Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 19, Issue 2, Pages 383-389Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.cnsns.2013.06.015
Keywords
Lie group analysis of differential equations; Filtration equations; Two-phase filtration; Nonlinear self-adjointness; Symmetries; Conservation laws
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The paper is devoted to investigation of group properties of a one-dimensional model of two-phase filtration in porous medium. Along with the general model, some of its particular cases widely used in oil-field development are discussed. The Buckley-Leverett model is considered in detail as a particular case of the one-dimensional filtration model. This model is constructed under the assumption that filtration is one-dimensional and horizontally directed, the porous medium is homogeneous and incompressible, the filtering fluids are also incompressible. The model of chromatic fluid filtration is also investigated. New conservation laws and particular solutions are constructed using symmetries and nonlinear self-adjointness of the system of equations. (c) 2013 Elsevier B.V. All rights reserved.
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