Performance analysis of fractured wells with elliptical SRV in shale reservoirs

A stimulated reservoir volume (SRV) exists around fractured wells in unconventional shale reservoirs, which leads to the flow characteristics of the fluid that are different from those in unstimulated formations. The existence of elliptical flow near vertical fractures is especially common and can provide a more comprehensive analysis than classical radial flow. This paper presented a new prediction composite model for fractured wells with elliptical SRV to analyze well performance in shale reservoirs. We developed the dual-porosity model to describe both the stimulated region and the unstimulated region in elliptical shale reservoirs. The gas flow follows Fick's Law between the matrix and the fractures due to the pressure difference and the concentration difference. In addition to the Laplace transform and Stehfest's algorithm, we also incorporate the modified Mathieu equations, including the angular Mathieu equation and the radial Mathieu equation, to obtain solutions of the elliptical flow model. The type curves are verified with the actual production data of the unconventional gas reservoir, and the sensitivities of the elliptical flow model are analyzed, including the inter-porosity coefficient λ, storativity ratio ω, adsorption index σ, and SRV size ξ1. The elliptical boundary characteristic parameter of SRV is a key parameter that is useful for describing and predicting the performances of fractured wells in composite shale reservoirs.