Abstract
This paper presents an object-oriented programming approach for the design of numerical homogenization programs, called JHomogenizer. It currently includes five functional modules to compute effective permeability and simple codes for computing solutions for flow in porous media. Examples with graphical output are shown to illustrate some functionalities of the program. A series of numerical examples demonstrates the effectiveness of the methodology for two-phase flow in heterogeneous reservoirs. The software is freely available, and the open architecture of the program facilitates further development and can adapt to suit specific needs easily and quickly.
Similar content being viewed by others
References
Amaziane, B.: Global behavior of compressible three-phase flow in heterogeneous porous media. Transp. Porous Media 10, 43–56 (1993)
Amaziane, B., Bourgeat, A., Koebbe, J.: Numerical simulation and homogenization of two-phase flow in heterogeneous porous media. Transp. Porous Media 6, 519–547 (1991)
Amaziane, B., Hontans, T., Koebbe, J.: Equivalent permeability and simulation of two-phase flow in heterogeneous porous media. Comput. Geosci. 5, 279–300 (2001)
Arbogast, T., Douglas, J., Hornung, U.: Derivation of the double porosity model of single phase flow via homogenization theory. SIAM J. Math. Anal. 21, 823–826 (1990)
Arbogast, T.: Computational aspects of dual-porosity models. In: Hornung, U. (ed.) Homogenization and Porous Media, pp. 203–223. Springer, Berlin Heidelberg New York (1997)
Badea, A., Bourgeat, A.: Homogenization of two phase flow through randomly heterogeneous porous media. In: Bourgeat, A. et al. (eds.) Proceedings of the Conference Mathematical Modelling of Flow Through Porous Media, pp. 44–58. World Scientific, Singapore (1995)
Badea, A., Bourgeat, A.: Numerical simulations by homogenization of two-phase flow through randomly heterogeneous porous media. In: Helmig, R. et al. (eds.) Notes on Numerical Fluid Mechanics, Modeling and Computation in Environmental Sciences , vol. 59, pp. 13–24 (1997)
Bakhvalov, N., Panasenko, G.: Homogenisation: Averaging Processes in Periodic Media Kluwer Academic Publishers, Dordrecht (1989)
Balls, D.: Numerical methods and simulation applied to optimize heating designs, Master’s Thesis, Utah State University, Logan, Utah (2004)
Bear, J., Bachmat, Y.: Introduction to Modeling of Transport Phenomena in Porous Media. Kluwer Academic Publishers, London (1991)
Bensoussan, A., Lions, J.L., Papanicolaou, G.: Asymptotic Analysis for Periodic Structures. North-Holland, Amsterdam (1978)
Bourgeat, A.: Two-phase flow. In: Hornung, U. (ed.) Homogenization and Porous Media, pp. 95–128. Springer, Berlin Heidelberg New York (1997)
Bourgeat, A., Hidani, A.: Effective model of two-phase flow in a porous medium made of different rock types. Appl. Anal. 58, 1–29 (1995)
Bourgeat, A., Kozlov, S.M., Mikelic, A.: Effective equations of two-phase flow in random media. Calc. Var. 3, 385–406 (1995)
Bourgeat, A., Jurak, M., Piatnitski, A.: Averaging a transport equation with small diffusion and oscillating velocity. Math. Methods Appl. Sci. 26, 95–117 (2003)
Bourgeat, A., Piatnitski, A.: Approximation of effective coefficients in stochastic homogenization, Ann. Inst. Henri Poincaré B 40, 153–165 (2004)
Brezzi, F., Fortin, M.: Mixed and Hybrid Finite Element Methods. Springer, Berlin Heidelberg New York (1991)
Ciarlet, P.G.: The Finite Element Method for Elliptic Problems. North-Holland, Amsterdam (1978)
Cioranescu, D., Donato, P.: An Introduction to Homogenization. Oxford University Press, Oxford (1999)
Farmer, C.L.: Upscaling: A review. Int. J. Numer. Meth. Fluids 40, 63–78 (2002)
Hornung, U.: Homogenization and Porous Media. Interdisciplinary Applied Mathematics. Springer, Berlin Heidelberg New York (1997)
Jikov, V.V., Kozlov, S.M., Oleinik, O.A.: Homogenization of Differential Operators and Integral Functionals. Springer, Berlin Heidelberg New York (1994)
Koebbe, J.: A computationally efficient modification of mixed finite element methods for flows problems with full transmissivity tensors. Numer. Methods Partial Differ. Equ. 9, 339–355 (1993)
Koebbe, J.: Homogenization-wavelet reconstruction methods for elliptic problems. Numer. Methods Partial Differ. Equ. 100, 1–35 (2002)
Koebbe, J.: Computational Homogenization and Multiscale Research Web Site. (2004) Available online at http://www.math.usu.edu/~koebbe/wwwHomog/
Koebbe, J.: JHomogenizer User’s Guide. (2004) Available at http://www.math.usu.edu/~koebbe/wwwHomog/
Koebbe, J., Thomas, R.: Wavelet construction based on homogenization. In: Proceedings of the XIII International Conference on Computational Methods in Water Resources, Calgary, Alberta, Canada 25–29 June 2000
Koebbe, J., Watkins, L., Thomas, R.: Characterization and upscaling of sedimentary depositional formations using archetypal analysis and homogenization. In: Proceedings of the Third International IMACS, Jackson, Wyoming, USA, 9–12 July 1997
Panfilov, M.: Macroscale Models for Flow Through Highly Heterogeneous Porous Media. Kluwer Academic, Dordrecht (2000)
Renard, P., DeMarsily, G.: Calculating equivalent permeability: A review. Adv. Water Resour. 20, 253–278 (1997)
Roberts, J.E., Thomas, J.M.: Mixed and hybrid methods. In: Ciarlet, P.G., Lions, J.L. (eds.) Handbook of Numerical Analysis, Finite Element Methods (Part 1), Vol. II, pp. 524–639, North-Holland, Amsterdam (1991)
Sanchez-Palencia, E.: Non-Homogeneous Media and Vibration Theory. Springer, Berlin Heidelberg New York (1980)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Amaziane, B., Koebbe, J. JHomogenizer: a computational tool for upscaling permeability for flow in heterogeneous porous media. Comput Geosci 10, 343–359 (2006). https://doi.org/10.1007/s10596-006-9028-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10596-006-9028-4