Fracture Critical Length Estimative Using Percolation Theory and Well Logging Data

Groundwater transport in crystalline rocks follows pathways along fractured zones because of low primary porosity and permeability in such formations. Fractured systems encompass an imbricated set of joints and fractures with different lengths, apertures and orientations resulting in complex permeable systems with heterogeneous groundwater transport properties. Geophysical well logging has proved effectiveness in detecting depth levels with denser fracture distributions as well as the apparent aperture of fractures contributing to groundwater flow. In many cases, the extension spanned by a fracture network cannot be directly inferred because it may extend beyond the radius of investigation of common well logging probes, thus preventing quantitative estimation of critical length for lateral extension a connected fractured system may have. Here we apply a percolation theory model to estimate the critical length as inferred from the linear density of fracture distribution observed at the borehole wall with an optical imaging probe. Our results are analyzed with electrical well logging data (normal resistivity and single-point resistance) cross borehole slug tests using a set of three boreholes. A critical length of 3.9 m was inferred with a percolation model which revealed consistency with the cross borehole slug tests from two wells situated 10 m and 30 m in the vicinity of the monitored borehole. Our results suggest the utility of inferring critical percolation lengths from fracture parameters obtained using standard well logging imaging techniques with potential applications to evaluate groundwater resources, characterize contaminated sites and provide geotechnical information for works in fractured formations.