Novel Model for Rate Transient Analysis in Stress-Sensitive Shale Gas Reservoirs

Technical advances in hydraulic fracturing and horizontal drilling technologies enable shale to be commercially exploited. Due to the technical and economic limitations of well testing in shale gas plays, rate transient analysis has become a more attractive option. After hydraulic fracturing, flow mechanisms in multiple scaled pores of shale become extraordinarily complicated: adsorption in nanopores, diffusion in micropores, and non-Darcy flow in macropores. Moreover, shale gas reservoirs are stress-sensitive because of ultralow permeability and diffusivity in a matrix. Furthermore, the porosity and permeability of natural fractures are stress-dependent as well. Accounting for all of these complex flow mechanisms, especially the aforementioned stress-sensitive parameters, a semianalytical production solution of a multiple fractured horizontal well (MFHW) can rapidly predict the entire production behavior. Scholars have done much work on the complex flow mechanisms of shale. Most models regarded permeability as a stress-sensitive parameter while diffusivity and porosity were considered to be a constant. However, diffusivity and porosity were proved to be stress-sensitive as experimental science developed. In this study, we present a novel semianalytical model for rate transient analysis of MFHW, which simultaneously incorporates multiple stress-sensitive parameters into flow mechanisms. Substituting stress-dependent parameters (diffusivity, porosity, and permeability) into governing equations resulted in strong nonlinearities, which was solved by employing the perturbation method. Production behaviors with only stress-sensitive permeability were compared with multiple stress-dependent parameters. The new model with multiple stress-sensitive parameters declined slower than the permeability-sensitive model, and the new model matched better with the field data. In addition, the effects of major stress-sensitive parameters on production decline curves were analyzed by the proposed model. The sensitivity analysis indicated that different parameters had their own degree of sensitivity intensity and influence on the production period. Finally, 1001 wells from the Marcellus shale play were divided into three well groups. Estimated inversion values of reservoir parameters from the three well groups and relevant single wells were consistent with the field data. The inverted values of single wells fluctuate within the inversion values of well groups, which indicates that the production behavior of well groups could be a guide for rate transient analysis of a single well in shale gas reservoirs.