An Efficient Numerical Hybrid Model for Multiphase Flow in Deformable Fractured-Shale Reservoirs
- Xia Yan (China University of Petroleum (East China); Heriot-Watt University) | ZhaoQin Huang (China University of Petroleum (East China)) | Jun Yao (China University of Petroleum (East China)) | Yang Li (Sinopec) | Dongyan Fan (China University of Petroleum (East China)) | Hai Sun (China University of Petroleum (East China)) | Kai Zhang (China University of Petroleum (East China))
- Document ID
- Society of Petroleum Engineers
- SPE Journal
- Publication Date
- August 2018
- Document Type
- Journal Paper
- 1,412 - 1,437
- 2018.Society of Petroleum Engineers
- Hydro-mechanical coupling, Embedded discrete fracture model, Shale reservoirs, Extended finite element method, Multiphase flow
- 16 in the last 30 days
- 307 since 2007
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After hydraulic fracturing, a shale reservoir usually has multiscale fractures and becomes more stress-sensitive. In this work, an adaptive hybrid model is proposed to simulate hydromechanical coupling processes in such fractured-shale reservoirs during the production period (i.e., the hydraulic-fracturing process is not considered and cannot be simulated). In our hybrid model, the single-porosity model is applied in the region outside the stimulated reservoir volume (SRV), and the matrix and natural/induced fractures in the SRV region are modeled using a double-porosity model that can accurately simulate the matrix/fracture fluid exchange during the entire transient period. Meanwhile, the fluid flow in hydraulic fractures is modeled explicitly with the embedded-discrete-fracture model (EDFM), and a stabilized extended-finite-element-method (XFEM) formulation using the polynomial-pressure-projection (PPP) technique is applied to simulate mechanical processes. The developed stabilized XFEM formulation can avoid the displacement oscillation on hydraulic-fracture interfaces. Then a modified fixed-stress sequential-implicit method is applied to solve the hybrid model, in which mixed-space discretization [i.e., finite-volume method (FVM) for flow process and stabilized XFEM for geomechanics] is used. The robustness of the proposed model is demonstrated through several numerical examples. In conclusion, several key factors for gas exploitation are investigated, such as adsorption, Klinkenberg effect, capillary pressure, and fracture deformation. In this study, all the numerical examples are 2D, and the gravity effect is neglected in these simulations. In addition, we assume there is no oil phase in the shale reservoirs, thus the gas/water two-phase model is used to simulate the flow in these reservoirs.
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An, F., Cheng, Y., Wu, D. et al. 2013. The Effect of Small Micropores on Methane Adsorption of Coals From Northern China. Adsorption 19 (1): 83–90. https://doi.org/10.1007/s10450-012-9421-3.
Barenblatt, G., Zheltov, I. P., and Kochina, I. 1960. Basic Concepts in the Theory of Seepage of Homogeneous Liquids in Fissured Rocks [Strata]. J. Appl. Math. Mech. 24 (5): 1286–1303. https://doi.org/10.1016/0021-8928(60)90107-6.
Berryman, J. G. 2002. Extension of Poroelastic Analysis to Double-Porosity Materials: New Technique in Microgeomechanics. J. Eng. Mech. 128 (8): 840–847. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:8(840).
Beskos, D. E. and Aifantis, E. C. 1986. On the Theory of Consolidation With Double Porosity—II. Int. J. Eng. Sci. 24 (11): 1697–1716. https://doi.org/10.1016/0020-7225(86)90076-5.
Biot, M. A. 1941. General Theory of Three-Dimensional Consolidation. J. Appl. Phys. 12: 155–164. https://doi.org/10.1063/1.1712886.
Blasingame, T. A. 2015. Reservoir Engineering Aspects of Unconventional Reservoirs. Oral presentation given at the Ask the Expert Session 3, Doha, 6–9 December.
Bochev, P. B., Dohrmann, C. R., and Gunzburger, M. D. 2006. Stabilization of Low-Order Mixed Finite Elements for the Stokes Equations. SIAM J. Numer. Anal. 44 (1): 82–101. https://doi.org/10.1137/S0036142905444482.
Bower, A. F. 2009. Applied Mechanics of Solids. Boca Raton, Florida: CRC Press.
Cai, L., Ding, D.-Y., Wang, C. et al. 2015. Accurate and Efficient Simulation of Fracture–Matrix Interaction in Shale-Gas Reservoirs. Transport Porous Med. 107 (2): 305–320. https://doi.org/10.1007/s11242-014-0437-x.
Cao, P., Liu, J., and Leong, Y.-K. 2016. A Fully Coupled Multiscale Shale Deformation-Gas Transport Model for the Evaluation of Shale Gas Extraction. Fuel 178 (15 August): 103–117. https://doi.org/10.1016/j.fuel.2016.03.055.
Cipolla, C. L., Lolon, E. P., Erdle, J. C. et al. 2010. Reservoir Modeling in Shale-Gas Reservoirs. SPE Res Eval & Eng 13 (4): 638–653. SPE-125530-PA. https://doi.org/10.2118/125530-PA.
Civan, F., Devegowda, D., and Sigal, R. F. 2013. Critical Evaluation and Improvement of Methods for Determination of Matrix Permeability of Shale. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September–2 October. SPE-166473-MS. https://doi.org/10.2118/166473-MS.
COMSOL. 2005. COMSOL Multiphysics User’s Guide, Version 333. Burlington, Massachusetts: COMSOL Inc. (10 September).
Cook, A. M., Myer, L. R., Cook, N. G. W. et al. 1990. The Effects of Tortuosity on Flow Through a Natural Fracture. In Rock Mechanics Contributions and Challenges, Proc., 31st US Symposium on Rock Mechanics, ed. W. A. Hustrulid and G. A. Johnson, 371–378. Rotterdam, The Netherlands: A. A. Balkema.
Cook, R. D. 1989. Concepts and Applications of Finite Element Analysis. Hoboken, New Jersey: John Wiley & Sons.
Dongyan, F., Jun, Y., Hai, S. et al. 2015. A Composite Model of Hydraulic Fractured Horizontal Well With Stimulated Reservoir Volume in Tight Oil & Gas Reservoir. J. Nat. Gas Sci. Eng. 24 (May): 115–123. https://doi.org/10.1016/j.jngse.2015.03.002.
Douglas, D. H. 1975. Guidance System for a Horizontal Drilling Apparatus. US Patent No. 3,907,045.
Fan, X., Li, G., Shah, S. N. et al. 2015. Analysis of a Fully Coupled Gas Flow and Deformation Process in Fractured Shale Gas Reservoirs. J. Nat. Gas Sci. Eng. 27/2 (November): 901–913. https://doi.org/10.1016/j.jngse.2015.09.040.
Freeman, C. M. 2010. A Numerical Study of Microscale Flow Behavior in Tight Gas and Shale Gas. Presented at the SPE Annual Technical Conference and Exhibition, Florence, Italy, 19–22 September. SPE-141125-STU. https://doi.org/10.2118/141125-STU.
Garipov, T. T., Karimi-Fard, M., and Tchelepi, H. A. 2014. Fully Coupled Flow and Geomechanics Model for Fractured Porous Media. Presented at the 48th US Rock Mechanics/Geomechanics Symposium, Minneapolis, Minnesota, 1–4 June. ARMA-2014-7460.
Giger, F. M., Reiss, L. H., and Jourdan, A. P. 1984. The Reservoir Engineering Aspects of Horizontal Drilling. Presented at the SPE Annual Technical Conference and Exhibition, Houston, 16–19 September. SPE-13024-MS. https://doi.org/10.2118/13024-MS.
Gong, B., Karimi-Fard, M., and Durlofsky, L. J. 2008. Upscaling Discrete Fracture Characterizations to Dual-Porosity, Dual-Permeability Models for Efficient Simulation of Flow With Strong Gravitational Effects. SPE J. 13 (1): 58–67. SPE-102491-PA. https://doi.org/10.2118/102491-PA.
Howard, G. C. and Fast, C. R. 1970. Hydraulic Fracturing. Richardson, Texas: Society of Petroleum Engineers.
Hu, L., Winterfeld, P. H., Fakcharoenphol, P. et al. 2013. A Novel Fully-Coupled Flow and Geomechanics Model in Enhanced Geothermal Reservoirs. J. Pet. Sci. Eng. 107 (July): 1–11. https://doi.org/10.1016/j.petrol.2013.04.005.
Huang, Z., Winterfeld, P. H., Xiong, Y. et al. 2015. Parallel Simulation of Fully-Coupled Thermal-Hydro-Mechanical Processes in CO2 Leakage Through Fluid-Driven Fracture Zones. Int. J. Greenh. Gas Contr. 34 (March): 39–51. https://doi.org/10.1016/j.ijggc.2014.12.012.
Huang, Z., Yan, X., and Yao, J. 2014. A Two-Phase Flow Simulation of Discrete-Fractured Media Using Mimetic Finite Difference Method. Commun. Computat. Phys. 16 (3): 799–816. https://doi.org/10.4208/cicp.050413.170314a.
Hubbert, M. K. and Willis, D. G. 1957. Mechanics of Hydraulic Fracturing. Petroleum Transactions, AIME, Vol. 210, 153–168. SPE-686-G.
Jenny, P., Lee, S. H., and Tchelep, H. A. 2004. Adaptive Multiscale Finite-Volume Method for Multiphase Flow and Transport in Porous Media. Multiscale Model. Simul. 3 (1): 50–64. https://doi.org/10.1137/030600795.
Jiang, J. and Younis, R. M. 2016. Hybrid Coupled Discrete-Fracture/Matrix and Multicontinuum Models for Unconventional-Reservoir Simulation. SPE J. 21 (3): 1009–1027. SPE-178430-PA. https://doi.org/10.2118/178430-PA.
Jurus, W. J., Whitson, C. H., and Golan, M. 2013. Modeling Water Flow in Hydraulically-Fractured Shale Wells. Presented at the SPE Annual Technical Conference and Exhibition, New Orleans, 30 September–2 October. SPE-166439-MS. https://doi.org/10.2118/166439-MS.
Karimi-Fard, M., Durlofsky, L. J., and Aziz, K. 2004. An Efficient Discrete-Fracture Model Applicable for General-Purpose Reservoir Simulators. SPE J. 9 (2): 227–236. SPE-88812-PA. https://doi.org/10.2118/88812-PA.
Karimi-Fard, M., Gong, B., and Durlofsky, L. J. 2006. Generation of Coarse-Scale Continuum Flow Models From Detailed Fracture Characterizations. Water Resour. Res. 42 (10), W10423, 13 pages. https://doi.org/10.1029/2006WR005015.
Karlsson, H., Jacques, G. E., Hatten, J. L. et al. 1992. Method and Apparatus for Horizontal Drilling. US Patent No. 5,148,875.
Khalili, N. 2003. Coupling Effects in Double Porosity Media With Deformable Matrix. Geophys. Res. Lett. 30 (22): 4-1–4-3. https://doi.org/10.1029/2003GL018544.
Khoei, A. R. 2015. Extended Finite Element Method: Theory and Applications. Hoboken, New Jersey: John Wiley & Sons.
Khoei, A. R., Hosseini, N., and Mohammadnejad, T. 2016. Numerical Modeling of Two-Phase Fluid Flow in Deformable Fractured Porous Media Using the Extended Finite Eement Method and an Equivalent Continuum Model. Adv. Water Resour. 94 (August): 510–528. https://doi.org/10.1016/j.advwatres.2016.02.017.
Kim, J. and Moridis, G. J. 2012. Numerical Studies on Coupled Flow and Geomechanics With the Multiple Porosity Model for Naturally Fractured Tight and Shale-Gas Reservoirs. Presented at the 46th US Rock Mechanics/Geomechanics Symposium, Chicago, 24–27 June. ARMA-2012-296.
Kim, J. and Moridis, G. J. 2014. Gas Flow Tightly Coupled to Elastoplastic Geomechanics for Tight- and Shale-Gas Reservoirs: Material Failure and Enhanced Permeability. SPE J. 19 (6): 1110–1125. SPE-155640-PA. https://doi.org/10.2118/155640-PA.
Kim, J., Sonnenthal, E. L., and Rutqvist, J. 2012. Formulation and Sequential Numerical Algorithms of Coupled Fluid/Heat Flow and Geomechanics for Multiple Porosity Materials. Int. J. Numer. Meth. Eng. 92 (5): 425–456. https://doi.org/10.1002/nme.4340.
Kim, J., Tchelepi, H. A., and Juanes, R. 2011. Stability and Convergence of Sequential Methods for Coupled Flow and Geomechanics: Fixed-Stress and Fixed-Strain Splits. Comput. Meth. Appl. Mech. Eng. 200 (13–16): 1591–1606. https://doi.org/10.1016/j.cma.2010.12.022.
Kim, N. H. 2014. Introduction to Nonlinear Finite Element Analysis. Berlin: Springer Science & Business Media.
Klinkenberg, L. 1941. The Permeability of Porous Media to Liquids and Gases. API-41-200.
Langmuir, I. 1917. The Constitution and Fundamental Properties of Solids and Liquids. J. Franklin Institute 183: 102–105.
Lee, S. H., Lough, M., and Jensen, C. 2001. Hierarchical Modeling of Flow in Naturally Fractured Formations With Multiple Length Scales. Water Resour. Res. 37 (3): 443–455. https://doi.org/10.1029/2000WR900340.
Leverett, M. 1941. Capillary Behavior in Porous Solids. Trans. AIME 142 (1): 152–169. SPE-941152-G. https://doi.org/10.2118/941152-G.
Li, L. and Lee, S. H. 2008. Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media. SPE Res Eval & Eng 11 (4): 750–758. SPE-103901-PA. https://doi.org/10.2118/103901-PA.
Liu, F. and Borja, R. I. 2010. Stabilized Low-Order Finite Elements for Frictional Contact With the Extended Finite Element Method. Comput. Meth. Appl. Mech. Eng. 199 (37–40): 2456–2471. https://doi.org/10.1016/j.cma.2010.03.030.
Liu, J., Chen, Z., Elsworth, D. et al. 2011. Interactions of Multiple Processes During CBM Extraction: A Critical Review. Int. J. Coal Geol. 87 (3–4): 175–189. https://doi.org/10.1016/j.coal.2011.06.004.
McClure, M. W., Babazadeh, M., Shiozawa, S. et al. 2016. Fully Coupled Hydromechanical Simulation of Hydraulic Fracturing in 3D Discrete-Fracture Networks. SPE J. 21 (4): 1302–1320. SPE-173354-PA. https://doi.org/10.2118/173354-PA.
Minkoff, S. E., Stone, C. M., Bryant, S. et al. 2003. Coupled Fluid Flow and Geomechanical Deformation Modeling. J. Pet. Sci. Eng. 38 (1–2): 37–56. https://doi.org/10.1016/S0920-4105(03)00021-4.
Moghaddam, R. N., Aghabozorgi, S., and Foroozesh, J. 2015. Numerical Simulation of Gas Production From Tight, Ultratight and Shale-Gas Reservoirs: Flow Regimes and Geomechanical Effects. Presented at EUROPEC 2015, Madrid, Spain, 1–4 June. SPE-174323-MS. https://doi.org/10.2118/174323-MS.
Moinfar, A., Varavei, A., Sepehrnoori, K. et al. 2012. Development of a Novel and Computationally-Efficient Discrete-Fracture Model to Study IOR Processes in Naturally Fractured Reservoirs. Presented at the SPE Improved Oil Recovery Symposium, Tulsa, 14–18 April. SPE-154246-MS. https://doi.org/10.2118/154246-MS.
Moinfar, A., Varavei, A., Sepehrnoori, K. et al. 2013. Development of a Coupled Dual Continuum and Discrete Fracture Model for the Simulation of Unconventional Reservoirs. Presented at the SPE Reservoir Simulation Symposium, The Woodlands, Texas, 18–20 February. SPE-163647-MS. https://doi.org/10.2118/163647-MS.
Ortega, J. M. and Rheinboldt, W. C. 1970. Iterative Solution of Nonlinear Equations in Several Variables. Cambridge, Massachusetts: Academic Press.
Pruess, K. 1985. A Practical Method for Modeling Fluid and Heat Flow in Fractured Porous Media. SPE J. 25 (1): 14–26. SPE-10509-PA. https://doi.org/10.2118/10509-PA.
Rahm, D. 2011. Regulating Hydraulic Fracturing in Shale Gas Plays: The Case of Texas. Energ. Policy 39 (5): 2974–2981. https://doi.org/10.1016/j.enpol.2011.03.009.
Ren, G., Jiang, J., and Younis, R. M. 2016. Fully Coupled Geomechanics and Reservoir Simulation for Naturally and Hydraulically Fractured Reservoirs. Presented at the 50th US Rock Mechanics/Geomechanics Symposium, Houseon, 26–29 June. ARMA-2016-364.
Ren, G., Jiang, J., and Younis, R. M. 2017. Fully-Coupled XFEM-EDFM Hybrid Model for Geomechanics and Flow in Fractured Reservoirs. Presented at the SPE Reservoir Simulation Conference, Montgomery, Texas, 20–22 February. SPE-182726-MS. https://doi.org/10.2118/182726-MS.
Ryder, R. T. 1996. Fracture Patterns and Their Origin in the Upper Devonian Antrim Shale Gas Reservoir of the Michigan Basin: A Review. Open-File Report No. 96–23, US Geological Survey, Reston, Virginia.
Sheng, M., Li, G., Shah, S. et al. 2012. Extended Finite Element Modeling of Multi-Scale Flow in Fractured Shale-Gas Reservoirs. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 8–10 October. SPE-159919-MS. https://doi.org/10.2118/159919-MS.
Song, W., Yao, J., Li, Y. et al. 2016. Apparent Gas Permeability in an Organic-Rich Shale Reservoir. Fuel 181 (1 October): 973–984. https://doi.org/10.1016/j.fuel.2016.05.011.
Tran, D., Settari, A., and Nghiem, L. 2004. New Iterative Coupling Between a Reservoir Simulator and a Geomechanics Module. SPE J. 9 (3): 362–369. SPE-88989-PA. https://doi.org/10.2118/88989-PA.
Versteeg, H. and Malalasekera, W. 1995. An Introduction to Computational Fluid Dynamics: The Finite Volume Method. Gambrills, Maryland: Pearson Education.
White, J. and Borja, R. 2008. Stabilized Low-Order Finite Elements for Coupled Solid-Deformation/Fluid-Diffusion and Their Application to Fault Zone Transients. Comput. Meth. Appl. Mech. Eng. 197 (49–50): 4353–4366. https://doi.org/10.1016/j.cma.2008.05.015.
Winterfeld, P. H. and Wu, Y.-S. 2016. Simulation of Coupled Thermal/Hydrological/Mechanical Phenomena in Porous Media. SPE J. 21 (3): 1041–1049. SPE-173210-PA. https://doi.org/10.2118/173210-PA.
Witherspoon, P. A., Wang, J. S. Y., Iwai, K. et al. 1980. Validity of Cubic Law for Fluid Flow in a Deformable Rock Fracture. Water Resour. Res. 16 (6): 1016–1024. https://doi.org/10.1029/WR016i006p01016.
Wu, Y. S., Li, J., Ding, D. et al. 2014. A Generalized Framework Model for the Simulation of Gas Production in Unconventional Gas Reservoirs. SPE J. 19 (5): 845–857. SPE-163609-PA. https://doi.org/10.2118/163609-PA.
Yan, X., Huang, Z., Yao, J. et al. 2016a. An Efficient Hybrid Model for Fractured Reservoirs. Sci. China Technol. Sci. 59 (10): 1609–1616. https://doi.org/10.1007/s11431-016-6104-4.
Yan, X., Huang, Z., Yao, J. et al. 2016b. An Efficient Embedded Discrete Fracture Model Based on Mimetic Finite Difference Method. J. Pet. Sci. Eng. 145 (September): 11–21. https://doi.org/10.1016/j.petrol.2016.03.013.
Yan, X., Huang, Z., Yao, J. et al. 2016c. Theoretical Analysis of Fracture Conductivity Created by the Channel Fracturing Technique. J. Nat. Gas. Sci. Eng. 31 (April): 320–330. https://doi.org/10.1016/j.jngse.2016.03.038.
Yu, W. and Sepehrnoori, K. 2014a. Simulation of Gas Desorption and Geomechanics Effects for Unconventional Gas Reservoirs. Fuel 116 (15 January): 455–464. https://doi.org/10.1016/j.fuel.2013.08.032.
Yu, W. and Sepehrnoori, K. 2014b. An Efficient Reservoir-Simulation Approach To Design and Optimize Unconventional Gas Production. J Can Pet Technol 53 (2): 109–121. SPE-165343-PA. https://doi.org/10.2118/165343-PA.
Zeng, Q., Yao, J., and Shao, J. 2018. Numerical Study of Hydraulic Fracture Propagation Accounting for Rock Anisotropy. J. Pet. Sci. Eng. 160 (January): 422–432. https://doi.org/10.1016/j.petrol.2017.10.037.
Zerzar, A. and Bettam, Y. 2004. Interpretation of Multiple Hydraulically Fractured Horizontal Wells in Closed Systems. Presented at the Canadian International Petroleum Conference, Calgary, 8–10 June. PETSOC-2004-027. https://doi.org/10.2118/2004-027.
Zhang, T., Ellis, G. S., Ruppel, S. C. et al. 2012. Effect of Organic-Matter Type and Thermal Maturity on Methane Adsorption in Shale-Gas Systems. Organ. Geochem. 47 (June): 120–131. https://doi.org/10.1016/j.orggeochem.2012.03.012.
Zhang, W. and Kobaisi, A. M. 2017. A Globally Coupled Pressure Method for the Discretization of the Tensor-Pressure Equation on Non-K-Orthogonal Grids. SPE J. 22 (2): 679–698. SPE-184405-PA. https://doi.org/10.2118/184405-PA.