A numerical study of two-phase flow models with dynamic capillary pressure and hysteresis

TL;DR

This paper investigates two-phase flow models incorporating dynamic capillary pressure and hysteresis, using numerical methods to simulate saturation and pressure overshoot phenomena with validation against experimental data.

Contribution

It introduces a numerical framework for modeling two-phase flow with dynamic capillary effects and hysteresis, demonstrating improved simulation of overshoot phenomena.

Findings

Numerical schemes effectively capture saturation and pressure overshoot.

Model results align well with experimental observations.

The approach demonstrates the importance of hysteresis in flow modeling.

Abstract

Saturation overshoot and pressure overshoot are studied by incorporating dynamic capillary pressure, capillary pressure hysteresis and hysteretic dynamic coefficient with a traditional fractional flow equation in one dimension. Using the method of lines, the discretizations are constructed by applying Castillo-Grone's mimetic operators in the space direction and explicit trapezoidal integrator in the time direction. Convergence tests and conservation property of the schemes are presented. Computed profiles capture both the saturation overshoot and pressure overshoot phenomena. Comparisons between numerical results and experiments illustrate the effectiveness and different features of the models.