Effective Flow Properties for Cells Containing Fractures of Arbitrary Geometry

Abstract

Summary Hydrocarbon production from unconventional resources such as shale usually entails stimulation by hydraulic fracturing, which results in nonplanar (curved) fractures. However, most reservoir models assume that the induced fractures are planar for the sake of simplicity. Considering the growing interest of the petroleum industry in better understanding production from these resources, we develop a fracture-cell model to capture the effects of fracture nonplanarity on transport properties. To build a realistic reservoir model for a fractured formation, we must account for three types of interactions: matrix-matrix (M-M), matrix-fracture (M-F), and fracture-fracture (F-F). The transport properties of the M-M interaction are based on laboratory measurements. In this study, we analytically determine the transport properties of the two other types of interactions (M-F and F-F). For this purpose, we account for the aperture size and spatial location of the fracture. As a result, we provide effective porosity and effective anisotropic permeabilities for a reservoir cell that contains a fracture inside it. The reservoir cell with transport properties that are modified is a fracture cell. We implement the fracture-cell model in a reservoir simulator and perform analyses for a single fracture and for multiple intersecting fractures; these fractures are nonplanar. The analyses include both single- and multiphase flow models and show that the hydrocarbon pressure inside the reservoir is strongly dependent on the fracture geometry when the matrix permeability is smaller than 1 µd. Thus, it is crucial to model the fracture geometry more accurately in unconventional reservoirs with ultralow permeabilities such as shale. One can easily implement the developed fracture-cell model in reservoir simulators, and there is no local refinement around the fracture. The main advantage of the proposed model is its simplicity, conjoined with its ability to capture the nonplanarity of the fracture. The developed model has major applications for understanding production from formations that are heavily fractured.