Production decline analysis for a multi-fractured horizontal well considering elliptical reservoir stimulated volumes in shale gas reservoirs

Multi-fractured horizontal wells (MFHWs) are an effective technique for developing shale gas reservoirs. After fracturing, stimulated reservoir volumes (SRVs) invariably exist around the wellbore. In this paper, a composite elliptical SRV model for each hydraulic fracturing stage is established, based on micro-seismic events. Both the SRV and the outer regions are assumed as single-porosity media with different formation physical parameters. Based on unstructured perpendicular bisection (PEBI) grids, a mathematical model considering Darcy flow, diffusion and adsorption/desorption in shale gas reservoirs is presented. The numerical solution is obtained by combining the control volume finite element method with the fully implicit method. The model is verified by a simplified model solution. The MFHW Blasingame production decline curves, which consider elliptical SRVs in shale gas reservoirs, are plotted by computer programming. The flow regions can be divided into five flow regimes: early formation linear flow, radial flow in the SRV region, transient flow, pseudo radial flow and boundary dominated flow. Finally, the effect of six related parameters, including the SRV area size, outer region permeability, SRV region permeability, Langmuir pressure, Langmuir volume and diffusion coefficient, are analyzed on type curves. The model presented in this paper can expand our understanding of MFHW production decline behaviors in shale gas reservoirs and can be applied to estimate reservoir properties, the SRV area, and reserves in these types of reservoirs by type curve matching.