A Simple Analytical Model for Oil Production from Partially Fractured Reservoirs to Estimate Size of Finite Fracture Networks

Most oil reservoirs are partially fractured, characterized by finite fracture networks (FFNs) in a sea of isolated fractures. It is necessary to determine size and shape of each FFN explicitly for reservoir simulation. FFN size is correlated with fracture connectivity, which is a function of fracture density, length, and angular scatter. Oil production from FFNs exhibits a long-term dual-porosity behavior. The initial fast rate (Phase I) represents depletion of matrix within FFN, and the subsequent gradual decline phase represents radial flow from the matrix outside the FFN perimeter. Thus, FFN size can be calculated from the cumulative oil production from Phase I, taking into account the pore volume, oil compressibility, and pressure decline. It is not always possible to identify the dual-porosity behavior by visual inspection. A mathematical model is needed to estimate FFN size. For this purpose, a set of three fundamental equations are derived for production rate, cumulative production, and pressure as a function of time. The model is a modified and simplified version of material balance equations with easy analytical solution. It is designed for fractured reservoirs with layer-bound fractures. Production is single-phase black oil under depletion drive. The analytical model was tested on four vertical wells. The unknown parameters such as FFN size, size of well drainage area, and fracture aperture are adjusted until an optimum fit to actual production data is obtained. FFN elliptical shape is estimated from average fracture strike and strike standard deviation. The results are validated by FFN size, fracture length, and aperture measurements from borehole images. The results are approximate but sufficient for preliminary mapping of FFNs with location and size and other critical attributes including fracture drainage area, matrix block size, fracture aperture, and permeability in partially fractured reservoirs.