Theoretical aspects for estimating anisotropic saturated hydraulic conductivity from in-well or direct-push probe injection tests in uniform media

Hydraulic conductivity and its anisotropy are fundamental aquifer properties for groundwater flow and transport modeling. Current in-well or direct-push field measurement techniques allow for relatively quick determination of general conductivity profiles with depth. However, capabilities for identifying local scale conductivities in the horizontal and vertical directions are very limited. Here, we develop the theoretical basis for estimating horizontal and vertical conductivities from different types of steady-state single-well/probe injection tests under saturated conditions and in the absence of a well skin. We explore existing solutions and a recent semi-analytical solution approach to the flow problem under the assumption that the aquifer is locally homogeneous. The methods are based on the collection of an additional piece of information in the form of a second injection (or recirculation) test at a same location, or in the form of an additional head or flow observation along the well/probe. Results are represented in dimensionless charts for partial validation against approximate solutions and for practical application to test interpretation. The charts further allow for optimization of a test configuration to maximize sensitivity to anisotropy ratio. The two methods most sensitive to anisotropy are found to be (1) subsequent injection from a lateral screen and from the bottom of an otherwise cased borehole, and (2) single injection from a lateral screen with an additional head observation along the casing. Results may also be relevant for attributing consistent divergences in conductivity measurements from different testing methods applied at a same site or location to the potential effects of anisotropy. Some practical aspects are discussed and references are made to existing methods, which appear easily compatible with the proposed procedures.