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Three-dimensional finite element simulation of three-phase flow in a deforming fissured reservoir. (English) Zbl 1138.76387

Summary: The development of a capacity to predict the exploitation of structurally complicated and fractured oil reservoirs is essential for the rational use of investment capital. A poor understanding of how the reservoir behaves during production may lead to inept, costly and inefficient development schemes. The mathematical formulation of a three-phase, three-dimensional fluid flow and rock deformation in fractured reservoirs is hence presented. The present formulation, consisting of both the equilibrium and multiphase mass conservation equations, accounts for the significant influence of coupling between the fluid flow and solid deformation, an aspect usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretise the governing equations in space and a finite difference scheme is used to march the solution in time. The final set of equations, which contain the additional cross coupling terms as compared to similar existing models, are highly non-linear and the elements of the coefficient matrices are updated implicitly during each iteration in terms of the independent variables. A field scale example is employed as an alpha case to test the validity and robustness of the currently formulation and numerical scheme. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered.

MSC:

76M10 Finite element methods applied to problems in fluid mechanics
76T30 Three or more component flows
86A05 Hydrology, hydrography, oceanography
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[1] Aifantis, E. C., Introducing a multi-porous medium, Developments Mech., 9, 46-69 (1985)
[2] Aziz, K.; Settari, A., Petroleum Reservoir Simulation (1979), Applied Science Publishers: Applied Science Publishers London
[3] Bai, M.; Elsworth, D.; Roegiers, J. C., Modelling of naturally fractured reservoir using deformation dependent flow mechanism, Int. J. Rock. Mech. Min. Sci. Geomech., 30, 1185-1191 (1993)
[4] Bai, M.; Meng, F.; Roegiers, J. C.; Abousleiman, Y., Modelling two-phase fluid flow and rock deformation in fractured porous media, (Thimus; etal., Poromechanics (1998), Balkema: Balkema Rotterdam) · Zbl 0933.74062
[5] Bai, M.; Meng, F.; Elsworth, D.; Abousleiman, Y.; Roegiers, J. C., Numerical modelling of coupled flow and deformation in fractured rock specimens, Int. J. Numer. Anal. Meth. Geomech., 23, 141-160 (1999) · Zbl 0933.74062
[6] Barenblatt, G. I.; Zheltov, I. P.; Kochina, I. N., Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech., USSR, 24, 1286-1303 (1960) · Zbl 0104.21702
[7] J.G. Berryman, H.F. Wang, The elastic coefficients of double-porosity models for fluid transport in jointed rock, UCRL-JC-119722, 1995; J.G. Berryman, H.F. Wang, The elastic coefficients of double-porosity models for fluid transport in jointed rock, UCRL-JC-119722, 1995
[8] Biot, M. A., General theory of three dimensional consolidation, J. Appl. Phys., 12, 155-163 (1941) · JFM 67.0837.01
[9] H.Y. Chen, L.W. Teufel, Coupling fluid-flow and geomechanics in dual-porosity modeling of naturally fractured reservoirs, Paper SPE 38884 presented at SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 1997; H.Y. Chen, L.W. Teufel, Coupling fluid-flow and geomechanics in dual-porosity modeling of naturally fractured reservoirs, Paper SPE 38884 presented at SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 1997
[10] Cho, T. F.; Plesha, M. E.; Haimson, B. C., Continuum modelling of jointed porous rock, Int. J. Numer. Anal. Meth. Geom., 15, 333-353 (1991) · Zbl 0825.73613
[11] Firoozabadi, A.; Thomas, L. K., Sixth SPE comparative solution project: dual-porosity simulators, JPT, 42, 710-715 (1990)
[12] Ghafouri, H. R.; Lewis, R. W., A finite element double porosity model for heterogeneous deformable porous media, Int. J. Numer. Anal. Meth. Geom., 20, 831-844 (1996)
[13] Hughes, T. J.R., The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Dover Reprinted Series (2000), Dover: Dover New York · Zbl 1191.74002
[14] Khaled, M. Y.; Beskos, D. E.; Aifantis, E. C., On the theory of consolidation with double porosity-III a finite element formulation, Int. J. Numer. Anal. Meth. Geom., 8, 101-123 (1984) · Zbl 0586.73116
[15] Khalili, N.; Valliappan, S., Unified theory of flow and deformation in double porous media, Eur. J. Mech A/Solid, 15, 321-336 (1996) · Zbl 0942.74013
[16] Lewis, R. W.; Ghafouri, H. R., A novel finite element double porosity model for multiphase flow through deformable fractured porous media, Int. J. Numer. Anal. Meth. Geom., 21, 789-816 (1997)
[17] Lewis, R. W.; Schrefler, B. A., The Finite Element Method in the Static and Dynamics Deformation and Consolidation of Porous Media, 2nd Ed. (1998), Wiley: Wiley Chichester · Zbl 0935.74004
[18] I. Masters, W.K.S. Pao, R.W. Lewis, Coupling temperature to double porosity deformable porous media, Int. J. Numer. Meth. Engrg. 49 (2000) 421-438; I. Masters, W.K.S. Pao, R.W. Lewis, Coupling temperature to double porosity deformable porous media, Int. J. Numer. Meth. Engrg. 49 (2000) 421-438 · Zbl 0972.74066
[19] Oda, M., Permeability tensor for discontinuous rock masses, Geotechnique, 35, 483-495 (1985)
[20] W.K.S. Pao, Coupling Flow and Subsidence model for Petroleum Reservoir. Fractured Reservoir Project, Confidential report submitted to UWS, NGI, BP-AMOCO, Total Fina Elf and Norwegian Research Council, 1998; W.K.S. Pao, Coupling Flow and Subsidence model for Petroleum Reservoir. Fractured Reservoir Project, Confidential report submitted to UWS, NGI, BP-AMOCO, Total Fina Elf and Norwegian Research Council, 1998
[21] Pao, W. K.S.; Masters, I.; Lewis, R. W., Integrated flow and subsidence simulation for hydrocarbon reservoir, (Seventh Annual Conference of ACME’99 (1999)), 175-178
[22] W.K. Pao, Aspects of continuum modelling and numerical simulations of coupled multiphase deformable non-isothermal porous continua, PhD Dissertation, Mech. Engrg. Dept., University of Wales Swansea, Swansea, UK, 2000; W.K. Pao, Aspects of continuum modelling and numerical simulations of coupled multiphase deformable non-isothermal porous continua, PhD Dissertation, Mech. Engrg. Dept., University of Wales Swansea, Swansea, UK, 2000
[23] W.K.S. Pao, R.W. Lewis, I. Masters, A fully coupled hydro-thermo-poro-mechanical model for black oil reservoir simulation, Int. J. Numer. Anal. Meth. Geom. 25 (2001) 1229-1256; W.K.S. Pao, R.W. Lewis, I. Masters, A fully coupled hydro-thermo-poro-mechanical model for black oil reservoir simulation, Int. J. Numer. Anal. Meth. Geom. 25 (2001) 1229-1256 · Zbl 1016.74023
[24] Schrefler, B. A.; Gawin, D., The effective stress principle: incremental or finite form, Int. J. Numer. Anal. Meth. Geom., 20, 785-815 (1996)
[25] Schrefler, B. A.; Simoni, L., Comparison between different finite element solutions for immiscible two-phase flow in deforming porous media, (Beer, G.; etal., Comp. Meth. Adv. Geomech. 2 (1991)), 1215-1220
[26] Singh, B., Continuum characterization of jointed rock masses. Part I: the constitutive equations, Int. J. Rock Mech. Min. Sci. Geomech. Abstr., 10, 311-335 (1973)
[27] Thomas, L. K.; Dixon, T. N.; Pierson, R. G., Fractured reservoir simulation, (SPERE (1983)), 42-54
[28] Valliappan, S.; Khalili-Naghadeh, N., Flow through fissured porous media with deformable matrix, Int. J. Numer. Meth. Eng., 29, 1079-1094 (1990) · Zbl 0704.73082
[29] Van Golf-Racht, T. D., Fundamental of Fractured Reservoir Engineering (1982), Elsevier: Elsevier Amsterdam
[30] Warren, J. E.; Root, P. J., The behaviour of naturally fractured reservoir, Trans. AIME, SPEJ, 228, 244-255 (1963)
[31] Wilson, R. K.; Aifantis, E. C., On the theory of consolidation with double porosity, Int. J. Engng. Sci., 20, 1009-1035 (1982) · Zbl 0493.76094
[32] R.W. Zimmerman, G. Chen, G.S. Bodvarsson, A dual-porosity reservoir model with improved coupling term, 17th Stanford Geothermal Reservoir Engineering Workshop, January 27-29, 1992; R.W. Zimmerman, G. Chen, G.S. Bodvarsson, A dual-porosity reservoir model with improved coupling term, 17th Stanford Geothermal Reservoir Engineering Workshop, January 27-29, 1992
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