An ICLS-based method for solving two-phase seepage free surface considering compressible gas in porous media

Abstract

The current seepage free surface methods can represent the seepage free surface when the gas escapes freely, but they cannot handle this situation when involving the confined gas, because they either ignore the gas or assume that the gas is incompressible. However, the compressibility of confined gas has an important effect on the seepage free surface. To address this problem, a novel approach based on the improved conservation level set (ICLS) method is proposed to represent accurate free surface especially considering compressible gas in two-phase seepage. The water–air two phases are both governed by the seepage governing equation and the generalized Darcy's law. Considering the compressibility of gas, the air density needs to be updated as the pore gas pressure changes according to the ideal gas law. The free surface is implicitly captured by the ICLS method, which exhibits better mass conservation property and more precise surface information. The new approach can be easily generalized without limitation of discretization schemes. Regardless of whether the gas can escape freely or not, the proposed method has the ability to describe precise free surface. The accuracy and capacity of present work are validated with several numerical examples.