Modeling and Simulation of Non-Darcy Flow in Porous Media

Abstract

Abstract Consideration of non-Darcy flow effects is essential to adequately model high-velocity flow effects. The relationship between velocity and pressure loss relies on the Forchheimer equation, which includes an empirically derived non-Darcy flow coefficient. The key issue in analyzing the non-Darcy flow is to accurately determine the non-Darcy coefficient. In this work, a semi-theoretical equation is proposed to estimate the non-Darcy coefficient for heterogeneous, porous media. It was determined that two previous theoretical models, parallel-type and serial-type, are upper and lower bounds to the proposed general correlation. The proposed equation can be used to predict the non-Darcy coefficient in porous media where parallel-type and serial-type models are deficient due to heterogeneity and directional permeability. The semi-theoretical equation was incorporated into a two-dimensional, single-phase gas flow simulator. This simulator was applied to a series of flow experiments where nitrogen was horizontally injected at various flow rates and in several directions into a 3-inch diameter by 3/8-inch thick heterogeneous core wafer. Results from the simulator successfully matched the experimental data, subsequently verifying the proposed correlation. In some directions, parallel-type or serial-type model was as good as the proposed correlation to be used to predict the non-Darcy coefficient; however, in one direction, the proposed correlation was better. The general equation for the non-Darcy coefficient has been verified by comparing differential pressures from simulations and their counterparts from the wafer non-Darcy flow experiments. The equation will help investigators to reach a better estimation of the non-Darcy effect in porous media. Furthermore, the modeling of the non-Darcy flow developed in this paper can easily be incorporated into a reservoir simulator to account for non-Darcy effect at high velocities.