Estimation of spatial covariance of log conductivity from particle size data

We derive analytical relationships between the spatial covariance of the (natural) logarithm of hydraulic conductivity (K) and that of representative soil particle sizes and porosity. The latter quantities can be directly measured during routine sedimentological analyses of soil samples and provide a way of incorporating K estimates into groundwater flow models at a relatively modest experimental cost. Here we rely on widely used empirical formulations requiring measurements of representative particle diameters and, in some cases, of medium porosity. We derive exact formulations relating the spatial covariance of these quantities and K and present workable approximations on the basis of perturbation methods. Our formulations provide a direct link between key geostatistical descriptors of sedimentological and hydraulic parameters of heterogeneous aquifers which can be employed in classical estimation and simulation procedures. The approach and theoretical results are tested on an extensive data set comprising 411 particle size curves collected at 12 boreholes in a small-scale alluvial aquifer.