Abstract
We present a set of algorithms for sequential solution of flow andtransport that can be used for efficient simulation of polymerinjection modeled as a two-phase system with rock compressibility andequal fluid compressibilities. Our formulation gives a set ofnonlinear transport equations that can be discretized with standardimplicit upwind methods to conserve mass and volume independent of thetime step. In the absence of gravity and capillary forces, thesplitting is unconditionally stable and the resulting nonlinear systemof discrete transport equations can be permuted to lower triangularform by using a simple topological-sorting method from graphtheory. This gives an optimal nonlinear solver that computes thesolution cell by cell with local iteration control. The single-cellsystems can be reduced to a nested set of nonlinear scalar equationsthat can be bracketed and solved with standard gradient orroot-bracketing methods. The resulting method givesorders-of-magnitude reduction in runtimes and increases the feasibletime-step sizes. For cases with gravity, the same method can beapplied as part of a nonlinear Gauss--Seidel method. Altogether, ourresults demonstrate that sequential splitting combined with standardupwind discretizations can become a viable alternative to streamlinemethods for speeding up simulation of advection-dominated systems
