A new analytical model for abnormal diffusion in stress-sensitive shale gas reservoirs

Analytical models have been developed to analyze transient pressure behaviors of multiple hydraulically fractured horizontal wells in a shale gas reservoir. In this work, an improved analytical model was developed to consider transport mechanisms more comprehensively, including adsorption, Knudson diffusion and surface diffusion in shale matrix, as well as pressure-dependent permeability, dual-porosity media, abnormal diffusion in the Stimulated Reservoir Volume (SRV) region, and non-Darcy flow in each hydraulic fracture. Subsequently, we used the new model to carry out parametric studies to investigate transient pressure behaviors on main flow features such as the shale gas reservoirs’ various diffusion, stress sensitive, abnormal diffusion and non-Darcy flow. The composite diffusion changes the inter-porosity flow to an earlier time. Stress-sensitive shale results in a faster decline of pressure and pressure derivatives. The abnormal diffusion, in the form of a time-fractional flux law to describe the sub-diffusion mechanism, delays early linear flow stage and then causes a larger pressure drop.