Two-phase flow, dissolution and transport in porous media: A numerical model using a collocation-based parallel algorithm

The transport and dissolution of slightly soluble Denser-than-water Non-Aqueous Phase Liquids (DNAPL) can be simulated using a two-phase flow model that permits interphase mass transport across the DNAPL-water interface. The model consists of four mass balance equations: two phase flow equations are used to define phase distribution and velocity field, and two species transport equations are used to define the distribution of the DNAPL dissolved in the water phase and the water dissolved in the DNAPL phase. In addition, the model contains constitutive relations describing the relationships between saturation and capillary pressure, relative permeability and saturation, and kinetic interphase mass exchange and saturation. Moreover, a hysteresis algorithm is used to describe the emplacement of residual DNAPL and subsequent removal by dissolution kinetics.; Computationally the model employs an implicit in time collocation discretization with a Picard linearization of the nonlinear terms. A decoupled approach allows for the iterative sequential solution of the flow and transport equations. Holding the composition of each phase fixed, evaluation of the flow equations depends on the flow regimes. Three flow regimes can exist in different parts of the computational domain, and the numerical algorithm utilizes appropriate dependent variables to describe each regime. First, both phases are present and mobile: saturation is treated as a function of capillary pressure, and the strongly coupled pressure based phase balance equations are evaluated simultaneously. Second, both phases are present, but the DNAPL phase is at an immobile residual state: saturation becomes a function of dissolution kinetics, and the weakly coupled pressure based water balance and saturation based DNAPL balance equations are solved sequentially. Third, the DNAPL phase is absent: only the pressure based water balance equation is solved. Given a solution to the flow equations the weakly coupled transport equations are evaluated sequentially.; A block iterative matrix splitting scheme, called Parallel Solution Collocation (PSC), allows the discretized domain to be solved as a series of independent subdomains. This algorithm is found to be ideally suited for parallel processing.