Nonlinear Model for Gas Flow into a Horizontal Well from a Shale Reservoir with a Branched Fracture Network

Abstract

We propose a mathematical model describing gas flow from a fractured shale reservoir into a horizontal well. Based on Langmuir adsorption theory and Darcy’s law, we have obtained a basic solution using a combination of a point source function, an integral of a Bessel’s function, and the Poisson summation formula. We plotted typical curves for the dimensionless pressure and its derivative on a log-log scale. We analyze the stages of gas flow from the shale formation to the horizontal well and the factors influencing it.