Network modelling of yield-stress fluid flow in disordered porous media

Yield-stress fluid flow occurs in many industrial applications, including in porous systems during enhanced oil recovery and membrane emulsification. However, the high computational cost of computational fluid dynamics (CFD) simulations for yield-stress fluids hinders the study of these large-scale systems. In this work, we develop a fully-predictive network model for flow through 2D disordered porous media that obtains a solution in minutes on a single CPU core, considerably faster than the days or weeks required by CFD with multiple CPU cores. Our model generates network nodes using a Voronoi tessellation, extracts geometric parameters accounting for the topology of the domain, and numerically solves mass and momentum conservation equations with a Newton-Raphson solver. We accurately predict the pressure drop and velocity field of flows with and without wall slip, validating our results against CFD simulations produced in-house and from the literature. Wall slip is ubiquitous in real-world flows of these materials, dramatically decreasing friction at solid-fluid interfaces and changing the overall resistance in porous networks. Thus, it was imperative that we accounted for this phenomenon in our model.