An adaptive solution domain algorithm for solving multiphase flow equations

Abstract

An adaptive solution domain (ASD) finite-element model for simulating hydrocarbon spills has been developed that is computationally more efficient than conventional numerical methods. Coupled flow of water and oil with an air phase at constant pressure is considered. In the ASD formulation, the solution domain for water- and oil-flow equations is restricted by eliminating elements from the global matrix assembly which are not experiencing significant changes in fluid saturations or pressures. When any nodes of an element exhibit changes in fluid pressures more than a stipulated tolerance τ, or changes in fluid saturations greater than tolerance τ 2 during the current time step, it is labeled active and included in the computations for the next iteration. This formulation achieves computational efficiency by solving the flow equations for only the part of the domain where changes in fluid pressure or the saturations take place above stipulated tolerances. Examples involving infiltration and redistribution of oil in 1- and 2-D spatial domains are described to illustrate the application of the ASD method and the savings in the processor time achieved by this formulation. Savings in the computational effort up to 84% during infiltration and 63% during redistribution were achieved for the 2-D example problem.