A new approach for phase transitions in miscible multi-phase flow in porous media

The tightly coupled, strongly nonlinear nature of non-isothermal multi-phase flow in porous media poses a tough challenge for numerical simulation. This trait is even more pronounced, if miscibility is also considered. A primary reason why inclusion of miscibility tends to be problematic are the difficulties stemming from phase transitions: on the one hand, phase transitions need to be included since the presence or absence of fluid phases has a major impact on the flow behavior; on the other hand, convergence of the nonlinear solver may be severely affected if they are not handled robustly. In this work, we present a mathematically sound approach to include phase transitions in the nonlinear system of equations: first, the transition conditions are formulated as a set of local inequality constraints, which are then directly integrated into the nonlinear solver using a nonlinear complementarity function. Under this scheme, Newton–Raphson solvers exhibit considerably more robust convergence behaviour compared to some previous approaches, which is then illustrated by several numerical examples.