A sequential mass and enthalpy based algorithm for computing multiphase, multicomponent heat and mass transfer in porous media

This work describes the component-mass based compositional and thermal model for heat and mass transfer originally proposed by Acs et al (1982) for nonisothermal multi-phase multi-component compressible flows in porous media. Our model incorporates capillary pressures, thermal effects, phase partitioning and allows up to n components in the phase composition. The scheme is also an extension of the algorithms and models presented by Bell-Colella-Trangenstein (BCT) (1989). None of these methods explored thermal modeling, some of them introduced decoupled approaches, others introduced high order schemes for isothermal flows, but none went as far as to include most of the physical processes involved in complex applications such as steam injection for soil and groundwater remediation. This work presents an algorithm which consists of conditions of thermodynamic equilibrium, an equation of state for the volume balance between the fluid and the rock void, Darcy's law for the volumetric flow rates, models for the capillary pressures between the fluid phases, energy transport, component-mass conservation equations and K-value phase equilibrium packages. These relations are combined to form a decoupled pressure equation and a modified system of conservation equations analogous to the classical fractional flow models available in the literature. The sequential formulation of the flow equations forms the basis for the numerical solution for the system, which is similar to the one used in Vega-Landeau et al (1998). The numerical computations illustrate the robustness, speed and high performance of the method. The execution of the fully decoupled model demonstrates the modularity of the algorithm, its potential for multiprocessor computing, and the ease of future module updates depending on the requirements of the user. New issues are identified in the current work that open interesting paths for future research in the world of computational fluid dynamics and heat transfer in porous media.