Multiscale Pore Network Model for Two-Phase Flow in Porous Media

Viscous effects are important for many applications in two-phase flow through porous media. These effects, such as viscous fingering and stable displacement, can be predicted by current dynamic pore network models. However, these models have severe time-step restrictions which limit their usage to small domains. In order to overcome this limitation, we propose a multiscale pore network model for primary drainage. The proposed model is applicable to typical flow scenarios where capillary forces are dominant at the pore scale and viscous forces at larger scales.

In our model, the pore network is divided into subnetworks smaller than a characteristic length below which capillary forces dominate (see Figure 1). The algorithm to advance the fluid interfaces within each subnetwork consists of three steps: 1) The saturation rate of each subnetwork is obtained by solving a two-phase meso-scale mass balance equation over the domain of subnetworks. In this step, both the viscous and capillary forces are taken into account. 2) An invasion percolation algorithm is then used to locally advance the fluid-fluid interfaces within each subnetwork until a new saturation value is matched. Here, the viscous forces are neglected. 3) The parameters for the meso-scale mass balance equation are updated based on the updated fluid configurations in each subnetwork.

An important feature of our pore network model is that it maintains consistency of both fluid occupancy (see Figure 2) and fluxes at subnetwork interfaces. In addition, it is straightforward to parallelize the solution algorithm. Exemplary results are presented and compared to results obtained with an existing dynamic pore network model.