Adaptive dynamic/quasi-static pore network model for efficient multiphase flow simulation

Abstract

Pore-scale simulation is increasingly used to study various phenomena that cannot be reproduced by conventional Darcy-based simulators. Direct numerical simulation on systems larger than a few millimeters is too computationally demanding. Pore network modeling (PNM) is a practical way to study the flow at pore scale for a representative elementary volume (REV) in a reasonable time. Pore network models can be divided into dynamic and quasi-static models. Dynamic models explicitly consider the competition between capillary and viscous forces. As they require pressure gradient calculation, they can be computationally expensive. Quasi-static models assume that the flow is only driven by capillary forces and avoids the need for pressure computations. Although they are very computationally efficient, the usage of these models is limited to capillary-dominated flow regimes obtained generally at low capillary numbers. We propose to combine the two approaches in an adaptive model, taking advantage of the speed of a quasi-static algorithm when the flow is governed by capillary forces, and that can simulate viscous effects when they are significant. We propose a criterion to localize the pressure solution in important areas to enhance the computational efficiency of the algorithm even in viscous dominated regimes. In this paper, we first describe our adaptive pore network model. Then, we show that using the capillary number as a switching criterion is not good enough to characterize the domain where the flow is controlled by capillary forces. Therefore, we present a newly defined criterion to switch between the dynamic and quasi-static flow regimes. Finally, we present several test cases where we show that the adaptive algorithm can considerably improve the computational performance of the pore network simulator without losing accuracy of the solution by treating large regions of models with the quasi-static algorithm. For capillary-dominated regimes, the observed speed-up can reach 16,000 for one million-node 3D networks. For viscous dominated regimes, the speed-up can reach 43 for one million-node 3D networks.