A continuum approach to multiphase flows in porous media

The volume averaging technique is revisited for multiphase flows in isotropic rigid porous media/packed columns. The tortuosity effect is introduced into the averaging procedure for gradients and flow velocities. Seven averaging rules are derived including summation, product, gradient and divergence rules. Closures are proposed for the evaluation of the extra surface/intrinsic phase integral terms arising from the averaging of the divergence of a flux. Applying the volume averaging rules, the governing equations for multiphase flows are obtained. Both inertia and interphase interactions are retained in the volume averaged equations. Therefore, the governing equations derived in this study can he used to solve for the problems of multiphase flows in packed distillation and absorption towers. It is found that the dispersion term is present in the continuity equation as well as the momentum equations.