Abstract
A finite volume dicretization has been used to solve compositional flow in porous media. Secondary migration in fractured rocks has been the main motivation for the work. Multipoint flux approximation has been implemented and adaptive local grid refinement, based on domain decomposition, is used at fractures and faults. The parallelization method, which is described in this paper, strongly promotes code reuse and gives a very high level of parallelization despite low implementation costs. The programming framework is also portable to other platforms or other applications. We have presented computer experiments to examine the parallel efficiency of the implemented parallel simulator with respect to scalability and speedup.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Aavatsmark, I., Barkve, T., Bøe, Ø., and Mannseth, T., Discretization on unstructured grids for inhomogeneous, anisotropic media. Part I: Derivation of the methods, SIAM J. Scient. Comput. 19 (1998), 1700–1717.
Aavatsmark, I., Barkve, T., Bøe, Ø., Reiso, E., and Teigland, R., Multipoint flux approximation for faults and grid refinement, submitted, 1999.
Bear, J. and Bachmat, Y., Introduction to Modeling of Transport Phenomena in Porous Media, Kluwer Academic Publishers, Dordrecht, Netherlands, 1990.
Bernardi, C., Maday, Y., and Patera, A. T., A new nonconforming approach to domain decomposition: the mortar element method, Nonlin. PDEs and their Applications, College de France Seminar, XI, 1992.
Bruaset, A. M., Cai, X., Langtangen, H. P., and Tveito, A., Numerical solution of PDEs on parallel computers utilising sequential simulators. Technical Report, University of Oslo, Depart. of Inform., Oslo, Norway, 1998.
Dahle, H. K., Espedal, M. S., and Sævareid, O. Characteristic, Local grid refinement techniques for reservoir flow problems, Numerical Methods for Partial Differential Equations 6 (1992), 279–309.
Edwards, M. G., M-matrix flux splitting for general full tensor discretization operators, J. Comput. Physics, 1999, to appear.
Edwards, M. G., Cross flow tensors and finite volume approximation with deferred correction Comput. Methods Appl. Mech. Eng. 151 (1998), 143–161.
Ewing, R. E., Lazarov, R. D., and Vassilevski, P. S., Local refinement technique for elliptic problems on cell-center grids, I; Error analysis Math. Comp. 56 (1991), 437–461.
Fladmark, G.E., A numerical method for local refinement of grid blocks applied to reservoir simulation, Internal Report, 1982, Norsk Hydro, Bergen, Norway.
Fladmark, G.E., Secondary oil migration: Mathematical and numerical model, Internal Report, 1995, Norsk Hydro, Bergen, Norway.
Reme, H., The preconditioning and multi-point flux approximation methods for solving secondary oil migration and upscaling problems, Dr. Scient. Thesis, Math. Dept., University of Bergen, Norway, 1999.
Teigland, R., On multilevel methods for numerical reservoir simulation, Dr. Scient. Thesis, Math. Dept., University of Bergen, Norway, 1991.
Verweij, J. M., Hydrocarbon migration systems analysis, Elsevier, Amsterdam, 1993.
Wachspress, E. L., Iterative Solution of Elliptic Systems and Applications to the Neutron Diffusion Equations of Reactor Physics, Prentice-Hall Inc, Englewood Cliffs, 1966.
Welte, D. H., Horsfield, B., and Baker, D. R., Petroleum and Basin Evolution, Springer-Verlag, Berlin, 1997.
Wong, T. W., Firoozabadi, A., and Aziz, K., The relationship of the volume balance method of compositional simulation to the Newton-Raphson method, SPE Reservoir Structure Symp., 5 (1990), 414–422.
Øye, G. Å., An object-oriented parallel implementation of local grid refinement and Domain decomposition in a simulator for secondary oil migration, Dr. Scient. Thesis, Math. Dept., University of Bergen, Norway, 1999.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Reme, H., Øye, G.Å., Espedal, M.S., Fladmark, G.E. (2000). Parallelization of a Compositional Reservoir Simulator. In: Chen, Z., Ewing, R.E., Shi, ZC. (eds) Numerical Treatment of Multiphase Flows in Porous Media. Lecture Notes in Physics, vol 552. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45467-5_21
Download citation
DOI: https://doi.org/10.1007/3-540-45467-5_21
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67566-2
Online ISBN: 978-3-540-45467-0
eBook Packages: Springer Book Archive