Equation-of-State Based Tie-Simplex Parameterization for Multiphase Thermal-Compositional Simulation

Enhanced Oil Recovery (EOR) processes usually involve complex phase behaviors between the injected fluid (e.g., steam, hydrocarbon, CO2, sour) and the in-situ rock-fluid system. Several fundamental questions remain regarding equation-of-state computations for mixtures than can form three, or more, phases at equilibrium. In addition, numerical and computational issues related to proper coupling of the thermodynamic phase-behavior with multiphase flow multi-component transport must be resolved in order to model the behaviors of large-scale EOR processes accurately and efficiently.
We describe a general negative-flash method for multi-component, thermal systems that can form three, or more, fluid phases. We prove that the new method is convergent to the unique solution. Based on our multiphase negative-flash technique, we have developed an adaptive tie-simplex parameterization framework for thermal-compositional simulation. We also prove that the tie-simplexes change continuously as a function of pressure, temperature, and composition. The continuity of the parameterized compositional space allows for interpolation in pressure and temperature using a limited number of tie-simplexes. We show that the tie-simplex framework constrains thermodynamic computations, and converges to the global minimum of the Gibbs free energy in a system that can form any number of phases.
The extended negative-flash approach accounts rigorously for tie-simplex degeneration (critical behavior) across phase boundaries. We study the behaviors of thermal-compositional reservoir displacement processes across a wide range of fluid mixtures, pressures, and temperatures. The focus is on the complex behaviors of the tie-triangles and tie-lines associated with three-phase, thermal steam-injection problems in heterogeneous formations. The algorithms that capture the complex combinations of the appearance and disappearance of multiple phases are described in detail. This tie-simplex based parameterization framework is integrated with a general-purpose reservoir simulator, and its accuracy and computational efficiency is demonstrated for several challenging compositional (CO2, four phase sour-gas) and thermal-compositional (steam) models. The nonlinear behaviors are analyzed in terms of the particular displacement process, miscible/immiscible dynamics, number of components, and sensitivity to time step size.