Alternative linearization of water table kinematic condition for unconfined aquifer pumping test modeling and its implications for specific yield estimates

SummaryAn alternative linearization of the nonlinear kinematic condition at the water table used in unconfined aquifer flow theory is proposed. It simulates the downward propagation of the water table, during water extraction via a pumping well, as a diffuse process controlled by a dimensionless linearization parameter, βD. The limiting value of βD = 0 corresponds to the solution of Neuman (1972) whereas that of βD → ∞ corresponds to the early-time Theis solution. Using the solution obtained with this linearization, data collected during a pumping test conducted at the Boise Hydrogeophysical Research Site in Idaho, US, were analyzed. The estimates of hydraulic conductivity and specific storage obtained in this study compare well with those obtained with the other models. The most significant improvement is in the estimated value of specific yield, with the proposed model yielding values that are close to those expected from known porosity values (n ∼ 0.25) at the site. The results show that meaningful estimates of specific yield can be obtained by treating the water table as a diffuse moving material boundary, without recourse to more complex models for water table decline or inclusion of unsaturated zone flow.

Research highlights
► The nonlinear kinematic condition at water table is linearized to include a diffusion term.
► This treatment implies diffuse propagation of water table during pumping tests, controlled by a linearization parameter, βDβD.
► βDβD can take values on [0, ∞], with βD=0βD=0 corresponding to Neuman (1972).
► βDβD modifies the slope of log–log drawdown-time curve in the intermediate-time range.
► Resulting model significantly improves estimates of specific yield (Sy ∼ 0.2) for an aquifer where other models yield anomalously low values (∼0.02).