Solutions of Trilinear Flow for a Fractured Horizontal Well in Shale Gas Reservoirs

Abstract

A novel flow solution was developed as a contribution to understanding the complex transport mechanism in shale gas reservoir. Hydraulic fracturing by horizontal wells is commonly done to enhance production in a shale gas reservoir. Unlike conventional gas reservoir, flow in shale gas reservoirs is involved with multiple physical phenomena, namely Darcy’s law, Knudsen’s diffusion, and gas adsorption. The objective of this study is to revisit a trilinear flow solution and adapt it for a fractured horizontal well in a shale gas reservoir to study pressure transient behavior. The fractured shale reservoir is considered as a dual-porosity medium with diffusion in matrix and adsorption at pore–grain interface and divided into three zones, i.e., (1) rejuvenated fracture zone (RFZ), (2) non-rejuvenated fracture zone (NRFZ), and (3) hydraulic fracture zone (HFZ). The wellbore pressure solution could be obtained via Laplace’s transform and inversion using Stehfest’s algorithm, based on which the following flow regimes can be interpreted, i.e., (1) bilinear flow, (2) formation linear flow, (3) boundary-dominated flow, (4) transition flow, and (5) the total system flow. Sensitivity analyses were conducted by changing such parameters as storage ratio, inter-porosity flow coefficient, adsorption index, reservoir diffusivity, hydraulic fracture conductivity, hydraulic fracture spacing, and reservoir boundary. The new solution was verified by comparison with a published model, and both gave similar calculation results. It provides with a simpler and faster method to analyze pressure transient in multiple-fractured horizontal well in shale gas reservoir, making it easily implemented in practice.