GAS FLOW SIMULATION USING THE DARCY-FORCHHEIMER EQUATION

Abstract

We discuss the modeling of gas ow in the reservoir, described by the equations of Darcy and Darcy- Forchheimer. Mathematical modeling of uid ow in porous media is the most crucial element in understanding the processes in oil and gas production; it is used when choosing the optimal option for developing oil and gas elds. The primary ltration law is the linear Darcy equation. However, it is known that this equation is not ful lled at high ltration velocities due to the manifestation of inertial forces. In problems of nonlinear ltration, the motion of liquid and gas is most accurately described by the two-term Darcy-Forchheimer law. The work aimed at studying the nonlinear law of Darcy-Forchheimer ltration in the bottom-hole zone of a gas well. In the course of the research, we performed a comparative analysis of the application of Darcy and Darcy-Forchheimer equations. To achieve this goal, we formulated the following tasks: to study the ltration process’s mathematical models, simulate the bottom-hole zone of a gas well, and compare the laws of Darcy and Darcy-Forchheimer. To obtain visual results, we used mathematical modeling. For the numerical solution of differential equations, we used the nite element method. The software implementation was carried out on the FEniCS computational package, which simpli es the solution of equations by the nite element method. We conclude that we got overestimated ow rates of gas wells when using the Darcy law, and using the Darcy- Forchheimer law, we were able to get data close to the actual ow rates. The simulations showed that the use of the Darcy-Forchheimer law is applicable for modeling gas ltration in actual conditions.