Modeling the Scale-Dependent Relationship Between Effective and Slug Test-Determined Saturated Hydraulic Conductivities

Slug tests are commonly used to measure saturated hydraulic conductivity in wells. How accurately do such tests, which are strongly influenced by aquifer properties close to the well screen, represent the larger-scale effective saturated hydraulic conductivity of a heterogeneous aquifer? To help answer this question we numerically-simulated steady-state and transient flows in 37 different 2-dimensional heterogeneous fields using Modflow. Each field consisted of 59,049 individual saturated hydraulic conductivity (K) values, grouped into hydrofacies with varying degrees of spatial structure and different length scales. An effective saturated hydraulic conductivity, (K-eff), was computed from the equilibrium fluxes in the steady-state simulations using Darcy's law. For the transient flow simulations a well was located at random in each field, and a slug of water was added. The resulting head response data were then analyzed by the Jacob-Bredehoft-Papadopoulos method yielding the slug test saturated hydraulic conductivity (K-slug). Three replicate slug test simulations were performed in each field. For fields comprised of only a few large hydrofacies with no spatial structure, the relationship between ln(K-eff) and ln(K-slug) was poor (coefficient of determination, R-squared = 0.25). The resulting regression equation indicated the slug test results underestimate K-eff except for the most conductive fields. In contrast, a strong relationship was found between ln(K-eff) and ln(K-slug) (R-squared = 0.94) for fields comprised of many small hydrofacies arranged in a nested spatial structure. In this case K-eff was overestimated except for the most conductive fields. Considering all of the fields together it was possible to predict ln(K-eff) from ln(K-slug) with a mean absolute percent error (MAPE) of 57%. Averaging results for the three replicate slug tests reduced the MAPE associated with the prediction of ln(K-eff) to 28%.