Analytical Solution for Shale Gas Productivity of a Multiple-Fractured HorizontalWell Based on a Diffusion Model

摘要

An analytical solution is developed for the shale gas productivity of a multiple-fractured horizontal well based on a diffusion model and a trilinear flow pattern. The shale gas reservoir is divided into three flow regions: hydraulic-fracture region, micro-fracture network or dual-porosity region, and pure-matrix region. For the pure-matrix region, a transient diffusion equation is solved based on our previous diffusivity model developed for the shale matrix. For the micro-fracture network region, a modified dual-porosity model is proposed wherein both the free and adsorbed gases in the shale matrix flow into the micro-fracture network through a pseudo-steady diffusion process. These gases then form conflux at the hydraulic fractures and continue to the wellbore. A dimensionless solution is obtained for the bottom-hole pressure in the Laplace domain considering the skin effect. An analytical solution is obtained for the gas production rate in a real-time domain through a partial Taylor series simplification and Laplace inverse transform. This analytical solution is compared with the field data of the shale gas produced from a fractured horizontal well located in southwestern China, and a good agreement is observed. Finally, a parametric study is conducted to quantify the effects of key parameters on the gas production rate. The parameters include the bottom-hole pressure, half-length of the hydraulic fracture, permeability of the hydraulic fracture, block size of the shale matrix, and pore size within the shale matrix. These results show that the analytical solution can be used to estimate the enhancement of the shale gas recovery through hydraulic fracturing.