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

作者：Lauser A^*; Hager C; Helmig R; Wohlmuth B

来源：Advances in Water Resources, 2011, 34(8): 957-966.

DOI：10.1016/j.advwatres.2011.04.021

• Phase transition
• Phase state
• Multi-phase flow
• Semismooth Newton
• 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.

• 出版日期2011-8