JULY 1-3 GROUND WATER/SURFACE WATER NTERACTONS AWRA SUMMER SPECULLTP CONF~NCR 22 32 CZ- PDG- ANALYSS OF NFLTRATED STREAM WATER TO A PUMPNG WELL Xunhong Chen' and Xi Chen' ABSTRACT: Pumping of groundwater near a stream indues the infiltration of stream water into the nearby aquifers, and this indued stream infiltration may result in onems about water quality at the well. This paper analyzes the migration proess of the infiltrated stream water toward a pumping well. MODFLOW is used to simulate the surfae water infiltration from a shallow stream to an alluvial aquifer, and MODPATH is used to reord the loations of the infiltrated water partiles during their movement to the well. Pathelines were plotted over a ross-setion, whih is perpendiular to the stream and ontains the pumping well, to show the hydrauli onnetivity between the pumping well and the stream. The area of influene zone, as well as the travel time, was used to haraterize the migration proesses of the stream water partiles. Generally, the movement of the infiltrated stream water in the nearby aquifer is very slow, and it often takes more than six months for the infiltrated stream water to arrive at the pumping well loated only several hundred meters from the stream. A number of variables redue the hydrauli onnetivity and thus the migration proess between the stream and the well. They inlude a deep pumping well, a short pumping duration and small pumping rate, a larger distane between the stream and the pumping well, a smaller vertial hydrauli ondutivity, a low-permeability streambed, an aquitard loated below the stream but above the top of the well sreen, and a regional hydrauli gradient toward the stream. KEY TERMS: Stream infiltration; partile traking; pathlines; influene zone. NTRODUCTON When groundwater withdrawal ours in an aquifer near a stream, the one of depression generated an interept the stream after a suffiiently long period of pumping. As soon as a hydrauli gradient from the stream to the aquifer is established, the stream begins to disharge surfae water to the aquifer. When water quantity is onemed, it is an issue of streamflow depletion; if the stream water has been polluted, it is also an issue of aquifer ontamination. For areas where the pumping well is for water supplies, analysis of the migration proess for the infiltrated stream water, as well as its arrival time to the well, is neessary for well head protetion. Although Wilson (1993) and Conrad and Beljin (1996) reognized the important assoiation of stream depletion to water quality issues, detailed analyses of the migration proess of the infiltrated stream water in the aquifer were not provided. Chen (21) evaluated the travel time and pathlines of the infiltrated water for stream-aquifer systems where a fully penetrating stream and pumping well, as well as an isotropi aquifer, must be assumed. His analysis learly demonstrated that although a slow proess, the infiltrated water will eventually arrive at the pumping well for a given period. His analysis foused on the migration proess over the x-y areal plane that does not haraterize the vertial features of the partile movement. Vertial flow omponents ommonly exist around the streams that partially penetrate aquifers. ' Conservation and Survey Division and Shool of Natural Resoure Sienes, University of Nebraska- Linoln, Linoln, NE 65, xhen2@unl.edu. 511
The objetive of this study is to analyze the movement of stream water partiles over a vertial ross-setion where the vertial and horizontal features of the migration proesses an be losely examined. A three-dimensional stream-aquifer model is designed to simulate the stream water infiltration and migration; pathlines are onstruted to show the hydrauli onnetivity between the pumping well and the stream. The effet of a number of hydrologi parameters on the migration proess of the infiltrated stream water in the nearby aquifers will be evaluated. These parameters inlude three groups: aquifer features, well plaement and operation, and regional hydrauli gradients. METHOD The groundwater flow in the area of the pumping well and the stream an be expressed suh that,, where h is the hydrauli head; K,, K,, and K, are the hydrauli ondutivity along the x, y, and z diretions; S, is the speifi storage of the aquifer; and R is a general sink/soure term that is intrinsially positive and defines the volume of inflow to the systems per unit volume of aquifer per unit time (Anderson and Woessner 1992). To simulate pumping R = -Wp. Numerial solutions of equation (1) an be seen from MDonald and Harbaugh (19). The rate of the flow from the stream to the aquifer is alulated from the differene of hydrauli heads in the stream and the adjaent aquifer ell (MDonald and Harbaugh 19): = C,#,. (H,,,.- h) (2) where Q,,, is the flow between the stream and the aquifer, H,,, is the head in the stream, h is the head at the node in the ell underlying the stream reah, C,,, is the hydrauli ondutane of the stream-aquifer interonnetion: where K,i,, is the hydrauli ondutivity of the streambed material, Lr,,, is the length of the stream hannel in the ell, W is the width of the stream hannel in the ell, and M is the thikness of the riverbed material. t is apparent that the volume of stream water infiltrating the aquifer is the funtion of streambed ondutane C,i, and (Hriv- h). After the stream water enters the aquifer, it moves toward the pumping well. The migration proesses is ontrolled by aquifer properties and other hydrologi variables. n this study, the movement of water partiles in the nearby aquifer was traed out using MODPATH (Pollok, 199a, 199b, 1994). Partiles were plaed in the stream-aquifer interfae to represent the stream water that will first enter the aquifer as soon as a hydrauli gradient from the stream to the aquifer is produed by the pumping well. These stream water partiles will then migrate toward the pumping well under the influene of the veloity field. MODPATH reords the oordinates of the partile moving paths until the partile reahes the well. Pathlines are plotted using the oordinates to show the onnetivity between the stream and the well. The part of aquifers where the pathlines have passed through is onsidered to be replaed by stream water, and if the stream water has been polluted, the part of aquifer is onsidered ontaminated. A 3-D stream-aquifer model was built using MODFLOW. The domain dimension is 1 m in length (x diretion) and 1 m in width (y diretion), and 3 m in thikness (z diretion). 512
The aquifer is unonfined. n the x diretion, spaing of nodes is from 2.5 m for the area between the stream and the well to 1 m for the area near the boundary; in the y diretion, spaing of nodes is from 5 m near the well to 1 m near the boundary; and in the z diretion, a onstant spaing of nodes (3 m) is used. The numbers of olumns in the x diretion varies from 163 to 21 depending on the distane between the well and stream. The numbers of rows in y diretion and in z diretion are onstant for eah simulation senario and they are 15 and 1, respetively. The stream is 5 m wide and 3 m deep. RESULTS Simulations were onduted to analyze the effets of aquifer properties, well plaement and operation, and regional hydrauli gradient on the migration of the infiltrated stream water in the nearby aquifer. The pathlines were plotted to show the influene area between the stream and the well. A larger influene area indiates a better hydrauli onnetion between the stream and well. The travel time is alulated for eah pathline. The pathlines were onstruted only over a vertial profile that ontains the pumping well and intersets the stream perpendiularly. A total of 36 water partiles were distributed along the stream-aquifer interfae in this ross-setion. Partiles moving over this profile take a shorter time arriving at the pumping well than those of other profiles. Effets of the Aquifer Properties Alluvial aquifers often have a strong anisotropy with a larger horizontal hydrauli ondutivity than the vertial one. Pumping test results suggest that the ratio of Kx/K, an he from 1 to 1 (Chen, 199; Chen et al., 1999; Ayers et al., 199; MGuire and Kilpatrik, 199). A number of simulations were onduted to analyze the effets of aquifer anisotropy on the migration of infiltrated stream water. The pathlines for K,/K, = 1 and 1 are plotted in Figures la and lb. The area overed by the pathlines is the influene zone where the infiltrated stream water has replaed the groundwater. As indiated by the two figures, a stronger vertial anisotropy leads to a redution in the vertial extension of the influene zone. The pumping ontinued for 365 days at a onstant rate of 4 m3/d. Additional simulations were onduted to analyze the role of an aquitard in ontrolling the migration of the infiltrated stream water. The aquitard layer is loated at the elevation below the stream but above the sreen of the pumping well. Figure 2 shows the pathlines of the stream water for two aquifers with a layer of aquitard. The hydrauli ondutivity values (K2) of the aquitard used for the two simulations were.1 and 1 m/d. t is believed that the layer of aquitard redues the hydrauli onnetivity between the stream and the well, and thus results in a smaller rate of stream infiltration. As indiated by Figure 2, rarely have any water partiles arrived at the pumping well after a period of 365-day pumping at a onstant rate of 4 m3/d. The infiltrated stream water did not penetrate the aquitard of K2 =.1 d d. (Figure 2a). The values of K, and K, in other layers of the model were 1 d d. Effets of the Well Operations and Plaement The well operations are referred to as the pumping rate and pumping duration; the well plaement inludes the depth of the well sreen loated in the aquifer and the distane from the 513
._ 2 2 3 3.- ;E T 2 9-. WE $ 1 = B - g 1 2 3 4 5 2 3 4 5 Figure 1. Pathlines of nfiltrated Stream Water Affeted by Aquifer Anisotropy. 3 3 - E._ 2 g x 2 2 m - D 5 W ii 1 - E 1 3 E a 9 2 3 4 5 2 3 4 5 Figure 2. Pathlines of nfiltrated Stream Water Affeted by An Aquitard. - 3 E ; ii 2-1 = 2 3 4 5-3 E.g 2 m D ii 1 z 2 3 4 5 b Figure 3. Pathlines of nfiltrated Stream Water Affeted by Pumping Rates 3._._ 2 : 2 z 1 = 3.e! 1 2 3 4 5 6 2 3 4 5 ix Figure 4. Pathlines of nfiltrated Stream Water Affeted by Well Loations. a 51 4
stream. Both the well operations and the well plaement affet hydrauli gradients between the stream and the well, and therefore affet the geometry of the influene zone. t is apparent that a higher pumping rate and a shorter distane between stream and the pumping well will shorten the arrival time of the infiltrated stream water to the well. Figure 3 shows the pathlines of two pumping rates, Q = 12 and 24 m3/d, respetively. After a 365- day period of pumping, no infiltrated stream water has arrived at the pumping well for the smaller pumping rate (Figure 3a); in ontrast, some stream water partiles that migrate in the shallow part of the aquifer have arrived at the pumping well for the larger pumping rate (Figure 3b). The earliest arrival time for this pumping rate is 3 15 days. The values of K, and K, are 1 m/d and KJK, = 1. Figure 4 shows the pathlines of the infiltrated stream water for two loations of pumping well, L = 3 and 15 m from the stream, respetively. After a ontinuous pumping of 365 days at a rate of Q = 4 m3/d, no stream water gets to the pumping well loated 3 m from the stream (Figure 4a). However, when L is only 15 m, 34 out of 36 water partiles that were released from the stream reahed the pumping well (Figure 4b). Effets of Regional Hydrauli Gradients Simulations were onduted to analyze the role of regional hydrauli gradient toward the stream. A gradient of.1 m/m was assumed in the model and thus the stream gained water from the aquifer before pumping began. The well pumped water for 365 days at rate of 4, m3/d. Pathlines in Figure 5 demonstrate that, during the pumping period, the partiles only in the right-hand side of the-stream (1 6 partiles) leak into the aquifer and move toward the well. However, the other 2 partiles are inapable of infiltrating into the aquifer, apparently beause the reversal of hydrauli gradients from the stream to the well has not been formed during the pumping period. As a result, the extension of the influene zone in Figure 5 is restrited in the upper layers of the aquifer. The hydrologi onditions used for this simulation were the same as those used in the simulation for Figure 1 b exept for there was regional hydrauli gradient. g 2-1 32 3 4 5 Figure 5. Pathlines of Stream Water Affeted by Regional Hydrauli Gradient. CONCLUSONS Generally, in the part of aquifer just under the stream-aquifer interfae, the infiltrated water migrates primarily downward where a vertial flow omponent is dominant and ontrols the path of the water partiles. For the area between the stream and the well, the migration path of the stream water is mainly in the horizontal diretions. A three-dimensional flow field is also signifiant near a partially sreened well. The migration proess is generally very slow, partiularly in the area near the stream; it speeds up when the water partiles get loser to the pumping well. The required time for a water partile to arrive at the well varies signifiantly and 515
is dependent on the initial loations along the stream-aquifer interfae. t often requires more than six months for the water partile, whih moves along the pathlines of the largest veloity, to arrive at a well that is loated only a ouple of hundred meters from the stream and is pumped at a high rate (for example, gallons per minute). When the horizontal hydrauli ondutivity is onstant, a derease in the vertial hydrauli ondutivity generally redues the hydrauli ondutivity between the well and the stream. That is beause a vertial flow omponent exits under the stream and the vertial hydrauli ondutivity plays a role in affeting the veloity field. An aquitard ourring in the layer below the stream but above the well sreen an redue the stream infiltration signifiantly. Well plaement and operation have a strong impat on the migration proess of the infiltrated stream water. For stream-aquifer systems where there is a regional hydrauli gradient toward the stream, the hydrauli onnetivity from the stream to the well is weaker than those systems where the river stage and the groundwater level are the same before pumping. Only when a reversal of hydrauli gradient from the stream to the aquifer is established does the stream begin to disharge water to the aquifer. REFERENCES Anderson, M. P., and W. M. Woessner, 1992. Applied Ground Water Modeling, Simulation of Flow and Advetive Transport. Aademi Press, n. San Diego, 31 p. Ayers, J. F., X. H. Chen, and D. Gosselin, 199. Behavior of nitrate-nitrogen movement around a pumping high-apaity well: a field example. Ground Water 6(2): 325-337. Chen, X. H., 199. Assessment of hydrauli properties from an alluvial aquifer near Grand sland, Nebraska. Journal of Amerian Water Resoures Assoiation 24(3): 63-616. Chen, X.H, J. Goeke, and S. Summerside, 1999. Hydrauli properties and unertainty analysis for an unonfined alluvial aquifer. Ground Water 37 (6): 45-54. Chen, X. H. 21. Migration of indued-infiltrated stream water into nearby aquifers due to seasonal ground water withdrawal. Ground Water 39(5): 721-72. Conrad, L. P., and M. S. Beljin, 1996. Evaluation of an indued infiltration model as applied to glaial aquifer systems. Water Resoures Bulletin 32(6): 129-122. MDonald, M. G., and A. W. Harbaugh, 19. Modular three-dimensional finite-differene groundwater flow model. Tehniques of water-resoures investigations of U. S. Geologial Survey. Book 6, CH. A, 576p. MGuire, V. L., and J. M. Kilpatrik, 199. Hydrogeology in the viinity of the Nebraska Management Systems Evaluation Area (MSEA) site, entral Nebraska, U. S. Geologial Survey Water-Resoures nvestigations Report 97-4266,25 p. Pollok, D. W., 199a. Doumentation of omputer programs to ompute and display pathlines using results from the U.S. Geologial Survey modular three-dimensional finite-differene ground-water flow model, US. Geologial Survey Open-File Report 9-31. Pollok, D. W., 199b. Doumentation of GKS-based MODPATH-PLOT, US. Geologial Survey Open-File Report 9-622. Pollok, D. W., 1994. User's Guide for MODPATHMODPATH-PLOT, Version 3: A Partile Traking Post-proessing Pakage for MODFLOW, the U. S. Geologial Survey Finite Differene Ground-water Flow Model, Reston, Virginia. Wilson, J. L., 1993. ndued infiltration in aquifers with ambient flow. Water Resoures Researh 29 (1): 353-3512. 516