Semi-analytical solution for pressure transient analysis of a hydraulically fractured vertical well in a bounded dual-porosity reservoir

We study the role of a hydraulic fracture on the pressure transient behavior of a vertical well producing from a bounded (or finite) dual-porosity formation. A combination of Laplace transform (LT) and the finite Fourier cosine transform (FFCT) are used to solve the diffusivity equation. The presented analysis allows identification of five flow regimes, including: 1) early linear flow, 2) volumetric depletion of natural fractures, 3) natural-fracture radial flow, 4) transition from natural-fracture radial flow to total (natural fractures and matrix) radial flow, and 5) pseudo-steady state flow. The results reveal that the interporosity flow coefficient, storativity ratio, natural fracture permeability anisotropy, and reservoir size play significant roles on the identified flow regimes compared to the hydraulically fractured well location and reservoir shape. The developed solution can be useful for well test analysis by generating a new set of type curves or can be applicable to a forward model for estimating parameters of reservoir. This study presents a new semi-analytical solution which finds application in well testing of hydraulically fractured wells in dual-porosity formations.