Semi-analytical solution for productivity evaluation of a multi-fractured horizontal well in a bounded dual-porosity reservoir

Development of horizontal drilling and multi-stage fracturing technologies makes the production of unconventional reservoirs economically and practically feasible. We study the productivity of the multi-fractured horizontal well (MFHW) in a bounded dual-porosity formation. The infinite conductivity fracture case is modeled by combining the Laplace transform (LT) and finite Fourier cosine transform (FFCT). The model is implemented to finite conductivity cases by applying the distributed volumetric sources (DVS) method. The model outputs are verified by comparing them with the results of the separation of variables technique. Different possible flow regimes are observed. The capability of the finite conductivity solution method for optimizing the fracture geometry is approved. The effects of the interporosity coefficient and storativity ratio as the dual-porosity parameters on the productivity of a bounded dual-porosity reservoir are studied by conducting a sensitivity analysis. Similar to single-porosity reservoirs, it is found that the optimum fracture design based on the pseudo-steady state flow regime leads to a higher productivity in the transient flow regimes in the dual-porosity cases. Finally, the proposed approach is used to perform an economic optimization of the hydraulic fracture design. This research study assists researchers and engineers to make better/more accurate fracture design in various applications such as production from unconventional petroleum reservoirs and remediation in fractured underground porous systems.