Theory of transient streaming potentials associated with axial-symmetric flow in unconfined aquifers

We present a semi-analytical solution for the transient streaming potential response of an unconfined aquifer to continuous constant rate pumping. We assume that flow occurs without leakage from the unit below a transverse anisotropic aquifer and neglect flow in the unsaturated zone by treating the water-table as a moving material boundary. In the development of the solution to the streaming potential problem, we impose insulating boundary conditions at land surface and the lower boundary of the lower confining unit. We solve the problem exactly in the double Laplace—Hankel transform space and obtain the inverse transforms numerically. The solution is used to analyse transient streaming potential data collected during dipole hydraulic tests conducted at the Boise Hydrogeophysical Research Site in 2007 June. This analysis yields estimates of aquifer hydraulic parameters. The estimated hydraulic parameters, namely, hydraulic conductivity, transverse hydraulic anisotropy, specific storage and specific yield, compare well to published estimates obtained by inverting drawdown data collected at the field site

Theory of transient streaming potentials in coupled unconfined aquifer-unsaturated zone flow to a well

A semianalytical solution is presented for transient streaming potentials associated with flow to a pumping well in an unconfined aquifer, taking into account the effect of flow in the unsaturated zone above the water table. Flow in the unsaturated zone is modeled with a linearized form of Richards\u27 equation using an exponential model for soil moisture retention and unsaturated hydraulic conductivity. Archie\u27s law is invoked for unsaturated electrical conductivity. The unsaturated electrokinetic coupling coefficient is modeled with a decaying exponential, where the maximum value is at and below the water table. The coupled flow and electrokinetic problem is solved using Laplace and Hankel transforms. The results of the model predicted behavior are presented and compared to that observed in laboratory simulations of pumping tests. The early time polarity reversal predicted the model is observable in the experiments. Other nonmonotonic streaming potential behaviors predicted by the model are also evident in experimental measurements. The model is used to estimate hydraulic parameters from SP data and these compare well to those obtained from drawdown data. For example, a hydraulic conductivity of 3.6 × 10−4 m/s is obtained from SP data compared to 3.4 × 10−4 m/s from drawdown data