Persistent-variable thermal compositional simulation of multiphase flow with phase separation in porous media

Abstract: Thermal compositional multiphase flow in porous media with phase transitions involves complex nonlinear interactions among flow, transport, and phase equilibrium. This paper presents a persistent-variable formulation for thermal compositional flow using enthalpy to formulate the energy balance and the local equilibrium problem. Equilibrium conditions are derived from a thermodynamically consistent minimization problem using a persistent set of variables, allowing for seamless integration of equilibrium calculations into a fully coupled flow and transport model. This formulation does not require phase stability tests and provides a continuous and full mathematical description of the multiphysics system, suitable for challenging non-isothermal scenarios. To tackle the nonlinearities arising from phase transitions, we embed a local solver for the thermodynamic subproblem within a global Newton solver for the fully implicit system. The local solver exploits the locality of the subproblem for parallelization and leverages the modularity of the persistent-variable formulation for both isothermal and isenthalpic equilibrium conditions locally. We demonstrate the capability of our approach to simulate complex high-enthalpy systems, including narrow-boiling phenomena. The impact of the embedded local solver is analyzed through numerical experiments, demonstrating a reduction in global nonlinear iterations of up to 23 \% with increased use of the local solver. The number of local iterations is controlled with a local solver tolerance and no significant impact on the global iteration number was observed for local residual tolerances as high as $1e-3$. The persistent-variable approach using enthalpy and the modularity of the embedded local solver advance the usage of equilibrium calculations in multiphase flow simulations and are suitable for high-enthalpy applications.