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Journal of Porous Media
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ISSN Imprimir: 1091-028X
ISSN En Línea: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v12.i12.20
pages 1139-1152

Analytical and Numerical Solution for One-Dimensional Two-Phase Flow in Homogeneous Porous Medium

Michal Benes
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic
Radek Fucik
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic
Jiri Mikyska
Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Trojanova 13, 120 00 Prague, Czech Republic
Tissa H. Illangasekare
Center for Experimental Study of Subsurface Environmental Processes, Colorado School of Mines, USA

SINOPSIS

The article presents a comparison of a semianalytical and a numerical approach to a one-dimensional flow-function model of two-phase flow through a homogeneous porous medium which is used for validation of more complex numerical models of two-phase flow. The flow-function model equation can be treated analytically to obtain an implicit formula for the saturation, which is resolved iteratively. This approach, originally derived by McWhorter and Sunada (1990; 1992), is used in its improved version so that we are able to readily obtain the wetting-phase saturation for all parameter values. To enlarge the class of admissible boundary and initial conditions, we propose another approach which relies on a numerical algorithm which solves the flow-function model equation, based on the finite-difference method in space and time, yielding values of the solution at given time moments and on a spatial grid of positions. Our approach is demonstrated in a series of one-dimensional computations showing the accuracy, efficiency, and generality of the proposed algorithms.


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