Stream depletion by a pumping well including the effects of nonlinear variation of captured evaporation from a phreatic aquifer

Hydrological Sciences Journal-journal Des Sciences Hydrologiques, 2004

A study was made to develop a model that can be used to predict the steady-state stream depletion rates caused by a continuous pumping well located in a water table aquifer. The effects of nonlinear variation of evaporation with the depth to water table on steady-state stream depletion rate were investigated using model results. Dimensional analysis was used to determine the relationship between the scaled steady-state stream depletion, the scaled pumping distance, the scaled hydraulic conductivity, and the scaled initial depth to the water table. A dimensionless graph was developed for a wide range of these parameters. Analysis of this graph showed that the steady-state stream depletion rate decreases as the pumping distance between the well and the stream increases. The dimensionless graph also showed that steady-state stream depletion rates strongly depended on the initial position of the water table. Analysis indicated that, as the saturated conductivity increased, the effect of the initial position of the water table on the magnitude of stream depletion rate was more influential. Analysis also showed that, as the value of saturated conductivity decreased, the relative error produced by the assumption that at steady state all the pumped water is captured from the evaporation, also decreased.

Aquifer drawdown and variable-stage stream depletion induced by a nearby pumping well

2015

A stream depletion phenomenon has been studied for many decades and different analytical models were developed to find the effect of a pumping well on a nearby stream. Most developed models consider a constant stream stage or neglect the variation in stream stage. This is not the case in reality where stream flow and level continuously vary over time. In this paper a new analytical model was developed considering variation in stream flow (i.e. stream stage). The developed model considers the recession of stream flow and its impact on stream depletion and drawdown. A Comparison between the developed solution and the existing ones shows a significant discrepancy when the stream flow varies.

Empirical relationships for estimating stream depletion by a well pumping near a gaining stream

Ground Water, 2005

Siting wells near streams requires an accurate estimate of the quantity of water derived from the river due to pumping. A number of hydrogeological and hydraulic parameters influence this value. This study estimates stream depletion under steady-state conditions for a variety of hydrogeological systems. A finite differences model was used to analyze several hydrogeological situations, and for each of these the stream depletion was estimated using an advective transport method. An empirical equation for stream depletion was obtained for the case of a stream that partially penetrates the aquifer and a pumping well that is screened over a portion of the aquifer. The derived equation, which is valid for both isotropic and anisotropic conditions, expresses stream depletion as a function of the unit inflow to the river, the discharge of the pumping well, the well screen length, the distance between the river and pumping well, the wetted perimeter, and a new parameter called ''overlap,'' which is defined to be the distance between the riverbed and the top of well screen. The overlap parameter makes it possible to consider indirectly the vertical component of flow, which is accentuated when the well is screened below the streambed. The formula proposed here should be useful in deciding where to locate a pumping well and to decide the appropriate length of its screen.

Drawdown and stream depletion induced by a nearby pumping well

Journal of Hydrology, 2012

Stream depletion Drawdown Stream leakage Groundwater/surface water interaction Superposition principle s u m m a r y This study derives two dimensional analytical solutions for drawdown and stream depletion resulting from a pumping well near a stream. The solutions were obtained for both line-width and finite-width streams in unconfined/confined aquifers, based on the principle of superposition. These solutions are general enough to be used for different hydrogeological settings within both unconfined and confined aquifers.

An evaluation of analytical solutions to estimate drawdowns and stream depletions by wells

Water Resources Research, 1991

Analytical solutions for computing drawdowns and streamflow depletion rates often neglect conditions that exist in typical stream-aquifer systems. These conditions can include (I) partial penetration of the aquifer by the stream, (2) presence of a streambed clogging layer, (3) aquifer storage available to the pumping well from areas beyond the stream, and (4) hydraulic disconnection between the stream and the well. A methodology is presented for estimating extended flow lengths and other parameters used to approximate the increased head losses created by partially penetrating streams and clogging layer resistance effects. The computed stream depletion rates and drawdown distributions from several analytical solutions were compared to those obtained using a two-dimensional groundwater flow model. The stream geometry was approximated as a semicircle. Numerical simulation results indicate that, because of the use of simplifying assumptions, the analytical solutions can misrepresent aquifer drawdown distributions and overestimate stream depletion rates. Assuming that a correct simulation of the stream depletion phenomenon is provided by the numerical model, the error associated with each of the simplifying assumptions was determined. At a time of 58.5 days after pumping began, errors in computed stream depletion rates due to neglect of partial penetration were 20%, those due to neglect of clogging layer resistance were 45%, and those due to neglect of storage in areas beyond the stream were 21%. Neglecting hydraulic disconnection had only a minor effect (i.e., an error of 1% only at a time of 58.5 days after pumping began) on computed stream depletion rates and a noticeable effect on aquifer drawdown distributions. groundwater withdrawals near a stream, the water table can be lowered below the streambed elevation, thereby severing the saturated exchange between the stream and the aquifer, creating disconnection, and forming an unsaturated zone Copyright 1991 by the American Geophysical Union. Paper number 91WR00001. 0043-1397/91/91WR-00001 $05.00 below the streambed (Figure 1 c). Under these conditions, as long as the water level in the stream does not change, a further drawdown of the water table due to pumping does not significantly affect the seepage rate from the stream. Several analytical solutions are available for computing drawdowns and stream depletions caused by pumping near a stream [e.g., Theis, 1941; Glover and Balmer, 1954; Jacob, 1950; Hantush, 1965]. These solutions typically incorporate image well theory to predict the rate at which a pumping well depletes flow in a nearby stream. The solutions are based on simplifying assumptions, e.g., (1) the stream fully penetrates the aquifer, (2) the stream and the aquifer are hydraulically connected, (3) the streambed is unclogged, (4) the stream is infinitely long and straight, and (5) the aquifer underlying the stream is isotropic, semi-infinite in extent, of constant transmissivity, and that only horizontal flow (i.e., Dupuit flow) occurs in the aquifer. To account for the effects of vertical seepage from streams that only partially penetrate the full aquifer thickness and whose beds and banks are much less permeable than the aquifer, the method of additional seepage resistances [e.g., Streltsova, 1974] has often been applied [Hantush, 1965]. This technique extends the actual distance between the stream and the pumping well by an additional length, horizontal flow through which results in head losses equivalent to the additional losses created by partial penetration and clogging layer effects. Extended flow lengths based on the Hahtush [1965] solution are, however, smaller than those based on the Jacob [1950] solution. The new "effective distance" replaces the actual distance between the stream and the well as used in the Theis [1941] solution.

A revisit of drawdown behavior during pumping in unconfined aquifers

Water Resources Research, 2011

1] 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. (2011), A revisit of drawdown behavior during pumping in unconfined aquifers, Water Resour. Res., 47, W05502,

Drawdown and Stream Depletion Produced by Pumping in the Vicinity of a Partially Penetrating Stream

Ground Water, 2001

Commonly used analytical approaches for estimation of pumping-induced drawdown and stream depletion are based on a series of idealistic assumptions about the stream-aquifer system. A new solution has been developed for estimation of drawdown and stream depletion under conditions that are more representative of those in natural systems (finite width stream of shallow penetration adjoining an aquifer of limited lateral extent). This solution shows that the conventional assumption of a fully penetrating stream will lead to a significant overestimation of stream depletion (> 100%) in many practical applications. The degree of overestimation will depend on the value of the stream leakance parameter and the distance from the pumping well to the stream. Although leakance will increase with stream width, a very wide stream will not necessarily be well represented by a model of a fully penetrating stream. The impact of lateral boundaries depends upon the distance from the pumping well to the stream and the stream leakance parameter. In most cases, aquifer width must be on the order of hundreds of stream widths before the assumption of a laterally infinite aquifer is appropriate for stream-depletion calculations. An important assumption underlying this solution is that stream-channel penetration is negligible relative to aquifer thickness. However, an approximate extension to the case of nonnegligible penetration provides reasonable results for the range of relative penetrations found in most natural systems (up to 85 %). Since this solution allows consideration of a much wider range of conditions than existing analytical approaches, it could prove to be a valuable new tool for water management design and water rights adjudication purposes.

Stream Depletion by Groundwater Pumping in Leaky Aquifers

Journal of Hydrologic Engineering, 2008

We present a simple approach to assess stream depletion by groundwater pumping in aquifers with leakage from an underlying source bed. The hydrogeological setting consists of a leaky aquifer that is hydraulically connected to a stream of shallow penetration. Under such conditions, the pumping rate is partially supported by the depletion of an adjacent stream. We quantify this phenomenon by

Effects of Streambed Conductance on Stream Depletion

Water, 2015

Stream depletion, which is the reduction in flow rate of a stream or river due to the extraction of groundwater in a hydraulically connected stream-aquifer system, is often estimated using numerical models. The accuracy of these models depends on the appropriate parameterization of aquifer and streambed hydraulic properties. Streambed conductance is a parameter that relates the head difference between the stream and aquifer to flow across the stream channel. It is a function of streambed hydraulic conductivity and streambed geometry. In natural systems, streambed conductance varies spatially throughout the streambed; however, stream depletion modeling studies often ignore this variability. In this work, we use numerical simulations to demonstrate that stream depletion estimates are sensitive to a range of streambed conductance values depending on aquifer properties. We compare the stream depletion estimates from various spatial patterns of streambed conductance to show that modeling streambed conductance as a homogeneous property can lead to errors in stream depletion estimates. We use the results to identify feasible locations for proposed pumping wells such that the stream depletion due to pumping from a well within this feasible region would not exceed a prescribed threshold value, and we show that incorrect assumptions of the magnitude and spatial variability of streambed conductance can affect the size and shape of the feasible region.

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