Pressure transient and rate decline analysis for hydraulic fractured vertical wells with finite conductivity in shale gas reservoirs

Producing gas from shale strata has become an increasingly important factor to secure energy over recent years for the considerable volume of natural gas stored. Unlike conventional gas reservoirs, gas transport in shale reservoirs is a complex process. In the organic nano pores, slippage effect, gas diffusion along the wall, viscous flow due to pressure gradient, and desorption from Kerogen coexist; while in the micro fractures, there exist viscous flow and slippage. Hydraulic fracturing is commonly used to enhance the recovery from these ultra-tight gas reservoirs. It is important to clearly understand the effect of known mechanisms on shale gas reservoir performance. This article presents the pressure transient analysis (PTA) and rate decline analysis (RDA) on the hydraulic fractured vertical wells with finite conductivity in shale gas reservoirs considering multiple flow mechanisms including desorption, diffusive flow, Darcy flow and stress sensitivity. The PTA and RDA models were established firstly. Then, the source function, Laplace transform, and the numerical discrete methods were employed to solve the mathematical model. At last the type curves were plotted and different flow regimes were identified. The sensitivity of adsorption coefficient, storage capacity ratio, inter-porosity flow coefficient, fracture conductivity, fracture skin factor, and stress sensitivity were analyzed. This work is important to understand the transient pressure and rate decline behaviors of hydraulic fractured vertical wells with finite conductivity in shale gas reservoirs.