Transient flowmeter test: semi-analytic crossflow model

Abstract

The transient flowmeter test (TFMT) provides more information about the well–aquifer system than the traditional quasi-steady-state flowmeter test (QFMT). The TFMT duration may be much shorter than that of a QFMT, which is desirable at highly contaminated sites where the extracted water has to be treated as hazardous waste. Here we present the TFMT model that accounts for inter-layer crossflow, a thick skin surrounding the well, and wellbore storage. The model is derived under the simplifying assumptions of the pseudo-steady-state inter-layer crossflow and the uniform wellface flux within each layer. The semi-analytic solution is inverted numerically from the Laplace domain to the time domain. Layer and skin parameters are estimated from the TFMT data via the modified Levenberg–Marquardt algorithm. The estimation is robust when the initial parameter guesses are close to their true values. Otherwise, a computationally expensive search among the local minima of the objective function is necessary to find the parameter estimates. The modeling errors and the associated parameter estimation errors are evaluated in a number of synthetic TFMTs and compared to the corresponding results obtained with a general numerical model that relaxes the two simplifying assumptions. The TFMT provides reasonably accurate estimates of hydraulic conductivities for the aquifer layers and the damaged skins and order-of-magnitude estimates of layer specific storativities and hydraulic conductivities for the normal skin. The skin specific storativities should not be estimated from a TFMT. Multi-rate TFMTs with a step-variable pumping rate yield significantly more accurate parameters than constant-pumping-rate TFMTs. The calculated modeling errors may be useful in estimating the magnitude of parameter estimation errors from the TFMT. Our field tests in a coastal aquifer at the Lizzie Site in North Carolina (USA) demonstrate the feasibility of a TFMT for aquifer characterization. The downhole hydraulic conductivity profiles from our field and synthetic TFMTs are consistent with the corresponding profiles from QFMTs.