Well testing model for multi-fractured horizontal well for shale gas reservoirs with consideration of dual diffusion in matrix

Shale gas reservoir is typical unconventional reservoir, itʹs necessary to take advantage of multi-stage fractured horizontal well so as to develop those kinds of reservoirs, which can form high conductivity hydraulic fractures and activate natural fractures. Due to the existence of concentration gap between matrix and fractures, desorption gas can simultaneously diffuse into the natural fractures and hydraulic fractures. This process can be called dual diffusion. Based on the triple-porosity cubic model, this paper establishes a new well testing model of multi-stage fractured horizontal well in shale gas reservoir with consideration of the unique mechanisms of desorption and dual diffusion in matrix. Laplace transformation is employed to solve this new model. The pseudo pressure transient responses are inverted into real time space with stehfest numerical inversion algorithm. Type curves are plotted, and different flow regimes in shale gas reservoirs are identified and the effects of relevant parameters are analyzed as well. Considering the mechanism of dual diffusion in matrix, the flow can be divided into five regimes: early linear flow; pseudo-steady state inter-porosity flow; the diffusion from matrix into micro-fractures; the diffusion from matrix into hydraulic fractures and boundary-dominated flow. There are large distinctions of pressure response between pseudo steady state diffusion and unsteady state diffusion under different value of pore volume ratio. Itʹs similar to the feature of pseudo-steady state inter-porosity flow, diffusion coefficient and Langmuir parameters reflect the characters of pseudo-steady state diffusion. The numbers of stage of hydraulic fractures have certain impact on the shape factor of matrix and the inter-porosity coefficient. This new model is validated compared with some existing models. Finally, coupled with an application, this mew model can be approximately reliable and make some more precise productivity prediction.