To build a realistic reservoir model of 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 matrix–matrix interaction (M–M) are based on lab measurements. Our goal in this research is to analytically determine the transport properties of the two other types of interactions (M–F and F–F). As a result, we provide effective anisotropic transport properties for a reservoir cell that contains a fracture inside it—a fracture cell model. This fracture cell model can easily be implemented in reservoir simulators, without the 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.

We have tested the fracture cell model and have also applied it to multiple intersecting non-planar (curved) fractures. The fracture patterns were generated using a geostatistics-based approach. The fracture pattern with no preferred orientation could be taken as an example of a relatively brittle shale formation with an isotropic stress field. The fracture pattern embraces two disconnected fractures that are on the top and top left of the reservoir. The disconnected fractures (with no influence on the iso-pressure contours) could be representative of those activated during stimulation or of non-sealed natural fractures if they remain open under confined boundary conditions.

                    km = 1 microdarcy     

                    km = 100 nanodarcy  

                     km = 10 nanodarcy    

                                                                        1 yr                           3 yr                         7 yr

Pressure distributions of the fractured reservoir (100 ft x 100 ft) under constant-bottom-hole-pressure production obtained using the fracture cell model. The spatial locations of the low pressures are consistent with those of the fractures connected to the well from the bottom of the reservoir.

Representative article

1. Sakhaee-Pour, A., and Wheeler, M. F. (2016). Effective flow properties for cells containing fractures of arbitrary geometry. SPE Journal, 21(03), 965–80.