Adaptive Mesh Refinement for One-Dimensional Three-Phase Flow with Phase Change in Porous Media

This article presents a detailed analysis of the implementation of the adaptive mesh refinement (AMR) technique to one-dimensional three-phase flows in heterogeneous porous media, including phase change. Since this is a particularly complex, highly nonlinear problem, many difficulties had to be resolved. A specific refining procedure and refinement criterion are proposed to deal with discontinuous saturations across interfaces between different rock types. In addition, we propose an alternative numerical algorithm to avoid difficulties in applying previous multilevel or multigrid algorithms to advance the solution on the AMR grids. Numerical examples, focused on steam injection modeling, show that the AMR technique is fast and has good accuracy.