Multiphase flow model of the transition between Darcy flow and Forchheimer flow

This study proposes a convenient definition of the Forchheimer number for multiphase to derive a generalized Darcy-Forchheimer model. Based on this, a numerical tool using control volume finite difference method has been developed to simulate two-phase inertial immiscible and incompressible flow in nondeformable homogeneous porous media. The numerical tool has been validated by comparing the results to those obtained using a semi-analytical solution to the Buckley-Leverett problem with inertial effects and showing good agreement with the analytical solution. This study also proposes a new method to determine the critical Forchheimer number for the transition between Darcy flow and Forchheimer flow for both single phase and multiple phases and obtains the critical values for both water and CO2 by using the new method and experimental data in the literature. These critical Forchheimer numbers are then incorporated into the multiphase model. A comparison between the classical Darcy flow model and the Darcy-Forchheimer flow is conducted to reveal the importance of non-Darcy effect for high velocity case. This study provides a useful tool for future analysis and comprehension of multiphase Darcy-Forchheimer flow.