(246f) Multiphase Compositional Space Parameterization for General-Purpose Thermal-Compositional Simulation

Modeling the phase behavior associated with compositional flow simulation of systems that form more than two fluid phases (e.g., steam, sour gas, or CO2 injection) is a challenging problem. In addition to the coupling of thermodynamics with the nonlinear equations of flow and transport, accurate phase-state identification for mixtures that form three (or more) phases, as function of pressure, temperature and composition, is the subject of active research. We describe a general negative-flash method for multi-component thermal systems that can form an arbitrary number of fluid phases, including a convergence proof. This extended negative-flash approach integrates quite nicely with flow simulation based on adaptive tie-simplex compositional space parameterization. We prove that tie-simplexes change continuously with pressure, temperature, or along a continuous trajectory in compositional space. Continuation of the tie-simplex space provides theoretical justification for the tie-simplex based flow modeling, in which interpolation in pressure and temperature for a limited number of tie-simplexes is performed during a simulation run. We also show how a tie-simplex associated with a given composition can degenerate as a function of pressure and temperature. Based on these ideas, we have developed a unified compositional space parameterization framework that is applicable for any three-phase system (with any multiphase degeneration pattern) over wide ranges of pressure. We focus on the complex behaviors of the tie-triangles and tie-lines associated with three-phase, steam-injection problems. The algorithms that capture the degeneration of the tie-triangles into tie-lines are described in detail. We also demonstrate how the miscibility of oil and gas phases can be modeled in steam systems. Interpolation in the parameterized compositional space is used to identify the phase-state and proves to be as reliable as a 'conventional' phase-stability test for three-phase mixtures. We demonstrate the effectiveness of the framework using several compositional steam-injection problems with complex behaviors.