Stable and Efficient Time Integration of a Dynamic Pore Network Model for Two-Phase Flow in Porous Media

Frontiers in Physics

Kjelstrup, Signe¹  Vassvik, Morten²  Gjennestad, Magnus Aa.²  Hansen, Alex² 

[1] PoreLab, Department of Chemistry, Norwegian University of Science and Technology, Norway;PoreLab, Department of Physics, Norwegian University of Science and Technology, Norway

关键词: Porous media;    Two-phase flow;    Pore network model;    Time integration;    Numerical methods;    Low capillary number;    stability;   

DOI  :  10.3389/fphy.2018.00056

学科分类：物理（综合）

来源: Frontiers

【 摘 要 】

We study three different time integration methods for a dynamic pore network model for immiscible two-phase flow in porous media. Considered are two explicit methods, the forward Euler and midpoint methods, and a new semi-implicit method developed herein. The explicit methods are known to suffer from numerical instabilities at low capillary numbers. A new time-step criterion is suggested in order to stabilize them. Numerical experiments, including a Haines jump case, are performed and these demonstrate that stabilization is achieved. Further, the results from the Haines jump case are consistent with experimental observations. A performance analysis reveals that the semi-implicit method is able to perform stable simulations with much less computational effort than the explicit methods at low capillary numbers. The relative benefit of using the semi-implicit method increases with decreasing capillary number Ca, and at Ca ~ 10^-8 the computational time needed is reduced by three orders of magnitude. This increased efficiency enables simulations in the low-capillary number regime that are unfeasible with explicit methods and the range of capillary numbers for which the pore network model is a tractable modeling alternative is thus greatly extended by the semi-implicit method.

【 授权许可】

CC BY