Two-dimensional modified Darcy model for calculating seepage problems in underground gas storage reservoirs

Abstract

The management and control of underground gas storage (UGS) require comprehensive optimization of multiple factors. However, the high computational cost of reservoir simulations severely limits the sensitivity and accuracy of UGS control optimization. To address this limitation, this study proposes a modified two-dimensional (2D) Darcy model for rapid simulation of immiscible phase displacement in reservoirs. This model represents a simplified equation of the conventional three-dimensional (3D) two-phase reservoir displacement problem. Compared to the traditional 2D Darcy model, our modified version incorporates a gravity compensation factor and a path compensation factor, designed to account for vertical terrain variations and gravitational effects neglected during dimensional reduction. Through comparative analysis with 3D benchmark models, we demonstrate both the critical role of gravity forces and the limitations of conventional 2D Darcy equations. The modified 2D Darcy model shows significantly improved alignment with 3D simulation results while reducing computational costs by over 70% without compromising model stability. Due to the compensatory modification of the simplified model based on the 2D Darcy equation describing the behavior of force action. So it cannot only be used to describe the gas injection problem of underground gas storage. And theoretically, it can be generalized to analyze three-phase (oil–gas–water) migration in complex reservoirs under Darcy flow regimes.