Numerical Simulation of Natural Gas Flow in Shale Reservoirs with Thermodynamic Equation of State: A Comparative Study

Abstract

Abstract Production from unconventional reservoirs like shale gas has increased considerably in the past few years due to the advancement in twofold, i.e., horizontal drilling and hydraulic fracturing technologies. Although there has been some success in increasing gas production from shale reservoirs, unfortunately, the physicochemical processes that take place in the shale formations remain challenging and are not completely understood. Unlike conventional reservoirs, shale reservoirs are characterized by very small porosity and extremely low-permeability. Gas flow in this tight formation involves complex flow processes such as Knudsen diffusion, Klinkenberg effect, adsorption and desorption, strong rock-fluid interaction, rock deformation, etc. Furthermore, because of high pressure and high temperature reservoir conditions the gas behaves as real gas. In this work, our shale gas mathematical model is built based on the dual-porosity dual-permeability model that incorporates the complex flow processes mentioned above as well as the thermodynamic calculations. Peng-Robinson equation of state (PR-EOS) was used to calculate the gas density and compressibility factor by solving the cubic equation. In the numerical method implementation we combine the finite difference method with the experimenting pressure field approach to solve the pressure equations for the matrix and fracture systems in the dual-porosity dual-permeability model. This combination greatly reduces the computational cost when solving the large systems of pressure equations of the matrix and fracture. In this approach, a set of predefined pressure fields is generated in the solution domain such that the undetermined coefficients are calculated from these pressure fields. In the numerical example, we considered a shale reservoir with single production well. Comparison between real gas and ideal gas is studied and the result shows that considering the real gas behavior generates higher cumulative production, which implies that the gas transport capacity is higher than the ideal gas case. The result also indicates that considering real gas behavior in the model would increase the production and retard the decline curve. Therefore, it is very important to incorporate the real gas behavior into the model in order to be able to forecast the production accurately.