Element-based Formulations for Coupled Flow, Transport, and Chemical Reactions a Report Submitted to the Department of Energy Resources Engineering of Stanford University in Partial Fulfillment of the Requirements for the Degree of Master of Science

A numerical modeling of coupled flow, transport, and chemical reactions is critical to understand the dynamic processes in natural porous media and manage subsurface resources, such as CO2 sequestration, water aquifers, and oil reservoirs. In this work, two molar formulations for coupled flow, transport, and chemical reactions are proposed, namely, the overall-composition and the element formulations. Both formulations assume an element-based statement of the governing equations, which are composed of the element mass-conservation equations, chemical reactions, phase-equilibrium, and constraint relations. A general treatment of the solid phase is employed, and the formulations allow for any component to exist in any phase. In the two proposed formulations, the primary equations set is composed of the element conservation equations and the kinetic reactions. The overall fraction for an element is introduced in the element formulation and used as a primary variable. The standard low-order finite-volume, fully-implicit method, which is widely used in reservoir simulation, is the basis for discretizing the equations. In the new formulations, variable substitution due to phase appearance, or disappearance, is not required; however, the equilibrium relations are treated separately from the mass conservation equations and solved using exact flash calculations. The element formulation is demonstrated using a simple model problem, which describes one-dimensional CO2 injection into water containing NaCl salt, and with only one equilibrium precipitation-dissolution reaction involving NaCl salt. A two-step phase-behavior computation procedure is