Fluid flow in fractured reservoirs: Exact analytical solution for transient dual porosity model with variable rock matrix block size

Abstract

Dual porosity reservoirs consist of two comparatively independent systems of fractures and matrix blocks with high and low permeability values, respectively. Semi-analytical and numerical studies on naturally fractured reservoirs have been already cited in the literature. The present study focuses on investigation of a linear double porosity model of a semi-infinite-acting naturally fractured reservoir using an exact analytical method. Different matrix block size distributions are embedded into a transient model to consider the effects of heterogeneity in fractured formations. In order to take into account transient fracture-matrix exchange, an analytical method is proposed to solve the coupled fracture and matrix equations. Gauss Legendre quadrature is employed to evaluate the double integral of general transient solution. Moreover, the corresponding shape factor was evaluated in a double porosity transient model coupled with variable matrix block size distribution. Results demonstrated that matrix block size distributions strongly affect the fluid transfer during the early time region. Also, the presented model was employed to generate interference test curves which in turn were studied to investigate the impacts of storativity ratio and matrix block size distributions on the fracture-matrix fluid transfer. Results illustrated that a series of obtained pressure data from an observational well along with the proposed model may be considered a robust method in fracture intensity assessment. Fast sensitivity analysis and very efficient computational cost are the benefit of the derived analytical solutions with respect to previous numerical solutions.