Electrical resistivity—hydraulic conductivity relationships in glacial outwash aquifers

Empirical field relationships between the apparent formation factors from surface resistivity soundings and hydraulic conductivity from pumping tests in fresh water granular aquifers usually show positive correlations. These relationships can be adequately explained by theory if consideration is taken of in situ field conditions. A sound theoretical basis for relating apparent formation factor to pertinent hydrogeophysical parameters in homogeneous isotropic sand is a three-phase parallel resistor model which explicity includes parameters of porewater resistivity, grain size and shape, porosity, tortuosity, and intergranular surface conductance. The veracity of the theoretical model is supported by data from laboratory tests. The model demonstrates that intergranular surface conductance is an important factor at small grain sizes and high porewater resistivities, operating to lower the apparent formation factor. The model further shows that direct relationships between hydraulic conductivity and formation factor are weak in the normal range of porewater resistivity, being strongly dependent on porosity. When systematic variation of in situ porosity and aquifer layering effects are considered, a simulated field curve relating the apparent formation factor to hydraulic conductivity is shown to compare favorably with the comparable curve from field data for thirteen pumping test sites in southern Rhode Island. Both theoretical and empirical results demonstrate a useful positive correlation between aquifer apparent formation factor and hydraulic conductivity. Quantitative interpretation, however, is imprecise because of nonuniqueness of interpretation and inherent variation in important aquifer parameters, especially porosity.