Compressibility, Porosity, and Permeability of Shales Involving Stress Shock and Loading/Unloading Hysteresis
- Faruk Civan (University of Oklahoma)
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- December 2019
- Document Type
- Journal Paper
- 2,458 - 2,481
- 2019.Society of Petroleum Engineers
- stress, compressibility, permeability, porosity, hysteresis
- 27 in the last 30 days
- 191 since 2007
- Show more detail
- View rights & permissions
|SPE Member Price:||USD 12.00|
|SPE Non-Member Price:||USD 35.00|
This paper presents the theory, formulation, and correlation of the compressibility, porosity, and permeability of shale reservoirs by considering the effects of stress shock causing a slope discontinuity and loading/unloading hysteresis. The slope discontinuity occurs because the relative contributions of the matrix or fracture change at a critical effective stress depending on whether the process is loading or unloading. The hysteresis phenomenon occurs because of partially reversible and irreversible deformations of the various shale rock constituents by various processes during loading and unloading. Two successful modeling approaches are developed for describing the stress dependency of the petrophysical properties of porous rock formations. The first approach implements a kinetic model leading to a modified power-law equation, and the second approach applies an elastic cylindrical pore-shell model leading to a semianalytical equation. The primary advantage of the kinetic model is its applicability to any stress-dependent property, including strain, void ratio, porosity, pore compressibility, and permeability, thus making it a universal method. The semianalytical equation derived from an elastic cylindrical pore-shell model is applicable only for correlation of permeability. Both approaches are shown to yield high-quality correlations of the properties of porous rocks with effective stress by honoring the slope discontinuity observed at a critical effective stress.
|File Size||1 MB||Number of Pages||24|
Al-Wardy, W. and Zimmerman, R. W. 2004. Effective Stress Law for the Permeability of Clay-Rich Sandstones. J Geophys Res Solid Earth 109 (B4): 10 pages. https://doi.org/10.1029/2003JB002836.
Bernabé, Y. 1986. The Effective Pressure Law for Permeability in Chelmsford Granite and Barre Granite. Int J Rock Mech Min Sci 23 (3): 267–275. https://doi.org/10.1016/0148-9062(86)90972-1.
Biot, M. A. 1941. General Theory of Three-Dimensional Consolidation. J Appl Phys 12 (2): 155–164. https://doi.org/10.1063/1.1712886.
Biot, M. A. and Willis, D. G. 1957. The Elastic Coefficients of the Theory of Consolidation. J Appl Mech 24: 594–601.
Byerlee, J. D. and Zoback, M. D. 1975. Permeability and Effective Stress: Geologic Notes. AAPG Bull 59 (1): 154–158. https://doi.org/10.1306/83D91C40-16C7-11D7-8645000102C1865D.
Carman, P. C. 1937a. The Determination of the Specific Surface of Powder: I. J Soc Chem Ind 57: 225.
Carman, P. C. 1937b. Fluid Flow Through Granular Beds. Trans Inst Chem Eng 15: 150–167.
Carman, P. C. 1956. Flow of Gases Through Porous Media. London: Butterworths.
Civan, F. 2000. Reservoir Formation Damage-Fundamentals, Modeling, Assessment, and Mitigation, first edition. Houston, Texas: Gulf Publishing Company.
Civan, F. 2011. Porous Media Transport Phenomena. Hoboken, New Jersey: John Wiley & Sons.
Civan, F. 2017. Phenomenological Correlation of Pressurization/Depressurization Hysteresis of Stress-Dependent Porosity and Permeability of Shale Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 9–11 October. SPE-187041-MS. https://doi.org/10.2118/187041-MS.
Civan, F. 2018a. Effect of Stress Shock and Pressurization/Depressurization Hysteresis on Petrophysical Properties of Naturally-Fractured Reservoir Formations. Paper presented at the SPEWestern RegionalMeeting, Garden Grove, California, 22–27April. SPE-190081-MS. https://doi.org/10.2118/190081-MS.
Civan, F. 2018b. Stress Dependency of Permeability Represented by an Elastic Cylindrical Pore-Shell Model: Comment on Zhu et al. (Transp Porous Med (2018) 122: 235–252). Transp Porous Med 127 (3): 573–585. https://doi.org/10.1007/s11242-018-1213-0.
Dickinson, G. 1953. Reservoir Pressure in Gulf Coast Louisiana. Am Assoc Pet Geol Bull 37 (2): 410–432.
Dong, J. J., Hsu, J. Y., Wu, W. J. et al. 2010. Stress-Dependence of the Permeability and Porosity of Sandstone and Shale From TCDP Hole-A. Int J Rock Mech Min Sci 47 (7): 1141–1157. https://doi.org/10.1016/j.ijrmms.2010.06.019.
Gangi, A. F. 1978. Variation of Whole and Fractured Porous Rock Permeability With Confining Pressure. Int J Rock Mech Mining Sci 15 (5): 249–257. https://doi.org/10.1016/0148-9062(78)90957-9.
Gensterblum, Y., Ghanizadeh, A., Cuss, R. J. et al. 2015. Gas Transport and Storage Capacity in Shale Gas Reservoirs—A Review. Part A: Transport Processes. J Unconventional Oil Gas Res 12: 87–122. https://doi.org/10.1016/j.juogr.2015.08.001.
Ghabezloo, S., Sulem, J., Guedon, S. et al. 2009. Effective Stress Law for the Permeability of a Limestone. Int J Rock Mech Min 46 (2): 297–306. https://doi.org/10.1016/j.ijrmms.2008.05.006.
Gutierrez, M., Katsuki, D., and Tutuncu, A. 2015. Determination of the Continuous Stress-Dependent Permeability, Compressibility and Poroelasticity of Shale. Mar Pet Geol 68: 614–628. https://doi.org/10.1016/j.marpetgeo.2014.12.002.
Heller, R., Vermylen, J., and Zoback, M. 2014. Experimental Investigation of Matrix Permeability of Gas Shales. AAPG Bull 98 (5): 975–995. https://doi.org/10.1306/09231313023.
Hoholick, J. D., Metarko, T., and Potter, P. E. 1984. Regional Variations of Porosity and Cement; St. Peter and Mount Simon Sandstones in Illinois Basin. AAPG Bull 68 (6): 753–764.
Jaeger, J. C., Cook, N. G. W., and Zimmerman, R. W. 2007. Fundamentals of Rock Mechanics. Hoboken, New Jersey: Blackwell Publishing.
Jones, F. O. 1975. A Laboratory Study of the Effects of Confining Pressure on Fracture Flow and Storage Capacity in Carbonate Rocks. J Pet Technol 27 (1): 21–27. SPE-4569-PA. https://doi.org/10.2118/4569-PA.
Jones, F. O. and Owens, W. W. 1980. A Laboratory Study of Low Permeability Gas Sands. J Pet Technol 32 (9): 1631–1640. SPE-7551-PA. https://doi.org/10.2118/7551-PA.
Jones, C., Somerville, J., Smart, B. et al. 2001. Permeability Prediction Using Stress Sensitive Petrophysical Properties. Pet Geosci 7 (2): 211–219. https://doi.org/10.1144/petgeo.7.2.211.
Kozeny, J. 1927. Uber Kapillare Leitung des Wasser im Boden. In Proc., Sitzungsbericht der Akademie der Wissenschaften, Wien, 136, 271–306.
Kümpel, H.-J. 1991. Poroelasticity: Parameters Reviewed. Geophys J Int 105 (3): 783–799. https://doi.org/10.1111/j.1365-246X.1991.tb00813.x.
Kwon, O., Kronenberg, A. K., Gangi, A. F. et al. 2001. Permeability of Wilcox Shale and Its Effective Pressure Law. J Geophys Res 106 (B9): 19339–19353.
Lamé, G. 1852. Leçons sur la Théorie Mathématique de l’Élasticité des Corps Solides. Paris: Bachelier.
Lei, Q., Xiong, W., Yuan, J. et al. 2007. Analysis of Stress Sensitivity and Its Influence on Oil Production From Tight Reservoirs. Presented at the SPE Eastern Regional Meeting, Lexington, Kentucky, 17–19 October. SPE-111148-MS. https://doi.org/10.2118/111148-MS.
Morris, J. P., Lomov, I. N., and Glenn, L. A. 2003. A Constitutive Model for Stress-Induced Permeability and Porosity Evolution of Berea Sandstone. J Geophys Res 108 (B10): 2485. https://doi.org/10.1029/2001JB000463.
Morrow, C. A., Shi, L. Q., and Byerlee, J. D. 1984. Permeability of Fault Gouge Under Confining Pressure and Shear Stress. J Geophys Res Solid Earth 89: 3193–3200. https://doi.org/10.1029/JB089iB05p03193.
Nelson R. 1975. Fracture Permeability in Porous Reservoirs: Experimental and Field Approach. PhD dissertation, Texas A&M University, College Station, Texas.
Nur, A. and Byerlee, J. 1971. An Exact Effective Stress Law for Elastic Deformation of Rock With Fluids. J Geophys Res 76: 6414–6419. https://doi.org/10.1029/JB076i026p06414.
Ostensen, R. W. 1986. The Effect of Stress-Dependent Permeability on Gas Production and Well Testing. SPE Form Eval 1 (3): 227–235. SPE-11220-PA. https://doi.org/10.2118/11220-PA.
Paterson, M. S. 1978. Experimental Rock Deformation: The Brittle Field. New York: Springer-Verlag.
Qiao, L. P., Wong, R. C. K., Aguilera, R. et al. 2012. Determination of Biot’s Effective-Stress Coefficient for Permeability of Nikanassin Sandstone. J Can Pet Technol 51 (3): 1–5. SPE-150820-PA. https://doi.org/10.2118/150820-PA.
Schmoker, J. W. and Halley, R. B. 1982. Carbonate Porosity Versus Depth: A Predictable Relation for South Florida. Am Assoc Pet Geol Bull 66 (12): 2561–2570.
Seeburger, D. A. and Nur, A. A. 1984. Pore Space Model for Rock Permeability and Bulk Modulus. J Geophys Res 89 (B1): 527–536. https://doi.org/10.1029/JB089iB01p00527.
Shi, J. -Q. and Durucan, S. 2016. Near-Exponential Relationship Between Effective Stress and Permeability of Porous Rocks Revealed in Gangi’s Phenomenological Models and Application to Gas Shales. Int J Coal Geol 154–155: 111–122. https://doi.org/10.1016/j.coal.2015.12.014.
Sigal, R. F. 2002. The Pressure Dependence of Permeability. Petrophysics 43 (2): 1–11. SPWLA-2002-v43n2a3.
Silvano, S. 2010. Mathematical Model of the Lame’ Problem for Simplified Elastic Theory Applied to Controlled-Clearance Pressure Balances. Arxiv ID: 2010arXiv1007.0813S. New York: Cornell University.
Teklu, T. W., Zhou, Z., Li, X. et al. 2016a. Experimental Investigation on Permeability and Porosity Hysteresis in Low-Permeability Formations. Presented at the at the SPE Low Perm Symposium, Denver, Colorado, 5–6 May. SPE-180226-MS. https://doi.org/10.2118/180226-MS.
Teklu, T. W., Zhou, Z., Li, X. et al. 2016b. Cyclic Permeability and Porosity Hysteresis in Mudrocks—Experimental Study. Presented at the 50th US Rock Mechanics/Geomechanics Symposium, Houston, Texas, 26–29 June. ARMA-2016-108.
Walls, J. and Nur, A. 1979. Pore Pressure and Confining Pressure Dependence of Permeability in Sandstone. Presented at the 7th Formation Evaluation Symposium, Canadian Well Logging Society, Calgary, 5–7 May.
Walsh, J. B. 1981. Effect of Pore Pressure and Confining Pressure on Fracture Permeability. Int J Rock Mech Min Sci 18 (5): 429–435. https://doi.org/10.1016/0148-9062(81)90006-1.
Wang, S. and Civan, F. 2005. Preventing Asphaltene Deposition in Oil Reservoirs by Early Water Injection. Presented at the Production Operations Symposium, Oklahoma City, Oklahoma, 17–19-April. SPE-94268-MS. https://doi.org/10.2118/94268-MS.
Wenlian, X., Tao, L., Min, L. et al. 2016. Evaluation of the Stress Sensitivity in Tight Reservoirs. Pet Explor Dev 43 (1): 115–123. https://doi.org/10.1016/S1876-3804(16)30013-1.
Yale, D. P. 1984. Network Modeling of Flow, Storage, and Deformation in Porous Rocks. Dissertation, Stanford University, Stanford, California (August 1984).
Yan, C., Cheng, Y., Deng, F., et al. 2017. Permeability Change Caused by Stress Damage of Gas Shale. Energies 10 (1350): 1–11. https://doi.org/10.3390/en10091350.
Yarushina, V. M., Bercovici, D., and Oristaglio, M. L. 2013. Rock Deformation Models and Fluid Leak-Off in Hydraulic Fracturing. Geophys J Int 194: 1514–1526. https://doi.org/10.1093/gji/ggt199.
Yarushina, V. M. and Podladchinov, Y. Y. 2014. (De)compaction of Porous Viscoelastoplastic Media: Model Formulation. J Geophys Res Solid Earth 120 (6): 4146–4170. https://doi.org/10.1002/2014JB011258.
Zhu, S. Y., Du, Z., Li, M. et al., 2018. A Semi-Analytical Model for Pressure-Dependent Permeability of Tight Sandstone Reservoirs. Transp Porous Med 122 (2): 235–252. https://doi.org/10.1007/s11242-018-1001-x.
Zhu, W. and Wong, T.- F. 1997. The Transition From Brittle Faulting to Cataclastic Flow: Permeability Evolution. J Geophys Res 102 (B2): 3027–3041. https://doi.org/10.1029/96JB03282.
Zimmerman, R. W. 1991. Compressibility of Sandstones, Developments in Petroleum Science, 29. Amsterdam, The Netherlands: Elsevier.
Zoback, M. D. and Byerlee, J. D. 1975. The Effect of Microcrack Dilatancy on the Permeability of Westerly Granite. J Geophys Res 80 (5): 752–755. https://doi.org/10.1029/JB080i005p00752.