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A one‐dimensional moving grid solution for the coupled non‐linear equations governing multiphase flow in porous media. 2: Example simulations and sensitivity analysis
Author(s) -
Gamliel Amir,
Abriola Linda M.
Publication year - 1992
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.1650140105
Subject(s) - multiphase flow , curvature , porous medium , flow (mathematics) , mathematics , finite element method , grid , mechanics , mathematical analysis , geometry , physics , porosity , materials science , thermodynamics , composite material
This paper presents numerical examples for the moving grid finite element algorithm derived in Part Ito solve the non‐linear coupled set of PDEs governing immiscible multiphase flow in porous media in one dimension. Examples include single‐ and double‐front simulations for two‐ and three‐phase flow regimes and incorporating a mass sink. The modelling approach is shown to achieve significant savings in computation time and memory allocation when compared with fixed grid solutions of equivalent accuracy. This work includes sensitivity analyses for the parameters which are incorporated in the grid adaptation method, including the curvature weights, artificial viscosity and artificial repulsive force. It is found that the curvature weights are exponential functions of the negative ratio of the square root of the domain length to the number of discrete nodes. These weighting parameters are also shown to depend upon the shape of the front. On the basis of the examined simulations, it is recommended that artificial viscosity be neglected in the solution of the coupled non‐linear set of PDEs governing multiphase flow in porous media. Similarly, use of a repulsive force is found to be unnecessary in simulations involving the migration of two liquid phases. For multiphase flows incorporating a gas phase it is recommended to use a non‐zero value for the repulslive force to avoid development of an ill‐conditioned nodal distribution matrix. An equation to evaluate the repulsive force under these circumstances is suggested.