Mass balance errors in modeling two-phase immiscible flows: causes and remedies

Abstract

Mass balance accuracy of two-phase immiscible flow models used for contaminant hydrology applications is examined through comparisons of finite element and finite difference solutions of the pressure-based and pressure-saturation formulations. The influence of model formulation and initial conditions on mass balance performance is explored. Model simulations demonstrate that accurate solutions for multiphase flow problems can be obtained with either finite element or finite difference, pressure-based or pressure-saturation formulations, if coefficients and initial conditions are properly treated. In the pressure-based formulation, capacity coefficients arise from the expansion of the saturation variables in terms of capillary pressure. Mass balance accuracy depends upon the proper evaluation of the capacity coefficients when the capillary pressure—saturation relation is nonlinear. Capacity coefficient approximations for finite element pressure-based models are developed which preserve elemental expansion of the saturation derivative. These approximations are shown to produce good mass balance results and accurate solutions, in contrast with traditional finite element approaches. When the organic liquid is initially absent from a domain, simulations reveal that mass balance accuracy is obtained only when the initial pressure distribution is established from a zero capillary pressure condition. The influence of matrix mass lumping and the minimum value of the capacity coefficient on model performance is also investigated.