Hydrocarbon production from unconventional resources such as shale usually entails stimulation by hydraulic fracturing, which results in non-planar (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 non-planarity on transport properties.

To build a realistic reservoir model for a fractured formation, three types of interactions must be accounted for: matrixmatrix (M-M), matrix-fracture (M-F), and fracture-fracture (F-F). The transport properties of the matrix-matrix interaction (MM) are based on lab 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 whose transport properties 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 non-planar. 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 microD. Thus, it is crucial to model the fracture geometry more accurately in unconventional reservoirs with ultra-low permeabilities such as shale.

The developed fracture cell model can easily be implemented in reservoir simulators, and there is no need for local refinement around the fracture. The main advantage of the proposed model is its simplicity, conjoined with its ability to capture the non-planarity of the fracture. The developed model has major applications for understanding production from formations that are heavily fractured.

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