Верификация численной методики моделирования двухфазных потоков несмешивающихся неньютоновских жидкостей в пористых средах

The paper presents the results of the development and verification of a computational technique for modeling two-phase immiscible flows in porous media, taking into account the transfer of polymers that change the rheology of fluids in the process of their flow. The mathematical model is based on the Navier–Stokes equations and the VOF method. The model includes a convective-diffusion concentration transfer equation with a constant effective diffusion coefficient. Within the framework of this model, the rheology of the displacing fluid is described by a nonlinear model of viscoplastic media (Herschel–Bulkley) based on the generalized viscosity approach. The rheological parameters of the model depend on the local polymer concentration. To regularize the effective viscosity and eliminate infinite values, an approach with exponential regularization of the shear rate at small values is used. The developed calculation methodology has been tested and verified to show that the numerical solutions found with this methodology are qualitatively and quantitatively in good agreement with known analytical solutions and with numerical solutions obtained using the Ansys Fluent reference CFD solver