# embeddings_queue

created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35372-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 16, "chroma:document": "inFigure 8.10 . The intersection point is at the 101st data point, which corresponds to\nthe closure time of 27.95 minutes and closure pressure of 5790 psi ( Fig. 8.10 ).\nA comparison between the results by our proposed technique and G-function anal-\nysis is presented in Table 8.2 . As can be seen, according to our analysis, fracture\nclosure happens slightly after the closure point by G-function. The reason for this\nClosure time = 27.8 min\nClosure pressure = 5822 psi\nClosure G           = ~ 0.126\nClosure point (#)   = 93\nFigure 8.9 G-function plot of field example 1.\nData points #Signal Energy, BHPClosure time = 27.95 min & closure pressure of 5790 psi\nClosure point (#)   = 101AB\nFigure 8.10 Distribution of the noise energy at decomposition level 3 (D 3) for the field example 1\n(Eltaleb et al., 2020 ).233 Fracture diagnostic testing"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae353ea-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 17, "chroma:document": "difference could be that the closure point by our technique is the complete closure of\nthe fracture, while the closure point by the G-function method is the start of the clos-\ning process.\n8.6.1.2 Field example 2\nFig. 8.11 shows the analysis of DFIT by G-function for this case. In this test, an aver-\nage of 0.28 bpm of water was injected into the formation for 12 minutes. Pressure\nfall-off was recorded after shut-in for B77 minutes, with a sampling rate of 1 second.\nAs can be seen in the figure, the closure pressure and closure time are estimated to be\n26756 psi and 822 seconds, respectively. The closure occurred at the 98th data point\nin the data set. This example is relatively straightforward to analyze using the\nG-function technique.\nThe figure below shows the energy distribution plot of decomposition level 3 (D 3).\nWe can notice that energy magnitude is declining, then leveling off to a minimum\nlevel until the end of the test. The closure point is identified from the intersection of"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35462-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 17, "chroma:document": "regions A and B, as indicated by the dashed line in Fig. 8.12 . The intersection point is\nat the 37th data point, which corresponds to the closure time of B14 minutes.\nThe summary of the results of the proposed methodology for field example 2 and\nits comparison with G-function analysis is presented in Table 8.3 . As can be seen,\nunlike field example 1, our method suggests an earlier fracture closure compared with\nthe G-function methods. The difference between the closure pressures of the two\nmethods is about 2000 psi. In this case, our method indicates the G-function underes-\ntimates the closure pressure. However, as shown in the field Case 1, this is not always\nthe case as many parameters affect the fracture closure.\nClosure time       = 822 \ns \nClosure pressure = 26,756 psi \nClosure G           = 0.27 \nClosure point (#)   = 98 \nFigure 8.11 G-function plot of the field example 2 ( Eltaleb et al., 2020 ).234 Unconventional Shale Gas Development"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae354da-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 18, "chroma:document": "8.6.1.3 Field example 3\nFigs. 8.13 and 8.14 show the analysis of DFIT by G-function for the example. In this\nDFIT, fracture fluid was injected into the formation for 12 minutes. The Pressure fall-off\nwas recorded after shut-in for B165 minutes, with a sample rate of 1 second. Also, the\nwater hammer signature in the early portion of the derivative G3dp/dGis an indication\nof a tight formation. The slight increase of the derivative G3dp/dGafter the closure\nattributes to fracture growth after pump shut-in. The fracture closure pressure using the\nG-function method is estimated to be 2656 psi and closure time of 13.6 minutes.\nThe analysis of the same data set via the energy distribution plot is shown in\nFig. 8.15 . The closure pressure is explicitly identified when energy magnitude levels\noff from region A to region B. The closure point is identified from the intersection\nbetween regions A and B, as indicated by the dashed line in Fig. 8.15 . The\nClosure time = 761 s\nClosure point (#)   = 37B"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3555c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 18, "chroma:document": "Closure time = 761 s\nClosure point (#)   = 37B\nData points #Signal Energy, BHPA\nFigure 8.12 Distribution of the noise energy at decomposition level 3 (D 3) for the field example 2\n(Eltaleb et al., 2020 ).\nFigure 8.13 G-function plot of the field example 3 ( Eltaleb et al., 2020 ).235 Fracture diagnostic testing"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae355d4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 19, "chroma:document": "intersection point is at the 93rd data point, which corresponds to a closure pressure of\n2708 psi and a closure time of 13.5 minutes.\nThe results of both methods for this case are summarized in Table 8.4 . In this case,\nsimilar to field example 2, the fracture closure happens before the closure identified by\nthe G-function technique. The closure pressure using our technique, in this case, is\nfollowing the methods presented by McClure et al. (2014) andWang and Sharma\n(2017) in the sense that the closure happens earlier than the G-function. However,\none needs to compare the methods more closely for a better conclusion. Also, note\nthat the models presented by Maclure and Wang almost always pick the closure before\nthe G-function. However, as shown in example 1, this is not always the case with our\nmethod. Moreover, this method is not restricted to any assumption and solely depends\non the recorded data and its quality.\n8.6.1.4 Field example 4"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3564c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 19, "chroma:document": "on the recorded data and its quality.\n8.6.1.4 Field example 4\nFig. 8.16 shows an analysis of DFIT of the fourth field example that is analyzed in this\npaper. Water is injected with an average rate of 2.8 bbl/min for 3 minutes into a\nClosure pressure = 2702 psi & Closure time = 13.5 min\nClosure point (#) = 94 BA\nData points #Signal Energy, BHP\nFigure 8.15 A summary of the results for field example 3 and its comparison with G-function\n(Eltaleb at al., 2020 ).\nClosure time = 13.6 min\nClosure G            = 0.28\nClosure pressure = 2656 psi\nClosure point (#) = 101\nFigure 8.14 Zoomed G-function plot of the field example 3 ( Eltaleb et al., 2020 ).236 Unconventional Shale Gas Development"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae356ce-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 20, "chroma:document": "formation that has 140 ft thickness, 9.7% porosity, and 0.58 mD permeability. The\npressure fall-off has been observed for 26 hours, with a sampling rate of 1 second.\nThe data, beyond 32 hours of shut-in time and corresponding to GB565, is ignored\nin the analysis because there is an observed pressure increase due to fluid heating\nup (Amini, Soliman, & House, 2015; Soliman, 1986 ). From G3dp/dGsignature\n(red line), a natural fracture system can be inferred. However, closure cannot be accu-\nrately identified since multiple straight line candidates can be plotted. The possible clo-\nsure points corresponding to closure pressures of 13,539, 13,068, and 12,815 psi. We\nwere given analysis for this case by an oil company, indicating the closure pressure as\n13,544 psi (first tangent line).\nThe analysis of this DFIT using the proposed technique yields more affirmative\nresults about the interpretation of the pressure data. The decomposition level (D 3) has"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35750-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 20, "chroma:document": "been used in this example. As shown in Fig. 8.17 , two regions of energy levels are rec-\nognized as A and B as follows:\n\u0081Region A : The energy decline describes the closing of the hydraulic fracture. The\nintersection between regions A and B would be the minimum stress for hydraulic\nfractures (closure pressure 513,521 psi, closure time 546 minutes, and closure\npoint (#) 52600).\n\u0081Region B : The energy levels off as the pressure continue to decline but no further\nreduction in the noise, indicating no physical changes are happening in the system,\nand the hydraulic fracture is completely closed.\nA summary of results from our proposed methodology and G-function is presented\ninTable 8.5 . As can be seen, in this case, although multiple closures were possible on\ntheG3dp/dGplot, the wavelet technique showed an obvious minimum energy level\nT closure =45 min\nP closure   = 13,539  psi \nT closure =294 min\nP closure   = 13,068  psi \nT closure   = 713 min\nP closure   = 12,815  psi"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae357c8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 20, "chroma:document": "T closure   = 713 min\nP closure   = 12,815  psi \nFigure 8.16 G-function plot of the field example 4 ( Eltaleb et al., 2020 ).237 Fracture diagnostic testing"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3584a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 21, "chroma:document": "that matched with the G-function analysis. This is an advantage of our proposed tech-\nnique as it does not limit it to a specific rock type and job parameter.\n8.6.2 Effect of natural fracture and temperature\nCurrent techniques for estimating the closure stress often contradict each other, reach-\ning up to 2000 psi difference in the identified closure stress. This discrepancy is due to\ntwo main reasons, (1) the underlying assumptions of these techniques, (2) ultra-tight\npermeability, natural fractures, and heat exchange.\nEltaleb, Rezaei, Soliman, and Dindoruk (2021) proposed a signal processing tech-\nnique for analyzing DFIT in geothermal reservoirs, where it showed several advantages\nover traditional methods in evaluating in-situ stresses. Because of the changing temper-\nature during the test, conventional techniques may yield inaccurate results. To show\nthe temperature effect on DFIT in geothermal reservoirs, two FORGE field cases are"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae358cc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 21, "chroma:document": "analyzed using the conventional and modified G-function analyses and the proposed\nsignal processing technique.\n8.6.3 Utah FORGE example (effect of heat exchange)\nA series of injection tests were performed in 2019 to estimate in situ stresses and for-\nmation parameters. Nine different test cycles have been performed, including pump-\nin/flow back and pump-in/shut-in. For this section, we focused on the pump in\nshut-in only.\nIn this test, water was injected at the rate of 15 BPM into FORGE formation\nthrough a 3.5-inch diameter tubing in Well 58 /C032 in April 2019. Series of fracture\ninjection/shut-in tests and Injection/flow-back tests were performed, as shown in\nFig. 8.18 . In this study, the results from DFIT 1 and DFIT 2 are analyzed.\nBoth temperature and pressure data have been analyzed for the first and second\nDFITs using the developed methodology before considering the temperature and\ncompressibility effect. Also, the pressure was analyzed after applying the corrections"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3594e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 21, "chroma:document": "to pressure. The energies of the noise in pressure and temperature were plotted\nData points #Signal Energy, BHPFracture closure pressure = 13,521                       psi & Closure time = 46\nminute\nClosure point (#) = 2600AB\nFigure 8.17 Distribution of the noise energy at decomposition level 3 (D 3) for the field example 4\n(Eltaleb et al., 2020 ).238 Unconventional Shale Gas Development"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae359c6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 22, "chroma:document": "against time. Our methodology for interpretation of pressure energy for unconven-\ntional reservoirs shows a negative slope in the energy distribution plot that is indicative\nof energy change in the system attributed to fracture closure. However, in geothermal\nreservoirs, the expected change of injected fluid temperature has a significant impact\non the observed pressure signal. It, therefore, may lead to an ambiguous estimation of\nthe rock in-situ stresses. Consequently, it is essential to include the effect of the frac-\nturing fluid \u2019s temperature change in DFIT. As shown in Fig. 8.19 , during water injec-\ntion into the hot formation, heat convection dominated as the temperature decreases.\nThe temperature energy shows two distinctive regions, indicated by the yellow and\nblack lines in Fig. 8.19 . Contrary to the pressure energy, the recorded temperature\nnoise energy AC decays in a constant slope until the end of the test, which attributes"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35a3e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 22, "chroma:document": "to a decrease in the heat exchange rate as the system reaches equilibrium.\nDetailed analyses of the two DFITs in Fig. 8.19 are given in the following section.\n8.6.4 DFIT 1\nFig. 8.20 shows the G-function of the pressure analysis in DFIT 1. As can be seen, the\nclosure, in this case, is equal to B4200 psi, which is 200 psi lower than what was\nidentified from the wavelet analysis in Fig. 8.19 . The closure pressure using our tech-\nnique, in this case, is in accordance with the methods presented by McClure et al.\n(2014) andWang and Sharma (2017) in the sense that the closure happens earlier than\nthe G-function (i.e., G-function underestimates closure).\nFigure 8.18 The diagnostic test on Utah FORGE geothermal reservoir (granite) ( Eltaleb et al., 2021 ).239 Fracture diagnostic testing"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35ac0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 23, "chroma:document": "Figure 8.19 Energy distribution of the noise in the recorded pressure and temperature in the semi-\nlog plot ( Eltaleb et al., 2021 ).\nFigure 8.20 G-function analysis of DFIT 1 before applying the corrections ( Eltaleb et al., 2021 ).240 Unconventional Shale Gas Development"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35b42-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 24, "chroma:document": "The energy distribution of the noise in the pressure and temperature data are plot-\nted in Fig. 8.21 . As can be seen, there are two drops in the level of noise in the pres-\nsure data. These drops correspond to 4400 psi and 3800 psi. After the second drop, the\nlevel of noise in the pressure data remains constant. However, the noise in the temper-\nature shows a different trend. The temperature curve shows only one sharp drop in\nthe noise and a continuous drop in the noise after that.\nWe think that the first drop in the pressure noise is the closure pressure, and the\nsecond drop might be due to the shearing of the natural fracture planes, as discussed\nbyNadimi et al. (2020) . The temperature plot confirms the closure because, BC, the\nmajority of the noise will be from the conduction and convection, with the former\nbecome dominant. However, after the fracture closure, the noise in the temperature\ndata will be from conduction and vanish as the system reaches equilibrium."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35bc4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 24, "chroma:document": "The method that was developed by Soliman (1986) accounts for the fracturing fluid\ncompressibility and temperature. The technique works up until the closure moment.\nAccording to the method, the fracturing temperature and compressibility cause the\npressure fall-off to be higher than what it should be in reality. In this study, the thermal\nconductivity and fluid compressibility were assumed to be 300 310261/psi and\n50310261//C14F, respectively. Fig. 8.22 shows the corrected pressure for DFIT 1.\nFigure 8.21 Energy distribution of the noise in the pressure and temperature for DFIT 1 ( Eltaleb\net al., 2021 ).241 Fracture diagnostic testing"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35c46-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 25, "chroma:document": "Based on the corrected pressure, one may apply the conventional G-function\nagain. After applying the correction for temperature, the closure pressure would be\npicked at 3900 psi, which is 400 psi lower than the closure identified from the wavelet\nin DFIT 1. This shows that the conventional G-Function is not suited for ultra-tight\nand hot reservoirs ( Fig. 8.23 ).\nThe energy distribution of the noise in the corrected pressure is not plotted, but it\ncan be shown that the correction of the pressure will not affect the wavelet results.\nThis is an advantage of our technique over conventional analytical methods.\n8.6.5 DFIT 2\nIn this injection test cycle, 183 bbl was pumped into the formation. The pumping\nschedule started with pumping 8 at 3800 psi; then, the rate was increased to 15 bpm at\n5000 psi. The pump stopped and the pressure was allowed to fall off for B15 hours.\nThe conventional G-function analysis of DFIT 2 without considering the effect of"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35cc8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 25, "chroma:document": "the temperature and fracturing fluid \u2019s compressibility is shown in Fig. 8.24 . In this\ncase, the closure using G-function analysis is identified as 4300 psi.\nThe distribution of the noise energy in the recorded pressure and temperature\nis shown in Fig. 8.25 . As can be seen in this example, three levels of energy are\nFigure 8.22 Corrected pressure for compressibility and temperature for DFIT 1 ( Eltaleb et al., 2021 ).242 Unconventional Shale Gas Development"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35d4a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 26, "chroma:document": "distinguished. The vertical line on the pressure plot shows where the closure pressure\nshould be picked from our proposed methodology. The closure, in this case, is equal to\n4350 psi, which is in accordance with the previous analysis on the FORGE. Also, we\nobserved a constant level of noise energy before the closure in the temperature noise.\nFigure 8.23 G-Function analysis of the corrected pressure of DFIT 1 ( Eltaleb et al., 2021 ).\nFigure 8.24 G-function analysis of DFIT 2 before applying the corrections ( Eltaleb et al., 2021 ).243 Fracture diagnostic testing"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35e76-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 27, "chroma:document": "Figure 8.25 Energy distribution of the noise in the pressure and temperature for DFIT 2 ( Eltaleb\net al., 2021 ).\nFigure 8.26 Corrected pressure for compressibility and temperature for DFIT 2 ( Eltaleb et al., 2021 ).244 Unconventional Shale Gas Development"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35ef8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 28, "chroma:document": "This constant noise level is due to convection. After the closure point, the temperature\nnoise reduces gradually until the temperature stabilizes to the in-situ reservoir\ntemperature.\nThe correction of the pressure, accounting for the temperature and fluid compress-\nibility, is shown in Fig. 8.26 . As can be seen, the pressure difference can reach up to\n1000 psi that can result in erroneous conclusions.\nThe G-Function analysis of the corrected pressure is shown in Fig. 8.27 . As can\nbe seen, the G-function method again underestimates the closure. After applying the\ntemperature effect, its underestimation is more apparent.\n8.7 Summary\nIn this chapter, conventional and newly developed approaches for fracture diagnostics\nare reviewed. Fracture tests are typical pre- and posttreatment tools to estimate several\nreservoirs and design variables. Typically, in all of the tests, a small amount of fluid is\npumped into the reservoir, and a short fracture is created. The diagnostics can be cate-"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35f7a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 28, "chroma:document": "gorized into three main groups: direct far-field techniques, direct near-wellbore tech-\nniques, and indirect fracture diagnostics. In this chapter, we reviewed the indirect\nfracture diagnostics methods that are conducted on recorded response pressure and\nrate from the wellbore. Sometimes, a combination of several methods is good for hav-\ning a better understanding of the interesting parameters.\nFigure 8.27 G-Function analysis of the corrected pressure of DFIT 2 ( Eltaleb et al., 2021 ).245 Fracture diagnostic testing"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae35ffc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 29, "chroma:document": "References\nAmini, K., Soliman, M. Y., & House, W. V. (2015). A three dimensional thermal model for hydraulic\nfracturing. Technical conference and exhibition. SPE-174858-MS; Society of Petroleum Engineers,\nHouston.\nBarree, R. D., Barree, V. L., & Craig, D. (2007). Holistic fracture diagnostics. Rocky mountain oil & gas\ntechnology symposium. Society of Petroleum Engineers.\nBarree, R. D., Miskimins, J., & Gilbert, J. (2015). Diagnostic fracture injection tests: Common mistakes,\nmisfires, and misdiagnoses. SPE Production & Operations ,30(02), 84 /C098.\nBarree, R. D., & Mukherjee, H. (1996). Determination of pressure dependent leakoff and its effect on\nfracture geometry. SPE annual technical conference and exhibition. Society of Petroleum Engineers.\nBurrus, C. S., Gopinath, R. A., & Guo, H. (1998). Introduction to wavelets and wavelet transforms: A primer\n(1st ed). Prentice Hall.\nCastillo, J. L. (1987). Modified fracture pressure decline analysis including pressure-dependent leak-off."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3607e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 29, "chroma:document": "Low permeability reservoirs symposium. Society of Petroleum Engineers.\nCinco-Ley, H., & Samaniego, V. F. (1981). Transient pressure analysis for fractured wells. Journal of\nPetroleum Technology ,1766 .\nC i p o l l a ,C .L . ,&W r i g h t ,C .A .( 2 0 0 0 ) .S t a t e - o f - the-art in hydraulic fr acture diagnostics. Paper presented at the\nSPE Asia Pacific oil and gas conference and exhibition .A v a i l a b l ef r o m https://doi.org/10.2118/64434-MS ,\nBrisbane, Australia.\nCleary, M. P., Johnson, D. E., Kogsb\u00f8ll, H. H., Owens, K. A., Perry, K. F., De Pater, C. J., ... ...\nMauro, T. (1993). Field implementation of proppant slugs to avoid premature screen-out of hydraulic fractures\nwith adequate proppant concentration .Low permeability reservoirs symposium . Society of Petroleum\nEngineers.\nCraig, D. P., & Blasingame, T. A. (2006). Application of a new fracture-injection/fall-off model accounting for\npropagating, dilated, and closing hydraulic fractures .SPE gas technology symposium . Society of Petroleum"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36100-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 29, "chroma:document": "Engineers.\nCramer, H., & Grenader, U. (1959). The Nyquist frequency is that frequency whose period is two sampling inter-\nvals.Probability and Statistics: The Harald Cramer Volume (p. 434) Almqvist & Wiksell.\nEltaleb, I., Rezaei, A., Siddiqui, F., Awad, M. M., Mansi, M., Dindoruk, B., & Soliman, M. Y. (2020).\nAnalysis of fracture injection tests using signal processing approach .Unconventional resources technology conference,\n20/C022 July 2020 (pp. 3994 /C04007). Unconventional Resources Technology Conference (URTeC).\nEltaleb, I., Rezaei, A., Soliman, M. Y., & Dindoruk, B. (2021). A signal processing approach for analysis\nof fracture injection test in geothermal reservoirs: A case study on the Utah FORGE formation. SPE\nhydraulic fracturing technology conference and exhibition .\nFelsenthal, M. (1974). Step-rate tests determine safe injection pressures in floods. Oil Gas Journal (United\nStates) ,72(43)."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36182-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 29, "chroma:document": "States) ,72(43).\nHoward, G. C., & Fast, C. R. (1957). Optimum fluid characteristics for fracture extension .Drilling and production\npractice . American Petroleum Institute.\nHubbert, M. K., & Willis, D. G. (1972). Mechanics of hydraulic fracturing. American Association of\nPetroleum Geologists ,18.\nHyden, Ron E., & Stegent, Neil A. (1996). Pump-in/shutdown tests key to finding near-welibore\nrestrictions. Paper presented at the Permian basin oil and gas recovery conference . Available from https://doi.\norg/10.2118/35194-MS , Midland, TX.\nLiu, G., Ehlig-Economides, C., & Sun, J. (2016). Comprehensive global fracture calibration model .SPE Asia\nPacific hydraulic fracturing conference . Society of Petroleum Engineers.\nMarongiu-Porcu, M., Ehlig-Economides, C. A., & Economides, M. J. (2011). Global model for fracture fall-\noff analysis .North American unconventional gas conference and exhibition . Society of Petroleum Engineers."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36204-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 29, "chroma:document": "Marongiu-Porcu, M., Retnanto, A., Economides, M. J., & Ehlig-Economides, C. (2014). Comprehensive\nfracture calibration test design .SPE hydraulic fracturing technology conference . Society of Petroleum\nEngineers.\nMayerhofer, M. J., & Economides, M. J. (1997). Fracture-injection-test interpretation: Leakoff coefficient\nvs. permeability. SPE Production & Facilities ,12(04), 231 /C0236.246 Unconventional Shale Gas Development"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3627c-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 30, "chroma:document": "McClure, M., Bammidi, V., Cipolla, C., Cramer, D., Martin, L., Savitski, A., ...Voller, K. (2019). A\ncollaborative study on DFIT interpretation: Integrating modeling, field data, and analytical techni-\nques. Paper presented at the SPE/AAPG/SEG unconventional resources technology conference,\nDenver, CO. Unconventional Resources Technology Conference (URTEC).\nMcClure, M. W., Blyton, C. A., Jung, H., & Sharma, M. M. (2014). The effect of changing fracture compli-\nance on pressure transient behavior during diagnostic fracture injection tests .SPE annual technical conference and\nexhibition . Society of Petroleum Engineers.\nMcClure, M. W., Jung, H., Cramer, D. D., & Sharma, M. M. (2016). The fracture-compliance method\nfor picking closure pressure from diagnostic fracture-injection tests (see associated supplementary dis-\ncussion/reply). SPE Journal ,21(04), 1 /C0321.\nMohamed, I. M., Azmy, R. M., Sayed, M. A. I., Marongiu-Porcu, M., & Economides, C. (2011)."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae362fe-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 30, "chroma:document": "Evaluation of after-closure analysis techniques for tight and shale gas formations .SPE hydraulic fracturing technol-\nogy conference . Society of Petroleum Engineers.\nMohamed, Y. (2016). Soliman, Ph.D., P.E., NAI; Ron Dusterhoft. Fracturing Horizontal Wells (McGraw-Hill\nEducation: New York, Chicago, San Francisco, Athens, London, Madrid, Mexico City, Milan, New Delhi,\nSingapore, Sydney, Toronto . Available from https://www.accessengineeringlibrary.com/content/book/\n9781259585616 .\nMukherjee, H., Larkin, S., & Kordziel, W. (1991). Extension of fracture pressure decline curve analysis to fis-\nsured formations .Low permeability reservoirs symposium . Society of Petroleum Engineers.\nNadimi, S., Forbes, B., Moore, J., Podgorney, R., & McLennan, J. D. (2020). Utah FORGE:\nHydrogeothermal modeling of a granitic based discrete fracture network. Geothermics ,87, 101853.\nNolte, K. G. (1979). Determination of fracture parameters from fracturing pressure decline .SPE annual technical"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36380-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 30, "chroma:document": "conference and exhibition . Society of Petroleum Engineers.\nNolte, K. G. (1986). A general analysis of fracturing pressure decline with application to three models.\nSPE Formation Evaluation ,1(06), 571 /C0583.\nNolte, K. G. (1991). Fracturing-pressure analysis for nonideal behavior. Journal of Petroleum Technology ,43\n(02), 210 /C0218.\nPan, H., Firoozabadi, A., & Fotland, P. (1997). SPE Production & Facilities .\nPercival, D. B., & Walden, A. T. (2000). Wavelet methods for time series analysis . Cambridge: Press\nSyndicate of The University of Cambridge.\nPokalai, K., Kulikowski, D., Johnson, R. L., Haghighi, M., & Cooke, D. (2016). Development of a new\napproach for hydraulic fracturing in tight sand with pre-existing natural fractures. The APPEA Journal ,\n56(1), 225 /C0238.\nPolikar, R. (2001). Multiresolution analysis: The discrete wavelet transform. Retrieved from The\nWavelet Tutorial: Available from http://users.rowan.edu/ Bpolikar/WTpreface.html ."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36402-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 30, "chroma:document": "Rioul, O., & Vetterli, M. (1991). Wavelet and signal processing. IEEE SP Magazine ,38.\nSavitski, Alexei A., & John, W. Dudley (2011). Revisiting Microfrac in-situ stress measurement via flow\nback \u2014A new protocol. Paper presented at the SPE annual technical conference and exhibition . Available\nfrom https://doi.org/10.2118/147248-MS , Denver, CO, USA, October.\nSiddiqui, F., Soliman, M. Y., House, W., & Ibragimov, A. (2016). A new analysis technique for inter-\npreting injection/shut-in tests. Hydraulic Fracturing Quarterly .\nSingh, P. K., Agarwal, R. G., & Krase, L. D. (1987). Systematic design and analysis of step-rate tests to\ndetermine formation parting pressure. Paper presented at the SPE annual technical conference and exhibition .\nAvailable from https://doi.org/10.2118/16798-MS , Dallas, TX, September.\nSoliman, M.Y. (1986). Technique for considering fluid compressibility and temperature changes in mini-frac analysis."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3647a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 30, "chroma:document": "Paper presented at the SPE annual technical conference and exhibition . SPE 15370. Society of Petroleum\nEngineers, New Orleans, LA.\nSoliman, M.Y., and A.A. Daneshy. Determination of Fracture Volume and Closure Pressure From\nPump-In/Flowback Tests. Paper presented at the Middle East Oil Show, Bahrain, November 1991.\nAvailable from https://doi.org/10.2118/21400-MS .\nSoliman, M. Y., & Gamadi, T. (2012). Testing tight gas and unconventional formations and determination of clo-\nsure pressure .SPE/EAGE European unconventional resources conference & exhibition-from potential to produc-\ntion. European Association of Geoscientists & Engineers.247 Fracture diagnostic testing"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae364fc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 31, "chroma:document": "Soliman, M. Y., & Kabir, C. S. (2012). Testing unconventional formations. Journal of Petroleum Science and\nEngineering ,92, 102 /C0109.\nSoliman, M. Y., Craig, D. P., Bartko, K. M., Rahim, Z., & Adams, D. M. (2005). Post-closure analysis to\ndetermine formation permeability, reservoir pressure, residual fracture properties .SPE Middle East oil and gas\nshow and conference . Society of Petroleum Engineers.\nSoliman, M. Y., Miranda, C., & Wang, H. M. (2010). Application of after-closure analysis to a dual-\nporosity formation, to CBM, and to a fractured horizontal well. SPE Production & Operations ,25(04),\n472/C0483.\nStehfest, H. (1970). Algorithm 368: Numerical inversion of Laplace transforms [D5]. Communications of the\nACM ,13(1), 47 /C049.\nTan, H. C., McGowen, J. M., Lee, W. S., & Soliman, M. Y. (1988). Field application of Minifrac analysis to\nimprove fracturing treatment design .California regional meeting (pp. 591 /C0612)."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3657e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 31, "chroma:document": "Unal, E., Siddiqui, F., Soliman, M. Y., & Dindoruk, B. (2019a). Wavelet analysis of DFIT data to identify\nfracture closure parameters .SPE hydraulic fracturing technology conference and exhibition . Society of Petroleum\nEngineers.\nUnal, E., Siddiqui, F., Rezaei, A., Eltaleb, I., Kabir, S., Soliman, M. Y., & Dindoruk, B. (2019b). Use of\nwavelet transform and signal processing techniques for inferring interwell connectivity in waterflooding operations .\nSPE annual technical conference and exhibition . Society of Petroleum Engineers.\nUnal, E., Rezaei, A., Siddiqui, F., Likrama, F., Soliman, M., & Dindoruk, B. (2019c). Improved understand-\ning of dynamic fracture behavior in unconventional horizontal wells using wavelet transformation .SPE annual\ntechnical conference and exhibition . Society of Petroleum Engineers.\nValk\u00f3, P., & Economides, M. J. (1995). Hydraulic fracture mechanics . United Kingdom: Wiley.\nWang, H., & Sharma, M. M. (2017). New variable compliance method for estimating in-situ stress"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36600-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/3-s2.0-B9780323901857000169-main.pdf", "page": 31, "chroma:document": "and leak-off from DFIT data. Paper presented at the SPE annual technical conference and exhibition , San\nAntonio, TX, USA, October.248 Unconventional Shale Gas Development"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36682-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "SPE\u0010 169539\u001006\nDiagnostic Fracture Injection Tests: Common Mistakes, Misfires, and \nMisdiagnoses \nR.D. Barree, J.L. Miskimins, and J.V. Gilbert, Barree & Associates \nCopyright 2014, Society of Petroleum Engineers \n \nThis paper was prepared for presentation at the SPE Western North American and Rocky Mountain Joint Regional Meeting held in Denver, Colorado, USA , 16\u201318 April 2014. \n \nThis paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been \nreviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its \nofficers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohi bited. Permission to"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36704-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "reproduce in print is restricted to a n abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright. \n \n \nAbstract \nOver the last twenty years, Diagnostic Fracture Injection Tests, or DFIT\u2019s, have evolved into commonly  used techniques that \ncan provide valuable information about the reservoir, as well as hydraulic fracture treatment parameters. Thousands are \npumped every year in both conventional and unconventional reservoirs. Unfortunately, many tests that are pumped provide \npoor or no results due to either problematic data acquisition or incorrect analysis of the acquired data. \nThis paper discusses common issues and mistakes made while acquiring DFIT data. Guidelines on how to avoid these \nerrors and secure the best possible data are provided including data resolution, pump rates, test duration, and fluid selection."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36826-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "Rules of thumb are provided to estimate the time required to reach fracture closure and establish stable reservoir transients for \nanalysis. \nThe last part of the paper addresses potential (and commonly observed) problems in the analysis of the DFIT. The se \nissues can be magnified in tight gas and shale reservoirs due the long data acquisition times and the subtle pressure transients \nthat can occur. Specific issues that are discussed include poor ISIP data from perforation restriction, loss of hydrostatic head, \ngas entry and the resulting phase segregation, the use of gelled fluids, and errors in after closure analysis. \n \n \nIntroduction \nDiagnostic fracture inject ion tests or DFIT\u2019s are small pump-in treatments performed to gather data to help design follow-up \nhydraulic fracturing treatments, as well as to characterize the subject reservoir. DFIT\u2019s have their basis in co nventional mini-"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae368b2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "frac treatments; however, they are subtly different and are intended to acquire significantly more data for fracture design and \nexecution and reservoir description. Conventional mini-frac treatments have historically been focused on acquiring very \nspecific treatment desig n parameters, such as fluid efficiencies and leakoff values, however, DFIT\u2019s are intended to expand \nthat role and acquire additional data such as reservoir pore pressure, detailed closure and fracture gradients, process zone \nstresses (PZS), transmissibility values which can be converted into reservoir permeability values, and leak-off mechanisms. \nThe advent of unconventional reservoirs have added even more value to DFIT testing, as most of the information gained is \ncomparable to traditional pressure transient tests, which are impractical to run in tight sand and shale systems since the time \nto analyzable pseudo-radial flow can be months, if not years."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36934-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "to analyzable pseudo-radial flow can be months, if not years. \nA generic DFIT test is shown in Figure 1. The wellbore is first filled at low to moderate rate, until a positive surface \npressure response is observed. With low to moderate wellbore compressibility, the pressure should rise quickly until initial \nbreakdown occurs. Breakdown will either be indicated by a sharp drop in pressure as a new fracture initiates (as at point 1 in \nFigure 1), or a plateau in pressure as existing fractures are opened and extended. Once a breakdown event is observed, the \ninjection rate should be increased to the maximum rate allowed by available horsepower, or to 75% of the planned treatment \nrate of the main frac, whichever is achievable. A constant rate is then held for 3-5 minutes (step 2 in Figure 1) , after which a \nrapid step-down can be conducted. The step-down test is separate from the actual DFIT but is commonly run at the end of the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae369ac-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 0, "chroma:document": "pump-in to determine perforation and ne ar-wellbore frictional pressure losses. The rate is then immediately reduced to zero, \nto obtain the instantaneous shut-in pressure (ISIP, shown as step 4) and the falloff pressure is monitored for as long as \npossible or as long as necessary to acquire the desired data. Even when high friction is not expected, the step-down is \nrecommended to make identification of ISIP easier. More specific details of how to pump DFIT tests and recommended \nacquisition procedures are discussed later in this paper. \n \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36a2e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 1, "chroma:document": "2  SPE 169539  \n \n \nFigure 1:  Generic DFIT procedure. Initial breakdown is achieved at point 1; a constant  rate is held for 3 -5 minutes indicated by  point \n2; point 3 shows a rapid step -down; point 4 indicates ISIP; and point 5 shows falloff.  \n \n \nThis paper not intend ed to provide specific  instructions on the basics of how to  analyze  DFIT tests, as that information is \ndescribed in detail in other papers ( Barree, et al, 2009; Barree, 1998 ). Rather, as the title implies, it aims to aid in the \nacquisition  of useful and analyzable data , as well as  provide hints to common problems that occur either during the pumping \nof the test or during the analysis of the results . It is not uncommon to hear statements that disparage the test , however, most \nof the  problems  can be attributed to failed te sts that do not provide any useful data  because they we re pumped  or analyzed"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36ab0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 1, "chroma:document": "incorrectly . This is a valid concern \u2013 these tests cost additional time and money, and if they fail to provide usable  information \nvalue is lost or d estroyed . However, more often than not, it is the quality of the acquired data  and how the acquisition does \n(or does not) take place  that i s the root issue. I f appropriate steps are taken and quality data acquired, the tests are quite valid \nand correct int erpretation can shed light on what the reservoir is trying to  say. \nThis paper tries to address these acquisition issues, provide guidance on acquiring quality data, and discuss some common \nmistakes that happen during analysis procedures. If these steps are  addressed, the success rate of the treatments should \nincrease significantly.  Most of t he examples in this paper focus  on unconventional, tight hydrocarbon systems, however, all \npoints are equally  applicable to conventional  reservoirs . \n \n \nRecommended Acquis ition Procedure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36b32-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 1, "chroma:document": "Recommended Acquis ition Procedure  \nEvery time fluid is pumped into a formation, there is a risk of formation damage.  Therefore, fluid injections of any kind \nshould be minimized  and be conducted under controlled conditions. However, at the same time, enough fluid must be \ninjected under fracturing conditions  to adequately contact the reservoir and provide conditions under which the desi red \nparameters can be measured.  \nA DFIT is a fracture test, and must be conducted at a stable fracturing rate. I t does not take extremely h igh rates to initiate \nand propagate a fracture  in low to moderate permeability formations . In milli -Darcy range permeabilities, rates of 1 -2 BP M \nare frequently high enough to exceed  fracturing pressure. Approximate  rates that cause fracture extension  in a giv en situation \ncan be calculated using radial Darcy\u2019s Law , as shown in Equation 1. To extend a fracture the injection rate must be high"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36baa-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 1, "chroma:document": "enough to generate a pressure differential  (\uf044psafe) greater than the net fracture extension pressure, FG*D -p. \nFor micro - and nano -Darcy systems, the necessary rates are even lower. Figure 2  shows a graph relating the generated \npressure for a variety of reservoir permeabilities. In an effort to pump enough fluid to adequately contact the reservoir, do so \nin a relatively short amount of time, and provide a safety factor, rates of 5 -6 BPM, or even slightly higher, 7-8 BPM, have \nproven to  be very successful in providing good results. This maximum rate is recommended to be held for 3 -5 minutes, as \nshown in Figure 1, which results i n ~600-1800 gallons of fluid being injected.  \n \n) (ln] )* [( 10 917.46\nmax,\nsrrp p D FGkh Xq\nwesafe\ni\n\uf02b\uf02d\uf044\uf02d\uf03d\uf02d\n\uf06d\uf062\n    (1) \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36c2c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 2, "chroma:document": "SPE 169539   3 \n \nWhere,  qi,max  =  injection rate in bbl/min  \nk  =  permeability of undamaged formation, md  \nh  =  net thickness, ft  \nFG  =  fracture gradient, psi/ft  \nD  =  depth, ft  \n\u0394psafe  =  safety margin, psi  \np  =  reservoir pressure, psi  \n\u03bc  =  viscosity of injected fluid, cp  \n\u03b2  =  formation volume factor  \nre  =  drainage radius, ft  \nrw  =  wellbore radius, ft  \ns  =  skin \n \n \n \n \nFigure 2 : Rate necessary to initiate a fracture at various reservoir permeabilities. Assumes a reservoir depth of 7000 ft, fracture \ngradient of 0.8 psi/ft,  normal hydrostatic pore gradient,  formation thickness  of 20 ft, and a water fluid system.  \n \nData resolution fo r the entire injection and falloff period is a critical co mponent. Common pumping gauge resolutions of \n5-10 psi are not adequate for DFIT acquisition , since the intent of the treatment is look for subtle variations in the derivative"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36cae-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 2, "chroma:document": "of the pressure versus time. Low resolution gauges can miss th ese data and render the test unusable . It is recommended to use \ngauges that have a resolution of at least 0.01 \u2013 0.10 psi, with a sampling rate of one measurement per second during the \npumping period  and through fract ure closure . This sampling rate can then be expanded during the falloff period after closure . \nDuring the post-closure falloff period, a sampling rate of up to one measurement every 30 seconds is adequate  and achievable \nwith appropriate gauge memory systems . \nTwo k ey parameter s in the analysis of a DFIT  is the time and volume of injection  (Barree, et al, 2009; Barree, 1998) , \ntherefore, the injection schedule  must be recording precisely. Ideally, it is measured digitally in conjunction with the pressure \nduring the injection period, however, if this is not possible or is not done, extremely detailed notes must be kept that detail"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36d26-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 2, "chroma:document": "the pumping start/stop times and any rate changes  and times of such made during the procedure . If the data are recorded in \ndetail, a rate schedule can then be recreated during analysis.  \nFluid selection for the treatment is a common question \u2013 what is the best option? In general, a Newtonian, non -wall \nbuilding fluid should be used. This is one area that differs significantly from traditional mini -fracs, which commonly inject \ngelled or other non -Newtonian fluid systems , specifically to measure fluid efficiency . For DFIT purposes, water, diesel, or \nsome other type of non -wall building fluid should be u sed. The reason for t his is demonstrated by Figures 3 -5. Figure 3  \ndemonstrates t he conventional fluid loss model as a one -dimensional solution for linear transient flow with constant pressure \nboundary conditions. The f luid pressure at the fracture face is assumed constant with time and the far -field pore pressure is"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36d9e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 2, "chroma:document": "assumed to be constant. Initially the pressure gradient, and the associated leakoff rate, is very high. With time, the transient \nmoves further into the reservoir and the g radient (and rate) decr ease. This solution shows  rate decreasing linearly with the \nsquare -root of time.  \n0.0000010.000010.00010.0010.010.1110100\n0.0001 0.001 0.01 0.1 1 10 100 1000\nPermeability (md)Rate (BPM)Downloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36e20-857d-11ee-bb1c-0242ac1c000c
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metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 3, "chroma:document": "4  SPE 169539  \nFigure 4  then shows leakoff  modeled as a combination of series flows. The figure roughly describes a high permeability \nfar-field reservoir zone, a near -fracture invaded zone,  and a thin wall filter -cake zone. In series flow , the total pressure drop \nthrough the system is the sum of the pressure drops through each zone. Using Darcy\u2019s Law  in linear fashion , each pressure \ndrop can be determined from the length and permeability of each zone. When even a thin film of very high flow resistance is \npresent, such as the filter -cake, the flow capacity of the least conductive region dominates the system. When this filter -cake is \ndeposited on a  fracture wall, as demonstrated in Figure 5 , most of the pressure drop is taken across the filter -cake during \nleakoff. The far -field pressure grad ient is much less than expected  when compu ted based on the leakoff rate, and t he after -"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36ea2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 3, "chroma:document": "closure analysis yields an estimate of reservoir flow capacity , i.e. k h, that is much too high and is inconsistent with the \nobserved closure time.  \n \n \n \nFigure 3 : Conventional fluid loss model as a one -dimensional solution for linear transient flow with constant pressure boundary \nconditions . \n \n \n \n \nFigure 4 : Leakoff  modeled as a combination of series flows  for permeabilities of 100 md, 1 md, and 0.001 md.  \n \n \n \nFigure 5 : When a filter -cake is deposited on a fracture wall most of the pressure drop is taken across the filter -cake during leakoff  \nunlike that shown in Figure 3 which de monstrates the pressure drop in an undamaged system.  \n \nAs a last acquisition component , isolation of the wellhead after pumping ends is required in order to eliminate any  \ninadvertent pressure transients that might be caused by mechanical or logistical issues. Since DFIT analysis uses derivatives,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36f1a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 3, "chroma:document": "any large changes or \u201cbumps\u201d in press ure, can inadvertently alter, invalidate the test , or render it impossible to analyze . Any \npressure bleedoff that might occur during rig -down  can render the test useless. Likewise, if pressure measurements are being \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae36f92-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "SPE 169539   5 \nacquired using long-term gauges that will remain in place after the pumping equipment is removed, care must be taken during \nother r outine field operations that these  gauges are not disturbed in any way.  \n \n \nComm on Acquisition Issues  \nAs noted above, a DFIT consists of i nject ing water or other clean fluid above fra cture extension pressure, creating  a stable \nfracture geometry, shut ting down injection and watch ing the pressure decay to evaluate leakoff mechanism and find fracture \nclosure, and then evaluating  the after-closure pressure decline using appropriate reservoir transient solution s. If any of these \nsteps are compromised during acquisition of the data, the data c an be unusable. This section discusses common acquisition \nissue s. \nAs noted in the previous section and shown in Figures 3 -5, it should be stressed that a Newtonian, non -wall building fluid"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37014-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "must be used  when pumping the treatment , if any reservoir propertie s are to be obtained from the analysis . Using gelled or \nother non -Newtonian fluids can disrupt the after -closure pressure gradient and ma sk the reservoir flow capacity. Another  \ncommon issue that is also a  holdover from old style mini -frac treatments is the use of multiple pump -ins. DFIT\u2019s should be \nconsidered  as \u201cone and done\u201d. If the treatment is not pumped correctly the first time, a second attempt is almost pointless, as \nthe reservoir conditions have now been altered by the first injection and , in low pe rmeability systems , the created pressure \ntransients will not have dissipated by the time the second attempt is usually made.  The assumptions required for valid \nanalysis of a pulse test do not allow for superposition of multiple injections.  A second attempt can possibly be made if the \nfirst attempt was not too invasive, however, remember that the pressure transient may take days if not weeks to fully \ndissipate."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37096-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "dissipate.  \nNot acquiring falloff data for a long enough period is also a com mon acquisition is sue. Specifically h ow long to plan on \nletting the falloff period be recorded for different reservoir types is disc ussed in following sections of this paper, however, it \nsuffices to say here that the time period will be longer than the pumping equipment wil l physically stay on location. \nTherefore, secondary gauges that remain after the pumping equipment is removed are generally required. A common issue \nwith these secondary, long -term gauges is that they are not opened to the wellhead when the treatment is pu mped. Since these \nsecondary gauge s are commonly calibrated to a slightly different level than the pump gauges, if the two data sets are \noverlapped there will often be a  difference in the readings . Since the analysis of DFIT\u2019s calls for pressure derivatives , any \ndifference in readings will show as a slope change and will provide false indications of reservoir conditions on the analysis ."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3710e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "The secondary long -term gauges must be opened to the wellhead during the pumping period also to eliminate this issue.  In \nany case, accurate calibration of all pressure gauges should be tested and assured.  \nAdditional field operational issues that can cause acquisition problems are frozen  or temperature -affected  wellheads and \noffset reservoir interruptions. Pre cautions should be  taken for wells in winter conditions to prevent freezing of the surface \ngauges. Even if the gauges don\u2019t fully freeze, temperature fluctuations can impact the pressure readings, therefore, insulati ng \nthe wellheads during the falloff periods is often helpf ul to prevent these pressure movements. Thermal fluid expansion or \ncontraction in the wellbore will affect bo th surface and down -hole gauges.  Some people assume that a down -hole gauge will \nbe in a constant temperature environment, and will therefore not be  affected. In a low compressibility fluid -filled wellbore the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37186-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "coefficient of thermal expansion, coupled with density driven convection currents, will still cause a pressure change \nthroughout the wellbore volume . \nAgain, the behavior of pressure transients i s critical to that analysis of the treatment \u2013 if the pressure changes are caused \nby anything but the reservoir  and fracture response , the treatment can provide false readings. This is also the case if the \nreservoir itself is upset by any pressure changes such as pumping offset hydraulic fracturing treatments. A quiet environment \nin both the surface and downhole environments is needed for optimal data acquisition.  \nOne final acquisition precaution relates to the step -down portion of the test. It is strongly recommended to use a step -\ndown test versus a step -up test for t he reasons displayed in Figure 6. Figure 6  shows the treating pressure for increasing rates \n(overlapped by the pink line) and then the treating pressure for decreasing rates. The hysteresis in the curve is obvious and"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37244-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "indicates that during the initial rate increase period, the wellbore is still experiencing breakdown periods and changes in t he \noverall net pressure and fracture extension period.  In many cases, the number of perforations open to i njection changes with \neach increase in pump rate. The step -down period does a better job of measuring the frictional change information that is \ndesired rather than the complexity of friction and fracture extension components combined.  \n \n \nCommon Analysis Mis takes  \nIn addition to the acquisition issues previously mentioned , there are also several common analysis mistakes after the DFIT \ndata is acquired. The following sections discuss some of these more common errors and ways that they can be avoided (if \npossibl e). \n \nIncorrect ISIP Determination  \nAnalysis of a pressure falloff begins with determination of the instantaneous shut -in pressure (ISIP). This value is taken to"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae372c6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 4, "chroma:document": "represent the fracture extension pressure, when corrected to bottomhole conditions, and the frac ture extension gradient. The \ndifference between the ISIP and determined closure pressure is taken as the net pressure in the fracture, or as a measure of the Downloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3733e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 5, "chroma:document": "6  SPE 169539  \nresistance of the rock to facture extension, or process -zone stress  (PZS) . Since net pressure dete rmines fracture width, and to \na large degree height (due to the expectation that confining stress contrast controls containment) the accurate determination  of \nISIP is critical to any later analysis and fracture geometry modeling.  \n \n \nFigur e 6: A step -rate analysis chart showing increasing rate (step -up) measurements versus decreasing rate (step -down) \nmeasurements. Note the hysteresis exhibited between the two curves.  \n \n \nIn many cases the ISIP is not obvious, and does not occur immediately after shut-in. When a substantial near -well \npressure drop exists, either through poor perforation efficiency or, more commonly, high near -wellbore tortuosity, injection \nat the fracture entrance may not stop for some time after the surface injection stops. The am ount of continued injection after"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae373b6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 5, "chroma:document": "shut-in, the amount of excess frictional pressure that must dissipate, and the time required for decompression of the wellbore \nfluids depends on the severity of the near -well restriction to flow and the compressibility of the wellbore volume.  \nFigure 7 shows a fairly extreme case with an apparent ISIP of about 3640 psi at surface. The pressure falls nearly 1800 psi \nin the first few minutes after shut -in, with an injection rate of only 4 bpm. This DFIT was conducted through perforations in \nthe toe of a cemented horizontal well. Inside diameter of the pipe was 4.0 inches and total depth of the well was \napproximately 15,000 feet. The wellbore was filled with fresh water for the test. Before any meaningful analysis can be done,  \nan ISIP must be selected somewhere between 3640 psi and 1750 psi. If a value significantly below the pressure at shut -in \n(3640 psi) is used, the excess pressure drop must be explained."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37438-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 5, "chroma:document": "Figure 7 : Rate and pressure chart for a test with extremely high entry friction . \n20002500300035004000450050005500\n0 5 10 15 20 25 30 35 40\nPump rate, bpmTreating Pressure, psi\nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae374b0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 6, "chroma:document": "SPE 169539   7 \n \nTotal compressibility of the wellbore described can be estimated from the water compressibility (3.0e -6/psi) and wellbore \nvolume (233 bbl). Expansion of the pipe should also be considered. Using the thi n-walled cylinder equation (Eq. 2 ), the \nchange in volume of the wellbore can be estimated, where d is the pipe diameter, t is the wall thickness, p is the internal \npressure change, and E is the modulus of the steel (30.0e6 psi).  \n \nd\ntEpd\uf044\uf03d\n22\n     (2) \n \nWhere,  p  =  internal pressure  change, psi  \nd  =  pipe diameter, in  \nt  =  wall thickness, in  \nE = modulus of steel, psi  \n \nCombining the water and pipe compressibility, the pressure of the fluid in the wellbore will change by approximately \n1170 psi for every 1 bbl of volume change. This re lationship can be used with an estimate of pressure drop due to tortuosity, \nassuming a square -root of rate linear relation, to estimate the frictional pressure drop driven by fluid expansion, and the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3753c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 6, "chroma:document": "expansion rate after shut -down. With an injection rate o f 4 bpm at shut -in, a frictional pressure drop of 1940 psi result s from \na tortuosity factor of 970 psi/ \uf0d6(bpm). In the first second after shut -in, this rate decreases the wellbore volume by 0.0667 bbls, \ncausing the pressure to drop from 3640 to 3562 psi. As  the fluid continues to expand, the injection rate drops, and the inlet \nfrictional pressure decays. Figure 8  shows a plot of the pressure decay computed from this simple relation, compared to the \nobserved pressure decline in the test.  \n \n \n \nFigure 8 : Actual  (thin blue line)  and computed  (thick blue line)  pressure decay after shut -in, accounting for near -well tortuosity and \nwellbore decompression . \n \nThe thin blue line is the  measured surface pressure for the test and the heavy line is the computed wellbore pressure with \nthe frictional pressure drop calculated from a constant tortuosity factor. The injection rate declines from 4 bpm at the inst ant"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae375c8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 6, "chroma:document": "of shut -in to 1.0 bpm after 2 5 seconds, and finally to less than 0.05 bpm after 200 seconds. Perforation pressure drop and \nother  factors are ignored in this analysis. The main point is that wellbore storage and decompression can drive injection after \nshut-in for a long time, in excess  of several minutes, and can account for large pressure drops. With large wellbore volumes, \ntypical of extended reach horizontal wells and larger pipe sizes, this effect becomes more pronounced. Any gas or more \ncompressible fluid in the wellbore will exten d the blow -down period even longer.  \nNow that the source and duration of the early pressure  decay is accounted for, what is the actual representative ISIP? One \nmethod that can help is to extrapolate the pressure versus log of time curve, as shown in Figure 9, back to the point of shut -in. \nThis construction suggests that some effect of wellbore fluid expansion may be felt for as long as 18 minutes after shut -in,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3764a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 6, "chroma:document": "and gives an estimated effective ISIP of 1766 psi. This may be a lower -bound of ISIP, but is a goo d starting estimate.  \n \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae376cc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 7, "chroma:document": "8  SPE 169539  \n \n \nFigure 9 : Extrapolation of the pressure versus log time to approximate ISIP . \n \nThe validity of the ISIP estimate can often be verified by examination of the log -log plot of pressure change from the \nassumed ISIP after shut -in and th e semi -log derivative of the pressure difference curve versus shut -in time. This plot, shown \nin Figure 10 , should produce parallel lines of the pressure difference (blue Delta Pressure) and derivative (red) during the pre -\nclosure period. The magnitude of t he derivative should be the pressure difference multiplied by the slope of the derivative \ncurve. In the example, when the pressure difference curve is 300 psi at closure and the derivative is roughly 0.28 (the slope ) \ntimes that value. Note that any change to the estimated ISIP value will move the pressure difference curve but will have no \neffect on the derivative curve slope or position on the plot. When a stable linear derivative is apparent through the pre -closure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37744-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 7, "chroma:document": "data, this method provides an effective f inal check, but is not always infallible.  \n \n \n \nFigure 10 : Log -log plot of pressure difference and derivative versus time . \n \nBasic Selection of Closure  \nBasic DFIT analysis should be covered in sufficient detail in SPE 107877 (2009), but some mistakes in the most basic \ninterpretation of the G -function diagnostic semi -log derivative continue to be made by many analysts. Figure 11 shows a \nDFIT with variable fracture compliance, or storage during closure, where the closure time and pressure have been mistakenly \ndiagnosed.  In the original  analysis the clo sure time and pressure were identified by the positions of the red lines, at a closure \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae377c6-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 8, "chroma:document": "SPE 169539   9 \ntime of G=14 and P=3960 psi. The correct closure time is G=32 and P=3640 psi. This discrepancy wi ll obviously affect any \ninterpr etation of closure stress for calibration of a geomechanical model or stress profile, and will impact estimates of \nformation flow capacity and post -frac production. The red arrows in Figure 11 indicate other incorrect closure events that are \noften selected  by mistake. The one correct closure event is shown by the blue arrow, after the end of the variable compliance \nand linear closure periods. The error in closure stress also leads to an error in the interpretation of fracture net extensio n \npressure. This af fects the predicted width of the fracture, and therefore directly impacts the computed fracture length, through \nconservation of injected volume. Predicted fracture height may also be affected, depending on the strength and stress of the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3783e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 8, "chroma:document": "confining layers. I n short, if the wrong analysis results are applied to the calibration of any fracture design model, the results \nwill be incorrect.  \n \n \nFigure 11: G -Function  derivative plot for variable compliance during closure, with incorrect closure picks.  \n \n \nEffect of Injection Time versus Pump Rate  \nAssuming a high enough injection rate is used so that the rock is dilated to its ultimate capacity, the width of the fracture  \nwill be determined by the net pressure generated, modulus of the rock, and some characteristic dim ension of the fracture. The \ntheoretical basis of the G -function analysis assumes that the fracture adheres to Perkins -Kern -Nordgren geometry \nassumptions (Nolte, 1979). While this assumption is not necessarily valid, it implies that the generated fracture h eight will be \nthe controlling dimension. This leads to a somewhat circular argument as net pressure, which is  proportional  to fracture"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae378c0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 8, "chroma:document": "width, and fracture compliance (H/E) are directly linked in this model. A confined height, for a constant modulus, means the \nnet pressure must be higher for a given frac width. A higher net pressure implies the ability to break through more barriers \nand possibly generate more fracture height, thus increasing compliance. The system should stabilize at an equilibrium \nfracture height, width, and net pressure for a given injection rate and fluid system.   \nFor a DFIT to be valid , an injection rate must be selected that will generate a net pressure and fracture geometry that is \nrepresentative of the main frac. In practical terms, that means that the highest possible injection rate for the test will le ad to \nthe most representative r esults. Once a stable net pressure and fracture geometry is achieved, a higher injection rate will cause \nthe fracture to grow faster, but should not alter the width or height significantly. This assumption deviates from the classi cal"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37960-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 8, "chroma:document": "PKN assumptions wherei n all net pressure is generated solely through frictional pressure gradient of the moving fluid. More \nrealistic analysis of DFIT results requires that there be some resistance to fracture propagation inherent in the rock. This has \nbeen referred to as \u201cproc ess zone stress,\u201d \u201cfracture toughness,\u201d \u201crock strength,\u201d and by other names, although each carries \ncertain different connotations regarding the mechanism of resistance to fracture growth. A very low injection rate will \ndevelop less net pressure, therefore less fracture height and width, and will not strain the rock to its ultimate limit. This can \nresult in missing the evolution of secondary shear fractures  that can affect compliance, leakoff rate, and system permeability. \nThe original theoretical models ass umed the rock to be linearly elastic and homogeneous, with no consideration that shear \nfailure could exist."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae379d8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 8, "chroma:document": "failure could exist.  \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37a50-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 9, "chroma:document": "10  SPE 169539  \nAssuming a stable net pressure and fracture geometry are achieved, the fracture volume to surface area, or fracture width, \nwill remain constant for  any duration of injection. That implies that a fracture with height of 50 feet and length of 300 feet \nwill close in the same time as a fracture 50 feet tall and 600 feet in length , as long as leakoff flux per unit area is the same in \nboth cases . For this reason the time to closure is not a function of injected volume, and is insensitive to rate as long as a high \nenough rate is achieved to reach a stable failure and fracture propagation condition. In fact, time to closure is a function of \npumpi ng time and n ot volume injected.  \nThe theoretical calculation for time to closure depends on the integration of the leakoff rate through  each ele ment of the \nfracture face as it s being created, and during the closure process. For single -phase flow, with no damage to the face of the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37ad2-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 9, "chroma:document": "fracture (such as a gel filtercake), the leakoff rate through each element of fracture face should decrease linearly with the  \nsquare -root of time since exposure of the face element.  For a slow injection rate each element of the face of the fra cture is \nexposed for a longer time, so the leakoff rate from the total fracture face will be much slower at shut -in than for the high rate \ninjection case.  \n \n \nFigure 1 2: Pressure transients established by low rate (A) and high rate (B) injection.  \n \nFigure 1 2 shows conceptually the radius of investigation of the leakoff pressure transients at three times for a low rate (A) \nand high rate (B) injection scenario. The center point  represents the wellbore or point of fracture initiation. The inner set of \npoints re present the fracture half-length  for some point near the middle of the injection period. In case A , the pressure \ntransient has penetrated a much larger distance into the formation , due to the longer injection time at low rate,  and the leakoff"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37b4a-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 9, "chroma:document": "rate is much lower than in case B. In the case B example, the same fracture length is reached at a much shorter injection time \nso the pressure transient cannot travel as far from the fracture face, and leakoff rate is faster than in case A. The second set of \npoints rep resents the fracture position at the end of injection. In case A , the pressure transients along the length of the fracture \nhave travelled a greater distance into the formation, leakoff rate through each element of fracture surface is much lower \n(following the square -root of time function), and therefore time to reach closure is significantly longer than in case B. In the \nhigh rate case, the entire fracture length is established with a short time of exposure o f all elements of the fracture surface and \nleakof f rate through each element remains high.  \nFor the same injected fluid volume the fracture of case B may be slightly longer than the case A fracture, but the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37bc2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 9, "chroma:document": "difference is not linear with rate. In case B , the leakoff rate is higher throughout the injection  period but the fluid efficiency is \nalso higher. All this assumes a similar net pressure and fracture compliance in both cases A and B .  \nA second result of the impact of rate is apparent from Figure 12. In the low rate (case A) condition, the pressure tran sient \nat closure, represented by the outer ellipse, has reached a nearly pseudo -radial flow case very quickly after closure. In case B \nthe transient remains in pseudo -linear flow for a very long time after closure. For this reason many people, generally th ose \nconcerned with application of classical pressure transient theory, recommend very low injection rates. This recommendation \nis based solely on the desire to establish a pseudo -radial flow period within a practical test duration. Unfortunately, in the re al \nworld where rocks are not isotropic, homogeneous, and linearly  elastic, with no  inherent resistance to fracture growth, the use"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37c44-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 9, "chroma:document": "of a very low injection rate makes the test essentially useless for fracture diagnostics. These tests seek to approach a matr ix \ninjection/falloff test and should not be considered  as valid diagnostic  fracture injection tests as the information critical to \nfracture design will all be compromised. Another failing of the low rate test is that the height of the zone contacted will r arely \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37cbc-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 10, "chroma:document": "SPE 169539   11 \n(in the real world that means effectively never) be the perforated p ay height. Therefore any permeability or even KH estimate \nwill probably not match post -frac production.  \n \nSize of Generated Fractures  \nMost people consider a short -duration fracture injection test to be too small to effectively evaluate enough reservoir \nvolume to be applicable for post -frac production . Figure 1 3 shows the estimated fracture  half that would be generated for a 30 \nfoot fracture height, with a fracture width of 0.1 inches, given 100% fluid efficiency. These may seem to be arbitrary input \nassumpt ions, but are reasonable for water injection in \u201ctypical\u201d rocks of 3 -4 million psi Young\u2019s Modulus with a net pressure \nof 1000 psi and very low system permeability. The estimated fracture length can be directly multiplied by fluid efficiency to  \ncorrect for  leakoff in higher permeability systems, and corrected by the ratio of created to assumed fracture height, if it is \nknown."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37d3e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 10, "chroma:document": "known.  \n \n \n \nFigure 1 3: Fracture half -length created as a function of pumping time and rate . \n \nNote that for the recommended rate of 10 bpm, a pumping time of 5 minutes generates a fracture half -length of more than \n600 feet, when leakoff during the 5 -minute injection period is negligible. This is very likely the case in a shale or ultra -tight \nsand or carbonate reservoir s. Extending the pumping ti me to 10 minutes increases the created length to almost 1200 feet and \nincreases the time to closure by increasing the average exposure time of all fracture face elements. Clearly, in tight rocks,  \nthese are not \u201csmall\u201d fractures and the formation surface ar ea exposed is statistically significant. For the 5 -minute, 10 bpm \ninjection case , the surface are a of one of the four fracture wing faces exposed is 18,000 square feet.  \n \nDesign of Test Duration  \nLonger pumping times allow more time for penetration of the i nduced pressure transient. Given a stable fracture"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37dc0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 10, "chroma:document": "geometry, the time required to close the fracture by leaking off a fixed volume to surface -area ratio of fluid in the fracture can \nbe related to the system permeability. A good approximation for time t o closure is given in Equation 3 : \n \nkttp\nc3\uf03d\n     (3) \n \nWhere,  tc =  time to fracture closure, min  \ntp =  pumping time, min  \nk =  permeability of leakoff system, md  \n \nWhere t c is the time to reach fracture closure (minutes), t p is the pumping time (minutes), and k is the permeability of the \nleakoff system connected to the fracture face, including any secondary permeability enhancement due to induced shear fa ilure \nof the host rock. Figure 1 4 is a plot of the estimated closure tim e for pumping times of 2 to 20 minutes ove r a range of system \npermeabilities  from 100 nano -darcies (0.0001 md) to 1 md. For convenience the time scale has been converted to hours of \nshut-in."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37e38-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 10, "chroma:document": "shut-in.  \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37eb0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 11, "chroma:document": "12  SPE 169539  \n \n \n \nFigure 1 4: Approximate time to reach fracture closure for va rious pumping times . \n \nNote that for a 5 -minute injection period into a 0.1 md formation, fracture closure occurs in about 0.2 hours (12 minutes). \nIn these moderately high permeability formations, where this technique was first applied, extending the pumpin g time may \nnot be a serious concern. For this 0.1 md rock, a pump time of 20 minutes will still reach fracture closure in about one hour  of \nshut-in time. Note that for higher permeability formations closure can happen too quickly to be easily identified wh en other \nfactors such as wellbore friction and compressibility are considered.  \nAt 0.01 md, the 5 -minute pumping time requires 2 -3 hours to reach closure. For a 0.001 md formation, which is not \natypical for what are considered commercial tight silt or shal e reservoirs, closure can take up to 24 hours after a 5 -minute"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37f5a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 11, "chroma:document": "injection. If the system permeability is actually in the 100 -nano -darcy range, closure can take up to ten days following a 5 -\nminute injection. When system permeability is this low , the created fracture length will be large, and the pressure transient \nestablished at closure will remain in a pseudo -linear flow regime for a very long time.  \nOnce the fracture has closed, some time is required for a stable reservoir transient flow regime to be establ ished. On a log -\nlog plot of pressure change versus shut -in time, a safe and realistic lag time is \u00bd of a log cycle in time after closure. That \nroughly means that no data should be analyzed for any reservoir flow regime, including pseudo -linear flow, until three times \nthe closure time has elapsed. So, using the 0.01 md, 5 -minute injection case, allow 2 -3 hours for closure and 6 -9 hours after \nshut-in to the start of a valid reservoir flow regime. For the 0.001 md case, that is 24 hours to closure and 3 days o f shut -in"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae37fe6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 11, "chroma:document": "for any useful reservoir information.  \nA goo d example of the time lag required to reach a stable reservo ir transient  is shown in Figure 1 5. After some non -linear \nleakoff behavior (including some mechanical noise in the data), there is an obvious break in the semi -log derivative curve  at \nthe closure time of 52 minutes after shut -in.  The derivative continues to curve until the first indication of a valid reservoir \npseudo -linear flow transient, at about 185 minutes after shut -in. The derivative cont inues to steepen, and approaches a \nnegative unit slope that some may be tempted to analyze as a pseudo -radial reservoir flow regime. For the purposes of this \ndiscussion, the important consideration is that any reservoir transient must take time to develop.  Expecting a sharp break in \nthe derivative curve immediately after closure to represent a reservoir flow transient is simply not reasonable."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3805e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 11, "chroma:document": "Downloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae380d6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 12, "chroma:document": "SPE 169539   13 \n \n \nFigure 1 5: Log -log pressure change versus shut -in time plot showing closure and start of pseudo -linear flow.  \n \nIf we follow the assumptions for the PKN fracture geometry, and assume that linear transient flow governs fracture \nleakoff flow up until closure, then the time required for the induced pressure transient to establish a pseudo -radial flow \nregime can be comp uted from the definition of t Dxf. For pseudo -radial flow , a value of t Dxf = 1.0  (at least)  must be reached i n \nthe falloff period. Equation 4  gives the time, in hours, to reach pseudo -radial flow (t pr) as a function of reservoir storativity, \npermeability, and fracture length.  \n \nktxCtDxfft\npr0002637.02\uf066\uf06d\uf03d\n     (4) \n \nWhere,  tpr =  time to reach pseudo -radial flow, hours  \n\u03c6 =  porosity, fraction  \n\u03bc = fluid viscosity, cp  \nCt = total reservoir compressibility, 1/psi  \nxf = fracture half -length, ft  \nk =  permeability of leakoff system, md"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38158-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 12, "chroma:document": "k =  permeability of leakoff system, md  \n \n \nEquation 4  has been solved for t Dxf=1 for a gas reservoir case with viscosity of 0.02 cp, porosity of 8%, and total reservoir \ncompressibility of 3.0e -5/psi. The time, in days, require d to reach the fully developed pseudo -radial flow period, according to \nthese a ssumptions, is shown in Figure 1 6. Daltaban and Wall (1998) suggest that pseudo -radial flow may not be identified \nuntil t Dxf=2 for an infinite conductivity fracture, or t Dxf=3 fo r a uniform flux fracture.  The assumptions used in Figure 1 6 are, \ntherefore, somewhat optimistic.  \nConsider a moderate permeability DFIT in a 0.1 md systems with a pump time of 5 minutes at 10 bpm. The generated \nfracture will close in about 15 minutes and have a fluid efficiency of about 50%. According to Figure 13, the generated \nfracture half-length  would be approximately 300 feet, for a fracture height of 30 feet (the default assumed height in the plot)."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae381da-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 12, "chroma:document": "Using the rule of thumb for start of after closure analysis, a pseudo -linear transient may develop in about 45 minutes after \nshut-in. If the created f racture is planar, constant height, and follows the assumptions for a homogeneous system permeability \nunder li near flow during closure, Figure 16 shows that a pseudo -radial flow regime should theoretically not be established \nuntil 2 -3 days after shut -in.  \n \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3825c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 13, "chroma:document": "14  SPE 169539  \n \n \nFigure 16: Time, in days, to theoretically reach pseudo-radial reservoir transient flow conditions for a gas reservoir for various \nsystem permeabilities. \n \nConducting the same analysis with a 0.001 md system permeability leads to a predicted closure time of 27 hours, start of \npseudo-linear flow after 83 hours, or 3.5 days, and start of pseudo-radial flow after about 1000 days of shut-in for a created \nfracture half-length of about 500 feet (83% efficiency). This implies that expecting pseudo-radial flow behavior in a DFIT in \nunconventional reservoirs is unreasonable. No combination of pump rate and pumping time will establish a stable fracture \ngeometry and result in stabilized pseudo-radial flow in a practical test duration with system permeability less than about 0.01 \nmd. Attempting to induce early onset of pseudo-radial flow by conducting the test at very low rate, or very short duration,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae382fc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 13, "chroma:document": "compromises the geometry of the fracture and the validity of any data associated with fracture extension criteria. If a test is to \nbe conducted as an injection/falloff test for reservoir properties, then it should not be confused as a diagnostic of fracture \nextension or closure conditions. Low rate, and small volume tests are then compromised by the inability to achieve \nbreakdown of many perforations or uniform injection over a predictable formation height. \nWhy do some DFITs appear to enter a pseudo-radial flow period, based on the negative unit slope of the semi-log \nderivative on the log-log pressure-time plot, or based on the after-closure flow regime analysis plot? The most plausible \nanswer is that fractures do not adhere to the simple planar geometry of a PKN fracture that is assumed in the derivation of the \nG-function equations and the conventional after-closure solution of the diffusivity equation. A more likely, or at least"}


created_at: 2023-11-17 19:17:23
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id: 9ae38374-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 13, "chroma:document": "plausible, image of the fracture system created in an unconventional reservoir is shown in map view in Figure 1 \u001a.  \n \n \n \nFigure 1\u001a: Complex, non-planar, fracture system with coalescing transient pressure fields. \n \nIf a complex, non-planar fracture system develops during injection, leakoff will occur through each face of all fracture \nstrands. Even with high volumetric fluid efficiency, the primary fracture will be much shorter than predicted for a planar \nfracture, as shown in Figure 12, and normally assumed in theory. Time to closure, based on the G-function, will be \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae383f6-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 14, "chroma:document": "SPE 169539   15 \nproportional to the overall surface area to fracture volume ratio at shut -in, whether the fracture is planar  or not. For this \nreason, the permeability estimated from the G -function closure time, and given in Barree et al, 2009,  is a reliable estimate of \nthe permeability of the system contacted by the induced fracture(s). The leakoff rate will be affected slightl y by the \noverlapping of the transient pressure envelopes around each fracture, but time required to leak off the fluid volume in the \nfracture system should be related to net pressure and system flow capacity or permeability. Some crossflow between fracture  \nstands opening against different normal stresses should be expected. This can lead to the variable storage signature seen  in G-\nfunction derivative analysis. Low compliance in the fracture systems coupled with a large exposed surface area can also lead"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3846e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 14, "chroma:document": "to the pressure -dependent permeability signature. Since both of these phenomena are commonly observed, it is reasonable to \nassume that complex fracture systems in unconventional reservoirs are common.  \nAs shut -in time progresses the overlapping transient pres sure envelopes with coalesce into what appears to be a more \nradial flow geometry, illustrated by the outer ellipse in Figure 16. As this pressure transient dissipates in to the far -field it will \nappear as a radial flow signature on the diagnostic derivativ e plots. However, this radial flow pattern does not conform to the \nassumptions inherent in the after -closure pseudo -radial flow solution. This solution is based on the assumption of a single \nplanar fracture with a transient evolving from a linear flow patt ern along the face of a single created fracture, which \ntransitions to a radial flow pattern over a dimensionless time proportional to the assumptions in Equation 4 and Figure 12."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae384f0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 14, "chroma:document": "The net result is that an apparent pseudo -radial flow regime develops much fa ster than would be the case for a single planar \nfracture of equivalent fluid efficiency. Any transmissibility derived from the apparent pseudo -radial flow time function may \nbe orders of magnitude too high to represent the actual flow capacity of the reserv oir system. The problem and errors in \ninterpretation are compounded when the radial flow or Horner analysis techniques are applied when a true pseudo -radial flow \npattern does not exist at all.  \n \nPhase Segregation and Gas Entry  \nDuring the falloff period , while the well is sitting undisturbed, gas entry from the formation can occur.  For the ideal case \nof a sealed wellbore under isothermal conditions, the volume of the gas bubble remains constant as it rises. With no mass \ntransfer from the gas to the wellbore fluid, the moles of gas in the bubble remains constant, therefore its pressure remains"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38568-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 14, "chroma:document": "constant as it rises. If a single gas bubble floats from the perfs to the surface under these conditions , the surface pressure wil l \nrise to the original bottomhole press ure and the pressure at the perf oration s will double. In reality, leakoff from the well is not \nidentically zero, the increased pressure generated by the rising bubble causes an increase in leakoff rate, the gas temperatu re \ndecreases somewhat during transit , and some gas may dissol ve in the wellbore fluid, therefore,  a very small gas bubble \nentering at the perforations can cause a large pressure upset  as demonstrated in Figure 1 8. Figure 1 9 shows the effects of gas \nentry on an actual treatment.  \n \n \n \nFigure 1 8: Schematic showing a gas bubble that enters from the perforations can generate increased pressures at it rises to the \nsurface.  \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae385e0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 15, "chroma:document": "16  SPE 169539  \n \nFigure 1 9: The complete data set for a long -term injection test in an over -pressured formation is shown. The minimum pressure \nrecorded at surface was 743 psi after 2.5 hours of falloff. The pressure increases after that time until about 9 hours of fal loff.  For \npurposes of analysis, the end of the valid data occurs before the minimum pressure point at 2.5 hours. The later pressur e rise is \ncaused by entry of small gas bubbles at the perforations which rise in the wellbore fluid column.  \n \n \nLoss of Hydrostatic Head  \nThe loss of the hydrostatic head effectively terminates a DFIT test. Bottomhole gauges can and are installed to acquire data in \ncertain circumstances, however, these will not aid in extending the test if the hydrostatic column starts to fall. In these cases, \nthe bottomhole gauge will record  the weight of the fluid standing above the gauge. The fluid column is supported by a  partial"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38658-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 15, "chroma:document": "vacuum between the fluid level in the well and the sealed wellhead. The rate of fluid level fall is then controlled more by t he \nrate of vaporization of the wellbore fluid than the reser voir transmissibility. Figure 20 shows a typical pressure resp onse for a \nbottomhole gauge in a well with falling fluid level.  \nThe data for the first few hours of falloff accurately represent the ISIP and initial leakoff rate and closure of the fractur e. \nThe remaining data, covering about a week of shut -in, shows almost no change in the pressure on the gauge because the fluid \nhead  above the gauge is nearly constant. Analysis of this part of the pressure falloff will give no  useful reservoir or  fracture \ninformation. Figure 2 1 shows the log -log plot for this falloff, and provides a useful clue for identifying the falling fluid level \ncase. As the fluid level begins to drop, the pressure deriv ative (magenta line in Figure 2 1) exhibits a large negative slope."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae386d0-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 15, "chroma:document": "Once the fluid level in the well stabilizes, and begins to drop at a rate controlled by vaporization of the fluid at the surf ace, \nthe derivative assumes a positive, nearly straight -line, slope of about \u00bd. During this period , the fluid at the surface of the \nstanding column is effectively boiling (fluid pressure equals vapor pressure), and the heat of phase transformation causes th e \nfluid temperature to drop. This increases fluid density, driving a convection cell which replaces the colder surface fluid with  \nwarmer fluid from below. The important point here, is that analysis of the pressure -time data in this case cannot provide \nuseful r eservoir or fracture data.  \n \n \nFigure 20: Bottomhole gauge response with falling fluid level, or surface pressure on vacuum.  \n3/22/200322:00\n3/23/200300:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00\n3/23/200318:00\nTime0100020003000400050006000A\n0.00.51.01.52.02.53.03.5B Wellhead Pressure (psi) Slurry Rate (bpm)A B\nCustomer: Job Date: Ticket #:"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38752-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 15, "chroma:document": "Customer: Job Date: Ticket #:\nWell Desc: UWI:GohWin v1.6.3\n18-Dec-06 15:35\nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae387de-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 16, "chroma:document": "SPE 169539   17 \n \n \n \nFigure 2 1: Log -log derivative an d pressure difference for a bottomhole gauge  with falling fluid level.  \n \nThere are three practic al ways to avoid this problem: f irst, use a fluid of low enough density so that hydrostatic wellbore \nhead is less than reservoir pressure. That can be achieved in some cases by using oil (a surface gauge can then be used) if t he \nreservoir is not badly unde r-pressured. Second, use a bottomhole gauge and bottomhole shut-in or isolation tool (that work s). \nThe example in Figures 20 and 2 1 was run with a bottomhole shut -in tool and memory gauge, but the shut -in tool leaked. The \nthird methods is to vent the wellh ead when the surface pressure drops to zero. This will allow the fluid level to fall to a \npressure in equilibrium with the reservoir. Fracture closure will often occur before the wellhead pressure drops to zero, and"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38860-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 16, "chroma:document": "the closure time and pressure will be wi thin acceptable accuracy. After closure there will be an extended transient period as \nthe fluid level seeks equilibrium. After that, the pressure decay to reservoir conditions  will be analyzable, but all reservoir \ntransients will be delayed. Corrections ca n be made for the added injection volume in the after -closure calculations.  \n \nCommon Mistakes in After -Closure Analysis  \nThe following example is one of many and shows some extremely common mistakes in DFIT after -closure analysis. The \nexample is not intende d to disparage any particular software or analyst and identifying information about the specific test has \nbeen hidden or removed whenever possible. The test data were acquired with a botto mhole gauge and the test was pumped \nthrough the toe perforations in a horizontal well. Figure 2 2 (a and b) show the G -function diagnostic derivatives for the test ,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae388d8-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 16, "chroma:document": "computed in two different software packages. The result s are essentially the same, with closu re pressures of 22.463 and \n22.419 MPa , respectively. The semi -log derivative shows variable storage and a long after -closure transient period. This part \nof the analysis is consistent across almost all software. The slight  difference in the value of G at cl osure may be due to slight \ndifferences in the computed pumping time.  \n \n \n  \n(a)                                                                                                  (b)  \n \nFigure 2 2: G-function diagnostic derivative plots from different software anal ysis systems . \n \nOnce ISIP and closure are identified, the net extension pressure can be computed from the difference. In this ca se, the \nISIP is slightly different due to wellbore expansion effects of short duration. The next step in the analysis is the log -log plot \nof pressure change from IS IP versus shut -in time. Figure 2 3 (a and b) show these plots from the two analysis packages."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3895a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 16, "chroma:document": "Downloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae389d2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 17, "chroma:document": "18  SPE 169539  \n \n(a)                                                                                             (b) \n \nFigure 2 3: Log -log pressure  change versus time after shut -in, with semi -log derivative . \n \nAfter the end of the variable storage period, and for a very brief time prior to closure, the plot in Figure 2 3(a) shows a \npositive \u00bd slope derivative corresponding to a linear fracture leakoff mechanism. After closure the derivative falls on a \nnegative slope that is slightly shallower than -1/2. Through the entire test , the flow regime does not develop into an ideal \npseudo -linear flow regime, and certainly shows no evidence whatsoever of a pseud o-radial f low regime. The plot in Figure \n23(b) identifies the late time slope at -1/2 (shown in the green text box), which is an approximation.  \nThe next step in the analysis should be to extrapolate the after -closure pressure decline to estimate reservoir  pore pressure."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38a4a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 17, "chroma:document": "Since the pseudo -linear flow regime is not fully developed, the extrapolation of the Cartesian linear flow plot will probably \ngive a pressure estimate that is slightly too high. Use of the Cartesian radial flow plot i s not warranted at all.  Figure 2 4(a) \nshows the construction and extrapolation of the Cartesian linear flow plot, with an extrapolation to a pore pressure of 17.5 5 \nMPa. Figure 2 4(b) shows the construction and extrapolation of the Cartesian radial flow plot that was presented in t he other \nanalysis. This extrapolation gives a reservoir pore pressure of 18.03 MPa.  \n \n \n \n(a)                                                                                                  (b) \n \nFigure 2 4: Pressure versus linear and radial time functions for linear extrapolation to reservoir pore pressure . \n \nIn this case , the difference in the estimated pressure is probably insignificant (about 3%), although in many cases the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38ac2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 17, "chroma:document": "same error in flow regime identification can lead to pressure errors of up to 30%. A m ore serious  error develops if the wrong \nflow regime, and wrong pore pressure are used in the Horner or radial -flow solution for reservoir transmissibility. The best \nway to assure that the after -closure flow regime is correctly identified is to use the Tall ey et al (1999) log -log flow regime \nplot. This plot displays the difference between calculated bottomhole pressure and static reservoir pressure (p* or p i) as a \nfunction of the square of the linear -flow time function. Entering the wrong pore pressure chang es the shape and position of \nthe pressure difference curve, but does not alter the shape and position of the derivative curve.  \nFigure 2 5 (a and b) show the two after -closure flow regime plots for the same test data. Figure 2 5(a) shows the plot using \nthe po re pressure estimated from the linear flow extrapolation. The straight line connecting the beginning and end of the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38b3a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 17, "chroma:document": "assumed linear flow period has the required slope of \u00bd. Clearly the derivative falls on a significantly lower sl ope, which is \nconsistent with the slope of the  semi -log derivative in Figure 2 4(a). The pressure difference curve is forced to fall on the \u00bd \nslope and be separated from the derivative by approximately 2x because of the selection of the pore pressure value derived \nfrom the extrapol ation of the Cart esian linear flow plot (Figure 2 4(a)). \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38bb2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 18, "chroma:document": "SPE 169539   19 \n \n \n \n(a)                                                                                          (b) \n \nFigure 2 5: Log -log of well pressure minus static reservoir pressure versus square of the linear flow time function . \n \nFigure 25 (b) shows the plot with the pore pressure picked from the Cartesian radial flow extrapolation. This value forces \nthe pressure difference curve to approach a -1 slope, and to fall on top of the derivative curve. Clearly, the deriva tive is not on \na -1 slope, and is still, in fact, of a slope less than -1/2. There appears to be a consistent trend in the industry to force a \npseudo -radial solution out of a DFIT analysis, even when the data clearly show that no such flow regime exists. T he final \nresults of this error in flow regime identification, and the forcing of an imposed incorrect analysis is most obvious in the \ncomputed reservoir transmissibility. Figure 25(b) indicates an estimate permeability of more than 0.1 md, which is consist ent"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38c70-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 18, "chroma:document": "with a transmissibility of more than 0.8 md -m/cp. These results can be reproduced in the software used for the case (a) results \nwhen the same mistakes are made. The closure time of G=20, from Figure 21, is more consistent with a system permeability \nof less than 0.002 md and transmissibility of less than 0.014 md -m/cp.  \nApplying the other relations described in this paper to this example gives a clearer interpretation of a consistent result. \nThe average pump rate for the test was 0.6 m3/m (3.7 bpm) with a pump time of 9.5 minutes. Fluid efficiency estimated from \nclosure time is 90% with a transverse storage factor of 91%. Based on Figure 13, this should generate a fracture half-length  \nof about 100m (320 ft). The rule of thumb for closure from Figure 14, assuming a permeability of about 0.002 md, is 10 \nhours. Actual closure time was 688 minutes (11.4 hours). A valid linear flow reservoir transient may be expected after 30"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38cfc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 18, "chroma:document": "hours, but a fully developed pseudo -linear flow regime never developed, even up to the  end of the test at 330 hours (13.8 \ndays). According to Figure 16, a pseudo -radial flow regime consistent with a single planar fracture should not be expected \nbefore 300 days. Clearly any results obtained from a forced radial flow analysis are not valid.  \nA final comment about the use of the Horner plot in after -closure analysis is warranted. The Horner plot is only valid, and \nshould only be relied upon, when a fully developed pseudo -radial flow regime is identified  in the data. The conditions \ndescribed abo ve for the use of the Cartesian radial flow analysis must also be met for the Horner extrapolation to be valid. In \npractical terms, that means that extrapolation of an apparent straight line at the end of a Horner plot will almost always be  \nwrong. Both the  Cartesian radial flow analysis and Horner plots can be extrapolated to the pore pressure derived from a"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38d74-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 18, "chroma:document": "pseudo -linear flow analysis (if the pseudo -linear flow regime exists) , to obtain a maximum upper bound of reservoir \ntransmissibility. Be aware that thi s estimate may be at least an order of magnitude too high.  \n \nConclusions  \nDFIT tests can provide a wide variety of data to aid in designing hydraulic fracturing treatments and characterizing the \nsubject reservoir. However, there are many factors associated with data collection and analysis that can result in poor or \nincorrect results. This paper attempts to describe  some of the common problems  and to help prevent some common errors  \noften observed in DFIT execution and analysis. These issues (and their possib le solutions) include:  \n \n\uf0b7 DFIT\u2019s should be pumped with a New tonian, non -wall building fluid;  \n\uf0b7 Multiple pump -ins must be avoided;  \n\uf0b7 The tests must be planned to allow for closure and  enough falloff time to enter linear flow at a minimum. This \ntime period may be several days, if not weeks, in low permeability systems;"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae38dec-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 18, "chroma:document": "\uf0b7 Use step -down  not step -up tests  to determine near wellbore and perforation friction;  \n\uf0b7 Correct ISIP determination  is cri tical to further analysis of the test. Wellbore compressibility and other factors \nmust be taken into consideration;  \n\uf0b7 The tests must b e of adequate duration and rate  (shortest practical duration at highest practical rate) ; \n\uf0b7 The possibility of p hase segregatio n and gas entry  must be considered;  \nDownloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3921a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 19, "chroma:document": "20  SPE 169539  \n\uf0b7 Loss of hydrostatic head  will likely render the test useless , even with bottomhole gauges,  unless certain \nadditional steps are taken; and,  \n\uf0b7 Not al l tests result in pseudo -radial flow regimes , and, i n fact, reaching pseud o-radial conditions is more the \nexception to the ru le. There are numerous reasons for f alse indications of pseudo -radial. To avoid these, full \nintegration of the test results must be considered and the physics of the solution must be respected.  \n \nConsiderat ion of these points and the other s listed in this paper will lead to i mproved data acquisition and analysis , which \nin turn,  will lead to better tests, better results, and ultimately better predictions of production and reserve recovery.  \n \nReferences  \nBarree,  R.D. 1998. Applications of Pre -Frac Injection/Falloff Tests in Fissured Reservoirs \u2013 Field Examples. Paper SPE 39932 presented  at"}


created_at: 2023-11-17 19:17:23
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id: 9ae392b0-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 19, "chroma:document": "the SPE Rocky Mountain Regional/Low -Permeability Reservoirs Symposium and Exhibition, Denver, CO, 5 -8 April.  \nBarree, R.D., Ba rree, V.L, and Craig, D.P. 2009. Holistic Fracture Diagnostics: Consistent Interpretation of Prefrac Injection Tests Using \nMultiple Analysis Methods SPE Prod & Oper 24(3): 396 -406. SPE 107877 -PA. DOI 10.2118/107877 -PA. \nDaltaban, T. S. and Wall, C. G. 1998. Fundamenta l and Applied Pressure Analysis, Imperial College Press,  p438 . \nTalley, G. R., Swindell, T. M., Waters, G. A. and Nolte, K. G. 1999. Field Application of After -Closure Analysis of Fracture Calibration \nTests. Paper SPE 52220 presented a t the SPE Mid -Continent Operations Symposium, Oklahoma City, OK, 28 -31 March.  \nNolte, K. G. 1979. Determination of Fracture Parameters from Fracturing Pressure Decline. Paper SPE 3841 presented at the Ann ual \nTechnical Conference and Exhibition, Las Vegas, NV, 23 -26 Sept. 23 -26."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/SPE-169539-MS.pdf", "page": 19, "chroma:document": "Downloaded from http://onepetro.org/SPEWRM/proceedings-pdf/14WRRM/All-14WRRM/SPE-169539-MS/1542530/spe-169539-ms.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 0, "chroma:document": "Transient Pressure Analysis \nfor Fractured Wells \nHeber Cinco-Ley, * SPE, Stanford U. \nFernando Samaniego-V., * SPE, Inst. Mexicano del Petr6leo \nSummary \nA new technique is presented for analyzing pressure \ntransient data for wells intercepted by a finite\u00ad\nconductivity vertical fracture. This method is based \non the bilinear flow theory, which considers transient \nlinear flow in both fracture and formation. It is \ndemonstrated that a graph of Pwf vs. tv. produces a \nstraight line whose slope is inversely proportional to \nhf(kfbf} Yz. New type curves are presented that \novercome the uniqueness problem exhibited by other \ntype curves. \nIntroduction \nA large amount of information concerning well test \nanalysis has appeared in the literature over the last \nthree decades. As a result of developments in this \narea, three monographs 1 ,2,3 and one book4 have \nbeen published covering different aspects of pressure \ntransient analysis. Ramey 5 also has presented a \nreview on the state of the art."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3940e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 0, "chroma:document": "review on the state of the art. \nThe analysis of pressure data for fractured wells \nhas deserved special attention because of the number \nof wells that have been stimulated by hydraulic \nfracturing techniques. A summary of the work done \non flow toward fractured wells' was presented by \nRaghavan 6 in 1977. \nIt was recognized early that intercepting fractures \ncan strongly affect the transient flow behavior of a \nwell7-9 and that, consequently, the application of \nclassical methods 10-12 to the analysis of transient \npressure data in this situation may produce erroneous \nresults. Several methods 13-24 were proposed to solve \nthis problem. \nThese analysis techniques consider a well in\u00ad\ntersected by either an infinite-conductivity vertical \nfracture or a uniform-flux vertical fracture. Cinco\u00ad\nLey et al.25 demonstrated that the assumption of \ninfinite fracture conductivity is valid whenever \n*Now with Petr61eos Mexicanos and U. Nacional de Mexico. \n0149\u00b72136/8110009\u00b77490$00.25"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39486-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 0, "chroma:document": "0149\u00b72136/8110009\u00b77490$00.25 \nCopyright 1981 Society of Petroleum Engineers of AIME \nSEPTEMBER 1981 the dimensionless fracture conductivity \n(kfbflkxf) ~300; all other cases; such as those \nrepresented by long or poorly conductive fractures, \nmust be analyzed by considering a finite-conductivity \nfracture model. \nExploitation of low-permeability gas reservoirs has \nrequired stimulation of wells by massive hydraulic \nfracturing (MHF) techniques. Vertical fractures of \nlarge horizontal extension are created as a result of \nthis operation; consequently, pressure drop along the \nfracture cannot be ne~lected. \nSeveral papers25-3 have been published on the \nbehavior of finite-conductivity vertical fractures. \nType-curve matching has been proposed as an \nanalysis method under these conditions; however, \nsome regions of the curves present a uniqueness \nproblem in the analysis. Barker and Ramey31 in\u00ad\ndicated that the use of published type curves becomes \npractical when a large span of pressure data is \navailable."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae394f4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 0, "chroma:document": "practical when a large span of pressure data is \navailable. \nThe purpose of this work is to present a new in\u00ad\nterpretation technique for early-time pressure data \nfor a well intercepted by a finite-conductivity vertical \nfracture, including the criteria to determine the end \nof wellbore storage effects. In addition, new type \ncurves are discussed to overcome the uniqueness \nproblem exhibited by previous curves at intermediate \nand large time values. \nTransient Pressure Behavior \nfor Fractured Wells \nConsider a vertically fractured well producing at a \nconstant flow rate, q, in an infinite, isotropic, \nhomogeneous, horizontal reservoir that contains a \nslightly compressible fluid of constant com\u00ad\npressibility c, and viscosity p.. The porous medium \nhas a permeability k, porosity 1>, thickness h, and \ninitial pressure Pi' \nLet us assume that the well is intercepted by an \nundeformable, fully penetrating vertical fracture of"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3956c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 0, "chroma:document": "undeformable, fully penetrating vertical fracture of \n1749 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae395e4-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 1, "chroma:document": "TABLE 1 -SI PREFERRED UNITS, CUSTOMARY UNITS, \nAND UNIT CONVERSION CONSTANTS \nParameter \nor Variable \nk \nh \nqo \nqg \np. \nB \n<P \nCt \np \nm(p) \nt \nIMPERMEABLE \nBOUNDARIES USED IN THESE SYSTEMS \nSI Preferred Units \np'm2 \nm \nm3/d \nm3/d \nPa\u00b7s \nm3/m3 \nfraction \nPa-1 \nkPa \nkPa2/Pa\u00b7s \nhours \n1,842 \n1,293 \n3.6x 10-9 \n34.97 \n24.57 \n0.3918 \n0.275 \nK \nm3/Pa Customary Units \nmd \nft \nSTBID \nMscf/D \ncp \nRB/STB \nfraction \npsi-1 \npsi \npsi2/cp \nhours \n141.2 \n1,424 \n2.637 x 10-4 \n44.1 \n444.75 \n8.128 \n81.97 \noR \ncu ft/psi \nWELLBORE \nFRACTURE \nh \nFig. 1 -Finite\u00b7conductivity vertical fracture in an infinite\u00b7 \nslab reservoir. \n, CASE \nf:>wD \nA \nF B D E \n\"', I< \ntDXf \nFig. 2 -Low\u00b7log graph of typical cases for fractured wells. \n!750 half-length xf' width bf, permeability kf' porosity \nr/>f' and total compressibility Cft (Fig. 1). The \nproperties of both the reservoir and the fracture are \nindependent of pressure and the flow in the entire \nsystem obeys Darcy's law. In addition, it is con\u00ad"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39652-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 1, "chroma:document": "system obeys Darcy's law. In addition, it is con\u00ad\nvenient to assume that pressure gradients are small, \ngravity effects are negligible, and flow entering the \nwell bore comes only through the fracture. \nWith these assumptions, the unsteady-state flow in \nthe system can be described by the diffusivity \nequation.! For details on the boundary conditions \nand a semianalytical solution for this flow problem, \nsee Ref. 25. \nThe general solution for the well bore flowing \npressure P wf for oil is given by25 \nkh(Pi-Pwf) \n----!....-B~- =PWD(tDxf,'Y/fD,CfDf) ...... (1) aoq J), \nand, for gas, \nwhere \n{3kt \ntDxf = r/>J),ctx}' ......................\u2022 (3) \n'Y/fD=~' ..\u2022...................... (4) \nkr/>jCft \nand \nCfDf= ~r;~ ....................... (5) \nP wD represents the dimensionless pressure drop; it is \na function of dimensionless time, t Dx ' dimen\u00ad\nsionless fracture hydraulic diffusivity, 'Y/ib, and di\u00ad\nmensionless fracture storage capacity, CfDJ. ao' ag, \nand {3 are unit conversion constants (see Table 1)."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae396ca-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 1, "chroma:document": "and {3 are unit conversion constants (see Table 1). \nCinco-Ley et at.25 showed that for practical values \nof dimensionless time the pressure behavior depends \non two parameters only: the dimensionless time t Dx.r' \nand the dimensionless fracture conductivity \n(kfb f) D\u00b7 The former was defined in Eq. 3 and the \nlatter may be obtained from Eqs. 4 and 5. By \ndefinition, the dimensionless fracture conductivity is \nkb (kfbf) D = ~k , ..................... (6) xf \nand it appears to be related to CfDf and 'Y/fD as \nfollows. \n(kfbf)D=7rCfDf'Y/fD. . ................. (7) \nFig. 2 shows the general behavior of a well with a \nfinite-conductivity vertical fracture. There, we show \na log-log graph of dimensionless wellbore pressure, \nPwD' vs. dimensionless time, tDX[\" For the sake of \nsimplicity only two cases are presented. Case 1 \nrepresents the behavior of a low-conductivity"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3974c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 1, "chroma:document": "represents the behavior of a low-conductivity \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae397c4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 2, "chroma:document": "~L--=~c5well ) \\ \nFracture \n(0) \nFRACTURE LINEAR FLOW \nFracture -----_/ \n(c ) \nFORMATION LINEAR FL()\\~ (b) \nB I LIN EAR FLO W \n\\ / \nFracture , . \nI \nWell \n\\ ~ \nPSEUDO-RADIAL FLOW \nFig. 3 -Flow periods for a vertically fractured well. \nfracture (kfbf) D =0.1; Case 2 considers a highly \nconductive fracture, (kfbf) D = 500. These cases \nwere selected because they exhibit all the features of \nthe transient pressure behavior for a fractured well. \nAn analysis of Fig. 2 shows that the transient \nbehavior of a well with a finite-conductivity vertical \nfracture includes several flow periods. Initially, there \nis a/racture linear flow characterized by a half-slope \nstraight iine; after a transition flow period, the \nsystem mayor may not exhibit a bilinear flow period, \nindicated by a one-fourth-slope straight line. As time \nincreases, a formation linear flow period might \ndevelop. Eventually, in all cases, the system reaches a \npseudoradial flow period (see Fig. 3). \nPoints A, F, and L in Fig. 2 represent the end of"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39846-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 2, "chroma:document": "Points A, F, and L in Fig. 2 represent the end of \nthe fracture linear flow period (half-slope straight \nline). The bilinear flow period (one-quarter-slope \nstraight line) is defined by Segments B-C and G-H; \nthis behavior is not present when the fracture has a \nhigh storage capacity and a high conductivity (lower \ncurve in Case 2). \nThe formation linear flow period is shown by the \nhalf-slope straight line between Points I and J, and it \nis only exhibited by fractures of high conductivity, \n(k fb f) D ~ 300. Points D and K show the beginning \nof the pseudoradial flow period. \nWe present a detailed description of both the \nfractured linear flow and the bilinear flow. The \nformation linear flow and the pseudoradial flow have \nbeen discussed in the literature. 14,15,17,19,22,25 \nSEPTEMBER 1981 Fracture Linear Flow Period \nThis behavior occurs at very small values of dimen\u00ad\nsionless time, and it is exhibited by all cases. During \nthis flow period, most of the fluid entering the well\u00ad"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae398be-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 2, "chroma:document": "this flow period, most of the fluid entering the well\u00ad\nbore comes from the expansion of the system within \nthe fracture and the flow is essentially linear, as \nshown in Fig. 3a. \nThe dimensionless pressure response at the \nwellbore is given by\u00b7 \nP D -2 ..j 1'('YIfDtD ............ (8) w -(kfbf) D -, 'Xf \nHence, for oil, \n_ _ 0ffoqB I p,t \nPwf-Pi b h ..,J k cJ> c ' ... ---. ---... (9) \nf f1ft \nand for gas, \n_ 0ffgqT I t m(pwf) -m(Pi) -b h ..,J k cJ> , \u2022\u2022\u2022\u2022\u2022 (10) \nj f jp,Ct \nwhere 0ffo and 0ffg are unit conversion constants. \nThese equations indicate that a log-log graph of \npressure vs. time yields a straight line whose slope is \nequal to one half. A graph of pressure or pseudo\u00ad\npressure vs. the square root of time also gives a \nstraight line whose slope depends on the fracture \ncharacteristics excluding the fracture half-length xf-\nThe fracture linear flow ends when \n\u00b7See Appendix A for derivation."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39990-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 2, "chroma:document": "\u00b7See Appendix A for derivation. \n1751 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39a08-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 3, "chroma:document": "2 \nP wD ----End of Straight \nLine O.21T \nFig. 4 -PwD vs. tb~l for a well with a finite\u00b7conductivity \nvertical fracture. \n_ 0.01 (kfbf) b tDxf- 2 ...........\u2022..... (11) \n'YIfD \nUnfortunately, this flow period occurs at a time too \nearly to be of practical use. \nBilinear Flow Period \nTo the best of our knowledge, this is a new type of \nflow behavior that has not been considered in the \nliterature. It is called bilinear flow because two linear \nflows occur simultaneously. One flow is a linear \nincompressiblejlow withinthefracture and the other \nis a linear compressible flow in the formation, as \nshown in Fig. 3b. A bilinear flow exists, as shown in \nAppendix A, whenever most of the fluid entering the \nwell bore comes from the formation and fracture tip \neffects have not yet affected the well behavior. \nLet us now examine this behavior in a log-log \ngraph of PwD vs. tDx (Fig. 2). In Case 1 \n[ (kjb f) D = 0.1], the bili6ear flow exists between \nPomts Band C after a transition flow period"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39a8a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 3, "chroma:document": "Pomts Band C after a transition flow period \nrepresented by Segment A-B. The pressure behavior \nfor the bilinear jlow exhibits a straight line whose \nslope is equal to one fourth. The duration of this \nperiod depends on both (kfbf) D and CfPf. Case 2 \n[(kfbf) D = 500] mayor may not exhibit the bilinear \nflow period, as shown by the upper and lower curves. \nThe upper curve for Case 2 corresponds to a low \nvalue for CfDf and does exhibit bilinear flow over a \nshort perioo of time (Segment G-H); however, the \n1752 -4 10 \nFig. 5 -Dimensionless time for the end of the bilinear flow \nperiod vs. dimensionless fracture conductivity. \nlower curve corresponding to a high value of CfDf does not exhibit the bilinear flow behavior because \nfracture tip effects are felt before this flow regime is \nestablished (Segment L-I). \nThe dimensionless wellbore pressure for the \nbilinear flow period is given by* \n7r \\1.1 \nPwD = r(1.25)..)2(k\nfb\nf) D t DXf' ......... (12) \nor \n2.45 II. \nPwD = ..) (kfb"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39b16-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 3, "chroma:document": "fb\nf) D t DXf' ......... (12) \nor \n2.45 II. \nPwD = ..) (kfb\nf) D t DXj\" ................ (13) \nThis equation indicates that a graph of PwD vs. \n{j t Dx produces a straight line whose slope is \n2.451..) (kfb f) D, intercepting the origin. Fig. 4 \npresents that type of graph for different values of \n(kfbf)D\u00b7 . \nAn important feature of this graph is that after the \nbilinear flow period (straight-line portion), the curves \nfor (kfbf) D :51.6 are concave downward and the \ncurves for (kfbf) D > 1.6 are concave upward. \nThe end 0 the straight-line portion of the curves \ndepends on the fracture conductivity and may be \nexpressed by \n0.1 \n\u00b7See Appendix A for derivation. \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39b8e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 4, "chroma:document": "0. \n<J \no \nFig. 6 -Graph for analysis of pressure data of bilinear \nflow. \n. [ ] -1.53 tDebf=O.0205 (kfbf}D-1.5 \nfor 1.6$ (kfbf) D $3, ........... (l4b) \nand \nt _ [ 4.55 _ 2.5] -4 \nDebf--J (kfbf) D \nfor (kiJf) D $1.6 ............... (l4c) \nFig. 5 shows a graphical representation of these \nequations. \nBilinear Fiow Analysis \nBilinear flow is exhibited by finite-conductivity \nfractures with a small dimensionless storage capacity; \nCfDf. Any attempt to analyze pressure data observed \nover this flow period using conventional methods (p \nvs. Yt or p vs. log t) will produce erroneous results. \nWe present the appropriate analysis method based on \nthe bilinear flow theory. \nBasic Equations and Graphs \nFrom Eq. 13, the pressure drop for oil may be ex\u00ad\npressed as \nSEPTEMBER 1981 Q \n<l \nOl o -1 \nSlope = 1/4 \nLog t \nFig. 7 -Log\u00b7log graph of pressure data for bilinear flow. \nand, for gas, \nwhere t:.p is the pressure (pseudopressure) change for \na given test. Both 0bfo and 0bfg are unit conversion"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39c10-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 4, "chroma:document": "a given test. Both 0bfo and 0bfg are unit conversion \nconstants and are given in Table 1. \nEqs. 15 and 16 indicate that the pressure change is \nboth inversely proportional to the square root of the \nfracture conductivity and directly proportional to the \nfourth root of time. \nAccording to Eqs. 15 and 16, a graph of t:.p vs. Vi \nproduces a straight line passing through the origin, \nwhose slope, m bf' for oil, is given by \nm -\u00b0bfoqBp, \nbf-h(kfbf} Y2(~p,Ctk} y. , ............ (17) \nand, for gas, \nm - \u00b0bfgqT \nbf-h(kfb\nf} 'I2(~p,ctk} y., .\u2022.......... (18) \nHence, the product h(kfbf} '12 can be estimated by \nusing the following equations. For oil, \nh (k b ) Y2 = \u00b0bfoqBp, (19) f f mbf(~p,Ctk} y., \u2022........... \nand, for gas, \n1753 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39c88-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 5, "chroma:document": "[lP \no \nFig. 8 -Bilinear\u00b7flow graph for a fracture with a flow \nrestriction near the well bore. \nThese equations indicate that values of reservoir \nproperties must be available to estimate the group \nh (kfbf) Y2 \u2022 Note that this analysis technique tends to \ndecrease the effect of the error introduced when poor \ninformation on reservoir properties (i.e., k, cp, and \net) is used. \nAll comments on the concavity of the curve in Fig. \n4 are valid for the curve in Fig. 6. \nFrom Eqs. 13 and 14, if (kfbf) D ??3, the \ndimensionless pressure drop at the end of the bilinear \nflow period is given by \n1.38 \n(PwD}ebf=- (kfbf}D ................. (21) \nHence, the dimensionless fracture conductivity can \nbe estimated using the following equation. \n1.38 (kfbf) D=- ................. (22) \n(PwD}ebf \n(p wD ) ebf can be calculated using Eq. 1 or Eq. 2 and \n(1\u00a5J) ebf or &n (p) ebf obtained from the bilinear \nflow graph. \nFrom Eqs. 15 and 16, a graph of log 1\u00a5J vs. log t \nyields a quarter-slope straight line (Fig. 7) that can be"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39d00-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 5, "chroma:document": "yields a quarter-slope straight line (Fig. 7) that can be \n. used as a diagnostic tool for bilinear flow detection. \nExtensions and Limitations \nThe region disturbed during bilinear flow includes \nonly the fracture and its vicinities because it occurs at \nearly time, even in partially penetrating fracture \nsystems. Thus, the equations and graphs discussed in \nthe previous section for bilinear flow can be extended \nto cases where the fracture does not penetrate the \n1754 llP \n,. /\" \\\\'.~ \n<#\\<1' \\.-\ns'-\n~\\.-O'\\ \n\\{c'r<!- ~ \n\",\\\\.-\\ ~ \nfvC,'\\ ~ \nI<!-\"'/\"\"''''-:~ \n\",.. \n\",.. PRESSURE BEHAVIOR WITH WELLBORE \n/\" /\" ?---- STORAGE EFFECTS \n4 \u00ab \nFig. 9 -Wellbore storage effect on the bilinear flow graph. \nentire thickness of the formation. This is possible \nsimply by using the fracture height, hf' instead ofthe \nformation thickness, h. \nIn cases where a flow restriction (low conductivity, \nturbulent flow) exists within the fracture in the \nvicinity of the well bore, bilinear flow still occurs and"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39d78-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 5, "chroma:document": "vicinity of the well bore, bilinear flow still occurs and \nthe pressure data analysis discussed cim be applied \n(see Fig. 8). An extra pressure drop, 1\u00a5Js' is created in \nthis case and the straight-line portion does not in\u00ad\ntercept the origin. These situations distort the \nstraight-line portion in the log-log graph. \nIf well bore storage affects the system, the bilinear \nflow pressure behavior may be masked, as shown in \nFig. 9, and data analysis becomes difficult (if not \nimpossible) with current interpretation methods. \nFlow Regime Identification \nand New Type Curves \nThe pressure behavior of a fractured well may exhibit \nseveral flow periods for practical values of time: \nbilinear flow, formation linear flow, and \npseudoradial flow. \nPressure data for each flow period should be \nanalyzed using a specific interpretation method (i.e., \nPw vs. Vi, Pw vs. Vi, and Pw vs. log t for bilinear, \nlinear, and pseudoradial flows, respectively). \nThe log-log graph has been used commonly as a"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39dfa-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 5, "chroma:document": "The log-log graph has been used commonly as a \ndiagnostic tool to detect different flow regimes in a \ntransient pressure test. The use of type curves in the \nanalysis of pressure data for fractured wells \nrepresents a major step in that area. The first type \ncurves for fractured wells were presented by \nGringarten et. af.19 Cinco-Ley et af.25 showed that \nthe infinite-conductivity vertical fracture solution of \nGringarten and Ramey17 behaves like the solution \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39e7c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 6, "chroma:document": "for a finite-conductivity vertical fracture of \n(k fb f ) D ~ 300; furthermore, they showed that the \numform-flux vertical fracture behaves as a variable\u00ad\nconductivity vertical fracture. The type-curve \nanalysis offers an advantage over the specific analysis \nmethods already mentioned because it can be applied \nto interpret at once pressure test data that correspond \nto different flow periods. In addition, the type-curve \nanalysis could indicate when the different graphical \ntechniques apply. \nExperience has shown that, in some cases, ap\u00ad\nplication of the type curves available for finite\u00ad\nconductivity vertical fractures does not yield unique \nresults. This is because the shape of pressure \nbehavior curves is similar for different values of \ndimensionless fracture conductivity over some \nregions of the type curves. A close inspection of Fig. \n2 indicates that the uniqueness problem can exist if \npressure data to be analyzed occur at either the \nbilinear flow period (one-fourth slope) or the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39ef4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 6, "chroma:document": "bilinear flow period (one-fourth slope) or the \npseudoradial flow period. \nA convenient presentation of the type curve \npublished by Cinco-Ley et al., 25 Ramey et al., 31 and \nAgarwal et al.29 is given in Fig. 10. We show a graph \nof log [PwD(kfbf}vl vs. log [tDx (kfbf}~l.* The \nmain feature of this graph is that for all values of \n(k fb J ) D the behavior of both bilinear flow (quarter \nslope) and the formation linear flow (half slope) is \ngiven by a single curve. Note that there is a transition \nperiod between the bilinear and linear flows. The \ndashed line in this figure indicates the approximate \nstart of the pseudoradial flow period (semilog \nstraight line). Also shown are the end of the bilinear \nflow and the start of the formation linear flow; the \ntime for the end of the bilinear flow from Fig. lO \nagrees with the results presented in Fig. 5. The groups \nof variables used in Fig. lO were derived in Appendix \nB, where it is shown that, for some values of fracture"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39f6c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 6, "chroma:document": "B, where it is shown that, for some values of fracture \nconductivity, bilinear flow ends when fracture tip \neffects are felt at the wellbore. \nAlthough many curves are presented for \n(kfbf) D > 207r, the shape of these lines is essentially \nthe same. The only difference is the duration of the \nformation linear flow (half slope); that is, the higher \nthe fracture conductivity, the longer the linear flow \nperiod. \nThe beginning of the formation linear flow occurs \nat tDxf (kfbf) b::::: 102; that is, \n100 \nt Dblf == 2 \u2022 \u2022 \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022.\u2022\u2022\u2022\u2022\u2022.\u2022.\u2022\u2022\u2022 (23) \n(kfbf) D \nThe end of this flow period is given by19 \ntDelf==0.016 .......................... (24) \nHence, the fracture conductivity may be estimated as \nfollows: \nlO (kfbf}D== ~, ................... (25) \n'ItDblf \n\u2022 A large-scale copy of this graph may be obtained from the authors. \nSEPTEMBER 1981 slope=-} \n'~~~~-'~6~2~--~'070~--,O~2~--~,~~~-,~~~~~,o8 \n2 t DX\nf (kf bflD \nFig. 10 -Type curve for vertically fractured wells. \nor"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae39fee-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 6, "chroma:document": "Fig. 10 -Type curve for vertically fractured wells. \nor \n(kfbf}D==1.25XlO-2j telf ........... (26) \ntblf \nThese equations apply when (k fbf) D ~ 100. \nFig. lO can be used as a type curve to analyze \npressure data for a fractured well. Pressure data on a \ngraph of log tlp vs. log t is matched on a type curve to \ndetermine (tlp}M' [PwD(kfbf}DlM, (t}M' [tDx \n. (kfbf}blM' [(k/b/}DlM, (tebf}M' (tblj}M' anl~ \n(tbssl J M' From thiS mformation, we can estimate the \nfollowing. \nDimensionless Fracture Conductivity. \nFormation Permeability. For oil, \nko = _Q!o,,-q_B_J1._ [PwD' (kfbf) DlM \nh(tlp}M [(kfbf}vlM ....... (27) \nand, for gas, \nk -Q!gqT [PwD' (kfbf) DlM \ng-h[~(p}lM [(kfbf}vlM ..... (28) \nFracture Half-Length. \n... (29) \nFracture Conductivity. \nEnd of Bilinear Flow. \nBeginning of Formation Linear Flow . \n1755 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a066-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 7, "chroma:document": "End of Wellbore \nStorage Effects \nFig. 11 -Type curve for well bore storage under bilinear \nflow conditions. \n-:: 102 \n.D \n.x-\na \no.~ 0. \n<l \n01 \n0 \n---' \n'fA Log t ----Approximate start \nof Semi log Straight \nLine \n10-2 L----'--------'-_-'----'--_1-----'--------'-_-'-----L_L----'--------'-\n10-4 10-2 102 104 106 108 \n2 \nt DX\nf ( kf bflD \nFig. 12 -Type-curve matching for data in bilinear and \ntransitional flow. \nQ \n<l \nOJ o \n---' \nLog t \nFig. 13 -Pressure data for a half\u00b7slope straight line in a \n10g\u00b7log graph. \n1756 Beginning of Semilog Straight Line. \nThese results can be obtained if a large span of \npressure data is available. It should be kept in mind \nthat specific analysis graphs must be used for dif\u00ad\nferent flow regimes to obtain a better estimate of \nboth fracture and reservoir parameters. \nNow we discuss cases where all pressure data fall \non a very small portion of the type curve and a \ncomplete set of information may not be obtained. \nCase 1. Pressure data exhibit one-fourth slope on a"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a0de-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 7, "chroma:document": "Case 1. Pressure data exhibit one-fourth slope on a \nlog-log graph (Fig. 7). According to the discussion \nin the previous section, these data correspond to the \nbilinear flow period and a unique match with Fig. 10 \ncannot be attained. The bilinear flow type of analysis \nis the only method available for this case to obtain \ninformation regarding the fracture characteristics \n(kfbf)\u00b7 \nA minimum value for fracture half-length, xf' can \nbe estimated from Eqs. 14a through 14c for tiie end \nof the bilinear flow; that is, for (kfbf) D ~ 3, we \nhave \n> 411O(3(k fbf)2tebf xf-\"<I c/>/l-ctk .. ............... (31) \nGenerally, wellbore storage affects a test at early \ntime; thus, it is expected to have pressure data \ndistorted by this effect, causing deviation from the \none-fourth slope characteristic of this flow period. \nFig. 11 may be applied to analyze pressure data for \nthis case even if the duration of the test is not enough \nto reach the one-fourth slope portion. It is important"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a160-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 7, "chroma:document": "to reach the one-fourth slope portion. It is important \nto note that pressure behavior in Fig. 11 for both \nwellbore-storage-dominated and bilinear-flow \nportions is given by a single curve that completely \neliminates the uniqueness matching problem. The \ncorrelating parameters FI (PwD) and F2 (tDxl) used \nin this figure are derived in Appendix C and aefined \nin Fig. 11. \nThe end of well bore stora~e effects in Fig. 11 \noccurs when F 2 (t Dx f) \"\" 2 x 10 ; that yields \n17.25 3/ c4 tews :::::--\"<1 2 4 \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 (32) \n(3 (kfbf) h c/>ctk \nFrom observation of the results presented in Fig. 11, \nwe can see that the end of well bore storage effects \noccurs three log cycles after the end of the unit slope. \nThis criterion is useful to determine whether the \nproper straight-line portion for bilinear flow analysis \nis chosen (see Fig. 9). If Fig. 11 is used as a type \ncurve, the following information may be obtained: \n[FI (PwD\u00bb)M' [F2(tDXf\u00bb)M' (i\u00a5J)M' and (t)M' \nHence, we can estimate the following."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a1d8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 7, "chroma:document": "Hence, we can estimate the following. \nWeI/bore Storage Constant. For oil, \nC= 27rDto(3qB/l-(t)M [FI (PwD\u00bb)M , ...... (33) \n(i\u00a5J)M [F2(tDXf\u00bb)M \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a25a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 8, "chroma:document": "1m.,....,.,\"\"\"\"\"\"\"\"\" \n~ +I+++t~ftHlttiH \n7 \n1++l+l~+l+~f!HlH-\n4 \nFig. 14 -Effective wellbore radius vs. dimensionless fracture conductivity for a vertical fracture. \nand, for gas, \nC= 2'1rcxg{3qT(t)M [FI (PwD)lM , ....... (34) \n[.::lm(p)lM [F2(tDXf)lM \nFracture Conductivity. For oil, \n_ 0.4 I ~ \\ cxoqBp,[FI (PwD) lM '13 \nkfbf- h2 ...j \u00a2ctk l (flp) M j' \n........................ (35) \nand, for gas, \nk b = 0.4 J ~ \\ cxgqI1FI (PwD)lM'I 3. \nf f h2 \u00a2ctk l [.::lm(p)lM j \n........................ (36) \nCase 2. Pressure data partially match the curve for \nthe transition period between bilinear and linear \nflows (Fig. 12). In this case, the remaining portion \nof the data may correspond to bilinear or linear flow \nand the type-curve match is unique because the \ntransition period has a characteristic shape. This \ncomment is valid for dimensionless fracture con\u00ad\nductivities, (kfbf) D ~57f. \nFrom the type-curve match of pressure data for \nthis case in Fig. 10, we obtain IPwD (kfbf) DlM'"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a2c8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 8, "chroma:document": "this case in Fig. 10, we obtain IPwD (kfbf) DlM' \n[tDxf (kfbf) blM, (M) M' and (flp) M' \nHence, for oil, \nSEPTEMBER 1981 and, for gas, \n(kfbf)_ cxgqT rpWD(kfbf)D]M' .(38) xf -h[.::lm(p)lM t \nFracture half-length and fracture conductivity. For \noil or gas, \n.... (39) \nand \nSince the formation permeability generally is \nknown from prefracture tests, the dimensionless \nfracture conductivity can be estimated by using \nresults from Eq. 37 or Eq. 38. Some of these results \nalso can be obtained from a specific analysis method \ncorresponding to the flow period exhibited by data \nother than the transition flow region (i.e., bilinear \nflow or linear formation flow, as discussed in the \nbilinear flow analysis section and in Ref. 14). \nIf all pressure data fall on the transition period of \nthe curve, type-curve matching (Fig. 10) is the only \nanalysis method available. \nCase 3. Pressure data exhibit a half-slope line on a \nlog-log graph. (Fig. 13). For this case there is no"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a340-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 8, "chroma:document": "log-log graph. (Fig. 13). For this case there is no \nunique match with Fig. 10; however, the linear flow \n1757 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a3b8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 9, "chroma:document": "P wD \nFig. 15 -Type curve for a finite-conductivity vertical \nfracture. \nanalysis presented by Clark 14 can be applied to \nobtain fracture half-length if formation permeability \nis known. In addition, a minimum value for the \ndimensionless fracture conductivity, (kfb J) D.' can \nbe estimated using Eq. 26. Note that tb/f In Fig. 13 \nrepresents a maximum value for the time of the \nbeginning of the linear flo~ period and t elf represents \na minimum value for the tIme of the end of the half \nslope. \nIf well bore storage effects are present at early \ntimes in a test for this case, the analysis can be made \nusing the type curve presented by Ramey and \nGringarten.21 \nCase 4. Pressure data partially match the curve jor \nthe pseudoradial flow period. If a large span of \npressure data is not available, a unique match would \nnot be obtained by using Fig. 10 because curves for different values of fracture conductivity are similarly \nshaped for the pseudoradial flow period. However,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a43a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 9, "chroma:document": "shaped for the pseudoradial flow period. However, \nthe transient pressure behavior shown in Fig. 10 can \nbe correlated to analyze these cases better. \nFor the pseudoradial flow period, a fractured well \nbehaves like an unfractured well with an effective \nwellbore radius being a function of dimensionless \nfracture conductivity, (kfbf) D. Fig. 14 presents a \ngraph of dimensionless effective wellbore radius, \nr~/xf' vs. dimensionless fracture conductivity, \n(kfbf) D. Notice that for large values of \n(k b f) D ( > 300), the dimensionless effective \nwefibore radius is 0.5, as mentioned by Prats et al. 8 \nIf the dimensionless time is defined by using r~ \ninstead of xf, a graph of Pwq vs. tDr~ t;>rovides a \nsingle curve for the pseudoradlal flow penod for all \nvalues of dimensionless fracture conductivity (see \nFig. 15). This curve provides an excellent tool for \ntype-curve analysis of pressure data partially falling \nin the pseudoradial flow period because the \nremaining data must follow one of the curves for"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a4c6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 9, "chroma:document": "remaining data must follow one of the curves for \ndifferent fracture conductivities. Fig. 14 must be \nused as an auxiliary curve to determine (kfbf) D \nwhen using Fig. 15. \nApplication of Fig. 15 to match pressure data \nprovides (PwD)M' (tDr )M' (tlp)M' (t)M' and \n[(kfbf) D]M. Hence, th~ following equations are \ngiven. \nReservoir Permeability. For oil, \nDloqBp. k= (PwD) M' ................ (41) h(tlp) M \n102r----------,----------~----------1I----------r_------~ \n.-\ntil a. \na. \nE \n<J o \n.D MdLCh Point \n[ot]M c 1 hour \n= 0.35 hour \nt '2 _ 5 hour ebf \n10~----------~----------~----------_t-------\nI \nI \nI \nI \n,-- ___ ~_O. \nI \nI o \nI 0 I - -,\u00ad\nI \nI \nBeginning of Senilog Straight Line 10. \nlo10-1~----~I--~~-----L---L._----i---~------~~~----~~ 3 2 1 101 107 '-_ .!.O-_ I 10-. I 10- _ 1 __ \n- - - - - - - - - - 2 1 102 /). t [hoursl \n10-2 10-1 t DXf (kf bflD 10 \nFig. 16 -Type-curve matching for Well A."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a548-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 9, "chroma:document": "Fig. 16 -Type-curve matching for Well A. \n1758 JOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a5c0-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 10, "chroma:document": "and, for gas, \n(XgqT k= (PwD) M. . ............ (42) \nh[~(p}lM \nEffective WeI/bore Radius. For oil or gas, \nr' =J (3k(t) M w cPJlCt (tDr ~) M\u00b7 ................. (43) \nBy using [(kfbj) DlM in Fig. 14, we obtain \n(r~/xj) Fig. 14; hence, \nr' Xj= [' j ..................... (44) \nr wlXj Fig. 14 \nThe pressure data falling in the pseudoradial flow \nperiod also must be analyzed using the semilog \nmethods to estimate k and r ~ . \nThe discussion in this section clearly indicates (as \nmentioned by Agarwal et af.29) that caution and \ndiligence should be exercised when applying the type\u00ad\ncurve matching technique. To perform the type of \nanalysis presented in the four cases, it is necessary to \nhave prefracture information. \nIt should be kept in mind that application of the \ntype-curve analysis method to pressure buildup tests \nis appropriate when the producing time is large. \nExamples of Application \nThree examples illustrate the application of several of \nthe methods and theory previously discussed. \nWell A"}


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topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 10, "chroma:document": "the methods and theory previously discussed. \nWell A \nA buildup test was conducted in this fractured well \nproducing in a low-permeability reservoir. Table 2 \npresents the information and results of the analysis \nfor this test. Fig. 16 shows a log-log graph of pressure \ndata. matching the type curve given in Fig. 10. Notice \nthat the first data points are influenced by well bore \nstorage and the rest of the data fall in both the \nbilinear and the transition flow periods. The match\u00ad\npoint results also are presented in Fig. 16. A \nminimum value for (k jb j ) D can be estimated from \nthe position of the last data point with respect to the \ntype curves; for this case, (kjbj}D min =511\". \nThe end of well bore storage occurs at ap\u00ad\nproximately 0.35 hour and the end of bilinear flow is \nat 2.5 hours. We also see that the formation linear \nflow period was not reached in this test. \nSince the test was not long enough to match a \ncurve for a specific value of (kjbj) D' this example"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 10, "chroma:document": "curve for a specific value of (kjbj) D' this example \ncorresponds to Case 2 in the type-curve-analysis \nsection. \nUsing the pressure data match and Eq. 38, we \nobtain \nkjbj _ 1,424x7,350x690x6.5 \nXj - 118x109 \n=0.3978 md-ftlft. \nSEPTEMBER 1981 TABLE 2 -TEST INFORMATION AND ANALYSIS RESULTS \nFORWELLA \nReservoir Data \nProduction rate q, MscflD \nProducing time tp, hours \nFormation thickness h, ft \nPorosity cJ>, fraction \nPermeability k, md \nFormation temperature T, oR \nAverage gas viscosity 1-', cp \nTotal compressibility ct, psi-1 \nFlowing well bore pressure Pwl, psia \nAnalysis Results \nk,b\n\" md-ft \nx\" ft \n(k:~'). md-ftlft \n(klbl)D \n,;.., ft Type-Curve \nAnalysis \n148 \n373 \n0.3978 \n15.9 \n171.6 7,350 \n2,640 \n118 \n0.1 \n0.025 \n690 \n0.0252 \n0.129x 10-3 \n1,320 \nBilinear \nFlow Analysis \n154 \n368 \n0.4185 \n-16.71 \n-169.3 \nFrom the time-match information and Eq. 39, we can \ncalculate \nJ 2.637 x 10 4 x 1 \n. 0.1 x 0.025 x 1.29 x 10-4 x 0.025 x 3.69 x 10-2 \n=373 ft. \nNow, application of Eq. 40 yields \nWe also can estimate"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 10, "chroma:document": "Now, application of Eq. 40 yields \nWe also can estimate \n(kjbj}D= kjbf ..!.. \nXj k \n0.3978 \n= 0.025 = 15.9. \nFrom Fig. 14, r~/xj=0.46. \n:. r~=373x0.46=171.6ft. \nFi~. 17 shows the bilinear flow graph [~(p) vs. \nllt ~ 1 for this example. Based on the information \nprovided by Fig. 16, the correct straight line is \ndrawn. The slope of this line is 1.62 X 108 psi2/cp\u00ad\nhr ~, and at the end of bilinear flow \nllm(p}ebj=2.05x 108 psi2/cp-hr~. Notice that the \npressure curve after the end of the bilinear flow \nperiod is concave upward, indicating that \n(kjbj) D > 1.6. \n1759 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 11, "chroma:document": "'\" 0. 10 ~ \nE \u2022 \n<J \no Cucve concave upwards ... (kfbf) D > 1.6 \n1~ V. IllI) (hour I \nFig. 17 -Bilinear flow graph for Well A. \nTABLE 3 -TEST INFORMATION AND ANALYSIS RESULTS \nFOR WEll B ' \nReservoir Data \nProduction rate q, MscflD \nProducing time tp, hours \nFormation thickness h, ft \nPorosity C/>, fraction \nPermeability k, md \nFormation temperature T, OR \nAverage gas viscosity p., cp \nTotal compressibility ct, psi-1 \nFlowing wellbore pressure Pwt, psia 1,675 \n1,800 \n85 \n0.11 \n0.0045 \n675 \n0.025 \n0.152x 10-3 \n1,250 \nAnalysis Results Type\u00b7Curve Bilinear \nAnalysis Flow Analysis \nktbt, md\u00b7ft \nXt, ft \n(k:~t), md.ftlft \n(ktbt)D \nr';\", ft \nFrom Eq. 20, 95.3 \n;;::692 \n::50.1377 \n::530.6 \n::5325 \n(kjbj) Yz = (444.75 X 7,350 X 690)/11.62 X 108 X 118 \n\u00b7(0.1 x 0.0252 x 1.29 x 10-4 xO.025)1~, \n:. (kjbj) = 154md-ft. \nUsing Eqs. 22 and 2, \n(k b ) D \"'\" 1.38 \nj j (0.025X1l8X2.05XI08) \n1,424 X 7,350 x 690 \n\"'\" 16.71. \n1760 109 \n0: u \nN~ \n'\" 0. \nCi 108 \nE \n<J Slope = 1/4 \nII t Ihours)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a836-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 11, "chroma:document": "0: u \nN~ \n'\" 0. \nCi 108 \nE \n<J Slope = 1/4 \nII t Ihours) \nFig. 18 -Log\u00b7log graph of pressure data for Well B. \nHence, \n154 ---- \"'\" 368 ft. 0.025 x 16.71 \nFrom Fig. 14, r:V1xj = 0.46. \n:.r:V =368 x 0.46 = 169.3 ft. \nWe see that the results obtained by using both the \nbilinear flow and the type-curve methods are ap\u00ad\nproximately the same; this fact increases confidence \nin the analysis performed. \nWellB \nA buildup test was run after fracturing this gas well. \nInformation about the test and results of analysis are \npresented in Table 3. A log-log graph of pressure \ndata (Fig. 18) indicates that the test was completely \ndominated by bilinear flow (quarter slope), \ncorresponding this example to Case 1 in the type\u00ad\ncurve-analysis section. \nThe bilinear flow graph (Fig. 19) yields a straight \nline whose slope, m bj' can be used to calculate \n(kjbj) usingEq. 20: \nor (kjbj) Yz = (444.75 x 1,675 x 675)/[0.92 x 108 \nx 85 x (0.11 x 0.025 x 1.52x 10-4 \nx 0.0045) ~], \nIf we assume that the last data point corresponds to"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 11, "chroma:document": "If we assume that the last data point corresponds to \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a944-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 12, "chroma:document": "0. u \n\"''::' U) \n0. \nco 9 \nQ \nE \n<J 2 \n(.H) last = 18 hours \nmbf = 0.92 x 108 ~, \ncp hrV\" \n2 \n1;4 1/4 (lit) (hour ) \nFig. 19 -Bilinear flow graph for Well B. 3 \nthe end of the bilinear flow period and (k fb f) D ~ 3, \nthen from Eq. 31, \n~ lOx2.637xlO-4X(95.3)2 X18 \nxf ~ 0.11 x 0.025 x 1.52 x lO -4 x 0.0045 \n=692 ft, \nand \nk b 95.3 ~ !S --=0.1377 md-ft/ft. xf 692 \nFromEq.6, \n( kfbf) 95.3 \n(k fb f) D = kx f !S -0-.0-04-5-x-6-9-2 ' \nFrom Fig. 14, r~/xf!S0.47; hence, r~ !S0.47 X 692, \nr~ !S325 ft. \nWelle \nAfter a flowing time of 1,890 hours, a buildup test \nwas run on this fractured oil well. Information for \nthe test and analysis results are presented in Table 4. \nFig. 20 shows a log-log graph of the pressure data; \nfrom this graph we can see that neither a one-fourth \nslope nor a half slope is exhibited by the data. This \nfigure also shows that pressure data match the curve \nfor (kfbf) D = 27r given in Fig. 15 and the last six \npoints fall on the semilog straight line."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3a9c6-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 12, "chroma:document": "points fall on the semilog straight line. \nFrom the pressure match obtained in Fig. 20 and \nEq. 41, we estimate \nk= 141.2 x 220 x 1.2 x 0.8 x 0.34 \n49x 100 \n=2.07md. \nSEPTEMBER 1981 101 r-----r---,---,---,---,-----, \nBeg~nning of Semllog \nStraight Llnc \n1031-- - -1-- -1--1-- - -\nI I I !>latch POl.nt \nI (tlp)1'-! = 100 psi \n(PWO)M '\" 0.34 ___ 1 ___ J._ \nI {6t)M = 1 hr \n1 (tDr~)M = 0.19 \n1 I ' \n10 '----- -L ___ 1 ____ 1 ___ ..J \n10-1 I 10 102 103 \nLIt (hours) \n10-2 L,-----'-:----'--,-----'--~---'7-----'-;;-----.J \n10-3 10-2 10-1 10 1 102 103 \nFig. 20 -Type\u00b7curve matching for Well C. \nTABLE 4 -TEST INFORMATION AND ANALYSIS RESULTS \nFORWELLC \nReservoir Data \nProduction rate q, STBID \nProducing time tp, hours \nFormation thickness h, ft \nPorosity </>, fraction \nViscosity /1-, cp \nTotal compressibility ct, psi-1 \nFormation volume factor 80, bbllSTB \nWell bore radius r w, ft \nFlowing well bore pressure Pw', pSia \nAnalysis Results \nk,md \n(k,btlo \nx\" ft \nk,b\" md-ft \nr;', ft \nS Type-Curve \nAnalysis \n2.07 \n211\" \n88.7"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3aa3e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 12, "chroma:document": "k,b\" md-ft \nr;', ft \nS Type-Curve \nAnalysis \n2.07 \n211\" \n88.7 \n1,156 \n36.89 \n-4.99 220 \n1,890 \n49 \n0.15 \n0.8 \n17.6x 10-6 \n1.2 \n0.25 \n1,704 \nSemi log \nAnalysis \n2.28 \n30.37 \n-4.8 \nUsing information from the time match in Eq. 43, \nr' _~ 2.637x 10 4 x2.07x 1 \nw-0.15xO.8xI7.6xlO 6xO.19 \n= 36.9 ft. \nFrom Fig. 14, r~/xf=0.415; hence, \n36.9 \nxf= 0.415 = 88.9 ft. \nThe skin factor is estimated by \nr 0.25 s=ln ~ =In-- = -4 99 \nr~ 36.9 .. \n1761 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 13, "chroma:document": "7.--------,-------,--------,---r----, \n6 \n5 \n2. 4 \n'\" ~ m = 307 psi/cycle \n-3 \nQ. \n<l \n2 \no \no \n10-1 00 \no 00 \n{l>p} : -47 psi // 1hr \n101 \nlit Ihours/ \nFig. 21 -Semi log graph for Well C. \nThe fracture conductivity is \nkjbj= {kjbj)nkXj \n=27rx 2.07 x 88.9= 1,156.2 md-ft. \nFig. 21 is a semilog graph for this example. The \ncorrect semilog straight line has a slope m = 307 \npsi/cycle and (ilp) Ihr = -47 psi. The formation \npermeability can be calculated as \nk = _16_2_._6_qB_fJ. \nmh \n162.6 x 220 x 1.2 x 0.8 = =2.28md. 307x49 \nThe skin factor is \nS=1.151[{Llp)lhr -log( k 2)+3.2275J \nm 1>fJ.ctrw \n[-47 = 1.151 -307 \n2.28 \n-log 0.15 xO.8 x 17.6x 10-6 x (0.25)2 \n+ 3.2275 J = -4.8. \nFinally, the effective wellbore radius is \nr~ =r we-s =0.25 e4.8 \n= 30.37 ft. \nThe results provided by both the type-curve \nanalysis and semilog analysis methods are in good \nagreement. From these examples it is demonstrated \nthat type-curve analysis, when applied properly, \nprovides an excellent diagnostic tool and a technique"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ab24-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 13, "chroma:document": "provides an excellent diagnostic tool and a technique \nto estimate both reservoir and fracture parameters. \n1762 Conclusions \nBased on the material presented in this work, the \nfollowing remarks are pertinent. \n1. The transient flow behavior of a vertically \nfractured well may exhibit four flow periods: (a) \nfracture linear flow, (b) bilinear flow, (c) formation \nlinear flow, and (d) pseudoradial flow. Bilinear flow \nis a new type of flow that has not been considered \nbefore. \n2. A new technique is presented to analyze data in \nthe bilinear flow period. It is shown that, during this \nflow period, a graph of pwj[or m (Pwj)] vs. Vi yields \na straight line whose slope is inversely proportional \nto h j{kjbj) Yz. \n3. New type curves are now available for pressure \nanalysis of fractured wells. The uniqueness problem \nin the analysis is reduced considerably with the use of \nthese type curves. \n4. Prefracture information about the reservoir is \nnecessary to estimate fracture parameters."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 13, "chroma:document": "necessary to estimate fracture parameters. \n5. The type-curve analysis method must be used \nsimultaneously with the specific analysis methods \n(Pwfvs. Vt,Pwjvs.1t, andpwjvs.log t) to produce \nreliable results. \nAcknowledgments \nPart of this work was develo,ped at Stanford U. and \nthe Inst. Mexicano del Petroleo. We are grateful to \nmany people, especially H.J. Ramey Jr. for his \nencouragement and helpful comments. \nNomenclature \nb j = fracture width \nB = formation volume factor \nc = compressibility \nC = well bore storage coefficient \nFI ,F2 = correlating parameters for well bore \nstorage \nh = formation thickness \nh j = fracture height \nk = permeability \nkjbj = fracture conductivity \n(k jb j) n = dimensionless fracture conductivity \nm = slope of semilog straight line, gas \npseudopressure \nmbj = slope of straight line for bilinear flow \nP = pressure \nq = well flow rate \nr w = wellbore radius \nr~ = effective well bore radius \ns = skin factor or Laplace space variable \nt = time \nilt = shut-in time"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ac1e-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 13, "chroma:document": "t = time \nilt = shut-in time \nT = reservoir temperature \nX,Y = space coordinates \nXj = fracture half-length \n(X,{3 = unit conversion constants \nr = gamma function \n'Y/ = hydraulic diffusivity \n1> = porosity \nfJ. = fluid viscosity \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ac96-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "Subscripts \nb= beginning \nbf = bilinear flow \ng gas \nD= dimensionless \ne = end \nf= fracture, flowing \ni = initial \n/f= linear flow \n0 oil \nt total \nxf based on xf \nw wellbore \nReferences \n1. Matthews, C.S. and Russell, D.G.: Pressure Buildup and \nFlow Tests in Wells, Monograph Series, SPE, DaJlas (1967) 1. \n2. Ramey, H.J. Jr., Kumar, A., and Gulati, M.S.: Gas Well Test \nAnalysis Under Water-Drive Conditions, AGA, Arlington, \nVA (1973). \n3. Earlougher, R.C. Jr.: Advances in Well Test Analysis, \nMonograph Series, SPE, Dallas (1977) 5. \n4. Theory and Practice of Testing of Gas Wells, third edition, \nEnergy Resources Conservation Board, Calgary, Alta. (1975). \n5. Ramey, H.J. Jr.: \"Practical Use of Modern Well Test \nAnalysis,\" paper SPE 5878 presented at the SPE 46th Annual \nCalifornia Regional Meeting, Long Beach, April 8-9, 1976. \n6. Raghavan, R.: \"Pressure Behavior of Wells Intercepting \nFractures,\" Proc., Invitational Well-Testing Symposium, \nBerkeley, CA, Oct. 19-21, 1977."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "Berkeley, CA, Oct. 19-21, 1977. \n7. Dyes, A.B., Kemp, C.E., and Caudle, B.H.: \"Effect of \nFractures on Sweep-Out Patterns,\" Trans., AI ME (1958) 213, \n245. \n8. Prats, M., Hazebroek, P., and Stickler, W.R.: \"Effect of \nVertical Fractures on Reservoir Behavior -Compressible\u00ad\nFluid Case,\" Soc. Pet. Eng. J. (June 1962) 87-94; Trans., \nAIME,225. \n9. Scott, J.O.: \"The Effect of Vertical Fractures on Transient \nPressure Behavior of Wells,\" J. Pet. Tech. (Dec. 1963) 1365-\n1369; Trans., AIME, 228. \n10. Horner, D.R.: \"Pressure Build-Up in Wells,\" Proc., Third \nWorld Pet. Cong., The Hague (1951) Sec. 11,503-523. \nII. Miller, C.C., Dyes, A.V., and Hutchinson, C.A. Jr.: \n\"Estimation of Permeability and Reservoir Pressure from \nBottom-Hole Pressure Build-Up Characteristics,\" Trans., \nAIME (1950) 189, 91-104. \n12. Matthews, C.S., Brons, F., and Hazebroek, P.: \"A Method \nfor Determination of Average Pressure in a Bounded \nReservoir,\" Trans., AIME (1954) 201,182-191."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ad90-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "Reservoir,\" Trans., AIME (1954) 201,182-191. \n13. RusseJl, D.G. and Truitt, N.E.: \"Transient Pressure Behavior \nin Vertically Fractured Reservoirs,\" J. Pet. Tech. (Oct. 1964) \n1159-1170; Trans., AIME, 231. \n14. Clark, K.K.: \"Transient Pressure Testing of Fractured Water \nInjection WeJls,\" J. Pet. Tech. (June 1968) 639-643; Trans., \nAIME,243. \n15. Millheim, K.K. and Cichowicz, L.: \"Testing and Analyzing \nLow-Permeability Fractured Gas WeJls,\" J. Pet. Tech. (Feb. \n1968) 193-198; Trans., AIME, 243. \n16. Raghavan, R., Cady, G.V., and Ramey, H.J. Jr.: \"Well-Test \nAnalysis for VerticaJly Fractured Wells,\" J. Pet. Tech. (Aug. \n1972) 1014-1020; Trans., AIME, 253. \n17. Gringarten, A.C. and Ramey, H.J. Jr.: \"Unsteady-State \nPressure Distributions Created by a WeJl With a Single In\u00ad\nfinite-Conductivity Vertical Fracture, Soc. Pet. Eng. J. (Aug. \n1974) 347-360; Trans., AIME, 257. \n18. Gringarten, A.C. and Ramey, H.J. Jr.: \"Unsteady-State \nPressure Distributions Created by a Well With a Single"}


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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "Pressure Distributions Created by a Well With a Single \nHorizontal Fracture, Partial Penetration or Restricted En\u00ad\ntry,\" Soc. Pet. Eng. J. (Aug. 1974) 413-426; Trans., AIME, \n257. \n19. Gringarten, A.C., Ramey, H.J. Jr., and Raghavan, R.: \n\"Applied Pressure Analysis for Fractured WeJls,\" J. Pet. \nTech. (July 1975) 887-892; Trans., AIME, 259. \nSEPTEMBER 1981 20. Wattenbarger, R.A. and Ramey, H.J. Jr.: \"Well Test In\u00ad\nterpretations of Vertically Fractured Gas WeJls,\" J. Pet. \nTech. (May 1969) 625-632; Trans., AIME, 246. \n21. Ramey, H.J. Jr. and Gringarten, A.C.: \"Effect of High\u00ad\nVolume Vertical Fractures on Geothermal Steam WeJl \nBehavior,\" Proc., Second United Nations Symposium on the \nUse and Development of Geothermal Energy, San Francisco, \nMay 20-29, 1975. \n22. Cinco, H., Ramey, H.J. Jr., and Miller, F.: \"Unsteady-State \nPressure Distribution Created by a Well With an Inclined \nFracture,\" paper SPE 5591 presented at the SPE 50th Annual \nTechnical Conference and Exhibition, Dallas, Sept. 30-0ct. 3, \n1975."}


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topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ae80-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "1975. \n23. Raghavan, R. and Hadinoto, N.: \"Analysis of Pressure Data \nfor Fractured Wells: The Constant-Pressure Outer Boun\u00ad\ndary,\" Soc. Pet. Eng. J. (April 1978) 139-150; Trans., AIME, \n265. \n24. Raghavan, R., Uraiet, A., and Thomas, G.W.: \"Vertical \nFracture Height: Effect on Transient Flow Behavior,\" Soc. \nPet. Eng. J. (Aug. 1978) 265-277. \n25. Cinco, H., Samaniego, F., and Domlnguez, N.: \"Transient \nPressure Behavior for a Well with a Finite-Conductivity \nVertical Fracture,\" Soc. Pet. Eng. J. (Aug. 1978) 253-264. \n26. Holditch, S.A. and Morse, R.A.: \"The Effects of Non-Darcy \nFlow on the Behavior of HydraulicaJly Fractured Wells,\" J. \nPet. Tech. (Oct. 1976) 1169-1178. \n27. Ramey, H.J. Jr., Barker, B., Arihara, N., Mao, M.L., and \nMarques, J.K.: \"Pressure Transient Testing of Hydraulically \nFractured Wells,\" paper presented at American Society \nTopical Meeting, Golden, CO, April 12-14, 1977. \n28. Cinco, H. and Samaniego, F.: \"Effect of Wellbore Storage"}


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topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3aef8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "28. Cinco, H. and Samaniego, F.: \"Effect of Wellbore Storage \nand Damage on the Transient Pressure Behavior of Vertically \nFractured WeJls,\" paper SPE 6752 presented at the SPE 52nd \nAnnual Technical Conference and Exhibition, Denver, Oct. 9-\n12,1977. \n29. Agarwal, R.G., Carter, R.D., and Pollock, C.B.: \n\"Evaluation and Prediction of Performance of Low\u00ad\nPermeability Gas WeJls Stimulated by Massive Hydraulic \nFracturing,\" J. Pet. Tech. (March 1979) 362-372; Trans., \nAIME,267. \n30. Barker, B.: \"Transient Flow to Finite-Conductivity Vertical \nFractures,\" PhD dissertation, Stanford U., Palo Alto, CA \n1977. \n31. Barker, B.J. and Ramey, H.J. Jr.: \"Transient Flow to Finite\u00ad\nConductivity Vertical Fractures,\" paper SPE 7489 presented \nat the SPE 53rd Annual Technical Conference and Exhibition, \nHouston, Oct. 1-3, 1978. \n32. Scott, J.O.: \"A New Method for Determining Flow \nCharacteristics of Fractured WeJls -Application to Gas WeJls \nin Tight Formations,\" paper 78-T-2, AGA 1978 Transmission"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3af7a-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 14, "chroma:document": "in Tight Formations,\" paper 78-T-2, AGA 1978 Transmission \nConference, Montreal, T-279-186. \nAPPENDIX A \nShort-Time Transient Pressure \nBehavior for a Well With \na Finite-Conductivity Fracture \nDerivation of Solution \nLet us consider the system described in the text of this \npaper. A fractured well produces at a constant flow \nrate from an infinite reservoir. At small time values, \nthe pressure behavior of the system is not affected by \nthe tips of the fracture. In addition, the flow in the \nformation is essentially linear and perpendicular to \nthe fracture plane. The reservoir and the fracture \nmay be treated as two different homogeneous \nregions. 25 \nIf the flow within the fracture is assumed to be \nlinear, the pressure behavior can be described by \na2pfD \na 2 + xD 2 apD I \n(kfbf) D aYD YD=O \n1763 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3aff2-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 15, "chroma:document": "= _1_ ap[D .................. (A-I) \n7JjD atDXj \nfor O<xD < 00, tDxj >0. \nInitial Condition. \nPfD =0, tDXj=O, O:s;xD <00. . .......... (A-2) \nBoundary Conditions. \napfD I = - 7r , tDx >0, \naXD XD=O (kfbf)D f \n. . . . . . . . . . . . . . (A-3) \nand \nlim PfD =0, tDxj >0, ............... (A-4) \nXD-OO \nwhere, in oilfield units, \n_ kh[Pi-Pf] \nPjD -141.2 qBJ.I. \nand kh [Pi -p] \nP D = 141.2 qBJ.I. \nx xD=-' xf \nY YD=-\u00b7 xf \nThe variables not included above are defined in the \ntext. P and P f represent the formation pressure and \nthe fracture pressure, respectively, x is the flow \ndirection in the fracture, and Y is the formation flow \ndirection perpendicular to the fracture plane. \nThe transient flow in the formation may be \ndescribed by \na2p ap D_~\u00b7O<y <00\u00b7 ~-!:I ' D ' aYD utDxj \ntDxj>O. . ................... (A-5) \nInitial Condition. \nPD =0; O<YD <00; tDXj=O ............. (A-6) \nBoundary Conditions. \nPD IYD=O =PfD; tDXj>O, .............. (A-7) \nand \nlim PD =0; tDxj>O ................. (A-8) \nYD-OO"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b074-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 15, "chroma:document": "and \nlim PD =0; tDxj>O ................. (A-8) \nYD-OO \n1764 The two partial differential equations are already \ncoupled by the boundary conditions. Application of \nthe Laplace transformation with respect to. time to \nEqs. A-I through A-8 and simplification yields \na2pfD 2 apD I + --\naXD2 (kfbf) D aYD Yd=O \ns _ \n= -PfD; O<xD < 00 ........... (A-9) \n7JjD \nBoundary Conditions . \napfD I = - 7r , \u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 (A-lO) \naXD Xd=O (kfbf) D \nlim PjD =0, ..................... (A-ll) \nXD-OO \nand \na2pD \naYD2 =SPD; O<YD<oo ............ (A-12) \nBoundary Conditions. \nPD IYD=O =PfD' .................... (A-l3) \nlim PD=O' ..................... . (A-14) \nYD-OO \nwhere \nPjD (xD' s) =\u00a3tDXj [PjD (XD,IDXj)]' \nand \nPD (YD' s) = \u00a3tDXj [PD (YD' tDXj) ]. \nNow let us define \nPD (r,s) = \u00a3YD [PD (YD,s)]. \nApplication of the Laplace transformation, with \nrespect tOYD, to Eq. A-12 yields \n2 ~ I ap D I ~ (A 15) r PD-rPD YD=O--a-- =sPD\u00b7\u00b7\u00b7-\n'YD YD=O \nBy solving for PD and considering Eq. A-l3, we \nobtain \n_ oPD I rPfD+ -a-"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b0f6-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 15, "chroma:document": "obtain \n_ oPD I rPfD+ -a-\n~ 'YD YD=O (A 16) PD= 2 \u2022 ...\u2022.\u2022.\u2022.. -r -s \nThe inversion of this equation with respect to Y D \nyields \na-\nP D = P jD cosh (...;s Y D) + : D I \n'YD YD=O \n................. (A-17) \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b178-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 16, "chroma:document": "From Eqs. A-14 and A-17, we can write \napD I - -- = -PfDYs. . ............. (A-18) \naYD YD=O \nNext, substitution of Eq. A-18 into Eq. A-9 allows \nus to write a partial differential equation with only \none dependent variable: \na2pfD _ S 2Ys_ \n2 - -+ PfD\u00b7 ........ (A-19) \naXD 'YlfD (kfbf) D \nThe solution of Eq. A-19 with boundary conditions \ngiven by Eqs. A-tO and A-II can be expressed as \n[ [ S 2Ys] Yz 7rexp -xD -+ \n-_ 'YlfD (kfbf) D ] prD-\np S 2Ys Yz \n(kfbf}DS[-+ b ] \n'YlfD (kf f) D \n....................... (A-20) \nThe pressure at the wellbore PwD is calculated at \nxD =0; thus, \n7r \nPwD = S 2Ys Y2\u00b7\u00b7 (A-21) \n(kfbf}D s[-+ ] \n'YlfD (kfbf}D \nFinally, the Laplace inversion of Eq. A-21 with \nrespect to 1 DXf produces \nPwD= ~ rDXf \n(kfbf) D 0 \n....................... (A-22) \nUnfortunately, Eq. A-22 is too complex to analyze \nboth the short-and long-time behavior of the \nsolution. Eq. A-21 may be used for this purpose. \nShort-Time Behavior \nThe short-time approximation of the solution can be"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b1fa-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 16, "chroma:document": "The short-time approximation of the solution can be \nobtained from Eq. A-21 by taking the limit as the \nvariable S approaches infinity. Thus, \n--~ PwD-(k\nfb\nf}DS312 ................. (A-23) \nInversion of this formula produces Eq. 8. \nLong-Time Behavior \nWe can obtain the solution for large values of time by \ntaking the limit of Eq. A-21 as S approaches zero; \nhence, \n7r \nPwD =::. ..J2(k\nfb\nf) D s5/4\u00b7 ............. (A-24) \nInverting Eq. A-24 produces Eq. 12. This solution \nalso may be obtained by considering incompressible \nflow within the fracture. \nSEPTEMBER 1981 Total Formation Flow \nEqs. A-18 and A-20 can be used to calculate the \nfraction of the well flow rate that is being produced \nfrom the formation. The formula for this case ap\u00ad\npears to be \nq formation = 1 _ exp( 41 DXr 2 ) \nq 7r2CfDf \n( 2..JIDxr ) . erfc . . ........ (A-25) \n7rCfDf \nFor small values of 1 Dx' the amount of fluid \ncoming from the formation {s negligible; however, at \nlarge values of 1 Dx' most of the produced fluid"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b27c-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 16, "chroma:document": "large values of 1 Dx' most of the produced fluid \ncomes from the formation. This illustrates the \nphysical behavior of the system. \nAPPENDIXB \nDerivation of Correlation Parameters \nfor Bilinear and Linear Flows \nIf we consider a fracture of length xf' Eq. A-4 \nbecomes \napfD I =0 ....................... (B-1) \naXD xD=1 \nUsing Eq. B-1 instead of Eq. A-4 and considering \nincompressible flow within the fracture, the Laplace \ntransformation solution for the problem stated in \nAppendix A is \npWD=(-7r+ E 27rexp[-2n \nn=O \n[~ (kfb~)D2 tJ )/(S(kl'tln \n.[~ (kfb~)D2 t) ............ (B-2) \nor \nPWD (kfbf)D3~( -<+ 00 E 27r eXPt -2n \nn=O \nHence, \n1 [ S ~] PWD(kfbf}D = (k\nfb\nf}D2! (k\nfb\nf}D2 ... (B-4) \nFrom Laplace inversion tables, \nPWD (kfbf) D =F[tDx/ (kfbf) D2]. . ..... (B-6) \n1765 Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b2f4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 17, "chroma:document": "Hence, a graph of Pw (kfbf)D vs. tDx (kfbf)2 . ld . I D f Yle s a smg e curve. \nFor small values of dimensionless time, Eq. B-3 \nyields Eq. A-24, corresponding to bilinear flow. \nThe long-time approximation of Eq. B-3 yields \n7r P WD ~ 2s312 ' .\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022\u2022 (B-7) \nwhich is the Laplace transform of the dimensionless \npressure for the formation linear flow. \nAPPENDIXC \nDerivation of Correlation Parameters \nfor Bilinear Flow with \nWellbore Storage Effects \nWhen well bore storage effects are considered in the \nflow problem defined in Appendix A, the boundary \ncondition at x D = 0 becomes \napfD I 7r (1-CDf apWD), . (C-l) \naXD xD=O (kfbf) D atDxf \nwhere \nC = C Df 27rA.c hx 2' ................... (C-2) \n'I' t f \nand C is the wellbore storage coefficient. \nIf flow within the fracture is considered in\u00ad\ncompressible and Eq. C-1 is taken instead of Eq. A-\n3, the solution for the wellbore pressure in the \nLaplace space is given by \n7r \nPwD = -V2(kfbf) D s5/4 + 7rCDfS2' \nwhich can be written as"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b376-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 17, "chroma:document": "7r \nPwD = -V2(kfbf) D s5/4 + 7rCDfS2' \nwhich can be written as \n1766 ...... (C-3) 4/3 C 4/3 s 5/4 \n(kfbf) D - _ ~Y2[ Df ] \nC 5/3 PwD-7r (k b ) 2/3 Df f f D \nCD//3s ~ \n+7r[ (kfbf)D2/3] j\" .. (C-4) \nFrom properties of the Laplace transformation, \n-I _1 [t] L !(as) -~F ~ ................... (C-5) \nHence, Eq. C-4 can be written as \n(kfbf)D2I3 =F[ (kfbf)D2I3 t ] \n(CDf) 113 PwD (CDf) 4/3 DXf' \n................... (C-6) \nThis means that the bilinear flow solutions including \nwell bore storage are represented by a single curve \nwhen graphed in terms of \n(k b ) 213 (k b ) 2/3 \n--\"\"f'--Lf'I::;'~;--PWD vs. f f ~/3 tDx' Cw (Cw) f \nSI Metric Conversion Factors \ncp x 1.0* E-03 = Pa\u00b7s \nft x 3.048* E-Ol = m \npsi x 6.894 757 E + 00 = kPa \n\u00b7Conversion factor is exact. JPT \nOriginal manuscript received in Society of Petroleum Engineers office Aug. \n10, 1978. Paper accepted for publication June 4, 1979. Revised manuscript \nreceived July 6,1981. Paper (SPE 7490) first presented at the SPE 53rd Annual"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b3f8-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-7490-pa.pdf", "page": 17, "chroma:document": "Technical Conference and Exhibition, held in Houston, Oct. 1-3, 1978. \nJOURNAL OF PETROLEUM TECHNOLOGY Downloaded from http://onepetro.org/JPT/article-pdf/33/09/1749/2226733/spe-7490-pa.pdf/1 by University of Houston, Mohamed Gabry on 18 July 2022"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b470-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 0, "chroma:document": "Citation: Gabry, M.A.; Eltaleb, I.;\nSoliman, M.Y.; Farouq-Ali, S.M. A\nNew Technique for Estimating Stress\nfrom Fracture Injection Tests Using\nContinuous Wavelet Transform.\nEnergies 2023 ,16, 764. https://\ndoi.org/10.3390/en16020764\nAcademic Editor: Maria Grazia\nDe Giorgi\nReceived: 2 December 2022\nRevised: 23 December 2022\nAccepted: 27 December 2022\nPublished: 9 January 2023\nCopyright: \u00a9 2023 by the authors.\nLicensee MDPI, Basel, Switzerland.\nThis article is an open access article\ndistributed under the terms and\nconditions of the Creative Commons\nAttribution (CC BY) license (https://\ncreativecommons.org/licenses/by/\n4.0/).\nenergies\nArticle\nA New Technique for Estimating Stress from Fracture Injection\nTests Using Continuous Wavelet Transform\u2020\nMohamed Adel Gabry *\n , Ibrahim Eltaleb\n , Mohamed Y. Soliman\n and Syed M. Farouq-Ali\nDepartment of Petroleum Engineering, The University of Houston, Houston, TX 77023, USA\n*Correspondence: magabry@cougarnet.uh.edu"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b4f2-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 0, "chroma:document": "*Correspondence: magabry@cougarnet.uh.edu\n\u2020 Society of Petroleum Engineers Technical Conference and Exhibition, Houston, TX, USA, 3\u20135 October 2022.\nAbstract: The diagnostic fracture injection test (DFIT) is widely used to obtain the fracture closure\npressure, reservoir permeability, and reservoir pressure. Conventional methods for analyzing DFIT\nare based on the assumption that a vertical well is drilled in ultra-low permeability reservoirs with\npotential multiple closures but fails to consider horizontal wells. There is still signi\ufb01cant debate about\nthe rigorousness and validity of these techniques due to the complexity of the hydraulic fracture\nopening and closure process and assumptions of conventional fracture detection methods. The\npaper introduces a new method for detecting fracture closure pressure using the continuous wavelet\ntransform (CWT). The new method aims to decompose the pressure fall-off signal into multiple levels"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b650-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 0, "chroma:document": "with different frequencies using the CWT. This \u201cshort wavy\u201d function is stretched or compressed and\nplaced at many positions along the signal to be analyzed. The wavelet then convoluted the signal\nyielding a wavelet coef\ufb01cient value. The signal energy is observed during the fracture closure process\n(pressure fall-off) and the fracture closure event is identi\ufb01ed when the signal energy stabilizes to\na minimum level. A prede\ufb01ned simple commercial fracture simulation case with known fracture\nclosure, \ufb02ow regime modeling, and actual \ufb01eld cases was used to validate the new methodology.\nKeywords: continuous wavelet transform; diagnostic fracture injection test; hydraulic fracture;\nminimum horizontal stress; geothermal reservoirs\n1. Introduction\n1.1. Scope of Study\nEstimating the minimum horizontal stress is a critical part of building formation\ngeomechanical models, designing hydraulic fractures, designing drilling schedules, etc."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b6e6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 0, "chroma:document": "Hydraulic fracturing design and execution need to calibrate the mechanical Earth model\nwith a reliable method. This is performed to identify the formation stresses. Classical\nmethods for obtaining the minimum horizontal stress of the formation relies on the open-\nhole well logs (Eaton (1969) [ 1]; Blanton and Olson (1999) [ 2]). These methods can be\ncategorized into two main techniques. The \ufb01rst technique relies on compressional and\nshear sonic waves to estimate dynamic geo-mechanical properties. The second technique\nuses correlations to calculate the dynamic properties of the rock from conventional well-\nlogging parameters, then calculates the minimum horizontal stress [3].\nThe actual in situ minimum principal stress of the formation is calculated by calibrating\nagainst the closure pressure from diagnostic pumping test [ 4]. That is performed by\npumping a small volume of non-wall building \ufb02uids to create a small fracture and then"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b768-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 0, "chroma:document": "analyze the pressure decline to know the pressure at which that fracture closes. That\nfracture closure pressure should be the average of the minimum principal stress for the\narea covered by the created fracture.\nAs no possible physical observation of the fracture propagation and closure in com-\nplicated subsurface formations, there are signi\ufb01cant debates surrounding the various\nmethodologies used to determine closure pressure. This is because of several reasons. The\nEnergies 2023 ,16, 764. https://doi.org/10.3390/en16020764 https://www.mdpi.com/journal/energies"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b7ea-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 1, "chroma:document": "Energies 2023 ,16, 764 2 of 29\n\ufb01rst reason is that the hydraulic fracture propagation and closure process are fairly compli-\ncated due to the formation stress state, the presence of natural fractures, heterogeneity, and\nthe anisotropy of the subsurface formations\u2019 properties. Conventional closure detection\nmethods have pre-set assumptions to simplify the state of the subsurface formation. Some\nof them may simplify the leak off to carter leak off, whilst other methods assume the\nconstant compliance or make certain assumptions regarding the \ufb02ow regimes or the state\nof injection. Many tests may deviate from the assumed pre-set conditions. The detected\nclosure be confused by the formation pressure response after the fracture closure. The\npressure change propagates in the formation and produces behavior that may be confused\nwith fracture closure detection.\nAlthough fracture closure is de\ufb01ned as the pressure at which a fracture closes, there"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b876-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 1, "chroma:document": "is an attempt to detect the contact pressure when the two fracture faces \ufb01rst come into\ncontact with one another. Assuming that closure pressure does not really exist, there is an\naperture between fracture faces. Complications regarding how the fracture propagates and\ncloses cause the interpreted fracture closure pressure debatable. In most cases, the industry\nworkers try various methods to determine the range of closure pressure. To date, there is no\nglobal technique that can detect closure without pre-assumptions. Each of the conventional\nmethods detects the closure from a speci\ufb01c point of view with certain pre-assumptions.\nThis paper introduces an innovative method to \ufb01nd the closure pressure using the wavelet\ntransform technique as a general technique without any pre-assumptions. It uses an\nindependent mathematical microscope to \ufb01nd the fracture closure pressure in the pressure\nfall-off signal. The new technique is validated using different ways: using simulated"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b90c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 1, "chroma:document": "synthetic pressure data from a fracture simulator and using \ufb02ow regime modeling by\nreverse calculating a pressure decay signal assumed to be both before fracture closure and\nafter fracture closure \ufb02ow regimes. The main advantage of this technique is that there is no\nneed to know formation parameters in advance or have a pre-prescribed testing procedure.\nSince the beginning of the 1990s, the science and engineering applications of wavelet\ntransform have increased at a remarkable growth rate. Thousands of peer-reviewed journals\nare now interested in wavelet transform applications covering numerous disciplines such\nas \ufb02uids, medicine, and fractal geometry. However, its use in the oil and gas industry\nand geothermal energy has been limited to date. A lot of the data recorded in multiple\ndisciplines are considered as signals to be analyzed to understand the physics-based\nmodels covering the many applications. For example, Germ\u00e1n-Sall\u00f3 et al. (2018) [ 5]"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3b998-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 1, "chroma:document": "introduced a method for crack detection in manufacturing systems using digital signal\nprocessing methods.\nSignal processing is widely used in the medical \ufb01eld to detect heart problems by\nanalyzing electrocardiography (ECG) signals. Research in the medical \ufb01eld deploys wavelet\ntransform to compare the ECG signals of a healthy heart to another ECG signal associated\nwith a diseased heart. The same methodology is adopted in the industrial application\nof signal processing to predict motor failure. For instance, the analysis of the vibration\nsignal of a motor can help detect bearing failure when the recorded signal is compared to a\nfunctional motor.\nWith the ongoing digitalization of the modern oil and gas industry and geothermal\nenergy industry, the same technique can be used in the analysis of hydraulic fracturing. In\nthis case, changes in pressure and rate over time are recorded during the fracture propa-\ngation stages, proppant placement, and fracture closure to determine what is happening"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ba1a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 1, "chroma:document": "thousands of feet below the Earth\u2019s surface during hydraulic fracturing treatment. The\nmost common methodology used by researchers for engineering wavelets applications is\nto try to \ufb01nd a correlation between the features detected from the signals and the actual\nphysical response of the system. The main problem with this methodology in hydraulic\nfracturing is the complexity of hydraulic fracturing propagation and closure due to fracture\nface roughness or natural fracture intensity and directions and a lot of other factors. This\nmay be complex not only because of the heterogeneity of the reservoir, but also because of\nthe interaction of the hydraulic fracture with natural fractures, \ufb01ssures, and other geologic"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3baa6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 2, "chroma:document": "Energies 2023 ,16, 764 3 of 29\nfeatures. Thus, all the complicating factors should be removed from the system to \ufb01nd a\nsignal representing a closure event in a homogeneous reservoir with no geologic complexi-\nties. In order to understand the CWT behavior during fracture closure, a numerical fracture\nsimulator is used in this study.\nThe application of wavelet analysis in the oil industry was pioneered twenty years\nago by Soliman et al. (2003) [ 6] as an application for well-test analysis and fracturing. The\nwavelet transform technique is a data transform technique that convolves the pressure\nand/or temperature data using a short wavy signal called \u201cwavelet\u201d. This convolution can\nbe performed at discrete points in the discrete wavelet transform (DWT) or continuously\nusing the CWT. The wavelet transform provides a representation of the pressure signal\nby letting the translation and scales of the wavelets vary continuously. This enables the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3bb32-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 2, "chroma:document": "analyst to \ufb01nd the details of the pressure data by observing the wavelet energy spectrum\nfor the monitored signal (pressure and/or temperature).\nAs the DWT is computationally cheaper, it was used as the \ufb01rst step to detect fracture\nclosure. The main disadvantage of using the DWT is its requirement of a uniform sampling\nrate and the detected closure pressure changes with an increasing level of decomposition.\nSoliman, Unal, Siddiqui, Rezaei, and Eltaleb (2019) [7,8] initiated a methodology to detect\nthe fracture closure pressure using the DWT. Determining the closure pressure in this\nmethodology is based on analyzing the detail levels to pick the time when the variance\nchanges. Eltaleb et al. (2020) [ 9] and Eltaleb et al. (2021) [ 10] improved the rigor of the\ntechnique using an energy density plot. The technique was compared to the G-function\ntechnique and showed good agreement. The DWT technique involves a multiresolution"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3bbbe-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 2, "chroma:document": "wavelet decomposition that breaks the (recorder pressure) signal into high pass (noise) and\nlow pass (approximation) components at various levels. The plot of energy distribution\nin time is constructed using the energy of the high pass component (noise) at different\ndecomposition levels. These plots provide means of capturing the physical changes in\nthe fracture system through pressure fall-off. They represented the noise energy in the\nrecorded pressure at different frequency levels. The closure pressure in this methodology\nwas determined based on changes in the noise energy of the recorded pressure and where\nit drops to a minimum stabilized level.\nThis paper introduces a closure detection technique similar to that introduced by\nEltaleb et al. (2021) [ 10], however, using the CWT. Using the CWT does not need a\nuniform sampling rate and captures all signal details. CWT can be used as a method for\ndetecting the fractal dimension which is one of the key features of complex wavelets that"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3bc40-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 2, "chroma:document": "is sometimes referred to as a \u201cmathematical microscope\u201d to detect the features. Using\nCWT was recommended by Fatmir (2020) through personal communication. CWT can\nbe used as a \ufb01lter to detect the signal features. It has the \ufb02exibility to be used with or\nwithout a uniform sampling rate. Thus, it could be validated using any type of data. This\nnew method was applied to both the fracture simulator data and actual \ufb01eld data. The\nsynthetic data were produced using a commercially available fracture simulator developed\nby Barree (1983) [ 11] based on fracture propagation and closure simulation principles with\nprede\ufb01ned fracture closure. Azlinda et al. (2010) [ 12] showed good agreement between the\nused fracture simulator with down-hole events in a stacked \ufb02uvial pay system. The CWT\ntechnique showed success with the actual real \ufb01eld data conducted on one of the oil and\ngas \ufb01elds and in another case in a geothermal reservoir.\n1.2. History of Closure Pressure Detection Techniques"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3bccc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 2, "chroma:document": "1.2. History of Closure Pressure Detection Techniques\nThe basic concept of classical methods of closure event detection from the pressure\ndecay of the diagnostic fracture injection test is combining the basic concepts of well\ntesting and hydraulic fracture analysis. After hydraulic fracturing was \ufb01rst introduced by\nClark (1949) [ 13], it was recognized that hydraulic fracturing could be used as a method\nto estimate the magnitude of minimum principal stress (Hubbert and Willis (1957) [ 14];\nGodbey and Hodges (1958) [ 15]; Kehle (1964) [ 16]; Haimson and Fairhurst (1967) [ 17];\nHickman and Zoback (1983) [ 18]). The main idea was to pump \ufb02uid at a pressure higher"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3bd58-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 3, "chroma:document": "Energies 2023 ,16, 764 4 of 29\nthan the fracturing pressure, to initiate a hydraulic fracture and propagate it through the\nformation. The minimum principal stress can be estimated from pressure measurements\nduring and after injection. Nolte (1979) [ 19] extended the applicability of fracturing tests\nby developing analytical techniques that can be used to estimate \ufb02uid leak-off parameters.\nThese techniques can be used to obtain the leak-off rate of complex \ufb02uids such as linear gel\nor cross-linked gel. These tests are typically called mini-frac tests (McLennan and Roegiers,\n(1982) [ 20]) or fracture calibration tests (Mayerhofer and Economides (1993) [ 21]). This is\nperformed to estimate the ef\ufb01ciency of the fracturing \ufb02uid after the interpretation of the\nminimum horizontal stress. One of the most widely used functions to obtain the closure\npressure is G-function (Nolte (1979) [ 19]). Several techniques have subsequently been"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3bdda-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 3, "chroma:document": "published as essential parts of the analysis, including those by Castillo (1987) [ 22] as well\nas Barree and Mukherjee (1996) [ 23]. Further modi\ufb01cations for the analysis were added,\nfor example, by Mayerhofer and Economides (1993) [ 21] and Mayerhofer et al. (1995) [ 24]\nshowed how to remove the \ufb01lter cake effect and its effect on the \ufb02uid leak-off factor from\nthe analysis. The recent development of the shale gas reservoirs came out with a new test\nthat uses the non-wall building \ufb02uid instead of the cross-linked gel or linear gel. It is called\nthe \u201cdiagnostic fracture injection test\u201d (DFIT). It is routinely performed in unconventional\nreservoirs due to the incapability to \ufb02ow the well to do a pressure transient analysis. The\nDFIT is used to obtain the best estimates for stress, permeability, and pore pressure (Craig\nand Brown (1999) [25]. The analysis of pressure decay data has two parts.\nThe \ufb01rst part of the DFIT analysis is called \u201cPre-closure analysis methods\u201d which"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3be66-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 3, "chroma:document": "are usually based on techniques from Nolte (1979) [ 19] and Mayerhofer and Economides\n(1993) [ 21], Mayerhofer et al. (1995) [ 24], Barree and Mukherjee (1996) [ 23], and Barree\net al. (2009) [ 26]. These methods are used to estimate the closure pressure and calibrate\nthe minimum principal stress. The second part is called \u2018Post-closure\u2019 analysis methods\nwhich are usually based on techniques from conventional well testing (Gu et al. (1993) [ 27];\nSoliman et al. (2005) [ 28]; Craig and Blasingame (2006) [ 29]) or the \u2018linear \ufb02ow time\nfunction\u2019 technique developed by Nolte et al. (1997) [ 30]. Due the development of uncon-\nventional reservoirs, multiple DFIT interpretation techniques have recently been developed\nby Marongiu-Porcu et al. (2011; 2014) [ 31,32], Soliman and Kabir (2012) [ 33], Soliman and\nGamadi (2012) [ 33], Cramer and Nguyen (2013) [ 34], Padmakar (2013) [ 35], Wallace et al.\n(2014) [ 36], Meng et al. (2014) [ 37], Craig (2014) [ 38], Zanganeh et al. (2018) [ 39], and\nHawkes et al. (2018) [40]."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3bef2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 3, "chroma:document": "Hawkes et al. (2018) [40].\nOne of the noticeable techniques is the compliance method that was recently intro-\nduced by McClure et al. (2014; 2016) [ 41,42] and Jung et al. (2016) [ 43]. This technique\nusually leads to an earlier and higher stress estimate in contrast to the commonly used\ntangent method (Barree et al. (2009) [ 26]) which is considered a modi\ufb01cations to Nolte\u2019s\n(1979) [ 19] technique. The technique introduced a new concept which is contact pressure\ninstead of closure pressure. McClure et al. (2016) [ 42] and Jung et al. (2016) [ 43] per-\nformed detailed DFIT simulations considering the effect of a residual aperture fracture\nafter the contact between the fracture walls. Simulations indicate that, in low permeabil-\nity formations, the contacting of the fracture walls causes the magnitude of the pressure\nderivative to increase, resulting in a pressure signal that was previously interpreted as\nthe height recession or closure of transverse fractures (Barree et al. (2009) [ 26]. Wang"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3bf7e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 3, "chroma:document": "and Sharma (2017) [ 44] reproduced these \ufb01ndings and proposed a modi\ufb01ed approach for\nestimating stress called the \u2018variable compliance method\u2019. Currently, there are two main\nclosure detection techniques that are used by the industry, the tangent method, and the\ncompliance method.\nThe initial technique of the G function introduced by Nolte (1979) [ 19] relied on several\nassumptions for the pumping and shut-in periods with some simpli\ufb01ed concepts of how a\nfracture propagates and closes. Nolte (1979) [ 19] provided the G time function to detect\nthe changes in the pressure during the shut-in period of the diagnostic pumping. The\nsecond derivative (GdP/dG) is used to detect the closure. The closure de\ufb01ned by this\ntechnique is the pressure at a time when the deviation from the straight line starting from"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c05a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 4, "chroma:document": "Energies 2023 ,16, 764 5 of 29\nzero in GdP/dG occurs. The detailed equations for the G time function were discussed\nby Nolte (1979) [ 19]. Castillo (1987) [ 22] added the condition that dP/dG should be with\nzero slopes at the same point. The tangent method was introduced to cope with the\ncomplicated fracture closure as a modi\ufb01cation for the Nolte (1979) [ 19] technique. The\ntangent method proposed four types of leak-off in the formation during the closure, normal\nleak-off, pressure-dependent leak-off, transverse storage leak-off or height recessions, and\ntip extension leak-off. It is taken from a plot of GdP/dG versus G. A straight line is\ndrawn from the origin to the tangent to the curve. The closure pressure is de\ufb01ned as the\npressure when the GdP/dG starts to deviate downward. The pressure at that point is\ntaken as the tangent method stress estimate. The tangent method was developed to match\nnumerical simulations by Barree and Mukherjee (1996) [ 23] and Barree et al. (2009) [ 26]."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c0dc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 4, "chroma:document": "Their work introduced a G-function signature for each type of leak-off. Each type of leak-\noff can characterize speci\ufb01c reservoir properties such as the presence of natural fractures,\nthe presence of lower permeability streaks or weak barriers surrounding the pay zone.\nThe tangent method in many cases shows a monotonic increase which makes the closure\npressure too low to be identi\ufb01ed. The tangent method is affected by the formation response\nafter the fracture closure. It is normally associated with the square root of time and log\u2013log\nanalysis, as recommended by Baree et al. (2009) [ 26]. The pre-closure \ufb02ow regime and\npost-closure \ufb02ow regimes should be identi\ufb01ed to support the closure detected using the\ntangent method. The second derivative of pressure to the square root of time should show\na local peak at the closure. The relations between the log\u2013log, square root of time, and\ntangent method were discussed in detail by Baree et al. (2009) [ 26]. The log\u2013log technique"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c15e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 4, "chroma:document": "and square root of time method can be combined as the \u201cHolistic Fracture Diagnostics\u201d as\ndescribed by Baree et al. (2007) [45].\nThe compliance method for estimating stress was developed from mathematical\nsolutions of the fracture closure process (McClure et al. (2016) [ 42]). As per the compliance\nmethod, the very early part of the shut-in is ignored as the pressure drops very rapidly.\nThis part of the transient is ignored because it is caused by the dissipation of near-wellbore\ntortuosity related to the initiation of a transverse hydraulic fracture from a horizontal\nwell. The straight section of the pressure versus G-time plot can be extrapolated back to\nthe y-intercept to estimate the pressure in the far-\ufb01eld fracture at shut-in (the so-called\neffective initial shut-in pressure). After the initial period, the pressure curve settles into\nan approximately straight line. The \u2018compliance method\u2019 of estimating stress identi\ufb01es\nthe contact pressure at the point where the derivative increased from the minimum and"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c1e0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 4, "chroma:document": "subtracts 75 psi to account for a stress shadow from the residual aperture (McClure et al.\n(2019) [ 46]). The 75 psi adjustment is based on a numerical simulation that matches the\n\ufb01eld DFITs (McClure et al. (2019) [46]).\nWhen the fracture walls contact, the stiffness increases, and the storage coef\ufb01cient\ndrops as per Sneddon (1946) [ 47]. This causes the dP/dG to increase when the fracture walls\ncome into contact. McClure et al. (2016 [ 42], 2019 [ 46]) note that, because of the roughness\nof the fracture walls, the \ufb02uid pressure may be higher than the minimum principal stress\nwhen the walls come into contact. Thus, it is recommended to estimate the closure pressure\nas 75 psi lower than the contact pressure based on numerical simulations. The contact\npressure is estimated by plotting the magnitude of dP/dG and identifying the point where\nthis derivative reaches a minimum and begins to increase. This is the so-called \u2018compliance\u2019"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c26c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 4, "chroma:document": "method stress estimate. It is noticeable that the \u2018compliance method\u2019 is close to the classical\nmethod by Nolte (1979) [ 19]. However, an upward de\ufb02ection in dP/dG is not always seen\nin the shut-in transients.\nIn a lot of cases, dP/dG continuously decreases during the shut-in. McClure et al.\n(2019) [ 46] discussed the possible causes of the lack of an upward de\ufb02ection. That may\nbe due to the excessive near-wellbore tortuosity as the fracture closes almost immediately\nafter shut-in. The monotonic dP/dG might arise from the continued fracture propagation\nafter shut-in. One of the key assumptions of G-function is that the fracture does not\npropagate after shut-in. This makes the G-function not accurate in many cases. McClure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c2f8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 5, "chroma:document": "Energies 2023 ,16, 764 6 of 29\net al. (2019) [ 46] recommended interpreting tests with a monotonic dP/dG as indicating\n\u2018rapid closure\u2019 in vertical wells where the near wellbore tortuosity is usually minimal and\nsupplementing dP/dG plots with plots of \u2018relative stiffness\u2019 versus pressure. The relative\nstiffness is not a normalized value calculated to be proportional to the system stiffness.\nIn tests where near-wellbore tortuosity is possible, McClure et al. (2019 [ 46]; 2022 [ 48])\nrecommended declining to provide a stress estimate and labeling the stress uninterpretable.\nMcClure et al. (2022) [ 48] found that \ufb01fty-nine percent of cases showed a clear upward\nde\ufb02ection; twenty-\ufb01ve percent of cases showed an adequate upward de\ufb02ection; and sixteen\npercent of cases showed no indication of an upward de\ufb02ection (i.e., a monotonic decrease\nin dP/dG).\nFrom the previous discussions, closure detection is still open for research and needs"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c384-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 5, "chroma:document": "more studies to understand the complications of fracture closure without pre-assumptions\nand fewer data requirements, which is the main advantage of wavelet transform techniques.\n2. Methodology\n2.1. Wavelet Transform\nWavelet transform is a mathematical transformation applied to signals to obtain\ninformation that is not readily available. This signal can be pressure or any parameter\nrecorded during \ufb01eld operations. In practice, most signals are in the time domain in their\nraw format and plotted as a time\u2013amplitude representation of the signal. As a result,\nthis is not always the best representation of the signal for most signal processing-related\napplications; hence, the most valuable features are usually hidden in the signal frequency.\nSeveral transformations may be used to analyze the acquired signals. Fourier trans-\nforms (FTs) are the most widely used signal processing technique that gives signal frequency\ninformation. However, it does not provide timely information on which those frequency"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c406-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 5, "chroma:document": "components exist. FT works best in the analysis of stationary signals whose time domain\nis periodic; then, the time domain signal can be converted into a combination of sine and\ncosine waves to in\ufb01nity duration (Rioul and Vetidsaerli (1991) [49]).\nOne modi\ufb01cation for the Fourier transform is the windowed Fourier transform (WFT).\nIt is a tool for extracting local-frequency information from the non-stationary signal. The\nsignal is divided into small stationary segments through window functions whose width\nmust equal the part of the signal where it is stationary. As discussed by Kaiser (1994) [ 50],\nWFT is prone to inaccurate results due to the aliasing of high- and low-frequency compo-\nnents that do not fall within the window function proposed by the technique. Wavelet\ntransform (WT) has a dynamical frequency spectrum and can represent the signals in\nboth the time and frequency domains. Figure 1 summarizes the difference between each"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c47e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 5, "chroma:document": "signal representation. As the wavelets analysis has a high dynamical frequency and a high\nresolution in both frequency and time domains, it is preferred for signals with a wide range\nof dominant frequencies and time\u2013frequency localization independence.\nWavelet transform analysis uses small wavelike functions known as wavelets. Math-\nematically, it can be de\ufb01ned as the convolution of the signal with the wavelet function.\nFigure 2 shows a few of the most common wavelet types.\nWavelets can be manipulated through translation (i.e., moving the wavelets along\nthe time axis) and scale (i.e., stretching and squeezing the wavelet at a particular point in\ntime). The scale and translation of wavelets govern parameters (b) and (a), respectively, in\nEquation (1).\nT(a,b)=1\u221aa\u222b\u221e\n\u2212\u221ex(t)\u03c8\u2217(t\u2212b\na)\ndt (1)\nThe Equation (1) comprised both the signal x(t), which could represent the pressure,\ntemperature, or any time series data, as well as the ( \u03c8\u2217(t\u2212b)/a) mother wavelet function."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c50a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 5, "chroma:document": "The wavelet transform works by superimposing the wavelet function on an arbitrary signal,\nas illustrated in Figure 3. Time segments A and B, where both the wavelet and original\nsignal agree (positive or negative), will result in a large positive transformation value of"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c58c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 6, "chroma:document": "Energies 2023 ,16, 764 7 of 29\nthe integral given by Equation (1). On the contrary, in regions C, D, and E, when the\nwavelet and the signal have opposite signs, the overall transformation results in a negative\ncontribution to T(a,b).\nFigure 1. Comparison between different signal representations.\nFigure 2. Shapes of different wavelet transform families.\nFigure 3. Mechanism of wavelet transform [51]."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c618-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 7, "chroma:document": "Energies 2023 ,16, 764 8 of 29\nWhen using complex wavelets, the resulting coef\ufb01cient consists of both real and\nimaginary parts. Fourier transforms of complex wavelets are zero for negative frequencies.\nTherefore, we can separate the phase and frequency components within the signal using\ncomplex wavelets. For instance, taking Fourier to transform the Mexican hat wavelet\nand then performing an inverse Fourier transform after neglecting the zero components\nin the Fourier transform will create a complex wavelet. It produces a less oscillatory\ntransform than in the case of real wavelets because a complex wavelet only responds to\nthe non-negative frequencies of the particular real signal. Therefore, it outperforms real\nwavelets in detecting and tracking instantaneous frequencies (Guerrero, A.P ., and Paredes,\nG. E. (2018) [52]). Complex wavelet transform is used in our analysis, which is de\ufb01ned by\nEquation (2) where the \ufb01rst part is the normalization factor, the second part is the complex"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c69a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 7, "chroma:document": "sinusoid, and the \ufb01nal part is the Gaussian bell curve.\n\u03c8(t)=1\n\u03c01/4ei2\u03c0f0te\u2212t2/2(2)\nTo inspect the multi-scale dimensional characteristics of a signal using complex\nwavelets, the Wavelet Transform Modulus (WTM) can be calculated using Equation (3).\nT(a,b)=\u221a\n[Re(T(a,b))]+[Im(T(a,b))] (3)\nOne of the main features of the signals that can be observed and analyzed to identify\nthe system properties is the analysis of signal energy. For any signal, the total energy\ncontained in a signal, x(t), is de\ufb01ned as its integrated squared magnitude as in Equation (4)\nwith the condition that the signal must contain \ufb01nite energy.\nE=\u222b\u221e\n\u2212\u221e|x(t)|2dt (4)\nThe relative contribution of the signal energy contained at a speci\ufb01c scale (a) and\nlocation (b) is given by the two-dimensional wavelet energy density function:\nE(a,b)=|T(a,b)|2(5)\nThe plot E(a)versus time (different location parameters b values) at different dilation\nparameter values (scale) (a) can be plotted in a plot called a scalogram. From the scalogram,"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c71c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 7, "chroma:document": "the location and scale of dominant energetic features within the signal can be detected from\nthe scale-dependent wavelet energy spectrum of signal E(a)at a speci\ufb01c scale. A plot of\nE(a,b)as a function of time and frequency is known as a scalogram. Scalograms are usually\nplotted with a logarithm and a scale axis. For example, Figure 4 shows a scalogram for The\nNino3 SST monthly climate time data series analyzed using Morlet wavelets (Torrence and\nCompo (1998) [53]), as discussed by Addison, P .S. (2016) [51].\nThe features that are detected at small scales, the compressed wavelet, are the rapidly\nchanging details (\ufb01ne features) that cause high frequency in the signal while the features\nthat are detected at large scales (stretched wavelet) are the slowly changing details (coarse\nfeatures) that cause high frequency in the signal."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c7a8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 8, "chroma:document": "Energies 2023 ,16, 764 9 of 29\nFigure 4. Example for the wavelet transform analysis of the monthly climate temperature (Nino3 SST)\ntime series data: ( a) The Ni\u00f1o3 SST time series data; and ( b) the local wavelet power spectrum using\nthe wavelet transform analysis of ( a) using the Morlet wavelet (Torrence and Compo (1998) [53]).\n2.2. CWT Fracture Closure Detection Technique\nIn this study, a new innovative technique to \ufb01nd a closure pressure using the CWT\ntechnique is introduced. The main idea behind estimating the minimum stress using the\ndiagnostic fracture injection test is to create a small fracture at a constant rate and then\nshut down the pumps and observe the pressure at which the fracture closes. The closure\npressure is the minimum average of the minimum stress for the area covered by the fracture\ncreated by the DFIT. The pressure during the shut-in and the observation period represents\nthe closure process of the formation. The main goal is to detect and magnify the pressure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c82a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 8, "chroma:document": "changes that re\ufb02ect the fracture\u2019s closure event. The pressure signal during the shut-in\nperiod after DFIT is analyzed using the CWT technique with a complex Morlet wavelet to\nobtain the signal energy. The complete work\ufb02ow for the CWT closure detection technique\nis shown in Figure 5. The technique starts by getting the coef\ufb01cient of CWT using the\ncomplex Morlet wavelets at multiple scales (from zero up to a scale of 256) and then getting\nthe wavelet transform modulus (WTM) using Equation (3) as a scalogram. The scalogram\nof signal energy is plotted using a log scale. The scalogram can be averaged to the average\nof the log signal energy of all scales. Fracture closure as a dominant feature can be identi\ufb01ed\nby the average of all log signal energies at several wavelet scales. The average of the log of\nsignal energy can be plotted with time. The plot can be used to detect the closure event as\nseen in Figure 5.\nFracture closure can be identi\ufb01ed with the two following features: the fracture closure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c8b6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 8, "chroma:document": "starts with a peak in the average of the log signal energy, which represents the fracture walls\ncoming into contact, then the drop in log signal energy level to a minimum stabilized level,\nwhich represents reaching the equilibrium state. The characteristics of fracture closure\ncan be seen in Figure 6. When the real \ufb01eld data are analyzed, high oscillatory signal\nenergy may be observed due to the noise of real \ufb01eld data. That may be due to several\nreasons, and the fracture faces are not smooth faces and the closure does not happen in\nsubsurface formation instantaneously, or there is noise in the pressure data, or due to that,\nthe equilibrium state is still disturbed with the DFIT."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c938-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 9, "chroma:document": "Energies 2023 ,16, 764 10 of 29\nFigure 5. Fracture closure detection work\ufb02ow using the CWT closure detection technique.\nFigure 6. Fracture closure pressure using CWT closure detection technique.\n2.3. Summary\nThe new CWT fracture closure detection technique can be conducted as the following\nsteps: The \ufb01rst step is to apply the CWT using a complex Morlet wavelet for the pressure\nsignal starting from the start of DFIT pumping to obtain the CWT coef\ufb01cient at different\nscales up to (a = 256) as per Equation (1) and then obtain the wavelet transform modulus\n(WTM) as per Equation (4) from the complex continuous wavelet coef\ufb01cient. This can\nbe followed by the calculation of signal energy using Equation (2). Considering fracture\nclosure is a dominant feature so it can be detected by averaging the log of signal energy\nvalues at each time point for different scales (up to scale (a) = 256). From the plotted signal\naverage log energy versus time, the start and the end of the fracture closure event can"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3c9c4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 9, "chroma:document": "be identi\ufb01ed with the following characteristics. The start of the fracture closure which\nrepresents the contact of two fracture faces can be recognized by a peak in average signal\nlog energy at the start of the fracture closure. The fracture closure can be identi\ufb01ed by the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ca50-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 10, "chroma:document": "Energies 2023 ,16, 764 11 of 29\ndrop in signal average log energy level to a minimum stabilized level. The start of the\nminimum stabilized level characterizes the end of the fracture closure event.\n3. Results and Discussion\n3.1. Validation Using Fracture Simulation\nThe numerical simulations in this study were performed using the commercial pla-\nnar 3D fracture simulator introduced by Barree (1983). The simulator integrates a \ufb01nite\ndifference formulation for the \ufb02uid \ufb02ow calculation within the fracture with an integral\nequation for fracture width. Fluid pressure and fracture width solutions are sequentially\ncoupled based on the linear-elastic solution of the deformation for an in\ufb01nite half-space\nwith a concentrated load. This relies on Poiseuille\u2019s equation along with the continuity\ncondition. It uses a pressure-dependent leak-off model for the effect of natural fractures.\nThis simulation is solved using \ufb01nite differences with a regular grid. The shear-rate and"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3cad2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 10, "chroma:document": "time-dependent laboratory \ufb02uid test data are used to model the \ufb02uid rheology. Proppant\ntransport is coupled with \ufb02uid \ufb02ow and iteratively solved for proppant distribution in\nfractures. The simulator is widely used by the oil and gas industry and its fracture geometry\nis validated by downhole events in a stacked \ufb02uvial pay system as per Nur. Azlinda et al.\n(2010) [12].\nTo test the new CWT closure detection technique using fracture simulation, grids for\nthe synthetic model are created with ideal properties; the idealized reservoir model has\n25 ft. of the sand body between two shale barriers with a sharp stress contrast and constant\nvalues for reservoir characteristics and geo-mechanical parameters. High-stress contrast\nbetween the pay zone and the surrounding shale zones is assumed. It is assumed that\nthe reservoir is tight (the formation permeability is 5 micro Darcy) and a simulation run\nwas conducted with a \ufb02uid volume (10,000 gallons of KCL water) of diagnostic fracture"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3cb5e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 10, "chroma:document": "injection test with the typical pumping rate of 8 bbl/min followed by 700 min of leak-off.\nThis is a standard DFIT procedure that is followed by the oil/gas industry. The KCL\nwater is commonly used to prevent clay swelling and it is a non-wall building \ufb02uid with\nviscosity changes with temperatures. The concentration of KCL is dependent on the needed\nhydrostatic for the DFIT. The pumping rate is selected to be 8 bbl/min as the maximum\nof the range of the DFIT pumping rate (3\u20138 bbl/MIN). The geomechanical and reservoir\nproperties are shown in Figure 7. The perforation shot per foot is selected to be six shots per\nfoot. The DFIT pumping schedule is implemented in the fracture simulator as per Figure 8.\nThe simulation model showed fracture propagation followed by complete fracture closure\nat 153 min when the average width is equal to zero, as shown in Figure 9. The complete\nclosure pressure is 5075 psi as per the fracture simulation."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3cc12-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 11, "chroma:document": "Energies 2023 ,16, 764 12 of 29\nFigure 7. The mechanical Earth model and reservoir properties for the fracture simulation model\nused to test the CWT closure detection technique.\nFigure 8. Synthetic model 1 pumping chart.\nFigure 9. Average width pro\ufb01le for synthetic model 1."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3cc9e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 12, "chroma:document": "Energies 2023 ,16, 764 13 of 29\nThe pressure from the fracture stimulation was analyzed with CWT to obtain the\naverage energy over wavelet scales (up to scale (a) = 256). The average log signal energy\nwas plotted against the time to detect the fracture closure in Figure 10. The energy signal in\nFigure 10 showed a peak at a time of 149 min which happens at a bottom-hole pressure of\n5095 psi. That pressure represents the start of the closure. The complete closure is when\nthe signal average energy drops to a stabilized level. As shown in Figure 10, the CWT\ntechnique showed a closure pressure at 5075 psi.\nFigure 10. Fracture closure pressure detection using the CWT technique for synthetic model 1.\nTo understand how the average log signal energy responds to fracture closure, the\nchange in the average width pro\ufb01le created by the fracture simulator is plotted as a semi-\nlog scale against time to magnify the changes in width during the closure. That is to be"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3cd2a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 12, "chroma:document": "compared with the average log signal energy to understand how the CWT closure detection\ntechnique detected fracture closure. It can be noticed that the difference in the average\nwidth pro\ufb01le reached zero at the same time when the average log signal energy reached\nthe stabilized level, as seen in Figure 11.\nThe limitations of the conventional methods are the assumptions behind each method.\nFor example, the G-function, square root, time, and log\u2013log are based on well-testing con-\ncepts, built on a constant pumping rate and shut-in. Therefore, the variable-rate pumping\nschedule does not ideally \ufb01t the basic concepts of these methodologies. However, the\nintroduced CWT closure detection is a technique that does not rely on built-in assump-\ntions. It depends on the wavelet transform acting as a global mathematical microscope\nto obtain the physical response of the signal. The closure detection technique was tested\nfor a variable pumping rate case. A pumping schedule with a variable pumping rate was"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ce06-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 12, "chroma:document": "simulated using the same ideal homogeneous geomechanical parameters used in Figure 7.\nThe pumping rate started at 4 bbl/min and then increased to 8 bbl/min and \ufb01nally to\n10 bbl/min, as shown in Figure 12. The simulation model showed fracture propagation\nand then complete fracture closure at 184.5 min, where the average width is equal to zero\nas shown in Figure 13."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ce92-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 13, "chroma:document": "Energies 2023 ,16, 764 14 of 29\nFigure 11. Comparison between the change in average width pro\ufb01le and CWT closure detection\ntechnique plot.\nFigure 12. Synthetic model 2 pumping chart."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3cf14-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 14, "chroma:document": "Energies 2023 ,16, 764 15 of 29\nFigure 13. Average width pro\ufb01le for synthetic model 2.\nThe simulation for synthetic example 2 yielded the same closure pressure of 5075 psi\nbut at a time of 184.5 min. That is what was expected using as the pumping rate changed\nfrom the synthetic model 1. The pressure from the fracture stimulation was analyzed\nwith the CWT closure detection technique by plotting the average of the log signal energy\nagainst time. From Figure 14, it is clear that the signal energy showed a peak at 169 min,\nrepresenting the bottom hole pressure of 5095 psi, which represents the start of the closure\nprocess. The complete closure pressure is at the moment when the signal average energy\ndrops to a stabilized level at a time of 184.5 min (closure pressure = 5075 psi). As shown\nin Figure 14, the CWT analysis yielded a closure pressure at 5075, the fracture closure is\nthe same as in the \ufb01rst synthetic model since the geomechanical parameters are the same."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3cfa0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 14, "chroma:document": "However, the closure time changed due to a change in the pumping rate and \ufb02uid volume.\nFigure 14. Signal average log energy using CWT for synthetic model 2.\n3.2. Validation Using Flow Regime Modeling\nTo further test the new technique with the complicated nature of the fracture closure, a\nnew approach was developed. This approach may be used to validate the CWT technique\nusing \ufb02ow regime modeling with a synthetic pressure decay signal that has no noise and\nrepresents the characteristic \ufb02ow regimes that happen before and after fracture closure. The\n\ufb02ow regime is identi\ufb01ed by the rate of change in pressure with time. A set of \ufb02ow regimes\nwere assumed to obtain a synthetic pressure leak-off signal that has a rate of change in\npressure representing those \ufb02ow regimes, then the wavelet transform technique was tested"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d022-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 15, "chroma:document": "Energies 2023 ,16, 764 16 of 29\nto know how the CWT closure detection technique detects the closure. Various pre-closure\nand post-closure \ufb02ow regimes can be identi\ufb01ed on the log\u2013log \u2206t d\u2206p /d\u2206t versus \u2206t\nplot. Table 1 shows the \ufb02ow regimes that happen pre-closure and post-closure and their\ncorresponding slopes on the log\u2013log \u2206td\u2206p /d\u2206t versus \u2206t. The basic concept can be\nvisualized as given in Figure 15. Table 1 the \ufb02ow regimes that happen pre-closure and\npost-closure and their corresponding slopes on the log\u2013log \u2206t d\u2206p /d\u2206t versus \u2206t.\nTable 1. The \ufb02ow regimes that happen pre-closure and post-closure and their corresponding slopes\non the log\u2013log \u2206t d\u2206p /d\u2206t versus \u2206t.\nThe Slope of the log\u2013log \u2206t d\u2206p/d\u2206t vs.\u2206t Flow Regime\nHalf slope (1/2) Pre-closure Linear \ufb02ow regime\nQuarter slope (1/4) Pre-closure bilinear \ufb02ow regime\nNegative half-slope ( \u22121/2) Post-closure linear \ufb02ow regime\nNegative three-fourth slope ( \u22123/4) Post-closure bilinear \ufb02ow regime\nNegative unit slope ( \u22121) Post-closure pseudo radial \ufb02ow regime"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d0a4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 15, "chroma:document": "Negative unit slope ( \u22121) Post-closure pseudo radial \ufb02ow regime\nFigure 15. Transient \ufb02ow regimes before and after fracture closure.\nPre-closure and post-closure \ufb02ow regimes can be identi\ufb01ed using the semi-log pressure\nderivative on the log\u2013log plot of \u2206p vs.\u2206t during the shut-in period following the fracture\ninjection test. A pseudo linear \ufb02ow period is identi\ufb01ed by parallel (1/2) slope lines on the\nlog\u2013log \u2206p\u2206t and\u2206t d\u2206p/d\u2206t\u2206t plot up until fracture closure as seen in Figure 16a,b.\nBilinear \ufb02ow can be identi\ufb01ed by parallel (1/4) slope lines on log\u2013log \u2206pwf versus \u2206t and\n\u2206t d\u2206p/d\u2206t versus \u2206t prior to fracture closure as seen in Figure 16c.\nAfter closure, the pseudo linear formation \ufb02ow period is identi\ufb01ed by a ( \u22121/2) slope\nof the semi-log derivative of the pressure difference on the same plot, and pseudo radial\n\ufb02ow is identi\ufb01ed by a ( \u22121) slope of the semi-log derivative on the log\u2013log plot, as seen in\nFigure 16a,b. It is dif\ufb01cult to obtain all the \ufb02ow regimes in one real \ufb01eld case. Thus, the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d126-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 15, "chroma:document": "perfect fracture closure log\u2013log plot can be synthetically created assuming \ufb02ow regime\nslopes and then calculating the pressure decay signal as seen in Figure 17. The slopes that\nwere assumed are the slopes of the log\u2013log plot of \u2206t d\u2206p/d\u2206t vs.\u2206t for each period of\npressure decay signal are shown in Table 2."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d1b2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 16, "chroma:document": "Energies 2023 ,16, 764 17 of 29\nFigure 16. (a) Normal leak off log\u2013log plot; ( b) pressure-dependent leak off log\u2013log plot; and ( c) tip\nextension log\u2013log plot (Barree et al. (2009) [26]).\nTable 2. The slopes of the log\u2013log plot of \u2206t d\u2206P/d\u2206t vs.\u2206t for the reverse-calculated pressure\ndecay signal.\nStart, min. End, min.The Slopes of\nthe log\u2013log Plot\nof\u2206t d\u2206P/d\u2206t\nvs.\u2206tPressure at\nStart, psi.Pressure at\nEnd, psi.\n0 5 Pumping period Pumping period Pumping period\n5 15 0.3 12,000 11,692\n15 40 0.5 11,692 11,499\n40 50 0.25 11,499 11,445\n50 200 \u22120.5 11,445 11,216\n200 360 \u22121 11,216 11,168"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d234-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 17, "chroma:document": "Energies 2023 ,16, 764 18 of 29\nThe pressure decay signal and its corresponding \ufb02ow regimes are shown in Figure 17.\nThe synthetic pressure decay signal can be used to illustrate that the wavelet transform\ndetects the features within the signal itself and not only the noise associated with it. It can\nalso be used to investigate the response of each closure detection technique. The synthetic\npressure decay signal was analyzed using each technique as if it was real \ufb01eld data.\nFigure 17. Synthetic reverse-calculated pressure decay signal.\nThe application of the conventional technique, the tangent method (Barree et al.\n(2009) [ 26]), showed that dP/dG monotonically decreases so it can be either rapid closure\nor it is not valid to be analyzed using the compliance method (Mcclure et al. (2022) [ 48]).\nHowever, the effective shut-in pressure is 11,850 psi which is delayed from the pump\nshut-down time by a minute and a half. There is no rise in dP/dG. The tangent method"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d2b6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 17, "chroma:document": "using GdP/dG detected the closure pressure at 11,445 psi which represents the end of the\nlinear pre-closure \ufb02ow regime. The dP/dG and GdP/dG are shown in Figure 18. The\npre-closure bilinear \ufb02ow regime is ignored by the tangent method. The application of the\nCWT closure detection technique detected the closure at the same point of the change\nfrom the bilinear \ufb02ow regime to the after-fracture-closure linear \ufb02ow regime. It accurately\ndetected the transition period between pre-closure and post-closure, as can be seen in\nFigure 19. The fracture closure is usually identi\ufb01ed at the end of the pre-closure linear \ufb02ow,\nbut this is not accurate as the pre-closure bilinear \ufb02ow can be detected in several real \ufb01eld\ncases. However, that bilinear \ufb02ow period is very short and cannot be observed in many real\n\ufb01eld cases. CWT closure detection technique detected the transition between pre-closure\nand post-closure with a clear peak. The change in \ufb02ow regime between the pre-closure"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d338-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 17, "chroma:document": "and post-closure periods can also be identi\ufb01ed with smaller and smoother peaks. The\nclosure pressure detected using the CWT technique matches the most accurate de\ufb01nition of\ncomplete fracture closure.\nFigure 18. Tangent method (dP/dG and GdP/dG) for the synthetic reverse-calculated pressure\ndecay signal.\nThe large peak matches the closure process as seen in Figure 19. This is when the\nfracture closes and the \ufb02ow starts to follow a formation linear \ufb02ow regime. This includes\nthe period of bilinear \ufb02ow where the formation and fracture \ufb02ow together and each of them"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d3ba-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 18, "chroma:document": "Energies 2023 ,16, 764 19 of 29\nshows a linear \ufb02ow regime. The multiple peaks that are shown in the reverse-calculated\npressure decay signal are not shown in fracture simulation synthetic data as the fracture\nsimulation did not include the post-closure reservoir \ufb02ow regimes. It only simulates\nhydraulic fracture propagation and closure.\nFigure 19. Closure pressure detection using the CWT technique for the synthetic reverse-calculated\npressure decay signal.\n3.3. Application of CWT on Real Field Data\nThe main challenge for any technique is to be applied to real \ufb01eld data. We compared\nthe closure pressure of a real \ufb01eld DFIT case estimated using the CWT technique to the\nconventional methods such as the tangent method, log\u2013log, and square root of the time and\ncompliance methods. This was performed to determine how the CWT closure detection\ntechnique stands up against other techniques used in the industry. Thus, two real \ufb01eld\ncases, wells X-01 and X-02 were selected for the analysis of the new CWT technique. The"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d446-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 18, "chroma:document": "well 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\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d4d2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 18, "chroma:document": "with 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d554-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d5e0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 19, "chroma:document": "There 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\nwas also tested on a very tight reservoir. The well X-02 was perforated through granite"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d662-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 19, "chroma:document": "formation, which is the typical geothermal formation type, and then pumped the DFIT as\nper the pumping schedule shown in Figure 25."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d6e4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d766-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d7fc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 21, "chroma:document": "detected 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d87e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d90a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3d98c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3da18-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3daa4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 25, "chroma:document": "4. 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\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."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3db26-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 25, "chroma:document": "8. 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.;\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."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3dba8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 25, "chroma:document": "of 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.\nCon\ufb02icts of Interest: The authors declare no con\ufb02ict of interest."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e008-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e0e4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 26, "chroma:document": "4. 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\nEvents by Analyzing the Energy of Rate and Pressure Signals. In Proceedings of the SPE Annual Technical Conference and"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e166-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 26, "chroma:document": "Exhibition, 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\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e1f2-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 26, "chroma:document": "Data 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]\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."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e274-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 26, "chroma:document": "19. 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.\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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e2f6-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e378-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "October 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.\n30. Nolte, K.; Maniere, J.; Owens, K. After-closure analysis of fracture calibration tests. In Proceedings of the SPE Annual Technical"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e404-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "Conference 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]\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e486-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "shale 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-\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e512-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "method. 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\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]"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e594-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "44. 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\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."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e616-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-00764.pdf", "page": 27, "chroma:document": "Sci.1946 ,187, 229\u2013260.\n48. 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e698-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/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\npeople or property resulting from any ideas, methods, instructions or products referred to in the content."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e7c4-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e850-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 0, "chroma:document": "*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\nobserving wellbore deformation, the SIMFIP tool determines the minimum principal stress, while"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e8d2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 0, "chroma:document": "strain 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-\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e954-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 0, "chroma:document": "experimental 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\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3e9e0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 0, "chroma:document": "fracture 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ea62-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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\nthe stimulation mode of a fracture. EGS Collab has undertaken a sequence of experiments"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3eae4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 1, "chroma:document": "involving 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\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3eb70-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 1, "chroma:document": "the 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\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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ebf2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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\nof the cage on the borehole wall (clamps correspond to points A and B in Figure 3). When"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ec7e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 2, "chroma:document": "the 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\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ed00-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 2, "chroma:document": "and 2019 during hydrofracturing experiments in boreholes drilled from drifts at the mine\n4890 ft and 4101 ft below ground surface (BGS), respectively."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ed82-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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)\nwhere Sfis the fracture stiffness, Wis the average fracture width, and Shmin is the minimum"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ee0e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 3, "chroma:document": "principal 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ee9a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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,\nand the probe stiffness. The main test cycles are then conducted. These tests are the"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ef1c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 4, "chroma:document": "classical 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\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ef9e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 4, "chroma:document": "10 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f020-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f0ac-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 5, "chroma:document": "164 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\nE1-I 164 tests (Guglielmi et al. (2022) [8]).\nNameInjection Duration\n(min:sec)Injection\nVolume, LAvg. Injection\nRate, L/minShut-In\nDuration, h"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f12e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 5, "chroma:document": "Volume, 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f1ba-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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\n(shut-in) in Figure 7 are almost identical. In E1-I 164 Test 3 is somewhat more complex"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f23c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 6, "chroma:document": "because 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f2be-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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\nmeasurements indicate reactivation of a cemented natural fracture set between the two"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f340-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 7, "chroma:document": "SIMFIP 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.\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f3c2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 7, "chroma:document": "shut-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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f444-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f4c6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 8, "chroma:document": "SIMFIP 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]).\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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f548-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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\nestimated from a plot of pressure versus cumulative \ufb02ow-back volume. A straight line is"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f5ca-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 9, "chroma:document": "drawn 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.\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f64c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 9, "chroma:document": "(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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f6d8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f750-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 10, "chroma:document": "creasing 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\nof the SIMFIP . These results indicate that conventional techniques may fail in analyzing\ncomplex or non-ideal tests."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f7dc-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 10, "chroma:document": "complex 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f868-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f8e0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f962-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3f9da-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 13, "chroma:document": "Figure 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\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3fa48-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 13, "chroma:document": "than 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3fac0-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3fb42-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 14, "chroma:document": "error) 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\ntest 4. It shows the average log signal energy using CWT of pressure versus time during"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3fbba-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 14, "chroma:document": "the 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3fc28-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3fcaa-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3fd22-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 16, "chroma:document": "closure 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3fd90-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3fe08-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 17, "chroma:document": "fracture 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\nTV4100 Test 7 19.03 (2760) 18.61 (2700) 42 10"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3fe80-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3fef8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 18, "chroma:document": "6. 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\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ff70-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 18, "chroma:document": "[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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae3ffde-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4004c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae400c4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 19, "chroma:document": "8. 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.\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."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4013c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 19, "chroma:document": "Sci.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.;\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."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae401b4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 19, "chroma:document": "15. 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.\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."}


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id: 9ae40236-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 19, "chroma:document": "18. 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae402b8-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40330-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/energies-16-02807.pdf", "page": 20, "chroma:document": "22. 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4042a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae404a2-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 0, "chroma:document": "turing 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 \nAt the present time there is no direct and simple \nprocedure for evaluating the basic parameters achieved"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4051a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 0, "chroma:document": "procedure 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 \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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4059c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 0, "chroma:document": "unit 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 \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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40614-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 0, "chroma:document": "would 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 \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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4068c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/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 = \nnCR /t (l+p) p 0"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40704-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 1, "chroma:document": "L = \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 \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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae4077c-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 1, "chroma:document": "In 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\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."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae407f4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 1, "chroma:document": "fracture 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 \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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40876-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 1, "chroma:document": "will 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae408ee-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/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 \nin-situ closure pressure of the formation, and E' is"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40970-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 2, "chroma:document": "in-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 \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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae409e8-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 2, "chroma:document": "Fig. 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 \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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40a6a-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 2, "chroma:document": "the 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. \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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40aec-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 2, "chroma:document": "any 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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40b64-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40be6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 3, "chroma:document": "time, 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 \nFig. 3, versus the actual ~hut-in time ~t. The field"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40c5e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 3, "chroma:document": "Fig. 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) \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."}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40ccc-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 3, "chroma:document": "fracture 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 \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)"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40d30-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 3, "chroma:document": "2CHP 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: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40d9e-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
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{"source": "drive/MyDrive/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 \nfluid efficiency than would result from the lower"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40e52-857d-11ee-bb1c-0242ac1c000c
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{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 4, "chroma:document": "fluid 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 \nterms in (21). However, more directly, noting that the \nterm in parentheses of the denominator of (25) relates"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40ed4-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 4, "chroma:document": "term 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\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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40f42-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 4, "chroma:document": "loss 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 \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"}


created_at: 2023-11-17 19:17:23
topic: persistent://default/default/8e5da3e9-8391-4ad8-a826-4d5919dbf381
id: 9ae40fa6-857d-11ee-bb1c-0242ac1c000c
encoding: FLOAT32
metadata:
{"source": "drive/MyDrive/Fracture closure Reviews/spe-8341-ms.pdf", "page": 4, "chroma:document": "tion, 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"}


