Reservoir Simulation using Mixed Methods, a Modified Method Characteristics, and Local Grid Refinement

The simulation of multiphase and multicomponent fluid flows of ten requires large coupled systems of nonlinear partial differential equations. These equations are convection-dominated with important local diffusive effects. An operator-splitting technique is used to address these different phenomena. Convection is treated by time stepping along the characteristics of the associated pure convection problem, and diffusion is modelled via Galerkin method for miscible displacement and a Petrov-Galerkin method for immiscible displacement. Accurate approximations of the fluid velocities needed in the modified method of characteristic time-stepping procedure are obtained by mixed finite element methods. Adaptive local grid refinement methods are then presented to resolve the moving internal boundary layers which arise and often govern the mass transfer between the phases. Local grid refinement techniques are also described for mixed finite element methods around wells and other fixed singularities. Due to the large size of many applications, efficiency in computation is critical. Concepts of domain decomposition for dynamic adaptive grid refinement are presented. Numerical results for both miscible and immiscible displacements will be presented.