A Semi-Analytical Model of a Hydraulically Fractured Horizontal Well with Pre-Darcy Flow and Stimulated Reservoir Volume in a Radial Composite Shale Reservoir

Summary Due to the low porosity and permeability of the shale matrix, multi-fractured horizontal well (MFHW) is one of the most well-known technologies to promote the withdrawal of shale oil. It is a great challenge to characterize the flow behavior by coupling pre-Darcy flow in pores of the shale matrix and Darcy flow inside fractures, particularly in the radial composite shale reservoir with stimulated reservoir volume (SRV). Because the semi-analytical method can contribute to revealing the flow mechanism of the MFHW, the approach to efficiently obtain a suitable and exact semi-analytical solution becomes a key issue. In this work, to couple the modified point-source solution of the shale matrix with the numerical solution of fractures,we developed a semi-analytical solution to analyze the impact of pre-Darcy flow and SRV properties on the pressure behavior of the MFHW. Moreover, we used a local grid refinement method to verify the accuracy of the newly developed semi-analytical solution. The results show that the radial flow regime in the dimensionless pressure derivative will obviously disappear due to the pre-Darcy flow. Pre-Darcy flow in the SRV zone is adverse to the late production of the MFHW after the pseudolinear flow regime, while pre-Darcy flow in the unstimulated reservoir volume (USRV) zone is beneficial to increase the production during the regional interporosity flow regime. Meanwhile, the “groove” can be recognized from the pressure derivative curves, which mainly depend on the mobility ratio and the storage capacity ratio. In addition, due to the uneven distribution of fractures, the pressure derivative during the pseudoradial flow regime significantly deviates from 1/(2N).