Estimating size of finite fracture networks in layered reservoirs

Conductive fractures in petroleum reservoirs may be totally isolated or fully interconnected. There is an intermediate state between the two extremities. Partially fractured reservoirs include finite fracture networks (FFN), which are bundles of interconnected fractures embedded in a sea of isolated fractures. Devising measures for sizes of FFNs is crucial in estimating critical engineering aspects such as productivity index, production decline rate and expected ultimate recovery of wells especially in reservoirs with low matrix porosity and permeability. Here, we present results of statistical evaluation of FFN size in relation to fracture connectivity which is in essence the number of fracture intersections per fracture. The analysis is based on a large number of stochastic 2-dimensional (2D) Poisson models of sub-vertical layer bound fractures. Fracture length in the models has log normal or truncated power distribution and fracture strike has circular normal distribution. The models may have single or multiple fracture sets and various truncation modes with different probabilities.

The analysis shows that number of fracture intersections per fracture can be accurately estimated by a fracture connectivity index, which is defined as product of facture scan-line density, average fracture length and sine of strike standard deviation. The statistically significant finding of this study is that the number of fractures within a FFN is an exponential function of fracture connectivity index. All three fracture properties defining the index can be measured on borehole image logs. Hence it should be possible to estimate fracture connectivity and corresponding FFN size from borehole image data. The analysis pertains to 2D fracture connectivity which is always the lower bound of number of fracture intersections in 3-dimensions. Therefore the exponential relationships must also hold for actual 3-dimensional layer-bound fractures with variable dips.