The performance of complex-structure fractured reservoirs considering natural and induced matrix block size, shape, and distribution

Abstract

This paper introduces an analytical approach for the performance of the fractured reservoir considering the impact of the matrix block size, shape, and distribution. The objective is better understanding the roles of the variable interporosity flow systems, fracture flowing systems, and reservoir matrix heterogeneity in the responses of the wellbore pressure drop, flow rate, cumulative production, and productivity index. This understanding could help to eliminate the uncertainties and increase the accuracy in characterizing the conventional and unconventional reservoirs where very complex structures of a significant disorder in the matrix block size, shape and distribution could be existed in the porous media.The study uses the well documented multilinear flow model to describe the pressure distribution in the naturally fractured reservoirs depleted by multiple hydraulic fractures considering different matrix block sizes, shapes, and distributions. The analytical models of the flow rate, cumulative production, and the productivity index are also developed in this study from the multilinear flow model. The reservoirs of interest are assumed to have stimulated porous media extending between hydraulic fracture and unstimulated volume extending beyond the fracture tips toward the reservoir boundary. The unstimulated reservoir volume is assumed consisting of uniformly distributed single matrix block size and shape because there is no impact for the hydraulic fracturing process. While the stimulated reservoir volume is considered consisting of a variable matrix block size, shape, and distribution because of the impact of hydraulic fracture propagation. The petrophysical properties of the two porous media, as well as the storativity and interporosity flow coefficient, are assumed functions of the matrix characteristics in the two volumes. The matrix block dimensions (radius or length) are correlated exponentially with the distance from the hydraulic fracture face toward the no-flow boundary between these fractures. Three fracture-matrix fluid flux functions are developed for the reservoirs where the matrix blocks could have a spherical, slab, and cylindrical configuration.The study has reached several conclusions. A positive impact on the reservoir performance is seen when the matrix block size becomes small or when the small size matrix blocks control the distribution of the blocks in the porous media. Reservoir performance is enhanced also when there are several matrix block sizes compared to a single size or very few sizes. It is observed that the reservoirs with spherical blocks may give better performance than the reservoir with slab or cylindrical matrix blocks. In terms of matrix block size and distribution, heterogeneous reservoirs may have a higher productivity index than homogenous reservoirs. The variable matrix block size and distribution in the stimulated reservoir volume is more beneficial than the unstimulated volume. The novel point presented in this paper is developing several analytical models for the wellbore pressure drop, flow rate, cumulative production, and productivity index of hydraulically fractured reservoirs with a consideration given to the matrix block size, shape, and distribution.