A Decomposed Fracture Network Model for Characterizing Well Performance of Fracture Networks on the Basis of an Approximated Flow Equation

Abstract

Abstract The gridless analytical and semianalytical methodologies can provide credible solutions for describing the well performance of the fracture networks in a homogeneous reservoir. Reservoir heterogeneity, however, is common in unconventional reservoirs, and the productivity can vary significantly along the horizontal wells drilled for producing such reservoirs. It is oversimplified to treat the entire reservoir matrix as homogeneous if there are regions with extremely nonuniform properties in the reservoir. However, the existing analytical and semianalytical methods can only model simple cases involving matrix heterogeneity, such as composite, layered, or compartmentalized reservoirs. A semianalytical methodology, which can model fracture networks in heterogeneous reservoirs, is still absent; in this study, we propose a decomposed fracture network model to fill this gap. We discretize a fractured reservoir into matrix blocks that are bounded by the fractures and/or the reservoir boundary and upscale the local properties to these blocks; therefore, a heterogeneous reservoir can be represented with these blocks that have nonuniform properties. To obtain a general flow equation to characterize the transient flow in the blocks that may exhibit different geometries, we approximate the contours of pressure with the contours of the depth of investigation (DOI) in each block. Additionally, the borders of each matrix block represent the fractures in the reservoir; thus, we can characterize the configurations of complex fracture networks by assembling all the borders of the matrix blocks. This proposed model is validated against a commercial software (Eclipse) on a multistage hydraulic fracture model and a fracture network model; both a homogeneous case and a heterogeneous case are examined in each of these two models. For the heterogeneous case, we assign different permeabilities to the matrix blocks in an attempt to characterize the reservoir heterogeneity. The calculation results demonstrate that our new model can accurately simulate the well performance even when there is a high degree of permeability heterogeneity in the reservoir. Besides, if there are high-permeability regions existing in the fractured reservoir, a BDF may be observed in the early production period, and formation linear flow may be indistinguishable in the early production period because of the influence of reservoir heterogeneity.