Abstract
In this paper a new numerical method for nonlinear system of partial differential equations which describes motion of a two-phase compressible fluid in microscopic porous medium in a class of discontinuous functions is suggested. For this aim, at first, the system of equations is split in two equations according to physical parameters. First one with respect to water saturation, and the other one with respect to pressure. Then, the special auxiliary problem having some advantages over the main problem is introduced. This auxiliary problem permits to develop the efficient numerical algorithm for obtaining the solution. Using the solution of the auxiliary problem, the solution of the main problem, which expresses all the physical properties is found.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Aziz, K., Settari, A.: Petroleum Reservoir Simulation. Elsevier Applied Science Pub., London (1979)
Buckley, S.E., Leverett, M.C.: Mechanism of Fluid Displacement in Sands. Trans. AIME 146, 107–116 (1942)
Collins, R.E.: Flow of Fluids through Porous Materials. Penn-Well Books, Tulsa (1976)
Muskat, M.: The Flow of Homogeneous Fluids through Porous Medium. McGraw-Hill, New York (1946)
Rasulov, M.A.: Numerical Solution of One Dimensional Filtration of Three Phase Compressible Fluid Through Medium in a Class of Discontinuous Functions. Appl. Math. Comput. 167(2), 1249–1266 (2005)
Rasulov, M.A.: Finite Difference Scheme for Solving of Some Nonlinear Problems of Mathematical Physics in a Class of Discontinuous Functions. Baku (1996) (in Russian)
Rasulov, M.A., Abasov, M.T.: To the Theory Filtration of Three-Phase Mixes in View of Them Compressible. Soviet Math. Dokl. USSR 325(1), 130–133 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Sinsoysal, B., Rasulov, M. (2009). Efficient Numerical Method of the 1D Motion of Two-Phase Fluid through Porous Medium in a Class of Discontinuous Functions. In: Margenov, S., Vulkov, L.G., Waśniewski, J. (eds) Numerical Analysis and Its Applications. NAA 2008. Lecture Notes in Computer Science, vol 5434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00464-3_62
Download citation
DOI: https://doi.org/10.1007/978-3-642-00464-3_62
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-00463-6
Online ISBN: 978-3-642-00464-3
eBook Packages: Computer ScienceComputer Science (R0)