# embeddings_queue

created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890896-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 18, "chroma:document": "technique stands up against other techniques used in the industry. Thus, two real \ufb01eld\ncases, wells X-01 and X-02 were selected for the analysis of the new CWT technique. The\nwell X-01 was perforated against a conventional oil sandstone reservoir. The well X-02 was\nperforated against a deep high temperature (400 degrees Fahrenheit) granite reservoir as\na conventional example for geothermal energy reservoirs. The well X-01 was perforated\nthrough a sandstone formation. One thousand gallons of water were pumped at a rate of\n8 bbl/min through a 10 ft perforated interval as a typical DFIT pumping schedule. This\nwas selected as the well site by the operating company. The pressure fall-off was observed\nfor 110 min, as shown in Figure 20. The CWT closure detection technique showed that the\nclosure started at a pressure of 7400 psi (start of closure) and ended at 6600 psi (complete\nclosure). As shown in Figure 21, the start of closure can be distinguished by increased"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8908f0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 18, "chroma:document": "closure). As shown in Figure 21, the start of closure can be distinguished by increased\nenergy levels followed by a drop in the average of signal log energy. The complete closure\npressure is when the level of energy drops to a lower level. The oscillatory signal energy\nwith real \ufb01eld data may be due to the complexity of fracture closure in addition to the\npresence of noise in the pressure signal observed in real \ufb01eld data."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890940-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 19, "chroma:document": "Energies 2023 ,16, 764 20 of 29\nFigure 20. Pumping chart for well X-01.\nFigure 21. Closure pressure detection using CWT closure detection technique for well X-01.\nApplication of classical conventional methods, tangent method (Barree et al. (2009) [ 26]),\nshowed that closure pressure is the same as what the CWT closure detection technique\ndetected. The closure pressure is 6600 psi as per the tangent method shown in Figure 22.\nThe log\u2013log technique detected the closure at the same pressure (6600 psi). The closure\npressure is the point at which the fracture linear \ufb02ow ended (slope of 0.5 at \u2206td\u2206p/d\u2206t\nvs.\u2206t log\u2013log plot) and the formation linear \ufb02ow started (slope of \u22120.5 at\u2206t d\u2206p/d\u2206t vs.\n\u2206t log\u2013log plot) as shown in Figure 23. The square root of the time method detected the\nclosure at the same point of 6600 psi, as seen in Figure 24. The compliance method (Mcclure\net al. (2022) [ 48]) using dP/dG vs. G-time plot did not show a clear signature for the closure."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89099a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 19, "chroma:document": "et al. (2022) [ 48]) using dP/dG vs. G-time plot did not show a clear signature for the closure.\nThere is no rise-up in dP/dG, as shown in Figure 22. However, there is a zero slope period\nat a pressure of approximately 7700 psi which can be de\ufb01ned as a closure. According to\nMcClure et al. (2019) [ 46], the DFIT is invalid due to the high near-wellbore tortuosity or the\nfracture may appear to be closed earlier than it should. The closure pressure value picked\nby the CWT technique matched the classical closure detection techniques. In addition to\nthat, CWT showed both the start and end of the fracture closure period. Table 3 lists the\nclosure pressure detected using each methodology for well X-01. The closure detected using\nthe CWT technique only used the pressure decline data without any information about the\npumping period or formation properties. In the well X-01 case, the CWT technique was\napplied to analyze the classic DFIT in a conventional sandstone formation. However, it"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8909ea-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 19, "chroma:document": "applied to analyze the classic DFIT in a conventional sandstone formation. However, it\nwas also tested on a very tight reservoir. The well X-02 was perforated through granite\nformation, which is the typical geothermal formation type, and then pumped the DFIT as\nper the pumping schedule shown in Figure 25."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890a3a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 20, "chroma:document": "Energies 2023 ,16, 764 21 of 29\nFigure 22. Tangentmethod (dP/dG and GdP/dG) for well X-01.\nFigure 23. Closure detection using the log\u2013log method for well X-01."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890a94-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 21, "chroma:document": "Energies 2023 ,16, 764 22 of 29\nFigure 24. Closure detection using the square root time method for well X-01.\nFigure 25. Pumping schedule for well X02.\nTable 3. Fracture closure pressure for well X-01.\nMethod Closure Pressure,psi\nTangent method (G-function) technique 6600 psi\nLog\u2013log technique 6600 psi\nSquare-root time technique 6600 psi\nCompliance method Invalid DFIT\nCWT fracture closure detection techniqueStart of fracture closure = 7400 psi, complete\nfracture closure = 6600 psi\nThe application of the CWT closure detection technique showed oscillatory signal\nenergy. That may be due to a noise in the pressure signal recorded during the shut-in period\nor the presence of natural fractures in granite formations. The presence of natural fractures\nis con\ufb01rmed with the image log of the well as shown in Figure 26. Natural fractures may\ncause noise and aggressive \ufb02uctuations in the pressure decay signal. The CWT technique"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890ae4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 21, "chroma:document": "cause noise and aggressive \ufb02uctuations in the pressure decay signal. The CWT technique\ndetected the start of fracture closure at the pressure of 5300 psi and complete fracture closure\nto be 4700 psi, as shown in Figure 27. The application of the tangent method (Barree et al.\n(2009) [ 26]) using GdP/dG showed fracture closure at the same complete fracture closure\nthat the CWT technique detected (4700 psi), as shown in Figure 28. This was con\ufb01rmed"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890b34-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 22, "chroma:document": "Energies 2023 ,16, 764 23 of 29\nby the square root of time, as seen in Figure 29. However, the log\u2013log plot showed the\nfracture closure at 4523 psi, as seen in Figure 30. The closure pressure is detected at the\nend of before the closure bilinear \ufb02ow regime. The application of the compliance method\n(Mcclure et al. (2022) [ 48]) showed the contact pressure to be 5625 psi as the dP/dG starts\nto rise up from the minimum at 5700 psi so the contact pressure is at 75 psi of that pressure,\nas seen in Figure 28. The main advantage of the CWT technique is that it illustrates the\ncon\ufb02ict between the tangent methods and the holistic fracture diagnostic technique and\ncaptured the full image of the fracture closure process. Table 4 showed the comparison\nbetween various techniques for well X-02.\nFigure 26. Formation image log for well X-02 indicating the presence of natural fractures in the\ngranite reservoir."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890b84-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 23, "chroma:document": "Energies 2023 ,16, 764 24 of 29\nFigure 27. Closure identi\ufb01cation using a CWT closure detection technique for well X02.\nFigure 28. Tangent method (dP/dG and GdP/dG) for well X-02.\nWith the application of the CWT closure detection technique on real data cases, fracture\nclosure can be detected at a lower maximum scale or higher maximum scale than that used\nin the study (a = 256) based on the noise of the data and the time of the signal. The selected\nmaximum scale is iterative until fracture closure is identi\ufb01ed. The signal energy scalogram\ncan be used as a guide for the maximum value for the maximum scale used. That is because\nwhen the scale (wavelet scale (a)) increases more than required, it can miss the fracture\nclosure event. The value for the maximum scale (wavelet scale (a)) may depend on several\nfactors such as the length of the pressure decay signal, the complexity and the duration of\nfracture closure, and the level of noise that is in the pressure decay signal."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890bd4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 24, "chroma:document": "Energies 2023 ,16, 764 25 of 29\nFigure 29. Closure identi\ufb01cation using the square root of time technique for well X-02.\nFigure 30. Closure detection using the log\u2013log analysis technique for well X-02 (closure identified when\nthe slope of changes from 1/4 (pre-closure bilinear flow) to \u22121/2 (post-closure formation linear)).\nTable 4. Fracture closure pressure for well X-02.\nMethod Closure Pressure, psi\nTangent method (G-function) technique 4700 psi\nLog\u2013log technique 4523 psi\nSquare-root of time technique 4700 psi\nCompliance method 5625 psi\nCWT fracture closure detection techniqueStart of fracture closure = 5300 psi, complete\nfracture closure = 4700 psi"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890c24-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 25, "chroma:document": "Energies 2023 ,16, 764 26 of 29\n4. Conclusions\nCWT can be used as a general mathematical microscope to analyze the output of\nthe physical systems (i.e., the diagnostic fracture injection test) to understand the process\nof fracture closure. That can be used for multiple purposes in oil\ufb01eld operations and\ngeothermal reservoir operations. Time\u2013frequency analysis for a pressure decay signal using\nCWT reliably detects the closure pressure. The following conclusions can be concluded\nfrom previous discussions:\n1. The average of the log signal energy versus time calculated using CWT characterizes\nthe closure event as a local increase in the signal log energy followed by a drop in the\nsignal log energy to a minimum stabilized level.\n2. The proposed technique has shown good agreement with synthetic fracture simula-\ntor data.\n3. The application of the CWT technique matched the classical closure detection tech-\nniques in real \ufb01eld cases with no pre-assumptions and less available data."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890c7e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 25, "chroma:document": "niques in real \ufb01eld cases with no pre-assumptions and less available data.\n4. The pressure decay signal re\ufb02ects the physical process of fracture closure and the\naverage signal energy using CWT is just a mathematical independent magni\ufb01cation\nfor the pressure decay.\n5. The start of the fracture closure can be identi\ufb01ed with the CWT closure detection\ntechnique at the local peak of average signal energy. Fracture closure ends when the\naverage signal energy reaches the minimum stabilized level. Those characteristics\nmatched numerical simulation, \ufb02ow regime modeling, and real \ufb01eld cases. The\ntechnique is consistent, reliable, and can ef\ufb01ciently detect fracture closure.\n6. The CWT closure detection technique can be used to analyze the real \ufb01eld data and\ncan detect a reliable closure pressure compared to current methods.\n7. The CWT closure detection technique can detect fracture closure regardless of the noise"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890cce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 25, "chroma:document": "7. The CWT closure detection technique can detect fracture closure regardless of the noise\nthat may accompany the real \ufb01eld pressure signal, it showed accurate fracture closure\nin synthetic data when there was no noise included in the pressure decay signal.\n8. The new technique has no built-in assumptions and works on the pressure decay\nsignal during the shut-in period.\n9. Using CWT to detect the closure can be generalized to detect the features from oil\ufb01eld\nsignals such as rate, torque, and drilling vibrations. Another perspective of the CWT\nclosure detection technique is using the CWT wavelet transform to investigate the\nnatural fracture in the subsurface formations.\n5. Patents\nThis study was \ufb01led under U.S. Patent Application No. 63/412,269 on 30 Septem-\nber 2022, and entitled \u201cSYSTEMS AND METHODS FOR MONITORING SUBSURFACE\nEVENTS USING CONTINUOUS WAVELET TRANSFORMS.\u201d\nAuthor Contributions: Conceptualization, M.A.G. and I.E.; methodology, M.A.G.; software, I.E.;"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890d28-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 25, "chroma:document": "EVENTS USING CONTINUOUS WAVELET TRANSFORMS.\u201d\nAuthor Contributions: Conceptualization, M.A.G. and I.E.; methodology, M.A.G.; software, I.E.;\nvalidation, I.E.; supervision, M.Y.S. and S.M.F.-A.; writing\u2014original draft, M.A.G. and I.E.; writing\u2014\nreview and editing, M.Y.S. and S.M.F.-A. All authors have read and agreed to the published version\nof the manuscript.\nFunding: This research received funding from HESS Corporation, Shell PLC, and Halliburton Energy\nService, members of the hydraulic fracturing consortium at the University of Houston.\nInstitutional Review Board Statement: Not applicable.\nInformed Consent Statement: Not applicable.\nData Availability Statement: The data presented in this study are available on request from the\ncorresponding author.\nAcknowledgments: We thank HESS Corporation, Shell PLC, and Halliburton Energy Service, mem-\nbers of the hydraulic fracturing consortium at the University of Houston, for sponsoring this work."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890d78-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 25, "chroma:document": "bers of the hydraulic fracturing consortium at the University of Houston, for sponsoring this work.\nCon\ufb02icts of Interest: The authors declare no con\ufb02ict of interest."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890dc8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 26, "chroma:document": "Energies 2023 ,16, 764 27 of 29\nAbbreviations\nThe following abbreviations are used in this manuscript:\n\u2206t Shut in time\na Dilation parameter or scale\nb Transportation parameter\nCWT Continuous wavelet transform\nDFIT Diagnostic fracture injection test\nDWT Discrete wavelet transform\nFT Fourier transform\nG G-time function\nP Pressure\nt Time\nT Wavelet transform modulus\nWFT Windowed Fourier transform\nWT Wavelet transform\nReferences\n1. Eaton, B.A. Fracture gradient prediction and its application in oil\ufb01eld operations. J. Pet. Technol. 1969 ,21, 1353\u20131360. [CrossRef]\n2. Blanton, T.; Olson, J.E. Stress magnitudes from logs: Effects of tectonic strains and temperature. SPE Reserv. Eval. Eng. 1999 ,\n2, 62\u201368. [CrossRef]\n3. Zain-Ul-Abedin, M.; Henk, A. Building 1D and 3D Mechanical Earth Models for Underground Gas Storage\u2014A Case Study from\nthe Molasse Basin, Southern Germany. Energies 2020 ,13, 5722. [CrossRef]"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890e22-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 26, "chroma:document": "the Molasse Basin, Southern Germany. Energies 2020 ,13, 5722. [CrossRef]\n4. Xing, P .; McLennan, J.; Moore, J. In-Situ Stress Measurements at the Utah Frontier Observatory for Research in Geothermal\nEnergy (FORGE) Site. Energies 2020 ,13, 5842. [CrossRef]\n5. Germ\u00e1n-Sall\u00f3, Z.; Strnad, G. Signal processing methods in fault detection in manufacturing systems. Procedia Manuf. 2018 ,\n22, 613\u2013620. [CrossRef]\n6. Soliman, M.; Ansah, J.; Stephenson, S.; Mandal, B. Application of wavelet transform to the analysis of pressure-transient data.\nSPE Reserv. Eval. Eng. 2003 ,6, 89\u201399. [CrossRef]\n7. Unal, E.; Siddiqui, F.; Soliman, M.; Dindoruk, B. Wavelet analysis of DFIT data to identify fracture closure parameters. In\nProceedings of the SPE Hydraulic Fracturing Technology Conference and Exhibition, The Woodlands, TX, USA, 5\u20137 February 2019.\n8. Awad, M.M.; Eltaleb, I.; Mansi, M.; Rezaei, A.; Soliman, M.; Farouq-Ali, S.; Dindoruk, B. Interpretation of Hydraulic Fracturing"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890e90-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 26, "chroma:document": "8. Awad, M.M.; Eltaleb, I.; Mansi, M.; Rezaei, A.; Soliman, M.; Farouq-Ali, S.; Dindoruk, B. Interpretation of Hydraulic Fracturing\nEvents by Analyzing the Energy of Rate and Pressure Signals. In Proceedings of the SPE Annual Technical Conference and\nExhibition, Virtual, 27\u201329 October 2020.\n9. Eltaleb, I.; Rezaei, A.; Siddiqui, F.; Awad, M.; Mansi, M.; Dindoruk, B.; Soliman, M. Analysis of fracture injection tests using\nsignal processing approach. In Proceedings of the SPE/AAPG/SEG Unconventional Resources Technology Conference, Virtual,\n20\u201322 July 2020.\n10. Eltaleb, I.; Rezaei, A.; Soliman, M.; Dindoruk, B. A signal processing approach for analysis of fracture injection test in geothermal\nreservoirs: A case study on the utah FORGE formation. In Proceedings of the SPE Hydraulic Fracturing Technology Conference\nand Exhibition, Virtual, 4\u20136 May 2021.\n11. Barree, R. A practical numerical simulator for three-dimensional fracture propagation in heterogeneous media. In Proceedings of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890eea-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 26, "chroma:document": "11. Barree, R. A practical numerical simulator for three-dimensional fracture propagation in heterogeneous media. In Proceedings of\nthe SPE Reservoir Simulation Symposium, San Francisco, CA, USA, 15\u201318 November 1983.\n12. Mohammad, N.A.; Miskimins, J.L. A Comparison of Hydraulic-Fracture Modeling With Downhole and Surface Microseismic\nData in a Stacked Fluvial Pay System. SPE Prod. Oper. 2012 ,27, 253\u2013264. [CrossRef]\n13. Clark, J. A hydraulic process for increasing the productivity of wells. J. Pet. Technol. 1949 ,1, 1\u20138. [CrossRef]\n14. Hubbert, M.K.; Willis, D.G. Mechanics of hydraulic fracturing. Trans. AIME 1957 ,210, 153\u2013168. [CrossRef]\n15. Godbey, J.; Hodges, H. Pressure measurements during formation fracturing operations. Trans. AIME 1958 ,213, 65\u201369. [CrossRef]\n16. Kehle, R.O. The determination of tectonic stresses through analysis of hydraulic well fracturing. J. Geophys. Res. 1964 ,69, 259\u2013273.\n[CrossRef]"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890f3a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 26, "chroma:document": "16. Kehle, R.O. The determination of tectonic stresses through analysis of hydraulic well fracturing. J. Geophys. Res. 1964 ,69, 259\u2013273.\n[CrossRef]\n17. Haimson, B.; Fairhurst, C. Initiation and extension of hydraulic fractures in rocks. Soc. Pet. Eng. J. 1967 ,7, 310\u2013318. [CrossRef]\n18. Hickman, S.H.; Zoback, M.D. The interpretation of hydraulic fracturing pressure-time data for in situ stress determinations.\nInWorkshop on Hydraulic Fracturing Rock Stress Measurements ; National Academy Press: Washington, DC, USA; 1981; pp. 103\u2013127.\n19. Nolte, K.G. Determination of fracture parameters from fracturing pressure decline. In Proceedings of the SPE Annual Technical\nConference and Exhibition, Las Vegas, NV , USA, 23\u201326 September 1979.\n20. Roegiers, J.-C.; McLennan, J.D.; Schultz, L.D. In-Situ Stress Determinations In Northeastern Ohio. In Proceedings of the 23rd U.S.\nSymposium on Rock Mechanics (USRMS), Berkeley, CA, USA, 25\u201327 August 1982."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890f8a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 26, "chroma:document": "Symposium on Rock Mechanics (USRMS), Berkeley, CA, USA, 25\u201327 August 1982.\n21. Mayerhofer, M.; Economides, M. Permeability estimation from fracture calibration treatments. In Proceedings of the SPE Western\nRegional Meeting, Anchorage, Alaska, 26\u201328 May 1993."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b890fda-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "Energies 2023 ,16, 764 28 of 29\n22. Castillo, J. Modi\ufb01ed fracture pressure decline analysis including pressure-dependent leakoff. In Proceedings of the SPE/DOE\nJoint Symposium on Low Permeability Reservoirs, Denver, CO, USA, 18\u201319 May 1987.\n23. Barree, R.; Mukherjee, H. Determination of pressure dependent leakoff and its effect on fracture geometry. In Proceedings of the\nSPE Annual Technical Conference and Exhibition, Denver, CO, USA, 6\u20139 October 1996.\n24. Mayerhofer, M.; Ehlig-Economides, C.; Economides, M. Pressure transient analysis of fracture calibration tests. J. Pet. Technol.\n1995 ,47, 229\u2013234. [CrossRef]\n25. Craig, D.P .; Brown, T.D. Estimating pore pressure and permeability in massively stacked lenticular reservoirs using diagnostic\nfracture-injection tests. In Proceedings of the SPE Annual Technical Conference and Exhibition, Houston, TX, USA, 3\u20136\nOctober 1999."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "fracture-injection tests. In Proceedings of the SPE Annual Technical Conference and Exhibition, Houston, TX, USA, 3\u20136\nOctober 1999.\n26. Barree, R.D.; Barree, V .L.; Craig, D. Holistic fracture diagnostics: Consistent interpretation of prefrac injection tests using multiple\nanalysis methods. SPE Prod. Oper. 2009 ,24, 396\u2013406. [CrossRef]\n27. Gu, H.; Elbel, J.; Nolte, K.; Cheng, A.D.; Abousleiman, Y. Formation permeability determination using impulse-fracture injection.\nIn Proceedings of the SPE Production Operations Symposium, Oklahoma City, OK, USA, 21\u201323 May 1993.\n28. Soliman, M.; Ansah, J. Methods and Systems for Using Wavelet Analysis in Subterranean Applications. U.S. Patent 6,978,211, 20\nDecember 2005.\n29. Craig, D.P .; Blasingame, T.A. Application of a new fracture-injection/falloff model accounting for propagating, dilated, and\nclosing hydraulic fractures. In Proceedings of the SPE Gas Technology Symposium, The Woodlands, TX, USA, 1\u20133 April 2006."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "closing hydraulic fractures. In Proceedings of the SPE Gas Technology Symposium, The Woodlands, TX, USA, 1\u20133 April 2006.\n30. Nolte, K.; Maniere, J.; Owens, K. After-closure analysis of fracture calibration tests. In Proceedings of the SPE Annual Technical\nConference and Exhibition, San Antonio, TX, USA, 5\u20138 October 1997.\n31. Marongiu-Porcu, M.; Ehlig-Economides, C.A.; Economides, M.J. Global model for fracture falloff analysis. In Proceedings of the\nNorth American Unconventional Gas Conference and Exhibition, The Woodlands, TX, USA, 14\u201316 June 2011.\n32. Marongiu-Porcu, M.; Retnanto, A.; Economides, M.J.; Ehlig-Economides, C. Comprehensive fracture calibration test design. In\nProceedings of the SPE Hydraulic Fracturing Technology Conference, The Woodlands, TX, USA, 4\u20136 February 2014.\n33. Soliman, M.; Kabir, C. Testing unconventional formations. J. Pet. Sci. Eng. 2012 ,92, 102\u2013109. [CrossRef]"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8910e8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "33. Soliman, M.; Kabir, C. Testing unconventional formations. J. Pet. Sci. Eng. 2012 ,92, 102\u2013109. [CrossRef]\n34. Cramer, D.; Nguyen, D. Diagnostic fracture injection testing tactics in unconventional reservoirs. In Proceedings of the SPE\nHydraulic Fracturing Technology Conference, The Woodlands, TX, USA, 4\u20136 February 2013.\n35. Padmakar, A. Geomechanics coupled reservoir \ufb02ow simulation for diagnostic fracture injection test design and interpretation in\nshale reservoirs. In Proceedings of the SPE Annual Technical Conference and Exhibition, New Orleans, LA, USA, 30 September\u20132\nOctober 2013.\n36. Wallace, J.; Kabir, C.; Cipolla, C. Multiphysics investigation of diagnostic fracture injection tests in unconventional reservoirs. In\nProceedings of the SPE Hydraulic Fracturing Technology Conference, The Woodlands, TX, USA, 4\u20136 February 2014.\n37. Meng, C.; Wei, L.; Yuan, R.S.C. Coupled \ufb02uid \ufb02ow and geomechanics modeling for DFIT analysis in unconventional gas develop-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891142-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "37. Meng, C.; Wei, L.; Yuan, R.S.C. Coupled \ufb02uid \ufb02ow and geomechanics modeling for DFIT analysis in unconventional gas develop-\nment. In Proceedings of the International Petroleum Technology Conference, Kuala Lumpur, Malaysia, 10\u201312 December 2014.\n38. Craig, D.P . New type curve analysis removes limitations of conventional after-closure analysis of DFIT data. In Proceedings of\nthe SPE Unconventional Resources Conference, The Woodlands, TX, USA, 1\u20133 April 2014.\n39. Sullivan, M.; Zanganeh, B.; Springer, A.; Clarkson, C. Post-fracture pressure decay: A novel (and free) stage-level assessment\nmethod. In Proceedings of the SPE/AAPG/SEG Unconventional Resources Technology Conference, Denver, CO, USA, 22\u201324\nJuly 2019.\n40. Hawkes, R.; Bachman, R.; Nicholson, K.; Cramer, D.; Chipper\ufb01eld, S. Good Tests Cost Money, Bad Tests Cost More-A Critical\nReview of DFIT and Analysis Gone Wrong. In Proceedings of the SPE International Hydraulic Fracturing Technology Conference"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891192-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "Review of DFIT and Analysis Gone Wrong. In Proceedings of the SPE International Hydraulic Fracturing Technology Conference\nand Exhibition, Muscat, Oman, 16\u201318 October 2018.\n41. McClure, M.W. Diagnostic fracture-injection tests with complex fracture networks. Lead. Edge 2014 ,33, 546\u2013552. [CrossRef]\n42. McClure, M.W.; Jung, H.; Cramer, D.D.; Sharma, M.M. The fracture-compliance method for picking closure pressure from\ndiagnostic fracture-injection tests. SPE J. 2016 ,21, 1321\u20131339. [CrossRef]\n43. Jung, H.; Sharma, M.M.; Cramer, D.D.; Oakes, S.; McClure, M.W. Re-examining interpretations of non-ideal behavior during\ndiagnostic fracture injection tests. J. Pet. Sci. Eng. 2016 ,145, 114\u2013136. [CrossRef]\n44. Wang, H.; Sharma, M.M. New Variable Compliance Method for Estimating In-Situ Stress and Leak-Off from DFIT Data. In\nProceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 9\u201311 October 2017"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8911e2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "Proceedings of the SPE Annual Technical Conference and Exhibition, San Antonio, TX, USA, 9\u201311 October 2017\n45. Barree, R.D.; Barree, V .L.; Craig, D. Holistic fracture diagnostics. In Proceedings of the Rocky Mountain Oil & Gas Technology\nSymposium, Denver, CO, USA, 16\u201318 April 2007.\n46. McClure, M.; Bammidi, V .; Cipolla, C.; Cramer, D.; Martin, L.; Savitski, A.A.; Sobernheim, D.; Voller, K. A collaborative study on\nDFIT interpretation: Integrating modeling, \ufb01eld data, and analytical techniques. In Proceedings of the Unconventional Resources\nTechnology Conference, Denver, CO, USA, 22\u201324 July 2019; pp. 2020\u20132058.\n47. Sneddon, I.N. The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc. R. Soc. Lond. Ser. A Math. Phys.\nSci.1946 ,187, 229\u2013260.\n48. Mcclure, M.; Fowler, G.; Picone, M. Best practices in DFIT interpretation: Comparative analysis of 62 DFITs from nine different"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891232-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "48. Mcclure, M.; Fowler, G.; Picone, M. Best practices in DFIT interpretation: Comparative analysis of 62 DFITs from nine different\nshale plays. In Proceedings of the SPE International Hydraulic Fracturing Technology Conference & Exhibition, Muscat, Oman,\n11\u201313 January 2022.\n49. Rioul, O.; Vetterli, M. Wavelets and signal processing. IEEE Signal Process. Mag. 1991 ,8, 14\u201338. [CrossRef]"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 28, "chroma:document": "Energies 2023 ,16, 764 29 of 29\n50. Kaiser, G.; Hudgins, L.H. A Friendly Guide to Wavelets ; Springer: Berlin/Heidelberg, Germany, 1994; Volume 300.\n51. Addison, P .S. The Illustrated Wavelet Transform Handbook: Introductory Theory and Applications in Science, Engineering, Medicine and\nFinance ; CRC Press: Boca Raton, FL, USA, 2017.\n52. Guerrero, A.P .; Paredes, G.E. Linear and Non-Linear Stability Analysis in Boiling Water Reactors: The Design of Real-Time Stability\nMonitors ; Woodhead Publishing: Sawston, UK, 2018.\n53. Torrence, C.; Compo, G.P . A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 1998 ,79, 61\u201378. [CrossRef]\nDisclaimer/Publisher\u2019s Note: The statements, opinions and data contained in all publications are solely those of the individual\nauthor(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-00764.pdf", "page": 28, "chroma:document": "author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to\npeople or property resulting from any ideas, methods, instructions or products referred to in the content."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 0, "chroma:document": "Citation: Gabry, M.A.; Eltaleb, I.;\nSoliman, M.Y.; Farouq-Ali, S.M.\nValidation of Estimating Stress from\nFracture Injection Tests Using\nContinuous Wavelet Transform with\nExperimental Data. Energies 2023 ,16,\n2807. https://doi.org/10.3390/\nen16062807\nAcademic Editor: Rafael J. Bergillos\nReceived: 10 February 2023\nRevised: 6 March 2023\nAccepted: 8 March 2023\nPublished: 17 March 2023\nCopyright: \u00a9 2023 by the authors.\nLicensee MDPI, Basel, Switzerland.\nThis article is an open access article\ndistributed under the terms and\nconditions of the Creative Commons\nAttribution (CC BY) license (https://\ncreativecommons.org/licenses/by/\n4.0/).\nenergies\nArticle\nV alidation of Estimating Stress from Fracture Injection T ests\nUsing Continuous Wavelet T ransform with Experimental Data\u2020\nMohamed Adel Gabry *\n , Ibrahim Eltaleb\n , Mohamed Y. Soliman\n , S. M. Farouq-Ali\nDepartment of Petroleum Engineering, The University of Houston, Houston, TX 77023, USA\n*Correspondence: magabry@cougarnet.uh.edu"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 0, "chroma:document": ", S. M. Farouq-Ali\nDepartment of Petroleum Engineering, The University of Houston, Houston, TX 77023, USA\n*Correspondence: magabry@cougarnet.uh.edu\n\u2020 In Proceedings of the Society of Petroleum Engineers Hydraulic Fracture Technology Conference,\nThe Woodlands, TX, USA, 31 January\u20132 February 2023.\nAbstract: The article discusses the new technique for fracture closure pressure detection using\ncontinuous wavelet transform (CWT). The study focuses on calibrating the CWT technique and\ncomparing it with different techniques for closure detection. According to the article, traditional\nmethods for identifying the closure of hydraulic fracturing operations are based on assumptions\nthat can con\ufb02ict with one another, resulting in greatly varying approximations of closure pressure\nand duration. To address this issue, the article employs a set of diagnostic fracture injection tests\nthat utilize the Step-Rate Injection Method for Fracture In-Situ Properties tool (SIMFIP). By directly"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89143a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 0, "chroma:document": "that utilize the Step-Rate Injection Method for Fracture In-Situ Properties tool (SIMFIP). By directly\nobserving wellbore deformation, the SIMFIP tool determines the minimum principal stress, while\nstrain gauges monitor the opening and closing of fractures during multiple tests. The publicly\naccessible data are used to evaluate the accuracy of the new closure detection technique using CWT.\nThe \ufb01ndings indicate that the CWT method aligns with measurements of deformation and can identify\nthe impact of intricate closure events and pre-existing natural fractures. In conclusion, the article\nsuggests that the CWT technique shows great potential as an alternative to traditional approaches for\ndetecting closure pressure.\nKeywords: strain measurements; fracture closure; geothermal reservoirs; hydraulic fracture; DFIT\n1. Introduction\nUsing the continuous wavelet transform (CWT) as a fracture closure detection tech-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891480-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 0, "chroma:document": "1. Introduction\nUsing the continuous wavelet transform (CWT) as a fracture closure detection tech-\nnique and its validation using fracture simulation and \ufb02ow regime modeling with the\ndiscussion of its applications on real \ufb01eld cases was introduced by Gabry et al. (2023) [ 1].\nIn this paper, the CWT fracture closure detection technique was validated using \ufb01eld\nexperimental data. The fracture closure was identi\ufb01ed by measuring the rock deformation\nusing strain gauges while observing the pressure decline during the shut-in period. The\npressure decline data during the shut-in period were analyzed using the various existing\ntechniques such as the log\u2013log technique, square root of time technique, and tangent method\nthat were discussed in detail by Baree et al. (2009) [ 2]. The log\u2013log technique and square\nroot of time method can be combined with G function technique as the \u201cHolistic Fracture\nDiagnostics\u201d as described by Baree et al. (2007) [ 3]. The data are analyzed also using the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8914d0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 0, "chroma:document": "Diagnostics\u201d as described by Baree et al. (2007) [ 3]. The data are analyzed also using the\ncompliance method (McClure et al. (2016) [ 4]). The analyses were carried out while strain\ngauge data provided an actual change in fracture width and finally closure. This would\nprovide a deep understanding of the accuracy and validity of the various fracture closure de-\ntection techniques. Dutler et al. (2020) [ 5] used strain measurements to compare the various\nfracture closure detection techniques and showed that the tangent method gave the lowest\nminimum principal stress among the various conventional techniques. However, there\nare some issues with Dutler et al. [ 5] work. The main issue is that the injection protocol\ndoes not follow the main assumptions for G-function which assume a constant injection\nrate for a fairly long period. The test\u2019s injection period was analyzed and performed under\nEnergies 2023 ,16, 2807. https://doi.org/10.3390/en16062807 https://www.mdpi.com/journal/energies"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89153e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 1, "chroma:document": "Energies 2023 ,16, 2807 2 of 21\nconstant pressure instead. The methodology of the closure pressure detection from the\nmeasured strain data by Dutler et al. (2020) [ 5] did not follow the x-intercept rule intro-\nduced by Gulrajani and Nolte (2001) [ 6]. The EGS Collab project presented an occasion to\nvalidate reservoir modeling, while concurrently analyzing geophysical and other fracture\ncharacterization data, with the overarching objective of comprehending the fundamental\ncorrelation among stress, seismicity, and permeability enhancement. Strain gauges were\nutilized in experiments to determine rock deformation and measure wellbore displacement\nduring fracture propagation and closure. Observing the three-dimensional displacements\nof a hydraulic fracture during water injections at various depths in the crystalline rock of\nthe Sanford Underground Research Facility (USA) was undertaken in order to characterize"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89158e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 1, "chroma:document": "the Sanford Underground Research Facility (USA) was undertaken in order to characterize\nthe stimulation mode of a fracture. EGS Collab has undertaken a sequence of experiments\ninvolving the injection of fractures to determine the lowest principal stress through direct\nobservation of rock deformations, using the SIMFIP tool (Step-Rate Injection Method for\nFracture In-Situ Properties) as described by Guglielmi et al. (2020) [ 7], and (2022) [ 8]. The\ntool monitors the formation deformation as a fracture opens and closes during multiple\ntests. Guglielmi et al. (2022) [ 8] compared the measurements for four extended shut-in tests\nperformed in two different wellbores at the Sanford Underground Research Facility as part\nof the EGS Collab project against several fracture closure detection techniques. The tool is\nused by Eltaleb (2023) [9] to validate the new Pump-In Flowback Model.\n2. Material and Methods\n2.1. Cwt Fracture Closure Detection Technique"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8915de-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 1, "chroma:document": "used by Eltaleb (2023) [9] to validate the new Pump-In Flowback Model.\n2. Material and Methods\n2.1. Cwt Fracture Closure Detection Technique\nAs discussed by Gabry et al. (2023) [ 1], the new fracture closure detection technique is\na way to \ufb01nd fracture closure pressure using wavelet transform. The pressure signal during\nthe shut-in period after DFIT is analyzed using CWT with a complex Morlet wavelet.\nThe CWT analysis is applied to obtain signal average log energy at different scales. As\na dominant feature fracture closure can be identi\ufb01ed from the average of all signal energies\nat several wavelet scales. Figure 1 shows the work\ufb02ow to detect fracture closure using the\nCWT technique. Fracture closure is identi\ufb01ed by the two following features; the fracture\nclosure starts with a peak in signal average energy that drops into a stabilized level. Still,\nthere is a \ufb02uctuation in signal average log energy due to the noise of real \ufb01eld data. Fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89162e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 1, "chroma:document": "there is a \ufb02uctuation in signal average log energy due to the noise of real \ufb01eld data. Fracture\nfaces are not smooth and the fracture closure does not happen instantaneously, it takes\nup to several minutes to occur. The characteristics of fracture closure in the CWT fracture\nclosure detection technique can be seen in Figure 2.\nFigure 1. CWT fracture closure detection technique work\ufb02ow (Gabry et. al. (2023) [1])."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891692-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 2, "chroma:document": "Energies 2023 ,16, 2807 3 of 21\nFigure 2. Closure pressure using CWT fracture closure detection technique(Gabry et al. (2023) [1]).\n2.2. Validation Using Experimental Data from EGS Collab Project\nThe data published by the EGS Collab team were used to validate the newly introduced\nCWT fracture closure detection technique against the SIMFIP tool. The SIMFIP tool is based\non a double-packer hydro fracturing probe customized with a 6-component displacement\nFiber Bragg grating sensor. The sensor is integrated with the injection interval sealed between\nthe two packers, as seen in Figure 3a full description of the procedure used in the testing was\ndescribed by Guglielmi (2013) [ 10]. The injection interval is 2.41 m long. The displacement\nsensor is set in the center of the interval. It is a 0.24 m long and 0.1 m diameter pre-calibrated\naluminum cage connected to two-0.58 m long elements that allow clamping of both ends"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891764-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 2, "chroma:document": "aluminum cage connected to two-0.58 m long elements that allow clamping of both ends\nof the cage on the borehole wall (clamps correspond to points A and B in Figure 3). When\nthe tool is clamped, the cage is disconnected from the straddle packer system allowing it\nto measure the relative borehole wall deformation/displacement between the two anchors\nwhich are 1.4 m apart. When a fracture is propagating or closing, the SIMFIP sensor measures\nthe three-dimensional displacement of the wellbore. The sensitivity of the SIMFIP tool is at\nthe micron level. Guglielmi et al. (2022) [8] give further details of the tool.\nThe tests conducted by EGS Collab are short rate-controlled pumping periods followed\nby a long shut-in period. The shut-in period was planned to be at least a few hours. The\nSIMFIP measurements were recorded and synchronized during the testing cycle, the\ninjection is designed not to cause a fracture intersection and not to be drained into a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8917e6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 2, "chroma:document": "injection is designed not to cause a fracture intersection and not to be drained into a\nneighboring borehole. Guglielmi et al. (2022) [ 8] published an analysis of four injection\nsequences that were conducted using this tool. The measurements were taken in 2018\nand 2019 during hydrofracturing experiments in boreholes drilled from drifts at the mine\n4890 ft and 4101 ft below ground surface (BGS), respectively."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891854-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 3, "chroma:document": "Energies 2023 ,16, 2807 4 of 21\nFigure 3. SIMFIP probe. ( a) Design of the probe; ( b) Schematic concept of the borehole three-\ndimensional relative displacement between anchors A and B; ( c) Example of a SIMFIP displacement\nsignal captured across the activated hydrofracture during E1-I 164 Test 2. The red segment is the\ndisplacement during injection and growth of the fracture. The orange segment is the displacement\nduring shut-in. (Guglielmi et al. (2022) [8]).\n2.3. Theoretical Basis of Using SIMFIP Tool\nGulrajani and Nolte (2001) [ 6] explained how to estimate the magnitude of the closure\npressure from deformation measurements; when the fracture is open but not propagating,\nthere is an approximately linear relationship between deformation and pressure. The\nrock displacement is plotted versus pressure as per Figure 4. It is based on Equation (1)\n(Sneddon (1946) [11]; Gulrajani and Nolte (2001) [6]).\nW=P\u2212Shmin\nSf(1)"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 3, "chroma:document": "(Sneddon (1946) [11]; Gulrajani and Nolte (2001) [6]).\nW=P\u2212Shmin\nSf(1)\nwhere Sfis the fracture stiffness, Wis the average fracture width, and Shmin is the minimum\nprincipal stress. The extrapolation line of the \u2018open fracture\u2019 curve back to zero rock\ndisplacement response indicates the minimum principal stress as shown in Figure 4. When\nan inclined fracture that is aligned with the minimum horizontal stress ( Shmin) is reopened,\nthe normal stress acting on the fracture will exceed Shmin, potentially leading to irreversible\nshear. This scenario becomes more likely if the fracture walls contain asperities that come\ninto contact during the closure, causing a non-linear increase in stiffness, as outlined by\nBarton et al. (1985) [12])."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89193a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 4, "chroma:document": "Energies 2023 ,16, 2807 5 of 21\nFigure 4. Schematic of hydraulic fracture reopening/closure. (Gulrajani and Nolte (2001) [6]).\nThe asperities contact at a critical fracture width is Wc. If the fracture were perfectly\nsmooth, then Wcwould equal zero, and the straight line in Figure 4 would extrapolate to\nzero on the y-axis in Figure 4. In other words, the existence of nonzero width at fracture\nclosure Wcindicates the existence of the rough fracture face. A typical SIMFIP test consists\nof several injection cycles. During the \ufb01rst cycle, pressure increases gradually up to a\nmaximum value considered below the fracturing opening pressure. Then pressure is\nstepped down to the initial value. This cycle is used for quality control and to characterize\nthe hydro-mechanical response of the injection chamber that integrates the formation\nmechanical response, the effect of the mechanical coupling of both SIMFIP clamps, packers,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8919b2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 4, "chroma:document": "mechanical response, the effect of the mechanical coupling of both SIMFIP clamps, packers,\nand the probe stiffness. The main test cycles are then conducted. These tests are the\nclassical DFITs. The SIMFIP displacements data are affected by the injection pressure to\nthe orientation and activation mode of the created fracture. Therefore, several stimulation\ncycles may be necessary to get a clear understanding of displacement orientation and of\nthe local borehole tortuosity effects. The borehole displacements are also affected by the\nzone pressure. The displacements should be reversible when pressure is stepped back\nto the initial to be used to detect fracture closure. The fracture closure should be at zero\nfracture width.\n2.4. Experiments\u2019 Location\nThe injection tests were conducted at two boreholes, the E1-I and TV4100. The E1-I\nborehole on the 1490 m (4891 ft) level was 69 m (226 ft) long and slightly dipping from"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891a2a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 4, "chroma:document": "borehole on the 1490 m (4891 ft) level was 69 m (226 ft) long and slightly dipping from\nhorizontal as shown in Figure 5. The E1-I test was the stimulation of a zone at a measured\ndepth of 164 ft., which is called the E1-I 164 Tests. TV4100 was approximately 1249 m\n(4100 ft) long and vertical. The TV4100 tests were performed at measured depths between\n10 m (32.8 ft) and 44.98 m (147.6 ft), and these are referred to by test numbers TV4100 Test\n4 and TV4100 Test 7. The host rock for the tests was a metamorphic rock of the Sanford"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891aa2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 5, "chroma:document": "Energies 2023 ,16, 2807 6 of 21\nUnderground Research Facility (SURF) in South Dakota, USA (Kneafsey et al. (2019) [ 13],\n(2020) [14]; Guglielmi et al. (2021) [7]; Guglielmi et al. (2022) [8]).\n2.4.1. E1-I 164 Interval\nIn the E1-I 164 borehole which is located 4891 ft below the ground surface, the vertical\nstress magnitude is estimated to be around 41.8 MPa (6062 psi) based on the density\nof overlying rocks. The maximum horizontal stress, SHmax , is estimated to be 34 MPa\n(4931 psi), while the minimum horizontal stress, Shmin, is 21.7 MPa (3147 psi) based on\nKneafsey et al. (2020) [ 14], Singh et al. (2019) [ 15], and Wang et al. (2017) [ 16]. The borehole\nis drilled subparallel to the estimated Shmin. The type of host rock is a metamorphic rock\n(Poorman Formation). The 3D view of the injection borehole E1-I and monitoring wellbore\nE1-OT for E1-I 164 tests are shown in Figure 5.\nFigure 5. (a) Numerical model setting with the calculated fracture at the end of the injection for E1-I"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891b1a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 5, "chroma:document": "Figure 5. (a) Numerical model setting with the calculated fracture at the end of the injection for E1-I\n164 Test ( b) 3D view of the injection borehole E1-I and monitoring wellbore E1-OT (Guglielmi et al.\n(2020) [7]).\nThe E1-I 164 tests consisted of three propagation and shut-in steps, each step extending\nthe fracture length until it intersected an observation borehole located 10 m (32.8 ft) away\nfrom the injection well. Using basic modeling, a mixed mode of fracture growth best\nmatched the measurements in accordance with the normal stress regime (Guglielmi et al.\n(2021) [ 17]; Schoenball et al. (2020) [ 18]; Fu et al. (2021) [ 19]). Table 1 shows the injection\nprotocol conducted by EGS Collab team during E1-I 164 tests as reported by Guglielmi et al.\n(2022) [8]. The values of E1-I 164 Test 3 are calculated from the publicly published data.\nTable 1. Injection duration, total injection volume, average injection rate, and shut-in duration for"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891b88-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 5, "chroma:document": "Table 1. Injection duration, total injection volume, average injection rate, and shut-in duration for\nE1-I 164 tests (Guglielmi et al. (2022) [8]).\nNameInjection Duration\n(min:sec)Injection\nVolume, LAvg. Injection\nRate, L/minShut-In\nDuration, h\nE1-I 164 Test 1 10:00 2.1 0.21 2\nE1-I 164 Test 2 63:00 23 0.37 15\nE1-I 164 Test 3 20:00 75 5 15\nDue to the early loss of SIMFIP tool recording and the lack of available test calibration\ninformation, it is not feasible to estimate stress using the SIMFIP measurements from the\nE1-I 164 test 1 shut-in period. Additionally, the measurements failed to reach an asymptotic\nminimum width."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891c0a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 6, "chroma:document": "Energies 2023 ,16, 2807 7 of 21\nDuring E1-I 164 Test 2, the zone pressure was initially maintained at 13.8 MPa (2001 psi)\nfor approximately 5 min, after which it was raised to 20.7 MPa (3002 psi) for around 1 min.\nSubsequently, the protocol was changed from pressure-controlled to \ufb02ow rate-controlled,\nand the \ufb02ow rate was progressively increased in increments until it reached a maximum of\n0.4 L/min, where it was maintained for 57 min (Guglielmi et al., 2022) [ 8]). The pressure\nincreased to 26.8 MPa (3887 psi) and then decreased to a relatively constant value of\n26.7 MPa (3872 psi) just before the pump was stopped, and the zone was left shut in for 15 h\nas seen in Figure 6. The SIMFIP tool readings may be seen in Figure 7. The application of\nthe x-axis intercept con\ufb01rms the closure stress to be 21.4 MPa (3103 psi) as seen in Figure 7.\nThe displacement lines representing fracture reopening (injection) and fracture closure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891c6e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 6, "chroma:document": "The displacement lines representing fracture reopening (injection) and fracture closure\n(shut-in) in Figure 7 are almost identical. In E1-I 164 Test 3 is somewhat more complex\nbecause the injection started with one pump at 0.1 L/min for 83 min before the pump was\nchanged to a larger one. The SIMFIP tool showed the closure to a negative displacement\nvalue (\u221250 microns) as given in Figure 7. The test procedure may be the reason behind this\nobviously wrong value.\nFigure 6. E1\u2212I 164 Test 2 injection protocol with SIMFIP displacement normal and tangential to the\nactivated fracture during E1-I 164 Test 2. (Guglielmi et al. (2022) [8]).\nFigure 7. Rock displacement normal to the activated fracture versus zone pressure measured using\nSIMFIP tool for the E1-I 164 tests (Guglielmi et al. (2022) [8]).\n2.4.2. Tv4100 Interval\nEight SIMFIP tests in TV4100 intervals were conducted using the same SIMFIP tool\nprobe to monitor fracture displacement response at different depths along the 164 ft (50 m)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891cbe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 7, "chroma:document": "Energies 2023 ,16, 2807 8 of 21\ndeep borehole to build a stress pro\ufb01le and to characterize the stress variability along with\nthis pro\ufb01le. The complete data sets (injection protocol with SIMFIP tool readings) for tests 4\nand 7 and SIMFIP tool measurements were publicly published and discussed by Guglielmi\net al. (2022) [ 8]. Table 2 shows the Injection duration, total injection volume, average\ninjection rate, and shut-in duration for TV4100 tests.\nTable 2. Injection duration, total injection volume, average injection rate, and shut-in duration for\nTV4100 tests (Guglielmi et al. (2022) [8]).\nNameInjection Duration\n(min:sec)Injection\nVolume (L)Avg. Injection\nRate (L/min)Shut-In\nDuration (h)\nTV4100 Test 4 10:29 20.5 1.08 7\nTV4100 Test 7 12:21 45.2 2.15 16\nTest 4 had a constant 1.2 L/min injection rate for 10 min and 29 s followed by a\n7-h-long shut-in as shown in Figure 8. Guglielmi et al. (2022) [ 8] reported that the SIMFIP"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891d0e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 7, "chroma:document": "7-h-long shut-in as shown in Figure 8. Guglielmi et al. (2022) [ 8] reported that the SIMFIP\nmeasurements indicate reactivation of a cemented natural fracture set between the two\nSIMFIP anchors with the approximate orientation of 236 \u00b0/54\u00b0dip direction/dip angle.\nSIMFIP tool showed a more complex displacement response as compared to previous\ntests. Figure 8 shows high tangential displacement readings and a smooth normal closure\ndisplacement during shut-in. It is noticeable that at 2 min and 21 s after injection, the\nfracture opened with a limited normal displacement of about 5 microns. Using the SIMFIP\ntool it appears that fracture closure in this test is affected by complex hydro-mechanical\neffects as seen in Figure 9. The normal displacement drops to near zero during the shut-in\nperiod at 18.6 MPa (2700 psi) and then climbs back up.\nFigure 8. SIMFIP displacement normal and tangential to the activated fracture during TV4100 Test 4."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891d5e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 7, "chroma:document": "Figure 8. SIMFIP displacement normal and tangential to the activated fracture during TV4100 Test 4.\nDisplacements are plotted with injection pressure and injection \ufb02ow rate (Guglielmi et al. (2022 [ 8]).\nIn TV4100 Test 7, a 12:21 min, 2.8 L/min injection test was run, followed by a 16-h\nshut-in period as seen in Figure 10. There is a smooth variation of fracture opening and\nshearing during the shut-in period. This may indicate that one or more natural fracture\nsegments were reactivated between the SIMFIP anchors. The fracture opens to a maximum\nof 43 microns as seen in Figure 11."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891dae-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 8, "chroma:document": "Energies 2023 ,16, 2807 9 of 21\nEnergies 2023 ,1, 0 9 of 22\nFigure 9. Rock displacement normal to the activated fracture versus zone pressure measured using\nSIMFIP tool for the TV4100 test 4 (Guglielmi et al. (2022) [8]).\nFigure 10. Rock displacement normal and tangential to the activated fracture using SIMFIP tool\nduring TV4100 test 7. Rock displacements are plotted with injection pressure and injection \ufb02ow rate\n(Guglielmi et al. (2022) [8]).\nFigure 9. Rock displacement normal to the activated fracture versus zone pressure measured using\nSIMFIP tool for the TV4100 test 4 (Guglielmi et al. (2022) [8]).\nFigure 10. Rock displacement normal and tangential to the activated fracture using SIMFIP tool\nduring TV4100 test 7. Rock displacements are plotted with injection pressure and injection \ufb02ow rate\n(Guglielmi et al. (2022) [8]).\nEnergies 2023 ,1, 0 9 of 22\nEnergies 2023 ,1, 0 9 of 22\nFigure 9. Rock displacement normal to the activated fracture versus zone pressure measured using"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891dfe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 8, "chroma:document": "Energies 2023 ,1, 0 9 of 22\nFigure 9. Rock displacement normal to the activated fracture versus zone pressure measured using\nSIMFIP tool for the TV4100 test 4 (Guglielmi et al. (2022) [8]).\nFigure 10. Rock displacement normal and tangential to the activated fracture using SIMFIP tool\nduring TV4100 test 7. Rock displacements are plotted with injection pressure and injection \ufb02ow rate\n(Guglielmi et al. (2022) [8]).\nFigure 9. Rock displacement normal to the activated fracture versus zone pressure measured using\nSIMFIP tool for the TV4100 test 4 (Guglielmi et al. (2022) [8]).\nFigure 10. Rock displacement normal and tangential to the activated fracture using SIMFIP tool\nduring TV4100 test 7. Rock displacements are plotted with injection pressure and injection \ufb02ow rate\n(Guglielmi et al. (2022) [8]).\nFigure 11. Rock displacement normal to the activated fracture versus zone pressure measured using\nSIMFIP tool for the TV4100 test 7 (Guglielmi et al. (2022) [8])."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891e76-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 8, "chroma:document": "SIMFIP tool for the TV4100 test 7 (Guglielmi et al. (2022) [8]).\nFigure 11. Rock displacement normal to the activated fracture versus zone pressure measured using\nSIMFIP tool for the TV4100 test 7 (Guglielmi et al. (2022) [8])."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891ec6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 9, "chroma:document": "Energies 2023 ,16, 2807 10 of 21\nEstimating the minimum stress from the x-intercept in test TV4100 is somewhat\nchallenging because the observed data do not usually yield a smooth, ideal straight line, as\nis seen in the E1-I 164 tests. The EGS Collab team reported the presence of apparently \ufb01ve\ncemented natural fractures in the TV4100 test 4 intervals and ten cemented natural fractures\nin the TV4100 test 7 intervals. Some natural fractures contained a several-centimeter thick\nin-\ufb01lling cement and a centimeter-thick damage zone. Acoustic logs before and after both\ntests were compared and the EGS collab team concluded that there were no new fractures.\nThe stronger acoustic contrast indicates that the fractures had been reactivated. EGS Collab\nteam conducted a pump-in \ufb02ow-back test on TV4100 interval as the second cycle for test 7.\nUsing the analysis technique introduced by Plahn et al. (1997), the closure stress may be"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891f16-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 9, "chroma:document": "Using the analysis technique introduced by Plahn et al. (1997), the closure stress may be\nestimated from a plot of pressure versus cumulative \ufb02ow-back volume. A straight line is\ndrawn through the linear periods on the plot before and after closure, and the intercept\nis taken as the closure as per Guglielmi et al. (2022) [ 8]. The closure estimate of around\n18.6 MPa (2700 psi) as seen in Figure 12.\nFigure 12. Pressure versus cumulative \ufb02ow-back volume for the TV4100 test 7-Cycle 2 (Pump-in\n\ufb02ow-back test) (Guglielmi et al. (2022) [8]).\n3. Results\nThe \ufb01nal comparison between the compliance, tangent, log\u2013log, and square root of\ntime with the SIMFIP tool reading is shown in Table 3. The new CWT fracture closure\ndetection technique showed the most accurate fracture closure pressure compared with the\nphysical measurement using the SIMFIP tool in the four tests published by Guglielmi et al.\n(2022) [8].\nTable 3. Comparison of the closure events period of the four EGS Collab tests."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891f66-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 9, "chroma:document": "(2022) [8].\nTable 3. Comparison of the closure events period of the four EGS Collab tests.\nFracture Closure Pressure\nDetection TechniqueE1-I 164 Test 2 E1-I 164 Test 2 TV4100 Test 4 TV4100 Test 7\nUsing SIMFIP 21.37 MPa (3100 psi) 21.37 MPa (3100 psi)18.69 MPa\n(2712 psi)\u201319.2 MPa\n(2785 psi)18.6 MPa (2700 psi)\nUsing CWT fracture closure\ndetection TechniqueStart of closure =\n21.59 MPa (3132 psi)Start of closure =\n20.68 MPa (3000 psi)Start of closure =\n18.89 MPa (2740 psi)Start of closure =\n19.02 MPa (2760 psi)\nComplete closure =\n21.39 MPa (3103 psi)Complete closure =\n20.34 MPa (2950 psi)Complete closure =\n18.6 MPa (2700 psi)Complete closure =\n18.6 MPa (2700 psi)\nUsing Compliance MethodRapid closure\n20.68 MPa\n(3000 psi)\u201324.13 MPa\n(3500 psi)18.79 MPa (2725 psi) 17.06 MPa (2475 psi) 19.31 MPa (2800 psi)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891fac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 10, "chroma:document": "Energies 2023 ,16, 2807 11 of 21\nTable 3. Cont.\nFracture Closure Pressure\nDetection TechniqueE1-I 164 Test 2 E1-I 164 Test 2 TV4100 Test 4 TV4100 Test 7\nFracture closure pressure\nusing Tangent MethodLess than 15.17 MPa\n(2200 psi)Less than 15.17 MPa\n(2200 psi)Less than 15.17 MPa\n(2200 psi)18.61 MPa (2700 psi)\nUsing Nolte Technique 23.44 MPa (3400 psi) No closure signature 20.06 MPa (2910 psi) 21.90 MPa (3177 psi)\nUsing log\u2013log method No closure signature No closure signature No closure signature No closure signature\nUsing the square root of\ntime methodNo closure signature No closure signature No closure signature 18.6 MPa (2700 psi)\n4. Discussion\n4.1. Analysis of E1-I 164 Test 2\nThe application of the conventional G-function methods to E1-I 164 Test 2 is shown in\nFigure 13. Following the initial Nolte (1979) [ 20] technique detected the fracture closure at\n23.44 MPa (3400 psi) where GdP/dG deviated from linear. The GdP/dG curve continues in-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b891ffc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 10, "chroma:document": "23.44 MPa (3400 psi) where GdP/dG deviated from linear. The GdP/dG curve continues in-\ncreasing and does not reach a peak by the end of the test. The dP/dG curve showed a mono-\ntonic decrease reaching a minimum pressure of 15.17 MPa (2200 psi). The interpretation\nusing compliance (McClure et al. (2019) [ 21]) that is discussed by Guglielmi et al. (2022) [8]\nimplies a wide range of stress estimates from 20.68 MPa (3000 psi) to 24.13 MPa (3500 psi).\nIn essence, there was no agreement between the three methods. Using the classical square\nroot of time given in Figure 14 did not show any closure event signature. The log\u2013log\nanalysis Figure 15 showed a pre-closure linear \ufb02ow regime (slope of 1). The curve con-\ntinued to increase at a half slope line till the end of the test indicating no closure. The\nSIMFIP tool detected closure at 21.37 MPa (3100 psi). There was no agreement among the\nconventional techniques, however, the compliance technique gave the closest value to that"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89204c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 10, "chroma:document": "conventional techniques, however, the compliance technique gave the closest value to that\nof the SIMFIP . These results indicate that conventional techniques may fail in analyzing\ncomplex or non-ideal tests.\nFigure 13. Tangent method (dP/dG & GdP/dG) and relative stiffness plots for E1-I 164 Test 2\n(Guglielmi et al. (2022) [8])."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89209c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 11, "chroma:document": "Energies 2023 ,16, 2807 12 of 21\nFigure 14. Square root of time analysis for E1-I 164 Test 2.\nFigure 15. Log\u2013log analysis for E1-I 164 Test 2.\nApplication of CWT fracture closure detection technique to the SIMFIP tool observed\ndata is given in Figure 16 as signal average log energy of pressure versus time. Local\npeaks are clear at the pressure of 21.59 MPa (3132 psi) indicating initiation of closure and\nagain 3 min later at 21.4 MPa (3103 psi) with a stabilized energy level over a long period\nindicating complete fracture closure. These results compare very well with the SIMFIP tool\nmeasurements reported in Figure 7. These clearly show that CWT techniques work very\nreliably regardless of the level of complexity of the test."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8920e2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 12, "chroma:document": "Energies 2023 ,16, 2807 13 of 21\nFigure 16. Closure pressure detection using CWT technique for E1-I 164 Test 2.\n4.2. Analysis of E1-I 164 Test 3\nE1-I 164 Test 3 is even more complex than the previous case as it started with a low\npumping rate for a long period of time (almost 82 min of injection rate of 0.1 L/min) then\nthe pumping rate increased to 5 L/min for 20 min, followed by 15 h of the shut-in period\nas seen in Figure 17. The SIMFIP tool signature for E1-I 164 Test 3 was similar to E1-I 164\nTest 2, however, the rock displacement line during shut-in dropped back to a large negative\ndisplacement value of \u221250 microns at 19 MPa (2755 psi) as seen in Figure 7. The shut-in\nline intersection with zero displacements at 21.37 MPa (3100 psi). It con\ufb01rmed the same\nvalues of fracture closure pressure of 21.4 MPa (3100 psi).\nFigure 17. Injection pressure and injection \ufb02owrate for EI-164 test 3."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892132-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 13, "chroma:document": "Energies 2023 ,16, 2807 14 of 21\nThe application of conventional methods using the compliance method on this test\nshowed that the transient reaches a minimum dP/dG at a value yielding a contact pressure\nof 19.30 MPa (2800 psi) and a stress estimate of 18.78 MPa (2725 psi) as given in Figure 18.\nGdP/dG monotonically increases throughout the test implying that the fracture never\nclosed. This implies that the minimum stress is lower than the \ufb01nal pressure value of\n15.17 MPa (2200 psi). The compliance method stress estimate is 2.07\u20132.59 MPa (300\u2013375 psi)\nlower than the SIMFIP estimates, i.e., yields about a 10% error. The application of conven-\ntional log\u2013log and the square root of time did not show any fracture closure signature as\nseen in Figure 19. The compliance method is the only fracture closure detection technique\nthat showed an almost reasonable stress estimate.\nFigure 18. Tangent method plots (dP/dG & GdP/dG) for E1-I 164 test 3."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892182-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 13, "chroma:document": "that showed an almost reasonable stress estimate.\nFigure 18. Tangent method plots (dP/dG & GdP/dG) for E1-I 164 test 3.\nFigure 19. Square root of time analysis and log\u2013log analysis for E1-I 164 Test 3.\nThe application of the CWT fracture closure detection technique is shown in Figure 20.\nThe signal average log energy showed a local peak at the pressure of 20.68 MPa (3000 psi)\nwhich indicates the start of fracture closure. That peak is followed by a drop in the level\nof signal average energy to a long and stable value which indicates complete closure at\nthe pressure of 20.34 MPa (2950 psi). This value agrees very well with the value of closure\npressure that is observed by the SIMFIP tool as per Figure 7. The conventional techniques\ndetected the closure 1.034 MPa (150 psi) below the SIMFIP tool measurement. However,\nthe closure pressure detected using the CWT technique matches the start of stabilization of"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8921d2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 13, "chroma:document": "the closure pressure detected using the CWT technique matches the start of stabilization of\nthe shut-in pressure line in negative displacement measurements. The difference between\nclosure pressure values detected by CWT and the one detected by the SIMFIP tool is less\nthan 5%. The time of closure event between the start of fracture closure at 20.68 MPa\n(3000 psi) and complete closure at 20.34 MPa (2950 psi) is 20 min."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892218-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 14, "chroma:document": "Energies 2023 ,16, 2807 15 of 21\nFigure 20. Closure pressure detection using CWT fracture closure detection technique for E1-I 164\ntest 3.\n4.3. Analysis of TV4100 Test 4\nThe application of conventional methods using the compliance method on TV4100\ninterval test 4 showed that the transient reaches a minimum dP/dG and rises back up,\nyielding a contact pressure of 17.58 MPa (2550 psi) and a stress estimate of 17.06 MPa\n(2475 psi) as seen in Figure 21. The relative stiffness plot shows an upward de\ufb02ection\nat approximately 17.24 MPa (2500 psi) as seen in Figure 21. The GdP/dG curve is still\nbending upwards at the end of the transient. Thus, the tangent method interpretation\nindicates that the fracture never closed as GdP/dG monotonically increases. This would\nalso indicate that the stress should be lower than the \ufb01nal pressure of 15.17 MPa (2200 psi).\nThe compliance method stress estimate is 1.6\u20132.14 MPa (237\u2013310 psi) (approximately 10%"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892268-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 14, "chroma:document": "The compliance method stress estimate is 1.6\u20132.14 MPa (237\u2013310 psi) (approximately 10%\nerror) lower than the estimates from SIMFIP . The tangent method stress estimates are\neven lower. However, by applying the initial technique by Nolte (1979) [ 20] the closure\npressure is detected at 2910 psi where the GdP/dG deviated from linear. The application\nof conventional log\u2013log and the square root of time did not show any fracture closure\nsignature as seen in Figure 22. As a summary of TV4100 test 4, the fracture closure pressure\nis less than 15.17 MPa (2200 psi) using the tangent method such as the log\u2013log analysis and\nthe square root of time analysis, it is 17.06 MPa (2475 psi) using the compliance method, and\n20.06 MPa (2910 psi) using Nolte (1979) [ 20] technique. The closure pressure detected using\nthe SIMFIP tool ranges from 19.20 MPa (2785 psi) to 18.69 MPa (2712 psi). Figure 23 shows\nthe application of the continuous wavelet transform (CWT) technique to data of TV4100"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8922b8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 14, "chroma:document": "the application of the continuous wavelet transform (CWT) technique to data of TV4100\ntest 4. It shows the average log signal energy using CWT of pressure versus time during\nthe shut-in period. Several observations may be made from Figure 23. It shows a small\npeak at pressure 18.89 MPa (2740 psi) and a decrease of the signal average wavelet energy\nlevel starting from that peak till complete closure after 28 min at 18.61 MPa (2700 psi). This\nvalue matches the SIMFIP tool readings."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892308-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 15, "chroma:document": "Energies 2023 ,16, 2807 16 of 21\nFigure 21. Tangent method plots (dP/dG & GdP/dG) and relative stiffness plots for TV4100 test\n4(Guglielmi et al. (2022) [8]).\nFigure 22. The log\u2013log analysis and square root of time analysis plots for TV4100 test 4.\nFigure 23. Closure pressure detection using CWT for TV4100 interval test 4."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892358-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 16, "chroma:document": "Energies 2023 ,16, 2807 17 of 21\n4.4. Analysis of TV4100 Test 7\nThe application of conventional methods on TV4100 interval test 7 indicates that\ndP/dG plot may be considered as an \u2018adequate\u2019 indication of closure (McClure et al.,\n(2022) [ 22]) as seen in Figure 24. There is an upward de\ufb02ection in dP/dG, but it never\nreaches a minimum. The upward de\ufb02ection occurs at approximately 19.82 MPa (2875 psi),\nsuggesting a stress estimate of 19.31 MPa (2800 psi) as per Guglielmi et al. (2022) [ 8].\nOn the other hand, the relative stiffness plot, Figure 24, does not show a clear upward\nin\ufb02ection, the curve stayed \ufb02at in spite of the increase in pressure. The tangent method\nclosure estimate is around 18.61 MPa (2700 psi). The application of the initial technique by\nNolte (1979) [ 20] detected the closure at 21.90 MPa (3177 psi) at the deviation of GdP/dG\nfrom the linear. The application of square root of time showed a good signature for fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8923a8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 16, "chroma:document": "from the linear. The application of square root of time showed a good signature for fracture\nclosure at the pressure of 18.61 MPa (2700 psi), however, conventional log\u2013log does not\nshow the fracture closure behavior as seen in Figure 25. As a summary of TV4100 test 7, the\nfracture closure is 18.61 MPa (2700 psi) using the tangent method and 19.31 MPa (2800 psi)\nusing the compliance method, and the square root of time analysis showed the closure at\n18.61 MPa (2700 psi). All these values are close to the closure pressure detected using the\nSIMFIP tool (18.61 MPa (2700 psi)).\nFigure 24. Tangent method plots (dP/dG & GdP/dG) and relative stiffness plots for TV4100 test 7\n(Guglielmi et al. (2022) [8]).\nFigure 25. The log\u2013log analysis and the square root of time analysis plots for TV4100 test 7."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8923f8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 17, "chroma:document": "Energies 2023 ,16, 2807 18 of 21\nFigure 26 illustrates the application of the continuous wavelet transform (CWT) tech-\nnique to TV4100 test 7. It may be noticed that the signal average energy showed a small\npeak at pressure 19.03 MPa (2760 psi) and may also be noticed that the drop of the signal\naverage energy level may be identi\ufb01ed after 28 min at 18.61 MPa (2700 psi). This agreed\nvery well with the SIMFIP tool reading of closure pressure (18.61 MPa (2700 psi)). That\ncomplex fracture closure observed by the SIMFIP tool matches the gradual decline of the\nsignal average energy as seen in Figure 26. It is interesting to observe that the presence of\nnatural fracture dampens the wavelet signal average log energy.\nFigure 26. Closure pressure detection using CWT for TV4100 interval Test 7.\nThe number of natural fractures reported by The EGS Collab Team (Guglielmi et al.,\n(2022) [ 8]) can be compared with the time of fracture closure based on the new CWT"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892448-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 17, "chroma:document": "(2022) [ 8]) can be compared with the time of fracture closure based on the new CWT\nfracture closure detection technique as per Table 4. Plotting these two parameters yields\na linear relationship as given in Figure 27. This indicates that the new CWT closure\ntechnique may be used as a deep investigative tool to understand the complexity of the\nfracture closure process. More deformation/strain measurement experiments are needed\nto further investigate the relationship between the natural fracture intensity and types and\nits response on the signal average energy plot using the CWT technique.\nTable 4. Comparison of the closure events period of the four EGS Collab tests.\nTestPressure at Start of\nClosure Event,\nMPa (psi)Pressure at Start of\nClosure Event,\nMPa (psi)Period of Closure\nEvent, minNumber of Reported\nNatural Fractures\nE1-I 164 Test 2 21.59 (3132) 21.39 (3103) 3 0\nE1-I 164 Test 3 20.68 (3000) 20.34 (2950) 20 Not Reported\nTV4100 Test 4 18.89 (2740) 18.61 (2700) 28 5"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892498-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 17, "chroma:document": "E1-I 164 Test 2 21.59 (3132) 21.39 (3103) 3 0\nE1-I 164 Test 3 20.68 (3000) 20.34 (2950) 20 Not Reported\nTV4100 Test 4 18.89 (2740) 18.61 (2700) 28 5\nTV4100 Test 7 19.03 (2760) 18.61 (2700) 42 10"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8924de-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 18, "chroma:document": "Energies 2023 ,16, 2807 19 of 21\nFigure 27. The relationship between fracture closure periods vs. number of natural fractures reported\nin EGS Collab experiments.\n5. Conclusions\nThe new CWT closure detection technique showed an accurate match with the closure\npressure detected by the measurement of the rock displacement with the strain gauges. The\nfollowing conclusions can be concluded:\n1. The signal average energy using the CWT closure detection technique is a reliable\nmathematical independent magni\ufb01cation for the pressure decay. This has been con-\n\ufb01rmed using the SIMFIP tool.\n2. The presence of natural fracture dampens the peak of the indicating the start of closure\nas it makes the fracture closure a more gradual process causing the average signal\nenergy to drop in a more gradual manner.\n3. A linear relationship between the closure time can be detected by the new CWT\ntechnique and the number of natural fractures observed.\n6. Patents"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892538-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 18, "chroma:document": "3. A linear relationship between the closure time can be detected by the new CWT\ntechnique and the number of natural fractures observed.\n6. Patents\nThis study was \ufb01led as U.S. Patent Application No. 63/412,269 on 30 September 2022,\nand entitled \u201cSYSTEMS AND METHODS FOR MONITORING SUBSURFACE EVENTS\nUSING CONTINUOUS WAVELET TRANSFORMS\u201d.\nAuthor Contributions: Conceptualization, M.A.G. and I.E.; methodology, M.A.G.; software, I.E.;\nvalidation, I.E.; Supervision, M.Y.S. and S.M.F.-A.; Writing\u2014original draft, M.A.G.; Writing\u2014review\nand editing, M.Y.S. and S.M.F.-A. All authors have read and agreed to the published version of\nthe manuscript.\nFunding: This research received funding from HESS Corporation and Halliburton Energy Service,\nmembers of the hydraulic fracturing consortium at the University of Houston.\nInformed Consent Statement: Not applicable.\nData Availability Statement: The data that support the \ufb01ndings of this study are openly available on"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89257e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 18, "chroma:document": "Informed Consent Statement: Not applicable.\nData Availability Statement: The data that support the \ufb01ndings of this study are openly available on\n1 May 2022 in (https://gdr.openei.org/submissions/1250) and (https://gdr.openei.org/submissions/\n1229). Derived data supporting the \ufb01ndings of this study are available from the corresponding author\n[M.A.G.] on request.\nAcknowledgments: We thank HESS Corporation, and Halliburton Energy Service, members of the\nhydraulic fracturing consortium at the University of Houston, for supporting this work. We thank\nalso The EGS Collab team for conducting that remarkable experiments and publishing the results for\npublic use."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8925ce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 19, "chroma:document": "Energies 2023 ,16, 2807 20 of 21\nCon\ufb02icts of Interest: The authors declare no con\ufb02ict of interest.\nAbbreviations\nThe following abbreviations are used in this manuscript:\n\u2206t Shut-in time\nCWT Continuous wavelet transform\nDFIT Diagnostic fracture injection test\nG G-time function\nP Pressure\nSIMFIP Step-Rate Injection Method for Fracture In-Situ Properties.\nt Time\nReferences\n1. Gabry, M.A.; Eltaleb, I.; Soliman, M.Y.; Farouq-Ali, S.M. A New Technique for Estimating Stress from Fracture Injection Tests\nUsing Continuous Wavelet Transform. Energies 2023 ,16, 764. [CrossRef]\n2. Barree, R.D.; Barree, V .L.; Craig, D. Holistic fracture diagnostics: Consistent interpretation of prefrac injection tests using multiple\nanalysis methods. SPE Prod. Oper. 2009 ,24, 396\u2013406. [CrossRef]\n3. Barree, R.D.; Barree, V .L.; Craig, D. Holistic fracture diagnostics. In Proceedings of the Rocky Mountain Oil & Gas Technology\nSymposium, OnePetro, Denver, CO, USA, 16\u201318 April 2007."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892628-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 19, "chroma:document": "Symposium, OnePetro, Denver, CO, USA, 16\u201318 April 2007.\n4. McClure, M.W.; Jung, H.; Cramer, D.D.; Sharma, M.M. The fracture-compliance method for picking closure pressure from\ndiagnostic fracture-injection tests. SPE J. 2016 ,21, 1321\u20131339. [CrossRef]\n5. Dutler, N.; Valley, B.; Gischig, V .; Jalali, M.; Brixel, B.; Krietsch, H.; Roques, C.; Amann, F. Hydromechanical insight of fracture\nopening and closure during in-situ hydraulic fracturing in crystalline rock. Int. J. Rock Mech. Min. Sci. 2020 ,135, 104450.\n[CrossRef]\n6. Gulrajani, S.N.; Nolte, K.; Economides, M. Fracture evaluation using pressure diagnostics. Reserv. Stimul. 2000 ,2, 1.\n7. Guglielmi, Y.; Nussbaum, C.; Rutqvist, J.; Cappa, F.; Jeanne, P .; Birkholzer, J. Estimating perturbed stress from 3-D borehole\ndisplacements induced by \ufb02uid injection in fractured or faulted shales. Geophys. J. Int. 2020 ,221, 1684\u20131695. [CrossRef]"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89266e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 19, "chroma:document": "displacements induced by \ufb02uid injection in fractured or faulted shales. Geophys. J. Int. 2020 ,221, 1684\u20131695. [CrossRef]\n8. Guglielmi, Y.; Mcclure, M. Estimating Stress from Fracture Injection Tests: Comparing Pressure Transient Interpretations with\nIn-Situ Strain Measurements. In Proceedings of the 47th Workshop on Geothermal Reservoir Engineering, Stanford University,\nStanford, CA, USA, 7\u20139 February 2022.\n9. Eltaleb, I.; Soliman, M.Y. New Pump-In Flowback Model Veri\ufb01cation with In-Situ Strain Measurements and Numerical Simulation.\nEnergies 2023 ,16, 1970. [CrossRef]\n10. Guglielmi, Y.; Cappa, F.; Lan\u00e7on, H.; Janowczyk, J.B.; Rutqvist, J.; Tsang, C.F.; Wang, J. ISRM suggested method for step-rate\ninjection method for fracture in-situ properties (SIMFIP): Using a 3-components borehole deformation sensor. In The ISRM\nSuggested Methods for Rock Characterization, Testing and Monitoring: 2007\u20132014 ; Springer: Berlin/Heidelberg, Germany, 2013;\npp. 179\u2013186."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8926be-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 19, "chroma:document": "Suggested Methods for Rock Characterization, Testing and Monitoring: 2007\u20132014 ; Springer: Berlin/Heidelberg, Germany, 2013;\npp. 179\u2013186.\n11. Sneddon, I.N. The distribution of stress in the neighbourhood of a crack in an elastic solid. Proc. R. Soc. Lond. Ser. A. Math. Phys.\nSci.1946 ,187, 229\u2013260.\n12. Barton, N.; Bandis, S.; Bakhtar, K. Strength, deformation and conductivity coupling of rock joints. Int. J. Rock Mech. Min. Sci.\nGeomech. Abstr. 1985 ,22, 121\u2013140. [CrossRef]\n13. Kneafsey, T.J.; Blankenship, D.; Knox, H.A.; Johnson, T.C.; Ajo-Franklin, J.B.; Schwering, P .C.; Dobson, P .F.; Morris, J.P .; White,\nM.D.; Podgorney, R.; et al. EGS Collab project: Status and progress. In Proceedings of the 44th Workshop on Geothermal\nReservoir Engineering, Stanford University, Stanford, CA, USA, 11\u201313 February 2019.\n14. Kneafsey, T.J.; Blankenship, D.; Dobson, P .F.; Morris, J.P .; White, M.D.; Fu, P .; Schwering, P .C.; Ajo-Franklin, J.B.; Huang, L.;"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 19, "chroma:document": "14. Kneafsey, T.J.; Blankenship, D.; Dobson, P .F.; Morris, J.P .; White, M.D.; Fu, P .; Schwering, P .C.; Ajo-Franklin, J.B.; Huang, L.;\nSchoenball, M.; et al. The EGS collab project: Learnings from Experiment 1. In Proceedings of the 45th Workshop on Geothermal\nReservoir Engineering, Stanford University, Stanford, CA, USA, 10\u201312 February 2020; pp. 10\u201312.\n15. Singh, A.; Neupane, G.; Dobson, P .; Zoback, M.; Morris, J.; Fu, P .; Schwering, P .; Roggenthen, W.; Frash, L.; Kneafsey, T.; et al. Slip\ntendency analysis of fracture networks to determine suitability of candidate testbeds for the EGS Collab hydroshear experiment.\nIn Proceedings of the GRC Annual Meeting & Expo, Palm Springs, CA, USA, 15\u201318 September 2019.\n16. Wang, H.; Lee, M.; Doe, T.; Haimson, B.; Oldenburg, C.; Dobson, P . In-situ stress measurement at 1550-m depth at the kISMET\ntest site in Lead, SD. In Proceedings of the 51st US Rock Mechanics/Geomechanics Symposium, OnePetro, San Francisco, CA,\nUSA, 25\u201328 June 2017."}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 19, "chroma:document": "test site in Lead, SD. In Proceedings of the 51st US Rock Mechanics/Geomechanics Symposium, OnePetro, San Francisco, CA,\nUSA, 25\u201328 June 2017.\n17. Guglielmi, Y.; Cook, P .; Soom, F.; Dobson, P .; Kneafsey, T.; Valley, B.; Kakurina, M.; Niemi, A.; Tsang, C.F.; Tatomir, A.; et al.\nEstimating Stress From Three-Dimensional Borehole Displacements Induced by Fluid Injection in Different Types of Fractured or\nFaulted Rocks. In Proceedings of the 55th U.S. Rock Mechanics/Geomechanics Symposium, OnePetro, Virtual, 20\u201323 June 2021.\n18. Schoenball, M.; Guglielmi, Y.; Ajo-Franklin, J.B.; Cook, P .J.; Dobson, P .; Hopp, C.; Kneafsey, T.J.; Soom, F.; Ulrich, C. In-situ\nobservation of pre-, co-and post-seismic shear slip at 1.5 km depth. In Proceedings of the 51st U.S. Rock Mechanics/Geomechanics\nSymposium, San Francisco, CA, USA, 25\u201328 June 2017."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 20, "chroma:document": "Energies 2023 ,16, 2807 21 of 21\n19. Fu, P .; Schoenball, M.; Ajo-Franklin, J.B.; Chai, C.; Maceira, M.; Morris, J.P .; Wu, H.; Knox, H.; Schwering, P .C.; White, M.D.; et al.\nClose observation of hydraulic fracturing at egs collab experiment 1: Fracture trajectory, microseismic interpretations, and the\nrole of natural fractures. J. Geophys. Res. Solid Earth 2021 ,126, e2020JB020840. [CrossRef]\n20. Nolte, K.G. Determination of fracture parameters from fracturing pressure decline. In Proceedings of the SPE Annual Technical\nConference and Exhibition, OnePetro, Las Vegas, NV , USA, 23\u201326 September 1979.\n21. McClure, M.; Bammidi, V .; Cipolla, C.; Cramer, D.; Martin, L.; Savitski, A.A.; Sobernheim, D.; Voller, K. A collaborative study on\nDFIT interpretation: Integrating modeling, \ufb01eld data, and analytical techniques. In Proceedings of the Unconventional Resources\nTechnology Conference, Denver, CO, USA, 22\u201324 July 2019; Society of Petroleum Engineers: Richardson, TX, USA; pp. 2020\u20132058."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8927f4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/energies-16-02807.pdf", "page": 20, "chroma:document": "Technology Conference, Denver, CO, USA, 22\u201324 July 2019; Society of Petroleum Engineers: Richardson, TX, USA; pp. 2020\u20132058.\n22. Mcclure, M.; Fowler, G.; Picone, M. Best practices in DFIT interpretation: Comparative analysis of 62 DFITs from nine different\nshale plays. In Proceedings of the SPE International Hydraulic Fracturing Technology Conference & Exhibition, The Woodlands,\nTX, USA, 31 January\u20132 February 2023.\nDisclaimer/Publisher\u2019s Note: The statements, opinions and data contained in all publications are solely those of the individual\nauthor(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to\npeople or property resulting from any ideas, methods, instructions or products referred to in the content."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892844-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 0, "chroma:document": "SPE 8341 \nDETERMINATION OF FRACTURE PARAMETER~ \nFROM FRACTURING PRESSURE DECLINE \nby Kenneth G. Nolte, Member SPE-AIME, \nAMOCO Production Co. \ng. Copynght t979. Amencan Institute of Mming. Metallurgical. and Petroleum Engineers. Inc. SPE \nSociety of Petroleun Engineers of AIM E \nTh1s paper was presented at the 54th Annual Fall Techn1ca/ Conference and Exhibition of the Society of Petroleum Engineers of A/ME. held in Las Vegas. Nevada. September 23\u00b726. 1979. The matenal is sub,ect to correct1on by the \nauthor. Permiss1on to copy IS restncted to an abstract of not more than 300 words. Wnte 6200 N. Central Expy .. Dallas. Texas 75206. \nABSTRACT \nThis paper presents analyses which permit some of The basic assumptions for the applicability of the \nanalyses are that the fracture: \nthe parameters that quantify a fracture and the frac- 1. has essentially constant height. \nturing process to be estimated from the pressure decline"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 0, "chroma:document": "the parameters that quantify a fracture and the frac- 1. has essentially constant height. \nturing process to be estimated from the pressure decline \nfollowing fracturing. The primary assumptions are 2. propagates through a quasi-elastic formation with \nnegligible slip of bedding planes. consistent with those of current practice--a vertical \nfracture of essentially constant height, propagating \nthrough a quasi-elastic formation, with continuous 3. was created by a constant injection rate of a \npower-law fluid into two symmetric wings. displacements (i.e., no slip) at the planes bounding \nthe top and bottom of the fracture. The parameters \nwhich can be quantified from the pressure decline are 4. propagates continuously during pumping and prop\u00ad\nagation stops when pumping stops. the fluid loss coefficient, the fracture length and \nwidth, fluid efficiency, and time for the fracture to \nclose. 5. closes freely without significant interference \nfrom proppant. \nINTRODUCTION"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8928e4-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 0, "chroma:document": "width, fluid efficiency, and time for the fracture to \nclose. 5. closes freely without significant interference \nfrom proppant. \nINTRODUCTION \nAt the present time there is no direct and simple \nprocedure for evaluating the basic parameters achieved \nduring a fracture treatment, such as the length, width \nand fluid efficiency at the time the treatment ends. \nThere exist fracture models which permit estimation of \nfracture length and width based on assumed heights, \nfluid loss coefficient, fluid viscosity, and formation \nmodulus. However, at the end of the treatment there is \nno way of knowing if the assumed parameters were cor\u00ad\nrect, with the possible exception of fracture height \nnear the wellbore. Techniques for defining the frac\u00ad\nture geometry from production performance do not sat\u00ad\nisfy this need completely because of the time delay \nrequired for the data, and the inferred lengths and \nwidths (fracture conductivity) are average values over"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892934-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 0, "chroma:document": "required for the data, and the inferred lengths and \nwidths (fracture conductivity) are average values over \nsections which significantly contribute to production \nand are at best lower bounds on the actual dimensions \ncreated by the fracturing fluid. As the volume and \nunit cost of fluids used for a typical fracture treat\u00ad\nment continue to increase, so does the need for better \ndefinition of the fracture geometry created by a par\u00ad\nticular treatment in a particular zone. \nSUMMARY OF DERIVATIONS \nBa$ed on the concept of a vertical fracture as \npresented by Perkins and Kern2 and as extended by \nNordgren,4 relationships based on the fracturing pres\u00ad\nsure decline are derived in this paper. \nReferences and illustrations at end of paper. Since actual hydraulic fractures will deviate by \nvarying degrees at various times from these idealized \nassumptions, the utility of the analyses presented for \nany application will depend on the degree of deviation"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89297a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 0, "chroma:document": "assumptions, the utility of the analyses presented for \nany application will depend on the degree of deviation \nand the sensitivity to the deviation. The ultimate \nutility will depend on the ability to provide realistic \nengineering correlations and predictions. As discussed \nin the \"Discussion of Applications\" section, the most \nlikely deviations from assumptions 1, 4, and 5 above, \nwould produce estimates erring on the conservative side \nfor the fluid loss coefficient and length. \nIn the following, the derived relationships are \nsummarized with equation numbers corresponding to those \nin later sections of the paper. The relationships are \nexpressed in terms of the dimensionless shut-in time, \no = ~t/t , where ~t is the time since pumping stopped \n(shut-in~ and t is the pump time prior to shut-in. . 0 . \nThe rate of pressure decline at time o is \n4CH E' dP(8) p f(8) ~= TIH2S It \ns 0 (9) \nwith f(o) defined by the bounds"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 0, "chroma:document": "The rate of pressure decline at time o is \n4CH E' dP(8) p f(8) ~= TIH2S It \ns 0 (9) \nwith f(o) defined by the bounds \n-1 -1/2 2 (11+8 -18) > f (8) > sin [ (1+8) ] (3) Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 1, "chroma:document": "2 DETERMINATION OF FRACTURE PARAMETERS FROM FRACTURING PRESSURE DECLINE S\"'?E 8341 \nshown in Fig. 1. The symbols in the above and follow\u00ad\ning equations are defined at the end of the paper. 8 \nis deftned in Eq. 8 and shown graphically in Fig. 2. s \nThe difference in the decline pressure between \ntimes o\n0 and o is given by \n(15) \nand G(o,o\n0) is defined in Eq. 16 and shown on Fig. 3. \nThe above equation can be used with actual decline \npressures in a curve matching technique (Applications \nSection) which defines a match pressure \nP* = (17) \nthat determines the value of the variable group on the \nright-hand side for the given application, from which \none of the variables can be defined in terms of the \nremaining variables. It is noted that these equations \nare independent of the fracture length. \nThe volume of fluid lost to the formation during \npumping is given in terms of the bounds \nnCR L ft > V > ~ CR L /t p o L 3 p o (22) \nThe length of the fracture can be determined by \nL ="}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892a6a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 1, "chroma:document": "pumping is given in terms of the bounds \nnCR L ft > V > ~ CR L /t p o L 3 p o (22) \nThe length of the fracture can be determined by \nL = \nnCR /t (l+p) p 0 \nwith the variable \nor, 28 P/t = c~) P o P f u 7f\"i3 dP/dt s \n~p P = G(o,oo) 28 -6-P~(o-,-o--) \ns 0 (25) \n(26) \n(27) \nin which P is the wellbore pressure, above closure \npressure, at shut-in and dP/dt is evaluated at o. \nFigure 4 illustrates the pressure terms in the above \nexpressions. \nThe fluid efficiency during the treatment is given \nby the simple ratio \neff = _2_ __ l+p \nwith p defined above. \nCombining (1) and (7) gives \nQt\n0(1-eff) \nL = \nnCR /t p 0 (28) \n(31) for the fracture length in terms of the fluid efficiency \nand fluid loss coefficient. \nThe average fracture width, over the height and \nlength at the end of pumping is given by \nR \nw = TIC _E_ ft p R o (37) \nThe dimensionless shut-in time for the fractur~ to \nclose can be found by either of the expressions \n--1 wH ] (41) 0 = g [ \n2CH It p 0 \n0 -1 [~] = g 2"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892aba-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 1, "chroma:document": "close can be found by either of the expressions \n--1 wH ] (41) 0 = g [ \n2CH It p 0 \n0 -1 [~] = g 2 \nwhere g-l is the inverse function for g(o) given in \nFig. 1 and defined in Eq. 13. \nIn the remaining sections of the paper, the above \nexpressions are derived and discussed, with example \napplications given in a later section. \nDERIVATIONS \nBackground: There are two fundamentally different \nconcepts for the geometry of a constant-height vertical\u00ad\nfracture which lead to very different results. One \nconcept1 is that the fracture width is constant across \nthe height of the fracture. This requires the assump\u00ad\ntion that the formation bed being fractured is inde\u00ad\npendent of the beds above and below--that is, the beds \ncan slip freely of one another at their boundaries. \nThis assumption leads to the conclusion that the fluid \npressure required to extend the fracture decreases with \ntime. \nThe other concept, utilized by Perkins and Kern,2 \nassumes that there is no, or negligible, slip of bound\u00ad"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892b00-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 1, "chroma:document": "time. \nThe other concept, utilized by Perkins and Kern,2 \nassumes that there is no, or negligible, slip of bound\u00ad\naries along the horizontal planes which confine the \nfracture height. This assumption leads to the conclu\u00ad\nsion that the fluid pressure required ~o extend the \nfracture increases with time. \nSince the two concepts fundamentally differ only \nin the assumption of slip along bedding planes, the \napplicable concept for a given fracture application \ndepends on the potential for bedding plane slip. \nBedding plane slip is more likely at shallower depths \nthan at deeper depths due to the difference in over\u00ad\nburden stress on the planes and the resulting friction \nwhich must be overcome for slip to occur. \nMeasurements3 of bottom-hole pressures during \nmassive-hydraulic-fracturing in three different areas \nof North America, at depths greater than 7900 ft indi\u00ad\ncate that for these conditions the fracturing pressure \nincreases with time in a manner consistent with the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 1, "chroma:document": "cate that for these conditions the fracturing pressure \nincreases with time in a manner consistent with the \nconcept presented by Perkins and Kern2 and as extended \nby Nordgren.4 As a result of these measurements indi\u00ad\ncating the validity of the concepts presented by \nPerkins and Kern, the assumptions used in this paper \nwill be consistent with this reference and the refine\u00ad\nments presented by Nordgren. Nordgren presents an \nexcellent review and critique of these assumptions \nwhich will not be repeated in this paper. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892baa-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 2, "chroma:document": "K. G. NOLTE \nFluid Loss Coefficient: The basic equation used in \nthis paper is the continuity equation for flow down a \nfracture, and as presented by Nordgren4 is \n_ aQ(z,t) =A( ) + aA(z,t) (l) az z,t at. \nwhich states that the gradient of the flow rate is \nequal to the rate fluid is lost to the formation, per \nunit length, plus the time rate of fluid storage due to \ncross-sectional area change. The assumption for fluid \nloss, as critiqued in Ref. 4, that \n2CH p (2) \nwill be used in the following. C is the fluid loss \ncoefficient, H is the height over the fracture where \nfluid loss occRrs (e.g., sand section), and Tis the \ntime the fracture was created at point z. Also the \nassumption will be used that negligible slip occurs \nacross bedding planes and that the formation responds \nquasi-elastic. These assumptions yield2 \nA = !. wH 4 7TH2 \n2E' p (3) \nwhere H is the fractured height, w is the maximum \nfracture width at z, p is the pressure at z, above the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892bfa-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 2, "chroma:document": "A = !. wH 4 7TH2 \n2E' p (3) \nwhere H is the fractured height, w is the maximum \nfracture width at z, p is the pressure at z, above the \nin-situ closure pressure of the formation, and E' is \nthe effective plane-strain modulus across the fracture \nheight. The term \"effective\" refers to a constant \nmodulus which gives the same average width across the \nheight as for an actual case in which the fracture may \ncross several beds with different in-situ pressures and \nelastic properties. \nCombining Eqs. 1, 2, and 3 yields \n-~ = 3 + !. H2 l\u00a3 \naz It-T 2 E' at (4) \nassuming that H and E' do not change significantly with \ntime. \nIntegrating (4) over the length of the fracture \nyields \nL \n-Q(L) + Q(O) 2CH f dz \np It-T (z) 0 \n7T H2 L \nJ lE.d (5) + 2E' at z \n0 2CH L 7T H2 lE_ 0 ~f(t) + 2 ElL rt at (6) \n0 \nwhere \nIt L \nf (t) 0 J dz \nL lt-T(z) 0 (7) \nL \n1 J p dz s p p =-L s (8) \n0 \nt in (6) is the injection time prior to shut-in and P \niR (8) is the wellbore pressure. S is defined as the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892c4a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 2, "chroma:document": "L \n1 J p dz s p p =-L s (8) \n0 \nt in (6) is the injection time prior to shut-in and P \niR (8) is the wellbore pressure. S is defined as the \nratio of the average pressure to th~ wellbore pressure \nand is given by Eq. 13 of Appendix A and shown in \nFig. 2. f(t) is the average over the length of the \ninverse-root of the fracture's age. Combining (6), \n(7), and (8) gives \ndP = \ndt CH E' 4 p f (t) \n7T H2S It s 0 (9) \nThe pressure decline function, f, in (7) can be \nevaluated by an upper and lower bound. These bounds \ncome from Ref. 4 for the time of fracture creation, \nT(z), and require the assumptions that the height, \ninjection rate and the injected fluid are constant, and \nthat the fracture propagates continously during pumping \n(i.e., no flow restrictions such as a screen-out). The \nlower bound on the rate of fracture extension is for \nthe fluid-loss dominated case and assumes that the \nfirst term on the right-hand side of (1) dominates the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892c90-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 2, "chroma:document": "the fluid-loss dominated case and assumes that the \nfirst term on the right-hand side of (1) dominates the \nsecond term to the extent that the second term, for \nfluid storage, can be neglected. As shown in Ref. 4, \nthis assumption yields \nz(t) = L (t/t )1/2 \n0 (10) \nor \nt(z) = t (z/1)2 \n0 \nwhere z is the length at time t. The upper bound on \nthe rate of fracture extension is for the minimal fluid \nloss case and assumes the A term of .(1) can be neglect\u00ad\nted. For this case4 the equivalent exponent of time in \n(10) would be 4/5 for a Newtonian fluid. However, an \nequivalent result for a power-law fluid can be obtained. \nIntegrating (5), with respect to time and neglecting A, \nyields Q~ to be proportional to pL; and (9) of Appendix \nA gives pL to be proportional to L raised to the \nl+l/(2n+2) power, with n being the power-law fluid \nfor which C, H , H, and E' are assumed to be effective- exponent. Combining these two proportionalities yields \nly constant do~ the fracture."}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 2, "chroma:document": "for which C, H , H, and E' are assumed to be effective- exponent. Combining these two proportionalities yields \nly constant do~ the fracture. \nFurther assuming that the fracture is shut-in \n(i.e., Q(O) = 0) and free extension of the tip after \nshut-in has ceased (i.e., Q(L) = 0), and replacing the \nabove integrals by their average values over the length \n(5) can be expressed as 2n+2 \nz(t) = L (t/t )2n+3 \n0 (11) \nSince the exponent in (11) is less than unity for \nany positive value of n, a more conservative upper \nbound than (11) is 3 Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 3, "chroma:document": "4 DETERMINATION OF FRACTURE PARAMETERS FROM FRACTURING PRESSURE DECLINE SPE 8341 \nz (t) \nor \n-c (z) L t/t \n0 \nt z/L \n0 (12) \nas shown in Figure 5. This figure also shows that (10) \nand (12) give, respectively, lower and upper bounds for \nthe actual value of -c(z). These bounds can be used for \n-c(z) in (7) to bound the value of the integral which \ndefines f(t). It can be shown that using (10) and \n(11), respectively to evaluate (7) gives \n2 (ll+~t/t -/trtTt) 0 0 (13) \n. -1 -1/2 sin [(1-~t/t) ] \n0 (14) \nwhere f1 results from (12) and f2 from (10). ~t/t is \nthe dimensionless shut-in time in terms of the pum~ \ntime, t , and the time since shut-in, D.t. The total \ntime siRce pumping began is t = t + ~t. In the fol\u00ad\nlowing ~t/t will be denoted simp~y as 8. The above \nbounds for ~ are shown in Fig. 1. The bounds are \nsurprisingly close and differ by less than 10% for \nshut-in times greater than one-quarter the pumping \ntime, i.e., D.t/t > 0.25. As a result, either of the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892d80-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 3, "chroma:document": "shut-in times greater than one-quarter the pumping \ntime, i.e., D.t/t > 0.25. As a result, either of the \ntwo bounds can bg used without compromising the accu\u00ad\nracy of (9) due to the larger uncertainty in quantify\u00ad\ning the other parameters in (9). \nThe pressure difference between two shut-in times \ncan be found by integrating (9), using (13), between \nthe two times, i.e., from 80 too. This can be shown \nto give \nfor which \n0 = D.t/t \n0 \nD.P(o\n0,o) = P(o\n0) -P(o) \n4 C(o,o0) = TI\" [g(o) -g(o\n0)] \ng(o) = i [(l+o)3/2- o3/2-1] 3 (15) \n(16) \nGraphs of G(o,o ) and g(o) are shown in Figs. 3 \nand 1, respectively.0 Eq. (15), in terms of pressure \ndifferences, is more readily applied to field data than \n(9). In particular, (15) can be used in terms of curve \nmatching to determine one of the four variables; C, H , \nE', or H, if the other three can be quantified from p \nother sources. This is undertaken by plotting D.P(o\n0,o) from field data, for the 8 's corresponding to those in"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892dc6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 3, "chroma:document": "other sources. This is undertaken by plotting D.P(o\n0,o) from field data, for the 8 's corresponding to those in \nFig. 3, versus the actual ~hut-in time ~t. The field \ndata is plotted on the same log-log scale as Fig. 3, \nand then Fig. 3 is overlain the field data with the \nvertical axis of Fig. 3, for 8 = 1, aligning with t , \nthe pump time, of the field data. Then the val~e o~ ~p \nfrom the field data which corresponds to G(o,o\n0)=1 of \nFig. 3, is the match pressure and is equal to \n* p (17) \nThe curve-matching procedure is demonstrated in \nthe Applications Section. From this curve-matching \nprocedure, the determined value of P* is equal to the \nvariable group on the right-hand side of (17). If the \nvalue of H can be inferred from well logs, E' from the \nmechanicalpproperty tests on cores, and H from post\u00ad\nfracture temperature logs or other means, this pro\u00ad\ncedure would permit determination of the fluid-loss \ncoefficient. \nc (18)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892e16-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 3, "chroma:document": "fracture temperature logs or other means, this pro\u00ad\ncedure would permit determination of the fluid-loss \ncoefficient. \nc (18) \nIt is important to note that this expression for deter~ \nmining the fluid-loss coefficient is independent of the \nfracture length or the constant injection rate while \npumping. \nBefore leaving this section, the variation of \nwellbore pressure with respect to time during pumping \nwill be recorded for a power-law fluid. The relation\u00ad\nships for a Newtonian fluid were given in Ref. 4. \nCombining (11) of Appendix A with the bounds in (10) \nand (11) yields the following proportionalities for the \nexponent of time, \n1 \nP(t) a t2(2n+2) high fluid loss (19) \n1 \nP(t) a t2n+3 low fluid loss (20) \nfor the bounds on the rate of pressure increase. \nFracture Length and Fluid Efficiency: Approximations \nof the fracture length and fluid efficiency can be \nobtained from relationships derived in the previous \nsections. Integrating (5) with respect to time over"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892e66-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 3, "chroma:document": "obtained from relationships derived in the previous \nsections. Integrating (5) with respect to time over \nthe time of injection (i.e., 0 tot) and using (8) \nyields 0 \nQt \n0 t z ( t) \n2CHP J J \n0 0 \n2 + .!_ H L S p 2 E' p dz dt \nlt--c (z) \n(21) Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892eb6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 4, "chroma:document": "., SPE 8J41 K. G. NOLTE \nIn (21), the terms can be identified as the fluid \n~olume injected which is equal to the sum of the fluid \n~olume lost to the formation and the fluid volume \noccupying the fracture. Utilizing the bounds on frac\u00ad\nture growth rate and the corresponding bounds for T(z) \nin (10) and (12), the integral term in (1), whi.ch is 11Discussion of Applications11), then (25) would depend \nonly on the fluid-loss coefficient, the ISIP and the \nrate of pressure decline at some time after shut-in. \nthe volume of fluid lost, v1, can be shown to be bounded \nby The pressure decline ratio, pin (26), can be \nexpressed also in terms of the decline pressure differ\u00ad\nence defined in (15). It can be shown that combining \n(9), (15), and (26) gives \nrrCH L /t > V > ~ CH L /t p o L 3 p o (22) \nThe upper bound for V in (22), which results from \n(10), will be used in the rollowing in order to provide \nmore conservative estimates on the fracture length and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892f06-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 4, "chroma:document": "(10), will be used in the rollowing in order to provide \nmore conservative estimates on the fracture length and \nfluid efficiency than would result from the lower \nbound. As a result (21) can be expressed as \nQt \n0 (23) \nIn (23) L represents the total length of both \nwings of the fracture since Q represents the total \ninjection rate into both wings. Also, the subscript, \np, on S indicates that the appropriate condition to \nevaluate S is for pumping, which is given by Eq. 13 of \nApp. A and shown on Fig. 2. Solving for L from (23) \nyields \nL Q t \n0 (24) p (27) \nwhere P is the ISIP pressure above closure pressure and \n6P(8 ,8) is the difference in the decline pressure \nbetwgen times 8 and o. The pressure terms in (26) and \n(27) are illust~ated in Fig. 4. \nThe fluid efficiency, defined as the ratio of the \nvolume of fluid (i.e., slurry) in the fracture at shut\u00ad\nin to the volume pumped, can be obtained in a similar \nmanner as (25) by the previous identification of the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892f56-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 4, "chroma:document": "in to the volume pumped, can be obtained in a similar \nmanner as (25) by the previous identification of the \nterms in (21). However, more directly, noting that the \nterm in parentheses of the denominator of (25) relates \nto the total volume pumped and that the last term in \nthe parentheses is the proportion left in the fracture \n(denoted as p) it follows that the efficiency is \neff __ P_ = __ 1_-:-\n1 + p 1 + 1/p \nRearranging (28) yields \neff \nP = 1 -eff (28) \n(29) \nThe dependence of L on fracture height and forma- and \ntion modulus can be eliminated by using (9). Combining \nthis equation with the last term in the denominator of 1 + p 1 (30) (24) yields \nL \nor \nL \np 2CH f (8) S P \nrr[CH /t + p p ] \np 0 \n1T s It dP I d t s 0 \nQ t \n0 \nrrCH It (1 +p) p 0 \nS P/t \n2f(8) ~ dP/~t \ns (25) \n(26) \nin which f(8) can be selected as (14) to be consistent \nwith the bound used in (23), and is evaluated for some \nselected shut-in time, 8; dP/dt is the wellbore pres\u00ad"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892fa6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 4, "chroma:document": "with the bound used in (23), and is evaluated for some \nselected shut-in time, 8; dP/dt is the wellbore pres\u00ad\nsure decline rate at 8; and P is the instantaneous \nshut-in pressure (ISIP) above the formation closure \npressure. Assuming that the height over which fluid \nloss will occur, H , can be selected from well logs \n(e.g., net sectionpof sand) and the closure pressure \ncan be determined (e.g., as discussed in the section 1 -eff \nCombining (25) and (30) yields \nQt\n0(1 -eff) \nL (31) \nrrCH It p 0 \nfor the fracture length in terms of the fluid effi\u00ad\nciency and loss coefficient. \nFracture Width and Closure Time: From the expressions \nin previous sections, the average and maximum fracture \nwidths, and the time for the fracture to close can be \nfound. The volume of a fracture is \n(32) \nwhere w is the average width over the fracture length \nand height. Using the definition of S from Appendix A \nas the ratio of the average pressure over the fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b892ff6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 4, "chroma:document": "and height. Using the definition of S from Appendix A \nas the ratio of the average pressure over the fracture \nto the pressure at the wellbore (pressures referenced \nto the closure pressure) it follows that S also relates \nthe ratio of average width to maximum width. In addi\u00ad\ntion, the average width, w, over the height at a given \nfracture location is rr/4 times the maximum width.2 5 Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893046-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 5, "chroma:document": "6 DETERMINATION OF FRACTURE PARAMETERS FROM FRACTURING PRESSURE DECLINE SPE 8341 \nAs a result, the average width, w, is related to the \nmaximum width at the wellbore, W, by \n7T ss W: shut-in w = 4 (33) \n7T \nsP W: pumping w = 4 (34) \nDuring the period of shut-in, w is essentially constant \nand (33) and (34) relate the change of W during this \nshort period before to after shut-in. From the defini\u00ad\ntion of fluid efficiency \n(35) \nCombining (32) and (35), and substituting into (25) \ngives \nw = TICH it (1 + p) (eff)/H (36) p 0 \nand substituting (28) yields, at the end of pumping, \nw = 7TC1 It p \n0 \nC' = CH /H p (37) \nin which C' is the average fluid loss coefficient with \nrespect to the total fracture height, and p is the \ndecline pressure ratio given in. (26) or (27). \nFrom (34), the maximum width at the wellbore, at \nthe end of pumping, is \n4 w w = -;s \np \nwith w given by (37). (38) \nThe time for a fracture to close after shut-in is \ngiven in Appendix B and is found by integrating (9)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89308c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 5, "chroma:document": "4 w w = -;s \np \nwith w given by (37). (38) \nThe time for a fracture to close after shut-in is \ngiven in Appendix B and is found by integrating (9) \nfrom shut-in to the time to close using f1 (~t/t ) of \n(13). As a result, the following express~on is0deter\u00ad\nmined in Appendix B, \ng (!J.t/t ) = ---'w-'----\n0 2C' /t (39) \n0 \nwhere the time to close, !J.t, is the value of g(!J.t/t ), \ndefined in (16), which equals the right-hand side o~ \n(39). This expression assumes that the average width \nand average fluid loss coefficient can be estimated \nthrough the fracture design process. \nAnother expression for closure time can be obtained \nfrom pressure decline data shortly after the fracture \ntreatment which would be useful for estimating the \nadditional time for the fracture to close. This expres\u00ad\nsion is obtained by combining (37) and (39). \ng(!J.t/t ) = _:~!\u00a3_ \n0 2 (40) This expression depends only on the pressure decline \nratio given in (26) or (27)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8930dc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 5, "chroma:document": "g(!J.t/t ) = _:~!\u00a3_ \n0 2 (40) This expression depends only on the pressure decline \nratio given in (26) or (27). \nUsing symbolic notation, in terms of the inverse \nfunction of g, i.e., g-1, (39) and (40) can be rewritten \nfor the dimensionless closure time as \nt:.t/t \n0 \nt:.t/t \n0 \nAPPLICATIONS g-1 [ w ] \n2C'/t \n0 (41) \nIn this section the expressions derived previously \nwill be applied to fracturing pressure decline data for \ntreatments of three wells. More specific information \non the treatments is given in Table I. \nCase 1: This was a calibration treatment of 500 \nbbls in the Muddy J sand of the Denver Basin. The \ncalibration treatment was pumped without proppant to \ndetermine information on the tendency of fracture \nheight to increase with respect to volume and pressure, \nand on fluid-loss behavior of the zone. The treatment \nconsisted of polymer-emulsion fluid consisting of two\u00ad\nthirds condensate and one-third water with 50 lbs of \npolymer per 1000 gals."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89312c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 5, "chroma:document": "consisted of polymer-emulsion fluid consisting of two\u00ad\nthirds condensate and one-third water with 50 lbs of \npolymer per 1000 gals. \nFigure 6 shows the SP log from which a fluid-loss \nheight of 32 feet over the height of the fracture was \nestimated, and the post-fracture temperature log from \nwhich a fracture height of 60 ft. was estimated. \nFigure 7 shows a \"pump-in/flow-back\" determination of \nclosure pressure (discussed in next section) and the \nsurface pressure decline, after shut-in. The left-hand \nside of Fig. 8 shows a pressure difference plot con\u00ad\nstructed from the decline data and compatible with \nEq. 15 and Fig. 3. The right-hand side of Figure 8 \nshows a \"curve match\" of the master curves, Fig. 3, \nwith the field data from which a P~\\' value of 350 psi \nwas.obtained. The master curves are shown as dashed \nlines in Fig. 8. A discussion of the \"curve match\" \ninterpretation will be given in a later section. Using \nthe data from Table 1 and Eq. 18, the fluid-loss"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89317c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 5, "chroma:document": "interpretation will be given in a later section. Using \nthe data from Table 1 and Eq. 18, the fluid-loss \ncoefficient is estimated to be \nc \nE'H /t p 0 .00053 ft/lmin \nFrom Fig. 7, the instantaneous shut-in pressure above \nclosure pressure and the pressure decline difference \nbetween o=.S and 1.0 can be obtained as 800 and 210 \npsi, respectively. From Fig. 3, the value of \nG(.S,l.)=O.S9, and from Fig. 2 the S /S ratio is \nobtained as .88 for estimated valuespofsn=.75 and \na=l.O. Using the above data and Eq. 27, the pressure \ndecline ratio is \np 0.98 \nFrom Eq. 28, the fluid efficiency is \neff = 0.49 Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8931cc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 6, "chroma:document": "0 SPE 8341 K. G. NOLTE \nFrom the data above and Table I, the fracture length \n(tip to tip) can be estimated from Eq. 25 as \nL = 2700 ft \nFor Eq. 25, the injected volume, Qt , must be converted \nto ft.3 fo~ compatibility of units Rsed above and in \nTable I. Eq. 37 can be used to estimate the average \nwidth across the height and length from the above data, \nand yields \nw = 0.0094 ft 0.11 inch can be estimated. Forming a ratio of P<'~, Hz, and \n~ for the two cases gives \n0 \n(25'300 =.; 250150 = \u202263 \nH1 = .sox H2 = .80 x 150 120 ft \nfor the fracture height at the time of the pad shut-in \nThe maximum width can be found from w and Eq. 34 and is and indicates the fracture height changed very little \nW = 0.24 inch \nThe dimensionless time for the fracture to close is \ngiven by Eq. 41 and for p=0.98 is \n-1 0 = g (1.54) = 1.6 \n6t = ~ t = 1.6 X 100 \n0 160 min. \nwhere Fig. 1 can be used to evaluate g-1\u2022 The actual \nclosure time from Fig. 7 was 150 min. This is the only"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893212-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 6, "chroma:document": "6t = ~ t = 1.6 X 100 \n0 160 min. \nwhere Fig. 1 can be used to evaluate g-1\u2022 The actual \nclosure time from Fig. 7 was 150 min. This is the only \nparameter of those determined above which can be check\u00ad\ned with data. \nCase 2: This treatment consisted of 700,000 lbs \nof 20/40 sand and 300,000 gals of a cross-linked, \nwater-base fluid with 40 to 60 lb/1000 gals of polymer \nand a 5% hydrocarbon phase to reduce leakoff. The \ntreatment was stopped after 30,000 gals for about \n80 min. The data used in the following calculations \nneglects this first part of the treatment. The zone \ntreated was the same as for Case 1. A fluid-loss \nheight of 70 ft and fracture height of 150 ft were \nestimated from the appropriate logs for the treatment. \nThe surface pressure decline data is shown in Fig. 9 as \nis the pressure-difference \"curve match\". The master \ncurves are shown as dashed lines. Using the same \nequations as in Case 1, the following parameters are \nestimated for this treatment. \nP* = 300 psi"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893262-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 6, "chroma:document": "curves are shown as dashed lines. Using the same \nequations as in Case 1, the following parameters are \nestimated for this treatment. \nP* = 300 psi \nC = .00076 ft/lmin \np = 2.4 \neff = 0.59 \nL = 4600 ft \nw 0.43 in \nW = 0.86 in \n0 = 5.5; 6t = oto \n6t = 5.5 x 250 = 1380 min = 23 hrs \nThe well was flowed back before closure and, therefore, \nthe 23-hour closure estimate cannot be compared with \nactual data for this case. \nAs stated above, this treatment was stopped during \nthe pad, i.e., shut-in, after 30,000 gals and a pump \ntime of 25 minutes. An analysis of the decline data \n(not given here) after the pad shut-in gave a P* value \nof 150 psi. Using Eq. 17, and assuming that all param\u00ad\neters, except the pump time, t , and the height are the \nsame for the pad shut-in and tRe shut-in after the \ntreatment, the height at the time of the pad shut-in during the major portion of the treatment. \nCase 3: the final example uses data on pressure \ndecline reported by Novotny.5 The reported data is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8932b2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 6, "chroma:document": "Case 3: the final example uses data on pressure \ndecline reported by Novotny.5 The reported data is \nsummarized in Table 1. This treatment was 400 bbl of a \npolymer-emulsion fluid. From the decline data in this \nreference, a rate of decline of dP/dt=4.5 psi/min is \ninferred at a shut-in time of 40 minutes (i.e., o=l for \na 40-minute pump time). Equation 9 will be used to \nestimate the fluid-loss coefficient with a value of \nf(o=l)=0.78 from Fig. 1 and a B value from Fig. 2 of \n0.67 (assuming values of a=.75 ~nd n=.75). This equa\u00ad\ntion gives \nc nH2B s rt:\" dP \n4H Ef(o) dt = 0.00035 \np \nFrom the referenced decline data, an inferred value of \ninstantaneous shut-in pressure above closure pressure \nof P=780 psi is obtained, and from Fig. 2 a B /Bs \nvalue of 0.88. Using the above data, the pregsure \ndecline ratio is \n2B P/t \nP = f ( 0 ) n B P dP I~ t = 1. 8 7 \ns \nThe fluid efficiency, from Eq. 28 is \neff _P_ = .65 \n1 + p \nand estimating the length from Eq. 31 gives \nL Qt\n0(1-eff)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893302-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 6, "chroma:document": "s \nThe fluid efficiency, from Eq. 28 is \neff _P_ = .65 \n1 + p \nand estimating the length from Eq. 31 gives \nL Qt\n0(1-eff) \nnCH It p 0 5600 ft \nThe average width, over the height and length, and \nmaximum width at the wellbore, obtained from Eqs. 37 \nand 38, are \nw .0043 ft = 0.052 inch \nw 0.11 inch 7 Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "8 DETERMINATION OF FRACTURE PARAMETERS FROM FRACTURING PRESSURE DECLINE SPE 8341 \nThe time for the fracture to close is obtained from \nEq. 36 and Fig. 1 as \n6t = at = 4.0 X 40 = 160 min. \n0 \nThe estimated closure time of 160 min. and fluid effi~ \nciency are in reasonable agreement with that obtained \nfrom the referenced data. However, the above length is \nsignificantly greater and the above width is signifi\u00ad\ncantly less than those esimated in the cited reference. \nThese values can be brought in closer agreement by \nreducing the modulus for the referenced data from 107 \nto 6 x 106 psi, (i.e., similar to the value for the \nprevious cases). For the reduced modulus, the above \nparameters which would change and their resulting \nvalues are listed below \nc = .00055 ft/lmin \nL = 3400 ft -w = .087 in \nw = 0.18 in \nFor the reduced modulus, the above value of W is in \nreasonable agreement to the referenced value of 0.21. \nHowever, the referenced value of L=852 ft. is still"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893398-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "reasonable agreement to the referenced value of 0.21. \nHowever, the referenced value of L=852 ft. is still \nsigni~icantly different than the above value. It is \nnoted that the referenced values of fluid pumped, \nefficiency, and wellbore width are not consistent with \nthe referenced value of height. \nDISCUSSION OF APPLICATIONS \nThe \"curve match\" for Case 1, shown in Fig. 8, \nindicates that the data curve for 8=.25 is larger than \nthe theoretical pressure difference curve for 8=.25. \nThis indicates that the average rate of pressure \ndecline between 8=.25 and subsequent times is greater \nthan predicted by fluid loss to the formation alone. \nAn expianation is that the fracture is still extending \nafter time 8=.25. This explanation is supported by a \nnumerical simulator for fractures (similar to that \ndiscussed in Ref. 4) which has been extended to include \nfracture closure as well as extension. The continued \nextension for some time after shut-in is contrary to"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8933e8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "fracture closure as well as extension. The continued \nextension for some time after shut-in is contrary to \nthe assumption used to derive the expressions in this \npaper. However, the assumption of extension stopping \nat shut-in provides conservative estimates in that the \ndetermined fluid-loss coefficient will be greater and \nthe length less than in reality. This follows because \ncontinued extension creates larger rates of pressure \ndecline (proportional to estimated value of C) than for \nno extension, because the increased length reduces the \naverage fracture width (for a fixed volume of fluid) \nand thus reduces the pressure. Also, the additional \nextension creates new fracture area (i.e., fluid-loss \narea) not accounted for by the analysis which assumes \nno extension after shut-in. \nOther possible deviations from the assumptions, \nwhich would lead to conservative estimates of the \nfluid-loss coefficient and length, are interference"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893438-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "which would lead to conservative estimates of the \nfluid-loss coefficient and length, are interference \nfrom proppant and variable fracture height. If the \nfracture height is not essentially constant, it will \ntend to decrease away from the wellbore. This follows \nbecause the pressure decreases toward the tip as a \nresult of the pressure gradient required to maintain \nfluid flow; and since an increase in fracture height \nmost likely results from an increase in pressure, the \nfracture height will tend to decrease toward the tip. Therefore, the average fracture height will most likely \nbe equal to or less than that determined at the well\u00ad\nbore. The effect of proppant on fracture closure is to \nmake the system effectively stiffer which is equivalent \nto increasing the formation modulus. Either a stiffer \nfracture system than would actually occur without \nproppant, or a smaller than estimated average-fracture\u00ad\nheight would increase the pressure decline rate and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89349c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "proppant, or a smaller than estimated average-fracture\u00ad\nheight would increase the pressure decline rate and \nlead to estimating a larger than actual fluid-loss \ncoefficient. Since the effect of proppant is to \nincrease the decline rate, an indication of the effect \nof proppant on the match curves would be for the data \nvalues to deviate toward larger values than indicated \nby the theoretical curves. \nThe match curves in Fig. 8 also show that all the \ndata curves, except 8=.25, tail off to lower values \nthan the theoretical curves for times greater than 125 \nminutes. This indicates that the rate of fluid loss \nafter 125 minutes is less than predicted. An inter\u00ad\npretation of this observation is that for times greater \nthan 125 minutes the fracture walls are closing to\u00ad\ngether from the tip toward the wellbore, since there \nwas no proppant in this case. The closing of the \nunpropped fracture reduces the area for fluid loss in \nthe relatively high loss area of the tip and conse\u00ad"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8934ec-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "unpropped fracture reduces the area for fluid loss in \nthe relatively high loss area of the tip and conse\u00ad\nquently reduces the net rate of loss and pressure \ndecline. \nThe match curves for Case 2 also indicate fracture \nextension after 8=.25, or 63 minutes, but none after \no~0.5, or 125 minutes. The curves for this case do not \ntail-off to the same degree as for Case 1. \nFor Cases 1 and 2, a fracture closure pressure is \nrequired to determine the net fracture pressure above \nclosure, denoted by P. The closure pressures were \ndetermined for these cases by a procedure prior to the \ntreatments which consists of creating a fracture with a \nrelatively small amount of fluid and flowing the fluid \nback out of the fracture at a controlled rate through a \nchoke. The decline curve for the flow-back stage \n(e.g., Fig. 7) shows a recognizable dogleg of an in\u00ad\ncrease rate of decline at the closure pressure due to \nthe restriction to flow out of the fracture introduced"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89353c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "crease rate of decline at the closure pressure due to \nthe restriction to flow out of the fracture introduced \nas the fracture closes at the wellbore. \nSUMMARY OF APPLICATIONS \n1. The example cases given in this paper illustrate \nthat the parameters which describe the geometry of \na fracture can be obtained simply and directly \nfrom the pressure decline data after a treatment. \n2. Using the parameters determined from an actual or \ncalibration treatment (e.g., Case 1) improved \ndesigns can be achieved for future treatment in a \ngiven pay zone. \n3. In particular, the\"fluid-loss coefficient should \nbe similar for all treatments of a given zone for \nsimilar fluids. As a result, using a \"calibrated\" \nfluid-loss coefficient and using decline data from \nsubsequent treatments, the fracture height or the \nformation modulus, and the fracture length can be \nestimated for these treatments. \n4. The decline pressure ratio, p, obtained from \ndecline data only, provides estimates of the fluid"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89358c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 7, "chroma:document": "estimated for these treatments. \n4. The decline pressure ratio, p, obtained from \ndecline data only, provides estimates of the fluid \nefficiency and fracture closure time. \n5. The only direct check on the accuracy of the \nestimates provided by this analysis is the time \nfor the fracture to close. In the two cases where Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8935dc-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 8, "chroma:document": "SPE 8341 K. G. NOLTE 9 \nclosure time data exis.ted, the predicted time Wq1;1. \nin good agreement with the data. \nNOMENCLATURE \nA = cross-sectional area of fracture \nC = fluid-loss coefficient \nE' = plane strain modulus \n= E/(l-v2) \nE =Young's Modulus \neff = fluid efficiency \nf(o) =dimensionless pressure decline function, Eq. 7. \nG(o,o\n0) = dimensionless pressure \ndifference function, Eq. 16. \ng(o) = avg. decline rate function, Eq. 16. \nH = fracture height \nH = fluid-loss height p \nL = fracture length \nP = fracture pressure, above closure pressure, \nat wellbore and at shut-in \nP* =match pressure, Eq. 17. \n6P(o\n0,o) = pressure decline difference \ndP/dt = pressure decline rate \np = pressure at some point in fracture. \np = average pressure over length of fracture. \nQ = pump rate. \nt = time variable. \nt\n0 = pump time. \n6t = time since shut-in. \nw = maximum fracture width \nw = maximum fracture width \nin the fracture. \n-at \nat \nw = average width over height well bore. \nsome point"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89362c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 8, "chroma:document": "w = maximum fracture width \nw = maximum fracture width \nin the fracture. \n-at \nat \nw = average width over height well bore. \nsome point \nand length. \nz = distance v~riable down fracture. \na = denotes proportionality \nS = ratio of average and wellbore pressure. \nsp = value of s while pumping. \nSs = value of S while shut-in. \no = dimensionless shut~in time = 6t/t \n0 \n8\n0 = reference shut-in time for pressure \ndifferences. \nA = fluid loss per unit fracture length. \nv =Poisson's ratio. \nT = time of local fracture creation. \n!REFERENCES \n1. Khristianovic, S. A. and Zheltov, Y. P., \"Forma\u00ad\ntion of Vertical Fractures by Means of Highly \nViscous Liquid,\" Proc. Fourth World Pet. Gong., \n\u00b7Rome (1955). 2. \n3. \n4. \n5. \n6. Perkins, T. K., and Kern, L. R., \"Widths of \nHydraulic Fractures,\" J. Pet. Tech. (Sept., 1961). \nNolte, K. G., and Smith, M. B., \"Interpretation of \nFracturing Pressures,\" 54th Annual Tech. Con\u00a3. and \nExhib., Las Vegas (Sept., 1979). \nNordgren, R. P., \"Propagation of a Vertical"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89367c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 8, "chroma:document": "Fracturing Pressures,\" 54th Annual Tech. Con\u00a3. and \nExhib., Las Vegas (Sept., 1979). \nNordgren, R. P., \"Propagation of a Vertical \nHydraulic Fracture, ll Soc. Pet. Eng. Jour. (August, \n1972). \nNovotny, E. J., \"Proppant Transport,\" 52nd Annual \nTech. Conf. and Exhib., Denver (October, 1977). \nDobkins, T. A., \"Methods to Better Determine \nHydraulic Fracture Height,\" 54th Annual Tech. \nCon\u00a3. and Exhib., Las Vegas (Sept., 1979). \nAPPENDIX A \nFluid Flow in a Vertical Fracture \nIn the following, the power-law flow model will be \na.ssumed to represent the flow behavior of a fracturing \nfluid over the range of conditions generally encount\u00ad\nered in fracturing applications. The parameters for \nthis model, as used \u00b7in the following, are \nShear stress = k(shear rate)n \nFor this assumption, the pressure gradient2 is \n~ \ndz n \n=2k~ 2n+l w \nm = (2n+l)/n (1) \nfor flow of q (volumetric flow rate per unit height) \nbetween walls separated by the width w. The total flow"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8936c2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 8, "chroma:document": "~ \ndz n \n=2k~ 2n+l w \nm = (2n+l)/n (1) \nfor flow of q (volumetric flow rate per unit height) \nbetween walls separated by the width w. The total flow \nrate, Q, down both wings of the fracture is twice the \nrate down either wing and is found by rearranging (1) \nand integrating over the cross section. \nH/2 1/n Jq 1 Cdp L) Q = 2 dy = -m dz 2k \n-H/2 \nH/2 \nX J wm dy \n-H/2 \nor \n1/n \nQ = cL dp) Hifl cp (n) \n2k dz m (2) \nwhere \n1/2 m \n<j>(n) = J c~r d (Y) w H (3) \n-1/2 \nm = (2n+l)/n Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893712-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 9, "chroma:document": "10. DETERMINATION OF FRACT'ORE PARAMETERS FROM FRACTURING PRESSURE DECLINE SPE 8341 \nand W is the maximum cross-sectional width. In (2) the Also from (8), the pressure at the wellbore is \nassumptions were made that k and n are constant across \nthe section and that dp/dz is also constant across the \nsection, i.e., one-dimensional flow. Rearranging (2) \nyields the proportionality \ndp = Mk~t ~ \ndz HnW2n+l a w2n+l \nn \nM = 2 (<P (:)) m (2n+l) /n (4) 1 \np (11) \nForming the ratio of p, from (9), to the pressure at \nthe wellbore, P from (11), gives \np/P = ___ 1 ___ = 2n+2 = 8 (e+l) 2n+bn+a+3 \np = 8P (12) \nfor the pressure gradient down a constant height frac- Without a detailed discussion, it has been found from \nture. If the fracture responds elastically to internal a numerical fracture simulator (similar to that \npressure discussed in Ref. 4) that the appropriate approxima\u00ad\ntions for flow rate in (7) or (12) are \np sw (5) \nwhere Sis the fracture stiffness (i.e., S = E'/2H for"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893762-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 9, "chroma:document": "tions for flow rate in (7) or (12) are \np sw (5) \nwhere Sis the fracture stiffness (i.e., S = E'/2H for \na constant-height fracture in a homogeneous, infinite, \nelastic medium), (4) and (5) yield \np2n+l dp a kQn dz (6) \nfor which the fracture stiffness is assumed to be \nconstant. For the assumption of a homogeneous elastic \nmedium, the fracture cross section is elliptical2 with \na minor axis of W and a major axis of H. For this case \na numerical integration for <P(n) and M defined in (3) \nand (4) is possible and is shown graphically in \nFig. 10. \nAssuming k and Q have the exponential relation\u00ad\nships \nk k (2z/L) a \n0 (7) \nQ Q (2z/L)b \n0 \nalong the fracture, and integrating (6) from the tip \n(p=O, z=O) to some distance z toward the wellbore \nyields \n-(8) \nfor which n was assumed effectively to be constant. \nThe average value of p, along the length L of the \nfracture, from (8) is \nL \np = f J p (z) dz \n0 \n(e+l) \ne = (a+bn+l)/(2n+2) (9) \n(10) b = 0 shut-in \nss 2n+2 \n2n+3+a \n(13)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8937b2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 9, "chroma:document": "fracture, from (8) is \nL \np = f J p (z) dz \n0 \n(e+l) \ne = (a+bn+l)/(2n+2) (9) \n(10) b = 0 shut-in \nss 2n+2 \n2n+3+a \n(13) \nb = 1 pumping \nsP 2n+2 \n3n+3+a \nimplying a nearly constant flow rate, greater than \nzero, down the fracture for shut-in even though the \nflow rate is zero at the wellbore and fracture tip; \nand a linearly varying flow rate while pumping of Q \nat the wellbore to essentially zero at the fracture0 \ntip. From (7) the variation of k, or equivalently \nthe viscosity, can be represented as \na = 0 constant viscosity \na = 1 medium degradation (14) \na = 2 strong degradation \nwhere \"a\" reflects the \"order of magnitude\" decrease \nin fluid viscosity down the fracture due to tempera\u00ad\nture, shear and time degradation of fluid system. \nThe ratio of 8 for pumping, 8 , to that for \nshut-in, 8 , is found from (13) asp s \n8 _E.. = 2n+3+a = 1 _ n \n8s 3n+3+a 3n+3+a (15) \nFor the sake of completeness, the actual equality for \n(11) is \n1 \n{ s2n+l k Qn 1} 2n+2 \np(L) M' o 0 (16)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893802-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 9, "chroma:document": "8s 3n+3+a 3n+3+a (15) \nFor the sake of completeness, the actual equality for \n(11) is \n1 \n{ s2n+l k Qn 1} 2n+2 \np(L) M' o 0 (16) \n(a+bn+l) Hn \nwhere \n1 \nM' [ (2n+2)M] 2n+Z Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893852-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 10, "chroma:document": "SPE 8341 K. G. NOLTE \nwith M defined in (4). By using the relationship for \nM in terms of n in Fig. 10, it can be shown, surpris\u00ad\ningly, that M' in (16) is essentially independent of \nnand is equal to 2.53 \u00b1 0.5% over the range of n=0.4 \nto 1.0. In (16), Q is the total flow rate into both \nfracture wings, L i~ the length of a fracture wing, \nand Sis defined by (5). \nAPPENDIX B \nTime for Fracture to Close \nThe time for a fracture to close can be found \nfrom Eq. 9 of the text. Rewriting this equation\u00b7 \nresults in \n2H dP 8CHP f(t) \nE' dt = \nTIH S /t s 0 (1) \nand integrating over the shut-in time 6t (time for \npressure to go to zero) gives \n2H p \nE' (2) \nwhere P is the pressure at shut-in. Noting that the left-hand side of (2) is the maximum width W at the \nwellbore,2 and rewriting yields \n0 \nC' 6t/t \n0 f t CL.lt/t ) d6t = ci ws ) -1-\u00ad\no to s 2C'/t \n0 (3) \nThe integral can be shown to be equal to g(6t/t ) \ngiven in (16) of the text, if (13) of the text ~s"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8938a2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 10, "chroma:document": "o to s 2C'/t \n0 (3) \nThe integral can be shown to be equal to g(6t/t ) \ngiven in (16) of the text, if (13) of the text ~s \nused for f. C' is the average fluid-loss coefficient \nover the fracture height, and using (33), the term in \nparentheses on the right-hand side can b~ expressed \nin terms of the average fracture width, w, at shut\u00ad\nin. Therefore, (3) can be rewritten as \ng(6t/t ) \n0 = __ w __ \n2C'/t \n0 (4) \nTable 1 \nData for Example Well Analysis \nCase 1 Case 2 Case 3 (Ref. 5) \nTreatment Vol. (bbl) 500 6,400 400 \nTreatment Rate (BPM) 5 30 10 \nTreatment Time (min.) 100 250 40 \nFluid Type Poly. -Em. Cross-Lk. Poly. -Em. \nReservoir Depth (ft.) ?,900 8,000 10,000 \nTemperature (\u00b0F) 265 265 200 \nPermeability, (md) .01 .01 1.0 \nFracture Height (ft.) 60 150 60 \nFluid-Loss Height (ft.) 32 70 20 \nFormation Modulus (106 psi) 5 6 10 \nTime to Close (min.) 150 130"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8938f2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 10, "chroma:document": "Fracture Height (ft.) 60 150 60 \nFluid-Loss Height (ft.) 32 70 20 \nFormation Modulus (106 psi) 5 6 10 \nTime to Close (min.) 150 130 \nProppant No Yes Yes 11 Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 11, "chroma:document": "4 \n3 \n\u00a7: 2 = \n1 \n0 0.25 0.5 0. 75 1.0 1.5 2.0 3.0 4.0 6.0 \n1.5 \no = ~t/t0, Dimensionless Shut-in Time \nFig. 1 -Dimensionless time function versus rlimensionless time. \n0 2 0 2 0 21.0 \n/3p f3s 0.9 0.9 \n(Pumping) (Shut-in) \n0.8 0.8 \nco.. \n0 0.7 0.7 0.7 \nG) \nf3r/f3s :I 'i > 0.6 0.6 0.6 \n0.5 0.5 0.5 \n0.4 0.4 \n0 2 0 2 0 2 \nViscosity Exponent, a \nFig. 2 -Variation of S with viscosity exponent, Eq. 7 -Appendix A. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893988-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 12, "chroma:document": "-0 \"0 .. \"0 \n(!} \n.. c \n0 ... \n(.J c \n::::J 1 LL. \nQ) .8 (.J c .6 Q) .... \nQ) = c .4 \nQ) .... \n::::J en en .2 Q) .... \nCl. 0.25 0.5 1.0 1.5 2.0 3.0 5.0 \n0 -o-\n0.25 \n0.5 \n0.75 \n1.0 \n0.25 0.5 1.0 1.5 2.0 3.0 5.0 \nDimensionless Shut-in Time, o -~t/t0 \nFig. 3 -Master curves for pressure differences. \nPressure Decline Ratio, p, Eqs.26 & 27 \n/ / \n/ \n/ \n/(Slope / \np P/t0 P Proportional to --or -\ndP/dt ~P \n-------T \n~P (8o, o) \n-~ / 1 / = Plt0 \nz ~-~ Fracture _ _ _ _ _ :\\ _ dP I Slope ~Cit Closure Pressure I \n~t 0 - = 8=0 0.5 \u2022 t0 ~~----L---~1----L---~J \n~t == 0 0.5t0 t0 I I I ~ 1.0 \n0 t0 1 .5 t0 2t0 t, time \n1~\u2022--Pumping------+--Shut-in ---\nFig. 4 -Illustration of pressure terms for decline analysis. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8939d8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 13, "chroma:document": "..J \n........ \nN 1.0 \n/% / / /Upper bound, Eq.12 \n/...,._, z/L = t/t0 / \n/ 't (z) \n~------~A~-------r Lower Upper' \nbound Actual bound \nlog t/t0 1.0 \nFig. 5 -Bounds for rate of fracture extension and time \nof fracture creation. \nSP-Log \nFluid Loss 7850 \n..... -..c: ..... c. \nQ) c Post-Fracture \nTemperature Log \n7950 *See Ref.6 \nFig. 6 -Input data for analysis of case 1. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893a28-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 14, "chroma:document": "Pressure Decline After Fracturing-\n1800 \n'iii c. \nen 1400 \n\"-::I \nCl) \nCl) \nen \n\"-1200 a. \nen \nC.) \nca -1000 \"-::I en \n800 \n600 \n0 25 11 \n~P=210 Cl) \u2022 \n': 1000 \nQ) \n\"-Pump-in/ \nFlow-back \n::::1 \nCl) \nCl) \nQ) 0:: Closure \na, Pressure \n~ 600 ~750 psi \n~ ~~~~-\n::::1 0 en 2,min. \nJf--~---\nLOj OJ ol ~ Closure ill ~~ Pressure \n50 75 100 ~ 25 150 \nTime Since Shut-In, min. \nFig. 7 -Pressure decline for case 1. \nPressure Differences for Data Match of Data and Master Curves \n..lt . '[ 8001- o 25mm. \nIll 6001-\u2022 50 \n~ c 75 \n~ 400 ~ \u2022100 ... .! \n- 0 c \n~ 200-\n:::1 \nIll \nIll \nQ) ... 1-\n~ 100 r-\n~ \n(J \nQ) 0 \n\u2022 0 0 \n0 \n0 \n0 \u2022 a \u2022 0 \na \u2022 \u2022 a \u2022 \n\u2022 \n0 \u2022 100 +a=1 \nI ~0;6; \nI 0/ /./ p. =350 o / /e /I - ---/-\"-lei-- j I /, I \n0 /1 ' 0/ ( 1 ,t 1\u2022 G(o,o0l= 1 \nI \u2022 I I \no I '! f t\u2022 I I I !. \nI I I. I \nI ,\u2022 01 I \nI I I \u2022 \nI I 1 \n100 c I I I 50 ......_--'---!..----L---'-----'----....1 \n50 75 100 150 200 50 75 100 150 200 50 \nShut-in Time , min Shut-in Time, Min."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893a78-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 14, "chroma:document": "I I 1 \n100 c I I I 50 ......_--'---!..----L---'-----'----....1 \n50 75 100 150 200 50 75 100 150 200 50 \nShut-in Time , min Shut-in Time, Min. \nFig. 8 -Match of pressure differences for case 1. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893ae6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-8341-ms.pdf", "page": 15, "chroma:document": "Match of Data and Master Curves \n1/) a= 1.0 0. \nI o} ' r.n \n~ 0~ 0 o/ /. c: 400 p\u2022 =300 ~ / / \u2022\u2022 ~ \n1/) Q; ----o /1' -;\u2022-/J- 0. -\n~\u00b7 ~ \"-' ~\u00b7 I \u2022 a 0 \"\"7~~~~~. 1 .5 ~ o r.o\"' ' /a!. G(o,o0)=1 (3 ... 1.()\u2022 \n~ :I \n0 1/) \n1/) / ~~c\u00a7'0o/ I ..... r~. \n~ 2000 ~ \n'r::!\n0/y .1 J 1 ... \nll. Y ~ ~o I :I \n1/) \n1/) \n~ ... \nll. \n~ \n0 \nca 't :I \n(/) ~ c: \"'I o. (j o\u00b7l.-\u00b71 \n~ t = 250 0 50 0 \n0 100 400 \nShut-in Time, Min. \nFig. 9 -Decline data and pressure difference match for case 2. \n10 \n8 \nc \n~ 6 \n4 \n0.4 \n0.60 \n0.58 \nc 0.56 \n-$. \n0.54 \n0.52 \n0.4 37r \n16 0.6 0.8 \n~-------\nL Value Assumed \nin Ref.2 \n0.6 0.8 \nPower Law Exponent, n 1.0 \n1.0 \nFig. 10 -Dependence of geometry variables on exponent n. Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/79SPE/All-79SPE/SPE-8341-MS/2057509/spe-8341-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893b36-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 0, "chroma:document": "SPE-187038-MS\nFracture Closure Stress: Reexamining Field and Laboratory Experiments of\nFracture Closure Using Modern Interpretation Methodologies\nD. P. Craig, DFITpro.com; R. D. Barree, Barree & Assocs. LLC; N. R. Warpinski, Retired and T. A. Blasingame,\nTexas A&M University\nCopyright 2017, Society of Petroleum Engineers\nThis paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, USA, 9-11 October 2017.\nThis paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents\nof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect\nany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893b86-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 0, "chroma:document": "consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may\nnot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.\nAbstract\nDuring the 1990s, field and laboratory experiments measured hydraulic fracture creation, propagation,\nand closure, and the archived data represent the finest collection of measurements that can be used to\nevaluate fracture models and fracture closure interpretation methodologies. None of the current fracture\nclosure interpretation methods, including G-function derivative analysis, log-log storage diagnostics, and\nthe changing-compliance method have been evaluated versus the field and laboratory measured data.\nRecent papers have proposed fracture closure pressure interpretations that differ from established\nmethodologies, and under some circumstances, will result in a closure pressure that is higher than"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893bcc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 0, "chroma:document": "methodologies, and under some circumstances, will result in a closure pressure that is higher than\ntraditionally accepted. Thus, it seems an opportune time to reexamine the field and laboratory fracture\nclosure data using interpretation methodologies developed over the last twenty years.\nAdditional issues cloud closure pressure interpretations, including different definitions of fracture closure\nused in numerous publications, like mechanical fracture closure, hydraulic fracture closure, progressive\nfracture closure, and complete fracture closure. Evidence from downhole tiltmeters and finely-instrumented\nlaboratory experiments of fracture propagation and closure all demonstrate that residual width is retained\nafter closure. Consequently, closure is somewhat of a misnomer, and if a \"closed\" fracture remains open,\nthe relationship between what we interpret as fracture closure and the minimum horizontal stress needs to\nbe clearly defined based on measurements as opposed to simulation."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893c1c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 0, "chroma:document": "be clearly defined based on measurements as opposed to simulation.\nBased on field tiltmeter deformation and pressure measurements in hard rock formations, we find that\nG-function derivative analysis and the log-log storage diagnostic plot interpretations together provide a\nfracture closure pressure that is consistent with the minimum horizontal stress identified using tiltmeter-\nmeasured rock deformation. Additionally, the closure pressure interpretations, and corresponding minimum\nhorizontal stress, are invariant over multiple injection/falloff sequences of varying volume and time.\nField experiments exhibiting variable-storage/changing-compliance signatures were also observed, and the\nchanging-compliance method interpretations of fracture closure pressure are inconsistent with tiltmeter-\nmeasured rock deformation. Finally, we find the fracture re-opening pressure identified using tiltmeter"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893c6c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 0, "chroma:document": "measured rock deformation. Finally, we find the fracture re-opening pressure identified using tiltmeter\ndeformation and the fracture closure pressure interpreted using pressure falloff data are essentially equal."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893cbc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 1, "chroma:document": "2 SPE-187038-MS\nBased on laboratory measurements of fracture closure and pressure, we find that G-function derivative\nanalysis and the log-log storage diagnostic plot together provide a fracture closure interpretation generally\nconsistent with measured fracture closure, but despite attempts to define an objective closure identification\nmethodology, fracture closure signatures are often non-distinct and interpretations are subjective. In soft\nrock reservoirs, like unconsolidated sand, the fracture closure pressure interpretation does not correspond\nto the minimum horizontal stress, but in hard rock reservoirs, the fracture closure pressure identified using\nG-function derivative analysis and log-log storage diagnostic interpretations are approximately equal to the\nimposed minimum horizontal stress.\nIntroduction\nHydraulic fracture closure has been studied for decades by researchers inside and outside of the petroleum"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893d0c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 1, "chroma:document": "Introduction\nHydraulic fracture closure has been studied for decades by researchers inside and outside of the petroleum\nindustry. Even after decades of study, opinions vary widely with respect to the fracture closure process,\nthe identification of fracture closure pressure, and the relationship between hydraulic fracture closure\npressure and the minimum horizontal stress. Hydraulic fracture closure pressure is typically inferred from\npressure data during fracture initiation, re-opening, or falloff. While we recognize small-volume stress tests,\nfracture step-rate tests, fracture-injection/flow back tests, and fracture pulse tests are all used to infer closure\npressure, we focus our study on fracture closure interpretations from the analysis of pressure and time data\nduring a fracture-injection/falloff test (DFIT).\nNumerous models and methods exist for identifying fracture closure pressure from pressure versus time"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893d52-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 1, "chroma:document": "Numerous models and methods exist for identifying fracture closure pressure from pressure versus time\ndata recorded during injection/falloff sequences. In geophysics and rock engineering, Hayashi and Haimson\n(1991) provided a summary of commonly-used methods outside of petroleum engineering, and the authors\ndescribed a fracture closure process based on observations of laboratory fracture closure experiments.\nHayashi and Haimson suggested a 3-stage fracture closure process during the shut-in period following a\nfracture inducing or dilating injection. Stage 1 of the process begins at the end of fracture-tip extension after\nshut-in and as aperture along the entire fracture half-length decreases. According to Hayashi and Haimson,\nfracture closure begins at the fracture tip, which defines Stage 2 of the closure process, and continues as the\nopen width and fracture length decrease from the fracture tip back to the wellbore. Stage 3 of the process is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893e4c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 1, "chroma:document": "open width and fracture length decrease from the fracture tip back to the wellbore. Stage 3 of the process is\ndefined by \"complete\" closure of the hydraulic fracture, where complete closure allows for the possibility of\nresidual fracture width. Hayashi and Haimson define the pressure observed at fracture-tip closure (Stage 2)\nas the minimum horizontal stress. Although Hayashi and Haimson based their model on observed field and\nlaboratory closure data, they did not present fracture dimensions during closure to validate their proposed\nfracture closure process.\nSeveral derivative works have followed from the work of Hayashi and Haimson (1991), notably Raaen,\nSkomedal, Kj\u00f8rholt, Markstead, and \u00d8kland (2001) who recognized that a change in fracture compliance\nshould be observed as fracture closure begins at the fracture tip, and suggested a fracture-injection/flow\nback test and interpretation methodology to identify closure pressure from a change in fracture compliance."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893ece-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 1, "chroma:document": "back test and interpretation methodology to identify closure pressure from a change in fracture compliance.\nMcClure, Jung, Cramer, and Sharma (2015) extended the work of Raaen et al., and using simulations\nof synthetic cases and interpretations of field data, described a changing fracture-compliance method for\nidentifying fracture closure from pressure falloff data in the absence of flow back. Recently, Zanganeh,\nClarkson, and Hawkes (2017) have suggested a fracture closure process and closure pressure identification\nanalogous to that of Hayashi and Haimson (1991). Zanganeh, Clarkson, and Hawkes also suggest that the\nfracture closure pressure corresponding to the minimum horizontal stress is observed at the start of tip\nclosure, and base their conclusions on finite-element modeling of synthetic cases and interpretations of\nfield data.\nClassical fracture closure pressure interpretation methods include plotting the shut-in pressure and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893f28-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 1, "chroma:document": "field data.\nClassical fracture closure pressure interpretation methods include plotting the shut-in pressure and\npressure derivative versus the square root of time, which have been described by Middlebrook, Aud,\nHarkrider, and Hansen (1997). Perhaps the best known fracture closure pressure interpretation methodology"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893f6e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 2, "chroma:document": "SPE-187038-MS 3\nis G-function analysis, which was initially presented by Nolte (1979), and expanded to include G-function\nderivative analysis by Castillo (1987) and Barree and Mukherjee (1996). A \"holistic\" approach to fracture\nclosure interpretation that included a square-root of time plot, G-function derivative analysis, and a log-log\nstorage diagnostic plot was also presented by Barree, Barree, and Craig (2009). We assume for the purposes\nof this research that the de facto standard for closure pressure interpretation from fracture-injection/falloff\ndata is G-function derivative analysis combined with the log-log storage diagnostic plot.\nThe G-function is defined as follows\n(1)\nwhere the dimensionless loss-volume function at the end of pumping is defined by Valk\u00f3 and Economides\n(1999) as\n(2)\nand \u03b1N is Nolte's power-model growth exponent (\u00bd \u2264 \u03b1N \u2264 1) and \u0393 is the Euler gamma function. The\ndimensionless loss-volume function is defined at any time after the end of pumping and written as"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b893fbe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 2, "chroma:document": "dimensionless loss-volume function is defined at any time after the end of pumping and written as\n(3)\nwhere F is the hypergeometric function, dimensionless time is defined as \u0394tD = (t \u2013 te)/te, and te is the time\nat the end of pumping.\nClosure Interpretation and Leakoff Types\nG-function derivative analysis requires a Cartesian plot of three curves: bottomhole pressure versus the G-\nfunction; the derivative, dp w/dG, versus the G-function, and the derivative, Gdp w/dG, versus the G-function.\nG-function derivative analysis can be used to identify hydraulic fracture closure and has been classically\nused to identify several non-ideal leakoff types, including pressure-dependent leakoff, fracture-height\nrecession/transverse or variable storage, and fracture tip extension. Examples of the leakoff types commonly\nobserved have been provided by Barree, Barree, and Craig (2009) and Craig, Eberhard, and Barree (2000)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89400e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 2, "chroma:document": "observed have been provided by Barree, Barree, and Craig (2009) and Craig, Eberhard, and Barree (2000).\nFig. 1 contains graphs of the four common leakoff types and has been updated from that of Craig, Eberhard,\nand Barree to include variable storage/changing compliance. A brief review of the classical leakoff types\nis as follows.\nNormal leakoff  behavior occurs when fracture area is constant during shut-in and leakoff is through\na homogeneous rock matrix. With G-function derivative analysis, normal leakoff is indicated by a\nconstant derivative and when the derivative Gdp w/dG lies on a straight line extending from the origin.\nFracture closure is identified when the Gdp w/dG data deviate downward from the straight line.\nPressure-dependent leakoff  from dilated fractures/fissures is indicated by a characteristic \"hump\" in\nthe Gdp w/dG derivative that lies above an extrapolated straight line from the origin through the normal"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89405e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 2, "chroma:document": "the Gdp w/dG derivative that lies above an extrapolated straight line from the origin through the normal\nleakoff data. The fissure opening pressure is identified at the end of the hump when the Gdp w/dG\nderivative data begin to follow the extrapolated straight line. A period of normal leakoff behavior\nis generally observed before fracture closure is identified when the Gdp w/dG derivative data deviate\ndownward from the extrapolated straight line.\nFracture height recession or transverse storage or variable storage or changing compliance  during\nshut-in are indicated by G-function derivative analysis when the Gdp w/dG derivative data fall below\na straight line extrapolated through the normal leakoff data. Traditionally, hydraulic fracture closure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8940ae-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 3, "chroma:document": "4 SPE-187038-MS\nis identified when the Gdp w/dG derivative data deviate downward from the straight line; however,\nMcClure, Jung, Cramer, and Sharma (2015) argue that fracture closure should be identified as the\npressure corresponding to the beginning of variable storage or changing compliance. Storage and\ncompliance are related to system stiffness by a reciprocal relationship. For example, Craig and\nBlasingame (2005, 2006) and Craig (2014) define storage during fracture propagation and closure as\n(4)\nwhere C is the storage coefficient, cw is the wellbore-fluid compressibility, cf is fracture-fluid\ncompressibility, Vw is the volume of the wellbore, Vf is the volume of one wing of the fracture, Af is\nthe area of one wing of the fracture, and Sf is the fracture stiffness, which can be written in a general\nform for 2D-analytical expressions of fracture stiffness as\n(5)\nwhere c is constant, E' is the plane-strain modulus, and Lc is a characteristic length. McClure, Jung,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8940fe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 3, "chroma:document": "(5)\nwhere c is constant, E' is the plane-strain modulus, and Lc is a characteristic length. McClure, Jung,\nCramer, and Sharma (2015) frame their discussion of closure around system stiffness, which is the\nreciprocal of storage, that is, using the definitions of storage in Eq. 4, system stiffness is defined as\n(6)\nwhere Seff is a system stiffness. In another recent work, van den Hoek (2016) frames his discussion\nof fracture closure in terms of total compliance, which using the definitions in Eq. 4, he defines as\n(7)\nwhere Ct is a system compliance and Cf is a time-dependent fracture compliance, which van den\nHoek defined as\n(8)\nwhere h is the fracture height, L is the fracture half length, and E(m) is complete elliptical integral. van\nden Hoek (2016) provided an interesting modification in that he allowed a time-dependent fracture\ncompliance during the falloff. In other words, van den Hoek's solution, which was formulated based"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89414e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 3, "chroma:document": "compliance during the falloff. In other words, van den Hoek's solution, which was formulated based\non laboratory experiments of fracture closure, explicitly allows fracture height and or length recession\nbefore hydraulic fracture closure is observed.\nIt should be clear that discussions of variable storage, effective stiffness, and changing total\ncompliance all refer to the same phenomena during a fracture-injection/falloff sequence. In Fig.\n1, the graph labeled \"Fracture Height Recession/Transverse or Variable Storage\" illustrates the\nGdp w/dG derivative response during the closure process with variable storage, compliance, or"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8941c6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 4, "chroma:document": "SPE-187038-MS 5\nstiffness. Additionally, the figure illustrates the different interpretations of fracture closure based\non the changing fracture compliance method or the classical Gdp w/dG derivative interpretation\u2014a\ndifference of about 500 psi between the two interpretations in the Fig. 1 example.\nFracture tip extension , which occurs when a fracture continues to grow after injection is stopped, is\nindicated when the Gdp w/dG derivative data lie along a straight line that extrapolates above the origin.\nFigure 1\u2014Classical G-function derivative analysis qualitative interpretations.\nAs noted, Fig. 1 shows the traditional interpretation of leakoff types during a falloff, but other effects\ncan result in a non-linear Gdp w/dG derivative response. Barree and Miskimins (2016) summarized several\nadditional possibilities to explain Gdp w/dG derivative deviation from a \u2018normal\u2019 leakoff signature, and"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894216-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 4, "chroma:document": "additional possibilities to explain Gdp w/dG derivative deviation from a \u2018normal\u2019 leakoff signature, and\nin some cases, the root cause of the Gdp w/dG derivative deviation from normal leakoff may be either\nunknown or ambiguous. Additionally, combinations of the above leakoff-types can be observed in some data\nsets. Fracture-injection/falloff tests conducted at the toe of horizontal wells predominately exhibit variable\nstorage or changing compliance during the falloff, so the correct fracture closure interpretation is important\nfor determining a representative minimum horizontal stress.\nThe holistic analysis method (Barree, Barree, and Craig 2009) also requires a log-log plot of the derivative\ntd[p e \u2013 pw(t)]/dt plotted versus time, t, which we refer to here as the log-log storage diagnostic. Craig (2014)\nhas proved that the derivative td[p e \u2013 pw(t)]/dt is related to a constant-rate pressure transient solution as\nfollows.\n(9)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894266-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 5, "chroma:document": "6 SPE-187038-MS\nwhere pi is the initial reservoir pressure, pwsD is the slug-test pressure difference, and dimensionless pressure,\ndimensionless time, and the dimensionless storage coefficient are defined as\n(10)\n(11)\n(12)\nThe fracture closure process is a storage phenomenon, so storage consists of both wellbore and\nfracture storage components. In general, an observed deviation of the Gdp w/dG derivative off of the\nextrapolated straight line, for example, pressure-dependent leakoff, will result in an observed deviation of\nthe td[p e \u2013 pw(t)]/dt derivative on the log-log storage diagnostic plot, which signals a change in fracture\nstorage. Additionally, the deviation of the Gdp w/dG derivative identified as fracture closure coincides with\ndissipation of storage distortion of the pressure falloff data identified by the log-log storage diagnostic in\nsoft and hard rock types.\nThe above discussion of the fracture closure process and fracture closure identification are all based"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8942ac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 5, "chroma:document": "soft and hard rock types.\nThe above discussion of the fracture closure process and fracture closure identification are all based\non analytical or numerical models, and although the models are based on fundamental physics and sound\nprinciples, their validation is often based on interpretation, which can be ambiguous. Both laboratory\nand field experiments of hydraulic fracture propagation and closure have been completed over the last\ntwo decades; however, the results of fracture closure models have not been routinely tested against the\nexperimental observation.\nAnalysis and Interpretation of Data\nWe examined both field and laboratory data with the intent of validating fracture closure interpretation\nmodels and methodologies with known or carefully measured results. The field data include virtually all\nthe time, rate, pressure, and deformation measurements from the M-Site project that has been summarized"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8942fc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 5, "chroma:document": "the time, rate, pressure, and deformation measurements from the M-Site project that has been summarized\nby Peterson, et al (1996) and Warpinski, et al (1998). We recognize that we are not the first to analyze\nall, or portions, of the M-Site field measurements. The original interpretations relied on fracture closure\nidentification methods that preceded the development of G-function derivative analysis and the log-log\nstorage diagnostics; consequently, the original interpretations were often inconsistent between data sets and\nanalysts. Subsequent analysis of the M-Site field data, for example, the study presented by Gulrajani, Nolte,\nand Romero (2001), also noted inconsistent interpretations of the multiple data sets, which the authors\nrationalized was caused by repeated injections of increasing volume connecting higher-stress reservoir rock\nto the wellbore.\nOur intent is to provide a consistent interpretation of all relevant time, rate, pressure, and deformation"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89434c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 5, "chroma:document": "to the wellbore.\nOur intent is to provide a consistent interpretation of all relevant time, rate, pressure, and deformation\ndata recorded at the M-Site. Additionally, our objective is to use the downhole tiltmeter fracture re-opening\nand fracture closing deformation measurements to define the minimum horizontal stress. With the minimum\nhorizontal stress defined independently, we then compare fracture closure pressure interpretations from the\ndifferent methodologies to validate a closure model.\nMany laboratory experiments have also been completed of hydraulic fracture creation, propagation, and\nclosure. We use publicly-available laboratory data, where the minimum horizontal stress is experimentally\nimposed, to compare fracture closure pressure interpretations with the known solution to validate a closure\nmodel. Additionally, some publicly available data includes measurements of fracture dimensions that were"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89439c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 5, "chroma:document": "model. Additionally, some publicly available data includes measurements of fracture dimensions that were\nrecorded during closure, so the effect of changing storage (or changing compliance) can be evaluated with\nrespect to the fracture closure interpretations. Finally, we include a never-published laboratory experiment"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8943e2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 6, "chroma:document": "SPE-187038-MS 7\nwhere the minimum horizontal stress is experimentally imposed, and a blind test is used to compare the\ninterpreted fracture closure pressure to the known minimum horizontal stress.\nField Experiments of Fracture Closure\nPerhaps the most comprehensive, best-documented, and publicly available field data set of fracture closure\nwas recorded at the M-Site in the mid-1990s. While the scope of the M-Site project was much more\ncomprehensive than simply fracture closure determination, two separate hard rock, tight-gas sandstone\nformations were tested during the field experiments, and the results provide insight into the fracture\nclosure process and fracture closure pressure determination. Experiments in both sands included multiple\ninjections of varying injection volume, injection rate, falloff time, flow back periods, time between\ninjections, and observations of hydraulic fracture closure. Many injections were monitored by downhole"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894432-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 6, "chroma:document": "injections, and observations of hydraulic fracture closure. Many injections were monitored by downhole\ntiltmeters cemented in place in an offset wellbore along with microseismic imaging of fracture propagation\nfrom two arrays in adjacent wellbores. Fig. 2 shows a plan view of the surface location of the M-Site\nwells. The Monitor Well shown in Fig. 2 held six tiltmeters and a microseismic array cemented in place\nwhile a wireline-run microseismic array monitored events from MWX-3. Fig. 3 contains the location and\norientation of the tiltmeters in the Monitor Well along with the location of the triaxial seismic receivers\nwith respect to the B-Sand and C-Sand in the MWX-2 treatment well. Within Fig. 3, the measurement-\naxis orientation is shown for each tiltmeter, and for all tiltmeters the y-axis is essentially normal to the\nprimary fracture orientation in the treatment well, which is shown in Fig. 2. With the tiltmeter y-axes"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894482-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 6, "chroma:document": "primary fracture orientation in the treatment well, which is shown in Fig. 2. With the tiltmeter y-axes\nessentially normal to the primary fracture plane, the tiltmeters have proven to be extremely sensitive\nto the rock deformation resulting from small fracture-width changes in the treatment well. Additionally,\nthe deformation and tiltmeter response is virtually immediate with respect to rate or pressure changes in\nthe treatment well once the treating pressure exceeds the minimum horizontal stress. Additional M-Site\nwellbore configuration, experimental measurements, and experimental procedures have been exhaustively\ndocumented by numerous authors, including Warpinski et al (1995, 1996, 1997, 1998), Peterson, et al\n(1996), and Branagan, et al (1996a, 1996b, 1997a, 1997b).\nFigure 2\u2014Plan view of M-Site, including locations of treatment well\n(MWX-2) and Monitor Well (downhole tiltmeters). After Branagan, et al. 1996."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8944c8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 7, "chroma:document": "8 SPE-187038-MS\nFigure 3\u2014Tiltmeter placement within Monitor Well, and tiltmeter axis orientation. After Branagan et al. (1996).\nFor the purposes of this paper, the pressure, rate, and time data recorded during the injection/falloff\nsequences are interpreted using G-function derivative analysis and the log-log storage diagnostic plot\nto infer hydraulic fracture closure, and where relevant tiltmeter measurements are available, closure-\nstress interpretations are compared with tiltmeter-measured rock deformation. As noted, the downhole\ntiltmeters are extremely sensitive to deformation created by an opening or closing fracture; thus, the tiltmeter\nmeasurements provide the best direct indication of hydraulic fracture width changes in field experiments.\nInjection/falloff sequences were completed in both the B-sand and the C-sand. In the B-sand, a total of\n10 injection/falloff, or injection/falloff/flowback, sequences were recorded over a period of nine months"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894518-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 7, "chroma:document": "10 injection/falloff, or injection/falloff/flowback, sequences were recorded over a period of nine months\nwith different fluid types, volumes, injection rates, falloff period, and flowback period. The first three\ninjection/falloff sequences were three small volume and low rate classical stress tests to establish an\nestimated minimum horizontal stress. In the C-sand, a total of 8 injection/falloff, or injection/falloff/\nflowback, sequences were recorded with different fluid types, volumes, injection rates, falloff period, and\nflowback period. No small-volume stress tests were pumped in the C-sand in the MWX-2 wellbore.\nFracture re-opening experiments were pumped in both the B-Sand (Injection 4B) and the C-Sand\n(Injection 4C). Prior injections in both sands had created and propagated a hydraulic fracture, so the re-\nopening experiments were pumped at very low rates to observe the dilation of an existing fracture, which"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8945cc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 7, "chroma:document": "opening experiments were pumped at very low rates to observe the dilation of an existing fracture, which\nwould be indicated by the rock deformation measured by the tiltmeters. As previously noted, an existing\nfracture should dilate (open) as the pressure within the fracture exceeds the minimum horizontal stress.\nConversely, an existing fracture should contract (close) during a falloff to a residual-width. In hard rock (E\n> 1.8 \u00d7 106 psi [12.5 GPa]), the pressure observed at fracture closure (residual width) corresponds to the\nminimum horizontal stress. Thus, in both the B-Sand ( E = 4.57 \u00d7 106 psi [31.5 GPa]) and C-Sand (E = 5.25"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894626-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 8, "chroma:document": "SPE-187038-MS 9\n\u00d7 106 psi [36.2 GPa]) fracture re-opening and fracture closure should occur at the same pressure, which is\nequivalent to the minimum horizontal stress (within experimental error). In soft rock (E < 7.25 \u00d7 105 psi [5.0\nGPa]), which includes unconsolidated sand formations, fracture closure to a residual width can be observed\nat a pressure below the minimum horizontal stress (Dong and de Pater 2007).\nB-Sand Stress Tests and Fracture Closure Experiments\nB-Sand experiments at the M-Site began with three stress tests in November 1994. Fig. 4 shows graphs\nfor each of the three stress tests, which are labeled within each graph \"Stress Test #1,\" \"Stress Test #2,\"\nand \"Stress Test #3.\" For each injection/falloff sequence, Fig. 4 shows graphs of bottomhole pressure and\ninjection rate versus time; bottomhole pressure, the derivative of bottomhole pressure with respect to the G-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89466c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 8, "chroma:document": "injection rate versus time; bottomhole pressure, the derivative of bottomhole pressure with respect to the G-\nfunction, dp w/dG, and the product of the G-function and the derivative of bottomhole pressure with respect\nto the G-function, Gdp w/dG, plotted versus the G-function during the shut-in period; and a log-log storage\ndiagnostic graph of the fracture-pressure difference, pe \u2013 pw(t), and the product of time and the derivative of\nthe fracture-pressure difference with respect to time, td[p e \u2013 pw(t)]/dt, plotted versus time since the beginning\nof the injection.\nFigure 4\u2014MWX-2 stress tests recorded in November 1994."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8946bc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 9, "chroma:document": "10 SPE-187038-MS\nStress Test #1 was a very small injection of 41-gal of water pumped at injection rates of less than 20\ngal/min. For Stress Test #1 the 1994 interpretation of closure of (p c)1994 = 3,020 psi is shown along with\na new interpretation of the fissure-opening pressure, (p fis)2017 = 2,941 psi, and fracture closure pressure,\n(pc)2017 = 2,886 psi using G-function derivative analysis. The log-log storage diagnostic graph shows that\nthe fracture closure time interpreted using G-function derivative analysis corresponds to the dissipation of\nstorage distortion of the pressure falloff data.\nStress Test #2 was a slightly larger injection of 47-gal of water pumped at injection rates of less than 20\ngal/min. For Stress Test #2, the new interpretation includes a fissure opening pressure of ( pfis)2017 = 2,915\npsi, and hydraulic fracture closure pressure of (p c)2017 = 2,893 psi.\nStress Test #3 was again a slightly larger injection of 51-gal of water pumped at injection rates of less"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89470c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 9, "chroma:document": "Stress Test #3 was again a slightly larger injection of 51-gal of water pumped at injection rates of less\nthan 20-gal/min, but the test included a step-down in injection rates. G-function derivative analysis shows a\nfissure-opening pressure, (p fis)2017 = 2,960 psi, but the final recorded pressure during the falloff was ( pw)final\n= 2,938 psi, and G-function derivative analysis confirms that hydraulic fracture closure was not observed,\nwhich is indicated by the increasing Gdp w/dG derivative through the end of the recorded pressure data. The\nlog-log storage diagnostic also demonstrates that the end of storage distortion was not observed during the\nrecorded falloff, which is also indicated by the increasing derivative, td[p e \u2013 p w(t)]/dt.\nAfter a 19-bbl borate crosslinked-gel injection (Injection 1C) was completed, the fracture diagnostics\ncontinued with Injection 2B, Injection 3B, and Injection 4B, and the fracture closure diagnostic graphs are"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894752-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 9, "chroma:document": "continued with Injection 2B, Injection 3B, and Injection 4B, and the fracture closure diagnostic graphs are\nshown in Fig. 5 with each injection/falloff sequence labeled \"Injection 2B,\" \"Injection 3B,\" and \"Injection\n4B,\" respectively. Injection 2B consisted of 27.1 bbl of 2% KCl-treated water injected in step rates up\nto 3.3 bbl/min. There are several important features of Injection 2B to note. First, the step-rate injection\ncan theoretically be used to interpret fracture closure pressure from a graph of bottomhole pressure versus\ninjection rate; however, close examination of the bottomhole pressure and injection rate versus time graph\nfor Injection 2B clearly shows the pressure response was not smooth or constant at the lowest injection rate\nof 0.5-bbl/min; consequently, an interpretation of the fracture closure stress from the step-rate pressure data,\nlike that presented by Gulrajani, Nolte, and Romero (2001), is highly questionable."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8947a2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 10, "chroma:document": "SPE-187038-MS 11\nFigure 5\u2014MWX-2 Injections 2B (27 bbl), 3B (104 bbl), 4B (215 bbl) April 1995.\nSecond, the G-function derivative analysis graph clearly shows the \"sudden\" appearance of variable\nstorage or changing compliance during the falloff, which was not observed in any of the stress tests recorded\nbefore the crosslinked-gel Injection 1B. The fracture-compliance method interpretation suggests a fracture\nclosure pressure of (p c)\u0394Cbc = 3,208 psi, where the subscript \u2018\u0394Cbc\u2019 denotes variable storage/compliance\nbefore closure. Since the final recorded pressure before beginning flow back was ( pw)final = 2,893 psi, fracture\nclosure was not observed during the falloff based G-function derivative analysis. Additionally, the log-\nlog storage diagnostic clearly shows storage distortion is observed through the end of the recorded falloff\ndata; thus, hydraulic fracture closure was also not observed during the falloff based on the log-log storage\ndiagnostic."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89481a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 10, "chroma:document": "data; thus, hydraulic fracture closure was also not observed during the falloff based on the log-log storage\ndiagnostic.\nInjection 3B was a 104-bbl injection of 2% KCl-treated water, which except for a brief shut-down early\nin the test, was injected at a constant rate. The bottomhole pressure and injection rate versus time plot shows\nthe final recorded pressure during the falloff was (p w)final = 2,972 psi. The G-function derivative analysis\ngraph once again suggests variable storage/changing compliance was observed during the falloff. Using the\nfracture-compliance method, the fracture closure is (p c)\u0394Cbc = 3,308 psi. Fracture closure was not observed"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894860-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 11, "chroma:document": "12 SPE-187038-MS\nbased on G-function derivative analysis as indicated by the increasing derivative, Gdp w/dG, and based on the\nlog-log storage diagnostic plot, which shows an increasing derivative, td[p e \u2013 pw(t)]/dt, and corresponding\nstorage distortion of the pressure falloff.\nInjection 4B was a 214.7 bbl injection of 2% KCl-treated water with a brief shut-down during the\ninjection, but with a hydraulic fracture re-opening experiment included at the beginning of the injection.\nAs was observed in Injection 2B and Injection 3B, the G-function derivative analysis plot shows a strong\nindication of variable storage/changing compliance, and the fracture-compliance method closure pressure is\n(pc)\u0394Cbc = 3,330 psi. Conversely, fracture closure was not observed based on G-function derivative analysis\nand the log-log storage diagnostic plots, which both show increasing derivatives, Gdp w/dG and td[p e \u2013 pw(t)]/\ndt, respectively, through the end of the falloff data."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8948b0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 11, "chroma:document": "dt, respectively, through the end of the falloff data.\nAlthough the low-volume stress tests should have established a fracture closure pressure corresponding\nto the minimum horizontal stress, the test analyses remain pressure interpretations of fracture closure and\nare not a direct observation of closure. The tiltmeters, however, are a measurement of rock deformation\nas a function of increasing hydraulic fracture width. Consequently, a re-opening experiment where 2%\nKCl-treated water is slowly injected into an existing fracture, and the pressure gradually increases, should\nindicate measurable rock deformation as the pressure within the fracture exceeds the minimum horizontal\nstress (closure pressure) and the hydraulic fracture dilates.\nFig. 6 contains plots of bottomhole pressure and y-axis deformation of the tiltmeters at 4,628-ft (below\nthe B-Sand), 4,558-ft (within the B-Sand), 4,487-ft (above the B-Sand). In each figure, the tiltmeter"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894900-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 11, "chroma:document": "the B-Sand), 4,558-ft (within the B-Sand), 4,487-ft (above the B-Sand). In each figure, the tiltmeter\nmeasurements are essentially constant before the injection begins and as pressure starts to increase. As\nbottomhole pressure exceeds approximately 2,800 psi, deformation is observed in every tiltmeter. The\ntiltmeter measurements suggest existing-fracture dilation begins at approximately (p c)ReOpen  \u2248 2,800 psi,\nwhich may be the fracture opening pressure corresponding to the minimum horizontal stress. Each figure\nshows a vertical red dashed line that corresponds to the fracture closure pressure interpreted from the stress-\ntest data, 2,855 psi \u2264 (p c)2017 \u2264 2,893 psi and the black dashed line corresponds to the fracture closure stress\ninterpreted using the fracture-compliance method, which is 3,208 psi \u2264 (p c)\u0394Cbc \u2264 3,330 psi.\nFigure 6\u2014MWX-2 B-Sand Injection 4B re-opening experiment tiltmeters identifying deformation and fracture opening."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894946-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 11, "chroma:document": "Figure 6\u2014MWX-2 B-Sand Injection 4B re-opening experiment tiltmeters identifying deformation and fracture opening.\nUnfortunately, tiltmeter re-opening experiments also have uncertainty, for example, if the re-opening\ninjection rate is too high, deformation may be observed before reopening. The tiltmeter measurements\nare, however, consistent with the fracture closure pressure interpreted from G-function derivative analysis\nand log-log storage diagnostic. Additionally, the tiltmeter measurements seem to validate that the fracture\nclosure pressure interpretations based on identifying the dissipation of storage distortion correspond to the\nminimum horizontal stress. Conversely, the tiltmeter measurements are inconsistent with the findings of the\nfracture-compliance method for closure identification, that is, the fracture-compliance method interpreted\nclosure pressure may not correspond to the minimum horizontal stress. Fig. 6 does show a significant"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8949a0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 12, "chroma:document": "SPE-187038-MS 13\nincrease in deformation as the pressure exceeds approximately 3,100 psi, but the initial deformation is\nobserved as bottomhole pressure increases above approximately (p c)ReOpen  \u2248 2,800 psi.\nInjections 5B and 6B were both 400-bbl 40-lb/1,000-gal linear gel injections, and the pressure falloff did\nnot extend through hydraulic fracture closure for either injection/falloff sequence. Injection 7B consisted\nof the final KCl-treated water injection/falloff in the B-Sand, and the falloff did extend through hydraulic\nfracture closure. Fig. 7 shows the Injection 7B diagnostic plots, and the bottomhole pressure and injection\nrate versus time graph show that the injection consisted of 30.5-bbl of 2% KCl treated water at injection\nrates up to 19 bbl/min. Unlike Injection 2B, Injection 3B, and Injection 4B, but like the three stress tests, the\nleakoff-off type identified using G-function derivative analysis is pressure-dependent leakoff with a fissure-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8949f0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 12, "chroma:document": "leakoff-off type identified using G-function derivative analysis is pressure-dependent leakoff with a fissure-\nopening pressure of (p fis)2017 = 2,893 psi. G-function derivative analysis shows no indication of variable\nstorage/changing compliance, but it does indicate fracture closure was observed at ( pc)2017 = 2,855 psi, which\nis consistent with the three stress tests and validated by the tiltmeter measurements from the Injection 4B re-\nopening experiment. The log-log storage diagnostic also shows storage distortion dissipates as the fracture\ncloses, which is indicated by the decreasing derivative td[p e \u2013 p w(t)]/dt, after closure.\nFigure 7\u2014MWX-2 B-Sand Injection 7B -- 31 bbl KCl water prefrac DFIT August 1995.\nThe tiltmeter measurements during the re-opening experiment provided a clear indication of hydraulic\nfracture re-opening and dilation during the injection, but the measurements are not as definitive during"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894a40-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 12, "chroma:document": "fracture re-opening and dilation during the injection, but the measurements are not as definitive during\nclosure. For example, Fig. 8 contains a graph of bottomhole pressure and tiltmeter deformation recorded\nduring the pressure falloff for the tiltmeter located at 4,487-ft (above the B-Sand). Notice that as bottomhole\npressure falls below the re-opening pressure and falloff-interpreted fracture closure pressure, the tiltmeter\nmeasurements continue to show decreasing deformation, which suggests fracture width continues to\ndecrease. Examination of the tiltmeter measurements also shows that the data are relatively noisy; however,\nthe shape of the tiltmeter-measured deformation curve is similar to the pressure falloff curve, and the\ntiltmeter-measured deformation might follow relationships known to exist for fracture pressure falloff data."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894a86-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 13, "chroma:document": "14 SPE-187038-MS\nFigure 8\u2014MWX-2 B-Sand Injection 7B bottomhole pressure and tiltmeter (4,487 ft) falloff during shut-in.\nAs previously noted, Craig (2014) demonstrated that the derivative, td[p e \u2013 pw(t)]/dt, is related to a general\npressure transient solution as follows.\n(13)\nGenerally, an analytical solution for a fractured well is used to generate the pressure transient derivative,\nand the observed DFIT data are matched to an appropriate solution. The method is general, and any\nappropriate transient solution, including flow from an infinite- or finite-conductivity fracture, dual porosity\nreservoir, anisotropic reservoir, multiple producing fractures, etc., can be used in the matching process. For\nthe purposes of the current paper, it's important to note the behavior of the pressure-transient derivative,\nwhich is shown in Fig. 9. In Fig. 9, the increasing derivative is indicative of wellbore and fracture storage"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894ad6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 13, "chroma:document": "which is shown in Fig. 9. In Fig. 9, the increasing derivative is indicative of wellbore and fracture storage\ndistortion. Wellbore and fracture storage distortion dissipates as the curve reaches the apex and begins to\nfall. A closing fracture is a type of storage ( Craig and Blasingame 2005, 2006), and in most cases, fracture\nstorage affects the falloff data long after wellbore storage has dissipated. Thus, when the derivative, td[p e\n\u2013 p w(t)]/dt, is increasing, the fracture is still closing.\nFigure 9\u2014Pressure transient solution derivative versus dimensionless time."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894b30-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 14, "chroma:document": "SPE-187038-MS 15\nIn terms of the tiltmeter response, tiltmeter measurements peaked at the end of pumping, that is, the\nhydraulic fracture maximum width was observed at the end of pumping and pressure pe. Since tiltmeter\ndeformation is proportional to the fracture width, and the fracture width changes over time are a function\nof pressure, it's anticipated that the tiltmeter deformation-difference derivative, td[(u y)e \u2013 uy (t)]/dt, curve\nshould mirror the fracture pressure-difference derivative curve. In other words, we postulate that in a\nhomogeneous reservoir with normal leakoff, the tiltmeter deformation-difference derivative, td[(u y)e \u2013 uy(t)]/\ndt, will increase through hydraulic fracture closure. Similarly, if pressure-dependent leakoff is observed,\nthe tiltmeter deformation-difference derivative should show a positive \"hump,\" like the fracture pressure-\ndifference derivative."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894b76-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 14, "chroma:document": "the tiltmeter deformation-difference derivative should show a positive \"hump,\" like the fracture pressure-\ndifference derivative.\nOne issue, however, in attempting derivative analysis of tiltmeter data is the noise noted in Fig. 8. If finite-\ndifference differentiation of the noisy tiltmeter data is attempted, the noise will be amplified by the derivative\ncalculation, and the derivative may be of limited value. An alternative technique for calculating a \"noiseless\"\nunderlying derivative of noisy experimental data was developed by Chartrand (2011) and is called total\nvariation regularization. Fig. 10 illustrates the derivative calculation of the tiltmeter measurements (4,487\nft) using both \"smoothed\" central-difference calculations and total variation regularization. With a smooth\nderivative calculation, the tiltmeter deformation-difference derivative, td[(u y)e \u2013 uy (t)]/dt, should show\ntrends similar to the fracture pressure-difference derivative, td[p e \u2013 p w(t)]/dt."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894bc6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 14, "chroma:document": "trends similar to the fracture pressure-difference derivative, td[p e \u2013 p w(t)]/dt.\nFigure 10\u2014MWX-2 B-Sand Injection 7B tiltmeter du y/dt derivative\ncalculated with central-difference and total variation regularization.\nFig. 11 shows a log-log graph of the tiltmeter deformation-difference derivative versus time since the\nbeginning of pumping for the tiltmeters at 4,487-ft (above B-Sand), 4,558-ft (within B-Sand), and 4,628-\nft (below B-Sand). All three tiltmeter derivative curves have a similar behavior that includes a pressure-\ndependent leakoff \"hump\" followed by an increasing derivative until fracture closure is observed. Fig. 11\nalso contains a log-log plot of both the fracture pressure-difference derivative and the tiltmeter deformation-\ndifference derivative (4,558-ft within B-Sand), and shows how both exhibit a pressure dependent hump and\nan increasing derivative before hydraulic fracture closure is interpreted. Figs. 10 and 11 demonstrate that"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894c16-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 14, "chroma:document": "an increasing derivative before hydraulic fracture closure is interpreted. Figs. 10 and 11 demonstrate that\na characteristic tiltmeter deformation-derivative signature was observed and is consistent with pressure-\ninferred hydraulic fracture closure. While the tiltmeter deformation-derivative curves may not provide an\neasily-identified and definitive closure event, the tiltmeter deformation-difference derivative interpretation\nalong with the analog fracture pressure-difference derivative methodology provide convincing evidence of\nhydraulic fracture closure, and the closure pressure is consistent with the fracture re-opening and pressure-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894c5c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 15, "chroma:document": "16 SPE-187038-MS\nfalloff inferred fracture closure pressure. To our knowledge, a relationship between the deformation-\ndifference derivative and the pressure-difference derivative has not been studied. The trends observed in the\ntiltmeter and pressure data suggest additional research is warranted to mathematically define a relationship\nif one exists.\nFigure 11\u2014Comparison of tiltmeter deformation-difference derivatives, td[(u y)e-uy(t)]/dt, and comparison of\ntiltmeter deformation-difference derivative (4,558 ft) with observed fracture pressure-difference derivative, td\u0394p/dt.\nFracture Re-Opening Experiment \u2013 C-Sand\nThe C-Sand is located between 4,303-ft and 4,390-ft in the MWX-2 wellbore, and the experiments of interest\nfor the present paper are Injection 3C and Injection 4C, which includes a fracture re-opening experiment.\nInjection 1C, like Injection 1B in the B-Sand, was a 95-bbl injection of 40-lb/1,000-gal borate-crosslinked"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894cac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 15, "chroma:document": "Injection 1C, like Injection 1B in the B-Sand, was a 95-bbl injection of 40-lb/1,000-gal borate-crosslinked\ngel, and Injection 2C was a 40-lb/1,000-gal linear gel injection. Injection 3C was a 247-bbl injection of\n40-lb/1,000-gal linear gel, with a significant falloff period; however, fracture closure cannot be interpreted\nfrom the falloff data using G-function derivative analysis and the log-log storage diagnostic plot.\nFig. 12 contains a graph of bottomhole pressure and injection rate versus time, the G-function derivative\nanalysis plot, and the log-log storage diagnostic graph. The graph of bottomhole pressure and injection rate\nversus time shows a maximum injection rate of 19-bbl/min and a falloff that was recorded through a final\nbottomhole pressure of (p w)final = 2,956 psi. G-function derivative analysis suggests fracture closure was not\nobserved through the end of the falloff, and the log-log storage diagnostic also shows an increasing fracture"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894cfc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 15, "chroma:document": "observed through the end of the falloff, and the log-log storage diagnostic also shows an increasing fracture\npressure-difference derivative through the end of the falloff, which confirms storage was still distorting the\npressure falloff and suggests the fracture was still closing."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894d4c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 16, "chroma:document": "SPE-187038-MS 17\nFigure 12\u2014MWX-2 C-Sand Injection 3C DFIT Analysis.\nA fracture re-opening experiment was also conducted in the C-Sand, and Fig. 13 contains a graph of\nbottomhole pressure and injection rate during the re-opening. The injection rates were kept lower during\nre-opening as compared to the B-Sand re-opening experiment; thus, the tiltmeter re-opening deformation\nmeasurements may provide a more definitive fracture re-opening pressure. As shown in Fig. 13, the injection\nrates were maintained at generally less than 10-gal/min until fracture opening was observed. Fig. 14 contains\ngraphs of bottomhole pressure and tiltmeter deformation for the tiltmeters at 4,418-ft (below the C-Sand),\n4,348-ft (within the C-Sand), and 4,273-ft (above the C-Sand). Even with the noise in the tiltmeter-recorded\ndeformation, a fracture re-opening pressure of approximately (p c)ReOpen  \u2248 2,900 psi was observed. Pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894d9c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 16, "chroma:document": "deformation, a fracture re-opening pressure of approximately (p c)ReOpen  \u2248 2,900 psi was observed. Pressure\nfalloff analysis of the entire Injection 4C injection/falloff sequence is shown in Fig. 15. The final recorded\npressure during the falloff was (p w)final = 3,108 psi, which is clearly above the hydraulic fracture re-opening\nstress, and both G-function derivative analysis and the log-log storage diagnostic confirm that hydraulic\nfracture closure was not observed during the falloff, which is indicated by the increasing derivatives, Gdp w/\ndG and td[p e \u2013 p w(t)]/dt, respectively, through the end of the falloff data.\nFigure 13\u2014MWX-2 C-Sand Injection 4C Reopening Experiment."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894e0a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 17, "chroma:document": "18 SPE-187038-MS\nFigure 14\u2014MWX-2 C-Sand Injection 4C Reopening Experiment.\nFigure 15\u2014MWX-2 C-Sand Injection 4C DFIT Analysis\nSummarizing the findings from both the B-Sand and C-Sand injection/falloff and fracture re-opening\nexperiments, we observed the following.\n\u2022Fracture re-opening experiments using bottomhole pressure and tiltmeter deformation\nmeasurements suggest a B-Sand fracture re-opening pressure of (p c)ReOpen  \u2248 2,800 psi and a C-Sand\nre-opening pressure of (p c)ReOpen  \u2248 2,900 psi.\n\u2022Fracture closure pressure interpretations using G-function derivative analysis and the log-log\nstorage diagnostic suggest a fracture closure pressure approximately equivalent to the fracture re-\nopening pressure. In the B-Sand, the falloff-interpreted closure pressure was 2,855 psi \u2264 ( pc)2017 \u2264\n2,893 psi. However, the C-Sand injection/falloff sequences did not allow bottomhole pressure to\ndecline below pw(t) = 2,956 psi, but we can confidently state that the falloff analysis in the C-Sand"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894e5a-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 17, "chroma:document": "decline below pw(t) = 2,956 psi, but we can confidently state that the falloff analysis in the C-Sand\nsuggests a fracture closure pressure of (p c)C-Sand < 2,956 psi.\n\u2022Fracture closure pressure when interpreted using G-function derivative analysis and the log-\nlog storage diagnostic was invariant over multiple injection/falloff sequences, including different\nfluids, fluid volumes, and rates, and invariant over time.\n\u2022The fracture-compliance method interpretations of the G-function derivative, Gdp w/dG, in the B-\nSand injections suggested a fracture closure pressure of 3,208 psi \u2264 ( pc)\u0394Cbc \u2264 3,330 psi, which\nare inconsistent with the small-volume stress tests, holistic G-function derivative analysis, and the\nfracture re-opening experiments.\n\u2022Tiltmeter measurements during a pressure falloff do not exhibit an easily-identifiable and definitive\nclosure event."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894eaa-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 18, "chroma:document": "SPE-187038-MS 19\n\u2022Tiltmeter deformation-difference derivative curves are generally similar in shape and behavior to\nfracture pressure-difference derivatives; consequently, the deformation-difference derivative can\npotentially validate fracture closure and the end of storage distortion identified using G-function\nderivative analysis and the log-log storage diagnostic.\nLaboratory Experiments of Fracture Closure\nNumerous researchers have reported experiments of fracture propagation and closure under controlled\nlaboratory conditions. Cheung and Haimson (1989) looked at existing fracture closure interpretation\ntechniques, while also developing a new model of their own, for identifying fracture closure pressure\nfrom pressure falloff data. Their experimental method required multiple injection-falloff sequences with\nthe wellbore pressure falling to below 1 MPa before each subsequent injection, and their experiments"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894ef0-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 18, "chroma:document": "the wellbore pressure falling to below 1 MPa before each subsequent injection, and their experiments\nfocused as much on identifying the fracture re-opening pressure as the fracture closure pressure. Fig. 16\ncontains a graph of pressure and the Gdp w/dG derivative for injection \u2018a\u2019 of Test #10 for a Niagara dolomite\n(E > 6.3 \u00d7 106 psi [43.7 GPa]) fracture closure experiment. Injection \u2018a\u2019 was the first fracture-injection/\nfalloff in the sample, and it was the only injection/falloff sequence with sufficient analyzable before-\nclosure data. For example, only about 10 seconds of before-closure pressure data are available for analysis\nin Fig. 16, which is barely sufficient to identify trends. The raw experimental data were not available;\nhowever, Cheung and Haimson's Fig. 2 was digitized using publicly-available software (Rohatgi 2017),\nwhich provided the pressure and time data required to construct Fig. 16. While digitizing historical publicly-"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894f40-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 18, "chroma:document": "which provided the pressure and time data required to construct Fig. 16. While digitizing historical publicly-\navailable experimental data is sometimes necessary (and worthwhile), there is inevitably a loss of resolution;\nconsequently, the data scatter shown in Fig. 16 may not have existed in the original raw pressure and time\nrecording.\nFigure 16\u2014Niagara Dolomite Test #10 Injection \u2018a\u2019. After Cheung and Haimson (1989).\nThe graph illustrates a clear \"hump\" in the Gdp w/dG derivative, which based on Fig. 1, is interpreted\nas pressure-dependent leakoff. de Pater et al (1994) have found pressure-dependent leakoff in laboratory\nfracturing experiments of moderately hard sandstone, so the result is anticipated even though the sample\ncontains no obvious natural fractures or fissures. The closure pressure is interpreted to be 13.2 MPa, which\nis within 12% of the imposed 15 MPa minimum horizontal stress. While the interpretation reasonable, it is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894f90-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 18, "chroma:document": "is within 12% of the imposed 15 MPa minimum horizontal stress. While the interpretation reasonable, it is\nnonunique because of limited before-closure data and a noisy Gdp w/dG derivative. With very few before-\nclosure data points, and since virtually all the before-closure data is affected by pressure-dependent leakoff,\nthe log-log storage diagnostic is of limited value for a fracture closure interpretation in this case."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b894fd6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 19, "chroma:document": "20 SPE-187038-MS\nWhen reviewing laboratory data, it is useful to have fracture dimensions measured during closure to help\ncorrelate the pressure falloff to measured fracture dimensions. While Cheung and Haimson reported acoustic\nemissions during closure, fracture dimensions during closure were not reported. de Pater, Desroches,\nGroenenboom, and Weijers (1996) presented measurements of both pressure falloff and fracture dimensions\nwith respect to time for both sandstone (E \u2245 3 \u00d7 106 psi [20.4 GPa]) and cement paste. Fig. 17 contains a\ngraph of pressure, dp w/dG, and Gdp w/dG versus the G-function and a graph of fracture width at the wellbore,\nfracture radius, and Gdp w/dG versus the G-function. The data were digitized from Fig. 3 and Fig. 10 of de\nPater, Desroches, Groenenboom, and Weijers (1996) for the sandstone sample.\nFigure 17\u2014G-function derivative analysis and fracture dimensions during closure for SNV03. After de Pater, et al (1996)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895030-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 19, "chroma:document": "Figure 17\u2014G-function derivative analysis and fracture dimensions during closure for SNV03. After de Pater, et al (1996).\nG-function derivative analysis suggests fracture closure was not observed through the end of the recorded\npressure falloff data as indicated by the Gdp w/dG derivative following a straight line extrapolated from the\norigin. The imposed stress was 23 MPa, which coincides with the last recorded pressure. A definitive closure\nidentification using G-function derivative analysis would have required recording the pressure falloff below\n23 MPa; however, the Gdp w/dG derivative curve is consistent with the observed closure. In other words,\nclosure was not observed during the falloff, which is confirmed by the Gdp w/dG derivative curve.\nPressure-dependent leakoff is once again indicated during the falloff of the sandstone sample by the\nGdp w/dG derivative \"hump.\" Fig. 17 also shows that during the Gdp w/dG derivative pressure-dependent"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895080-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 19, "chroma:document": "Gdp w/dG derivative \"hump.\" Fig. 17 also shows that during the Gdp w/dG derivative pressure-dependent\nleakoff signature, both the fracture width and fracture radius were decreasing. As previously discussed, a\ndecreasing radius during the falloff increases fracture stiffness, which should result in decreasing storage\nand a changing compliance signature of the Gdp w/dG derivative, which is opposite of what is observed. In\nboth the Niagara dolomite and the Colton sandstone samples, any variable storage/changing compliance\nsignature that should be observed in the Gdp w/dG derivative, is masked by the pressure-dependent leakoff.\nThe fracture width change and radius change during closure confirm that the fracture was indeed closing\nfrom the fracture tip back to the wellbore, which is consistent with the closure process defined by Hayashi\nand Haimson (1991) and \"progressive fracture closure\" as defined Zanganeh, Clarkson, and Hawkes (2017)."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8950c6-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 19, "chroma:document": "and Haimson (1991) and \"progressive fracture closure\" as defined Zanganeh, Clarkson, and Hawkes (2017).\nHowever, the experiment also clearly shows that the minimum horizontal stress is not equivalent to the\npressure at tip-closure. At fracture-tip closure, the experimental data show a pressure of about 30 MPa, but\nthe imposed horizontal stress was only 23 MPa; thus, the conclusions of Zanganeh, Clarkson, and Hawkes\nare not supported by experimental data in a hard rock sample. In hard rock, a fracture closure pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895116-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 20, "chroma:document": "SPE-187038-MS 21\ncorresponding to the minimum horizontal stress is correctly identified by the traditional Gdp w/dG derivative\ninterpretation and the log-log storage diagnostic when the fracture closes to essentially the residual width\nat the wellbore.\nDong and de Pater (2007) presented a fracture closure experiment of a soft unconsolidated sand (E \u2245\n250,000 psi [1.7 GPa]), which makes a very interesting comparison with the hard-rock cases noted above.\nFig. 18 contains a graph of pw, dp w/dG, and Gdp w/dG versus the G-function along with a log-log graph of\nthe td[p e \u2013 pw(t)]/dt derivative versus time. A Gdp w/dG derivative interpretation suggests fracture closure\nis observed at G = 2.09 and a closure pressure of 3 MPa after periods of pressure-dependent and normal\nleakoff; however, the imposed stress during the experiment was 7 MPa. The td[p e \u2013 pw(t)]/dt derivative also\nshows the effects of pressure-dependent leakoff and fracture storage distortion until fracture closure was"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895166-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 20, "chroma:document": "shows the effects of pressure-dependent leakoff and fracture storage distortion until fracture closure was\nobserved. Fig. 19 is reproduced from Dong and de Pater (2007) and shows several CT scans of the hydraulic\nfracture during the pressure falloff. The CT scans shows that the fracture remains open with perhaps a small\ndecrease in aperture as the pressure declines below the imposed horizontal stress; however, it also shows\nthat the fracture closes as the pressure decreases to about 3 MPa. After the pressure falls below the imposed\nminimum horizontal stress, fracture closure begins at the tip and proceeds back to the wellbore until a\nresidual fracture width is observed. The CT scans graphically demonstrate that the Gdp w/dG derivative and\nthe log-log td[p e \u2013 pw(t)]/dt derivative accurately reflect fracture closure, that is, the methods can identify the\ndecrease to a residual fracture width and volume, but for soft rock, the closure pressure does not correspond"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8951ac-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 20, "chroma:document": "decrease to a residual fracture width and volume, but for soft rock, the closure pressure does not correspond\nto the minimum horizontal stress.\nFigure 18\u2014Soft unconsolidated sand closure experiment CTC08. After Dong and de Pater 2007."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8951fc-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 21, "chroma:document": "22 SPE-187038-MS\nFigure 19\u2014CT scans of fracture closure in a soft unconsolidated sand. After Dong and de Pater (2007).\nFig. 19 is also an excellent visualization of fracture-storage distortion. As previously noted, during\na fracture-injection/falloff test, storage has both wellbore and fracture components. In the laboratory\nexperiments, wellbore storage is minimized, so the primary contributor to storage distortion of the falloff\ndata is fracture closure when fluid is \"squeezed\" from the fracture into the formation as closure proceeds.\nFigs. 18 and Fig. 19 viewed in conjunction demonstrate that the storage distortion observed in the td[p e\n\u2013 pw(t)]/dt derivative is purely a function of the closing fracture. When the fracture finally closes, storage\ndistortion of the pressure falloff dissipates. The observation holds for field and laboratory data and is\nindependent of rock hardness.\nFig. 20 is an example provided by van Dam and de Pater (2017) of a closure experiment in a harder"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89524c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 21, "chroma:document": "independent of rock hardness.\nFig. 20 is an example provided by van Dam and de Pater (2017) of a closure experiment in a harder\nsample (E \u2245 1.3 \u00d7 106 psi [8.9 GPa]). The example was provided as a \"blind test\" where the imposed\nstress remained unknown until after an analysis was completed, and the examples illustrates the difficulty\nof interpreting fracture closure from laboratory data. The Gdp w/dG derivative shows a pressure-dependent\n\"hump,\" a variable storage/changing compliance \"dip,\" and a period of normal leakoff. A changing-\ncompliance interpretation results in a closure pressure of 20.16 MPa, which is 26% too high, and as was\ndemonstrated in the field experiments, a strict changing-compliance closure interpretation as advocated by\nMcClure, Jung, Cramer, and Sharma (2015), does not provide the correct closure pressure and minimum\nhorizontal stress. A classical interpretation resulted in a closure pressure of 14.32 MPa, and while the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89529c-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 21, "chroma:document": "horizontal stress. A classical interpretation resulted in a closure pressure of 14.32 MPa, and while the\nclassical interpretation is within 10.5% of the correct answer (16 MPa), it illustrates the difficulty in drawing\nthe correct Gdp w/dG derivative straight line during a G-function derivative analysis without a clear and\ndistinct deviation of the Gdp w/dG derivative off the straight line. It also shows that picking the end of storage\ndistortion using the td[p e \u2013 pw(t)]/dt derivative is helpful, but it is also not distinct since closure is observed\nas storage distortion dissipates and not necessarily at the apex of the td[p e \u2013 pw(t)]/dt derivative. In other\nwords, despite all attempts to make fracture closure identification objective using the Gdp w/dG and td[p e \u2013\npw(t)]/dt derivatives, the pressure falloff trends from laboratory experiments are often non-distinct and the\ninterpretation subjective, which can introduce some interpretation error\u2014for example, 12.5% for the hard"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8952e2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 21, "chroma:document": "interpretation subjective, which can introduce some interpretation error\u2014for example, 12.5% for the hard\ndolomite and 10.5% for the hard sandstone."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895332-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 22, "chroma:document": "SPE-187038-MS 23\nFigure 20\u2014Laboratory fracture-closure experiment (GNV06b) in moderately hard rock (E = 1.3 \u00d7 106 psi [8.9 GPa] and v = 0.21).\nConclusions\nBoth laboratory and field experiments of hydraulic fracture closure with measurements of fracture\ndimensions during the pressure falloff have been examined and the results compared to interpretations of\nclosure pressure from the pressure falloff and the relationship to the minimum horizontal stress. In two\nhard-rock microdarcy sandstone reservoirs, field experiments of fracture closure monitored by downhole\ntiltmeters suggested the following.\n\u2022Fracture re-opening experiments using bottomhole pressure and tiltmeter deformation\nmeasurements suggest a B-Sand fracture re-opening pressure of (p c)ReOpen  \u2248 2,800 psi and a C-Sand\nre-opening pressure of (p c)ReOpen  \u2248 2,900 psi.\n\u2022Fracture closure pressure interpretations using G-function derivative analysis and the log-log"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895382-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 22, "chroma:document": "re-opening pressure of (p c)ReOpen  \u2248 2,900 psi.\n\u2022Fracture closure pressure interpretations using G-function derivative analysis and the log-log\nstorage diagnostic suggest a fracture closure pressure approximately equivalent to the fracture re-\nopening pressure. In the B-Sand, the falloff-interpreted closure pressure was 2,855 psi \u2264 ( pc)2017 \u2264\n2,893 psi. However, the C-Sand injection/falloff sequences did not allow bottomhole pressure to\ndecline below pw(t) = 2,956 psi, but we can confidently state that the falloff analysis in the C-Sand\nsuggests a fracture closure pressure of (p c)C-Sand < 2,956 psi.\n\u2022Fracture closure pressure when interpreted using G-function derivative analysis and the log-\nlog storage diagnostic was invariant over multiple injection/falloff sequences, including different\nfluids, fluid volumes, and rates, and invariant over time.\n\u2022The fracture-compliance method interpretations of the Gdp w/dG derivative in the B-Sand injections"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89540e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 22, "chroma:document": "\u2022The fracture-compliance method interpretations of the Gdp w/dG derivative in the B-Sand injections\nsuggested a fracture closure stress of 3,208 psi \u2264 ( pc)\u0394Cbc \u2264 3,330 psi, which are inconsistent with\nthe small-volume stress tests, holistic G-function derivative analysis, and the fracture re-opening\nexperiments.\n\u2022Tiltmeter measurements during a pressure falloff do not exhibit an identifiable and definitive\nclosure event.\n\u2022Tiltmeter deformation-difference derivative curves are generally similar in shape and behavior to\nfracture pressure-difference derivatives; consequently, the deformation-difference derivative can\npotentially validate fracture closure and the end of storage distortion identified using G-function\nderivative analysis and the log-log storage diagnostic.\nLaboratory experiments of fracture closure in soft rock (E < 7.25 \u00d7 105 psi [5.0 GPa]) through hard\nrock (E \u2245 6.3 \u00d7 106 psi [43.7 GPa]) demonstrate that G-function derivative analysis and the log-log storage"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895468-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 22, "chroma:document": "rock (E \u2245 6.3 \u00d7 106 psi [43.7 GPa]) demonstrate that G-function derivative analysis and the log-log storage\ndiagnostic interpretations of pressure falloff data can generally identify hydraulic fracture closure although"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8954b8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 23, "chroma:document": "24 SPE-187038-MS\nthe trends in the falloff data are sometimes non-distinct and the interpretations subjective. Examination of\nlaboratory experiments of fracture closure also suggest the following.\n\u2022Measurements of fracture dimensions and pressure during closure show that fracture closure begins\nat the fracture tip and proceeds to the wellbore, which confirms the closure process of Hayashi and\nHaimson (1991); however, the pressure at tip closure did not correspond to the minimum horizontal\nstress.\n\u2022Although changing compliance was observed in samples based on measurements of fracture\ndimensions and pressure, the fracture closure pressure corresponding to changing compliance did\nnot correspond to the minimum horizontal stress.\n\u2022Fracture closure is observed as storage distortion of the pressure falloff dissipates, which\ncorresponds to closure at the wellbore and a near-residual fracture volume.\n\u2022In soft rock, like unconsolidated sand, G-function derivative analysis and the log-log storage"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8954fe-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 23, "chroma:document": "\u2022In soft rock, like unconsolidated sand, G-function derivative analysis and the log-log storage\ndiagnostic correctly interpret fracture closure, but the closure pressure does not correspond to the\nminimum horizontal stress.\n\u2022In hard rock, G-function derivative analysis and the log-log storage diagnostic correctly interpret\nfracture closure, and the fracture closure pressure is approximately equal to the minimum horizontal\nstress.\nAcknowledgment\nWe appreciate Hans de Pater providing the raw pressure and time data for CTC08 and the blind test.\nNomenclature\nAf= fracture area, L2\nB= formation volume factor, L3/L3\ncf= compressibility of fluid in fracture, Lt2/m\ncw= compressibility of fluid in wellbore, Lt2/m\nC= wellbore and fracture storage, L4t2/m\nCf= time-dependent fracture compliance, L4t2/m\nCs= slug-test storage coefficient, L4t2/m\nCt= system compliance, L4t2/m\nE= Young's modulus, m/Lt\nE'= Plane-strain modulus, m/Lt2\nE(m) = complete elliptical integral, dimensionless"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895558-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 23, "chroma:document": "Ct= system compliance, L4t2/m\nE= Young's modulus, m/Lt\nE'= Plane-strain modulus, m/Lt2\nE(m) = complete elliptical integral, dimensionless\nF= hypergeometric function, dimensionless\ng= loss-volume function, dimensionless\nG= G-function, dimensionless\nh= height, L, ft\nhf= fracture height, L, ft\nk= permeability, L2, md\nLf= fracture half-length, L, ft\np= pressure, m/Lt2\npws= wellbore pressure with variable flow rate, m/Lt2\npwc= wellbore pressure with constant flow rate, m/Lt2\nq= flow rate, L3/t\nSf= fracture stiffness, m/L4t2\nSeff= system stiffness, m/L4t2"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8955a8-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 24, "chroma:document": "SPE-187038-MS 25\nsfs= fracture-face skin, dimensionless\nt= time, t\ntLfD= Dimensionless time, dimensionless\nVw= wellbore volume, L3\nVf= fracture volume one wing, L3\nGreek\n\u03b1N= fracture growth exponent, dimensionless\n\u0394= difference, dimensionless\n\u03bc= viscosity, m/Lt, cp\n\u03c4= variable of substitution, dimensionless\n\u03d5= porosity, dimensionless\n\u0393= Euler gamma function, dimensionless\nSubscripts\nc= constant-rate\n\u0394Cbc = changing-compliance closure\nD= dimensionless\ne= end of injection\nfinal = last recorded\ni= property evaluated at initial conditions\n0= end of injection\ns= slug test\nw= wellbore\nr= reservoir\nReOpen = observed re-opening\nReferences\nBarree, R.D., Barree, V .L., and Craig, D.P. 2009. Holistic Fracture Diagnostics: Consistent Interpretation of Prefrac\nInjection Tests Using Multiple Analysis Methods. SPE Prod & Opers 29 (03). https://doi.org/10.2118/107877-PA\nBarree, R.D. and Mukherjee, H. 1996. Determination of Pressure Dependent Leakoff and Its Effects on Fracture Geometry."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8955f8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 24, "chroma:document": "SPE-36451-MS. https://doi.org/10.2118/36451-MS\nBranagan, P.T., Peterson, R.E., Warpinski, N.R., Wright, T.B. 1996b. Characterization of a Remotely Intersected Set\nof Hydraulic Fractures: Results of Intersection Well No. 1-B, GRI/DOE Multi-Site Project. Presented at the SPE\nAnnual Technical Conference and Exhibition, Denver, Colorado, U.S.A., 6-9 October. SPE-36452-MS. https://\ndoi.org/10.2118/36452-MS\nBranagan, P.T., Peterson, R.E., and Wilmer, R. 1997a. Measurements of Well-to-Well Conductivity Through a Propped\nHydraulic Fracture. Presented at the 1997 SPE Rocky Mountain Regional Meeting, Casper, Wyoming, U.S.A., 18-21\nMay. SPE-38375-MS. https://doi.org/10.2118/38375-MS\nBranagan, P.T., Warpinski, N.R., Peterson, R.E., Hill, R.E., and Wolhart, S.L. 1997b. Propagation of a Hydraulic Fracture\ninto a Remote Observation Wellbore: Results of C-Sand Experimentation at the GRI/DOE M-Site Project. Presented"}


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


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


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 25, "chroma:document": "Permeability Reservoirs Symposium and Exhibition, Denver, Colorado, USA, 12-15 March. SPE-60291-MS. https://\ndoi.org/10.2118/60291-MS\nde Pater, C.J., Weijers, L. Savic, M., Wolf, K.H.A.A., van den Hoek, P.J., and Barr, D.T. 1994. Experimental Study of\nNonlinear Effects in Hydraulic Fracture Propagation. SPE Prod & Facilities 9 (04). https://doi.org/10.2118/25893-PA\nde Pater, C.J., Desroches, J., Groenenboom, J., and Weijers, L. 1996. Physical and Numerical Modeling of Hydraulic\nFracture Closure. SPE Prod & Facilities 11 (02). https://doi.org/10.2118/28561-PA\nvan Dam, D.B. and de Pater, C.J. 2017. Personal communication.\nDong, Y . and de Pater, C.J. 2007. Closure of Hydraulic Fractures Visualized by X-ray CT Technique in Sand. Presented\nat the 1st Canada \u2013 U.S. Rock Mechanics Symposium, Vancouver, Canada, 27-31 May. ARMA-07-082.\nGulrajani, S.N., Nolte, K.G.,, Romero, J. 2001. Evaluation of the M-Site B-Sand Fracture Experiments: Evolution of a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 25, "chroma:document": "Gulrajani, S.N., Nolte, K.G.,, Romero, J. 2001. Evaluation of the M-Site B-Sand Fracture Experiments: Evolution of a\nPressure Analysis Methodology. SPE Prod & Facilities 16 (01). https://doi.org/10.2118/69206-PA\nHayashi, K. and Haimson, B.C. 1991. Characteristics of Shut-in Curves in Hydraulic Fracturing Stress Measurements\nand Determination of in Situ Minimum Compressive Stress. Journal of Geophysical Research 96 (B11) 18,311-321.\nhttps://onlinelibrary.wiley.com/doi/10.1029/91JB01867\nMcClure, M.W., Jung, H., Cramer, D.D., and Sharma, M.M. 2015. The Fracture-Compliance Method for Picking Closure\nPressure From Diagnostic Fracture-Injection Tests. SPE Journal 21 (04). https://doi.org/10.2118/179725-PA\nMiddlebrook, M.L., Aud, W.W., Harkrider, J.D., and Hansen, J.T. 1997. An Evolving Approach in the Analysis of Stress-\nTest Pressure-Decline Data. SPE Production & Facilities 12 (03). https://doi.org/10.2118/29599-PA"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 25, "chroma:document": "Test Pressure-Decline Data. SPE Production & Facilities 12 (03). https://doi.org/10.2118/29599-PA\nNolte, K.G. 1979. Determination of Fracture Parameters From Fracturing Pressure Decline. Presented at the 1979 SPE\nAnnual Technical Conference and Exhibition, Las Vegas, Nevada, USA, 23-26 September. SPE-8341-MS https://\ndoi.org/10.2118/8341-MS\nPeterson, R.E., Wolhart, S.L., Frohne, K.W., Branagan, P.T., Warpinski, N.R. and Wright, T.B. 1996. Fracture\nDiagnostics Research at the GRI/DOE Multi-Site Project: Overview of the Concept and Results. Presented at the\nSPE Annual Technical Conference and Exhibition, Denver, Colorado, U.S.A., 6-9 October. SPE-36449-MS. https://\ndoi.org/10.2118/36449-MS\nRaaen, A.M., Skomedal,, E., Kj\u00f8rholt, H., Markstead, P., and \u00d8kland,D. 2001. Stress determination from hydraulic\nfracturing tests: the system stiffness approach. Int. Journal of Rock Mechanics & Mining Science 38 (2001) 529-541."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 25, "chroma:document": "fracturing tests: the system stiffness approach. Int. Journal of Rock Mechanics & Mining Science 38 (2001) 529-541.\nRohatgi, A. 2017. WebPlotDigitizer. V3.12. June 2017. Austin, Texas, USA http://arohatgi.info/WebPlotDigitizer\nValk\u00f3, P.P. and Economides, M.J. 1999. Fluid-Leakoff Delineation in High-Permeability Fracturing. SPE Production &\nFacilities 14 (02) May. https://doi.org/10.2118/56135-PA\nvan den Hoek, P. 2017. A Simple Unified Pressure-Transient-Analysis Method for Fractured Waterflood Injectors and\nMinifractures in Hydraulic-Fracture Stimulation. SPE Production & Operations https://doi.org/10.2118/181593-PA\nWarpinski, N.R., Engler, B.P., Young, C.J., Peterson, R., Branagan, P.T., and Fix, J.E. 1995. Microseismic Mapping of\nHydraulic Fractures Using Multi-Level Wireline Receivers. Presented at the SPE Annual Technical Conference and\nExhibition, Dallas, Texas, U.S.A., 22-25 October. SPE-30507-MS. https://doi.org/10.2118/30507-MS"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/SPE_187038_(Craig)_Frac_Closure_Stress_Field_y_Lab_Experiments_Frac_Closure.pdf", "page": 26, "chroma:document": "SPE-187038-MS 27\nWarpinski, N.R., Branagan, P.T., Peterson, R.E., Fix, J.E., Uhl, J.E., Engler, B.P. and Wilmer, R. 1997. Microseismic\nand Deformation Imaging of Hydraulic Fracture Growth and Geometry in the C Sand Interval, GRI/DOE M-Site\nProject. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, U.S.A., 5-8 October.\nSPE-38573-MS. https://doi.org/10.2118/38573-MS\nWarpinski, N.R., Branagan, P.T., Peterson, R.E., Wolhart, S.L. 1998. An Interpretation of M-Site Hydraulic Fracture\nDiagnostic Results. Presented at the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium,\nDenver, Colorado, U.S.A., 5-8 April. SPE-39950-MS. https://doi.org/10.2118/39950-MS\nZanganeh, B., Clarkson, C.R., and Hawkes, R.V . 2017. Reinterpretation of Fracture Closure Dynamics During Diagnostic\nFracture Injection Tests. Presented at the 2017 SPE Western Regional Meeting, Bakersfield, California, USA, 23 April.\nSPE-185649-MS. https://doi.org/10.2118/185649-MS"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89594a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 0, "chroma:document": "SPE 16417 SPE/DOE \nSociety of \nPetroleum Engineers U.S. Department \nof Energy \nModified Fracture Pressure Decline Analysis Including \nPressure-Dependent Leakoff \nby J. L. Castillo* Dowell Schlumberger \n*Member SPE \nCopyright 1987, Society of Petroleum Engineers \nThis paper was prepared for presentation at the SPE/DOE Low Permeability Reservoirs Symposium held in Denver, Colorado, May 18-19, 1987. \nThis paper was selected for presentation by an SPE Program Committee following review of information contained in an abstract submitted by the \nauthor(s). Contents of the paper, as presented, have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the \nauthor(s). The material, as presented, does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Papers \npresented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89599a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 0, "chroma:document": "presented at SPE meetings are subject to publication review by Editorial Committees of the Society of Petroleum Engineers. Permission to copy is \nrestricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of \nwhere and by whom the paper is presented. Write Publications Manager, SPE, P.O. Box 833836, Richardson, TX 75083-3836. Telex, 730989 SPEDAL. \nABSTRACT \nNolte developed an analysis of the pressure \ndecline following a fracturing treatment to provide an \nestimate of fluid efficiency, fluid loss coefficient, \nand fracture geometry. This analysis has become an \nindustry standard for evaluating and improving the \ndesign of fracturing treatments. The derivations by \nNolte assume the leakoff coefficient is a pressure\u00ad\nindependent constant. This assumption is valid when \nleakoff is controlled by a compressible filter cake. \nIn cases where leakoff is primarily controlled by"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895a08-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 0, "chroma:document": "leakoff is controlled by a compressible filter cake. \nIn cases where leakoff is primarily controlled by \nfiltrate viscosity, by an incompressible filter cake, \nor by reservoir permeability and compressibility, the \nleakoff coefficient is pressure dependent, and, there\u00ad\nfore, declines during the closure period. Under these \ncircumstances, direct application of the Nolte tech\u00ad\nnique may not be appropriate, and could cause an \noptimistic estimate of fluid efficiency and leakoff \ncoefficient. \nThis paper introduces a new plot for fracture \npressure decline analysis that determines the pressure \nparameters (ISIP, Pc, P*) required in the Nolte leak\u00ad\noff calculations. The derivative of this plot may be \nused to identify the extension period, the closure \nperiod, and to assess the influence of pressure depen\u00ad\ndent 1 eakoff on fracture pressure decline. In order \nto account for pressure dependent 1 eakoff, equations \nare presented where the leakoff coefficient is treated"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895a62-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 0, "chroma:document": "to account for pressure dependent 1 eakoff, equations \nare presented where the leakoff coefficient is treated \nas a mathematical variable.\u00b7 The equations describe \nsimple linear relations applicable to the fracture \nclosure period. When these relations are plotted on \nReferences and illustrations at end of paper. Cartesian coordinates, the closure period is recog\u00ad\nnized by a straight line with slope proportional to \nthe 1 eakoff coefficient. As shown in the examples, \nthis modified approach is easily applied and provides \nnew insight to the fracture closure period. \nINTRODUCTION \nThe methodology currently used in fracture pres\u00ad\nsure decline analysis employs type-curve matching to \ndetermine a match pressure (P*) that is proportional \nto the leakoff coefficient.1'2 Data used in the curve \nmatch must correspond to the closure period. This \nperiod is usually interpreted as the 11linear11 region \nof a square-root of time plot or as the half-slope"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895ab2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 0, "chroma:document": "period is usually interpreted as the 11linear11 region \nof a square-root of time plot or as the half-slope \nregion of a log-log plot.3,4 Analysis of the square\u00ad\nroot plot or the log-log plot, however, is often \ninconclusive. To aid identification of the closure \nperiod, the closure pressure is usually determined \nprior to a calibration treatment from a stress test \n(e.g. pump-in flow-back test). \nA new plot is introduced that has the unique \nadvantage of providing all of the pressure variables \n(ISIP, Pc, P*) required in decline analysis. This \nplot is more easily applied than the Nolte type \ncurves, and is superior to the square-root of time \nplot because it uses a more precise relationship \nbetween decline pressure and time. When the deriva\u00ad\ntive of this plot is graphed against time, fracture \nextension after shut-in, fracture closure, and pres\u00ad\nsure dependent 1 eakoff can be observed. This plot \nenhances interpretation and identification of the"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895af8-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 0, "chroma:document": "sure dependent 1 eakoff can be observed. This plot \nenhances interpretation and identification of the \nclosure period. However, by no means should use of \nthis plot replace stress tests. \nWhen analysis of the derivative plot indicates a \ndependence of leakoff rate on pressure, a technique is \npresented to account for a declining leakoff coeffi\u00ad\ncient during closure. \n273 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895b48-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "2 MODIFIED FRACTURE PRESSURE DECLINE ANALYSIS \nINCLUDING PRESSURE-DEPENDENT LEAKOFF SPE 16417 \nDEVELOPMENT OF THE 11G-FUNCTION11 PLOT \nNolte1'2 has shown that, during closure, the \npressure difference between two shut-in times can be \nexpressed as \n1r\u2022C\u2022f \u2022It \n__ ...__P _ _._p \u2022 G(to,t*o) \n2 \u2022cf \n(l~t> ~t*) ( 1) \nwhere, ~t* is a reference time since shut-in, C is the \nleakoff coefficient, fp is the ratio of permeable area \nto gross area, tp is pump time, and t0 is dimension\u00ad\nless time (M/t ). Equations for cf (fracture's \ncompliance for wfdth) and G (dimensionless difference \nfunction) are given in Appendix A. \nA Nolte type-curve1 is constructed by selecting a \ndimensionless reference time (t11*) prior to closure \nand plotting G against t0 on log-log coordinates. The \nsame reference time is used to plot ~p against ~t \u00b7 on \nlog-log coordinates. A curve match is obtained by \noverlaying the curves, aligning the x axes so that ~t \ncorresponds to t0, and shifting along the y axis."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895b98-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "overlaying the curves, aligning the x axes so that ~t \ncorresponds to t0, and shifting along the y axis. \nOnce a match is obtained, a match point is selected, \nand the Nolte match pressure (P*) is computed from \n~P/G. The match pressure is equivalent to \nTI\u2022C\u2022f \u00b7It P* = p . p (2) \n2\u2022cf \nWhen compliance can be inferred, the leakoff \ncoefficient can be estimated from Equation 2. \nThe new plot proposed here makes note of the fact \nthat Equation 1 is a linear equation. Substituting \nEquation 2 into Equation 1, and selecting a reference \ntime of ~t* = 0.0 results in \nP(~t) = P*\u2022G(tD,O) + P(~t* = 0) (3) \nThis equation is in the familiar form of y = mx + \nb. Thus, a Cartesian plot of decline pressure against \nG (referred to below as the 11G-Function11 plot) should \nresult in a straight line during the closure period \nwith slope equal toP* andy-intercept equal to a \ntheoretical pressure at shut-in. The closure period \nis recognized by linearity; deviation from linearity"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "theoretical pressure at shut-in. The closure period \nis recognized by linearity; deviation from linearity \nidentifies the closure pressure. From this single \nplot, then, all of the pressure parameters ( Pc, P*, \n!SIP) required in the analysis calculations are \ninferred. \nInterpretation of the G-Function plot is enhanced \nby differentiating Equation 3 to give \ndP \nP* (4) \ndG \nA graph of dP/dG against ~t (referred to as the \nG-Function derivative plot) should provide a horizon\u00ad\ntal line during the closure period with a constant y\u00ad\naxis value of P*. The derivative, dP/dG, may be \ncomputed by using linear regression on a small number \nof data points (e.g. 5); the ~t value that corresponds \nto dP/dG is a time average of the points used. Example 1 \nFigures 1 and 2 are the G-Function and G-Function \nderivative plots, respectively, for a case where a \ncrosslinked HPG fluid was used in a gas well. Figure \n2 shows the G-Funct ion plot is 1 i near ( i .e. constant"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895c2e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "crosslinked HPG fluid was used in a gas well. Figure \n2 shows the G-Funct ion plot is 1 i near ( i .e. constant \nslope) from 10 to 32 minutes. The non-linearity from \nshut-in to 10 minutes is interpreted as fracture \nextension after shut-in, while the non-linearity after \n32 minutes implies that the fracture is closed. \nAn estimate of a theoretical !SIP is obtained by \ndrawing a line through the linear portion of the G\u00ad\nFunction plot and extrapolating to the y-axis (as \nindicated in Figure 1). The difference between the \ntheoretical !SIP and the observed !SIP corresponds to \na decrease in fracture width resulting from continued \nfracture extension after shut-in. Use of the theoret\u00ad\ni c a 1 I S I P i n t he Nolte e f f i c i en c y c a 1 c u 1 at i o n 2 s h o u 1 d \nprovide a lower bound estimate of fluid efficiency. \nFigure 3 is the square-root of time plot using \nthe same data as above; Figure 4 is the derivative \nplot of the square-root of time. As shown by Figure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895c7e-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "the same data as above; Figure 4 is the derivative \nplot of the square-root of time. As shown by Figure \n4, the square-root plot is never linear. Instead, the \nsquare-root plot exhibits an inflection when fracture \nclosure occurs. The inflection is observed as a \nchange in slope (from + to -) in the square-root \nderivative plot. The implication of this example is \nthat the square-root of delta time is not directly \nproportional to the pressure decline during fracture \nclosure. \nThe G-Functi on plot, therefore, represents the \nclosure period more accurately than the square-root of \ntime plot since G is linearly related to the pressure \ndecline. Both the G-Function plot and the square-root \nof time plot are enhanced by plotting their deriva\u00ad\ntives against time. \nPRESSURE DEPENDENT LEAKOFF \nNolte1'2 developed Equation 1 from an assumption \nthat the leakoff coefficient is independent of varia\u00ad\ntions in pressure. This assumption was shown to be"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895cce-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "that the leakoff coefficient is independent of varia\u00ad\ntions in pressure. This assumption was shown to be \nvalid when leakoff is controlled by a compressible \nfilter cake.2 When leakoff is primarily controlled by \nan incompressible filter cake, by filtrate viscosity, \nor by the reservoir, the leakoff coefficient is depen\u00ad\ndent on pressure.2,s During fracture closure, there\u00ad\nfore, the leakoff coefficient declines as the pressure \nin the fracture declines. As indicated by Equations 2 \nand 4, a declining 1 eakoff coefficient should result \nin a declining G-Function derivative plot. \nExample 2 \nFigures 5 and 6 are a G-Functi on plot and a G\u00ad\nFunction derivative plot, respectively, for a case \nwhere an oil reservoir was fractured with a waterfrac \nfluid (10 lb polymer per 1,000 gallons). The leakoff \ncontrol in this case is primarily due to the reser\u00ad\nvoir's compressibility and permeability; thus, the \n1 eakoff coefficient is pressure dependent. Ex ami na\u00ad"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895d1e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 1, "chroma:document": "voir's compressibility and permeability; thus, the \n1 eakoff coefficient is pressure dependent. Ex ami na\u00ad\ntion of the G-Function derivative plot in Figure 6 \nindicates a slope change at five minutes that corres\u00ad\nponds to fracture closure. The square-root plot in \nFigure 7 also exhibits an inflection at five minutes \n(as indicated in Figure 8). Observe that the G-Func\u00ad\ntion derivative plot in Figure 6 is not horizontal \nduring the closure period. This implies that, when \n274 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895d64-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 2, "chroma:document": "SPE 16417 J. L. CASTILLO 3 \n1 eakoff is pressure dependent, the 1 i near relation \nbetween decline pressure and the G-Function does not \nhold. In these cases, Equation 3 falls short of \naccurately predicting fracture pressure decline. \nEquations that account for pressure dependence \nare presented in the next section. These equations \nwere developed from an assumption of a direct rela\u00ad\ntionship between leakoff rate and a pressure-dependent \nleakoff coefficient. A more comprehensive relation\u00ad\nship, however, between leakoff rate and pressure \nshould be derived using superposition of the total \npressure hi story in the fracture. 6 Thus, the tech\u00ad\nnique proposed below provides a first-order correction \nfor pressure-dependent leakoff. \nSUMMARY OF EQUATIONS FOR PRESSURE DEPENDENT LEAKOFF \nDetermination of Pressure Dependent Leakoff \nCoefficient \nThe general form of the 1 eakoff coefficient as a \nfunction of fracture pressure above reservoir pressure \ncan be expressed as,s"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895db4-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 2, "chroma:document": "Coefficient \nThe general form of the 1 eakoff coefficient as a \nfunction of fracture pressure above reservoir pressure \ncan be expressed as,s \nC(z,t) = M \u2022 (~Pf,r(z,t) )u (5) \nThe ~pf r(z,t) term is the difference between \nfracture pres~ure (Pf) and reservoir pressure (Pr) at \na given position in the fracture (z) at a given time \n(t), i.e.: \n~pf r(z,t) = Pf(z,t) -Pr = , \nPn(z,t) + Pc -Pr \nwhere, \nPn = net pressure above closure \nPc = closure pressure (6) \nThe coefficients, M and u, are functions of the \nleakoff mechanism, and are given below for three cases \nof 1 eakoff control where pressure-dependence is si g\u00ad\nnificant:2,5 \nI: Reservoir Permeability and Compressibility \nu = 1 \nM = .001183 \u2022 lkr \u2022 $r \u2022 cr I ~r \nwhere, \nkr = permeability to reservoir fluid, md \n$r = porosity containing reservoir fluid \ncr = compressibility of reservoir fluid, \n~r = reservoir fluid viscosity, cp \nII: Viscosity of Fluid Filtrate \nu = 112 \nM = .001483 \u2022 v'kf \u2022 $f I ~f psi-1 where,"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895e04-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 2, "chroma:document": "~r = reservoir fluid viscosity, cp \nII: Viscosity of Fluid Filtrate \nu = 112 \nM = .001483 \u2022 v'kf \u2022 $f I ~f psi-1 where, \nkf =permeability to fracture fluid filtrate, md \n$f =porosity containing fracture fluid filtrate \n~f = fracture fluid filtrate viscosity, cp \nIII: Incompressible Filter Cake \nu = 112 \nM = function of filter cake properties \nAn estimate of the total effective leakoff coef\u00ad\nficient as a function of wellbore net pressure (Pnw) \ncan be approximated by \nC( t) = M \u2022 ( Pnw( t) \u2022 8 + pc -pr )u (7) \nwhere the 8 term is defined by Nolte as the ratio of \naverage net pressure in the fracture to well bore net \npressure.1'2 Values for 8 are provided in Appendix A \n(8 = 8p during pumping, 8 = 8s during shut-in). \nEquation 7 can be used to estimate C when M and u have \nbeen determined. The exponent u is selected based on \nthe supposed primary 1 eakoff mechanism. The coeffi\u00ad\ncient M may be graphically determined as discussed in \nthe next sections."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895e54-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 2, "chroma:document": "the supposed primary 1 eakoff mechanism. The coeffi\u00ad\ncient M may be graphically determined as discussed in \nthe next sections. \nDetermination of M for Reservoir Leakoff Control \nThe linear equation below was derived (see Appen\u00ad\ndix B) for the case where the primary mechanism of \n1 eakoff control is from the reservoi r\u2022 s permeabi 1 ity \nand compressibility (i.e. u = 1): \n-1r\u2022M\u2022f \u20228s\u00b7lf \nln[Pnw( ~t) \u20228s + Pc -Pr] = p p \u2022 G(t0,0) \n2 \u2022Cf \n+ ln[Pnw(O) \u2022Ss + Pc -Pr] (8) \nA plot of ln[Pnw(~t)\u20228s + Pc -Pr] against G \nshould yield a straight line during closure with slope \nproportional to M and a y-intercept from which a \ntheoretical ISIP can be inferred. After determining \nthe slope and y-i ntercept of this plot, M can be \ncalculated from \nM - -SLOPE \u20222 \u2022cf \nlT\u2022f 0 8S \u2022ft p p \nand a theoretical ISIP can be calculated from \nexp(yint) -Pc + Pr \nISIP = -------- + Pc \n8S (9) \n(10) \nNotice that calculation of the term ln[Pnw(~t) \u20228s \n+ Pc -Pr] requires an estimate of closure pressure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895e9a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 2, "chroma:document": "ISIP = -------- + Pc \n8S (9) \n(10) \nNotice that calculation of the term ln[Pnw(~t) \u20228s \n+ Pc -Pr] requires an estimate of closure pressure \nand reservoir pressure. Ideally, closure pressure \nwill have been estimated from a stress test and reser\u00ad\nvoir pressure wi 11 have been estimated from a tran\u00ad\nsient pressure test. \nDetermination of M for Filtrate Viscosity or Incom\u00ad\npressible Filter-Cake Leakoff Control \nThe equation below was derived (see Appendix B) \nfor the case where the primary mechanism of 1 eakoff \n275 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895eea-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 3, "chroma:document": "4 MODIFIED FRACTURE PRESSURE DECLINE ANALYSIS \nINCLUDING PRESSURE-DEPENDENT LEAKOFF SPE 16417 \ncontrol is from the viscosity of fracture fluid fil\u00ad\ntrate or from an incompressible filter cake (i.e. u ~ \n1/2): ~ \n[Pnw(~t)\u2022as + Pc-Pr]1/2 = \n+ [Pnw(O)\u2022as + Pc ~ Pr]1/2 ( 11) \nA plot of [Pnw(~t) \u2022as + Pc -Pr]1/2 against G \nshould yield a straight line during closure with slope \nproportional to M and a y-intercept from which a \ntheoretical ISIP can be inferred. After determining \nthe slope and y-i ntercept of this plot, M can be \ncalculated from \nSLOPE\u20224\u2022cf \nM = -~~~--..:.-\n'JT\u2022f \u2022as\u00b7lt p p (12) \nand a theoretical ISJP can be calculated from \n2 (yint) -Pc + Pr \nISIP = -----....,..-.- + Pc (13) \nas \nNotifh that cal cul ati on of the term [Pnw( 4t) \u2022 as + \nPc -PrJ requires an estimate of closure pressure \nand reservoir pressure. \nFluid Efficiency \nThe following equation was derived to include \npressure dependent l eakoff effects in Nol te\u2022 s fluid"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895f44-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 3, "chroma:document": "and reservoir pressure. \nFluid Efficiency \nThe following equation was derived to include \npressure dependent l eakoff effects in Nol te\u2022 s fluid \nefficiency calculation 2 based on dimensionless closure \ntime (t0c): \n.,.b -~2 -4ac \neff = (14) \n2a \nwhere, \na gdl gdu \nb gdu 2. gdl + 1 -Ks/ j c = gdl 1 (15) \nand, \ngdl gl(tDc) \n--\"--~ and gdu (16) \ngl ( O) \nKs = Nolte\u2022s correction for spurt (usually 1.0) \nAlso, \nj (17) Pnws = wellbore net pressure at shut-in \nm = slope of Nolte-Smith plot \nPc = closure pressure \nPr = reservoir pressure \nThe terms g1 and gu are the lower and upper \nbound, respectively, for Nolte\u2022s dimensionless loss\u00ad\nvolume function.1'2 Equations for these functions can \nbe found in Appendix A. Note that when pressure\u00ad\ndependence becomes negligible, the exponent u ap\u00ad\nproaches 0 and j in Equation 17 approaches unity. \nAPPLICATION \nRecall that Example 2 was characterized by a \ndeclining leakoff coefficient during closure (Figure"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b895f8a-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 3, "chroma:document": "APPLICATION \nRecall that Example 2 was characterized by a \ndeclining leakoff coefficient during closure (Figure \n6). Since the reservoir in this example was liquid \nfilled, and since the wall-building properties of the \nfluid were negligible, it was inferred that leakoff \ncontrol was primarily due to the reservoir. There\u00ad\nfore, Equation 8 was used to construct the specialized \nplot in Figure 9. The derivative plot (Figure 10) \nshows that Figure 9 is linear during the closure \nperiod. This implies that Equation 8 pro vi des a \nlinear relation during closure between functions of \npressure and time when leakoff is reservoir con\u00ad\ntrolled. Table 1 compares analysis results between \nEquations 1 and 2 (pressure independence) and Equa\u00ad\ntions 7, 8, and 9 (pressure dependence). Notice that \nif data near closure had been used in the Nolte type\u00ad\ncurve match, a P* value of 1,270 psi would have been \nestimated resulting in a C value of .0038. This value"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b896002-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 3, "chroma:document": "curve match, a P* value of 1,270 psi would have been \nestimated resulting in a C value of .0038. This value \nis 25% less than the value calculated from Equation 7 \nwhen pressure-dependence is considered. \nCONCl-USIONS \nA new plot (G-Function plot) has been introduced \nthat is superior to the square-root of time plot. The \nsquare-root plot uses an approximate relationship \nbetween pressure and time, whereas the G-Function plot \nuses a more precise relationship (gquation 5), When \nthe derivative of the G-Function plot is graphed \nagC!i nst time, phenomena such as fracture extension \nafter shut-in, fracture closure, and pressure-depen ... \ndent 1 eakoff can be observed, To account for pres\u00ad\nsure-dependence, first-order approximation functions \nare provided (Equations 8, 11) to correct for a de\u00ad\nclining leakoff coefficient during closure. These \nfunctions tend to linearize the relation between \npressure and time during the closure period. As shown"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b896052-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 3, "chroma:document": "functions tend to linearize the relation between \npressure and time during the closure period. As shown \nin Example 2, ignoring pressure dependence can result \nin an optimistic estimate of the leakoff coefficient. \nNOMENCLATURE \na = viscosity degradation coefficient \nAf = fracture area, ft2 \ncf = fracture compliance for width, ft/psi \nC = leakoff coefficient, ft/lrnln \nE1 = plane-strain modulus, psi \neff = \nf = p \nf(tp) \ng (to) = fluid efficiency \nratio of permeable area to gross area \ndimensionless loss-rate function \ndimensionless loss-volume function \n276 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8960a2-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 4, "chroma:document": "SPE 16417 J. L. CASTILLO 5 \nG(t0,t*0) dimensionless difference function \nHg =gross fracture height, ft \n!SIP = instantaneous shut-in pressure, psi \nk = permeability, md \nL = fracture half-length, ft \nM = leakoff proportionality constant \nn\u2022 behavior index of fracturing fluid \nP pressure, psi \nPc closure pressure, psi \nPr = reservoir pressure, psi \nPn = net pressure above closure, psi \nPnw = wellbore net pressure, psi \nP* = Nolte Match Pressure, psi \n~t = delta time since shut-in, minutes \n~t* = reference time since shut-in, minutes \nt = p pump time, minutes \nto = dimensionless delta time ( t.t/tp) \nu = exponent for leakoff \nVi = injected volume , ft 3 \nw = average fracture width, ft \nz ::: position in fracture \nS = ratio of average net pressure to wellbore \nnet pressure \n~P(~t,~t*) = pressure difference between ~t and ~t* \n~Pf,r =difference between fracture and reservoir \npressure \n~s = Nolte\u2022s correction for spurt \n~ = porosity \n~ = viscosity, cp \nREFERENCES"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8960f2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 4, "chroma:document": "~Pf,r =difference between fracture and reservoir \npressure \n~s = Nolte\u2022s correction for spurt \n~ = porosity \n~ = viscosity, cp \nREFERENCES \n1. Nolte, K. G.: 110etermination of Fracture Parame\u00ad\nters from Fracturing Pressure Decline Analysis, .. \npaper SPE 8341 presented at the 1979 SPE Annual \nTechnical Conference and Exhibition, Las Vegas, \nSept. 23-26. \n2. Nolte, K. G.: 11A General Analysis of Fracturing \nPressure Decline Analysis With Application to \nThree Models,11 SPEFE (Dec. 1986) 571-583. \n3. \n4. \n5. Elbel, J. L. et al.: 11Stimulation Study of Cot\u00ad\ntage Grove Formation, .. J. Pet. Tech. (July 1984) \n1199-1205. \nNolte, K. G.: 11Fracture Design Considerations \nBased on Pressure Analysis ,11 paper SPE 10911 \npresented at the SPE Cotton Valley Symposium, \nTyler, May 1982. \nHoward, G. C. and Fast, C. R.: \ning, Monograph Series, SPE, \n( 1970) , Vo 1 \u2022 2. Hydraulic Fractur\u00ad\nRichardson, Texas \n6. Nolte, K. G.: Personal communication, Feb. 1987. APPENDIX A"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b896142-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 4, "chroma:document": "( 1970) , Vo 1 \u2022 2. Hydraulic Fractur\u00ad\nRichardson, Texas \n6. Nolte, K. G.: Personal communication, Feb. 1987. APPENDIX A \nCalculation of Fracture Compliance (cf): \nThe fracture\u2022s compliance for width is given by \nNolte as: \n'IT. ss \ncf = -~ \u2022 \n2 \u2022E I r- -\nHg PK \n2 \u2022L \n32 \n--z\u2022L \n31T --KGD \nRadial (A1) \nwhere E1 is the plane-strain modulus, Hg is gross \nfracture height, Lis hydraulic half-length, and Sis \nthe ratio of average net pressure in the fracture to \nthe well bore net pressure at shut-in. Nolte reports \nvalues of s during closure (ss) and during pumping \n( Sp) as f o ll ows : \n[2n+2)./(2n.+3+a~\u00b7 PK Ss 0. 9 KGD \n0.925 Radial \nand, \nn\u2022 \na ~2n+2)/(3n+3+aJ.\u00b7 PK\u00b7. Sp = ~ 0.85 KGD \n? Radial \nBehavior index of fracture fluid \nNolte viscosity degradation correction \n0 for no degradation \n1 for moderate degration \n2 for severe degradation (A2) \n(A3) \nThe Sp value for the radial model is expected to \nbe much less than unity.2 \nOnce efficiency has been determined, the following"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b896188-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 4, "chroma:document": "(A3) \nThe Sp value for the radial model is expected to \nbe much less than unity.2 \nOnce efficiency has been determined, the following \nequation from Nolte2 can be used to estimate fracture \nhalf-length (L): \nr-2 ~ \nHg \u2022L PK \nVi \u2022eff\u2022E1 2 \nss . 2 \u2022Hg \u2022L KGD (A4) \n16 3 -\u00b7L Radial \n31T \nwhere, '---\ninjected vo 1 ume \nnet pressure immediately after shut-in \nOnce compliance has been determined, average \nhydraulic width in the fracture at shut-in can be \nestimated from: \n(A5) \nCalculation of the G-Function: \nThe G-Function is calculated from Nolte\u2022sl,2 \ndimensionless loss-volume function (g) as follows: \n4 \n\u2022 [g(t0) .. g(O)] (A6) \n'IT \n277 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


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


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 5, "chroma:document": "change of fracture volume can be related to the rate \nof change of average fracture width (w): \ndw \n-Af \u00b7-= q(t) \ndt (B3) \nBased on Nolte\u2022 s definition of compliance, the \nrate of change in average fracture width can be re\u00ad\nlated to the rate of change in net pressure: \ndw dPnw \n(B4) \ndt dt \nSubstituting B3 and B4 into B2 cancelling Af, and \nrearranging terms results in an equation that relates \nrate of change in pressure to dimensionless time: \n-dPnw \ndt 2\u2022M\u2022fp\u2022{Pnw\u2022Ss + Pc-Pr}u \nCf\u2022~ \nSeparating variables results in: \n-dPnw 2\u2022M\u2022f \u00b7It \n_ ____.,P _ _._P \u2022 f ( t D) d t D \ncf {Pnw\u2022Ss + Pc -Pr}u (B5) \n(B6) \nIntegrating B6 between shut-in (tD=O) and some \nlater time using u=l and u=l/2 provides the relations \npresented in this paper. \n278 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


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


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


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 7, "chroma:document": "Figure 4. Square-Root Derivative Plot (Example 1). \n6,200 \n6,000 \n,_ \n\"iii \n~ 5,aoo \nLaJ \nl:t: \n::::> \nVl 5,600 Vl \nLaJ \nl:t: a.. \n5,400 \n5,200 L..._ __ ___l ____ __.J.. ___ .....J.... __ .....J._ ___ ~---...l------' \n0 0.1 0.2 0.3 0.4 .0.5 0.6 0. 7 \nG FUNCTION \nFigure 5. Pressure vs. the G-Function (Example 2). \n~ 2,500 .--..----------------------------------, \na. -\nLaJ > i= 2,000 \n~ \n~ \nLaJ c \n1-1,500 \nz \n0 a.. \nI \nLO 1,000 \n(!) \n\"C ' 500 a.. \n\"C 0 \nFigure 6. Fracture Closed \n2 3 4 5 6 7 a 9 10 11 12 \nDELTA TIME SINCE SHUT -IN (min) \nG-Function Derivative Plot (Example 2). \n280 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


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


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-16417-ms.pdf", "page": 8, "chroma:document": "..... 0.6 z \n0 \nD... \nI 0.4 Ill 0 \nFigure 10. 2 3 4 s s 7 a 9 10 11 12 \nDELTA TIME SINCE SHUT -IN (min) \nPressure Function (u=l) Derivative Plot \n( Ex amp 1 e 2 ) \u2022 Downloaded from http://onepetro.org/SPERMPTC/proceedings-pdf/87LPR/All-87LPR/SPE-16417-MS/3233786/spe-16417-ms.pdf/1 by University of Houston user on 27 October 2023"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 0, "chroma:document": "SPE-215017-MS\nBest Practices in DFIT Interpretation - Comparative Analysis of 80 DFITs in\nthe Canadian Montney Shale Play\nClaudio Virues , Alexandra Robertson, and Bruce Sendecki , Alberta Energy Regulator\nCopyright 2023, Society of Petroleum Engineers DOI 10.2118/215017-MS\nThis paper was prepared for presentation at the 2023 SPE Annual Technical Conference and Exhibition held in San Antonio, Texas, USA, 16 - 18 October 2023.\nThis paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents\nof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect\nany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89644e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 0, "chroma:document": "consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may\nnot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.\nAbstract\nCurrent practice for conducting minifrac or diagnostic fracture injection tests has been changing with time.\nThe Alberta Energy Regulator (AER) has a pressure and deliverability testing directive that has guidance\non those tests. This guidance was updated in late 2021. Many operators from the Canadian Montney shale\nplay submit minifracs to AER, 80 of these minifracs were summarized statistically in this paper. Closure,\nreservoir pressure, and permeability were the main analyzed parameters in the paper scope.\nRequirements for pressure and deliverability tests are set out by this newly updated directive. Industry\nuses minifrac in horizontal wells with multistage fracture treatments when developing unconventional"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 0, "chroma:document": "uses minifrac in horizontal wells with multistage fracture treatments when developing unconventional\nreservoirs. Closure, initial reservoir pressure is commonly being determined with the common well test.\nHolistic or tangent vs. compliance method are compared for closure pressure in this paper. Readers are\neager to replicate results, so for After Closure Analysis (ACA) methods equations that govern the analysis\nare provided in detail.\nPublished or commercially available holistic and compliance models are compared for closure pressure.\nPublished or commercially available ACA Soliman and Nolte methods are compared for permeability\nand reservoir pressure. Horizontal wells in 80 unconventional shale field case studies are presented. The\nfact that the signature of closure pressure is not apparent is a significant finding. Similarity of closure\npressure outcomes or estimates for tangent vs compliance is remarkable. Differentiation of reservoir"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 0, "chroma:document": "pressure outcomes or estimates for tangent vs compliance is remarkable. Differentiation of reservoir\npressure determination for either linear or radial flow are observed. Interpretation on net pressure impact is\nevaluated and ultimately differentiation on ACA permeability determination is assessed. Analogous shale\nplays operators in USA and current Canadian Montney Shale play operators will find practical and direct\nimplications. To calculate effective fracture half length and optimize fracture design and well spacing\naccurate permeability values are needed. To design hydraulic fractures with geomechanics applications\naccurate closure pressure values are essential. To conduct Rate Transient Analysis (RTA) for resources and\nreserves assessment in similar unconventional shale plays accurate initial reservoir pressure as an input is\nfundamental.\nComparing analytically closure pressure methods in unconventional shale plays is novel. In addition,"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 0, "chroma:document": "fundamental.\nComparing analytically closure pressure methods in unconventional shale plays is novel. In addition,\npracticing engineers or well testing interpreters will find the comparison of different after closure analysis\nrelevant.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
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 1, "chroma:document": "2 SPE-215017-MS\nIntroduction\nThe AER requires pressure data to better manage the Montney resource play by understanding regional\npressure trends. Pressure analysis is also important to confirm the resource estimate used for annual reserves\nreporting in ST98 Alberta Energy Outlook. As part of contributions towards modernization, the AER has\nrevised the pressure and deliverability testing of oil and gas wells directive to include a minifrac testing and\nsubmission requirement. To ensure licensees and operators could submit minifrac results and data, AER\nrevised the PAS file in early 2020.\nHorizontal multistage wells with important volumes of treatment fluids are being used by industry in\nthe development of unconventional or tight reservoirs. In these reservoirs, build up tests are not providing\na representative initial reservoir pressure post-completion mainly due to extended shut-in time needed."}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 1, "chroma:document": "a representative initial reservoir pressure post-completion mainly due to extended shut-in time needed.\nInstead, minifrac, fracture injection or fall-off test has become the go to well test as far as determination of\ninitial reservoir pressure in unconventionals.\nProppant-less minifracs are normally executed before the principal hydraulic fracture treatment.\nMinifrac's intent is generate a short fracture while injecting in order for the formation to be broken down.\nTherefore, while the pressure is falling down, the closure of the short fracture could be observed. Small\ninjected volumes of typically water, normally less than 16 m3, are used in these low rate tests. Less than\n15 minutes are normally used for total injection to be concluded, with the pressure falling (fall-off) over\ntypically a period of two weeks.\nDuring injection and fall-off periods the data on pressure is collected. Pressure is uploaded, smoothed"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b896d7c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 1, "chroma:document": "typically a period of two weeks.\nDuring injection and fall-off periods the data on pressure is collected. Pressure is uploaded, smoothed\nand filtered for analysis in order to extract stress estimates, pore pressure and permeability. While assisting\nproduction and pressure analysis, being inputs for reservoir models, aiding to reserves quantification or\nstimulation assessment, determination of pore pressure and permeability is extremely important. Once\npressure data is analyzed and interpreted, leak-off coefficients, gradient of fracture pressure and closure of\nfracture pressure or minimum principal stress (or S min) could aid fracture design.\nGeology of Montney\nIn late 2013, NEB, AER and BC MoNGC assessed collaboratively the Montney geological formation's\nsaleable, and not conventional oil resources.\nIn Alberta and British Columbia in the 1950's, industry was focusing only on dolostone/sandstone"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 1, "chroma:document": "saleable, and not conventional oil resources.\nIn Alberta and British Columbia in the 1950's, industry was focusing only on dolostone/sandstone\nMontney reservoir for oil and gas discovery. Siltstone, which has far greater volume of rock with oil and\ngas in it but less permeable, surrounded the standard dolostone/sandstone reservoir at the time. Montney\nsiltstones had to wait until 2005 to be developed, when drilling horizontals and multistage hydraulic\nfracturing came roaring.\nThe Montney geological formation (Lower Triassic) is vast, approximately ~131,000 km2 (Figure 1).\nIts thickness is roughly on average 200 m, while thinning out at its eastern and northeastern flanks while\nspreading to over 300 m on the west before commencing with outcrops in the Rocky peaks.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


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


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 3, "chroma:document": "4 SPE-215017-MS\n\u2022Fluid Efficiency: accumulated volume within the fracture divided by the total fluid injected.\nThis paper will review two methods to pick closure:\n1.McClure et al (2019)\n2.Barree et al (2009)\nAfter Closure Analysis (ACA)\nAfter Closure Analysis is completed on fall-off data compiled after fracture closure. The workflow is akin\nto conventional pressure transient analysis.\nThere are two ACA techniques discussed in this paper: Nolte and Soliman/Craig\nPre-Closure \u2013 \"Compliance\" procedure from McClure et al. (2019)\nFigure 2  shows field and simulation data with indication of closure from the tangent method (blue) and\nindication of closure from the fracture-compliance method (orange).\nFigure 2\u2014Identification of closure from the tangent and compliance\nmethod in field and simulation data (Source: SPE Journal 21)\nDiagnostic plots.   Figure 3  (left) reveals a DFIT conducted in the Montney formation. The plot shows"}


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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 3, "chroma:document": "Diagnostic plots.   Figure 3  (left) reveals a DFIT conducted in the Montney formation. The plot shows\nmeasured calculated bottomhole pressure (BHP). When calculating fracture closure pressure, a hydrostatic\nadjustment would be added to convert from wellhead pressure (WHP) to BHP.\nFigure 3\u2014BHP Pressure (blue) and injection rate (orange) versus elapsed\ntime in hours (left) and BHP (blue) and dP/dG (red) versus G-time (right)Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


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


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 4, "chroma:document": "good. Appraising stress with these types of tests is considered best practice.\nFigure 5\u2014\"Weak\" (left) vs. \"No\" (right) indication of McClure closure\nThe plot on the right can be characterized as displaying \"no\" indication of closure. The dP/dG plot is\ndiminishing monotonically downward without modulating upward. Best practice is not to carry on with\nestimating stress from these types of tests.\nEstimating effective Instantaneous Shut-in Pressure (ISIP).   Figure 6  displays how to detect contact\npressure and determine effective ISIP.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 5, "chroma:document": "6 SPE-215017-MS\nFigure 6\u2014Identification of contact pressure and effective ISIP (Source: URTeC-2019-123)\nMinifrac Observations from real data \u2013 McClure et al (2019)\nEstimating effective ISIP and S min.   In Figure 7 , contact happens around G-time of ~7.8, contact pressure\nor closure pressure estimation is 53,908 kPa and for the S min estimation a subtraction of 515 kPa (75 psi)\nfrom fracture closure will be required. The effective ISIP, ~56,000 kPa, is assessed by identifying the point\nof minimum dP/dG and extrapolating the pressure versus G-time curve back to zero from this point. The\neffective ISIP is an assessment for the pressure in the far-field fracture at shut-in. This is the pressure actually\npresent in the fracture that is opening up and spreading the crack.\nFigure 7\u2014Well 6 \u2013 Identification of contact pressure, minimum dP/dG and effective ISIP\nPre-Closure \u2013 \"Holistic\" procedure from Barree et al. (2009)"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 5, "chroma:document": "Figure 7\u2014Well 6 \u2013 Identification of contact pressure, minimum dP/dG and effective ISIP\nPre-Closure \u2013 \"Holistic\" procedure from Barree et al. (2009)\nEstimating closure pressure and Smin.   Barree et al. (2009) proposed penciling in a straight line from\nthe origin to the tangent to the curve, near the peak, and recognizing this as the time of fracture \"closure\",\nbelieved to be equal to S min (see Figure 8 ). This is the so-called \"tangent\" method. Closure event is also\nmarked by a straight vertical dashed line in Figure 8 .Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 6, "chroma:document": "SPE-215017-MS 7\nFigure 8\u2014G-function plot (Source: SPE 107877)\nSupplementary pre-closure interpretations from the \"tangent\" method.\nLeak-off types.\n1.Normal Leak-off (NL)  (Figure 9 , left)\n2.Transverse Fracture Storage/Fracture Height Recession (TFS/FHR) ( Figure 9, right)\n3.Pressure Dependent Leak-off (PDL): (Figure 10, left)\n4.Fracture Tip Extension (FTE)  (Figure 10 , right).\nTable 1  shows a summary of the leak-off types for all 80 field case studies.\nFigure 9\u2014Normal leak-off (left) and transverse fracture storage/fracture height recession leak-off (right) \u2013 Source: S&P GlobalDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 7, "chroma:document": "8 SPE-215017-MS\nFigure 10\u2014Pressure dependent leak-off (left) and fracture tip extension leak-off \u2013 Source: S&P Global\nTable 1\u2014Summary of the leak-off types and whether McClure Closure was observed.\nLeak-Off Type McClure Closure Pressure\nWell 1 TFS / FHR n/a\nWell 2 NORMAL (NL) YES\nWell 3 TFS / FHR YES\nWell 4 TFS / FHR n/a\nWell 5 PDL n/a\nWell 6 TFS / FHR YES\nWell 7 TFS / FHR YES\nWell 8 TFS / FHR YES\nWell 10 PDL n/a\nWell 11 TFS / FHR YES\nWell 12 TFS/FHR n/a\nWell 13 PDL n/a\nWell 14 PDL n/a\nWell 15 PDL n/a\nWell 16 PDL n/a\nWell 17 PDL n/a\nWell 18 TFS / FHR n/a\nWell 19 TFS / FHR n/a\nWell 20 TFS / FHR n/a\nWell 21 PDL n/a\nWell 22 TFS / FHR n/a\nWell 25 TFS / FHR YES\nWell 26 TFS / FHR n/a\nWell 27 TFS / FHR YES\nWell 28 PDL n/a\nWell 29 TFS / FHR n/a\nWell 30 TFS / FHR n/aDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 8, "chroma:document": "SPE-215017-MS 9\nLeak-Off Type McClure Closure Pressure\nWell 31 TFS / FHR YES\nWell 32 TFS / FHR YES\nWell 33 NORMAL (NL) n/a\nWell 35 TFS / FHR n/a\nWell 36 TFS / FHR n/a\nWell 37 TFS / FHR YES\nWell 38 TFS / FHR n/a\nWell 39 TFS / FHR n/a\nWell 40 TFS / FHR n/a\nWell 41 NORMAL (NL) n/a\nWell 42 TFS / FHR n/a\nWell 44 NORMAL (NL) n/a\nWell 45 TFS / FHR n/a\nWell 46 NORMAL (NL) n/a\nWell 47 TFS / FHR n/a\nWell 48 TFS / FHR YES\nWell 49 TFS / FHR YES\nWell 50 NORMAL (NL) YES\nWell 52 TFS / FHR YES\nWell 53 TFS / FHR YES\nWell 54 FTE YES\nWell 55 TFS / FHR YES\nWell 56 TFS / FHR YES\nWell 57 TFS / FHR YES\nWell 58 TFS / FHR YES\nWell 59 NORMAL (NL) n/a\nWell 60 TFS / FHR YES\nWell 61 TFS / FHR YES\nWell 62 TFS / FHR YES\nWell 63 TFS / FHR YES\nWell 64 TFS / FHR YES\nWell 65 TFS / FHR YES\nWell 66 FTE YES\nWell 67 TFS / FHR YES\nWell 68 TFS / FHR YES\nWell 69 TFS / FHR YES\nWell 70 TFS / FHR YES\nWell 71 TFS / FHR YES\nWell 72 TFS / FHR YES"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 8, "chroma:document": "Well 66 FTE YES\nWell 67 TFS / FHR YES\nWell 68 TFS / FHR YES\nWell 69 TFS / FHR YES\nWell 70 TFS / FHR YES\nWell 71 TFS / FHR YES\nWell 72 TFS / FHR YES\nWell 73 TFS / FHR YESDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 9, "chroma:document": "10 SPE-215017-MS\nLeak-Off Type McClure Closure Pressure\nWell 74 TFS / FHR YES\nWell 75 TFS / FHR YES\nWell 76 TFS / FHR YES\nWell 77 TFS / FHR YES\nWell 78 TFS / FHR YES\nWell 79 TFS / FHR YES\nWell 80 TFS / FHR YES\nThe pivot chart in Figure 11  shows how many leak-off types show indication of McClure closure pressure\nvs. when it is not available (n/a). McClure closure is not found in pressure dependent leak-off.\nFigure 11\u2014Pivot chart for leak-off types\nMinifrac Observations from real data - Barree et al. (2009)\nWell 44 - Normal Leak-off G-function Analysis.   The field case in Figure 12 reveals some minor deviation\nfrom the perfect constant leak-off but is a notable example of the anticipated curve shape with a clear-cut\nindication of closure at Gc = 7.157.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 10, "chroma:document": "SPE-215017-MS 11\nFigure 12\u2014Well 44 - G-function\nWell 44- Normal Leak-off Sqrt(t) Analysis.   The plot in Figure 13 , reveals that the slope of the pressure\ncurve begins low, then rises and gets a maximum rate of decline at the inflection point, then diminishes\nagain after closure.\nFigure 13\u2014Well 44 - Sqrt(t) plot\nResults\nEstablished industry methodologies were compared. No one method is recommended over another. The\nanalysis performed demonstrates the ranges of outcomes between the alternative approaches.\nThe results are summarized in Table 2 . Thereafter, we discuss the clarity of the compliance closure\nresponse, a comparison between closure and net pressure from holistic vs. compliance method, estimation\nof permeability and pressure, and rate transient analysis implications.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 11, "chroma:document": "12 SPE-215017-MS\nTable 2\u2014Summary of the statistical comparisons, conditions for inclusion of a test in the comparison, and key findings\nComparisons Condition for Inclusion Key Findings\nComparison of DFITs showing strong,\nadequate, weak, or no \"compliance\" method\nindication of closureNo condition; all DFITs were\nincluded20% showed strong indication of closure,\n~24% showed adequate indication of closure,\n~9% showed weak indication of closure and\n~48% showed no indication of compliance\nclosure.\nComparison of closure pressure\nestimated from \"compliance\" versus\n\"tangent\" methodsMust have strong, adequate \"compliance\"\nindication of closureThe tangent method and compliance\nmethods provide similar closure pressure within\n8% difference.\nComparison of net pressure Must have strong or adequate\n\u2018compliance\u2019 indication\nof closureThe net pressure estimated using tangent\nclosure and ISIP is 10x higher than that estimated\nbased on compliance closure and effective\nISIP, or an average of ~17,000 kPa."}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 11, "chroma:document": "closure and ISIP is 10x higher than that estimated\nbased on compliance closure and effective\nISIP, or an average of ~17,000 kPa.\nComparison of permeability Must have either achieved radial\nand/or linear flowsPermeabilities estimates were of the same\norder of magnitude for Nolte and\nSoliman/Craig.\nComparison of pore pressure Must have either achieved radial\nand/or linear flowsPore pressure estimates were of the same\norder of magnitude for Nolte and\nSoliman/Craig.\nComparison of Xf \u221ak  and\nAf\u221akMust have at least achieved\nlinear flowEstimates are heavily dependent on assumptions\nof net pay. RTA estimates for Af\u221ak\nwere significantly higher, ~300x.\nDiscussion\nClarity of the \"compliance\" closure response\nFigure 14  shows the fraction of tests with strong, adequate, weak, and no \"compliance\" method indication\nof closure on the dP/dG plot.\nFigure 14\u2014Fraction of tests with strong (yellow), adequate (grey),\nweak (orange) and no (red) compliance indication of closure."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 11, "chroma:document": "Figure 14\u2014Fraction of tests with strong (yellow), adequate (grey),\nweak (orange) and no (red) compliance indication of closure.\nClosure pressure from the compliance method and tangent method\nFigure 15  shows a comparison of the dP/dG and G*dP/dG plots from a Montney DFIT.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 12, "chroma:document": "SPE-215017-MS 13\nFigure 15\u2014dP/dG as a function of G-time (left) and G*dP/dG as a function of G-time\n(right) plots from Montney DFITs (Source: Discussion of the Paper SPE-187038-MS)\nThe methods yield similar results as far as closure pressure is concerned. compliance closure pressure is\n~8% higher for this dataset. Table 3 displays a comparison between compliance closure pressure (McClure\net al 2019 ) vs. the holistic closure pressure.\nTable 3\u2014Summary of closure pressure values\nCompliance Closure\nPressure (kPa)Holistic Closure\nPressure (kPa)Delta Closure\nPressure (Xx)Delta Closure\nPressure (kPa)\nWell 1 n/a 49898\nWell 2 40,742 38721 1.1x 2021\nWell 3 43,600 39441 1.1x 4159\nWell 4 n/a 48658\nWell 5 n/a 37136\nWell 6 53,908 50979 1.1x 2929\nWell 7 45000 40154 1.1x 4846\nWell 8 40000 38306 1.0x 1694\nWell 9 n/a 46274\nWell 10 n/a 40993\nWell 11 25500 22849 1.1x 2651\nWell 12 n/a 48941\nWell 13 n/a 42201\nWell 14 n/a 50861\nWell 15 n/a 46387\nWell 16 n/a 32003\nWell 17 n/a 62545\nWell 18 n/a 43727"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 12, "chroma:document": "Well 12 n/a 48941\nWell 13 n/a 42201\nWell 14 n/a 50861\nWell 15 n/a 46387\nWell 16 n/a 32003\nWell 17 n/a 62545\nWell 18 n/a 43727\nWell 19 n/a 36657\nWell 20 n/a 48642\nWell 21 n/a 44425\nWell 22 n/a 39274\nWell 23 n/a 49202\nWell 24 n/a 32177Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


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


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 13, "chroma:document": "Well 56 43000 40475 1.1x 2525\nWell 57 59500 53083 1.1x 6417\nWell 58 44500 38359 1.2x 6141\nWell 59 n/a 55895\nWell 60 42000 38344 1.1x 3656\nWell 61 47000 43332 1.1x 3668\nWell 62 42000 37941 1.1x 4059\nWell 63 37500 36070 1.0x 1430\nWell 64 41000 37720 1.1x 3280Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 14, "chroma:document": "SPE-215017-MS 15\nCompliance Closure\nPressure (kPa)Holistic Closure\nPressure (kPa)Delta Closure\nPressure (Xx)Delta Closure\nPressure (kPa)\nWell 65 50020 45652 1.1x 4368\nWell 66 39000 37827 1.0x 1173\nWell 67 46000 42301 1.1x 3699\nWell 68 40000 36382 1.1x 3618\nWell 69 44000 40475 1.1x 3525\nWell 70 44000 40934 1.1x 3066\nWell 71 45000 41406 1.1x 3594\nWell 72 41500 39774 1.0x 1726\nWell 73 44000 39551 1.1x 4449\nWell 74 44500 39371 1.1x 5129\nWell 75 47000 42233 1.1x 4767\nWell 76 46000 41633 1.1x 4367\nWell 77 47000 43466 1.1x 3534\nWell 78 43500 39560 1.1x 3940\nWell 79 46000 42845 1.1x 3155\nWell 80 42500 38906 1.1x 3594\nAverage 44,472 42,667 1.08x 3,419\nEstimating Permeability and Pore Pressure \u2013 Nolte and Soliman/Craig\nNolte ACA Derivative.   Figure 16  represents the log-log diagnostic plot for well 2 used to confirm fracture\nclosure and identify the flow regimes developed after closure.\nFigure 16\u2014Well 2 - Log-log derivative (diagnostic) plot \u2013 Nolte radial flow"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 14, "chroma:document": "closure and identify the flow regimes developed after closure.\nFigure 16\u2014Well 2 - Log-log derivative (diagnostic) plot \u2013 Nolte radial flow\nNolte ACA Linear Flow.   If impulse linear flow is identified in the derivative plot, the fluid loss coefficients,\nCR and CT, can also be estimated.\nThe equations 1 , 2, 3 and 4 governing impulse linear flow are defined as:Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 15, "chroma:document": "16 SPE-215017-MS\n(1)\n(2)\n(3)\nFigure 17  represents the Well 2 fall-off data using Nolte's linear time function.\nFigure 17\u2014Well 2 - Fall-off data using minifrac linear time function for Nolte\nNolte ACA Radial Flow.   The equations 4 , 5, 6 and 7 governing impulse radial flow are defined as:\n(4)\n(5)\n(6)\n(7)\nFigure 18  represents the Well 3 fall-off data using Nolte's radial time function.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


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


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 17, "chroma:document": "18 SPE-215017-MS\nFigure 20  represents the Well 3 fall-off data using Soliman/Craig's radial time function. When radial flow\nis achieved after closure, this plot yields a constant slope. By fitting a straight line through the radial flow\ntrend, the analysis yields a kh of 0.0353 md.m and k = 1.26E-03md using net pay h = 28.1m.\nFigure 20\u2014Well 3 \u2013 Soliman/Craig analysis minifrac radial flow\nTable 4  summarizes the results of the 80 field cases.\nTable 4\u2014Summary of the permeability values for Nolte and Soliman/Craig After Closure Analysis for radial flow and key findings\nNolte Permeability\nRadial Flow\n(mD)Soliman/Craig\nPermeability Radial\nFlow (mD)Key Findings\nWell 1 3.96E-04 3.69E-04\nWell 2 7.67E-05 1.89E-04\nWell 3 7.30E-04 7.40E-04\nWell 4 4.65E-03 3.72E-03\nWell 5 4.30E-02 Radial flow not\nachieved (Soliman/Craig)\nWell 6 1.80E-04 1.90E-04\nWell 7 1.00E-02 9.10E-05\nWell 11 3.80E+00 3.24E+00\nWell 12 5.97E-03 6.00E-03\nWell 14 1.41E-02 1.29E-02\nWell 15 1.66E-03 1.60E-03"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 17, "chroma:document": "Well 7 1.00E-02 9.10E-05\nWell 11 3.80E+00 3.24E+00\nWell 12 5.97E-03 6.00E-03\nWell 14 1.41E-02 1.29E-02\nWell 15 1.66E-03 1.60E-03\nWell 16 8.07E-02 2.84E-02\nWell 20 3.10E-03 3.16-03\nWell 23 6.20E-03 2.00E-03\nWell 24 4.39E-02 4.36E-02\nWell 25 2.46E-04 2.46E-04\nWell 26 1.40E-04 1.60E-04\nWell 29 3.15E-04 3.04E-04\nWell 30 4.23E-03 Radial flow not\nachievedDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 18, "chroma:document": "SPE-215017-MS 19\nNolte Permeability\nRadial Flow\n(mD)Soliman/Craig\nPermeability Radial\nFlow (mD)Key Findings\n(Soliman/Craig)\nWell 33 1.00E-07 9.70E-08\nWell 34 1.58E-02 1.60E-02\nWell 35 1.50E-01 4.00E-02\nWell 36 3.98E-03 2.30E-03\nWell 37 8.45E+00 5.69E+00\nWell 38 1.03E-02 3.00E-03\nWell 39 3.20E-04 3.30E-04\nWell 41 2.50E-02 Radial flow not\nachieved\n(Soliman/Craig)\nWell 42 1.60E-03 1.60E-03\nWell 43 3.10E-01 3.08E-01\nWell 44 3.70E-03 3.80E-03\nWell 46 3.10E-04 3.10E-04\nWell 48 2.30E-02 2.24E-02\nWell 50 1.02E-03 Radial flow not\nachieved\n(Nolte)\nWell 62 2.40E-03 2.30E-03\nWell 65 1.20E-03 9.90E-04\nWell 80 3.96E-04 3.69E-04\nThe stacked chart in Figure 21  was used to display the relationship of part to whole over Nolte vs Soliman/\nCraig categories."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897650-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 18, "chroma:document": "The stacked chart in Figure 21  was used to display the relationship of part to whole over Nolte vs Soliman/\nCraig categories.\nFigure 21\u2014Stacked area chart for Nolte vs. Soliman/Craig permeability estimates using radial flow.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8976a0-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 19, "chroma:document": "20 SPE-215017-MS\nThe scatter chart in Figure 22  was used to compare Nolte and Soliman/Craig sets of permeability values\nfor radial flow. It shows the one-to-one relationship between both sets of values.\nFigure 22\u2014Scatter Chart for Nolte vs. Soliman/Craig permeability estimates using radial flow.\nThe histogram in Figure 23  shows the frequency of occurrence of values within both data sets, Nolte,\nand Soliman/Craig. Ranges of values are grouped into bins.\nFigure 23\u2014Histogram for Nolte vs. Soliman/Craig permeability estimates using radial flow.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8976e6-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 20, "chroma:document": "SPE-215017-MS 21\nA comparison of pore pressure estimated using Nolte and Soliman/Craig is shown in Table 5.\nTable 5\u2014Summary of the pore pressure for Nolte and Soliman/Craig ACA for radial and linear flow.\nNolte ACA Pore\nPressure Radial\nFlow (kPa)Nolte ACA Pore\nPressure Linear\nFlow (kPa)Soliman/Craig ACA\nPore Pressure Radial\nFlow (kPa)Soliman/Craig ACA\nPore Pressure Linear\nFlow (kPa)\nWell 1 28,013 26,000 28,058 26,560\nWell 2 31,187 30,562 31,700 30,467\nWell 3 29,735 29,188 29,781 29,287\nWell 4 40,377 39,912\nWell 5 29,120 29,210\nWell 6 43,432 41,413 42,350 41,182\nWell 7 31,105 31,101\nWell 8 24,639 23,193\nWell 11 17,014 15,059 16,895 13,749\nWell 12 37,390 36,302 37,397 35,362\nWell 14 41,783 40,870\nWell 15 39,140 39,133 35,699\nWell 16 31,830 31,799 31,674\nWell 17 82,400 79,110\nWell 18 30,397 30,400\nWell 19 27,448 27,370\nWell 20 36,971 35,796 37,022 35,228\nWell 21 31,085 31,102\nWell 22 29,108 28,689\nWell 23 41,763 41,758 41,257\nWell 24 25,981 25,985\nWell 25 26,870 26,871"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 20, "chroma:document": "Well 21 31,085 31,102\nWell 22 29,108 28,689\nWell 23 41,763 41,758 41,257\nWell 24 25,981 25,985\nWell 25 26,870 26,871\nWell 26 28,784 28,385 28,844 28,361\nWell 27 31,126 31,117\nWell 28 26,359\nWell 29 31,789 31,780\nWell 30 29,287 25,429\nWell 31 26,249 26,242\nWell 32 30,940 30,937\nWell 33 43,429 43,436\nWell 34 25,428 25,438\nWell 35 34,831 34,287 34,416 34,241\nWell 36 41,675 38,289 40,729 35,101\nWell 37 42,424 41,407 42,117 41,159\nWell 38 46,953 44,777 44,217 38,430\nWell 39 28,342 28,077 28,361 28,036Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897786-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 21, "chroma:document": "22 SPE-215017-MS\nNolte ACA Pore\nPressure Radial\nFlow (kPa)Nolte ACA Pore\nPressure Linear\nFlow (kPa)Soliman/Craig ACA\nPore Pressure Radial\nFlow (kPa)Soliman/Craig ACA\nPore Pressure Linear\nFlow (kPa)\nWell 40 24,911 22,801 24,866 22,676\nWell 41 43,230\nWell 42 37,073 37,116 30,547\nWell 43 27,083 25,622 27,084 25,924\nWell 44 37,914 37,058 37,920 27,154\nWell 46 31,267 31,262\nWell 47 29,967\nWell 48 38,105 36,533 38,072 37,830\nWell 49 27,647\nWell 50 32,097 32,142 33,210\nWell 51 44,104 43,188\nWell 52 27,197\nWell 53 27,741 27,711\nWell 54 30,607\nWell 55 30,273\nWell 56 29,024\nWell 57 39,255 37,361\nWell 58 25,492\nWell 59 24,103\nWell 60 29,127 29,106\nWell 61 32,655 32,593\nWell 62 28,748 28,740\nWell 63 26,154 23,335 26,162 23,276\nWell 64 28,904 28,896\nWell 65 38,074 35,506 37,819 34,912\nWell 66 25,348 25,385\nWell 67 29,848\nWell 68 29,482 29,454\nWell 69 29,024\nWell 70 25,001 24,986\nWell 71 27,632 27,564\nWell 72 28,010 27,998\nWell 73 28,908\nWell 74 26,322 26,286\nWell 76 27,551 27,559\nWell 77 28,927"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 21, "chroma:document": "Well 70 25,001 24,986\nWell 71 27,632 27,564\nWell 72 28,010 27,998\nWell 73 28,908\nWell 74 26,322 26,286\nWell 76 27,551 27,559\nWell 77 28,927\nWell 78 30,112 30,087\nWell 79 28,700 28,693\nWell 80 24,518 24,504Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 22, "chroma:document": "SPE-215017-MS 23\nThe clustered column chart in Figure 24 shows slightly higher estimates for radial flow vs. linear flow\nfor Nolte and Soliman/Craig methods.\nFigure 24\u2014Clustered column chart for Nolte vs. Soliman/Craig pressure estimates for linear and radial flow.\nNet pressure from the compliance method and tangent method\nThe \u2018compliance net pressure\u2019 is calculated as the \u2018effective ISIP\u2019 minus the estimate for compliance\nclosure pressure for the compliance closure the \u2018holistic net pressure\" is calculated as the \u2018ISIP\u2019 minus the\nestimate for holistic closure pressure. It is an estimate for the pressure driving crack propagation through\nthe formation \u2013 the amount that pressure exceeds closure pressure.\nThe holistic net pressures are on average about ~10x higher (~17,000 kPa higher). This comparison uses\nthe ~44% of the tests for which the compliance method closure pick was assessed as being \"strong\" or"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897876-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 22, "chroma:document": "the ~44% of the tests for which the compliance method closure pick was assessed as being \"strong\" or\n\"adequate\". Table 6  shows a summary of the net pressure values for Compliance and Holistic methods.\nTable 6\u2014Summary of Net Pressures using Holistic and Compliance with inputs.\nHolistic\nISIP (kPa)Compliance\n(Effective)\nISIP (kPa)Holistic Closure\nPressure (kPa)Compliance\nClosure\nPressure (kPa)Holistic Net\nPressure (kPa)Compliance Net\nPressure (kPa)\nWell 1 66,234 n/a 49,898 n/a 16,336 n/a\nWell 2 67,916 45,500 38,721 40,742 29,195 4,758\nWell 3 63,444 45,000 39,441 43,600 24,003 1,400\nWell 4 55,564 n/a 48,658 n/a 6,906 n/a\nWell 5 46,328 n/a 37,136 9,192 0\nWell 6 64,666 56,000 50,979 53,908 13,687 2,092\nWell 7 76,254 46,000 40,154 45,000 36,100 1,000\nWell 8 47,087 42,500 38,306 40,000 8,781 2,500\nWell 9 52,431 n/a 46,274 n/a 6,157 n/a\nWell 10 67,785 45,000 40,993 n/a 26,792 n/a"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 22, "chroma:document": "Well 8 47,087 42,500 38,306 40,000 8,781 2,500\nWell 9 52,431 n/a 46,274 n/a 6,157 n/a\nWell 10 67,785 45,000 40,993 n/a 26,792 n/a\nWell 11 26,751 26,500 22,849 25,500 3,902 1,000Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89790c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 23, "chroma:document": "24 SPE-215017-MS\nHolistic\nISIP (kPa)Compliance\n(Effective)\nISIP (kPa)Holistic Closure\nPressure (kPa)Compliance\nClosure\nPressure (kPa)Holistic Net\nPressure (kPa)Compliance Net\nPressure (kPa)\nWell 12 56,048 54,000 48,941 n/a 7,107 n/a\nWell 13 45,975 n/a 42,201 n/a 3,774 n/a\nWell 14 72,438 59,000 50,861 n/a 21,577 n/a\nWell 15 53,541 50,000 46,387 n/a 7,154 n/a\nWell 16 32,385 32,325 32,003 n/a 382 n/a\nWell 17 101,279 n/a 62,545 n/a 38,734 0\nWell 18 68,256 50,000 43,727 n/a 24,529 n/a\nWell 19 81,662 43,500 36,657 n/a 45,005 n/a\nWell 20 55,261 52,500 48,642 n/a 6,619 n/a\nWell 21 56,144 48,000 44,425 n/a 11,719 n/a\nWell 22 42,903 n/a 39,274 n/a 3,629 n/a\nWell 23 58,341 55,000 49,202 n/a 9,139 n/a\nWell 24 37,224 n/a 32,177 n/a 5,047 n/a\nWell 25 76,049 44,000 39,822 42,000 36,227 2,000\nWell 26 45,008 44,000 40,033 n/a 4,975 n/a\nWell 27 72,672 49,000 42,779 48,000 29,893 1,000\nWell 28 73,982 n/a 41,951 n/a 32,031\nWell 29 68,290 45,750 41,981 n/a 26,309 n/a\nWell 30 63,821 n/a 39,572 n/a 24,249 0"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b89795c-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 23, "chroma:document": "Well 28 73,982 n/a 41,951 n/a 32,031\nWell 29 68,290 45,750 41,981 n/a 26,309 n/a\nWell 30 63,821 n/a 39,572 n/a 24,249 0\nWell 31 51,506 41,750 37,289 41,000 14,217 750\nWell 32 77,376 46,000 40,722 43,000 36,654 3,000\nWell 33 66,448 n/a 50,727 n/a 14,217 n/a\nWell 34 42,298 n/a 31,641 n/a 10,657 n/a\nWell 35 68,408 54,500 45,609 n/a 16,740 n/a\nWell 36 59,604 55,750 48,477 n/a 11,127 n/a\nWell 37 55,169 54,500 49,933 52,000 5,236 2,500\nWell 38 54,820 54,500 50,366 n/a 4,454 n/a\nWell 39 68,227 47,500 37,965 n/a 30,262 n/a\nWell 40 42,880 39,500 35,101 n/a 7,779 n/a\nWell 41 62,933 n/a 58,321 n/a 4,612 n/a\nWell 42 52,207 51,000 45,132 n/a 7,075 n/a\nWell 43 48,682 n/a 40,327 n/a 8,355 n/a\nWell 44 54,807 54,000 46,743 n/a 8,064 n/a\nWell 45 47,548 45,500 40,408 n/a 7,140 n/a\nWell 46 67,523 n/a 43,833 n/a 23,690 n/a\nWell 47 53,237 n/a 41,213 n/a 12,024 n/a\nWell 48 53,638 54,000 48,611 52,811 5,027 1,189\nWell 49 77,084 44,000 37,157 41,000 39,927 3,000"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 23, "chroma:document": "Well 47 53,237 n/a 41,213 n/a 12,024 n/a\nWell 48 53,638 54,000 48,611 52,811 5,027 1,189\nWell 49 77,084 44,000 37,157 41,000 39,927 3,000\nWell 50 52,700 52,500 49,563 48,500 3,137 4,000Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b8979f2-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 24, "chroma:document": "SPE-215017-MS 25\nHolistic\nISIP (kPa)Compliance\n(Effective)\nISIP (kPa)Holistic Closure\nPressure (kPa)Compliance\nClosure\nPressure (kPa)Holistic Net\nPressure (kPa)Compliance Net\nPressure (kPa)\nWell 51 90,441 n/a 53,873 n/a 36,568 0\nWell 52 71,593 48,250 43,747 47,000 27,846 1,250\nWell 53 68,659 48,000 44,040 46,250 24,619 1,750\nWell 54 77,548 49,500 43,341 45,500 34,207 4,000\nWell 55 62,712 47,500 39,140 44,000 23,572 3,500\nWell 56 70,992 44,250 40,475 43,000 30,517 1,250\nWell 57 63,140 61,000 53,083 59,500 10,057 1,500\nWell 58 57,153 46,000 38,359 44,500 18,794 1,500\nWell 59 63,170 n/a 55,895 n/a 7,275 0\nWell 60 67,694 43,500 38,344 42,000 29,350 1,500\nWell 61 72,766 48,000 43,332 47,000 29,434 1,000\nWell 62 65,552 43,000 37,941 42,000 27,611 1,000\nWell 63 41,622 40,000 36,070 37,500 5,552 2,500\nWell 64 79,428 44,000 37,720 41,000 41,708 3,000\nWell 65 51,418 48,000 45,652 50,020 5,766 -2,020\nWell 66 72,990 47,250 37,827 39,000 35,163 8,250\nWell 67 60,842 47,750 42,301 46,000 18,541 1,750"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897a42-84a2-11ee-9ca1-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 24, "chroma:document": "Well 65 51,418 48,000 45,652 50,020 5,766 -2,020\nWell 66 72,990 47,250 37,827 39,000 35,163 8,250\nWell 67 60,842 47,750 42,301 46,000 18,541 1,750\nWell 68 60,527 41,000 36,382 40,000 24,145 1,000\nWell 69 70,992 44,500 40,475 44,000 30,517 500\nWell 70 76,096 48,000 40,934 44,000 35,162 4,000\nWell 71 71,998 46,000 41,406 45,000 30,592 1,000\nWell 72 69,560 44,500 39,774 41,500 29,786 3,000\nWell 73 72,033 44,500 39,551 44,000 32,482 500\nWell 74 78,979 45,000 39,371 44,500 39,608 500\nWell 75 60,774 48,000 42,233 47,000 18,541 1,000\nWell 76 70,560 47,000 41,633 46,000 28,927 1,000\nWell 77 75,124 47,250 43,466 47,000 31,658 250\nWell 78 71,225 47,500 39,560 43,500 31,665 4,000\nWell 79 57,788 47,000 42,845 46,000 14,943 1,000\nWell 80 53,923 43,000 38,906 42,500 15,017 500\nAverage 18,939 1,908\nIn hydraulic fracturing, higher net fracture pressures can have several implications:\n1.Enhanced fracture growth: high net fracture pressures help create and extend fractures in the target"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897a92-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 24, "chroma:document": "1.Enhanced fracture growth: high net fracture pressures help create and extend fractures in the target\nformation, allowing for greater contact with the reservoir and improved flow of oil and gas.\n2.Increased production rates: by generating larger and longer fractures, high net fracture pressures can\nenhance the productivity of a well, leading to increased production rates of oil and gas.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


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topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 25, "chroma:document": "26 SPE-215017-MS\n3.Reservoir connectivity: high net fracture pressures can help establish better connectivity between the\nwellbore and the reservoir, enabling the extraction of hydrocarbons from a larger area within the\nformation.\n4.Risk of fracture propagation: while high net fracture pressures can be advantageous, they also carry\nthe risk of unintended fracture propagation.\n5.Hydraulic fracturing fluid requirements: achieving high net fracture pressures may require larger\nvolumes of hydraulic fracturing fluid, which can pose logistical challenges, increase costs and\npotentially impact water availability in some regions.\nRate Transient Analysis\nRate Transient Analysis was conducted to make a comparison on values of Af\u221a k estimates using DFIT\nACA methodologies. The periods analyzed for RTA ranged from 1 day up to 75 days of production and\npressure data. Figure 25  shows a typical production and pressure profile for the wells analyzed."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 25, "chroma:document": "pressure data. Figure 25  shows a typical production and pressure profile for the wells analyzed.\nFigure 25\u2014Well 36 \u2013 Typical production and pressure profile used for rate transient analysis.\nSoliman/Craig ACA Linear Flow.   The equations 12, 13, 14 and 15 governing linear flow are defined as:\n(12)\n(13)\n(14)\n(15)\nFigure 26  shows minifrac linear flow plot for Soliman/Craig.Downloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 26, "chroma:document": "SPE-215017-MS 27\nFigure 26\u2014Well 3 - Soliman / Craig Analysis \u2013 Linear Flow\nTable 7  shows a summary of the Soliman -Craig estimates of Xf\u221ak, Af\u221ak and RTA estimates of Af\u221ak\n(linear flow). Wells with no or insufficient data are shown as non/available (n/a).\nTable 7\u2014Summary of the Soliman -Craig estimates of Xf\u221ak, Af\u221ak and RTA estimates of Af\u221ak (linear flow)\nSoliman / Craig\nLinear Flow\nXf \u221a k  (m*\u221amd)Assumed h\nNet Pay (m)Soliman / Craig Linear\nFlow Af\u221ak\n(m2 \u221amd)RTA Linear Flow\nAf\u221ak\n(m2 \u221amd)\nWell 1 0.03 45 1.35 7,595\nWell 6 0.06 15 0.9 788\nWell 9 9.64 45 434 n/a\nWell 12 0.39 15 5.85 13,753\nWell 15 0.05 10 0.5 41,668\nWell 16 2.87 15 43.05 3,970\nWell 20 0.21 15 3.15 4,805\nWell 21 0.34 20 6.80 n/a\nWell 26 0.05 15 0.75 1,163\nWell 35 5.68 20 113.6 769\nWell 36 0.14 15 2.1 5,748\nWell 37 70.87 20 1417 n/a\nWell 38 0.17 20 3.4 31,278\nWell 39 0.11 15 1.65 687\nWell 40 0.2 20 4 2,842\nWell 42 0.07 39 2.73 10,705\nWell 43 7.55 20 151 n/a\nWell 44 0.11 53 5.83 n/a\nWell 46 0.07 40 2.8 4,428"}


created_at: 2023-11-16 17:06:54
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 26, "chroma:document": "Well 40 0.2 20 4 2,842\nWell 42 0.07 39 2.73 10,705\nWell 43 7.55 20 151 n/a\nWell 44 0.11 53 5.83 n/a\nWell 46 0.07 40 2.8 4,428\nWell 48 1.16 15 17.4 3,748\nWell 50 0.12 20 2.4 n/aDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897c0e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 27, "chroma:document": "28 SPE-215017-MS\nSoliman / Craig\nLinear Flow\nXf \u221a k  (m*\u221amd)Assumed h\nNet Pay (m)Soliman / Craig Linear\nFlow Af\u221ak\n(m2 \u221amd)RTA Linear Flow\nAf\u221ak\n(m2 \u221amd)\nWell 65 0.18 17 3.06 6,224\nConclusions\nThis study reviews results from 80 DFITs from different operators in the Canadian Unconventional Montney\nshale play. The key findings are as follows:\na.A \u2018compliance method\u2019 closure/stress estimate is not apparent in the significant majority of DFITs in\nthe Canadian Montney formation.\nb.The compliance method and tangent method provide similar closure pressures. The compliance\nclosure pressure was ~8% higher than the tangent closure pressure on average. To estimate the\nminimum principal stress, a subtraction of a pressure constant from the compliance closure pressure\nis suggested by McClure et al. 2019 .\nc.The clarity of the \u2018compliance method\u2019 closure response varies in the Montney.\nd.The net pressure estimated based on tangent closure and \u2018ISIP\u2019 are ~10x higher on average than that"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897c5e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 27, "chroma:document": "d.The net pressure estimated based on tangent closure and \u2018ISIP\u2019 are ~10x higher on average than that\nestimated based on compliance closure and \u2018effective ISIP\u2019.\ne.7 cases were identified as normal leak-off (NL). 56 cases were identified as transverse fracture storage/\nfracture height recession (TFS/FHR). 9 cases out of 80 cases were identified as pressure dependent\n(PDL). 2 cases were identified as fracture tip extension (FTE). 6 cases were not clearly identified. As\nexpected, McClure closure was not found in PDL signatures.\nf.Nolte and Soliman-Craig ACA permeability estimates were of similar order of magnitude for linear\nor radial flow, respectively.\ng.Nolte and Soliman-Craig ACA pore pressure estimates for linear and/or radial flow were of similar\norder of magnitude for linear or radial flow, respectively. Pore pressure estimates for linear flow were\nslightly lower than for radial flow."}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897cae-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 27, "chroma:document": "order of magnitude for linear or radial flow, respectively. Pore pressure estimates for linear flow were\nslightly lower than for radial flow.\nh.As far as RTA implications, Xf\u221ak  and Af\u221ak  estimates from ACA methodologies are heavily dependent\non the assumption on whether the net pay has been partially or fully accessed. When Af\u221a k estimates\nfrom DFIT were compared with RTA estimates, the latter values were ~7,000x higher.\ni.The AER does not make recommendations or approve one single analysis method over another. The\nanalysis of the various methods demonstrates the range of possible outcomes and illustrates unique\nproperties of the Montney reservoir and can be used to optimize development.\nj.The ability to independently calculate reservoir pressure across the unconventional play allows better\nunderstanding the pressure variances of the Montney and enables more accurate resource estimation"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897cfe-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 27, "chroma:document": "understanding the pressure variances of the Montney and enables more accurate resource estimation\nof the play to be performed and reported. Without DFIT data, resource evaluation has been historically\nmore difficult.\nNomenclature\nAf= fracture area, L2, m2\nct= total compressibility, Lt2/m, kPa\u22121\nCT= total fluid loss coefficient, L/t\u00bd, m/min1/2\nFL1= Nolte linear flow time function, dimensionless\nFR1= Nolte radial flow time function, dimensionless\nG= G-function, dimensionless\nh= net pay, L, m\nk= permeability, L2, mdDownloaded from http://onepetro.org/SPEATCE/proceedings-pdf/23ATCE/3-23ATCE/D031S036R004/3290732/spe-215017-ms.pdf/1 by University of Houston user on 27 October 2023"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897d4e-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 28, "chroma:document": "SPE-215017-MS 29\nXf= fracture half-length, L, m\np= pressure, m/Lt2, kPa\npfo = fracture pressure measured at wellbore, m/Lt2, kPa\nq= flow rate, L3/t, m3/D\nQt= total injection volume, L3, m3\nt= time, hr\ntp= producing time, hr\nV= injection  volume, m3\n\u03c0= constant, dimensionless\n\u0394= difference, dimensionless\n\u00b5= viscosity, m/Lt, cp\n\u03a6= porosity, dimensionless\nSubscripts\na= adjusted\nc= closure\nD= dimensionless\ni= initial\nf= fracture\np= producing\nt= total\nw= wellbore\nReferences\nAlberta Energy Regulator Directive 040: Pressure and Deliverability Testing Oil and Gas Wells  https://www.aer.ca/\nregulating-development/rules-and-directives/directives/directive-040\nAlberta Energy Regulator Report ST98: Alberta Energy Outlook, https://www.aer.ca/providing-information/data-and-\nreports/statistical-reports/st98\nBarree, R.D. , H. Mukherjee . 1996 . Determination of pressure dependent leak-off and its effect on fracture geometry . Paper"}


created_at: 2023-11-16 17:06:54
topic: persistent://default/default/c01518eb-579a-4a9d-8cdf-22ca77573fa8
id: 6b897d94-84a2-11ee-9ca1-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/Fracture closure Reviews/spe-215017-ms.pdf", "page": 28, "chroma:document": "Barree, R.D. , H. Mukherjee . 1996 . Determination of pressure dependent leak-off and its effect on fracture geometry . Paper\nSPE 36424 presented at the SPE Annual Technical Conference and Exhibition, Denver, CO, doi: 10.21118/36424-MS\nBarree, R.D. 1998 . Applications of Pre-Frac Injection/Falloff Tests in Fissured Reservoirs\u2014Field Examples. Paper SPE\n39932 presented at the SPE Rocky Mountain Regional/Low-Permeability Reservoirs Symposium, Denver, 5\u20138 April.\nDOI: 10.2118/39932-MS .\nBarree, R.D. , V .L. Barree  and D.P. Craig. 2007 . Holistic fracture diagnostics, Paper SPE 107877 presented at the SPE\nRocky Mountain Oil & Gas Technology Simposium, Denver, CO, doi: 10.2118/107877-MS\nBarree, R. D., V . L. Barree, and D.P. Craig . 2009 . \"Holistic fracture diagnostics: consistent interpretation of prefrac\ninjection tests using multiple analysis methods\". SPE Production & Operations 24 ( 3): 396\u2013406."}


