Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T16:16:48.961Z Has data issue: false hasContentIssue false
  • English
  • Français

An Efficient Numerical Model for Immiscible Two-Phase Flow in Fractured Karst Reservoirs

Published online by Cambridge University Press:  03 June 2015

Zhao-Qin Huang ,
Jun Yao  and
Yue-Ying Wang
Zhao-Qin Huang
Affiliation:
School of Petroleum Engineering, China University of Petroleum, Qingdao 266555, Shandong, China
Jun Yao*
Affiliation:
School of Petroleum Engineering, China University of Petroleum, Qingdao 266555, Shandong, China
Yue-Ying Wang
Affiliation:
School of Petroleum Engineering, China University of Petroleum, Qingdao 266555, Shandong, China
*
Corresponding author.Email:[email protected]
Get access

Abstract

Numerical simulation of two-phase flow in fractured karst reservoirs is still a challenging issue. The triple-porosity model is the major approach up to now. However, the triple-continuum assumption in this model is unacceptable for many cases. In the present work, an efficient numerical model has been developed for immiscible two-phase flow in fractured karst reservoirs based on the idea of equivalent continuum representation. First, based on the discrete fracture-vug model and homogenization theory, the effective absolute permeability tensors for each grid blocks are calculated. And then an analytical procedure to obtain a pseudo relative permeability curves for a grid block containing fractures and cavities has been successfully implemented. Next, a full-tensor simulator has been designed based on a hybrid numerical method (combining mixed finite element method and finite volume method). A simple fracture system has been used to demonstrate the validity of our method. At last, we have used the fracture and cavity statistics data from TAHE outcrops in west China, effective permeability values and other parameters from our code, and an equivalent continuum simulator to calculate the water flooding profiles for more realistic systems.

Keywords

35B2735Q3076S05Fractured karst reservoirseffective permeability tensordiscrete fracture-vug network modeltwo-phase flowfull-tensor simulator
Type
Research Article
Information
Communications in Computational Physics , Volume 13 , Issue 2 , February 2013 , pp. 540 - 558
Copyright
Copyright © Global Science Press Limited 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1]Popov, P., Efendiev, Y. and Qin, G., Multiscale modeling and simulations of flows in naturally fractured karst reservoirs, Commun. Comput. Phys., 6(1) (2009), 162–184.Google Scholar
[2]Gulbransen, A. V., Hauge, V. L. and Lie, K. A., A multiscale mixed finite element method for vuggy and naturally fractured reservoirs, SPE J., 15(2) (2010), 395–403.Google Scholar
[3]Arbogast, T. and Lehr, L. H., Homogenization of a Darcy-Stokes system modeling vuggy porous media, Comput. Geosci., 10(3) (2006), 291–302.Google Scholar
[4]Arbogast, T. and Brunson, D. S., A computational method for approximating a Darcy-Stokes system governing a vuggy porous medium, Comput. Geosci., 11 (2007), 207–218.Google Scholar
[5]Popov, P., Qin, G. and Bi, L.et al., Multiscale methods for modeling fluid flow through nat-urally fractured carbonate karst reservoirs, SPE paper 110778, presented at the 2007 SPE Annual Technical Conference and Exhibition, Anaheim, California, USA, 11-14 November, 2007.Google Scholar
[6]Popov, P., Bi, L. F. and Efendiev, Y.et al., Multiphysics and multiscale methods for modeling fluid flow through naturally fractured carbonate reservoirs, SPE paper 105378, presented at the 15th SPE Middle East Oil & Gas Show and Conference, Bahrain, 11-14 March, 2007.Google Scholar
[7]Gulbransen, A. F., Hauge, V. L. and Lie, K. A., A multiscale mixed finite-element method for vuggy and naturally-fractured reservoirs, Paper SPE 119104, presented at the 2009 SPE Reservoir Simulation Symposium, Woodlands, Texas, USA, 2-4 February, 2009.CrossRefGoogle Scholar
[8]Arbogast, T. and Gomez, M. S. M., A discretization and multigrid solver for a Darcy-Stokes system of three dimensional vuggy porous media, Comput. Geosci., 13 (2009), 331–348.Google Scholar
[9]Huang, Z. Q., Yao, J. and Li, Y. J.et al., Permeability analysis of fractured vuggy porous media based on homogenization theory, Sci. China Tech. Sci., 53(3) (2010), 839–847.Google Scholar
[10]Yao, J., Huang, Z. Q. and Li, Y. J.et al., Discrete Fracture-Vug network model for modeling fluid flow in fractured vuggy porous media, Paper SPE 130287-MS, presenred at the Inter-national Oil and Gas Conference and Exhibition in China, 8-10 June 2010, Beijing, China, 2010.Google Scholar
[11]Huang, Z. Q., Yao, J. and Li, Y. J.et al., Numerical calculation of equivalent permeability tensor for fractured vuggy porous media based on homogenization theory, Commun. Comput. Phys., 9(1) (2011), 180–204.Google Scholar
[12]Qin, G., Bi, L. F. and Popov, P.et al., An efficient upscaling process based on a unified fine-scale multi-physics model for flow simulation in naturally fracture carbonate karst reservoirs, paper SPE132236-MS, presenred at the International Oil and Gas Conference and Exhibition in China, 8-10 June 2010, Beijing, China, 2010.Google Scholar
[13]Wu, Y. S., Qin, G. and Ewing, R. E.et al., A multiple-continuum approach for modeling multi-phase flow in naturally fractured vuggy petroleum reservoirs, Paper SPE 104173, presented at the 2006 SPE International oil & Gas Conference and Exhibition, Beijing, China, 5-7 De-cember, 2006.Google Scholar
[14]Kang, Z. J., Wu, Y. S. and Li, J.et al., Modeling multiphase flow in naturally fractured vuggy petroleum reservoirs, Paper SPE 102356, presented at the 2006 SPE Annual Technical Conference and Exhibition, San Antonio, Texas, USA, 24-27 September, 2006.Google Scholar
[15]Wu, Y. S., Qin, G. and Kang, Z. J.et al., A triple-continuum pressure-transient model for a naturally fractured vuggy reservoir, Paper SPE 110044, presented at the 2007 SPE Annual Technical Conference and Exhibition, Anaheim, California, USA, 11-14 November, 2007.CrossRefGoogle Scholar
[16]Snow, D., Rock-fracture spacing, openings and porosities, J. Soil Mech. Founda. Div. ASCE., 94 (1968), 73–91.CrossRefGoogle Scholar
[17]Berkowitz, B., Bear, J. and Braester, C., Continuum models for contaminant transport in frac-tured porous formations, Water Resour. Res., 24 (1988), 1225–1236.Google Scholar
[18]Van Golf-Racht, T. D., Fundamentals of Fractured Reservoir Engineering, Amsterdam Else-vier, 1982.Google Scholar
[19]Nakashima, T., Arihara, N. and Sutopo, S., Effective permeability estimation for modeling naturally fractured reservoirs, Paper SPE 68124, presented at 2001 SPE Middle East Oil Show, Bahrain, 2001.CrossRefGoogle Scholar
[20]Bogdanov, I.I., Mourzenko, V. V. and Thovert, J. F.et al., Effective permeability of fractured porous media in steady state flow, Water Resour. Res., 39(1) (2003), 1023–1040.Google Scholar
[21]Bogdanov, I. I., Mourzenko, V. V. and Thovert, J. F.et al., Effective permeability of fractured porous media with power-law distribution of fracture sizes, Phys. Rev. E, 76(3) (2007), 036309–036325.CrossRefGoogle ScholarPubMed
[22]Beavers, G. S. and Joseph, D. D., Boundary condition at a naturally permeable wall, J. Fluid Mech., 30 (1967), 197–207.Google Scholar
[23]Saffman, P. G., On the boundary condition at the surface of a porous medium, Stud. Appl. Math., 1 (1971), 93–101.Google Scholar
[24]Hearn, C. L., Simulation of stratified waterflooding by pseudo relative permeability curves, SPE J. Petrol. Tech., 7 (1971), 805–813.Google Scholar
[25]Talleria, M. S., Virues, C. J. J. and Crotti, M. A., Pseudo relative permeability functions limitations in the use of the frontal advance theory for 2-dimensional systems, Paper SPE 54004, presented at the SPE Latin American and Caribbean Petroleum Engineering Conference, Caracas, Venezuela, 21-23 April, 1999.CrossRefGoogle Scholar
[26]Pruess, K., Wang, J. S. Y. and Tsang, Y. W., On the therm.ohydrologic conditions near high-level nuclear wastes emplaced in partially saturated fractured tuff, part 2: effective continuum approximation, Water Resour. Res., 26(6) (1990), 1249–1261.Google Scholar
[27]van Lingen, P., Daniel, J. M., Cosentino, L. and Sengul, M., Single medium simulation of reservoirs with conductive faults and fractures, Paper SPE 68165 presented at the SPE Middle East Oil Show, Bahrain, 17-20 March, 2001.Google Scholar
[28]Abdel-Ghani, Rida, Single porosity simulation of fractures with low to medium fracture-to-matrix permeability contrast, Paper SPE 125565, presented at the 2009 SPE/EAGE Reservoir Characterization and Simulation Conference held in Abu Dhabi, UAE, 19-21 October, 2009.Google Scholar
[29]Aavatsmark, I., An introduction to multipoint flux approximations for quadrilateral grids, Comput. Geosci., 6(3-4) (2002), 405–432.Google Scholar
[30]Aavatsmark, I., Eigestad, G. T. and Klausen, R. A.et al., Convergence of a symmetric MPFA method on quadrilateral grids, Comput. Geosci., 11 (2007), 333–345.Google Scholar
[31]Chen, Q. Y., Wan, J. and Yang, Y.et al., Enriched multipoint flux approximation for general grids, J. Comput. Phys., 227(3) (2008), 1701–1721.Google Scholar
[32]Lipnikov, K., Shashkov, M. and Yotov, I., Local flux mimetic finite difference methods, Numer. Math., 112(1) (2009), 115–152.Google Scholar
[33]Raviart, P. A. and Thomas, J. M., A mixed finite element method for second order elliptic equations, Mathematical Aspects of Finite Element Methods (Galligani, I. and Magenes, E., eds.), Springer-Verlag, Berlin-Heidelberg-New York, pp. 292–315, 1977.CrossRefGoogle Scholar
[34]Chavent, G. and Jaffre, J., Mathematical Models and Finite Elements for Reservoir Simulation, North Holland, 1982.Google Scholar
[35]Brezzi, F. and Fortin, M., Mixed and Hybrid Finite Element Methods, Springer-Verlag, New York, 1991.CrossRefGoogle Scholar
[36]Aarnes, J. E., On the use of a mixed multiscale finite element method for greater flexibility and increased speed or improved accuracy in reservoir simulation, Multiscale Model. Simul., 2(3) (2004), 421–439.Google Scholar
[37]Aarnes, J. E., Gimse, T. and Lie, K.-A., An introduction to the numerics of flow in porous media using Matlab, Geometric Modelling, Numerical Simulation and Optimization: Applied Mathematics at SINTEF (Hasle, G., Lie, K.-A. and Quak, E., eds.), Springer, Berlin/Heidelberg, pp. 265–306, 2007.Google Scholar
[38]Afif, M. and Amaziane, B., On convergence of finite volume schemes for one-dimensional two-phase flow in porous media, J. Comput. Appl. Math., 145 (2002), 31–48.Google Scholar
[39]Afif, M. and Amaziane, B., Convergence of finite volume schemes for a degenerate convection-diffusion equation arising in flow in porous media, Comput. Methods Appl. Mech. Eng., 191 (2002), 5265–5286.Google Scholar
[40]Afif, M. and Amaziane, B., Numerical simulation of two-phase flow through heterogeneous porous media, Numer. Algorithms, 34 (2003), 117–125.Google Scholar
[41]Huang, Z. Q., Yao, J. and Wang, Y. Y.et al., Numerical study on two-phase flow through fractured porous media, Sci. China Tech. Sci., 54(9) (2011), 2412–2420.CrossRefGoogle Scholar