Analytical Model for Shale Gas Transportation from Matrix to Fracture Network

Abstract

Abstract The matrix of shale gas reservoirs has an extremely low permeability; therefore, fractured vertical wells and multi-stage fractured horizontal wells (MFHWs) are adopted in most cases for exploration purpose. In this context, studying the dynamic pressure in MFHWs in shale gas reservoirs not only provides an important means of obtaining the parameters of shale reservoirs, but also constitutes the basis of evaluating the productivity of shale gas wells. However, existing models for fractured horizontal wells have neglected the heterogeneity of shale gas reservoirs and the seepage mechanism in the nanopores of shale organic matter, and failed to take into account the differences among different occurrence spaces in gas flow characteristics. On that account, in this study, we combined dust gas model (DGM) and generalized Maxwell-Stefan model (GMS) to calculate the apparent permeability considering viscous flow, Knudsen diffusion, surface diffusion and desorption, and introduced these into the macro seepage model to establish a dynamic pressure analysis model considering reservoir heterogeneity and stress sensitivity effect of MFHWs in shale gas reservoirs. Based on the five-linear flow model, this study divides one reservoir into two top reservoir regions, two inner reservoir regions, two outer reservoir regions, and one artificial fracture region. Through analyzing the flow characteristics of different regions, it uses Laplace transformation and regular perturbation methods to solve the model; based on the analytical solution to this model, it plots the dynamic pressure curve and the dynamic productivity curve and carries out flow region division and sensitivity analysis. As indicated by the study results, the model established in this study fits relatively well with actual production data, has a reliable theoretical foundation, and can preferably describe the dynamic changes of pressure in the exploration process of shale gas wells.