Improving the Computational Efficiency of a Dynamic Pore Network Model - A Hybrid Approach for a Better Performance

Pore scale simulation is more and more used to study various pore scale phenomena that cannot be reproduced by conventional Darcy-based simulators. Dynamic pore network models are a method to study the flow at the pore scale without having to use the very precise and time consuming direct numerical simulators. However, these models are still very slow when applied to 3D core scale simulations. In fact, to reproduce the competition between viscous and capillary forces governing the immiscible flow in porous media, these models require computing many expensive pressure gradients. However, at low rates the displacement tends to become dominated by capillary forces and this means that, during drainage, the pores having the lowest capillary entry pressure are filled first. In this case, simple flow rules can be defined thus avoiding the pressure calculations. These simplified models are named quasi-static and can be only used when viscous forces do not influence the flow. In the literature, most researchers have used either a dynamic pore network or a quasi-static model. Since quasi-static algorithms are faster and are able to reproduce similar results to dynamic models at low rates, we propose to combine these two approaches in a hybrid algorithm taking advantage of the speed of quasi-static algorithms when the flow is governed by the capillary forces and that can simulate the viscous effects when they are important. We propose a criterion to localize the pressure solution to the important areas to enhance the computational efficiency of the algorithm even in viscous dominated regimes. In this paper, we first show that using the classical definition of 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 use the macroscopic capillary number as a criterion to switch between the dynamic and quasi-static flow regimes. Finally, we present several test cases where we show that the hybrid algorithm can considerably improve the computational performance of the pore network simulator without losing the accuracy of the solution. For capillary dominated regimes, the observed speed-up on 3D networks can reach 500 and 16000 for our industrial networks of 43000 and 1 million nodes, respectively. For viscous dominated regimes the speed-up on 3D networks can reach 5 and 30 for 43000 and 1 million nodes, respectively. This approach is compatible with a multiscale method for the pressure computations and will provide an additional speed-up.