Computing Brine Transport in Porous Media with an Adaptive-Grid Method

摘要

An adaptive grid finite difference method was applied to a model fornonisothermal, coupled flow and transport of brine in porous media. In the vicinity of rock salt formations the salt concentration in the fluid becomes large, giving rise to disparate scales in the salt concentration profiles. A typical situation, that of a sharp fresh salt water interface that moves in time, is considered. In such situations adaptive grid methods are more effective than standard fixed grid methods, since they refine the space grid locally and hence, provide for substantial reduction in number of grid points, memory use, and central processing unit time. The adaptive grid method considered, is a static, local uniform grid refinement method. Its main feature is that it is integrated on nested sequences of locally uniformly refined cartesian space grids, which are automatically adjusted in time to follow rapid spatial transitions. Variable time steps are used to cope with rapid temporal transitions, including a fast march to possible steady state solutions. For time stepping the implicit, second order Backward Differentiation Formula (BDF) scheme is used. Two specific example problems are numerically illustrated. The main physical properties involved are advection and dispersion, and in the case of dominant advection sharp fresh salt water interfaces arise.