Simulation of immiscible multiphase flow in porous media using a moving finite element algorithm.

A moving grid finite element method is developed to solve the nonlinear coupled set of partial differential equations (PDEs) governing immiscible multiphase flow in porous media in one dimension. This is one of the first research works to develop an adaptive grid algorithm to solve a coupled set of nonlinear PDEs. The model's algorithm is based on a time implicit st and ard Galerkin finite element method, with linear basis functions and an iterative Picard procedure. Grid adaptation may be accomplished after each iteration, every time step or every few time steps. The adaptation method is based upon a single equidistribution equation involving gradient and curvature criteria. This single equidistribution equation is employed in place of the more complex alternative which involves solving a multiobjective distribution problem, applying distribution criteria to all the PDEs variables. The simplification is achieved by assigning the largest gradient at each node as a representative gradient. Use of a single reduced equidistribution equation facilitates the incorporation of the adaptive grid algorithm in the numerical solver for a coupled set of nonlinear PDEs. This work includes sensitivity analyses for the parameters which are incorporated in the grid adaptation method, including curvature weighting parameters, artificial viscosity and artificial repulsive force coefficients. Consideration is also given to methods for preserving phase mass in the grid adaptation process. The FEM used herein incorporates a FEM chord slope analog for the saturation derivatives with respect to the capillary pressures to avoid oscillations in the solution of the capillary pressures and phase volume balance. This work includes a discussion of the implementation of a fixed organic chemical pressure boundary condition. The discussion shows that division of the boundary pressure into two parts, one which is applied to the boundary capillary pressure, and one which is applied to the nonorganic fluid boundary pressure to force this phase to flow away from the boundary, generates results similar to physical observations. The model is verified against the finite difference model of Abriola (1984). Its applicability and versatility are demonstrated through solution of complex two- and three-phase flow problems involving single and double fronts and a sink/source term. The model is shown to achieve significant savings in computation time and memory allocation, when compared with fixed grid solutions of equivalent accuracy.PhDCivil engineeringPetroleum engineeringMathematicsUniversity of Michiganhttp://deepblue.lib.umich.edu/bitstream/2027.42/162307/1/9001630.pd