A negative-flash tie-simplex approach for multiphase reservoir 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 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. This negative-flash approach is integrated with reservoir flow simulation based on adaptive tie-simplex parameterization of the compositional space. We prove that the tie-simplexes change continuously as a function of pressure, temperature, and composition. The continuity of the parameterized space allows for interpolation in pressure and temperature using a limited number of tie-simplexes. This extended negative-flash approach accounts rigorously for tie-simplex degeneration 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, 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. The accuracy and computational efficiency of this negative-flash, tie-simplex based approach is demonstrated for several challenging compositional (CO₂, 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.