Simplified Green-Ampt Model, Imbibition-Based Estimates of Permeability, and Implications for Leak-off in Hydraulic Fracturing

Predicting water imbibition into porous materials is important in a wide variety of fields, and hydraulic fracturing of low permeability hydrocarbon reservoirs has emerged as an application that is imposing a large water footprint. Reliable predictions of imbibition are needed to better manage water use, yet are challenging because of uncertainties in both the permeability and capillary pressure driving force. Here, this uncertainty is reduced through evaluating correlations between the permeability and the effective capillary pressure associated with the wetting front, P-c,P-f. These correlations allow elimination of P-c,P-f from the Green and Ampt equation and concentrate all uncertainties in fluxes on the effective permeability k. Over a wide range of k and porosities n, imbibition scales approximately with k(1/3). Although Leverett k(1/4) scaling for predicting P-c,P-f is shown to be inferior when tested with data spanning a wide range of n, it nevertheless predicted imbibition fairly well. From simple imbibition measurements, both the empirical and Leverett scaling approaches allow estimates of k that have root-mean-square deviations of about one order of magnitude relative to measurements that ranged over 10 orders of magnitude in k. Key Points The capillary pressure associated with the imbibition front can be approximated as a power function of permeability Scaling the wetting front capillary pressure to the permeability reduces uncertainty in the Green and Ampt imbibition equation A new correlation was developed to estimate permeabilities based on imbibition measurements