Applying Method of Characteristics to Determine Pressure Distribution in 1D Shale-Gas Samples

Abstract

Summary This paper examines application of the method of characteristics (MOC) to determine pressure distribution in a 1D matrix of shale gas. Because of gas expansion and local desorption in shale gas, pressure distribution changes during production. We developed a semianalytic MOC solution of gas flow in shale by use of the analogous-continuum approximation (apparent permeability). The MOC solution is derived with the inclusion of compressibility, gas-slippage effect, and desorption. Through quantitative comparison of pressure profiles and history plots, we used a simulation approach to verify the accuracy of the analytic solution. Results suggest that the simulation results are consistent with our MOC solution, which can also be used to evaluate impacts of different parameters on pressure distribution. Prediction of pressure distribution over time will greatly enhance approximation of reservoir performance.