Pore-scale network modeling of Ellis and Herschel–Bulkley fluids

Network modeling is used to study the flow in porous media of Ellis and Herschel–Bulkley fluids, which model a large group of time-independent non-Newtonian fluids. Previous work is extended to include yield-stress and shear-thickening phenomena. We use two topologically-disordered networks representing a sand pack and Berea sandstone. Analytical expressions for the volumetric flow rate in a single tube are derived and implemented in each pore and throat to simulate single-phase flow in the pore space. An iterative technique is used to compute the relationship between flow rate and pressure gradient across the whole network. The single tube behavior is compared to that of the network. Experimental data in the literature are compared to the network simulation results to validate the model and investigate its predictive capabilities. Good agreement is obtained in many cases. The flow of yield-stress fluids in porous media is analyzed. Two algorithms to predict the network threshold yield pressure are implemented and compared to the numerically computed threshold yield pressure of the network.