Simplified Green-Ampt model, imbibition-based estimates of permeability, and implications for leak-off in shale reservoirs

Predicting water imbibition into porous materials is important in a wide
variety of fields, yet is often 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, Pc,f. These correlations allow elimination of Pc,f from the
Green and Ampt equation, and concentrates all uncertainties in fluxes on
the effective permeability k. Over a wide range of k and n, imbibition
scales approximately with k1/3. Although Leverett k1/4 scaling for
predicting Pc,f is shown to be inferior when tested with data spanning a
wide range of porosities 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 1 order of magnitude relative to measurements that
ranged over 10 orders of magnitude in k.