DEVELOPMENT AND VERIFICATION OF A NOVEL DARCY SOURCE TERM FOR MULTIPHASE FLOW OF HERSCHEL-BULKLEY FLUIDS

This work presents the development and verification of a novel Darcy source term for multiphase flow in porous media based on Herschel-Bulkley rheology. The formulation preserves the Darcy-law structure and introduces a regularized apparent viscosity obtained from a capillary-bundle representation, recovering the Newtonian, power-law, and Bingham cases. The model was implemented in a custom OpenFOAM-based solver (upstreamFoam) with composition-dependent rheology, in which τ₀(yield stress), n (flow behaviour index), and µ_HB (Herschel-Bulkley consistency index) vary with the local mass fraction. The Buckley-Leverett verification results show excellent agreement with semi-analytical solutions for pure fluids of the Newtonian, power-law, Bingham, and Herschel-Bulkley types.