely, resulting in \ngreatly different permeability estimates from the method of Barree et al. (2015a), even though the \nperme ability was the same in all simulations.  \nIn the Utica DFIT , using the tangent method of picking closure, the time to closure is 1960 min. The \ninjection duration is 9.7 min. Therefore, the equation proposed by Barree et al. (2015a) implies that \npermeability  is equal to 1. 6 microdarcy. This estimate is almost 100 times too high."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8995a4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 14, "chroma:document": "permeability  is equal to 1. 6 microdarcy. This estimate is almost 100 times too high.  \n3.1.8 Permeability estimation from radial flow  \nAs discussed in Section 3.1 .5, we believe that the late -time transient in Figure 5 is false radial caused by \ninteraction of evolving fracture stiffness after contact with multiphase flow effects. However, for \ncomparison, we can use it to estimate permeability. The permeability -height product (kh) is estim ated using \nthe impulse radial solution (Section A.10.iv). Permeability is estimated by dividing kh by the estimate for \nheight. If PKN geometry is assumed, then height is known. If radial geometry is assumed, we use the mass \nbalance approach to estimate dia meter, and set height equal to diameter.  \nThe radial permeability estimate from the example dataset is 734 nd. This estimate is roughly 50x greater \nthan the estimates from the G -function and h -function methods. The overestimate  is consistent with"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8995f4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 14, "chroma:document": "than the estimates from the G -function and h -function methods. The overestimate  is consistent with \nexpectati on from simulation  results  and comparison with field data, as discussed in Section 3.1 .5. \nIn this case, the operator had already evaluated, and discarded, the radial permeability estimate. The \noperator\u2019s diagnostics and analysis (performed prior to this DF IT study) suggested that the permeability is \nin the range of 10 -20 nd, similar to the values calculated in Section 3.1 .7 (Cipolla et al., 2018).  \nWe observed a false radial signature in the majority of  field DFIT \u2019s that we reviewed from a gas reservoir, \ninvolving tests in the Montney, Marcellus, and Utica. False radial was also observed in every DFIT \nsimulation we performed of a gas reservoir. In these  cases, using the false radial yielded a large overestimate \nof permeability.  \n3.1.9 Estimating average aperture versus effective stress"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899644-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 14, "chroma:document": "of permeability.  \n3.1.9 Estimating average aperture versus effective stress  \nUsing the technique in Section A.14, it is possible to derive a n approximate  plot of average aperture versus \neffective stress. Figure 7 shows the inferred relationship for the Utica DFIT.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899694-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 15, "chroma:document": "URTeC 123   16 \n \nFigure 7: Approximate  average aperture versus Shmin minus pressure for the Utica DFIT.  \nFigure 7 indicates that the contact pressure (when the system begins to stiffen) occurs when inferred \naperture is around 2 mm. This is typical of the field data reviewed in this study: the aperture at the contact \npressure was usually inferred to be in th e range of 0.5 \u2013 3 mm.  \nIt is an important finding that the system begins to stiffen at an aperture on the order of millimeters. This \nfinding is consistent with the finding from Branagan et al. (1996) that the residual tilt at late -time was 20% \nof the maxi mum observed tilt, experimental results from (Suarez -Rivera et al., 2013) showing macroscopic \ncomplexity in hydraulic fracture geometry, and DFIT analyses from Wang and Sharma (2018).  \nMcClure et al. (2016) defined \u2018fracture closure\u2019 as being equivalent to  what we are now calling the \u2018contact"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8996e4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 15, "chroma:document": "McClure et al. (2016) defined \u2018fracture closure\u2019 as being equivalent to  what we are now calling the \u2018contact \npressure\u2019 \u2013 the pressure at which the walls begin to contact and the system stiffens. The problem with the \ndefinition from McClure et al. (2016) is that it may seem counterintuitive to define \u2018closure\u2019 as occurring \nat a point when the average fracture aperture is still substantial.  \n3.2 Comparison with simulation  \nA numerical simulation was performed based on the parameters inferred from the data ( Figure 8). The \nsimulation is performed with permeability of 14 nd, Shmin equal to 7975 psi, pore pressure equal to 6900 \npsi, and near -wellbore pressure drop coefficient of 1500 psi/bpm^(1/2). The simulations appear very similar \nto the actual da ta (Figure 1 and Figure 5). The log -log plot indicates a bend into a -1 slope after t he hump \nin t*dP/dt. The simulation shows a -1/2 slope after the -1 slope. This is not visible in the data, but the actual"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899734-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 15, "chroma:document": "in t*dP/dt. The simulation shows a -1/2 slope after the -1 slope. This is not visible in the data, but the actual \ntest terminated prior to 10^4 minutes, and the -1/2 slope in the simulation does not develop until after 10^4 \nminutes.  \nIn order to improve the match to data, it was necessary to vary the W0 and \ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53 parameters from the Willis -\nRichards et al. (1995) equation for fracture aperture after contact (Equation 1). This was necessary because \nthe shape of the aperture versus effective stress curve has a significant effect on the shape of the transient \nin the period after contact and prior to impulse flow. Permeability, pore pressure, and Shmin were not varied \nto match the data \u2013 the parameters were taken directly from the inte rpretation performed prior to running \nthe simulation.  \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89977a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 16, "chroma:document": "URTeC 123   17 \n \n \nFigure 8: DFIT simulation based on the Utica DFIT.  \n3.3 Other field examples  \nFigure 9 shows results from a DFIT performed in an oil well in the Wolfcamp shale (WHP is plotted without \nadjustment to BHP). Approximately 3000 psi of near -wellbore pressure drop dissipates in the first 30 \nminutes after shut -in. The dP/dG plot shows good indication o f contact, and the log -log plot shows a -1/2 \nslope after the hump in t*dP/dt. Using a radial fracture geometry, the G -function method yields a \npermeability estimate of 289 nd; the h -function method yields an estimate of 401 nd, and the impulse linear \ntrend  yields an estimate of 162 nd.   \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8997ca-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 17, "chroma:document": "URTeC 123   18 \n \nFigure 9: G-function and log -log plots for a DFIT performed in the Wolfcamp B. The G -function plot shows measured WHP.  \nDFIT\u2019s were performed in all five wells in this pad. All five were landed in the Wolfcamp B. They all show  \nthousands of psi of near -wellbore pressure drop and ha ve good indication of contact, as indicated from \ndP/dG increasing from a minimum. The estimates  of Shmin are all within 150 psi of each other. The G -\nfunction permeability estimates are: 168 nd, 212 nd, 289 nd, 188 nd, and 638 nd. The h -function \npermeability estimates are: 204 nd, 137 nd, 401 nd, 142 nd, and 619 nd. Three of the DFIT\u2019s show an \nindica tion of impulse linear. The impulse linear permeability estimates are 64 nd, 162 nd, and 44 nd. None \nof the DFIT\u2019s shown an indication of impulse radial.  \nFigure 10 shows a  dP/dG plot from a field DFIT in a vertical well the Lower Eagle Ford. As expected from"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89981a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 17, "chroma:document": "Figure 10 shows a  dP/dG plot from a field DFIT in a vertical well the Lower Eagle Ford. As expected from \na vertical well (in a non -thrust faulting regime), the near -wellbore tortuosity pressure drop is minimal. The \nestimate for Shmin is 12,076 psi. Assuming radial geometry , the G -function method permeability estimates \nis 171 nd, and the h -function method estimate is 126 nd.  \n \nFigure 10: dP/dG  and pressure versus G -time for a DFIT in a vertical well in the Lower Eagle Ford.  \n4. Discussion  \n4.1 Tests without a clear pick for contact pressure  \nThe clarity of the pick for contact pressure can be assessed from the separation between the minimum and \nmaximum dP/dG. If there is not good separation, a clear pick may also be possible if an inflection can be \nidentified from the relative stiffness plot. Nevertheless, in some tests, a clear pick is not possible. Figure 11 \nshows an example of a test with monotonically decreasing dP/dG and a smoothly, gradually increasing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89986a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 17, "chroma:document": "shows an example of a test with monotonically decreasing dP/dG and a smoothly, gradually increasing \nrelative stiffness.  \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8998ba-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 18, "chroma:document": "URTeC 123   19 \n \nFigure 11: G-function plot and relative stiffness plot for a  DFIT performed in the Middle Bakken (in Figure 11a, blue is pressure and red is \ndP/dG). It is not possible to identify the contact pressure or estimate Shmin.  \nBy performing simulations under a variety of conditions, we identified processes that can cause \nmonotonically decreasing dP/dG:  \n1. If a significant volume of fluid has been pumped into the formation prior to the DFIT, such that the \nDFIT involves reinjection into a pre -existing, previously -created hydraulic fracture.  \n2. If injection occurs directly into a h ighly conductive natural fracture.  \n3. If the hydraulic fracture intersects a highly conductive natural or pre-existing hydraulic fracture.  \n4. If the matrix permeability divided by formation fluid viscosity is sufficiently high (> 0.01-0.1 \nmd/cp).  \n5. If near -wellbore  pressure drop is very severe, masking the pressure transient in the far -field \nfracture."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89990a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 18, "chroma:document": "md/cp).  \n5. If near -wellbore  pressure drop is very severe, masking the pressure transient in the far -field \nfracture.  \nFor the first four scenarios listed above, dP/dG is monotonic because the fracture walls contact almost \ninstantly after shut -in (or perhaps, never fully separated) . If injection reopens a pre -existing hydraulic or \nnatural fracture, there is not any  \u2018toughness\u2019 that must be overcome  in order to propagate the effective \u2018tip\u2019 \nof reopening. As a result, the fracture opens just enough to conduct flow. After shut -in, the wall s contact \nvery rapidly, and fluid continues to flow outward into the rest of the pre -existing fracture. In scenario #3, \nthe fracture walls contact rapidly because fluid flows out into the pre -existing fracture. In scenario #4, the \nfracture walls contact ra pidly because growth is limited by leakoff, rather than resistance to propagation at"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89995a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 18, "chroma:document": "fracture walls contact ra pidly because growth is limited by leakoff, rather than resistance to propagation at \nthe tip. In scenario #5, the pinch -point caused by near -wellbore pressure drop is so severe that the real \npressure transient in the hydraulic fracture is not observed.  \nIf the test in Figure 11 was in a vertical well, it might be justifiable to assume  that there is not any near -\nwellbore tortuosity , and the ISIP could be taken as an estimate for Shmin (because of the 'rapid contact\u2019 \ninterpretations #1 -#4). But because this test is in a horizontal well, it is unclear whether to interpret that the \nfracture walls have rapidly contacted or to interpret that near-wellbore pressure drop is obscuring the true \ntransient (or a combination of both). Because of these uncertainties, a test in a horizontal well without cl ear \nevidence of a contact pressure cannot be confidently interpreted. In either vertical or horizontal wells, it"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8999a0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 18, "chroma:document": "evidence of a contact pressure cannot be confidently interpreted. In either vertical or horizontal wells, it \nwill be impossible to estimate fracture area and permeability because the net pressure cannot be estimated. \nIt might be possible to estimate pe rmeability from impulse radial flow. If impulse  linear or radial  flow is \nreached, it will be possible to estimate pore pressure.  \n4.2 Impact of the permeability estimate  \nRate-transient analysis (RTA) of production data in shale typically indicates linear fl ow. By matching the \nlinear flow equation to the production data, it is possible to derive an estimate for \ud835\udc34\u221a\ud835\udc58. However, without \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8999f0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 19, "chroma:document": "URTeC 123   20 \nan independent estimate for permeability, the RTA match is nonunique. With a DFIT permeability estimate, \nit is possible to uniq uely estimate effective fracture area from the \ud835\udc34\u221a\ud835\udc58 value taken from the RTA.  \nIn the Utica dataset, the false/invalid radial flow evaluation and the method from Barree et al. (2015a) yield \na 50-100-fold overestimate of permeability. Holding \ud835\udc34\u221a\ud835\udc58 constant, this implies that the effective fracture \narea (or if height is assumed, effect ive fracture length) will be underestimated by a factor of 7 -10.  \nThe analysis provided by Barree et al. (2015b) may be an example of the consequences of overestimated \npermeability in a gas reservoir. They analyze a gas shale well with DFIT -derived permeab ility and an RTA \nmatch to production data. They estimate the effective fracture length to be just 35 ft. Th is estimate  seems  \nimplausibly low . \nTo test the impact on net -present value, we history matched ResFrac simulations to the Utica well"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899a40-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 19, "chroma:document": "implausibly low . \nTo test the impact on net -present value, we history matched ResFrac simulations to the Utica well \nproduction data,  using either 1 microdarcy or 20 nd as the permeability estimate. Then, we performed a \nseries of simulations with different cluster and well spacing and performed simple economic calculation s \nof net-present value. The high and low permeability models yielded different optimal designs. Applying \nthe optimal design from the \u2018high permeability\u2019 model to the \u2018low permeability\u2019 model resulted in large \nreduction in net present value. The details of this comparison will be shown in a separate, standalone  paper. \nThe analysis shows that improved accuracy from the DFIT permeability estimate can improve fracture \ndesign and well placement and significantly increase return on investment.  \n5. Conclusions  \nBy integrating detailed nume rical simulations, field data, operator experience, and mathematical analysis,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899a86-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 19, "chroma:document": "5. Conclusions  \nBy integrating detailed nume rical simulations, field data, operator experience, and mathematical analysis, \nwe developed a step -by-step procedure for estimating stress, permeability, and pore pressure from DFIT\u2019s \nin low permeability formations.  \n\u2012 Near -wellbore pressure drop typically c auses 1000s of psi of pressure drop at early time in DFIT\u2019s \nin horizontal wells. If this occurs, then f or tens of minutes after shut -in, pressure measured in the \nwell is much higher than the pressure in the far -field hydraulic fracture. The effective ISIP (an \nestimate for the pressure in the fracture at shut -in) can be estimated from a G -function plot.  \n\u2012 Analogous to the g -function, the h -function is proportional to the cumulative volume of fluid leaked \noff from the fracture since the start of injection. Unl ike the g -function, the h -function accounts for \ndeviation from Carter leakoff as the pressure in the fracture decreases. The h -function is useful in"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899ad6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 19, "chroma:document": "deviation from Carter leakoff as the pressure in the fracture decreases. The h -function is useful in \nmathematical derivations used for permeability estimation and for the construction of a relative \nstiffness plot. \n\u2012 The G -function and h -function methods can be used to estimate permeability from the data prior to \nimpulse flow. We derive mass balance equations for jointly inferring permeability and fracture size. \nUnlike equations commonly used in the literature  (Valko and Economides, 1999) , these equations \nconsider wellbore storage and leakoff.  \n\u2012 Impulse linear flow can be used to estimate permeability as long as fracture area can be estimated. \nSimilar to the G -function and h -function methods, permeability can be jo intly estimated with area \nusing a mass balance equation.  \n\u2012 Simulations show that a variety of processes can cause the appearance of impulse radial, even in"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899b26-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 19, "chroma:document": "using a mass balance equation.  \n\u2012 Simulations show that a variety of processes can cause the appearance of impulse radial, even in \nsituations where flow is not actually radial. This problem is especially severe in gas shale, where \nfalse radial is common in both simulation results and in real data. Analysis based on false radial \nflow typically leads to a 10 -100x overestimate of permeability. Genuine radial is most likely to \noccur in low volume DFIT \u2019s and in formations with permeabilit y divided by viscosity greater than \n1 microdarcy/cp.  \n\u2012 The G -function and h -function permeability estimates are usually similar. The G -function method \nis more sensitive to error  due to  elevated dP/dG from near -wellbore pressure drop. With field data, \nimpulse  linear permeability estimates are usually 2 -5 times lower than the G -function and h -function"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899b76-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 19, "chroma:document": "impulse  linear permeability estimates are usually 2 -5 times lower than the G -function and h -function \nmethods. The G -function and h -function estimates may be impacted by multiphase effects or by Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899bc6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 20, "chroma:document": "URTeC 123   21 \npressure dependent permeability. Therefore, the impulse linear flow p ermeability estimate is \ntypically preferred for reservoir engineering calculations. If impulse linear flow is not available, the \nG-function or h -function methods may be adjusted downward by about 3-fold. There is moderate \nuncertainty in the permeability es timates, and modelers should have reasonable freedom to modify \npermeability  if needed to match production data.  \n\u2012 The magnitude of the minimum principal stress can be estimated by identifying the \u2018contact \npressure\u2019 which is the pressure at which the fracture  walls come into contact and the system begins \nto stiffen. The minimum principal stress can be estimated to be approximately 75 psi below the \ncontact pressure. This is effectively the \u2018compliance method\u2019 of picking \u2018fracture closure\u2019 (McClure \net al., 2016) . However, we have defined the new term \u2018contact pressure\u2019 to avoid confusion with a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899c0c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 20, "chroma:document": "et al., 2016) . However, we have defined the new term \u2018contact pressure\u2019 to avoid confusion with a \nvariety of other definitions of \u2018closure.\u2019 Rather than using a plot of G*dP/dG (as recommended by \nMcClure et al., 2016), we recommend identifying the contact pressure from  a plot of dP/dG or from \na relative stiffness plot.  \n\u2012 It is possible to approximately infer the relationship between aperture and effective stress. Field data \nshows that the average fracture aperture is between 0.5 -3 mm at the contact pressure, and continues  \nto be substantial when the fluid pressure is equal to the minimum principal stress. This is evidently \nthe manifestation of the roughness of in -situ hydraulic fractures.  \n\u2012 DFIT permeability estimates have direct implication for fracture design and can significantly impact \neconomic returns.  \n \nAcknowledgements  \nWe gratefully acknowledge the financial support of ConocoPhillips  Company , Hess Corporation, Shell"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899c5c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 20, "chroma:document": "economic returns.  \n \nAcknowledgements  \nWe gratefully acknowledge the financial support of ConocoPhillips  Company , Hess Corporation, Shell  \nInternational Exploration and Production Inc. , Equinor, Keane Group, Range Resources Corporation, an d \nApache Corporation.  We also want to recognize the important contributions of the study participants who \nare not listed as coauthors.  \n \nReferences  \nAyoub, J. A., D. P. Bourdet, Y. L. Chauvel. 1988. Impulse testing. SPE Formation Evaluation 3 (3): 534 -\n546, d oi: 10.2118/15911 -PA. \nBarree, R. D., H. Mukherjee. 1996. Determination of pressure dependent leakoff and its effect on fracture \ngeometry. SPE 36424. Paper presented at the 71st Annual Technical Conference and Exhibition, Denver, \nCO. \nBarree, R. D., V. L. Ba rree, and D. P. Craig. 2009. Holistic fracture diagnostics: Consistent interpretation \nof prefrac injection tests using multiple analysis methods. SPE 107877. Paper presented at the SPE Rocky"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899d24-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 20, "chroma:document": "of prefrac injection tests using multiple analysis methods. SPE 107877. Paper presented at the SPE Rocky \nMountain Oil & Gas Technology Symposium, Denver, CO.  \nBarree, R. D ., J. L. Miskimins, and J. V. Gilbert. 2015 a. Diagnostic fracture injection tests: common \nmistakes, misfires, and misdiagnoses. SPE Production & Operations 30 (2): 84-98, doi: 10.2118/169539 -\nPA. \nBarree, R. D., S. A. Cox, J. L. Miskimins, J. V. Gilbert, and  M. W. Conway. 2015b. Economic optimization \nof horizontal -well completions in unconventional reservoirs. SPE Production & Operations 3 (4): 293 -311, \ndoi: 10.2118/168612 -PA. \nBarree, R. D. and J. L. Miskimins. 2016. Physical explanations of non-linear derivatives in diagnostic \nfracture injection test analysis. SPE 179134 -MS. Paper presented at the SPE Hydraulic Fracturing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899d74-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 20, "chroma:document": "fracture injection test analysis. SPE 179134 -MS. Paper presented at the SPE Hydraulic Fracturing \nTechnology Conference, The Woodlands, TX.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899dc4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 21, "chroma:document": "URTeC 123   22 \nBarton, N., S. Bandis, K. Bakhtar. 1985. Strength, deformation and conductivity coupling of rock joints. \nInternational Journal of Rock Mechanics and Mining Sciences & Geomechanics Abstracts  22 (3): 121 -140, \ndoi: 10.1016/0148 -9062(85)93227 -9. \nBazan, Lucas W. and Bruce R. Meyer. 2015. Fracture complexity: analysis methodology and signat ure \npressure behavior of hydraulic fracture propagation from horizontal wellbores. SPE 176919. Paper \npresented at the SPE Asia Pacific Unconventional Resources Conference and Exhibition, Brisbane, \nAustralia.  \nBird, R. Byron, Warren E. Stewart, Edwin N. Ligh tfoot. 2006. Transport Phenomena, 2nd edition, John \nWiley & Sons, Inc.  \nBlanton, T. L. and J. E. Olson. 1999. Stress magnitudes from logs: Effects of Tectonic Strains and \nTemperature. SPE Reservoir Evaluation and Engineering 2 (1), 62 -68, doi: 10.2118/54653 -PA. \nBourdet, D., T. M. Whittle, and A. A. Douglas. 1983. A new set of type curves simplifies well test analysis."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899e14-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 21, "chroma:document": "Bourdet, D., T. M. Whittle, and A. A. Douglas. 1983. A new set of type curves simplifies well test analysis. \nWorld Oil: 95 -106. \nBranagan, P. T., N. R. Warpinski, B. Enger, and R. Wilmer. 1996. Measuring the hydraulic fracture -induced \ndeformation of reservoirs and adjacent rocks employing a deeply buried inclinometer arra y: GRI/DOE \nmulti-site project. SPE 36451. Paper presented at the SPE Annual Technical Conference and Exhibition, \nDenver, CO.  \nCarslaw, H. S., and J. C. Jaeger. 1959. Conduction of Heat in Solids. 2nd ed. Oxford University Press, Great \nBritain.  \nCastillo, J. L. 1987. Modified fracture pressure decline analysis including pressure -dependent leakoff. SPE \n16417. Paper presented at the SPE/DOE Low Permeability Reservoir Symposium, Denver, CO.  \nCipolla, Craig, Constance Gilbert, Aviral Sharma, and John LeBas. 2018. C ase history of completion \noptimization in the Utica. SPE 189838 -MS. Paper presented at the SPE Hydraulic Fracturing Technology"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899e64-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 21, "chroma:document": "optimization in the Utica. SPE 189838 -MS. Paper presented at the SPE Hydraulic Fracturing Technology \nConference and Exhibition, The Woodlands, TX.  \nClark, J. B. 1949. A hydraulic process for increasing the productivity of wells. Jo urnal of Petroleum \nTechnology 1 (1): 1 -8. \nCraig, David P., Ted D. Brown. 1999. Estimating pore pressure and permeability in massively stacked \nlenticular reservoirs using diagnostic fracture -injection tests. SPE 56600. Paper presented at the SPE \nAnnual Tech nical Conference and Exhibition, Houston, TX.  \nCraig, David P., Mike J. Eberhard, Chad E. Odegard, and Muthukumarappan Ramurthy. 2002. \nPermeability, pore pressure, and leakoff -type distributions in Rocky Mountain Basins. SPE 75717. Paper \npresented at the SP E Gas Technology Symposium, Calgary, Alberta, Canada.  \nCraig, David P. 2014. New type curve analysis removes limitations of conventional after -closure analysis"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899eb4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 21, "chroma:document": "Craig, David P. 2014. New type curve analysis removes limitations of conventional after -closure analysis \nof DFIT data. SPE 168988 -MS. Paper presented at the SPE Unconventional Resources Conference, The \nWoodlands, TX.  \nCraig, D. P. and T. A. Blasingame. 2006. Application of a new fracture -injection/falloff model accounting \nfor propagating, dilated, and closing hydraulic fractures. SPE 100578. Paper presented at the SPE Gas \nTechnology Symposium, Calgary, Al berta.  \nCraig, D. P., R. D. Barree, N. R. Warpinski, and T. A. Blasingame. 2017. Fracture closure stress: \nReexamining field and laboratory experiments of fracture closure using modern interpretation \nmethodologies. SPE 187038. Paper presented at the SPE Annu al Technical Conference and Exhibition, San \nAntonio, TX.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899f04-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 22, "chroma:document": "URTeC 123   23 \nCraig, David and Robert Jackson. 2017. Calculating the volume of reservoir investigated during a fracture -\ninjection/falloff test DFIT. SPE 184820. Paper presented at the SPE Hydraulic Fracturing Tech nology \nConference and Exhibition, The Woodlands, TX.  \nCramer, D. D. and D. H. Nguyen. 2013. Diagnostic fracture injection testing tactics in unconventional \nreservoirs. SPE 163863 . Paper presented at the SPE Hydraulic Fracturing Technology Conference, \nWoodla nds, TX.  \nCramer, D., Friehauf, K., Roberts, G., Whittaker, J. 2019. Integrating DAS, Treatment Pressure Analysis \nand Video -based Perforation Imaging to Evaluate Limited Entry Treatment Effectiveness. SPE 194334. \nPaper presented at the SPE Hydraulic Fractur ing Technology Conference, Woodlands, TX.  \nCrouch, S. L. and A. M. Starfield. 1983. Boundary Element Methods in Solid Mechanics . George Allen & \nUnwin (Publishers), Ltd."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899f4a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 22, "chroma:document": "Crouch, S. L. and A. M. Starfield. 1983. Boundary Element Methods in Solid Mechanics . George Allen & \nUnwin (Publishers), Ltd.  \nDelaney, Paul T., David D. Pollard, Joseph I. Ziony, and Edwin H. McKee. 1986. Field rel ations between \ndikes and joints: emplacement processes and paleostress analysis. Journal of Geophysical Research, 91 \n(B5): 4920 -4938, doi: 10.1029/JB091iB05p04920 . \nEaton, Ben A. 1969. Fracture gradient prediction and its application in oilfield operations.  Journal of \nPetroleum Technology 21 (10): 1353 -1360, doi: 10.2118/2163 -PA \nEconomides, Michael J. and Kenneth G. Nolte, eds. 2000. Reservoir Stimulation. Wiley.  \nEconomides, Michael and Tony Martin. 2008. Modern Fracturing \u2013 Enhancing Natural Gas Production.  \nEnergy Tribune Publishing.  \nEhlig -Economides, Christine A. and Michael J. Economides. 2000. Chapter 2: Formation characterization: \nWell and reservoir testing. In Reservoir Stimulation, eds, Michael J. Economides and Kenneth G. Nolte, \nWiley."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899f9a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 22, "chroma:document": "Well and reservoir testing. In Reservoir Stimulation, eds, Michael J. Economides and Kenneth G. Nolte, \nWiley.  \nGale, Julia F. W., Sara J. Elliott, and Stephen E. Laubach. 2018. Hydraulic fractures in core from stimulated \nreservoirs: core fracture description of HFTS slant core, Midland Basin, West Texas. Paper presented at the \nUnconventional Resources Technology Conference, Houst on, TX.  \nGodbey, J. K., H. D. Hodges. 1958. Pressure measurements during formation fracturing operations. \nPetroleum Transactions, AIME 213: 65 -69 \nGringarten, Alain C., Henry J. Ramey, R. Raghavan. 1974. Unsteady -state pressure distributions created \nby a wel l with a single infinite conductivity vertical fracture. SPE Journal 14 (4): 347 -360, doi: \n10.2118/4051 -PA. \nGu, H., J. L. Elbel, K. G. Nolte, A. H. D. Cheng, Y. Abousleiman. 1993. Formation permeability \ndetermination using impulse -fracture injection. SPE  25425. Paper presented at the Production Operations \nSymposium, Oklahoma City, OK."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b899fea-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 22, "chroma:document": "determination using impulse -fracture injection. SPE  25425. Paper presented at the Production Operations \nSymposium, Oklahoma City, OK.  \nGulrajani, Sunil N. and K. G. Nolte. 2000. Chapter 9: Fracture Evaluation using Pressure Diagnostics . In \nReservoir Stimulation, eds, Michael J. Economides and Kenneth G. Nolte, Wiley.  \nHaimson, Bezalel, Charles Fairhurst. 1967. Initiation and extension of hydraulic fractures in rocks. Society \nof Petroleum Engineers Journal 7 (3), doi: 10.2118/1710 -PA. \nHawkes, R. V., R. Bachman, K. Nicholson, D. D. Cramer, and S. T. Chipperfield. 2018. Good tests cost \nmoney, bad tests cost more \u2013 a critical review of DFIT analysis gone wrong. SPE 191458. Paper presented \nat the SPE International Hydraulic Fracturing Technology Conference and Exhibition, Muscat, Oman.  \nHickman, Stephe n H., Mark D. Zoback. 1983. The interpretation of hydraulic fracturing pressure -time data"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a03a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 22, "chroma:document": "Hickman, Stephe n H., Mark D. Zoback. 1983. The interpretation of hydraulic fracturing pressure -time data \nfor in -situ stress determination. In Hydraulic Fracturing Measurements, ed. M. D. Zoback and B. C. \nHaimson, 44 -54. Washington D.C., National Academy Press.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a080-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 23, "chroma:document": "URTeC 123   24 \nHorne, Rol and N. 1995. Modern Well Test Analysis: A Computer -Aided Approach, 2nd edition. Palo Alto, \nCA, Petroway, Inc.  \nHouze, Olivier P., Roland N. Horne, Henry J. Ramey. 1988. Pressure -transient response of an infinite \nconductivity vertical fracture in a reservoir  with double -porosity behavior. SPE Formation Evaluation 3 \n(3): 510 -518, doi: 10.2118/12778 -PA. \nHoward, George C. and C. R. Fast. 1957. Optimum fluid characteristics for fracture extension. Paper \npresented at the Spring Meeting of the Mid -Continental Distr ict, Division of Production, Tulsa, OK.  \nHubbert, M. K., D. G.  Willis. 1957. Mechanics of hydraulic fracturing. Journal of Petroleum Technology \n9 (6): 153 -168. \nJung, H., M. M. Sharma, D. D. Cramer, S. Oakes, and M. W. McClure. 2016. Re -examining interpreta tions \nof non -ideal behavior during diagnostic fracture injection tests. Journal of Petroleum Science and \nEngineering 145: 114 -136, doi: 10.1016/j.petrol.2016.03.016."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a0d0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 23, "chroma:document": "Engineering 145: 114 -136, doi: 10.1016/j.petrol.2016.03.016.  \nKamal, Medhat M., ed. 2009. Transient Well Testing, Vol. Monograph Series Vol. 23, Society  of Petroleum \nEngineers.  \nKehle, Ralph O. 1964. The determination of tectonic stresses through analysis of hydraulic well fracturing. \nJournal of Geophysical Research 69 (2): 259 -273, doi: 10.1029/JZ069i002p00259.  \nLee, J. and R. Wattenbarger. 1996. Gas Reser voir Engineering. Society of Petroleum Engineers.  \nLiu, Guoqing, Christine Ehlig -Economides, and Jianlei Sun. 2016. Comprehensive Global Fracture \nCalibration Model. SPE 181856. Paper presented at the SPE Asia Pacific Hydraulic Fracturing Conference, \nBeijing , China.  \nMarongiu -Porcu, Matteo, Christine A. Ehlig -Economides, and Michael John Economides. 2011. Global \nmodel for fracture falloff analysis. SPE  144028. Paper presented at the SPE North American \nUnconventional Gas Conference and Exhibition, The Woodlands , TX."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a120-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 23, "chroma:document": "Unconventional Gas Conference and Exhibition, The Woodlands , TX.  \nMarongiu -Porcu, Matteo, Albertus Retnanto, Michael J. Economides, Christine Ehlig -Economides. 2014. \nComprehensive fracture calibration test design. SPE 168634 . Paper  presented at the SPE Hydraulic \nFracturing Technology Conference, The Woodlands, TX.  \nMayerhofer, M. J. and M. J. Economides. 1993. Permeability estimation from fracture calibration \ntreatments. SPE 26039. Paper presented at the SPE Western Regional Meeting, Anchorage, AK.  \nMayerhofer, M. J., C. A. Ehlig -Economides, and M. J. Economides. 1995 . Pressure -transient analysis of \nfracture -calibration tests. SPE 26527. Journal of Petroleum Technology 47 (3): 231 -236. \nMcLennan, J. D., J. -C. Roegiers. 1982. How instantaneous are instantaneous shut -in pressures? SPE 11064. \nPaper presented at the 57th An nual Fall Technical Conference and Exhibition of the Society of Petroleum \nEngineers of AIME, New Orleans, LA."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a170-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 23, "chroma:document": "Paper presented at the 57th An nual Fall Technical Conference and Exhibition of the Society of Petroleum \nEngineers of AIME, New Orleans, LA.  \nMcClure, M. W. 2012. Modeling and characterization of hydraulic stimulation and induced seismicity in \ngeothermal and shale gas reservoirs. PhD The sis, Stanford University, Stanford, California.  \nMcClure, Mark W., Christopher A. J. Blyton, Hojung Jung, and Mukul M. Sharma. 2014. The Effect of \nChanging Fracture Compliance on Pressure Transient Behavior During Diagnostic Fracture Injection Tests . \nSPE 17 0956. Paper presented at the SPE Annual Technical Conference and Exhibition, Amsterdam, The \nNetherlands.  \nMcClure, Mark W., Hojung Jung, Dave D. Cramer, and Mukul M. Sharma. 2016. The fracture compliance \nmethod for picking closure pressure from diagnostic f racture injection tests. SPE Journal 21 (4): 1321 -1339,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a1c0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 23, "chroma:document": "method for picking closure pressure from diagnostic f racture injection tests. SPE Journal 21 (4): 1321 -1339, \ndoi: 10.2118/179725 -PA. Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a210-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 24, "chroma:document": "URTeC 123   25 \nMcClure, Mark. 2017. The spurious deflection on log -log superposition -time derivative plots of diagnostic \nfracture -injection tests. SPE Reservoir Evaluation & Engineering 20 (4 ), doi: 10.2118/186098 -PA. \nMcClure, Mark. 2019. Discussion of the Paper \u201cSPE -187038 -MS: Fracture Closure Stress: Reexamining \nField and Laboratory Experiments of Fracture Closure Using Modern Interpretation Methodologies .\u201d \narXiv:1904.07126  \nMcClure, Mark and Charles Kang. 2018. ResFrac Technical Writeup. arXiv:1804.02092 . \nMeng, Chunfang, Lingli Wei, Roger Yuan. 2014. Coupled fluid flow and geomechanics modeling for DFIT \nanalysis in unconventional gas development. Paper presented at the Intern ational Petroleum Technology \nConference, Kuala Lumpur, Malaysia, doi: 10.2523/18159 -MS. \nMukherjee, H. 1991. Extension of fracture pressure decline curve analysis to fissured formations. SPE \n21872. Paper presented at the Rocky Mountain Regional Meeting and Low-Permeability Reservoir"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a260-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 24, "chroma:document": "21872. Paper presented at the Rocky Mountain Regional Meeting and Low-Permeability Reservoir \nSymposium, Denver, CO.  \nNolte, Kenneth. 1979. Determination of fracture parameters from fracturing pressure decline. SPE 8341. \nPaper presented at the Annual Fall Technical Conference and Exhibition of the Society of Petroleum \nEngi neers, Las Vegas, NV.  \nNolte, K. G., J. L. Maniere, and K. A. Owens. 1997. After -closure analysis of fracture calibration tests. SPE \n38676. Paper presented at the 1997 Annual Technology Conference and Exhibition of the Society of \nPetroleum Engineers, San Antonio, TX.  \nPadmakar, A.  S. 2013. Geomechanics coupled reservoir flow simulation for diagnostic fracture injection \ntest design and interpretation in shale reservoirs. SPE 166201 . Paper  presented at the SPE Annual Technical \nConference and Ex hibition, New Orleans, LA.  \nPerkins, T. K., and J. A. Gonzalez. 1985. The effect of thermoelastic stresses on injection well fracturing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a2b0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 24, "chroma:document": "Perkins, T. K., and J. A. Gonzalez. 1985. The effect of thermoelastic stresses on injection well fracturing \n25(1): 78 -88, doi:  10.2118/11332 -PA. \nRaaen, A. M., E. Skomedal, H. Kjorholt, P. Markestad, D. Okland. 2001. Stress determ ination from \nhydraulic  fracturing tests: the system stiffness approach. International Journal for Rock Mechanics and \nMining Sciences  38 (4): 529 -541, doi: 10.1016/S1365 -1609(01)00020 -X. \nScholz, Christopher H. 2010. A note on the scaling relations for openi ng mode fractures in rock. Journal of \nStructural Geology 32, doi:  10.1016/j.jsg.2010.09.007 . \nShou, Keh -Jian, Eduard Siebrits, Steven L. Crouch. 1997. A higher order displacement discontinuity \nmethod for three -dimensional elastostatic problems. Internationa l Journal of Rock Mechanics and Mining \nSciences 34 (2): 317 -322, doi: 10.1016/S0148 -9062(96)00052 -6. \nSmith, Michael Berry  and Carl T. Montgomery. 2015. Hydraulic Fracturing . CRC Press."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a300-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 24, "chroma:document": "Smith, Michael Berry  and Carl T. Montgomery. 2015. Hydraulic Fracturing . CRC Press.  \nSneddon, I. N. 1946. The distribution of stress in the neighborhood of a crack in an elastic solid. Proceedings \nof the Royal Society of London Series A 187 (1009): 229 -260, doi: 10.1098/rspa.1946.0077  \nSoliman, M. Y.  and Talal Gamadi. 2012. Testing tight ga s and unconventional formations and \ndetermination of closure pressure. SPE 150948 . Paper  presented at the SPE/EAGE European \nUnconventional Resources Conference and Exhibition, Vienna, Austria.  \nSoliman, M. Y., C.S. Kabir. 2012. Testing unconventional format ions. Journal of Petroleum Science and \nTechnology 92-93: 102 -109, doi: 10.1016/j.petrol.2012.04.027.  \nSpivey, John P. and W. John Lee. 2013. Applied Well Test Interpretation. SPE Textbook Series, volume \n13."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a350-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 24, "chroma:document": "Spivey, John P. and W. John Lee. 2013. Applied Well Test Interpretation. SPE Textbook Series, volume \n13. \nStewart, George. 2011. Well Test Design and Analys is. PennWell Corp.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a396-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 25, "chroma:document": "URTeC 123   26 \nSuarez -Rivera, Roberto, Jeff Burghardt, Sergei Stanchits, Eric Edelman, and Aniket Surdi. 2013. The effect \nof rock fabric on fracture complexity for improving completion design and well performance. Paper \npresented at the International P etroleum Technology Conference, Beijing, China.  \nTheis, Charles V. 1935. The relationship between the lowering of the Piezometric surface and the rate and \nduration of discharge of a well using ground -water storage. Eos, Transactions, American Geophysical \nUnion 16 (2): 519 -524, doi: 10.1029/TR016i002p00519.  \nValko, P. P. and M. J. Economides. 1999. Fluid -leakoff delineation in high -permeability fracturing. SPE \nProduction & Facilities 14 (2), doi: 10.2118/56135 -PA. \nVogler, D., R. R. Settgast, C. Annavarapu, C. Madonna, P. Bayer, and F. Amann. 2018. Experiments and \nsimulations of fully hydro -mechanically coupled response of rough fracture exposed to high -pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a3e6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 25, "chroma:document": "simulations of fully hydro -mechanically coupled response of rough fracture exposed to high -pressure \ninjection. Journal of Geophysical Research: Solid Earth 123: 1186 -1200, doi: 10.1002/2017JB015057 .  \nWallace, J., C.  S. Kabir, C. L. Cipolla. 2014. Multiphysics investigation of diagnostic fracture injection \ntests in unconventional reservoirs. SPE 168620 . Paper  presented at the SPE Hydraulic Fracturing \nTechnology Conference, The Woodlands, TX.  \nWang, HanYi and Mukul M. Sharma. 2017. New variable compliance method for estimating in -situ stress \nand leak -off from DFIT data. SPE 187348. Paper presented at the SPE Annual Technical Conference and \nExhibition, San Antonio, TX.  \nWang, HanYi and Mukul M. Sharma. 2018. Estimating unpropped fracture conductivity and compliance \nfrom diagnostic fracture injection tests. SPE 189844. Paper presented at the SPE Hydraulic Fracturing \nTechnology Conference & Exhibition, The Woodlands, TX."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a436-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 25, "chroma:document": "Technology Conference & Exhibition, The Woodlands, TX.  \nWarpinski, Norman R. 1991. Hydraulic frac turing in tight, fissured media. Journal of Petroleum \nTechnology, 43 (2), doi:  10.2118/20154 -PA. \nWeijers, L., L. G. Griffin, H. Sugiyama, T. Shimamoto, S. Takada, K. K. Chong, J. M. Terracina, and C. \nA. Wright. 2002. The first successful fracture treatment  campaign conducted in Japan: Stimulation \nchallenges in a deep, naturally fractured volcanic rock. SPE  77678. Paper presented at the Annual Technical \nConference and Exhibition, San Antonio, TX.  \nWillis -Richards, J., K. Watanabe, H. Takahashi. 1996. Progress toward a stochastic rock mechanics model \nof engineered geothermal systems. Journal of Geophysical Research  101 (B8): 17481 -17496, doi: \n10.1029/96JB00882.  \nWitherspoon, P. A., J. S. Y. Wang, K. I wai, J. E. Gale. 1980. Validity of cubic law for fluid flow in a \ndeformable rock fracture. Water Resources Research 16 (6): 1016 -1024, doi: 10.1029/WR016i006p01016."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a486-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 25, "chroma:document": "deformable rock fracture. Water Resources Research 16 (6): 1016 -1024, doi: 10.1029/WR016i006p01016.  \nWright, Chris. 2000. Section 9E: Rate step -down test analysis \u2013 a diagnostic for fracture e ntry. In Reservoir \nStimulation, eds, Michael J. Economides and Kenneth G. Nolte, Wiley.  \nYew, Ching H. and Xiaowei Weng. 2015. Mechanics of Hydraulic Fracturing. Gulf Professional \nPublishing.  \nZanganeh, Behnam, Christopher R. Clarkson, Jack R. Jones. 2019. R einterpretation of flow patterns during \nDFITs based on dynamic fracture geometry, leakoff and afterflow. SPE 189840. Paper presented at the SPE \nHydraulic Fracturing Technology Conference, The Woodlands, TX.  \nZhang, Junjing, Anton Kamenov, D. Zhu, A.D. Hill.  2013. Laboratory measurement of hydraulic fracture \nconductivities in the Barnett Shale . SPE 163839 . Paper  presented at the SPE Hydraulic Fracturing \nTechnology Conference, The Woodlands, TX.  \nZoback, Mark. 2007. Reservoir Geomechanics. Cambridge University Press."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a4d6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 25, "chroma:document": "Technology Conference, The Woodlands, TX.  \nZoback, Mark. 2007. Reservoir Geomechanics. Cambridge University Press.  \n  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a526-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 26, "chroma:document": "URTeC 123   27 \nList of variables  \nA: fracture surface area; does not count both sides of the fracture \u2013 ie, defined so that a fracture with sides \nof length 1 ft has area of 1  ft^2 (ft^2; m^2)  \ncfl: compressibility of the fluid in the fracture (psi^ -1; MPa^ -1) \n\ud835\udc36\ud835\udc53: fracture conductivity (md -ft; m^3)  \n\ud835\udc36\ud835\udc53\ud835\udc37: dimensionless fracture conductivity  \nCL: leakoff coefficient (ft/min^0.5; m/s^0.5)  \nCnw: near -wellbore pressure drop coefficient (psi/(bpm)^.5; MPa/(m^3/s)^.5)  \nCt: total system storage coefficient (bbl/psi; m^3/MPa)  \nct: total formation compressibility (psi^ -1; MPa^ -1) \nCw: wellbore storage coefficient (bbl/psi; m^3/MPa)  \nE\u2019: Plane strain Young\u2019s modulus  \nFL: linear flow time function (dimensionless)  \nG: G-function (dimensionless)  \nGc: G-funct ion at closure (dimensionless)  \ng: g-function (dimensionless)  \ng0: g-function at shut -in (dimensionless)  \nH: H-function (psi -min^.5; MPa -s^.5)  \nh: h-function (psi -min^.5; MPa -s^.5); or formation height (ft; m)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a56c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 26, "chroma:document": "H: H-function (psi -min^.5; MPa -s^.5)  \nh: h-function (psi -min^.5; MPa -s^.5); or formation height (ft; m)  \nhf: fracture height (ft; m)  \nk: permeability (md; m ^2) \nLf: fracture length (ft; m)  \nm: mass of fluid in the wellbore/fracture system (lbs; kg)  \nP: fluid pressure (psi; MPa)  \nP0: effective fluid pressure at shut -in (estimate for effective ISIP) (psi; MPa)  \nPeff: effective fluid pressure (estimate for fluid pres sure in the fracture) (psi; MPa)  \n\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53: effective ISIP (psi; MPa)  \nPres: reservoir fluid pressure (psi; MPa)  \nPw,init: fluid pressure at the beginning of injection (psi; MPa)  \nQ: volumetric flow rate (bpm; m^3/s)  \nRf: fracture radius (ft; m)  \nrw: wellbore radius (ft; m)  \ns: skin factor (unitless)  \nSf,c: stiffness of a closed crack (psi/ft; MPa/m)  \nSf,o: stiffness of an open crack (psi/ft; MPa/m)  \nSrel: relative stiffness (min^ -.5; s^ -.5) \nSt: total system stiffness (psi/bbl; MPa/m^3)  \nt: time (various un its; s)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a5bc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 26, "chroma:document": "Srel: relative stiffness (min^ -.5; s^ -.5) \nSt: total system stiffness (psi/bbl; MPa/m^3)  \nt: time (various un its; s)  \nte: duration of injection (min; s)  \nV: volume of the wellbore/fracture system (bbl; m^3)  \nVf: volume of fluid in the fracture (bbl; m^3)  \nVinj: volume of fluid injected (bbl; m^3)  \nVL: volume of fluid leaked off from the fracture since the start of inj ection (bbl; m^3)  \n\ud835\udc49\ud835\udc3f\ud835\udc60: volume of fluid leaked off from the fracture since shut -in (bbl; m^3)  \nVslug: volume of fluid injected as part of a slug test (bbl; m^3)  \nW: fracture aperture (inches; m)  \nW0: fracture aperture when the walls come into contact (inches; m)  \nW0,max: numerical parameter; maximum allowed value of W0 in an element (inches; m)  \n\ud835\udefd: near -wellbore pressure drop exponent (unitless)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a60c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 26, "chroma:document": "W0,max: numerical parameter; maximum allowed value of W0 in an element (inches; m)  \n\ud835\udefd: near -wellbore pressure drop exponent (unitless)  \n\u0394\ud835\udc43\ud835\udc5b\ud835\udc64: pressure drop due to near -wellbore pressure drop (psi; MPa)  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a65c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 27, "chroma:document": "URTeC 123   28 \n\u0394\ud835\udc61: shut -in duration (min; s)  \n\u0394\ud835\udc61\ud835\udc5d\ud835\udc52\ud835\udc4e\ud835\udc58: shut -in duration at the peak value of G*dP/dG (min; s)  \n\u0394\ud835\udf0e\ud835\udc5b,\ud835\udc4f\ud835\udc4e\ud835\udc50\ud835\udc58: additional normal stress on the fracture due to opening (psi; MPa)  \n\ud835\udf02: fracturing efficiency (dimensionless)  \n\ud835\udf07: fluid viscosity (cp; MPa -s) \n\ud835\udf0e\ud835\udc5b: normal stress (psi; MPa)  \n\ud835\udf0e\ud835\udc5b,\ud835\udc50: contact stress (psi; MPa)  \n\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53: effective normal stress at which the aperture has decreased 90% from W0 (psi; MPa)  \n\ud835\udf0f: integration variable for time (min; s)  \n\ud835\udf19: porosity (unitless)  \n \nA. Appendix   \nThis appendix reviews the physics of a DFIT pr essure transient and provides mathematical derivation of \ninterpretation techniques. All equations are provided in consistent ( SI) units.  \nA.1 Decomposing the pressure derivative  \nFrom the chain rule, the derivative of pressure with respect to time can be wri tten as: \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61=\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc5a\ud835\udc51\ud835\udc5a\n\ud835\udc51\ud835\udc61,           (2) \nwhere P is pressure, m is mass of fluid in the wellbore/fracture system, and t is time. Starting from Equation"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a6ac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 27, "chroma:document": "\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61=\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc5a\ud835\udc51\ud835\udc5a\n\ud835\udc51\ud835\udc61,           (2) \nwhere P is pressure, m is mass of fluid in the wellbore/fracture system, and t is time. Starting from Equation \n2, McClure et al. (2016) showed that for a slightly compressible fluid:  \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61=1\n\ud835\udc36\ud835\udc61\ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc61,           (3) \nwhere dV\ndt is the leakoff rate  and Ct is the system storage coefficient (the volume of fluid released from the \nsystem per increment of pressure) . Equation 3 provides a framework for understanding DFIT pressure \ntransients. Changes in slope are caused by changes in either system storage coefficient or leakoff.  \nEquation  2 assumes that a single value of press ure can be used for the entire fracture. This implicitly \nassumes that the fracture is effectively infinite conductivity and neglects perforation and near -wellbore \npressure drop.  The effect of finite fracture conductivity is discussed in Section A.5.  \nA.2 Sy stem storage and contact"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a6f2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 27, "chroma:document": "pressure drop.  The effect of finite fracture conductivity is discussed in Section A.5.  \nA.2 Sy stem storage and contact  \nMcClure et al. (2016) show ed that the system stiffness ( and its reciprocal,  system storage) can be written \nas: \n\ud835\udc46\ud835\udc61=1\n\ud835\udc36\ud835\udc61= 1\n\ud835\udc36\ud835\udc64+\ud835\udc34\n\ud835\udc46\ud835\udc53+\ud835\udc49\ud835\udc53\ud835\udc50\ud835\udc53\ud835\udc59.          (4) \nwhere Cw is the wellbore storage coefficient, A is the area of the fracture, Sf is the fracture stiffness  (equal \nto the reciprocal of the derivative of average fracture aperture with respect to pressure) , Vf is the volume of \nthe fracture, and cfl is the compressib ility of the fluid in the fracture. Equation 4 is valid during injection, \nand after shut -in: before, during, and after contact . Raaen et al. (2001) performed a si milar decomposition \nof system stiffness for application to pumpin/flowback tests.  \nThe wellbore storage coefficient has two components \u2013 the compressibility of the fluid in the well and the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a742-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 27, "chroma:document": "The wellbore storage coefficient has two components \u2013 the compressibility of the fluid in the well and the \ncompressibility of the wellbore volume itself. Wellbore storage coe fficient can be estimated directly from \nthe injection data. At the beginning of injection, prior to breakdown or fracture opening, a plot of pressure \nversus cumulative injection volume forms a straight line. The slope is equal to the wellbore storage \ncoeff icient.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a792-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 28, "chroma:document": "URTeC 123   29 \nIn these derivations, v olumes and areas  are written  in terms of the full fracture volume and area, not the \nvolume and area of one-wing  of the fracture. Authors  sometimes  define terms using one-wing  of the \nfracture. We prefer not to follow this convention because  fractures can propagate radially, with complex \ngeometry, or asymmetrically, and so in the general case it is not always meaningful to refer to  \u2018one-wing\u2019 \nof a fracture . Also, sometimes authors define \u2018area\u2019 by counting both sides  of the fracture. This is not the \nconvention used in this paper. We define area according to the convention that a square fracture with length \nand height of 1 ft has an area of 1 ft2.  \nWe define the \u2018contact pressure\u2019  as being the pressure at which the fracture wa lls come back into contact  \nand the system begins to stiffen.  Prior to contact , the fracture stiffness can be written from an analytical"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a7e2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 28, "chroma:document": "and the system begins to stiffen.  Prior to contact , the fracture stiffness can be written from an analytical \nsolution based on the geometry of the fracture and the mechanical properties of the rock. The two common \ngeometry assump tions are radial and PKN. PKN fracture geometry applies to a fracture that has length \nmuch greater than height.  \nIf the fracture is radial, the stiffness is ( Table 2 -2 from Ehlig -Economides and Economides, 2000 ): \n\ud835\udc46\ud835\udc53,\ud835\udc5c(\ud835\udc5f\ud835\udc4e\ud835\udc51\ud835\udc56\ud835\udc4e\ud835\udc59 )=3\ud835\udf0b\ud835\udc38\u2032\n16\ud835\udc45\ud835\udc53,          (5) \nwhere Sf,o is the stiffness of an open crack, E\u2019 is the plane strain Young\u2019s modulus, and Rf is the radius.  If \nthe fracture has PKN geometry, the stiffness is written as:  \n\ud835\udc46\ud835\udc53,\ud835\udc5c(\ud835\udc43\ud835\udc3e\ud835\udc41 )=2\ud835\udc38\u2032\n\ud835\udf0b\u210e\ud835\udc53,          (6) \nwhere hf is the assumed fracture height.  Once contact  occurs, the fracture begins to stiffen because of contact \nstress created by the contacting fracture walls. The total stiffness can be written as (McClure et al., 2016):  \n\ud835\udc46\ud835\udc53=\ud835\udc46\ud835\udc53,\ud835\udc5c+\ud835\udc46\ud835\udc53,\ud835\udc50,          (7)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a832-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 28, "chroma:document": "stress created by the contacting fracture walls. The total stiffness can be written as (McClure et al., 2016):  \n\ud835\udc46\ud835\udc53=\ud835\udc46\ud835\udc53,\ud835\udc5c+\ud835\udc46\ud835\udc53,\ud835\udc50,          (7) \nwhere Sf,c is the additional stiffness due to contact. The contact stiffness is equal to:  \n\ud835\udc46\ud835\udc53,\ud835\udc50=1\n\ud835\udc51\ud835\udc4a\n\ud835\udc51\ud835\udc43,           (8) \nwhere W is the fracture aperture  (calculated as a function of effective normal stress) . Sometimes,  authors \ndifferentiate between fracture void aperture  and hydraulic aperture  (McClure, 2012),  but in this work, they \nare assumed to be equal.  \nPrior to contact, Sf,c is equal to zero. After contact, t he parameter Sf,c begins to increase  and asymptotically  \napproaches infinity as effective normal stress approaches infinity.  Sf,c can be calculated from an empirical \nrelation between aperture and effective normal stress.  \nThe resulting relation for contact stiffness is:  \n\ud835\udc46\ud835\udc53,\ud835\udc50=\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53\n9\ud835\udc4a0 (1+9(\ud835\udf0e\ud835\udc5b\u2212\ud835\udc43)\n\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53)2\n.         (9)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a882-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 28, "chroma:document": "The resulting relation for contact stiffness is:  \n\ud835\udc46\ud835\udc53,\ud835\udc50=\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53\n9\ud835\udc4a0 (1+9(\ud835\udf0e\ud835\udc5b\u2212\ud835\udc43)\n\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53)2\n.         (9) \nEquation 9 indicates that \ud835\udc46\ud835\udc53,\ud835\udc50 is nonzero at the moment of contact, which implies a discontinuous jump in \nstiffness at t he point of contact. It is unclear whether this is realistic . In future work, it would be worthwhile \nto explore alternatives to Equation 1 that allow a smooth increase from contact stiffness from zero as contact \noccurs.  \nEven after \u2018contact\u2019 has occurred a cross the entire fracture, the walls of the fracture are not literally touching \neverywhere along the fracture. Instead, asperities cause solid -to-solid contact across only a fraction of the \nfracture area. As effective stress increases, the percentage of ar ea with solid -to-solid contact increases. This \nprocess is implicit to  Equation 1. The equation to be used to capture average fracture aperture without"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a8d2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 28, "chroma:document": "process is implicit to  Equation 1. The equation to be used to capture average fracture aperture without \nperforming detailed modeling at the scale of individual asperities. As an example of the alternative \napproach, Vogler et al. (2018) performed small -scale modeling that captures individual asperities.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a922-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 29, "chroma:document": "URTeC 123   30 \nPrior to contact , force balance requires that fracture effective normal stress is equal to zero  (Crouch and \nStarfield, 1983) . After contact , the effective normal stress becomes compressive  and equal to the contact \nstress created by the contacting of the fracture walls. Contact stress can be calculated by solving for effective \nnormal stress in a constitutive equation. Using Equation 1, contact stress is:  \n\ud835\udf0e\ud835\udc5b\u2212\ud835\udc43=\ud835\udf0e\ud835\udc5b,\ud835\udc50=\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53  \n9 (\ud835\udc4a0\n\ud835\udc4a\u22121).        (10) \nBecause of fracture roughness, the fracture aperture is not zero at contact. This residual aperture creates a \nbackstress so that the  normal stress is slightly above Shmin when  the walls come into contact. Th e \nbackstress can be calculated as:  \n\u0394\ud835\udf0e\ud835\udc5b,\ud835\udc4f\ud835\udc4e\ud835\udc50\ud835\udc58 =\ud835\udc4a\ud835\udc46\ud835\udc53,\ud835\udc5c.          (11) \nThe fluid pressure is equal to Shmin when the backstress is equ al to the contact stress:  \n\ud835\udc4a\ud835\udc46\ud835\udc53,\ud835\udc5c=\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53  \n9 (\ud835\udc4a0\n\ud835\udc4a\u22121).         (12)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a972-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 29, "chroma:document": "The fluid pressure is equal to Shmin when the backstress is equ al to the contact stress:  \n\ud835\udc4a\ud835\udc46\ud835\udc53,\ud835\udc5c=\ud835\udf0e\ud835\udc5b,\ud835\udc5f\ud835\udc52\ud835\udc53  \n9 (\ud835\udc4a0\n\ud835\udc4a\u22121).         (12) \nThere is a discrete  change in the physics at the point when the walls come into contact  \u2013 the contact stress \nbegins to increase from zero. However, t here is no meaningful change in the physics or discernable signal \nin the transient when pressure is equal to  Shmin. Because  there is not a signal in the data when pressure \nreaches Shmin, the difference between contact pressure  and Shmin  is a source of uncertainty  when \nestimating Shmin . \nCraig and Blasingame (200 6) and Craig et al. (2017) define the total storage in a piece -wise fashion \u2013 \nneglecting different parts of the storage at different points during the test. In their definition, th e \ud835\udc34\n\ud835\udc46\ud835\udc53 term is \nnegligible after \u2018closure, \u2019 implying that Sf is infinite. This assumption does not appear to be well -founded. \nWith realistic values in Equation 4, the \ud835\udc34"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89a9b8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 29, "chroma:document": "With realistic values in Equation 4, the \ud835\udc34\n\ud835\udc46\ud835\udc53 term is not negligible until pressure is hundreds or thousands of \npsi below Shmin.  \nA.3 G -function analysis  \nThe G -function (also called G -time) is a monotonic transformation of \u0394\ud835\udc61 (shut-in time ). Nolte (1979) \nderived the G -function (also call ed G-time) such that, under reasonable assumptions, the cumulative leakoff \nafter shut -in is linearly proportional to G -time. A related function, the g -function, is derived to be linearly \nproportional to the cumulative leakoff from the start of injection (C astillo, 1987; Gulrajani and Nolte, 2000) : \n\ud835\udc49\ud835\udc3f(\u0394\ud835\udc61)=2\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\ud835\udc61\ud835\udc52\ud835\udc54(\u0394\ud835\udc61).          (13) \nThe G -function is defined as:  \n\ud835\udc3a(\u0394\ud835\udc61)=4\n\ud835\udf0b(\ud835\udc54(\u0394\ud835\udc61)\u2212\ud835\udc54(\u0394\ud835\udc61=0)).        (14) \nThe cumulative leakoff after shut -in is defined as:  \n\ud835\udc49\ud835\udc3f\ud835\udc60(\u0394\ud835\udc61)=2\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\ud835\udc61\ud835\udc52(\ud835\udc54(\u0394\ud835\udc61)\u2212\ud835\udc54(0))=\ud835\udf0b\n2\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\ud835\udc61\ud835\udc52\ud835\udc3a(\u0394\ud835\udc61).      (15) \nThe exact form of the G and g functions depend on assumptions about fracture growth. However, there is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89aa08-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 29, "chroma:document": "2\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\ud835\udc61\ud835\udc52\ud835\udc3a(\u0394\ud835\udc61).      (15) \nThe exact form of the G and g functions depend on assumptions about fracture growth. However, there is \nlittle practical difference between the different forms of the g and G -functions. For example, within \nreasonable ranges, the cumulative leakoff at shut -in can be bounded with \ud835\udc540=\ud835\udc54(\u0394\ud835\udc61=0) is a number in \nthe narrow range between 4/3 and \ud835\udf0b\n2 (Equation 30 of the appendix from Gulrajani and Nolte, 2001). The \nmost common form of the g -function is:  \n\ud835\udc54(\u0394\ud835\udc61)=4\n3[(1+\u0394t\nte)1.5\n\u2212(\u0394t\nte)1.5\n].        (16) Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89aa58-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 30, "chroma:document": "URTeC 123   31 \nBecause cumulative leakoff after shut -in is proportional to G -time, the derivative of cumulative leakoff \nwith respect to G -time is equal to a constant. In the ideal case, f racture stiffness is constant prior to contact , \nand so the total system storage (and  stiffness) are also constant prior to contact.  Therefore, from Equation  \n3, a plot of pressure versus G -time should form a straight line  (Castillo, 1987) : \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc3a=1\n\ud835\udc36\ud835\udc61\ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc3a=\ud835\udc50\ud835\udc5c\ud835\udc5b\ud835\udc60\ud835\udc61\ud835\udc4e\ud835\udc5b\ud835\udc61 .          (17) \nIf fracture geometry and mechanical properties of the rock are known, then Equation 17 can be solved for \nthe leakoff coefficient  (Nolte, 1979; Castillo, 1987; Gulrajani and Nolte, 2000) .  \nIf the fracture formed instantaneously during injection, then the G -function would be equivalent  the square \nroot of time . The square root s caling aris es because the G -function assumes  Carter leakoff. The G-function"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89aaa8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 30, "chroma:document": "root of time . The square root s caling aris es because the G -function assumes  Carter leakoff. The G-function \nis not exactly equal to the square root of time because accounts for the progressive growth of the fracture \nduring injection. As a result, t he duration of leakoff is a function of position along the fracture area. \nEquation 24 from  McClure (2017) provide s a succinct derivation of the G -function for the special case that \nthe fracture grows linearly with respect to time during injection.  \nA.4 Deviation from Carter leakoff  \nThe G -function  is derived based on the assumption of Carter leakoff (Nolte, 1979; Howard and Fast, 1957 ). \nFor the simple case with no filtrate zone or filtercake, Carter leakoff can be derived as the solution the 1D \ndiffusivity equation with a Dirichlet  (constant pressure)  boundary condition  (Bird et al., 2007) : \n\ud835\udc49\ud835\udc3f\ud835\udc60=4\ud835\udc34\u221a\u0394\ud835\udc61(\ud835\udc43\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\ud835\udf19\ud835\udc50\ud835\udc61\ud835\udc58\n\ud835\udf0b\ud835\udf07=4\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\u0394\ud835\udc61.       (18) \nThe leakoff coefficient is defined from Equation 18 as: \n\ud835\udc36\ud835\udc3f=(\ud835\udc43\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\ud835\udf19\ud835\udc50\ud835\udc61\ud835\udc58"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89aaf8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 30, "chroma:document": "\ud835\udc49\ud835\udc3f\ud835\udc60=4\ud835\udc34\u221a\u0394\ud835\udc61(\ud835\udc43\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\ud835\udf19\ud835\udc50\ud835\udc61\ud835\udc58\n\ud835\udf0b\ud835\udf07=4\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\u0394\ud835\udc61.       (18) \nThe leakoff coefficient is defined from Equation 18 as: \n\ud835\udc36\ud835\udc3f=(\ud835\udc43\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\ud835\udf19\ud835\udc50\ud835\udc61\ud835\udc58\n\ud835\udf0b\ud835\udf07.          (19) \nThe leakoff coefficient can be generalized to include the effect of filtrate invasion and filtercake formation. \nFiltercake does not form during a DFIT becaus e the injection is performed with water. Filtrate invasion is \nminor in DFIT\u2019s because of the low permeability and relatively large fracture surface area.  \nThe G-function assumption of Carter leakoff  is violated during a DFIT because pressure decreases over  \ntime (Castillo, 1987). As long as the change in the fracture pressure is relatively small relative to the \ndifference between ISIP (initial shut -in pressure) and the formation fluid pressure, then the leakoff rate is \nreasonably described by Carter leakoff.  But e ventually, the fluid pressure drops sufficiently far that there is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ab48-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 30, "chroma:document": "reasonably described by Carter leakoff.  But e ventually, the fluid pressure drops sufficiently far that there is \nsignificant deviation from Carter leakoff (Castillo, 1987) . The leakoff rate reduces relative to the rate that \nwould have occurred if Carter leakoff had continued. Because  \ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc3a is constant during  Carter leakoff , the \ndeviation causes  \ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc3a to decrease  (because leakoff occurs more slowly than if Carter leakoff had continued),  \nand so the derivative of pressure with respect to G -time begins to decrease.  This causes dP/dG  to decrease \nand G*dP/dG to bend downward. The peaking of G*dP/dG and t*dP/dt occurs during the progressive \ntransition from Carter leakoff  to late -time impulse behavior (McClure, 2017).  \nA.5 The effect of closure  \nEquation  3 provides a conceptual framework f or understanding the effect contact between the fracture \nwalls. When the fracture walls come into contact, stiffness begins to increase (Equation 7). Increasing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ab98-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 30, "chroma:document": "walls. When the fracture walls come into contact, stiffness begins to increase (Equation 7). Increasing \nstiffness c auses dP/dG to increase. Based on this insight, contact can be identified as occurring when dP/dG \nbegins to increase (McClure et al., 2016).  \nEquation  3 depends on the assumption that pressure in the fracture can be described with a single parameter, \nP. This is valid if the fracture is approximately infinite conductivity. The dimensionless fracture \nconductivity is defined as:  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89abde-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 31, "chroma:document": "URTeC 123   32 \n\ud835\udc36\ud835\udc53\ud835\udc37=\ud835\udc36\ud835\udc53\n0.5\ud835\udc58\ud835\udc3f\ud835\udc53,           (20) \nwhere \ud835\udc36\ud835\udc53 is fracture conductivity and Lf is fracture length. Fractures are \u2018infinit e conductivity\u2019 when \ud835\udc36\ud835\udc53\ud835\udc37 is \nabove approximately 300 (some authors use a lower threshold). From the cubic law, fracture conductivity \nis equal to (Witherspoon et al., 1980):  \n\ud835\udc36\ud835\udc53=\ud835\udc4a3\n12.           (21) \nFor a fracture with half -length of 150 ft and matrix permeability of 100 nanodarcies, the fracture will be \ninfinite conductivity as long as fracture aperture is greater than just 2 5 microns  (equivalent to conductivity \naround 1 md -ft). Zhang et al. (2013) measured the conductivity of unpropped fra ctures in the Barnett Shale \nand found that conductivity remained above 1 md -ft until effective normal stress exceeded 1000s of psi. \nFor unaligned fractures, the conductivity was even higher, and in -situ, fractures are probably rougher than \nin small -scale f ractures induced in the lab."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ac2e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 31, "chroma:document": "in small -scale f ractures induced in the lab.  \nFor permeability on the order of microdarcies or millidarcies, it becomes less likely that the fracture will \nremain infinitely conductive after contact. If dimensionless fracture conductivity drops sufficiently rapidly \nwith co ntact, then it is conceivable that nonnegligible pressure gradient could develop in the fracture. If this \noccurs, then contact would cause an apparent reduction in the \u2018leakoff rate,\u2019 \ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc3a, and this could potentially \ncause the pressure derivative to de crease, rather than increase, with contact.  \nIn the worst case, stiffness and leakoff rate could change in approximately equal amounts and result in no \nchange in \ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc3a with contact. This scenario is probably uncommon because it requires coincidental equ ality \nof two opposing effects, but probably occurs occasionally. Decreasing \ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc3a with contact (due to decreased"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ac7e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 31, "chroma:document": "of two opposing effects, but probably occurs occasionally. Decreasing \ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc3a with contact (due to decreased \ndimensionless fracture conductivity) has been confirmed by numerical simulation (McClure et al., 2016). \nIf this occurred, \ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc3a may decre ase monotonically after contact. If the fracture begins to become finite \nconductivity, it is possible that the conductivity could be spatially variable along the fracture area.  \nA.6. Impulse flow  \nCraig and Blasingame (2006) pointed out that the late time be havior of a DFIT can be described with \nimpulse flow solutions from conventional well test analysis. The impulse flow solution can be found by \ntaking the dimensionless time derivative of the nondimensionalized solution for constant -rate injection \n(Houze et al, 1988; Ayoub et al., 1988; Gu et al, 1993). For example, constant rate injection into an infinite \nconductivity fracture yields a scaling of \u0394\ud835\udc43\u221d(\u0394\ud835\udc61)1\n2 (Gringarten et al., 1974) . Therefore, the impulse"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89acce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 31, "chroma:document": "conductivity fracture yields a scaling of \u0394\ud835\udc43\u221d(\u0394\ud835\udc61)1\n2 (Gringarten et al., 1974) . Therefore, the impulse \nsolution for an infinite conductivity fracture is \u0394\ud835\udc43\u221d(\u0394\ud835\udc61)\u22121\n2. Late-time impulse transients can be used to \ninfer permeability and fluid pressure (Sections A.10.iii and 3.1.6). \nA.7 Near -wellbore pressure drop  \nIn field DFIT\u2019s in horizontal wells , there is usually always  a period of rapid pressure drop immediate ly after \nshut-in. At very early time, this pressure drop is due to the end of wellbore and perforation friction  (if the \nwell is perforated) . But subsequently, there can be  a period of rapid pressure drop  that may last tens of \nminutes or longer. During this  time, pressure commonly drops  by 1000s of psi. This behavior  is apparent  \nin most of the field data reviewed in this study.  \nNear -wellbore pressure drop can be modeled as a pressure difference between the wellbore and the fracture \n(Wright, 2000):  \n\u0394\ud835\udc43\ud835\udc5b\ud835\udc64=\ud835\udc36\ud835\udc5b\ud835\udc64\ud835\udc44\ud835\udefd,          (22)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ad1e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 31, "chroma:document": "(Wright, 2000):  \n\u0394\ud835\udc43\ud835\udc5b\ud835\udc64=\ud835\udc36\ud835\udc5b\ud835\udc64\ud835\udc44\ud835\udefd,          (22) \nwhere \ud835\udc36\ud835\udc5b\ud835\udc64 is a constant, Q is the volumetric flow rate from the well into the fractur e, and \ud835\udefd is an exponent \n(typically equal to 0.5).  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ad6e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 32, "chroma:document": "URTeC 123   33 \nAfter shut -in, flow at the wellhead is zero, but fluid continues to flow into the formation because of wellbore \nstorage. The flow rate Q can be estimated as:  \n\ud835\udc44=\ud835\udc36\ud835\udc64\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61.            (23) \n\u0394\ud835\udc43\ud835\udc5b\ud835\udc64 can be estimated from the equation:  \n\u0394\ud835\udc43\ud835\udc5b\ud835\udc64~\ud835\udc43\u2212\ud835\udc43\ud835\udc52\ud835\udc53\ud835\udc53,           (24) \nwhere P is the bottomhole pressure of the well and Peff is the \u2018effective\u2019 pressure estimated by extrapolating \nback to G -time equal to zero from the point of minimum dP/dG ( Section 3.1 .1). Peff is an estimate for the \nfluid pressure in the fracture, on the \u2018other side\u2019 of the near -wellbore pressure drop from the wellbore.  \nThese relations make it possible to plot the difference between well pressure and fracture pressure versus \nvolumetric flow rate and directly infer \ud835\udc36\ud835\udc5b\ud835\udc64.    \nA.8 The h -function  \nNolte (1979) derived the G -function to be proportional to the cumulative leakoff volume after shut -in and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89adbe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 32, "chroma:document": "A.8 The h -function  \nNolte (1979) derived the G -function to be proportional to the cumulative leakoff volume after shut -in and \nderived the g -function to be proportional to the total volume of fluid leaked off after the start of injection. \nBoth functions are derived assuming Carter leakoff.  Following a similar approach, it is convenient to define \nan \u2018h\u2019 function that is proportional to the cumulative leakoff volume  from the start of injection , but unlike \nthe g -function, accounts  for deviation fro m Carter leakoff caused by pressure change over time . This is \naccomplished using  a time -convolution integral of the  one-dimensional  constant pressure solution  (given \nby Equation 18). This approach is related to the method described by Mayerhofer and Economides (1993) \nand Mayerhofer et al. (1995) , who proposed a procedure  for estimating permeability using  an \napproximation to the leakoff rate and the n a convolution integral of the constant rate solution  (Section"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ae0e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 32, "chroma:document": "approximation to the leakoff rate and the n a convolution integral of the constant rate solution  (Section \nA.3.vii) , and is also related to the relative stiffness relations developed by Wang and Sharma (2018) .  \nThe cumulative leakoff from the start of pumping can be estimated as: \n\ud835\udc49\ud835\udc3f=4\ud835\udc34\u221a\ud835\udc58\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 \u222b(\ud835\udc43(\ud835\udf0f)\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\n\ud835\udc51\ud835\udf0f\u221a\u0394\ud835\udc61+\ud835\udc61\ud835\udc52/2\u2212\ud835\udf0f\ud835\udc51\ud835\udf0f\u0394\ud835\udc61+\ud835\udc61\ud835\udc52/2\n0=4\ud835\udc34\u210e(\u0394\ud835\udc61)\u221a\ud835\udc58\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 .   (25) \nThus, the h -function is defined as:  \n\u210e(\u0394\ud835\udc61)=\u222b(\ud835\udc43(\ud835\udf0f)\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\n\ud835\udc51\ud835\udf0f\u221a\u0394\ud835\udc61+\ud835\udc61\ud835\udc52/2\u2212\ud835\udf0f\ud835\udc51\ud835\udf0f\u0394\ud835\udc61+\ud835\udc61\ud835\udc52/2\n0.       (26) \nIf pressure versus time  is known , cumulative leakoff can be calculated  as: \n\ud835\udc49\ud835\udc3f(\u0394\ud835\udc61\ud835\udc58)\u22484\ud835\udc34\u221a\ud835\udc58\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 [(\ud835\udc430\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\u0394\ud835\udc61\ud835\udc58+\ud835\udc61\ud835\udc52\n2+\u2211 (\ud835\udc43\ud835\udc56\u2212\ud835\udc43\ud835\udc56\u22121)\ud835\udc58\n\ud835\udc56=1 \u221a\u0394\ud835\udc61\ud835\udc58\u2212\u0394\ud835\udc61\ud835\udc56].   (27) \nThe h -function is calculated  as: \n\u210e(\u0394\ud835\udc61\ud835\udc58)\u2248(\ud835\udc430\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\u0394\ud835\udc61\ud835\udc58+\ud835\udc61\ud835\udc52\n2+\u2211 (\ud835\udc43\ud835\udc56\u2212\ud835\udc43\ud835\udc56\u22121)\ud835\udc58\n\ud835\udc56=1 \u221a\u0394\ud835\udc61\ud835\udc58\u2212\u0394\ud835\udc61\ud835\udc56.     (28) \nAnalogous to the G -function, an H -function can be defined that is proportional to the volume of fluid leaked \noff since shut -in: \n\ud835\udc3b(\u0394\ud835\udc61)=\u222b(\ud835\udc43(\ud835\udf0f)\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\n\ud835\udc51\ud835\udf0f\u221a\u0394\ud835\udc61+\ud835\udc61\ud835\udc52/2\u2212\ud835\udf0f\ud835\udc51\ud835\udf0f\u0394\ud835\udc61+\ud835\udc61\ud835\udc52/2\n\ud835\udc61\ud835\udc52/2.       (29) \nThe H-function is calculated as:  \n\ud835\udc3b(\u0394\ud835\udc61\ud835\udc58)\u2248(\ud835\udc430\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)(\u221a\u0394\ud835\udc61\ud835\udc58+\ud835\udc61\ud835\udc52\n2\u2212\u221a\ud835\udc61\ud835\udc52\n2)+\u2211 (\ud835\udc43\ud835\udc56\u2212\ud835\udc43\ud835\udc56\u22121)\ud835\udc58"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ae5e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 32, "chroma:document": "\ud835\udc3b(\u0394\ud835\udc61)=\u222b(\ud835\udc43(\ud835\udf0f)\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\n\ud835\udc51\ud835\udf0f\u221a\u0394\ud835\udc61+\ud835\udc61\ud835\udc52/2\u2212\ud835\udf0f\ud835\udc51\ud835\udf0f\u0394\ud835\udc61+\ud835\udc61\ud835\udc52/2\n\ud835\udc61\ud835\udc52/2.       (29) \nThe H-function is calculated as:  \n\ud835\udc3b(\u0394\ud835\udc61\ud835\udc58)\u2248(\ud835\udc430\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)(\u221a\u0394\ud835\udc61\ud835\udc58+\ud835\udc61\ud835\udc52\n2\u2212\u221a\ud835\udc61\ud835\udc52\n2)+\u2211 (\ud835\udc43\ud835\udc56\u2212\ud835\udc43\ud835\udc56\u22121)\ud835\udc58\n\ud835\udc56=1 \u221a\u0394\ud835\udc61\ud835\udc58\u2212\u0394\ud835\udc61\ud835\udc56.    (30) \nCumulative leakoff after shut -in can be written as:  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89aea4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 33, "chroma:document": "URTeC 123   34 \n\ud835\udc49\ud835\udc3f\ud835\udc60(\u0394\ud835\udc61\ud835\udc58)\u22484\ud835\udc34\ud835\udc3b(\u0394\ud835\udc61\ud835\udc58)\u221a\ud835\udc58\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 .         (31) \nThe h -function can be calculated directly from pressure versus time data  and an  estimate of the reservoir \npressure, \ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60. Estimation of reservoir pressure is discussed in Section 3.1 .6. \nUnlike the G -function, Equation 25 does not rigorously account for the effect of the propagation of the \nfracture over time. Instead, leakoff during injection is approximated by assuming the fracture formed \ninstantaneously after a duration of injection of te/2. Although simple, this is a rea sonably accurate \napproximation. Equation 25 implies that the volume of fluid leaked off at shut -in is equal to:  \n\ud835\udc49\ud835\udc3f(\u0394\ud835\udc61=0)\u22484\ud835\udc34\u221a\ud835\udc58\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 [(\ud835\udc430\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\ud835\udc61\ud835\udc52\n2]=2\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\ud835\udc61\ud835\udc52 \u221a2.     (32) \nThe factor \u221a2 in Equation 32 is analogous to \ud835\udc54(\u0394\ud835\udc61=0)=\ud835\udc540 in Equation 13 (which is taken from the \nmore d etailed derivations of Nolte, 1979, and Gulrajani and Nolte, 2000). \ud835\udc540 is bounded within the range \n4/3 and \ud835\udf0b\n2, and \u221a2 lies within this range .   \nA.9 Relative stiffness"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89aef4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 33, "chroma:document": "4/3 and \ud835\udf0b\n2, and \u221a2 lies within this range .   \nA.9 Relative stiffness  \nUsing Equation  3 and Equation 25, it is possible to derive a \u2018relative stiffness\u2019 value ( Srel) that is linearly \nproportional to fracture stiffness:  \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61=(1\n\ud835\udc36\ud835\udc61 \ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc61)\u221d1\n\ud835\udc36\ud835\udc61\ud835\udc51\u210e\n\ud835\udc51\ud835\udc61.          (33) \n1\n\ud835\udc36\ud835\udc61\u221d\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61\n\ud835\udc51\u210e\n\ud835\udc51\ud835\udc61=\ud835\udc46\ud835\udc5f\ud835\udc52\ud835\udc59.           (34) \nUsing tabular data of pressure versus time and an estimate for formation fluid pressure, it is possible to \ndirectly calculate the relative stiffness:  \n\ud835\udc46\ud835\udc5f\ud835\udc52\ud835\udc59(\ud835\udc61\ud835\udc58)=\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61(\ud835\udc61\ud835\udc58)\n\ud835\udc51\u210e\n\ud835\udc51\ud835\udc61(\ud835\udc61\ud835\udc58)=\ud835\udc51\ud835\udc43(\ud835\udc61\ud835\udc58)\n\ud835\udc51\u210e(\ud835\udc61\ud835\udc58).         (35) \nA plot of relative stiffness versus pressure can be used to identify contact . When the relative stiffne ss \nincreases, this indicates that the fracture walls have come into contact (Wang and Sharma, 2018) .  \nBecause of near -wellbore pressure drop, the measured wellbore pressure after shut -in is typically higher \nthan the actual pressure in the far -field fractur e. To address this problem, the relative stiffness and the h -"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89af44-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 33, "chroma:document": "than the actual pressure in the far -field fractur e. To address this problem, the relative stiffness and the h -\nfunction can be calculated using an \u2018effective pressure,\u2019 Peff, that represents a best estimate for the true \npressure in the fracture (Section 3.1 .1).  \nA.10 Methods of estimating permeability  \nThe following sections describe methods for estimating permeability and leakoff coefficient. We \nrecommend estimating permeability from multiple techniques: the G -function technique, the h -function \ntechnique, impulse linear, and/or impulse radial. These estima tes use different parts of the data and can be \ncompared for consistency. At the end of this section, we review several common methods that are not \nrecommended.  \nA.10.i G -function technique  \nCombining with Equations 4 and 17: \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc3a=1\n\ud835\udc36\ud835\udc61 \ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc3a=\u2212\ud835\udf0b\n2 \ud835\udc34\ud835\udc36\ud835\udc3f\ud835\udc46\ud835\udc61\u221a\ud835\udc61\ud835\udc52=\u2212\ud835\udf0b\n2\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\ud835\udc61\ud835\udc52\n\ud835\udc36\ud835\udc64+\ud835\udc34"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89af94-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 33, "chroma:document": "recommended.  \nA.10.i G -function technique  \nCombining with Equations 4 and 17: \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc3a=1\n\ud835\udc36\ud835\udc61 \ud835\udc51\ud835\udc49\n\ud835\udc51\ud835\udc3a=\u2212\ud835\udf0b\n2 \ud835\udc34\ud835\udc36\ud835\udc3f\ud835\udc46\ud835\udc61\u221a\ud835\udc61\ud835\udc52=\u2212\ud835\udf0b\n2\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\ud835\udc61\ud835\udc52\n\ud835\udc36\ud835\udc64+\ud835\udc34\n\ud835\udc46\ud835\udc53+\ud835\udc49\ud835\udc53\ud835\udc50\ud835\udc53\ud835\udc59.       (36) Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89afe4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 34, "chroma:document": "URTeC 123   35 \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc3a can be directly estimated from the data. \ud835\udc49\ud835\udc53\ud835\udc50\ud835\udc53\ud835\udc59 is negligibly small and is omitted from the following \nequations. Assuming a radial crack, the leakoff coefficient can be calculated as:  \n\ud835\udc36\ud835\udc3f(\ud835\udc5f\ud835\udc4e\ud835\udc51\ud835\udc56\ud835\udc4e\ud835\udc59 )=\u2212\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc3a \ud835\udc36\ud835\udc64+16\ud835\udc45\ud835\udc533\n3\ud835\udc38\u2032\n\ud835\udf0b2\n2\ud835\udc45\ud835\udc532\u221a\ud835\udc61\ud835\udc52=\u2212\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc54 \ud835\udc36\ud835\udc64+16\ud835\udc45\ud835\udc533\n3\ud835\udc38\u2032\n2\ud835\udf0b\ud835\udc45\ud835\udc532\u221a\ud835\udc61\ud835\udc52.       (37) \nAssuming a fixed -height (PKN) crack, the leakoff coefficient can be calculated as:  \n\ud835\udc36\ud835\udc3f(\ud835\udc43\ud835\udc3e\ud835\udc41 )=\u2212\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc3a 2\ud835\udc36\ud835\udc64\n\ud835\udf0b+\ud835\udc3f\ud835\udc53\u210e\ud835\udc532\n\ud835\udc38\u2032\n\ud835\udc3f\ud835\udc53\u210e\ud835\udc53\u221a\ud835\udc61\ud835\udc52=\u2212\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc54 2\ud835\udc36\ud835\udc64+\ud835\udc3f\ud835\udc53\u210e\ud835\udc532\ud835\udf0b\n\ud835\udc38\u2032\n4\ud835\udc3f\ud835\udc53\u210e\ud835\udc53\u221a\ud835\udc61\ud835\udc52.       (38) \nEquations 37 and 38 cannot be solved direct ly because they require estimation of the fracture size, either \nradius or length. In addition, the PKN calculation requires an assumption of fracture height. It is not possible \nto estimate height solely from the DFIT. It needs to be estimated from ancillar y information, such as \nknowledge of a stress contrast creating height confinement. If wellbore storage is neglected and height is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b034-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 34, "chroma:document": "knowledge of a stress contrast creating height confinement. If wellbore storage is neglected and height is \nassumed, Equation 38 reduces to an equation that can  be solved directly for leakoff coefficient (Marongiu -\nPorcu et al., 2011).  \nRadius and length in Equations 37 and 38 can be estimated by writing a mass balance equation for the entire \nsystem:  \n\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57=\ud835\udc36\ud835\udc64(\ud835\udc43(\u0394\ud835\udc61)\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)+\ud835\udc34\n\ud835\udc46\ud835\udc53(\ud835\udc43(\u0394\ud835\udc61)\u2212\ud835\udc46\u210e\ud835\udc5a\ud835\udc56\ud835\udc5b )+2\ud835\udc34\ud835\udc36\ud835\udc3f\u221a\ud835\udc61\ud835\udc52\ud835\udc54(\u0394\ud835\udc61).    (39) \nEquation 39 states that the volume of fluid injected is equal to wellbore storage, fluid store d in the fracture, \nand leakoff. Equation 39 forms a system of two equations (with Equation 37 or 38) and two unknowns ( \ud835\udc36\ud835\udc3f \nand Rf or Lf). These equations can be solved to estimate leakoff coefficient and fracture extent. \ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61 is the \nmeasured pressure at the beginning of inje ction. The term \ud835\udc36\ud835\udc64(\ud835\udc43(\u0394\ud835\udc61)\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61) accounts for the net flow \ndue to wellbore stora ge. \nEquations 37, 38, and 39 must be evaluated at a particular point in time. We recommend evaluating dP/dG"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b084-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 34, "chroma:document": "due to wellbore stora ge. \nEquations 37, 38, and 39 must be evaluated at a particular point in time. We recommend evaluating dP/dG  \nat the minimum point in dP/dG . Because dP/dG is never constant, this point is probably distorted by both  \nnear-wellbore pressure drop and contact. As a result , it is an upper bound  on the true value of dP/dG and \nmay lead to an overestimate of leakoff coefficient. Nevertheless, it is the best  available point in  time to \nestimate dP/dG.  \nWe recommend evaluating Equation 39 at the effective ISIP ( Section 3.1 .1) in order to minimize the relative \nimpact of the Shmin uncertainty on the calculation of net pressure. Eq uation 39 is evaluated from the \nestimate of the effective ISIP, rather than the literal ISIP, because near -wellbore pressure drop elevates the \nliteral I SIP far above the actual pressure in the fracture at shut -in. \nOnce leakoff coefficient has been calculated, permeability can be calculated from Equation 19."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b0d4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 34, "chroma:document": "Once leakoff coefficient has been calculated, permeability can be calculated from Equation 19. \nA.10.ii h -function technique  \nThe assumption of Carter leakoff is a limitation of the G -function method. This limitation can be overcome \nusing the h -function method. Similar to Equation 39, we can write a mass balance on the system using the \nh-function to calculate leakoff:  \n\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57=\ud835\udc36\ud835\udc64(\ud835\udc43(\u0394\ud835\udc61)\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)+\ud835\udc34\n\ud835\udc46\ud835\udc53 (\ud835\udc43(\u0394\ud835\udc61)\u2212\ud835\udc46\u210e\ud835\udc5a\ud835\udc56\ud835\udc5b )+4\ud835\udc34\u210e(\u0394\ud835\udc61)\u221a\ud835\udc58\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 .    (40) \nAfter selecting appropriate values for A and Sf (for either rad ial or PKN geometry), Equation 40 contains \ntwo unknowns: permeability and fracture radius (or length). The problem is solved by evaluating the \nequation at two different points in time: at shut -in (using the effective I SIP) and at the point of maximum"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b11a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 34, "chroma:document": "equation at two different points in time: at shut -in (using the effective I SIP) and at the point of maximum \nG*dP/dG. The point of maximum G*dP/dG is reached a significant period of time after  the fracture walls Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b16a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 35, "chroma:document": "URTeC 123   36 \ncome into contact . The fracture still retains some aperture, but it is reasonable to assume that the great \nmajority of f luid has leaked off from the system. Specifically, we assume that 10% of the total injection \nvolume remains stored in the fracture at this point in time (the calculation is not strongly dependent on the \nprecise percentage that is assumed). This assumption yields:  \n0.9\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57=\ud835\udc36\ud835\udc64(\ud835\udc43\ud835\udc5d\ud835\udc52\ud835\udc4e\ud835\udc58 \u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)+4\ud835\udc34\u210e(\u0394\ud835\udc61\ud835\udc5d\ud835\udc52\ud835\udc4e\ud835\udc58 )\u221a\ud835\udc58\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 .      (41) \nRearrangement yields an equation for \ud835\udc34\u221a\ud835\udc58:  \n\ud835\udc34\u221a\ud835\udc58=0.9\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57\u2212\ud835\udc36\ud835\udc64(\ud835\udc43\ud835\udc5d\ud835\udc52\ud835\udc4e\ud835\udc58 \u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)\n4\u210e(\ud835\udee5\ud835\udc61\ud835\udc5d\ud835\udc52\ud835\udc4e\ud835\udc58 )\u221a\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 .         (42) \nEquation 40 can be solved for area:  \n\ud835\udc34=(\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57\u2212\ud835\udc36\ud835\udc64(\ud835\udc43(\u0394\ud835\udc61)\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)\u2212\ud835\udc34\u221a\ud835\udc58(4\u210e(\u0394\ud835\udc61)\u221a\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 ))\ud835\udc46\ud835\udc53\n\ud835\udc43\u2212\ud835\udc46\u210e\ud835\udc5a\ud835\udc56\ud835\udc5b.    (43) \n\ud835\udc34\u221a\ud835\udc58 can be calculated from Equation 42 and plugged into Equation 43. Appropriate r elations for A and Sf \nare plugged into Equation 43, assuming either radial or PKN geometry , and  the equation can be  solved for \neither radius or fracture length. Then, it is trivial to calculate area and permeability."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b1ba-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 35, "chroma:document": "either radius or fracture length. Then, it is trivial to calculate area and permeability.   \nWe recommend evaluating Equation 40 at \u0394\ud835\udc61 equal to zero (using the effective ISIP) in order to minimize \nthe relative effect of uncertainty in the estimate of Shmin. For the case of \u0394\ud835\udc61=0, Equation 40 reduces to:  \n\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57=\ud835\udc36\ud835\udc64(\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)+4(\ud835\udc34\u221a\ud835\udc58)(\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\ud835\udc61\ud835\udc52\n2\u221a\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 +\ud835\udc34\n\ud835\udc46\ud835\udc53 (\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc46\u210e\ud835\udc5a\ud835\udc56\ud835\udc5b ). (44) \nFor radial geometry, the radius is calculated as:  \n\ud835\udc45\ud835\udc53=\u221a3\ud835\udc38\u2032[\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57\u2212\ud835\udc36\ud835\udc64(\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)\u22124(\ud835\udc34\u221a\ud835\udc58)(\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\ud835\udc61\ud835\udc52\n2\u221a\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 ]\n16(\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc46\u210e\ud835\udc5a\ud835\udc56\ud835\udc5b ) 3\n     (45) \nFor PKN geometry, the fracture length is calculated as:  \n\ud835\udc3f\ud835\udc53=2\ud835\udc38\u2032[\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57\u2212\ud835\udc36\ud835\udc64(\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)\u22124(\ud835\udc34\u221a\ud835\udc58)(\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\ud835\udc61\ud835\udc52\n2\u221a\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 ]\n\u210e\ud835\udc532\ud835\udf0b(\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc46\u210e\ud835\udc5a\ud835\udc56\ud835\udc5b ).     (46) \nA.10.iii Impulse linear  \nThe late time behavior of a DFIT can be interpreted like an impulse test from classical well test analysis \n(Craig and Blasingame, 2006). The late -time analytical solution for linear flow with constant rate injection"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b20a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 35, "chroma:document": "(Craig and Blasingame, 2006). The late -time analytical solution for linear flow with constant rate injection \nis (Gringarten et al., 1974):  \n\ud835\udc43=\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60+\ud835\udc44\n\ud835\udc34\u221a\ud835\udf07\n\ud835\udf0b\ud835\udc58\ud835\udc50\ud835\udc61\ud835\udf19\u221a\u0394\ud835\udc61,         (47) \nwhere Q is the volumetric injection rate. Taking the derivative of the nondimensionalized form of th e \nequation, we can find the solution for injection of a volume of fluid Vslug into the system  (Houze et al, 1 988; \nAyoub et al., 1988; Gu et al, 1993 ). \ud835\udc49\ud835\udc60\ud835\udc59\ud835\udc62\ud835\udc54 should take wellbore storage into account:   \n\ud835\udc43=\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60+\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57\u2212\ud835\udc36\ud835\udc64(\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)\n2\ud835\udc34\u221a\ud835\udf07\n\ud835\udf0b\ud835\udc58\ud835\udc50\ud835\udc61\ud835\udf191\n\u221a\u0394\ud835\udc61.       (48) \nEquation 48 can be rearranged to calculate \ud835\udc34\u221a\ud835\udc58 from the slope of a plot of pressure versus 1\n\u0394\ud835\udc611/2. Once \ud835\udc34\u221a\ud835\udc58 \nhas been estimated, radius (or length) and permeability can be estimated from Equations 45 and 46.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b25a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 36, "chroma:document": "URTeC 123   37 \nA.10.iv Impulse radial  \nThe late -time analytical solution for radial flow with constant rate injection is (Theis, 193 5; Horne, 1995):  \n\ud835\udc43\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60=\ud835\udc44\ud835\udf07\n2\ud835\udf0b\ud835\udc58\u210e[0.5(\ud835\udc59\ud835\udc5b(\ud835\udc58\u0394\ud835\udc61\n\ud835\udf19\ud835\udf07\ud835\udc50\ud835\udc61\ud835\udc5f\ud835\udc642)+0.80907 )+\ud835\udc60].      (49) \nTherefore, impulse radial is the derivative of the constant rat e solution ( Houze et al, 1988; Ayoub et al., \n1988; Gu et al, 1993 ): \n\ud835\udc43\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60=(\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57\u2212\ud835\udc36\ud835\udc64(\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61))\ud835\udf07\n4\ud835\udf0b\ud835\udc58\u210e1\n\u0394\ud835\udc61.        (50) \nEquation 50 can be rearranged to show that the permeability -thickness product , \ud835\udc58\u210e, can be calculated from \nthe slope of a plot of pressure versus 1\n\u0394\ud835\udc61. To calculate permeability, it is necessary to m ake an estimate for \nh, the height of the permeable formation. If well logs indicate that there is a clear \u2018pay\u2019 zone with higher \npermeability than surrounding formations, then the thickness of this zone can be used for h. Alternatively, \nif well logs indica te strong height confinement, then the fracture can be assumed to have known height, and \nthis value can be used for h."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b2e6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 36, "chroma:document": "if well logs indica te strong height confinement, then the fracture can be assumed to have known height, and \nthis value can be used for h.  \nIf there is not clear indication of height confinement and there is a not a single \u2018high permeability\u2019 pay \nzone, we recommend using a ra dial fracture geometry and setting h equal to 2 Rf. For known kh (estimated \nfrom Equation 50), then k is approximately equal to (\ud835\udc58\u210e)\ud835\udc52\ud835\udc60\ud835\udc61\n2\ud835\udc45\ud835\udc53. Equation 44 becomes:  \n\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57=\ud835\udc36\ud835\udc64(\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)+4(\ud835\udf0b\ud835\udc45\ud835\udc532\u221a(\ud835\udc58\u210e)\ud835\udc52\ud835\udc60\ud835\udc61\n2\ud835\udc45\ud835\udc53)(\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc60)\u221a\ud835\udc61\ud835\udc52\n2\u221a\ud835\udf19\ud835\udc50\ud835\udc61\n\ud835\udf0b\ud835\udf07 + 16\ud835\udc45\ud835\udc533\n3\ud835\udc38\u2032  (\ud835\udc43\ud835\udc3c\ud835\udc46\ud835\udc3c\ud835\udc43 ,\ud835\udc52\ud835\udc53\ud835\udc53\u2212\ud835\udc46\u210e\ud835\udc5a\ud835\udc56\ud835\udc5b ) \n            (51) \nEquation 51 is a cubic equation for Rf. It can be solved with a nonlinear solver and then used to estimate h \nand k.  \nA.11 The linear flow time function  \nSometimes, impulse interpretations are performed with the \u2018linear flow time function\u2019 defined by Gulrajani \nand Nolte (2000) as:  \n\ud835\udc39\ud835\udc3f=2\n\ud835\udf0bsin\u22121\u221a\ud835\udc61\ud835\udc50\n\u0394\ud835\udc61,          (52)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b336-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 36, "chroma:document": "and Nolte (2000) as:  \n\ud835\udc39\ud835\udc3f=2\n\ud835\udf0bsin\u22121\u221a\ud835\udc61\ud835\udc50\n\u0394\ud835\udc61,          (52) \nwhere tc is the shut -in time to \u2018closure.\u2019 \ud835\udc39\ud835\udc3f is only defined for  \u0394\ud835\udc61\u2265\ud835\udc61\ud835\udc50. \ud835\udc34\u221a\ud835\udc58 is estimated from impulse \nlinear flow using a plot of pressure versus \ud835\udc39\ud835\udc3f or \ud835\udc39\ud835\udc3f\u22121. \ud835\udc58\u210e is estimated from impulse radial flow using a plot \nof pressure versus \ud835\udc39\ud835\udc3f2 or \ud835\udc39\ud835\udc3f\u22122.  \nEquation 52 can be understood by considering the behavior of the arcsine function as its argument \napproaches zero:  \nlim\n\ud835\udc65\u21920sin\u22121\ud835\udc65=\ud835\udc65.          (53) \nTherefore, once \ud835\udc61\ud835\udc50+\u0394\ud835\udc61 is substantially larger than tc, \ud835\udc39\ud835\udc3f can be approximated as:  \n\ud835\udc39\ud835\udc3f\u22482\n\ud835\udf0b\u221a\ud835\udc61\ud835\udc50\n\u0394\ud835\udc61.           (54) \nFor \u0394\ud835\udc61 equal to 2\ud835\udc61\ud835\udc50, the approximation is accurate within 11%. For \u0394\ud835\udc61 equal to 10\ud835\udc61\ud835\udc50, the approximation is \naccurate within 2%.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b386-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 37, "chroma:document": "URTeC 123   38 \nThus, for most practical purposes, a plot of pressure ve rsus \ud835\udc39\ud835\udc3f is equivalent to a plot of pressure versus \nreciprocal square root of time, and a plot of pressure versus \ud835\udc39\ud835\udc3f2 is equivalent to a plot of pressure versus \nreciprocal time. A plot of \ud835\udc39\ud835\udc3f\u22122 is equivalent to a plot of pressure versus time.  \nThe FL function is significantly different from 2\n\ud835\udf0b\u221a\ud835\udc61\ud835\udc50\n\ud835\udee5\ud835\udc61 in the period from \u0394\ud835\udc61=\ud835\udc61\ud835\udc50 to \u0394\ud835\udc61=2\ud835\udc61\ud835\udc50 (it is not defined \nprior to tc). Should FL be used if data is not available for \u0394\ud835\udc61 greater than 2\ud835\udc61\ud835\udc50? Possibly, but interpreters \nshould keep in mind the assump tions underlying FL. It is derived assuming that Carter leakoff occurs until \nclosure, and then there is zero leakoff after closure (Nolte et al., 1997; page 76 from Carslaw and Jaeger, \n1959). But in reality, leakoff rate gradually deviates from Carter leak off as pressure decreases in a system \ncoupled with nonlinear evolution of system storage (Section A.13). Because of this simplification, the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b3d6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 37, "chroma:document": "coupled with nonlinear evolution of system storage (Section A.13). Because of this simplification, the \nperiod from \u0394\ud835\udc61=\ud835\udc61\ud835\udc50 to \u0394\ud835\udc61=2\ud835\udc61\ud835\udc50 is the period when the assumptions underlying FL are least reliable. After \nthis p eriod, FL is similar to the impulse solution.  \nA.12 Estimating efficiency  \nFracture efficiency, \ud835\udf02, is defined as the volume of fluid remaining  in the fracture at shut -in divided by the \nvolume of fluid injected into the fracture (the total injection volume minus wellbore storage). A classical \nequation for estimating efficiency is (Equation 9 -60 from Gulrajani and Nolte, 2001):  \n\ud835\udf02=\ud835\udc3a\ud835\udc50\n2+\ud835\udc3a\ud835\udc50,           (55) \nwhere \ud835\udc3a\ud835\udc50 is G-time at \u2018closure.\u2019  \nEquation 55 is derived assuming the same assumptions discussed in Section A.11 : Carter leakof f occurs \nuntil \u2018closure,\u2019 at which point there is zero fluid remaining in the fracture. Conventionally, Equation 55 \nwould be applied with the tangent m ethod for picking closure. But there has been substantial deviation from"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b426-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 37, "chroma:document": "would be applied with the tangent m ethod for picking closure. But there has been substantial deviation from \nCarter leakoff by the time of the tangent closure pick. As discussed in Section 3.1 .9, due to fracture \nroughness, there is likely to be significant fluid remaining the fracture at the  point of contact, and even \nwhen pressure is equal to or less than Shmin. Because of the offsetting effect of different approximations, \nEquation 55 often yields a reasonable approximation  of efficiency in many cases if applied with the tangent \nmethod of picking closure.  \nAlternatively, efficiency can be estimated after estimating leakoff coefficient and/or permeability using the \ntechniques in Section A.10. Then, cumulative leakoff at shut -in can be estimated from Equation 13, and \nefficiency  can be calculated  directly by applying mass balance (including the effect of wellbore storage):  \n\ud835\udf02=\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57\u2212\ud835\udc36\ud835\udc64(\ud835\udc43\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)\u2212\ud835\udc49\ud835\udc3f(\u0394\ud835\udc61=0)\n\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57\u2212\ud835\udc36\ud835\udc64(\ud835\udc43\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61).         (56)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b476-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 37, "chroma:document": "\ud835\udf02=\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57\u2212\ud835\udc36\ud835\udc64(\ud835\udc43\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61)\u2212\ud835\udc49\ud835\udc3f(\u0394\ud835\udc61=0)\n\ud835\udc49\ud835\udc56\ud835\udc5b\ud835\udc57\u2212\ud835\udc36\ud835\udc64(\ud835\udc43\u2212\ud835\udc43\ud835\udc64,\ud835\udc56\ud835\udc5b\ud835\udc56\ud835\udc61).         (56) \nA.13 Estimating pore pressure with a short shut -in \nSometimes, DFIT\u2019s are not performed with sufficient shut -in duration to reach impulse linear or radial. A \nsimple numerical simulation and history match can be used to provide a rou gh estimate for fluid pressure.  \n1. Assume W0 and Pres. \n2. Use the h -function method to integrate the measured pressure data (after conversion to Peff) and use \nthe method in Section A.10.ii to infer leakoff coefficient and fracture surface area. Use the \nestimated  area and assumed fracture geometry to calculate Sf,o. \n3. Numerically solve the following equation for a DFIT pressure transient (derived from Equation 3): \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61(\ud835\udc34\n\ud835\udc46\ud835\udc53+\ud835\udc36\ud835\udc64)=\ud835\udc51\ud835\udc49\ud835\udc3f\n\ud835\udc51\ud835\udc61.         (57) Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b4c6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 38, "chroma:document": "URTeC 123   39 \n\ud835\udc51\ud835\udc49\ud835\udc3f\n\ud835\udc51\ud835\udc61 is the leakoff rate, calculated from Equation 25. When the calculated aperture reaches Wo, the \nfracture stiffness is increased to account for the c ontribution of Sf,c, as discussed in Section A.1.ii. The \nintegration can be solved numerically with explicit Euler:  \n\ud835\udc43\ud835\udc58=\ud835\udc43\ud835\udc58\u22121+(\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61)\n\ud835\udc58\u0394\ud835\udc61,         (58) \nwhere (\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc61)\n\ud835\udc58 is calculated from Equation 57. \n4. Check to see if the timing and value of the peak in t*dP /dt has been accurately predicted. If not, go \nback to Step 1 and select new values for W0 and Pres. Iterate until convergence.  \nA.14 Generating plots of aperture versus effective normal stress  \nWang and Sharma (2018) propose  a method for estimating aperture versus pressure. The technique in this \nsection is conceptually similar. From Equation 35, the derivative of P with respect to h is proport ional to \nsystem stiffness. Therefore, neglecting wellbore storage, we can write:  \n\ud835\udc51\ud835\udc43\n\ud835\udc51\u210e\n(\ud835\udc51\ud835\udc43\n\ud835\udc51\u210e)\ud835\udc5a\ud835\udc56\ud835\udc5b\ud835\udc46\ud835\udc53\n\ud835\udc34=\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc49.           (59)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b516-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-2019-123-ms.pdf", "page": 38, "chroma:document": "system stiffness. Therefore, neglecting wellbore storage, we can write:  \n\ud835\udc51\ud835\udc43\n\ud835\udc51\u210e\n(\ud835\udc51\ud835\udc43\n\ud835\udc51\u210e)\ud835\udc5a\ud835\udc56\ud835\udc5b\ud835\udc46\ud835\udc53\n\ud835\udc34=\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc49.           (59) \nThe permeability estimation methods in Section A.10 yield estimates of fracture area and stiffness prior to \ncontact, Sfo. Next, estimate the derivative of pressure with respect to aperture:  \n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc4a=\ud835\udc34\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc49.           (60) \nIf we assume that aperture at the peak of G*dP/dG  is an arbitrary, small value, 3.28e -5 ft, then we can \nperform an integral to  roughly approximate  average fracture aperture as a function of pressure:  \n\ud835\udc4a(\ud835\udc43)=3.28\u221710\u22125 +\u222b1\n\ud835\udc51\ud835\udc43\n\ud835\udc51\ud835\udc4a\ud835\udc51\ud835\udc43\ud835\udc43\n\ud835\udc43\ud835\udc5d\ud835\udc3a,        (61) \nwhere \ud835\udc43\ud835\udc5d\ud835\udc3a is the pressure at the peak G* dP/dG. Figure 7 shows a result from this procedure.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/19URTC/2-19URTC/D023S030R001/1138462/urtec-2019-123-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b566-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 0, "chroma:document": "URTeC: 3717105 \n \nImprovement in the Characterization of Vaca Muerta With DFIT Type \nCurves Analysis \n \nCristian F. Gonz\u00e1lez* and Ignacio Arhancet \u2020, YPF S.A. \n\u2020 Now with TotalEnergies \n \nCopyright 2022, Unconventional Resources Technology Conference (URTeC) DOI 10.15530/urtec-2022-3717105 \n \nThis paper was prepared for presentation at the Unconventional Resources Technology Conference held in Houston, Texas, USA, \n20-22 June 2022. \nThe URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted \nby the author(s). The contents of this paper have not been reviewed by URTeC and URTeC does not warrant the accuracy, reliability, \nor timeliness of any information herein. All information is the responsibility of, and, is subject to corrections by the author(s). Any \nperson or entity that relies on any information obtained from this paper does so at their own risk. The information herein does not"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b5b6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 0, "chroma:document": "person or entity that relies on any information obtained from this paper does so at their own risk. The information herein does not \nnecessarily reflect any position of URTeC. Any reproduction, distribution, or storage of any part of this paper by anyone other than the \nauthor without the written consent of URTeC is prohibited.   \n \nAbstract \nNatural decline of conventional fields and the good results in the development of USA shale plays motivated \nYPF, Argentina\u2019s National Oil Company, to start in 2010 the exploitation of unconventional resources. \nVaca Muerta Formation in Neuqu\u00e9n Basin was selected among others because of its excellent petrophysical \nand geomechanical properties. Since then, more than 1000 wells have been drilled and completed across \nthe basin proving that Vaca Muerta is a world-class unconventional play. \nIdentification of sweet spots, optimization in drilling and completion of shale wells and a proper field"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b606-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 0, "chroma:document": "Identification of sweet spots, optimization in drilling and completion of shale wells and a proper field \ndevelopment plan require a good dynamic characterization of the reservoir. In conventional reservoirs this \nwas traditionally performed by a series of tools in which well tests were a key part to get reservoir pressure \nand permeability. Because of the extremely low permeability of shale reservoirs, classical well testing is no \nlonger a practical tool to estimate these parameters. Diagnostic Fracture Injection Tests (DFITs) are one of \nthe few methodologies that allows estimation of reservoir transmissibility and pore pressure in \nunconventional reservoirs. DFITs are also useful to obtain closure pressure, a geomechanical parameter \nnecessary to define the stress state. \nHowever, DFITs interpretation by conventional methodology, also known as holistic approach, is not \nalways successful because it requires specific flow regimes during decline time to correctly estimate"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b656-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 0, "chroma:document": "always successful because it requires specific flow regimes during decline time to correctly estimate \nreservoir parameters. Additionally, as DFIT tests are generally pumped through horizontal well\u2019s toe prior \nto completion stage, they must compete against fracture bundle efficiency given its high costs of standby. \nAll of this, results in short shut-in times leading to a poor DFIT interpretation efficiency [i.e., low \npercentage of tests with confident reservoir data (closure pressure, reservoir pressure and transmissibility)]. \nThis paper describes how using type-curves methodology, YPF increased the number of valid results from \nDFITs improving the characterization of Vaca Muerta. Better mapping of pore pressure and knowledge of \ntypical ranges of permeability were possible after reanalyzing more than 100 DFITs. \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b69c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 1, "chroma:document": "URTeC 3717105  2 \n \nIntroduction \nThe focus towards development of low permeability reservoirs during recent years has changed the way to \nget reservoir parameters from a well testing perspective. Diagnostic Fracture Injection Test (DFIT) has \nemerged as one of the few tools that allows to estimate pore pressure and permeability in unconventional \nreservoirs. Because of this, data acquisition plans usually include DFITs in wells of different locations and \nlanding zones.  \nYPF has led exploration, appraisal, and early development stages of Vaca Muerta shale in Argentina during \nthe first ten years (2010-2020). In that period, 135 DFITs were executed across the Neuqu\u00e9n basin to capture \nkey information (stress state, pore pressure and reservoir permeability) necessary to characterize the \nreservoir and identify sweet spots. Fig. 1 shows the location of DFITs in a map of Vaca Muerta\u2019s area.  \n \nFig. 1- Location of DFITs in Vaca Muerta during 2010-2020."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b6ec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 1, "chroma:document": "Fig. 1- Location of DFITs in Vaca Muerta during 2010-2020. \nThose tests were interpreted following the classical best practices for DFIT analysis known as holistic \napproach (Barree et al, 2007). Analysis of results indicated that almost 90% of tests had a closure pressure \nestimation but only half of them presented a reservoir pressure calculation. Transmissibility values were \nonly present in around 10% of tests. That poor outcome in reservoir parameters can be explained by the \nlimitations of the traditional approach that are described in the following section.  \nConsidering the previous situation and with the objective of improving those numbers and extracting more \nvalue from DFITs, reservoir and stimulation engineering teams evaluated new interpretation techniques. \nDr. David Craig\u2019s work in type curves applied to DFITs (Craig, 2014) was considered a good alternative \nbecause it removes the main limitation of after closure analysis (ACA)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b73c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 1, "chroma:document": "because it removes the main limitation of after closure analysis (ACA). \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b78c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 2, "chroma:document": "URTeC 3717105  3 \n \nLimitations of Traditional Approach in Unconventionals \nCurrent most common procedure of DFITs interpretation is mainly based on Ken Nolte\u2019s works and it is \nwell described in Barree et al (2007). This approach, known as holistic, relies on proper flow regime \nidentification using different diagnostic graphs and special mathematical functions of time (e.g., G-function \ntime, Squared linear flow time, etc.) \nLeak-off type and closure pressure are not always simple to determine in before closure analysis (BCA) of \nunconventional wells using the holistic approach. Horizontal wells promote complex fracture growth \ngeometries that result in early events that disturb the G-Function plot\u2019s curves and can lead to different \ninterpretations generating uncertainty in in-situ minimum stress estimation. \nIn after closure analysis (ACA), correct estimation of pore pressure requires reaching specific flow regimes:"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b7dc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 2, "chroma:document": "In after closure analysis (ACA), correct estimation of pore pressure requires reaching specific flow regimes: \npseudolinear or pseudoradial. On the other hand, transmissibility or permeability calculation is only \npossible in pseudoradial flow. \nPseudolinear flow is expected to be developed in DFITs pumped in unconventional reservoirs after several \nhours of pressure decline while pseudoradial flow would be extremely rare due to its low permeability. \nBecause of this, DFITs in unconventionals are considered a good tool for initial pressure estimation but not \nso much for transmissibility or permeability calculation.  \nIn practice, pseudolinear flow is not always present in unconventional reservoirs DFITs due to lack of \nsufficient shut-in time or because of fracture-rock system complexities that result in non-ideal reservoir \nsignatures. Regarding interpretation, the use of auxiliary lines with characteristic slopes in flow regime"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b82c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 2, "chroma:document": "signatures. Regarding interpretation, the use of auxiliary lines with characteristic slopes in flow regime \nidentification graphs sometimes promotes that the analysts see that specific flow regime even when it is not \npresent or it is not fully developed yet, leading to wrong estimations in reservoir parameters.  \nOn the operational side, as DFITs are generally pumped through horizontal well\u2019s toe prior to completion \nevent, shut-in times are limited by fracture set\u2019s schedule and its high cost of standby. Consequently, fall \noff registration time is usually lower than desirable for low permeability rocks. \nAll of this, results in many tests with poor interpretation outcomes and it has led some operators to stop \npumping DFITs in horizontal wells and question its validity.  \nType-Curves Methodology in DFITs \nDavid Craig (2014) presented a new method for DFIT analysis based on type curves whose main advantage"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b872-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 2, "chroma:document": "Type-Curves Methodology in DFITs \nDavid Craig (2014) presented a new method for DFIT analysis based on type curves whose main advantage \nis that no specific flow regime is needed to estimate reservoir pressure and permeability overcoming the \nprincipal problem of the holistic approach. This new methodology also provides an alternative way to \nestimate closure pressure which is particularly useful in horizontal wells where classic technique is \nsometimes ambiguous. \nDFIT type-curves analysis is analogous to classic well testing, i.e., it uses special derivatives to aid the \nmatching process between field data and different theoretical models (type curves) and, in contrast to the \ntraditional method, integrates all data in a unique analytical solution. Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b8c2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 3, "chroma:document": "URTeC 3717105  4 \n \nAs DFITs consist of a small injection of fluid followed by a long shut-in time, it could be practically \nconsidered as a slug test or short-flow transient test. Craig and Blasingame (2006) demonstrated that DFITs \ncould be modeled with a variable-storage slug test solution. Additionally, slug tests pressure response could \nbe transformed into an equivalent constant-rate drawdown by deconvolution (Peres et al, 1989). This allows \nthe use of conventional constant-rate type curves for DFIT analysis. \n \nFig. 2- Schematic of DFIT transformation into an equivalent constant-rate drawdown. \nThe problem is that cited transformation requires knowing the initial pressure which it is one of DFIT\u2019s \nobjectives. In 2008, David Craig found out, after differentiating the slug test solution, that the same semi-\nlog derivative used in the log-log plot of holistic approach can be matched to a special derivative of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b912-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 3, "chroma:document": "log derivative used in the log-log plot of holistic approach can be matched to a special derivative of \nconstant-rate type curves (Eq. 1). This was the missing part that made possible to calculate the initial \npressure and completed the matching process. \n \n\ud835\udc61\u0bbd\u0bd7\u0be3\u0ce2\u0cb5\n\u0bd7\u0be7\u0cb5\u11e3\u11e7\u11e4\u11e7\u11e5\n\u0bbd\u0bbf\u0bc2\u0bcd \u0be6\u0bd8\u0be0\u0bdc\u0b3f\u0b6a\u0b6d\u0b65\u0bd7\u0bd8\u0be5\u0bdc\u0be9\u0bd4\u0be7\u0bdc\u0be9\u0bd8= \u2212\ud835\udc5d\u0bea\u0be6\u0bbd(\u0b34) \u00d7 \ud835\udc36 \u0be6\u0bbd\u0e15\n\u0be6\u0be7\u0be2\u0be5\u0bd4\u0bda\u0bd8\n\u0bd6\u0be2\u0bd8\u0bd9\u0bd9\u0bdc\u0bd6\u0bdc\u0bd8\u0be1\u0be7 \u00d7 \ud835\udc61 \u0bbd\u0bd7\u0c2e\u0be3\u0ce2\u0cce\u0cb5\n\u0bd7\u0be7\u0cb5\u0c2e\u11e3\u11e7\u11e7\u11e4\u11e7\u11e7\u11e5\n\u0bd6\u0be2\u0be1\u0be6\u0be7\u0bd4\u0be1\u0be7\u0b3f\u0be5\u0bd4\u0be7\u0bd8  \u0bd7\u0be5\u0bd4\u0bea\u0bd7\u0be2\u0bea\u0be1\n\u0b36\u0be1\u0bd7 \u0be2\u0be5\u0bd7\u0bd8\u0be5 \u0bd7\u0bd8\u0be5\u0bdc\u0be9\u0bd4\u0be7\u0bdc\u0be9\u0bd8 (Eq. 1) \nAnother important conclusion of Craig\u2019s work is that fracture closure is a storage phenomenon. Storage \neffects are recognized by unit-slope and superposition of pressure and first derivative curves in well testing \ndiagnostic plots.  Hence, fracture closure pressure could be identified as the point where both curves \nseparate from each other and deviates from unit slope. This provides an alternative to tangent method \n(holistic technique), and it is especially useful in horizontal wells where complex signatures during closure \nare common."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b962-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 3, "chroma:document": "(holistic technique), and it is especially useful in horizontal wells where complex signatures during closure \nare common. \nThe procedure for analyzing DFITs with type curves can be resumed as: \n1. Match semi-log derivative of DFIT data with a constant-rate second order derivative type \ncurve. Different constant storage coefficients can be used to construct the set of type curves. \n2. Calculate initial pressure from a matching point (MP) using the following equation: \n\ud835\udc5d\u0bdc= \ud835\udc5d\u0bea(\u0be7\u0cd0)\u2212\u0b35\n\u0be3\u0ce2\u0cde\u0cb5(\u0c2c)\u0bbc\u0cde\u0cb5\u124e\u0be7\u0ccf\u0cdb\u0ce2(\u0cdf)\n\u0ccf\u0cdf\n\u0b3f\u0be7\u0cb5\u0ccf\u0c2e\u0cdb\u0ce2\u0cce\u0cb5(\u0cdf\u0cb5)\n\u0ccf\u0cdf\u0cb5\u0c2e\u124f\n\u0bc6\u0bc9(Eq. 2) \n3. Once initial pressure has been estimated, constant-rate pressure and first derivative can be \ncalculated. The slug test (DFIT) has been transformed into an equivalent constant-rate \ndrawdown. \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b9b2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 4, "chroma:document": "URTeC 3717105  5 \n \n4. Overlap preceding curves with type curves. Perhaps, it could be necessary to slightly adjust \ninitial pressure to refine matching. \n5. Transmissibility can be calculated from a matching point over the pressure curve.  \n\u0bde\u0bdb\n\u0c13= (141.2)(24) \ud835\udc5d\u0bea\u0be6\u0bbd(\u0b34)\ud835\udc36\u0be6\u0bbd(\ud835\udc5d\u0b34\u2212\ud835\udc5d\u0bdc)\u1248\u0be3\u0ce2\u0cce\u0cb5(\u0cdf\u0cb5)\n\u222b\u0d6b\u0be3\u0ce2(\u0cdf)\u0b3f\u0be3\u0cd4\u0d6f\u0bd7\u0be7\u0cdf\n\u0c2c\u1249\n\u0bc6\u0bc9(Eq. 3) \n6. Fracture closure pressure is determined from the point where pressure and first derivative \ndeviate from unit slope and separate from each other. \nPrevious workflow considers a constant storage coefficient. In cases when variable storage is evident (e.g., \nnon-ideal leak-offs during fracture closure), the effect could be incorporated in type curves and equations \n(Craig, 2014). \nExamples of Application \nIn this section, two examples of application to Vaca Muerta\u2019s wells are presented and compared with the \nholistic approach. Detailed discussion about how well compared both methodologies for each parameter is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89b9f8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 4, "chroma:document": "holistic approach. Detailed discussion about how well compared both methodologies for each parameter is \npresented in the following section adding more wells to the analysis. \nWell A is an exploratory vertical well where a 3 barrel-DFIT was pumped in the lower section of Vaca \nMuerta and pressure decline was registered for 64 hours. Fig. 4 groups the set of graphs that are normally \nused for DFIT holistic interpretation. ACA shows a long pseudolinear flow period; hence, initial pressure \ncan be estimated with confidence using traditional technique and can be compared with type-curve method. \nAdditionally, a pump-in flowback rebound test (PIFBRT) was executed in well A after the DFIT providing \nan alternative estimation of closure pressure for comparison.  \nFig. 3 shows the type-curve match using Craig\u2019s methodology and Table 1 resumes the results of \ninterpretation by both methods. Pore pressure estimation is consistent between methods, being slightly"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ba48-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 4, "chroma:document": "interpretation by both methods. Pore pressure estimation is consistent between methods, being slightly \ngreater (+1%) for type-curve analysis. Regarding closure pressure, the tangent-line technique (holistic \napproach) does not provide an easy way to determine closure in this case because of a tip extension leak-\noff signature (no local maximum in dP/dG derivative and tangent line on GdP/dG does not pass through \nthe origin). The interpreted value is slightly lower (-2%) than the PIFBRT estimation but it has a high \ndegree of uncertainty. Type-curve closure pressure is in contrast a little bit greater (+1%). Despite the small \ndifference, the type-curve analysis yielded an acceptable estimation of closure pressure, and it is a simple \nalternative when the classical approach is ambiguous.  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bac0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 5, "chroma:document": "URTeC 3717105  6 \n \n \nFig. 3- DFIT type-curve match for well A. \n \nFig. 4- Conventional DFIT analysis of well A. Upper left: Log-log diagnostic plot. Upper right: G-function plot. Lower left: ACA diagnostic plot. \nLower right: Linear flow function plot. \n \nMethod Closure Pressure \n[psi] Closure Gradient \n[psi/ft] Initial Pressure \n[psi] Pressure Gradient \n[psi/ft] Transmissibility \n[mD.ft/cP]  \nHolistic 9118 0.978 8258 0.887 - \nType Curve 9378 1.006 8348 0.895 1.4 \nPIFBRT 9278 0.995 - - - \nTable 1- DFIT interpretation results for well A. \nWell A \nWell A Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bb10-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 6, "chroma:document": "URTeC 3717105  7 \n \nSecond example corresponds to Well B, a horizontal well landed in a high TOC section of Vaca Muerta. \n36 barrels of fresh water were injected at 6 barrels per minute and shut-in lasted around 120 hours.  Fig. 6 \nshows the different specialized plots that were used for analyzing that DFIT under traditional workflow. A \nclear and long-lasting pseudoradial flow could be observed after fracture closure, then transmissibility and \ninitial pressure were estimated with a high degree of confidence (Table 2). \n \nFig. 5- DFIT type-curve match for well B. \n \nFig. 6- Conventional DFIT analysis of well B. Upper left: Log-log diagnostic plot. Upper right: G-function plot. Lower left: ACA diagnostic plot. \nLower right: Radial flow function plot. \n \nWell B \nWell B Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bb60-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 7, "chroma:document": "URTeC 3717105  8 \n \nFig. 5 is the plot of DFIT type-curve analysis for well B and results are presented in Table 2. Initial pressure \nestimation is almost identical in both methods and transmissibility is very similar, being slightly greater for \ntype-curve analysis but consistent with traditional estimation. Closure pressure was also determined with \nboth techniques. In this case, the closure point is very clear on the G-function plot hence its value is a good \nreference for comparison. Type-curve estimated a closure pressure 2% greater than the tangent line method. \n \nMethod Closure Pressure  \n[psi] Closure Gradient \n[psi/ft] Initial Pressure  \n[psi] Pressure Gradient \n[psi/ft] Transmissibility \n[mD.ft/cP]  \nHolistic 8146 0.851 7496 0.783 12.83 \nType Curve 8341 0.871 7507 0.784 14.21 \nTable 2- DFIT interpretation results for well B. \nValidation \nDFIT type-curve methodology was validated by comparison with holistic method results before further"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bbb0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 7, "chroma:document": "Validation \nDFIT type-curve methodology was validated by comparison with holistic method results before further \napplication. DFITs with clear pseudolinear or pseudoradial flow regimes were selected for this purpose so \nits results were reliable for validation. The comparison was divided considering the main parameters of \nDFITs interpretation: initial pressure, transmissibility, and closure pressure.     \n\u25cf  Initial Pressure \nInitial pressure estimations from 35 DFITs with pseudolinear flow and 7 with pseudoradial flow were \ncompared and plotted in Fig. 7. As it can be seen, linear regression gives practically unit slope and R2=1 \nindicating that both methods estimate almost identical values.   \n \nFig. 7- Crossplot and linear regression of initial pressure estimations with both methods. \n \n \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bc00-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 8, "chroma:document": "URTeC 3717105  9 \n \n\u25cf  Transmissibility  \nDue to few tests with pseudoradial flow in Vaca Muerta, 8 DFITs from tight sands were included in the \ncomparison. Fig. 8 shows the crossplot and linear regression. R-squared is 0.9972 and slope of the line is \naround 1.02. In general, type-curve transmissibilities are slightly greater than holistic\u2019s but are very close \nsince data practically lies in the 45\u00ba line. Considering the uncertainty in this parameter, these differences \nare totally acceptable for engineering use.   \n \nFig. 8- Crossplot and linear regression of transmissibility estimations with both methods. \n\u25cf  Closure Pressure \nClosure pressure estimations of 87 DFITs from both methods are plotted in Fig. 9. R-squared is 0.9998 and \nslope of the line is around 1.01 indicating that values for type-curves are on average slightly greater (+70-\n100 psi).  \nClosure pressure estimation from DFITs has generated a lot of debate in the industry since the fracture-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bc50-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 8, "chroma:document": "100 psi).  \nClosure pressure estimation from DFITs has generated a lot of debate in the industry since the fracture-\ncompliance method was presented by McClure et al (2016). This method results in closure pressures \nsignificantly greater (500 psi or more in some cases) than the tangent-line technique (holistic approach).  \nResults from Fig. 9 would preliminarily indicate intermediate values but closer to the tangent-line method \nsince differences are small. Nevertheless, application of fracture-compliance method to this dataset must \nbe performed to correctly compare between all these methods. Comparison with other techniques like \nPIFBRT, whenever it is available, would be desirable. \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bc96-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 9, "chroma:document": "URTeC 3717105  10 \n \n \nFig. 9- Crossplot and linear regression of closure pressure estimations with both methods. \nAnalysis of Type Curves Non-uniqueness  \nAs it is well known in well testing interpretation, type-curve matching is usually non-unique (i.e., data could \nbe matched with several type curves). This is also true for DFIT type curves, therefore, the impact of curve \nselection in pressure and transmissibility estimation was evaluated. \nA DFIT with a not fully developed post-closure flow regime (Fig. 10) was selected to evaluate a case of \nhigh uncertainty. Flow regime identification after fracture closure shows a slope of -0.15 in semi-log \nderivative after 80 hours that could be interpreted as a slow transition to pseudolinear flow. Conventional \nACA cannot be applied because pseudolinear flow is not developed.   \nTwo extreme type curves were selected to test sensitivity. Dimensionless storage coefficient of 0.09 (Fig."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bce6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 9, "chroma:document": "Two extreme type curves were selected to test sensitivity. Dimensionless storage coefficient of 0.09 (Fig. \n10) implies transition to a long pseudolinear flow regime (realistic case) and dimensionless storage \ncoefficient of 0.36 (Fig. 11) means short pseudolinear flow followed by pseudoradial flow (unlikely case). \nIn both cases, an acceptable match can be performed.  \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bd36-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 10, "chroma:document": "URTeC 3717105  11 \n \n \nFig. 10- Type-curve match with lower storage coefficient. \n \nFig. 11- Type-curve match with higher storage coefficient. \nTable 3 resumes the results of both interpretations. Closure pressure and initial pressure are independent of \nthe type curve selected for analysis since estimations are practically identical. This proves that type-curve \nmethodology is an excellent tool for closure and initial pressures estimations.  \n \nDimensionless \nStorage \nCoefficient  Closure \nPresure  \n[psi] Closure Gradient \n[psi/ft] Initial Pressure  \n[psi] Pressure Gradient \n[psi/ft] Transmissibility \n[mDft/cP]  \n0.09 8339 0.913 7474 0.818 1.22 \n0.36 8339 0.913 7489 0.820 3.38 \nTable 3- Results of different type curves interpretations. \nTransmissibility estimation, in contrast, does depend on what curve is used. For this example, a factor of 3 \nwas obtained between cases. This sensitivity can be seen as a weakness of the method but must be"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bd86-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 10, "chroma:document": "was obtained between cases. This sensitivity can be seen as a weakness of the method but must be \nconsidered that there are not many other alternatives to estimate transmissibility from DFITs, especially in \nCSD=0.09 \n-tDd2pwcD/dtD2 CSD=0.09 \npwcD \ntDdpwcD/dtD \n-tDd2pwcD/dtD2 \nClosure \nCSD=0.36 \n-tDd2pwcD/dtD2 CSD=0.36 \npwcD \ntDdpwcD/dtD \n-tDd2pwcD/dtD2 \nClosure Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bdcc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 11, "chroma:document": "URTeC 3717105  12 \n \nunconventional reservoirs where pseudoradial flow is extremely rare. In any case, transmissibility \nestimations from different type curves will result in the same order of magnitude.  \nResults \nFig. 12 shows the improvement in the percentage of DFITs with valid estimates for different parameters \nafter applying the type-curve methodology to over 100 tests in Vaca Muerta.   \nClosure pressure percentages were slightly improved from 87% to 91%. Type curves allowed reinterpreting \na few tests where closure was not clear or impossible to estimate with the tangent-line method.  \nBefore type-curve application only half of tests had an estimation of initial pressure. Type-curves rise the \npercentage to 80%, adding tests where no pseudolinear or pseudoradial flow were seen. \nSince transmissibility is only possible to be calculated in pseudoradial flow using the traditional approach,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89be1c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 11, "chroma:document": "Since transmissibility is only possible to be calculated in pseudoradial flow using the traditional approach, \nthe percentage of test was too low (roughly 1 of 10) before type curves implementation. That number \nimproved to 6 of 10 because of type-curves methodology. \n \nFig. 12- Comparison of percentage of DFITs with closure pressure, initial pressure, and transmissibility estimations before and after type-curves \napplication. \nApplications \nThe results presented in the previous section increased the data available for Vaca Muerta characterization. \nBetter areal coverage of closure and initial pressures across Neuqu\u00e9n basin resulted in better mapping of \nstress state and pore pressure. For pore pressure mapping, more data availability allowed to construct maps \nfor the different landing zones. All of this is key information for sweet spots identification. \nAnother example of application is knowledge of permeability ranges for Vaca Muerta. Permeability that"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89be6c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 11, "chroma:document": "Another example of application is knowledge of permeability ranges for Vaca Muerta. Permeability that \ncontributes to production in unconventionals [i.e., system permeability (matrix + fissures)] is impossible to \nestimate from classical tools such as well testing. Rock cores offer an alternative to knowing permeability, \nbut they are not very representative because of its small volume of investigation. DFIT type-curves analysis \nis an excellent tool for permeability estimation in unconventional reservoirs. \nFig. 13 shows a S-curve of DFIT\u2019s permeabilities for Vaca Muerta calculated from type-curves \ntransmissibilities. Error bars have been included in the graph to indicate the estimated uncertainty of \ncalculated permeabilities. \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bebc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 12, "chroma:document": "URTeC 3717105  13 \n \n \nFig. 13- S-curve of Vaca Muerta DFIT permeability. \n \nConclusions \n\uf0b7 Application of type-curves analysis allowed YPF S.A. to improve DFITs\u2019 interpretation \nefficiency resulting in better characterization of Vaca Muerta. \n\uf0b7 Type-curves methodology was validated by comparing results with classic approach in DFITs \nof reference (clear pseudolinear and pseudoradial flow). \n\uf0b7 Closure and initial pressure estimations are practically insensitive to the selected type curve. \nThis puts the type-curves method as one of the best ways to estimate reservoir pressure in \nunconventional reservoirs.    \n\uf0b7 Transmissibility estimation does depend on the type curve used in the analysis. Different \ninterpretations can differ as much as a factor of 3. Being one of the few methods to get \ntransmissibility in unconventional reservoirs, the authors consider it acceptable despite the \nrange of uncertainty."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bf0c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 12, "chroma:document": "transmissibility in unconventional reservoirs, the authors consider it acceptable despite the \nrange of uncertainty.  \n\uf0b7 Type-curves method provides an alternative way to estimate closure pressure which is \nparticularly useful in horizontal wells where complex pressure signatures are common. \n\uf0b7 Type curves are an excellent tool for improving the analysis of DFITs in unconventional \nreservoirs like Vaca Muerta. \nAcknowledgments \nThe authors would like to thank YPF S.A. for the permission to publish this paper and Dr. David Craig for \ncreating and sharing this powerful tool for DFITs analysis. \nNomenclature \nACA After Closure Analysis  \nBCA Before Closure Analysis  \nDFIT Diagnostic Fracture Injection Test  \nDownloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bf5c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 13, "chroma:document": "URTeC 3717105  14 \n \nMP Matching Point  \nPIFBRT Pump-In Flowback Rebound Test  \nTOC Total Organic Carbon  \nUSA United States of America  \n  \n\ud835\udc36\u0be6\u0bbd Dimensionless storage coefficient \n\ud835\udc3a G-function time \n\u210e Height \n\ud835\udc58 Permeability \n\ud835\udf07 Viscosity \n\ud835\udc5d\u0bdc Initial pressure \n\ud835\udc5d\u0b34 Pressure at end of injection \n\ud835\udc5d\u0bea Wellbore pressure \n\ud835\udc5d\u0bea\u0bbd Dimensionless wellbore pressure  \n\ud835\udc5d\u0bea\u0bd6\u0bbd Dimensionless constant-rate wellbore pressure  \n\ud835\udc5d\u0bea\u0be6\u0bbd Dimensionless slug-test wellbore pressure  \n\ud835\udc61 Time \n\ud835\udc61\u0bbd Dimensionless time \n\ud835\udc61\u0bd8 Time at end of injection \n \nReferences \nBarree, Robert David, Barree, Valencia L., and David Craig. \"Holistic Fracture Diagnostics.\" Paper \npresented at the Rocky Mountain Oil & Gas Technology Symposium, Denver, Colorado, U.S.A., April \n2007. doi: https://doi.org/10.2118/107877-MS  \nCraig, David P. \"New Type Curve Analysis Removes Limitations of Conventional After-Closure Analysis \nof DFIT Data.\" Paper presented at the SPE Unconventional Resources Conference, The Woodlands, Texas,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bfac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 13, "chroma:document": "of DFIT Data.\" Paper presented at the SPE Unconventional Resources Conference, The Woodlands, Texas, \nUSA, April 2014. doi: https://doi.org/10.2118/168988-MS  \nCraig, David P., and Thomas Alwin Blasingame. \"Application of a New Fracture-Injection/Falloff Model \nAccounting for Propagating, Dilated, and Closing Hydraulic Fractures.\" Paper presented at the SPE Gas \nTechnology Symposium, Calgary, Alberta, Canada, May 2006. doi: https://doi.org/10.2118/100578-MS  \nCraig, David P., and Robert A. Jackson. \"Calculating the Volume of Reservoir Investigated During a \nFracture-Injection/Falloff Test DFIT.\" Paper presented at the SPE Hydraulic Fracturing Technology \nConference and Exhibition, The Woodlands, Texas, USA, January 2017. doi: \nhttps://doi.org/10.2118/184820-MS  \nMcClure, Mark W., Jung, Hojung, Cramer, Dave D., and Mukul M. Sharma. \"The Fracture-Compliance \nMethod for Picking Closure Pressure From Diagnostic Fracture-Injection Tests.\" SPE J. 21 (2016): 1321\u2013"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89bff2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 13, "chroma:document": "Method for Picking Closure Pressure From Diagnostic Fracture-Injection Tests.\" SPE J. 21 (2016): 1321\u2013\n1339. doi: https://doi.org/10.2118/179725-PA  \nNolte, Kenneth G., and Michael B. Smith. \"Interpretation of Fracturing Pressures.\" Paper presented at the \nSPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, September 1979. doi: \nhttps://doi.org/10.2118/8297-MS  \nNolte, Kenneth G. \"Determination Of Fracture Parameters From Fracturing Pressure Decline.\" Paper \npresented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, September 1979. \ndoi: https://doi.org/10.2118/8341-MS  \nNolte, Kenneth G.. \"Fracturing-Pressure Analysis for Nonideal Behavior.\" J Pet Technol 43 (1991): 210\u2013\n218. doi: https://doi.org/10.2118/20704-PA  Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c042-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 14, "chroma:document": "URTeC 3717105  15 \n \nNolte, K.G., Mack, M.G., and W.L. Lie. \"A Systematic Method for Applying Fracturing Pressure Decline: \nPart I.\" Paper presented at the Low Permeability Reservoirs Symposium, Denver, Colorado, April 1993. \ndoi: https://doi.org/10.2118/25845-MS  \nNolte, K.G., Maniere, J.L., and K.A. Owens. \"After-Closure Analysis of Fracture Calibration Tests.\" Paper \npresented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, October 1997. doi: \nhttps://doi.org/10.2118/38676-MS  \nPeres, A. M. M., Onur, M., and A. C. Reynolds. \"A New General Pressure Analysis Procedure for Slug \nTests.\" Paper presented at the SPE California Regional Meeting, Bakersfield, California, April 1989. doi: \nhttps://doi.org/10.2118/18801-MS  \nTalley, G.R., Swindell, T.M., Waters, G.A., and K.G. Nolte. \"Field Application of After-Closure Analysis \nof Fracture Calibration Tests.\" Paper presented at the SPE Mid-Continent Operations Symposium,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c092-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/urtec-3717105-ms.pdf", "page": 14, "chroma:document": "of Fracture Calibration Tests.\" Paper presented at the SPE Mid-Continent Operations Symposium, \nOklahoma City, Oklahoma, March 1999. doi: https://doi.org/10.2118/52220-MS  \n Downloaded from http://onepetro.org/URTECONF/proceedings-pdf/22URTC/1-22URTC/D011S012R003/2801994/urtec-3717105-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c0e2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 0, "chroma:document": "SPE-201413-MS\nDFIT Analysis and Simulation: A Utica Shale Field Study\nJeffery Hildebrand, Jr. and Yu Liang , The University of Texas at Austin\nCopyright 2020, Society of Petroleum Engineers\nThis paper was prepared for presentation at the SPE Annual Technical Conference & Exhibition originally scheduled to be held in Denver, Colorado, USA, 5 \u2013 7\nOctober 2020. Due to COVID-19 the physical event was postponed until 26 \u2013 29 October 2020 and was changed to a virtual event. The official proceedings were\npublished online on 21 October 2020.\nThis paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents\nof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c132-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 0, "chroma:document": "any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written\nconsent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may\nnot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.\nAbstract\nSince 2010, hydrocarbon production from long horizontal wells targeting shales has become the norm for\nindustry leaders. Because of the steep decline rates, it is vital to understand the reservoir and its properties\nbefore going through with a full-scale fracture stimulation. Through the application of Diagnostic Fracture\nInjection Tests (DFIT), one can determine accurate estimates of closure pressure, net pressure, pore pressure,\nformation permeability, and induced fracture geometry. The Utica shale is among the most promising"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c182-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 0, "chroma:document": "formation permeability, and induced fracture geometry. The Utica shale is among the most promising\nreservoirs of the future, but there is limited information available discussing its properties. In SPE-196149-\nMS, we analyzed a DFIT from one horizontal well targeting the Utica. However, in order to fully understand\nthe Utica shale at scale, further analysis is required. In this study, we will present three additional horizontal\nwells targeting the Utica, and analyze the pressure and its derivative to accurately estimate the properties\nmentioned above.\nDFIT analysis is an advanced technique to accurately predict stress regimes and reservoir properties.\nHowever, interpretation of DFIT data is challenging, especially in shale formations. In this study, we\noverview the geologic properties of the Utica shale, discuss the development of DFIT analysis and its\ngoverning equations, then present the three data sets and resulting conclusions. We specifically discuss"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c1c8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 0, "chroma:document": "governing equations, then present the three data sets and resulting conclusions. We specifically discuss\nthe Tangent Line Method, the Compliance Method, and the Variable Compliance method in detail, while\ncomparing their underlying equations and assumptions to determine closure pressure. After-Closure analysis\nis then performed in order to verify fracture closure and identify flow regimes. Through linear regression\nof this data, pore pressure from a linear flow regime is extrapolated, and through numerical simulation, key\nreservoir properties, such as permeability and fracture geometry, are estimated for the Utica shale.\nThe DFIT interpretation and simulation results from this study are very insightful. Interpreting the GdP/\ndG function, the closure pressure ranges from 4,943 psi to 6,141 psi, contributing to a closure pressure\ngradient of 0.797 to 0.891 psi/ft for the Utica shale. Based on the pressure transient analysis, the pore"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c218-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 0, "chroma:document": "gradient of 0.797 to 0.891 psi/ft for the Utica shale. Based on the pressure transient analysis, the pore\npressure ranges from 3,238 psi to 4,064 psi, contributing to a pore pressure gradient of 0.486 to 0.616\npsi/ft for the Utica shale. Additionally, field wide ranges of reservoirs properties are presented, allowing\nindustry to further optimize their drilling and fracing techniques in the Utica shale. Two of the wells in this\nstudy are close in proximity and show very similar results both in After-Closure analysis and in pressure\nresponse curves. The third well displays a different GdP/dG response, leak off characteristics, pressureDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c268-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 1, "chroma:document": "2 SPE-201413-MS\ntransient behaviors, formation permeability, and fracture geometry. This variance in results can be attributed\nto regional differences in geology, stresses, and pressures. Therefore, operators need to consider regional\ndifferences in reservoir properties in order to enhance the development of Utica shale and unlock all potential\nrecoverable hydrocarbons.\nIntroduction\nSince 2010, hydrocarbon production from long horizontal wells targeting shales has become the norm for\nindustry leaders. Because of the steep decline rates, it is vital to understand the reservoir and its properties\nbefore going through with a full-scale fracture stimulation. Through the application of Diagnostic Fracture\nInjection Tests (DFIT), one can determine accurate estimates of closure pressure, net pressure, pore pressure,\nformation permeability, and induced fracture geometry. The Utica shale is among the most promising"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c2b8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 1, "chroma:document": "formation permeability, and induced fracture geometry. The Utica shale is among the most promising\nreservoirs of the future, but there is limited information available discussing its properties. In SPE-196149-\nMS, we analyzed a DFIT from one horizontal well targeting the Utica. However, in order to fully understand\nthe Utica shale at scale, further analysis is required. In this study, we will present three additional horizontal\nwells targeting the Utica, and analyze the pressure and its derivative to accurately estimate the properties\nmentioned above.\nGeological Overview of Utica Shale\nUnderlying many parts of the Northeast United States lies a vast, organic rich laminated shale that spans an\napproximate 115 square miles. Upper Ordovician in age, the Utica shale was deposited in the Appalachian\nbasin around 450 million years ago. The play has thickness ranging from less than 100 feet to over 500 feet"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c2fe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 1, "chroma:document": "basin around 450 million years ago. The play has thickness ranging from less than 100 feet to over 500 feet\nand depths ranging from 14,000 feet to just 2,000 feet below sea level. Outcrops of the Utica can even be\nobserved in Quebec; however, this area is far outside of the producing zone. All of the major rock units in\nthe Appalachian basin follow the same basic trend: thickness and depth to the southeast, while progressively\nthinning and uplifting with northwestward progression.\nCreated by some 1,182 wells logs, Figure 1 illustrates the stratigraphic nature of the Utica shale. The\nmajority of drilling activity has occurred in eastern Ohio for two main reasons: the Utica is at optimal depth\nranging from 6,000 ft - 9,000 ft and it's home to the wet gas/condensate region. Additionally, the Marcellus\noverlies the Utica in this area and the existing wellbores can serve as a re-entry point to the shallower target"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c34e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 1, "chroma:document": "overlies the Utica in this area and the existing wellbores can serve as a re-entry point to the shallower target\nafter the Utica wells become uneconomic. The oil window resides to the west of the production wells in\nFigure 1  and corresponds with GOR's of less than 10,000 scf/bbl. Conversely, the gas window resides to\nthe east of the production wells and corresponds with GOR's greater than 10,000 scf/bbl. The three defined\nhydrocarbon windows in the Utica can be defined by vitrinite reflectance (Ro), which is directly related\nto thermal maturity. The oil window has Ro values between 0.6% and 1.1% while the dry gas window\nhas values between 1.4% and 3.2%. A Ro value above or below these ranges suggests that no producible\nhydrocarbons exist in that interval. Because the Utica is Ordovician in age, the vitrinite reflectance is\ncalculated from bitumen and conodont reflectance data (U.S. Energy Information Administration, 2017 )."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c39e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 1, "chroma:document": "calculated from bitumen and conodont reflectance data (U.S. Energy Information Administration, 2017 ).\nConodonts are microfossils of small marine animals that lived from the Cambrian through Triassic periods.\nThese tiny, eel like animals are most frequently found in marine sedimentary rocks. When the surrounding\nrock is heated, the color of the conodonts change from light to dark. This is known as the conodont alteration\nindex or CAI. Because the change in color is irreversible, studying conodonts is a great way to determine\nthe maximum temperature a rock has endured. Oil generation is associated with a CAI range from 1 to 2\nand anything greater is likely to be gas dominated. Similar to vitrinite reflectance, the western Utica has\nCAI values between 1 and 2 while the eastern portion has values greater than 2.5.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c3ee-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 2, "chroma:document": "SPE-201413-MS 3\nFigure 1\u2014Structure map of the Utica formation ( U.S. Energy Information Administration, 2017).\nThe Utica was deposited on a carbonate shelf in a shallow marine environment, experiencing frequent\nalgal blooms and storms. Fossils suggest that the depositional environment was shallow, well oxygenated,\nand exposed to sunlight (West Virginia Geological and Economic Survey, 2020). However, due to the\ndominant presence of amorphinite in Utica cores, the region must have gone through seasonal anoxic periods\nin which dissolved oxygen in the sea plummeted and marine algae flourished. Interestingly enough, areas\nwith high organic material deposition had similar water depths to areas with low organic material deposition.\nThis was likely due to small moving currents and erosional surfaces created by storms throughout the region\n(U.S. Energy Information Administration, 2017 ).\nThe Utica has an average total organic content (TOC) of about 3.5% and an average carbonate content"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c43e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 2, "chroma:document": "(U.S. Energy Information Administration, 2017 ).\nThe Utica has an average total organic content (TOC) of about 3.5% and an average carbonate content\nof 25%. Due to the low carbonate content and high clay content, fracturing the Utica proves difficult. In\nreality, the majority of wells drilled in eastern Ohio are actually targeting the underlying Point Pleasant\nformation. The Lower Point Pleasant has an average TOC around 4.5% and has a much higher carbonate\ncontent of 40%-60%, making it a more productive and much easier rock to induce fractures (West Virginia\nGeological and Economic Survey, 2020 ).\nGenerally speaking, Gamma Ray (GR) and TOC are directly related when plotted against each other.\nOrdovician shales are unique in the sense that they do not follow this trend. The gamma ray values from these\nshales correlate almost exactly with carbonate content instead of TOC, unlike the overlying Marcellus shale."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c48e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 2, "chroma:document": "shales correlate almost exactly with carbonate content instead of TOC, unlike the overlying Marcellus shale.\nThe implications of this unique characteristic can be hugely beneficial to operators in the region if analyzed\ncorrectly. Because carbonate rich rocks are more brittle, they respond better to hydraulic fracturing. From\nFigure 2 , it seems that the Lexington/Trenton Formation may be the best target in this organic rich interval\ndue to the high carbonate and TOC content. However, the presence of clay particles creates matrix porosity,\nso the optimal target here is the lower organic rich member of the Point Pleasant Formation. In general, there\nis an increasing carbonate content and a decreasing clay content with depth in this organic rich interval.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c4d4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 3, "chroma:document": "4 SPE-201413-MS\nFigure 2\u2014GR log, carbonate content and TOC from the Eichelberger No. 1,\nAshland County, Ohio ( West Virginia Geological and Economic Survey, 2020).\nHigh in both calcite and clay content, the Utica shale is an extremely tight reservoir. With an average\npermeability range of 0.00008 to 0.003 mD and an average porosity range of 3.7% to 6%, data analyzation is\nparamount in the pursuit to unlock untapped reserves in the Utica shale. Through the utilization of diagnostic\nfracture injection tests, this goal can be achieved.\nDFIT Theory and Methods\nDiagnostic fracture injection tests (DFITs) have been referred to as a number of different names including\nfracture calibration tests, mini-frac tests, and injection fall-off tests. The test involves pumping a small\namount of fluid down a cased and perforated wellbore at a constant rate to induce a small fracture in the\nnear wellbore region. The well is then shut in and the pressure transient data is analyzed to obtain reservoir"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c524-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 3, "chroma:document": "near wellbore region. The well is then shut in and the pressure transient data is analyzed to obtain reservoir\nproperties and in situ stresses. Historically, DFITs were conducted to estimate frac design parameters such as\nleak off coefficient, fluid efficiencies, and minimum principal stress. In recent years, it has become possible\nto predict reservoir pore pressure, permeability, and fracture geometry through numerical simulation. DFITs\nlend countless advantages, which allow the industry to have a more comprehensive understanding of the\nreservoir before continuing with a full-scale frac stimulation.\nFigure 3  illustrates an idealized version of what a typical DFIT pressure as a function of injection rate\nwould look like. The bottom hole pressure increases linearly until the leak off pressure (LOP) and is usually\nassociated with a slope change, meaning a small fracture has been induced in the near wellbore rock matrix."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c574-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 3, "chroma:document": "associated with a slope change, meaning a small fracture has been induced in the near wellbore rock matrix.\nThe formation fully fractures at the formation breakdown pressure and the fractures propagate at the fracture\npropagation pressure until injection ceases. The well is then shut in and the pressure drops to the ISIP due\nto the loss of friction in the wellbore and in the newly induced fractures. The bottom hole pressure will then\ndecline into a linear and then into a radial flow regime. The closure pressure, which is defined by whenDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c5c4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 4, "chroma:document": "SPE-201413-MS 5\nthe planes of the newly induced fracture come into contact, is a proxy for minimum in situ stress and is\nestimated by the variable compliance method on a GdP/dG vs. G-time graph. It should be noted that it could\ntake months after a DFIT test for a well to exhibit a radial flow regime, which makes estimation of reservoir\npore pressure difficult.\nFigure 3\u2014Typical DFIT test data plotted with pressure vs. time ( Wang and Sharma, 2017).\nDFIT pressure data is generally split into two distinct groups: Before-Closure data (BC) and After-\nClosure data (AC), separated by the fracture closure pressure. Before-Closure data is used to estimate leak\noff and fracture geometry, assuming normal leak off behavior according to Carter's leak off. However,\nCarter's leak off oversimplifies leak off behavior and generally leads to severe over or underestimation\nof the minimum in situ stress. After-Closure data is mainly used to predict formation pore pressure and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c614-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 4, "chroma:document": "of the minimum in situ stress. After-Closure data is mainly used to predict formation pore pressure and\npermeability. Because only half of the data is being used in each case, the results can be misleading. Attempts\nhave been made in the past to bridge the gap between the two sets of data but the models were based on\nthe fundamentally flawed G-function assumptions. Up until the development of the variable compliance\nmethod, which assumes variable fracture stiffness and pressure dependent leak off, no mathematical model\nwas able to seamlessly integrate both regions of data.\nThe basic mathematical model underlying DFIT analysis contains two important components. The first\ncomponent assumes that the pressure derivative is constant with time throughout the induced entire fracture\nnetwork and is based on the material balance ( Hildebrand and Liang, 2019). Through derivation, it is found"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c664-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 4, "chroma:document": "network and is based on the material balance ( Hildebrand and Liang, 2019). Through derivation, it is found\nthat the leak off rate is proportional to the pressure derivative with respect to time. The second component,\nwhich is in a similar form to 1D diffusivity equation with constant pressure boundaries, is the Carter Leak\nOff Theory (Hildebrand and Liang, 2019). The Carter Leak Off Theory suggests that the leak off rate is\nproportional to the inverse of the square root of time, and assumes that the single-phase fluid in the fracture\nand in the formation are identical (Howard and Fast, 1957). Carter Leak Off Theory also assumes that fluid\npressure in the fracture is constant over time and that spurt loss is neglected ( Hildebrand and Liang, 2019).\nWith the integration of these two components, the basic mathematical model underlying DFIT analysis can"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c6aa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 4, "chroma:document": "With the integration of these two components, the basic mathematical model underlying DFIT analysis can\nbe written asDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c6fa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 5, "chroma:document": "6 SPE-201413-MS\n(1)\nwhere \u0394 P is the change in pressure after shut-in time, C is a constant that relates to comprehensive\ncompressibility and the leak off coefficient, \u0394t is the change in time after shut-in, A is the fracture surface\narea and Sf is the fracture stiffness/compliance. The basic mathematical model assumes that the fracture is\nformed at the time of shut-in and that the fracture stiffness Sf stays constant before fracture closure, varying\nonce the fracture walls initially come into contact. Consequently, the closure pressure is picked at the point\non the plot where pressure as a function of the square root of \u0394t first deviates from linearity. However,\nbecause of the underlying assumptions in the basic mathematical model, correct identification of closure\npressure by this method is not feasible.\nIn the following years, Nolte (1986a, 1986b , 1979 ) modified the leak off equation by assuming the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c74a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 5, "chroma:document": "pressure by this method is not feasible.\nIn the following years, Nolte (1986a, 1986b , 1979 ) modified the leak off equation by assuming the\nfractures form over a period of time instead of instantaneously at the time of shut in. Still used today for\nanalysis, the model is known as the G-function. Assuming power law fracture growth, negligible spurt loss,\nconstant fracture stiffness, constant fracture surface after shut in, and Carter Leak Off Theory, Nolte was\nable to provide an equation for fracture pressure as a function of dimensionless time and can be written as\n(2)\nwhere P is the pressure in the fracture, ISIP is the instantaneous shut-in pressure, CL is Carter's leak\noff coefficient that is a constant, te is the shut-in time, and G (\u0394tD) is the G-function as a function of a\ndimensionless time \u0394 tD. The dimensionless time \u0394 tD is defined as\n(3)\nThen G-function is defined as the following\n(4)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c79a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 5, "chroma:document": "dimensionless time \u0394 tD. The dimensionless time \u0394 tD is defined as\n(3)\nThen G-function is defined as the following\n(4)\nFluid efficiency is defined as the ratio of the pumped fluid that is stored in fractures to the total fluid that\nis pumped into the well. High fluid efficiency indicates that more fluid is stored in the fracture due to the\nlow leak off rate, and vice versa.\nFor high fluid efficiency, g (\u0394 tD) is defined by\n(5)\nFor low fluid efficiency, g (\u0394 tD) is defined by\n(6)\nNot long after the development of the G-function, Castillo (1987) began analyzing Nolte's pressure versus\nG-function plot under the assumption of normal leak off behavior (constant Carter leak off coefficient, leak\noff area, and stiffness). Similar to the basic mathematical model, Castillo determined that fracture pressure\nshould scale with G-function linearly before the fracture closure ( Hildebrand and Liang, 2019). As a result,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c7ea-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 5, "chroma:document": "should scale with G-function linearly before the fracture closure ( Hildebrand and Liang, 2019). As a result,\nhe interpreted the closure pressure should be picked at the point where the pressure first deviates from\nlinearity, and the slope of the line is used to calculate the leak off coefficient CL (Hildebrand and Liang,\n2019 ).\nHowever, when interpreting plots of pressure versus G-function, initial linearity is highly uncommon.\nUsually, these plots contain many points of inflection due to a multitude of factors and identifying a linear\ntrend is generally not clear. Due to the ambiguous nature of the straight-line method, correct identification\nof closure pressure is also not feasible. Recognizing the straight line method was unreliable, Barree et al."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c83a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 5, "chroma:document": "of closure pressure is also not feasible. Recognizing the straight line method was unreliable, Barree et al.\n(2009 , 1996 ) developed a new way to estimate closure pressure by the Tangent Line Method. In this method,Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c88a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 6, "chroma:document": "SPE-201413-MS 7\nBarree plotted GdP/dG versus G time and determined the closure pressure was the line tangent to the GdP/\ndG curve that also passed through the origin. Integrating this method with Castillo's pressure versus G time\ngraph, estimating the closure pressure became much more consistent. The tangent line method is still a\nwidely accepted method today, however the method has not been scientifically proven, which makes for an\ninteresting research topic (Wang and Sharma, 2017). By taking the derivative of pressure with respect to\nthe G-function of Equation 2, the equation of GdP/dG can be written as\n(7)\nNon-ideal transient behaviors are commonly observed when using the G-function to process field DFIT\ndata, including pressure dependent leak off, fracture tip extension, and height recession/transverse storage\nbehaviors, as depicted in Figure 4 .\nFigure 4\u2014Signatures of non-ideal leak off behaviors (a,b,c) on the G-function plots ( Barree et al., 2009 )."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c8da-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 6, "chroma:document": "behaviors, as depicted in Figure 4 .\nFigure 4\u2014Signatures of non-ideal leak off behaviors (a,b,c) on the G-function plots ( Barree et al., 2009 ).\nAdvancing this topic, McClure et al. (2016 , 2014 ) developed the Compliance method to estimate the\nfracture closure pressure at the point on the G-function plot where the trend starts to deviate from its original\nlinearity. Based on the Compliance method, Wang and Sharma (2019, 2018a, 2018b , 2017 ) suggest the\nVariable Compliance method to estimate the fracture closure pressure by addressing that fracture stiffness\ngradually increases as the fracture walls come into contact. As a result, the Variable Compliance method\nidentifies closure pressure at the average G-function time of the Tangent Line and Compliance methods.\nDFIT numerical simulation is an advanced method to estimate matrix permeability and fracture geometry,\nwhich are important to the development of unconventional assets. The DFIT numerical simulation of this"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c920-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 6, "chroma:document": "which are important to the development of unconventional assets. The DFIT numerical simulation of this\nmanuscript is based on the algorithm by Wang and Sharma (2019, 2018a , 2018b , 2017 ).\nThe differential form of mass balance, with the assumption of 1D leak-off into a semi-infinite formation,\ncan be presented as\n(8)\nWhere Ct is the total compressibility, k is the formation permeability and \u00f8 is the formation porosity. The\nboundary condition of Equation 8 can be written as\n(9)\nThe initial conditions of Equation 8 are written as\n(10)\n(11)\nWhere ISIP is the instantaneous shut-in pressure, Po is the initial reservoir pressure and Sf is the fracture\nstiffness. The net pressure is written asDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c970-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 7, "chroma:document": "8 SPE-201413-MS\n(12)\nWhere Shmin is the minimum principal stress and wf is the average fracture width. The minimum principal\nstress is assumed to be the closure pressure, and ISIP is estimated by extrapolation in this paper. Pnet and Sf\nare used to evaluate the induced fracture geometry based on expressions in Table 1 , as shown below.\nTable 1\u2014Fracture stiffness by different fracture geometry models (Wang and Sharma, 2017).\nFracture Geometry PKN KGD Radial\nFracture Stiffness\nThe pressure decline and GdP/dG behaviors during DFITs are simulated by Equation 8 with Equation\n9 constraining as the boundary condition; Equation 10 and 11 are governing Equation 8 as the initial\nconditions. One essential feature of this numerical simulation algorithm, which is based on the Variable\nCompliance method, is that this model is able to capture variable fracture stiffness and pressure-dependent\nleak-off during the progressive fracture closure process. The fracture geometry is estimated by Equation"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89c9c0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 7, "chroma:document": "leak-off during the progressive fracture closure process. The fracture geometry is estimated by Equation\n12 and Table 1 .\nThree DFIT Cases Targeting Utica Shale\nAccurate estimations of closure pressure, pore pressure, and permeability are essential to the successful\ndevelopment of a shale play. However, permeability of shale formations are low, thus interpretation of DFIT\ndata targeting shale formations is challenging. The Utica shale is one of the most promising unconventional\nplays in the United States, but there are not many publications discussing its closure pressure, pore pressure,\nand permeability. In SPE 196149-MS, we presented one set of DFIT data and its related interpretation. Here,\nthree additional DFIT cases are presented to give a comprehensive, field wide estimation of stress regimes\nand reservoir properties of the Utica shale.\nDFITs are performed on Well-A, Well-B, and Well-C with the locations of these three wells shown in"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ca10-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 7, "chroma:document": "and reservoir properties of the Utica shale.\nDFITs are performed on Well-A, Well-B, and Well-C with the locations of these three wells shown in\nFigure 5 . They are all horizontal wells with their horizontal intervals all being stimulated by hydraulic\nfracturing into multiple stages. The TVD and MD for the wells are as follows: 6,600 feet and 12,500 feet\nfor Well-A, 6,200 feet and 9,300 feet for Well-B, and 6,900 feet and 12,600 feet for Well-C. During each\nDFIT, water is injected into the targeted wellbore for approximately 15 minutes at a constant rate of around\n3.5 bbl/min. Figures 6  through 8 display the wellhead pressure and pump rate vs. time for Well-A, Well-\nB, and Well-C, respectively.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ca88-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 8, "chroma:document": "SPE-201413-MS 9\nFigure 5\u2014DFITs targeting the Utica shale were carried out on Well-A, Well-B and Well-C.\nFigure 6\u2014WHP and pump rate vs. time for the DFIT on Well-A.\nFrom Figure 6 , it can be determined that the leak off pressure (LOP), the fracture breakdown pressure\n(FBP), and the fracture propagation pressure (FPP) of Well-A are estimated to be 8,467, 9,126 and 8,938 psi.\nWhen the pump is shut down and the pump rate reads zero, the instantaneous shut-in pressure (ISIP) after\nadding hydrostatic reads 8,206 psi and quickly drops to 7,657 psi after one minute. This significant drop in\nISIP indicates that the friction and the tortuosity inside the wellbore are high and the fracture complexity near\nthe wellbore is significant, therefore the true ISIP is estimated by extrapolation to calculate net pressure andDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cace-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 9, "chroma:document": "10 SPE-201413-MS\nanalyze the G-function. At end of the DFIT, the pressure of Well-A drops to 4,762 psi, which is magnified\nin the inserted image. Similarly, Figures 7 and 8 show wellhead pressure and pump rate vs. time for wells B\nand C. Based on the plots, LOP, FBP, FPP, and ISIP are estimated to be 8,121, 8,629, 8,480, and 7,744 psi for\nWell-B, and 7,854, 8,668, 8,642, and 7,926 psi for Well-C. It should be noted that high wellbore tortuosity\nand significant fracture complexity are also observed in Well-B and Well-C due to the significant drop in\npressure after shut-in, therefore the extrapolated ISIPs are applied to the following analysis and simulation.\nFigure 7\u2014WHP and pump rate vs. time for the DFIT on Well-B.\nFigure 8\u2014WHP and pump rate vs. time for the DFIT on Well-C.\nBased on the field DFIT data from three wells, a plot of pressure and GdP/dG vs. G-function can be\nseen in Figure 9 . There is quite a bit of noise in GdP/dG response after the closure time, represented by"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cb1e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 9, "chroma:document": "seen in Figure 9 . There is quite a bit of noise in GdP/dG response after the closure time, represented by\nthe blue line, which is commonly observed in DFIT analysis. The noise in the data is smoothed by the\nButterworth filter with a smoothing coefficient of 0.11, and the filtered data is represented by the red line.\nThe G-functions of wells A and C experience a similar trend, while well B does not. Further analysis on\nthese trends is explained with the simulation results.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cb6e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 10, "chroma:document": "SPE-201413-MS 11\nFigure 9\u2014G-function plots for Wells A, B, and C, respectively.\nFigures 10  through 12 show closure pressure determination by the Tangent Line method, the Compliance\nmethod, and the Variable Compliance method for the three wells, as depicted by red, blue and turquoise\ndotes, respectively. The Compliance method suggests that fracture closure pressure is determined when\nGdP/dG response starts to deviate from expected linearity, and the Variable Compliance method is an\naverage result of the Tangent Line method and the Compliance method. Therefore, the Compliance method\nshows an upper bound while the Tangent Line method suggests a lower bound of closure pressure estimation.\nAs shown in Figure 10 , the closure pressure by the Tangent Line method for Well-A is estimated to be\n5,690 psi, contributing to a stress gradient of 0.862 psi/ft; 6,125 psi with 0.928 psi/ft by the Compliance"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cbbe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 10, "chroma:document": "5,690 psi, contributing to a stress gradient of 0.862 psi/ft; 6,125 psi with 0.928 psi/ft by the Compliance\nmethod, and 5,973 psi with 0.905 psi/ft by the Variable Compliance method. As shown above, the true ISIP\nis extrapolated to 6,300 psi when the square root of time reaches to zero, compared to the estimated ISIP\nof 8,206 psi from the pump schedule presented above. A net pressure of 327 psi is determined and applied\nto the fracture geometry estimation, which is discussed in the following simulation section. As a result, the\nWell-A DFIT analysis estimates that the closure pressure ranges from 5,690 psi to 6,125 psi, contributing\nto the stress gradient of 0.862 \u2013 0.928 psi/ft in this area.\nFigure 10\u2014Closure pressure determination by the Tangent, the Compliance"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cc0e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 10, "chroma:document": "to the stress gradient of 0.862 \u2013 0.928 psi/ft in this area.\nFigure 10\u2014Closure pressure determination by the Tangent, the Compliance\nand the Variable Compliance methods using the filtered Well-A DFIT data.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cc5e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 11, "chroma:document": "12 SPE-201413-MS\nFigure 11\u2014Closure pressure determination by the Tangent, the Compliance\nand the Variable Compliance methods using the filtered Well-B DFIT data.\nFigure 12\u2014Closure pressure determination by the Tangent, the Compliance\nand the Variable Compliance methods using the filtered Well-C DFIT data.\nFigure 11  demonstrates the closure pressure by the Tangent Line method for Well-B is estimated to be\n4,692 psi, contributing to a stress gradient of 0.757 psi/ft; 5,154 psi with 0.831 psi/ft by the Compliance\nmethod, and 4,943 psi with 0.797 psi/ft by the Variable Compliance method. The true ISIP is extrapolated\nto 5,700 psi when the square root of time reaches to zero, compared to the estimated ISIP of 7,744 psi from"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cca4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 11, "chroma:document": "to 5,700 psi when the square root of time reaches to zero, compared to the estimated ISIP of 7,744 psi from\nthe pump schedule. A net pressure of 757 psi is determined and applied to the fracture geometry estimation.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ccf4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 12, "chroma:document": "SPE-201413-MS 13\nAs a result, the Well-B DFIT analysis estimates that the closure pressure ranges from 4,692 psi to 5,154 psi,\ncontributing to the stress gradient of 0.757 \u2013 0.831 psi/ft in this area.\nFigure 12  presents the closure pressure by the Tangent Line method for Well-C is estimated to be 5,662\npsi, contributing to a stress gradient of 0.821 psi/ft; 6,416 psi with 0.929 psi/ft by the Compliance method,\nand 6,141 psi with 0.891 psi/ft by the Variable Compliance method. The true ISIP is extrapolated to 6,250\npsi when the square root of time reaches to zero, compared to the estimated ISIP of 7,926 psi from the\npump schedule. A net pressure of 109 psi is determined and applied to the fracture geometry estimation. As\na result, the Well-C DFIT analysis estimates that the closure pressure ranges from 5,662 psi to 6,416 psi,\ncontributing to the stress gradient of 0.821 \u2013 0.929 psi/ft in this area. Overall, the closure pressure ranges"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cd44-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 12, "chroma:document": "contributing to the stress gradient of 0.821 \u2013 0.929 psi/ft in this area. Overall, the closure pressure ranges\nfrom 4,943 psi to 6,141 psi in the Utica shale, contributing to the closure pressure gradient of 0.797 to 0.891\npsi/ft by the Variable Compliance method.\nA log-log pressure derivative plot vs. shut in time is used in this analysis to verify fracture closure and\nestimate the pore pressure, as shown in Figure 13 . Well-A, Well-B, and Well-C all experience similar after\nclosure-flow patterns: after the pump is shut down, the afterflow rate is greater than the leak-off rate in the\nfracture, causing the fracture to propagate in all directions. This signature is marked by a unit slope in the\nfigures. Once the injected fluid reaches the fracture tip, the fracture is propagating only into its longitude\ndirection and fracture length is increased, signaled by a zero slope. Following that, leak-off phenomenon"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cd94-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 12, "chroma:document": "direction and fracture length is increased, signaled by a zero slope. Following that, leak-off phenomenon\nstarts to govern the process, and fractures starts to close progressively. The peaks of the pressure derivative\nin the figures clearly indicate that the induced fracture is mechanically closed, verifying the fracture closure\ndetermination in the analysis above. After fracture closure time, reservoir flow starts to dominate the process\nand the pore pressure is estimated by pressure transient analysis. The adjacent reservoir fluid first flows in\nthe induced fracture by a 1D flowing pattern, resulting in a linear flow regime and implied by a slope of\n\u22120.5 on the pressure derivative plot, as shown by the red line in Figure 13. Well-B is a bit unique in the sense\nthat the pressure derivative experiences a significant drop after the peak pressure, and then reaches a linear\nflow regime marked by a \u22120.5 slope, where Well-A and Well-C reach linear flow immediately after the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cdda-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 12, "chroma:document": "flow regime marked by a \u22120.5 slope, where Well-A and Well-C reach linear flow immediately after the\nderivative peak. This observed signature could indicate that there are natural or secondary fractures existing\nnear Well-B, which is consistent with observations from its G-Function plot.\nFigure 13\u2014Before-Closure (BC) and After-Closure (AC) analyses by pressure derivative log-log plots for\nWell-A, Well-B and Well-C. Signature of linear flow regime is slope of \u22120.5 after the fracture closure time.\nTo estimate pore pressure, the pressure data in a linear flow regime is regressed linearly in a log-log\nplot of pressure vs. the inverse of square root of time, as shown in Figures 14 through 16. In general, pore\npressure by radial flow regime gives an upper bound estimation while linear flow gives a lower bound.\nFigure 14  demonstrates that the pore pressure of Well-A by linear flow regime is estimated to be 28.03 MPa"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ce2a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 12, "chroma:document": "Figure 14  demonstrates that the pore pressure of Well-A by linear flow regime is estimated to be 28.03 MPa\nor 4,064 psi, contributing to a pore pressure gradient of 0.616 psi/ft. Similarly, Figure 15  shows that the\npore pressure of Well-B by linear flow regime is estimated to be 22.33 MPa or 3,238 psi, contributing to a\npore pressure gradient of 0.522 psi/ft. Figure 16 indicates that the pore pressure of Well-C by linear flow\nregime is estimated to be 23.1 MPa or 3,351 psi, contributing to a pore pressure gradient of 0.486 psi/ft.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ce7a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 13, "chroma:document": "14 SPE-201413-MS\nAs a result, the pore pressure ranges from 3,238 psi to 4,064 psi, contributing to a pore pressure gradient\nof 0.486 to 0.616 psi/ft for the Utica shale.\nFigure 14\u2014Pore pressure of Well-A is estimated by pressure transient analysis.\nFigure 15\u2014Pore pressure of Well-B is estimated by pressure transient analysis.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ceca-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 14, "chroma:document": "SPE-201413-MS 15\nFigure 16\u2014Pore pressure of Well-C is estimated by pressure transient analysis.\nBy inputting the rock properties and fracture parameters into the simulator developed by Wang and\nSharma (2019 , 2018a , 2018b, 2017 ), DFIT numerical simulations are performed to match the historical\npressure and GdP/dG data for DFITs from Well-A, Well-B, and Well-C. The input parameters include\nporosity, viscosity, Poisson's ratio, injection volume, total compressibility, Young's modulus, and wellbore\nstorage coefficient. Figures 17 to 19 demonstrate that the simulated pressures and derivatives match with the\nfield DFIT data well. It should be noted that although the shape of the simulated results may not be exactly\nthe same, the most important aspect is making sure that the peaks of the GdP/dG (blue) and simulated\nresults (red) agree. This will validate that the closure pressure and permeability are accurate estimates. The"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cf10-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 14, "chroma:document": "results (red) agree. This will validate that the closure pressure and permeability are accurate estimates. The\nsimulated reservoir permeability for Well-A is 0.000041 mD, 0.002 mD for Well-B, and 0.000025 mD\nfor Well-C. The fracture geometry simulation is performed based on the material balance, the net pressure\ncalculation by Equation 12, and the fracture geometry calculation from Table 1 . With an assumption of a 50-\nfoot fracture height, the simulation results of fracture geometry are summarized in Table 2 . It should be noted\nthat the simulation results are consistent with the estimations from our reservoir and petrophysics studies.\nFigure 17\u2014Numerical simulation and history match of pressure and pressure derivative for Well-A DFIT data.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cf60-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 15, "chroma:document": "16 SPE-201413-MS\nFigure 18\u2014Numerical simulation and history match of pressure and pressure derivative for Well-B DFIT data.\nFigure 19\u2014Numerical simulation and history match of pressure and pressure derivative for Well-C DFIT data.\nTable 2\u2014Fracture length and width with different fracture geometries.\nWell A Well B Well C\nFracture Geometry Radial PKN Radial PKN Radial PKN\nEstimated Frac\nLength (ft)72.95 263.62 50.87 89.39 82.43 380.3\nFracture\nAverage Width\nat Shut-in (ft)0.01406 0.00891 0.02165 0.01969 0.00736 0.00413Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cfb0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 16, "chroma:document": "SPE-201413-MS 17\nThe G-function signatures of these DFITs, as depicted in Figure 9, are insightful. At the very beginning\nof the shut-in time, a minor hump in GdP/dG in Well-A and Well-C is seen, corresponding to an accelerated\nand considerable pressure drop. As discussed above, these wells are long horizontal wells and this minor\nGdP/dG hump results from wellbore tortuosity and fracture complexity. Therefore, it should be excluded\nfrom the closure pressure determination. After that, a major hump in GdP/dG appears and follows a\nclassic concave-up trend, which is a characteristic signature of pressure-loss-acceleration. Indicating that\nthe induced fracture is closed progressively and, thus closure pressure can be determined by the Compliance\nmethod. Height recession and transverse storage are the two main mechanisms contributing to the pressure-\nloss-acceleration signature. However, they are two different mechanisms from the perspective of physics."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89cff6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 16, "chroma:document": "loss-acceleration signature. However, they are two different mechanisms from the perspective of physics.\nHeight recession occurs when the induced fracture grows into overlying and/or underlying formations\nduring a DFIT, causing increasing stiffness and thus accelerating pressure drop rate. Transverse storage takes\nplace when fluid, expelled from transverse fractures due to fracture closure, enters into the induced fracture,\nand contributes to the increasing leak-off rate and accelerated GdP/dG. Besides these two mechanisms,\nMcClure (2016 , 2014 ) states that fracture closure is a dynamic process, and the concave upward trend is\nactually an indication that two fracture planes come into contact and stiffness is therefore increased. It is\ndifficult to confirm which mechanism is dominating without further supporting data, but the methodology to\ndetermine the closure pressure of a concave-up trend is consistent. On the contrary, Well-B does not display"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d064-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 16, "chroma:document": "determine the closure pressure of a concave-up trend is consistent. On the contrary, Well-B does not display\na hump at the beginning of shit in time. Instead, we observe a consistent concave down trend throughout the\ntest. This is a typical signature of pressure dependent leak off in a naturally fractured formation and generally\noccurs in a dual porosity system when the fluid loss rate varies with the pressure dependent permeability. The\npotential existence of secondary fractures near Well-B is also verified by the pressure derivative analysis, as\nshown in Figure 13 . It is common to observe a signature of tip extension in DFIT targeting shale formations,\nwhich usually leads to a questionable estimation of closure pressure. However, the DFIT results presented\nin this paper do not show characteristics of tip-extension, which is an indication of productive shale quality.\nAs seen from the simulated fracture geometries in Table 2 , we again see similarities between wells A"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d0b4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 16, "chroma:document": "As seen from the simulated fracture geometries in Table 2 , we again see similarities between wells A\nand C. In both radial and PKN geometry, the fractures exhibit the similar lengths and widths. These two\nwells are very close in proximity to each other and share similar depths, so it's physically meaningful that\nthese two wells experience similar results. Well-B is located further north on the trend and the results from\nthis study show that the differences in DFIT behaviors and simulation, including GdP/dG response, leak off\ncharacteristics, pressure transient behaviors, formation permeability, and frac geometries, can be attributed\nto regional geology, stresses, and pressures. Therefore, operators need to consider regional differences in\nreservoir properties in order to enhance the development of the Utica and unlock all potential producible\nhydrocarbons.\nConclusion\nThe objective of this study was to continue analysis on the Utica shale and its properties through multiple"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d0fa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 16, "chroma:document": "hydrocarbons.\nConclusion\nThe objective of this study was to continue analysis on the Utica shale and its properties through multiple\nDFITs across the extent of the play. In this study, we presented three additional wells to perform analysis\nand determined field wide ranges of closure pressure, pore pressure, net pressure, formation permeability,\nand fracture geometry. In this study, we first gave a geological overview of the Utica shale, then explained\nthe theories and methods behind DFITs, and finally presented a field wide range of reservoir characteristics\nand properties. The results from this study are encouraging and insightful, showing that there are regional\ndifferences across the shale and can be identified through the application of DFITs. The knowledge resulting\nfrom this study indefinitely creates value for the industry in the pursuit of unlocking hydrocarbons in the\nUtica shale. The analysis and results from this study provide the following conclusions:"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d14a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 16, "chroma:document": "Utica shale. The analysis and results from this study provide the following conclusions:\n\u2022As observed by all three wells, the sharp breakdown of pressure after shut in indicates that the\nfriction and the tortuosity inside the wellbores are high, and the fracture complexity near the\nwellbore is significant for horizontal wells and the Utica shale.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d19a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 17, "chroma:document": "18 SPE-201413-MS\n\u2022Interpreting the GdP/dG data by the Variable Compliance Method, the closure pressure ranges\nfrom 4,943 psi to 6,141 psi in the Utica shale, contributing to a closure pressure gradient of 0.797\nto 0.891 psi/ft.\n\u2022Calculating based on the closure stress and ISIP, the net pressure in the fractures from wells A, B,\nand C are 327, 757, and 109 psi, respectively.\n\u2022Based on G-function analysis, Wells A and C follow a classic concave-up trend, which is a\ncharacteristic signature of pressure-loss-acceleration, indicating that the induced fracture is closed\nprogressively. Well-B displays a consistent concave down trend, which is a typical signature of\npressure dependent leak off in a naturally fractured formation and generally occurs in a dual\nporosity system when the fluid loss rate varies with the pressure dependent permeability. This\nobservation is consistent with the pressure derivative analysis."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d1e0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 17, "chroma:document": "observation is consistent with the pressure derivative analysis.\n\u2022On the log-log plots of pressure derivative, Well-A, Well-B, and Well-C experience similar After-\nClosure flow patterns in general. The sharp decline in pressure derivative on the log-log plot after\nits peak indicate that there are natural and secondary fractures near Well-B. This observation is\nconsistent with the G-function analysis.\n\u2022From the linearly regressed log-log plot of pressure vs. the inverse of square root of time, the pore\npressure ranges from 3,238 psi to 4,064 psi, contributing to a pore pressure gradient of 0.486 to\n0.616 psi/ft for the Utica shale.\n\u2022Through numerical simulation, the formation permeability for Well-A is 0.000041 mD and\n0.000025 mD for Well-C. The numerical simulation shows that the formation permeability for\nWell-B is 0.002 mD, which is higher than Well-A and Well-C.\n\u2022Wells A and C show similar fracture geometries with an average frac length of 77.69 feet and width"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d230-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 17, "chroma:document": "\u2022Wells A and C show similar fracture geometries with an average frac length of 77.69 feet and width\nof 0.01071 feet in radial geometry, and an average frac length of 321.96 feet and width of 0.01304\nfeet in PKN geometry. For Well-B, the frac length is estimated 50.87 feet in radial geometry and\n89.39 feet in PKN geometry. The difference in fracture geometry indicates that Wells A and C are\nlocated in an area where induced fractures tend to propagate into longitude direction.\n\u2022As shown above, Wells A and C are very close in proximity and thus they display similar DFIT\nresults and reservoir properties. Well-B is well north of wells A and C, and it shows different\nGdP/dG response, leak off characteristics, pressure transient behaviors, formation permeability,\nand frac geometries. This variance can be attributed to regional differences in geology, stresses,\nand pressures.\nAcknowledgment\nThe authors wish to thank Dr. Mukul Sharma and Dr. Hanyi Wang for their continued support and guidance."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d280-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 17, "chroma:document": "and pressures.\nAcknowledgment\nThe authors wish to thank Dr. Mukul Sharma and Dr. Hanyi Wang for their continued support and guidance.\nNomenclature\nASurface area of fracture\nCA constant relevant to leak off coefficient and comprehensive compressibility\nCAI Conodont alteration index\nCLCarter's leak off coefficient\nCtTotal compressibility\nE\u2019Plane strain for Young's Modulus\nGR Gamma ray\nGOR Gas Oil Ratio\nhfFracture height\nISIP Instantaneous shut-in pressure\nkFormation permeabilityDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d2d0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 18, "chroma:document": "SPE-201413-MS 19\nLOP Leak off pressure\nPPressure in fracture\nPoInitial reservoir pressure\nPnetNet pressure\nRfFracture radius\nRoVitrinite reflectance\nSfFracture stiffness\nShminMinimum principal stress\nteShut-in time\nTOC Total organic content\nwfAverage fracture width\nxfFracture half-length\n\u0394PPressure difference after shut-in\n\u0394tTime difference after shut-in\n\u2206tDDimensionless time that is discussed in Equation 3\n\u03d5Formation porosity\nReference\nBarree, R.D.,  Barree, V .L.,  Craig, D., 2009 . Holistic Fracture Diagnostics: Consistent Interpretation of Prefrac Injection\nTests Using Multiple Analysis Methods. SPE-107877-PA 24, 396\u2013406. https://doi.org/10.2118/107877-PA\nBarree, R.D.,  Mukherjee, H., 1996 . Determination of Pressure Dependent Leakoff and Its Effect on Fracture Geometry, in:\nSPE-36424-MS. Presented at the SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers,\nSPE, p. 10. https://doi.org/10.2118/36424-MS"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d316-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 18, "chroma:document": "SPE, p. 10. https://doi.org/10.2118/36424-MS\nCastillo, J.L.,  1987 . Modified Fracture Pressure Decline Analysis Including Pressure-Dependent Leakoff, in: SPE-16417-\nMS. Presented at the Low Permeability Reservoirs Symposium, Society of Petroleum Engineers , SPE, p. 9. https://\ndoi.org/10.2118/16417-MS\nHildebrand, J.Jr.,  Liang, Y .,  2019 . DFIT Analysis and Simulation in Shale Formations: A Utica Case Study, in:\nSPE-196149-MS. Presented at the SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers ,\nSPE, p. 20. https://doi.org/10.2118/196149-MS\nHoward, G.C., Fast, C.R., 1957 . Optimum Fluid Characteristics for Fracture Extension, in: API-57-261. Presented at the\nDrilling and Production Practice, American Petroleum Institute, API, p. 10.\nMcClure, M.W.,  Blyton, C.A.J., Jung, H., Sharma, M.M., 2014 . The Effect of Changing Fracture Compliance on Pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d370-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 18, "chroma:document": "McClure, M.W.,  Blyton, C.A.J., Jung, H., Sharma, M.M., 2014 . The Effect of Changing Fracture Compliance on Pressure\nTransient Behavior During Diagnostic Fracture Injection Tests, in: SPE-170956-MS. Presented at the SPE Annual\nTechnical Conference and Exhibition, Society of Petroleum Engineers, SPE, p. 23. https://doi.org/10.2118/170956-MS\nMcClure, M.W.,  Jung, H.,  Cramer, D.D., Sharma, M.M., 2016 . The Fracture-Compliance Method for Picking Closure\nPressure From Diagnostic Fracture-Injection Tests (see associated supplementary discussion/reply) . SPE-179725-PA\n21, 1321 \u20131339 . https://doi.org/10.2118/179725-PA\nNolte, K.G.,  1986a . Determination of Proppant and Fluid Schedules From Fracturing-Pressure Decline. SPE-13278-PA\n1, 255\u2013265. https://doi.org/10.2118/13278-PA\nNolte, K.G., 1986b . A General Analysis of Fracturing Pressure Decline With Application to Three Models . SPE-12941-\nPA 1, 571\u2013583. https://doi.org/10.2118/12941-PA"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d3c0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 18, "chroma:document": "PA 1, 571\u2013583. https://doi.org/10.2118/12941-PA\nNolte, K.G.,  1979 . Determination Of Fracture Parameters From Fracturing Pressure Decline, in: SPE-8341-MS. Presented\nat the SPE Annual Technical Conference and Exhibition, Society of Petroleum Engineers, SPE, p. 16. https://\ndoi.org/10.2118/8341-MS\nU.S. Energy Information Administration, 2017 . Utica Shale Play Geology Review.\nWang, H.,  Sharma, M.M.,  2019 . A Novel Approach for Estimating Formation Permeability and Revisit After-Closure\nAnalysis from DFIT, in: SPE-194344-MS. Presented at the SPE Hydraulic Fracturing Technology Conference and\nExhibition, Society of Petroleum Engineers, SPE, p. 32. https://doi.org/10.2118/194344-MS\nWang, HanYi,  Sharma, M.M., 2018a. Estimating Unpropped Fracture Conductivity and Compliance from Diagnostic\nFracture Injection Tests, in: SPE-189844-MS. Presented at the SPE Hydraulic Fracturing Technology Conference and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d406-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 18, "chroma:document": "Fracture Injection Tests, in: SPE-189844-MS. Presented at the SPE Hydraulic Fracturing Technology Conference and\nExhibition, Society of Petroleum Engineers, SPE, p. 28. https://doi.org/10.2118/189844-MSDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d456-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-201413-ms.pdf", "page": 19, "chroma:document": "20 SPE-201413-MS\nWang, Hanyi,  Sharma, M.M.,  2018b . Estimating Fracture Closure Stress in Naturally Fractured Reservoirs With\nDiagnostic Fracture Injection Tests, in: ARMA-2018-225. Presented at the 52nd U.S. Rock Mechanics/Geomechanics\nSymposium, American Rock Mechanics Association, ARMA, p. 12.\nWang, H.,  Sharma, M.M.,  2017 . New Variable Compliance Method for Estimating In-Situ Stress and Leak-Off from DFIT\nData , in: SPE-187348-MS. Presented at the SPE Annual Technical Conference and Exhibition, Society of Petroleum\nEngineers , SPE, p. 40. https://doi.org/10.2118/187348-MS\nWest Virginia Geological and Economic Survey, 2020 . A Geologic Play Book for Utica Shale Appalachian Basin\nExploration [WWW Document] . URL http://www.wvgs.wvnet.edu/utica/playbook/index.aspx (accessed 8.2.20).Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/20ATCE/2-20ATCE/D022S061R029/2371481/spe-201413-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d4a6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 0, "chroma:document": "SPE-199690-MS\nDFIT Analysis and Interpretation in Layered Rocks\nShuang Zheng, Ripudaman Manchanda, HanYi Wang, and Mukul Sharma, The University of Texas at Austin\nCopyright 2020, Society of Petroleum Engineers\nThis paper was prepared for presentation at the SPE Hydraulic Fracturing Technology Conference and Exhibition held in The Woodlands, Texas, USA, 4-6 February\n2020.\nThis paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents\nof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect\nany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d4ec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 0, "chroma:document": "consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may\nnot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.\nAbstract\nDiagnostic fracture injection tests (DFITs) are often used to estimate formation properties such as closure\nstress, pore pressure, and matrix permeability. These estimations are typically based on analysis of pressure\ndata assuming the closure of simple planar fractures in homogeneous reservoirs. These interpretations\nare incorrect when dealing with complex reservoir environments such as layered reservoirs with different\nproperties and stresses. This paper investigates the impact of such complex environments on DFIT\ninterpretation and presents a systematic method to analyze the data.\nA 3-D implicitly integrated poroelastic fracture-reservoir-wellbore model is used to simulate DFITs."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d53c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 0, "chroma:document": "A 3-D implicitly integrated poroelastic fracture-reservoir-wellbore model is used to simulate DFITs.\nDFIT fracture propagation and well shut-in are simulated with implicitly computed fluid leak-off and\nfracture closure. The model is validated by simulating a DFIT for a homogeneous reservoir and the implicitly\ncalculated surface pressure is interpreted to obtain the simulation inputs (stress, pore pressure, permeability,\netc.). A multi-layer reservoir model is then built in the numerical simulation domain and a DFIT is simulated\nin the target layer. The properties and thickness of the layers are varied to analyze their impact on the\nobserved DFIT signature.\nWe analyze the impact of layer thicknesses, layer stresses, pressure and permeability of each layer, stress\ncontrast between the layers, fracture interaction with bedding planes and the rock roughness and hardness\nof each layer on the DFIT pressure signature. We show that the layer property variations can cause different"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d582-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 0, "chroma:document": "of each layer on the DFIT pressure signature. We show that the layer property variations can cause different\nbut characteristic DFIT pressure responses. Fracture propagation into layers with different stresses induces\nmultiple closure events in the observed pressure signature, which provides a quantitative representation of\nthe fracture height growth. The emergence of these closure events in the pressure signature are found to be\ndependent on the hardness and modulus of the rock layers and the fluid communication between the closing\nparts of the fracture. The DFIT signature patterns are also found to correlate with the interaction of the\nfracture with bedding planes (cross/arrest/divert) and provide valuable insights into fracture containment.\nIn this work we present best practices for performing DFIT analysis in layered reservoirs. Results from\nsimulated DFITs in layered reservoirs clearly show the effect of key heterogeneity parameters on DFIT"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d5d2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 0, "chroma:document": "simulated DFITs in layered reservoirs clearly show the effect of key heterogeneity parameters on DFIT\nresponses. The results from this work can be used to more accurately determine reservoir closure stress,\npore pressure, reservoir permeability, fracture compliance, fracture conductivity, and fracture containment\nin heterogeneous reservoirs.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d640-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 1, "chroma:document": "2 SPE-199690-MS\nIntroduction\nThe technology of multi-stage hydraulic fracturing in horizontal wells plays a key role in creating highly\nconductive flow channels connecting the wellbore with ultra-tight formations and this has led to the shale\nrevolution in North America. Diagonostic Fracture Injection Test (DFIT) has been an efficient method for\ndetermining formation properties, for example, fracture closure stress and pore pressure. A DFIT is usually\nperformed on a vertical data well or after the horizontal well is drilled and cemented and before the main\nhydraulic fracturing treatments start. A small amount of water is injected at low rate aiming to create a\nfracture and then the well is shut-in for several days while the pressure is recorded. During the shut-in, water\ngradually leaks into the reservoir and the fracture gradually closes. The fracture closure stress and pore\npressure can then be inferred from the closure and post-closure pressure data. Both analytical approaches"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d690-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 1, "chroma:document": "pressure can then be inferred from the closure and post-closure pressure data. Both analytical approaches\n(summarized in the Appendix) and numerical approaches (e.g., Zheng et al., 2019b; Zheng et al., 2019g; Ji\net al., 2019 ; Kamali and Ghassemi, 2019 ) have been developed for DFIT data interpretation.\nPrevious researchers have mainly focused on DFIT interpretations and simulations assuming a planar\nfracture geometry in a homogeneous reservoir, however, it is not uncommon for the fracture that is\ncreated to intersect several layers with different stress and mechanical/flow properties. This can have a\nbig impact on the DFIT signature since the mechanical properties (rock Young's modulus, Poisson's ratio,\nfracture touchness, rock surface roughness, stress state) and the flow properties (permeability, porosity, pore\npressure) may vary a lot between different layers. Bedding planes are commonly seen in shale formations."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d6d6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 1, "chroma:document": "pressure) may vary a lot between different layers. Bedding planes are commonly seen in shale formations.\nDuring a DFIT, bedding planes may be connected and opened by the hydraulic frcature and the hydraulic\nfracture may be arrested by the bedding planes or cross them and propagate further ( Tang and Wu, 2018).\nDFIT fractures interacting with bedding planes will significantly impact the final fracture geometry and\nleakoff rate during shut-in, and thus influence the pressure response (Wang and Sharma, 2019b). Very\ncomplicated DFIT pressure signals are commonly observed in field data. For example, a field example of\na G-function plot of the pressure and pressure derivative ( Figure 1) shows multiple humps. However, most\nDFIT interpretations in the past did not take the layer effect into consideration. The traditional analytical\ninterpretation approaches (as summarized in the Appendix) are inadequate in these complicated but real"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d726-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 1, "chroma:document": "interpretation approaches (as summarized in the Appendix) are inadequate in these complicated but real\nscenarios. Other numerical models (e.g. Ji et al., 2019 ; Kamali and Ghassemi, 2019) also fail to capture\nthese complex behaviors due to their inability to model rock heterogeneity.\nFigure 1\u2014Field example case of complex DFIT pressure response ( Zheng et al., 2019g ).\nIn this paper, we apply our fully integrated reservoir-fracture-wellbore simulator to DFIT simulations.\nThrough the fully integrated fracturing and reservoir simulation, we can for the first time, study the behavior\nof the DFIT pressure response in layered formations. To fully understand the impact of the layer properties\nwe vary different layer properties with the ultimate aim of identifying the key parameters that affect the\nDFIT interpretation. The effect of layer stress contrast, layer permeability, layer thickness, rock asperity"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d776-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 1, "chroma:document": "DFIT interpretation. The effect of layer stress contrast, layer permeability, layer thickness, rock asperity\nroughness, rock hardness, bedding planes on the closure stress and pore pressure estimation are clearly\nshown. Many of these factors are found to have a significant impact on the DFIT analysis. The paper isDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d7bc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 2, "chroma:document": "SPE-199690-MS 3\nstructured as follows: First, we provide a brief summary to our fully integrated simulator in the Model\nDescription section with the model domains, model physics and solution algorithms. Sensitivity studies\nand discussions of the effect of different layer properties on the DFIT response and interpretation are then\nprovided in the Results and Discussions section. A Conclusion section summarizing the key findings of this\npaper is included at the end of this paper.\nModel Description\nA fully integrated hydraulic fracturing and reservoir simulator is used in this paper to simulate a DFIT:\nhydraulic fracture propagation and shut-in. This simulator has been developed for designing and evaluating\npad scale fracturing treatments previously ( Zheng et al., 2019a; 2019b ; 2019c; Manchanda et al., 2019a;\n2019b ). It was then extended from a single-phase flow model to multi-phase black-oil flow model and from"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d80c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 2, "chroma:document": "2019b ). It was then extended from a single-phase flow model to multi-phase black-oil flow model and from\nsingle well fracturing simulator to an integrated fracturing and reservoir simulator. An energy balance model\nwas inporporated into the simulator to consider temperature changes ( Zheng et al., 2019d). The fully implicit\ngeomechanical hydraulic fracturing simulator was also extended to an integrated Equation-of-State based\ncompositional fracturing and reservoir simulator in recent work (Zheng et al., 2019e ; Zheng et al., 2019f).\nThis simulator couples the reservoir-fracture-wellbore system ( Figure 2) and has the capability to\nsimulate the lifecycle of wells: hydraulic fraturing, shut-in, flowback, primary production, and improved\noil recovery. Multiple physics in each domain are tightly coupled. Solid deformation, flow in the rock\nmatrix and the fracture, and temperature are modeled and solved in the reservoir domain. Fracture fluid"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d85c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 2, "chroma:document": "matrix and the fracture, and temperature are modeled and solved in the reservoir domain. Fracture fluid\nand proppant flow, and fracture width change are solved in the fracture domain. Slurry and proppant\ndistribution, wellbore storage, hydrostatic and friction pressure drops are considered in the wellbore domain.\nThe coupled, non-linear system of equations is solved using the Newton-Raphson method. An Implicit\npressure, explicit saturation/concentration based (IMPES/IMPEC) solution algorithm is shown in Figure\n3. After the solutions to the coupled system of equations are obtained, mesh topology change (fracture\npropagation, dynamic mesh refinement) is checked and looped until no more mesh topology changes are\nneeded. Then the fluid mass conservation equations and temperature equations in the reservoir and fracture\ndomain as well as the the proppant volume equations in the fracture domain are solved. The simulation enters"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d8ac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 2, "chroma:document": "domain as well as the the proppant volume equations in the fracture domain are solved. The simulation enters\nthe next time step after the phase behavior analysis (using correlations if black-oil model and using Equation-\nof-State if using a compositional model) is performed. Although only the IMPES/IMPEC algorithm is\nshown here, different sets of equation for different physics can be chosen to be coupled into the main Newton\niteration block or removed from the block with great flexibility. For example, the fluid mass conservation\nequations can be coupled into the main Newton iteration block, making the simulation fully implicit and\nthe solid deformation equation can be removed from the iteration block, making it a non-geomechanical"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d8fc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 2, "chroma:document": "the solid deformation equation can be removed from the iteration block, making it a non-geomechanical\nreservoir simulator. A detailed formulation of the simulator can be found in the references cited above.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d94c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 3, "chroma:document": "4 SPE-199690-MS\nFigure 2\u2014The coupled domains and physics of the fully integrated simulator ( Zheng et al., 2019d ).\nFigure 3\u2014The IMPES/IMPEC solution algorithm of the fully integrated simulator.\nThis simulator was first applied to fracture closure and DFIT modeling in Zheng et al., 2019b in which\nthe Barton-Bandis contact correction was incorporated to model fracture closure on asperities/proppants.\nThis simulator was successfully validated for DFIT simulation and applied to study the effect of depletionDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89d992-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 4, "chroma:document": "SPE-199690-MS 5\ninduced stress and pore pressure heterogeneity on DFIT closure stress and pore pressure estimation ( Zheng\net al., 2019g ). Readers are encouraged to read Zheng et al., 2019g for more details on the model validation.\nBase Case\nIn the Base Case, a small amount of fluid (2 m3) is injected into the wellbore in 5 minutes and then the well\nis shut-in for 10 days to mimic a DFIT job. The simulation domain is 400 \u00d7 400 m2 in the horizontal plane\nand 200 m in the height direction (Figure 4). The perforation clusters are placed in the middle of the domain.\nOther reservoir properties and completion design parameters are summarized in Table 3. The bottom hole\npressure versus time is computed and plotted in this simulation. The simulation involves propagation of a\nsingle vertical fracture from a horizontal wellbore drilled in a formation with layered stress heterogeneity."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89da64-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 4, "chroma:document": "single vertical fracture from a horizontal wellbore drilled in a formation with layered stress heterogeneity.\nThe stress distribution with the DFIT fracture initiation point is shown in Figure 5. The initial mesh size is 40\n\u00d7 10 \u00d7 10 m3 and is dynamically refined as can be seen from Figure 6. Grid convergence analysis (Zheng et\nal., 2019g ) is performed to determine the correct mesh size for a grid converged solution and it is found that\nwhen the smallest grid size reached 0.625 \u00d7 1.25 \u00d7 1.25 m3 by three levels of static refinement perpendicular\nto the wellbore direction and three levels dynamic refinement in all directions, the results will not change\nwith further mesh refinement. A plot of the fracture geometry with width distribution and pore pressure\ndistribution at the end of shut-in (t  = 10 days) is shown in Figure 6. In this figure, each fracture segment\nhas an area of 1.25 \u00d7 1.25 m2 and the length of the smallest grid perpendicular to the wellbore direction is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89dadc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 4, "chroma:document": "has an area of 1.25 \u00d7 1.25 m2 and the length of the smallest grid perpendicular to the wellbore direction is\n0.625 m. During fracture propagation and shut-in, fracturing fluid in the fracture leaks into the reservoir,\ncausing a pressure increase in the reservoir matrix adjacent to the fracture. The fracture width shows good\nagreement with the input layer stresses, with smaller widths being computed in the high stress layers.\nFigure 4\u2014Illustration of simulation domain, well location, and cluster locationDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89db5e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 5, "chroma:document": "6 SPE-199690-MS\nFigure 5\u2014Stress distribution in a vertical slice of the reservoir\nFigure 6\u2014Fracture geometry with width distribution and pore pressure distribution at the end of shut-inDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89dbc2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 6, "chroma:document": "SPE-199690-MS 7\nTable 1\u2014Reservoir properties and completion design in the Base Case\nParameter Value Unit Parameter Value Unit\nLength of the domain in the x-direction 400 m Initial stress in the x-direction ( Shmin) 35/36 MPa\nLength of the domain in the y-direction 400 m Initial stress in the y-direction ( Shmax) 51 MPa\nLength of the domain in the z-direction 200 m Initial stress in the z-direction ( Sv) 70 MPa\nPermeability 2e-19 m2 Vertical stress gradient 0.02262 MPa /m\nPorosity 0.08 Young's modulus of the rock 20 GPa\nCritical energy release rate 1000 Pa \u2219 m Poisson's ratio of the rock 0.25\nContact width 2e-4 m Fluid viscosity 0.001 Pa \u2219 s\nAsperity initial stiffness 5e8 Pa/m Total injection time 300 s\nWellbore volume 55 m3 Total injection volume 2 m3\nWell diameter 0.1397 m Number of perforations per cluster 2\nShut-in time 10 days Perforation diameter 0.0127 m\nFigure 7  shows the fracture contact area and fracture width distribution when shut-in time equals to"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89dc12-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 6, "chroma:document": "Figure 7  shows the fracture contact area and fracture width distribution when shut-in time equals to\n57, 67, 77, 87, 97, and 107 hours, respectively. As can be seen from Figure 7, the fracture maintains the\nlargest width in the middle low stress region and the two low stress regions below and above the middle\nlow stress region also have a large width as compared to the fracture tip regions and the high stress regions.\nThe fracture surfaces first fall in contact around the tips of the high stress regions followed by the internal\nfracture surface area in the high stress region. At about 97 h, all the fracture surfaces in the high stress region\ncome into contact on the rough asperities. During fracture closure, fracture width decreases, however, the\nfracture width in the low stress region is always higher than in the high stress region. Between time 97 h\nand 107 h, the fracture in the upper and lower low stress region closes first. The fracture in the middle low"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89dc58-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 6, "chroma:document": "and 107 h, the fracture in the upper and lower low stress region closes first. The fracture in the middle low\nstress region closes last.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89dca8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 7, "chroma:document": "8 SPE-199690-MS\nFigure 7\u2014Fracture contact area and fracture width at selected times during shut-in.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89dd16-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 8, "chroma:document": "SPE-199690-MS 9\nThe resulting pressure and G-function plot is shown in Figure 8. Since the stress contrast in the case is\nnot significantly large (1 MPa ), the fracture closure sequence in the high stress and low stress regions is\nnot very different. No double humps are observed in the G-function plot (they are not visually obvious).\nHowever, one can still observe that there is a small change in the pressure derivative between a G-time of 80\nand 100, which is caused by the non-uniform fracture closure event in different stress layers. By applying\nthe variable compliance method, the estimated closure stress value is about 35.6 MPa, which is an averaged\nvalue of the high stress value (36 MPa) and the low stress value (35 MPa ) input into the simulation.\nFigure 8\u2014G-function plot for the Base Case.\nResults and Discussion\nIn this section, we apply our numerical DFIT model to study the effect of different layer properties on the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89dd66-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 8, "chroma:document": "Results and Discussion\nIn this section, we apply our numerical DFIT model to study the effect of different layer properties on the\nDFIT signature and its interpretation. Based on the Base Case setup, we vary the layer properties including\nlayer stress contrast, layer permeability, layer thickness, layer rock stiffness and simulate DFIT fracture\npropagation during injection and fracture closure during shut-in. Bottom hole pressure is obtained and\nanalyzed. We also study the effect of bedding planes on the DFIT signature. From the simulation results, it\nis found that most of the layer properties have a very big impact on the DFIT signature and interpretation.\n1. Effect of layer stress contrast\nIn this subsection, we show two sets of simulations to investigate the effect of layer stress contrast on DFIT\nsignature and interpretation. In the first set of simulations, we modify the base case, in which the low stress"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ddac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 8, "chroma:document": "signature and interpretation. In the first set of simulations, we modify the base case, in which the low stress\nis fixed at 35 MPa  and the stress contrast is varied. Figure 9 shows the DFIT fracture geometry at the end\nof injection with a stress contrast of 1 MPa in Case (a) (Base Case), 3 MPa in Case (b), and 5 MPa in Case\n(c). The color scale depicts the fracture width distribution. It is observed that the magnitude of the stress\ncontrast significantly affects the DFIT fracture geometry and fracture width. In Case (a), the stress contrast\nis the smallest and it does not have a very big influence on fracture containment. The fracture grows in both\nlength and height in Case (a). By comparison, Case (b) has an intermediate stress contrast which limits the\nfracture height growth. Case (c) has the highest stress contrast, resulting in mainly length propagation of\nthe fracture in the low stress region. In the central low stress layer, Case (a) shows the largest fracture width"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89ddfc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 8, "chroma:document": "the fracture in the low stress region. In the central low stress layer, Case (a) shows the largest fracture width\nwhereas Case (c) shows the smallest fracture width.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89de4c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 9, "chroma:document": "10 SPE-199690-MS\nFigure 9\u2014Fracture geometry with color scale showing the fracture width distribution for\nstress contrast comparison. The stress contrasts are 1MPa in (a), 3MPa in (b), and 5MPa\nin (c), respectively. The middle layer where the fracture is initiated is a low stress layer.\nAfter injection, the well is shut-in for 20 days leaving the fracture to close gradually. The G-function plots\nof pressure and pressure derivative for each case are shown in Figure 10 . From the pressure plot, one can\nobserve different Instantaneous Shut-in Pressure (ISIP) for these three cases: the larger stress contrast case\ngives a large ISIP and vice versa, which is reasonable since more energy is needed to open the rocks under\nlarger compressive stress. One can also observe that cases with larger stress contrast close faster than the\ncases with low stress contrast. Double humps are observed in the pressure derivative plots in Case (b) and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89de9c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 9, "chroma:document": "cases with low stress contrast. Double humps are observed in the pressure derivative plots in Case (b) and\nCase (c) because of the lag time between fracture closure in the different stress layers are distinguishable\nwhile in Case (a) this time is not distinguishable and the two peaks merge into a single peak. Through DFIT\ninterpretation, the closure stresses correspond to the first and second humps in Case (b) are determined to be\n35.9 MPa  and 34.6 MPa , and the closure stresses correspond to the first and second humps in Case (c) are\ndetermined to be 36.7 MPa and 34.7 MPa using the tangent line method. In Case (b) and Case (c), the lower\nclosure stresses are almost same, but lower than the input low stress value (35 MPa). The higher closure\nstresses are 35.9 MPa  and 36.7 MPa , which are also lower than their input values (38 MPa and 40 MPa). As\nexpected, the tangent line method underestimates the closure stress. When the variable compliance method"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89deec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 9, "chroma:document": "expected, the tangent line method underestimates the closure stress. When the variable compliance method\nis used to estimate the layer closure stresses, better agreement with the input stresses is obtained: The closure\nstress in Case (b) and Case (c) are 37.4 MPa and 35.1 MPa, 38 MPa and 35.1 MPa, respectively. A very\ngood estimation to the lower stress is obtained and the estimation to the higher stress is improved. Table\n2 summarizes these results.\nFigure 10\u2014G-function plots of stress contrast comparison. The\nmiddle layer where the fracture is initiated is a low stress layer.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89df32-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 10, "chroma:document": "SPE-199690-MS 11\nTable 2\u2014Estimated closure stress corresponding to cases shown in Figure 9\nTangent\nline methodCompliance\nmethodVariable\ncompliance\nmethod\nCase (b)35.9 MPa\n34.6 MPa38.4 MPa\n35.5 MPa37.4 MPa\n35.1 MPa\nCase (c)36.7 MPa\n34.7 MPa38.5 MPa\n35.4 MPa38 MPa\n35.1 MPa\nIn the second set of simulations, we inverse the stress in the first set of simulations, while all other things\nremain the same. This means that the old high stress layers become the low stress layers and the old low\nstress layers become the high stress layers. In this set of simulations, the fracture is initiated in the high\nstress layer. The fracture geometries for different stress contrasts are shown in Figure 11 . Similarly, since\nthe stress contrast in Case (a) is only 1 MPa, it does not have a big restriction on the fracture geometry and\nfracture height growth, but one can still observe the the low width value in the central high stress layer."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89df82-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 10, "chroma:document": "fracture height growth, but one can still observe the the low width value in the central high stress layer.\nFrom Case (b) and (c), one can see that the DFIT fracture breaks through into the upper and lower low stress\nlayers and grows preferentially in the two low stress layers. Case (c) shows a better fracture containment\nand longer fracture length than Case (b) because of its higher layer stress contrast.\nFigure 11\u2014Fracture geometry with color scale showing the fracture width distribution for\nstress contrast comparison. The stress contrasts are 1MPa in (a), 3MPa in (b), and 5MPa\nin (c), respectively. The middle layer where the fracture is initiated is a high stress layer.\nThe G-function plots for the second set of simulations are shown in Figure 12 . It is observed that larger\nstress contrast gives early fracture closure. However, in this case, the fracture in the high stress layer closes,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89dfd2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 10, "chroma:document": "stress contrast gives early fracture closure. However, in this case, the fracture in the high stress layer closes,\nand consequently the wellbore will lose its hydraulic connection to the fracture. Compared to the previous\nset of simulations, in the current simulation set, the time lag between the two closure events is larger. This\nis because of the bottleneck in the fracture geometry which makes it easier to isolate the fracture portions\nin different stress layers. The closure stresses using tangent line method, the compliance method and the\nvariable compliance method are shown in Table 3. The tangent line method gives the best estimation of the\nlower closure stress. The closure stresses estimated from the variable compliance method area is overall\ncloser to the input layer stresses. In these three cases in Figure 12 , the fracture closes first in the high stress\nlayers, including the middle high stress layer where the wellbore goes through. This limits the hydraulic"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89e018-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 10, "chroma:document": "layers, including the middle high stress layer where the wellbore goes through. This limits the hydraulic\nconnectivity between the fracture in other layers and the wellbore and leads to a slow fracture closure, which\ncan be seen in Figure 12 where the stiffness keeps increasing slowly even at late G time. This \"slowly rising\ntail\" is comparable to the similar \"slowly rising tail\" as shown in Figure 1.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89e068-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 11, "chroma:document": "12 SPE-199690-MS\nFigure 12\u2014G-function plots of stress contrast comparison. The\nmiddle layer where the fracture is initiated is a high stress layer.\nTable 3\u2014Estimated closure stress corresponding to cases shown in Figure 11\nTangent\nline methodCompliance\nmethodVariable\ncompliance\nmethod\nCase (b)36.2 MPa\n35.3 MPa37.9 MPa\n35.7 MPa37.3 MPa\n35.5 MPa\nCase (c)37.2 MPa\n35.1 MPa38.4 MPa\n36.5 MPa38 MPa\n36.3 MPa\n2. Effect of layer thickness\nIn this subsection, we vary the layer thickness from the the Base Case. The stress contrast is fixed at 3 MPa\n(35 MPa  for low stress and 38 MPa for high stress). Different layer thickness has been tested: 5 m in Case\n(a), 10 m in Case (b), and 15 m in Case (c) as shown in Figure 13 . The fracture is initiated in the low stress\nlayer and it can be summarized that smaller layer thickness gives larger fracture surface area, longer fracture\nlength, smaller fracture height and smaller fracture width. The ratio of the area of the fracture portion in the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89e0b8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 11, "chroma:document": "length, smaller fracture height and smaller fracture width. The ratio of the area of the fracture portion in the\nlow stress layer to the total fracture area are 46.7%, 72.8%, and 87.7%, respectively.\nFigure 13\u2014Fracture geometry with color scale showing the fracture width distribution for layer\nthickness comparison. The stress contrast is 3MPa. The layer thicknesses are (a) 5m, (b) 10m,\nand (c) 15m, respectively. The middle layer where the fracture is initiated is a low stress layer.\nThe DFIT plots of the first set of simulations are shown in Figure 14. We observe that double humps\nare more likely to occur if more of the fracture area is in the high stress layer. In Figure 12, Case (a) hasDownloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89e0fe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 12, "chroma:document": "SPE-199690-MS 13\nthe largest proportion of fracture area in high stress layer whereas Case (c) has the smallest proportion of\nfracture area in the high stress layer. Case (b) lies between Case (a) and Case (c). As observed from Figure\n13 and Figure 14 , the time when fracture starts to closure follows the sequence Case (a) < Case (b) < Case\n(c), which is caused by the fact that under the same condition, the fracture width of Case (a) is the smallest\nwhile the width of Case (c) is the largest. More fracture propagates into high stress layer in Case (a), making\nthe signal from the high stress closure more pronounced and comparable to the low stress layer fracture\nclosure signal. This results in two humps in the pressure derivative plot. Comparatively speaking, most of\nthe fracture stays in the low stress layer in Case (b) and Case (c). For this reason, the ISIP also follows Case\n(a) > Case (b) > Case (c). The closure of the high stress layer fracture does not give a large enough fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89e14e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 12, "chroma:document": "(a) > Case (b) > Case (c). The closure of the high stress layer fracture does not give a large enough fracture\nstiffness increase and there is not a large enough gap between the different fracture areas, which leads to\nonly one hump in the pressure derivative plot for Case (b) and Case (c).\nFigure 14\u2014G-function plots of layer thickness comparison. The\nmiddle layer where the fracture is initiated is a low stress layer.\nIn the second simulation (Figure 15), the high stress layers and low stress layers are reversed, which\nmeans the fracture is initiated in the high stress layer. It can be observed the DFIT fracture tends to break out\nof the high stress layer and preferentially propagate in the low stress layer. The proportions of the fracture\nin the low stress layer are 54.1%, 75.1%, and 75.9%, respectively.\nFigure 15\u2014Fracture geometry with color scale showing the fracture width distribution for layer"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89e1c6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 12, "chroma:document": "Figure 15\u2014Fracture geometry with color scale showing the fracture width distribution for layer\nthickness comparison. The stress contrast is 3MPa. The layer thicknesses are (a) 5m, (b) 10m,\nand (c) 15m, respectively. The middle layer where the fracture is initiated is a high stress layer.Downloaded from http://onepetro.org/SPEHFTC/proceedings-pdf/20HFTC/2-20HFTC/D022S016R001/2428479/spe-199690-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89e216-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 13, "chroma:document": "14 SPE-199690-MS\nAll the three cases show two humps in the pressure derivative plots in Figure 16. In all the three cases,\nthe first hump corresponds to the closure of the fracture in the high stress layer whereas the second hump\ncorresponds to the closure of the fracture in the low stress layer. A larger proportion of fracture surface in\nthe high stress layer leads to a larger stiffness increase in the first closure event (fracture in high stress layer\ncloses). The magnitudes of the first hump are: Case (a) > Case (b) = Case (c), which agrees well with the\nfracture surface area ratio under high stress layer in the three cases. The fracture starts to close earliest in\nCase (c) and lastest in Case (a), as observed in Figure 15 . In these three cases in Figure 15 , the fracture\ncloses first in the high stress layers, including the middle high stress layer where the wellbore goes through."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89e266-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 13, "chroma:document": "closes first in the high stress layers, including the middle high stress layer where the wellbore goes through.\nThis limits the hydraulic connectivity between the fracture in other layers and the wellbore and leads to a\nslow fracture closure, which can be seen from Figure 15 where the stiffness keeps increasing slowly even\nat late G time.\nFigure 16\u2014G-function plots showing the effect of layer thickness.\nThe middle layer where the fracture is initiated is a high stress layer.\n3. Effect of rock stiffness and hardness\nIn this subsection, we study the effects of rock asperity stiffness on DFIT interpretation. The stress is uniform\nin all the layers. The rock asperity stiffness is varied by varying the initial normal stiffness parameter in\nthe Barton-Bandis contact correlation. Three cases have been run. In the small and large stiffness cases,\nthe initial normal stiffnesses are fixed at uniform values of 100 MPa/m and 500 MPa/m, respectively. In"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89e2ac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-199690-ms.pdf", "page": 13, "chroma:document": "the initial normal stiffnesses are fixed at uniform values of 100 MPa/m and 500 MPa/m, respectively. In\nthe mixed stiffness case (Figure 17 ), the initial normal stiffness value varies between 100 MPa/m and 500\nMPa /m in different layers. The DFIT G-function plot is shown in Figure 18 , from which one can see that the\nasperity stiffness has no impact on the fracture propagation but greatly affects the fracture closure period.\nThe DFIT fracture is found to close much faster in the small stiffness case than in the large stiffness case and\nthe mixed stiffness case lies in between the two uniform cases. From the Barton-Bandis correlation, one can\nsee that smaller initial normal stiffness will result in a smaller contact force. The contact force applied on\neach other's rough surface by the soft rock is much smaller than the hard rock, which lead to a fast fracture\nclosure in the soft rock. This is also obvious from Figure 17: The fracture residual width is much larger in"}


