A numerical study of two-phase flow with dynamic capillary pressure using an adaptive moving mesh method

TL;DR

This paper presents a numerical study of two-phase flow with dynamic capillary pressure, employing an adaptive moving mesh method to analyze saturation overshoot phenomena and validate results against laboratory data.

Contribution

It introduces an efficient adaptive moving mesh numerical method for modeling dynamic capillary pressure effects in two-phase flow, including non-monotonic saturation profiles.

Findings

Traveling wave solutions can be monotonic, non-monotonic, or plateau-shaped.

Numerical solutions match laboratory measurements of saturation overshoot.

The method effectively captures complex flow behaviors.

Abstract

Motivated by observations of saturation overshoot, this paper investigates numerical modeling of two-phase flow incorporating dynamic capillary pressure. The effects of the dynamic capillary coefficient, the infiltrating flux rate and the initial and boundary values are systematically studied using a travelling wave ansatz and efficient numerical methods. The travelling wave solutions may exhibit monotonic, non-monotonic or plateau-shaped behaviour. Special attention is paid to the non-monotonic profiles. The travelling wave results are confirmed by numerically solving the partial differential equation using an accurate adaptive moving mesh solver. Comparisons between the computed solutions using the Brooks-Corey model and the laboratory measurements of saturation overshoot verify the effectiveness of our approach.