Pumping In Unconfined Aquifers Research Articles

The Bredehoeft problem: Evaluating salvage during groundwater pumping in unconfined aquifers

During groundwater pumping from unconfined aquifers, evapotranspiration can be reduced as the water table drops, a process known as salvage. This phenomenon must be included in water balance assessments for accurate predictions of groundwater withdrawals. Although the salvage phenomenon has been well understood for a long time, i.e., since Theis’ pioneering studies, the models that were later developed by Bredehoeft always relied on numerical techniques to treat the inherent non-linearity, most commonly using MODFLOW. Analytical methods have been previously used with success for practical evaluation of water balance components such as stream depletion rates. This work presents a novel analytical solution of the Bredehoeft problem. It is a breakthrough in analytical evaluation of transient salvage losses induced by groundwater withdrawals due to declines of water table. We evaluate stream depletion and loss of storage in addition to salvage, using the new model. Detailed analysis of the solution using COMSOL software indicates that the linear approximation used in the analytical solution is accurate for most practical cases. Diagrams for drawdown, water balance and evaluation of solution accuracy are presented, considering a broad range of problem parameters. Results can be used for analyses of watershed-scale water balances.

A general analytical model for head response to oscillatory pumping in unconfined aquifers: effects of delayed gravity drainage and initial condition

Abstract. Oscillatory pumping tests (OPTs) provide an alternative to constant-head and constant-rate pumping tests for determining aquifer hydraulic parameters when OPT data are analyzed based on an associated analytical model coupled with an optimization approach. There are a large number of analytical models presented for the analysis of the OPT. The combined effects of delayed gravity drainage (DGD) and the initial condition regarding the hydraulic head are commonly neglected in the existing models. This study aims to develop a new model for describing the hydraulic head fluctuation induced by the OPT in an unconfined aquifer. The model contains a groundwater flow equation with the initial condition of a static water table, Neumann boundary condition specified at the rim of a partially screened well, and a free surface equation describing water table motion with the DGD effect. The solution is derived using the Laplace, finite-integral, and Weber transforms. Sensitivity analysis is carried out for exploring head response to the change in each hydraulic parameter. Results suggest that the DGD reduces to instantaneous gravity drainage in predicting transient head fluctuation when the dimensionless parameter a1=ϵSyb/Kz exceeds 500 with empirical constant ϵ, specific yield Sy, aquifer thickness b, and vertical hydraulic conductivity Kz. The water table can be regarded as a no-flow boundary when a1<10-2 and P<104 s, with P being the period of the oscillatory pumping rate. A pseudo-steady-state model without the initial condition causes a time-shift from the actual transient model in predicting simple harmonic motion of head fluctuation during a late pumping period. In addition, the present solution agrees well with head fluctuation data observed at the Savannah River site. Highlights. An analytical model of the hydraulic head due to oscillatory pumping in unconfined aquifers is presented. Head fluctuations affected by instantaneous and delayed gravity drainages are discussed. The effect of the initial condition on the phase of head fluctuation is analyzed. The present solution agrees well with head fluctuation data taken from field oscillatory pumping.

Cross‐correlation analysis and information content of observed heads during pumping in unconfined aquifers

Key Points cross‐correlation for pumping tests analysis in unconfined aquifers geological structure and variability are both considered during analysis cross‐correlation results are not axisymmetric

Comments on “A revisit of drawdown behavior during pumping in unconfined aquifers” by D. Mao, L. Wan, T.‐C. J. Yeh, C.‐H. Lee, K.‐C. Hsu, J.‐C. Wen, and W. Lu

Comments on “A revisit of drawdown behavior during pumping in unconfined aquifers” by D. Mao, L. Wan, T.‐C. J. Yeh, C.‐H. Lee, K.‐C. Hsu, J.‐C. Wen, and W. Lu

Replies to comments on “A revisit of drawdown behavior during pumping in unconfined aquifers” by Neuman and Mishra

Key Points Transition of water release mechanisms Heterogeneous, variably saturated flow equation Unconfined aquifers

A revisit of drawdown behavior during pumping in unconfined aquifers

In this study, the S‐shaped log‐log drawdown‐time curve typical of pumping tests in unconfined aquifers is reinvestigated via numerical experiments. Like previous investigations, this study attributes the departure of the S shape from the drawdown‐time behavior of the confined aquifer to the presence of an “additional” source of water. Unlike previous studies, this source of water is reinvestigated by examining the temporal and spatial evolution of the rate of change in storage in an unconfined aquifer during pumping. This evolution is then related to the transition of water release mechanisms from the expansion of water and compaction of the porous medium to the drainage of water from the unsaturated zone above the initial water table and initially saturated pores as the water table falls during the pumping of the aquifer. Afterward, the 1‐D vertical drainage process in a soil column is simulated. Results of the simulation show that the transition of the water release mechanisms in the 1‐D vertical flow without an initial unsaturated zone can also yield the S‐shaped drawdown‐time curve as in an unconfined aquifer. We therefore conclude that the transition of the water release mechanisms and vertical flow in the aquifer are the cause of the S‐shaped drawdown‐time curve observed during pumping in an unconfined aquifer. We also find that the moisture retention characteristics of the aquifer material have greater impact than its relative permeability characteristics on the drawdown‐time curve. Furthermore, influences of the spatial variability of saturated hydraulic conductivity, specific storage, and saturated moisture content on the drawdown curve in the saturated zone are found to be more significant than those of other unsaturated properties. Finally, a cross‐correlation analysis reveals that the drawdown at a location in a heterogeneous unconfined aquifer is mainly affected by local heterogeneity near the pumping and observation wells. Applications of a model assuming homogeneity to the estimation of aquifer parameters as such may require a large number of observation wells to obtain representative parameter values. In conclusion, we advocate that the governing equation for variably saturated flow through heterogeneous media is a more appropriate and realistic model that explains the S‐shaped drawdown‐time curves observed in the field.