Exercise 1 Solution: Effects of Well Location (Distance from Well to River)

The problem:

Exercise 1 requests that you consider the hypothetical desert-basin, stream-aquifer system, as illustrated in Figure 17 and answer the following questions. Does the position of the pumping well relative to the stream affect the response of the system? Specifically, how does it affect (1) the magnitude and timing of the effect of pumping on surface water, and (2) the relative sources of water to the well? What is the nature of these effects? Consider two alternative well locations—one further from the river and one closer to the river. Are any of these pumping scenarios sustainable? If you were a water manager for this stream-aquifer system, which well location would you consider preferable, and why? And are there any tradeoffs, such as the amount of drawdown in the pumping well?

How to run and analyze the model results:

If you have not already done so, it is useful to read Box 3, then run and post-process the results of the Base Case model of Case Study 1 before undertaking Exercise 1. To do this, first put the input files, MODFLOW-NWT executable code, and ModelMuse files for the Base Case of Case Study 1 on a Microsoft-OS computer by downloading the zip file “CaseStudy1–Models.zip“ from the online Supplementary Information for this book. Extract the “Case Study 1” folders and subfolders onto your personal computer. Then go through the steps described in Box 3.

Acquiring a file folder for Exercise 1:

Next download the zip file “Exercise1.zip“ from the online Supplementary Information for this book. To get you started, we have already copied the Base.Case input files into two new folders under the folder “Exercise 1” (Well.Closer.to.River.Case and Well.Further.from.River.Case); you can use these to simulate the cases with the well at two alternative locations — one closer to the river and the other further from the river. However, the files have not been modified yet, so if you execute either of these simulations without changes, you will get the base case result. We suggest you work from these two folders to analyze and develop solutions to Exercise 1. For convenience, we have also installed a copy of the executable code for MODFLOW-NWT in a location that will work with the batch files in these two folders.

Modifying Input Files to move the well:

Next, modify the input files in the Input.Files subfolders of the two folders “Well.Closer.to.River.Case” and “Well.Further.from.River.Case” to move the position of the well closer to and further from the river, respectively. For each variant, it might be easiest to modify the input file for the WEL Package manually using a text editor, such as Notepad. In this approach, you only have to modify the column coordinate in the pumping well data, which is the very last line of the file “Base.Case.wel”, which shows the well in row = 40 and column = 30. The stream is in column 40 so the new well will be half way between the base case well and the stream if it is placed in column 35. The mountains are to the left of column 1 so the new well will be half way between the base case well and the mountains if it is placed in column 15.

If you change the name of this file [or of any other input file], then you also have to make a corresponding change to the name of that file within file “Base.Case.nam”. If you change the name of the “name” file, then you have to make a corresponding change to its name in the file “Base.Case.bat”. You can run the modified problem by double-clicking on the batch file (named “Base.Case.bat”), assuming the folder “MODFLOW-NWT.Model” is at the same level as we setup in the zip file “Exercise1.zip”, that is, at the same level as the folders “Well.Closer.to.River.Case” and “Well.Further.from.River.Case”.

Alternatively, if you have the ModelMuse software on your Microsoft-OS computer, or download it as described in Box 3, you can modify the position of the well by opening the ModelMuse project file “Base.Case.gpt” and adjusting the well position therein, exporting the input files, and running the program from within ModelMuse. You will also be able to use ModelMuse to visualize the groundwater heads and drawdowns using the instructions from Box 3 to contour data from the name.fhd and name.fdn files.

Post-processing the new model results:

Box 3 provides step-by-step instructions for analyzing and plotting the water budgets and hydrographs, preparing contour maps of hydraulic head and drawdown, and computing streamflow gains and losses for the Base Case. For Exercise 1 repeat that process for the models with the well closer to and further from the stream. Once you complete the analysis for the other model, it is useful to include the results for all three cases in the same graph to facilitate comparison. Data from the model output of this exercise are included in spreadsheets located in the “DataSpreadsheets” subfolder of the “Exercise 1” folder.

Analysis of impact of well position on streamflow:

In assessing the effects of pumping on streamflow, it is important to remember that the river is interacting with the aquifer even under natural predevelopment conditions. Specifically, the river is losing water to the aquifer in the upstream reaches of the river and is gaining water from the aquifer in the lower downstream reaches of the river. This is clearly indicated by the predevelopment head distribution (Figure 20a). However, pumping the well disturbs these “natural” interactions.

After post-processing the streamflow result for the base case and the two cases with the well closer to and further from the stream, the results are compared at the end of the simulation (t = 200 years). The methods and steps used to calculate streamflow gains and losses are detailed in Box 3.

The results shown in Figure ExSol 1-1 indicate that the location of the well relative to the river has only a small effect (relative to the magnitude of the streamflow) on the streamflow profile along the river — certainly a smaller effect than that of the pumping itself. At the most downstream point, where the river leaves the area of the model, the flow is essentially the same for all three well locations. The same is true at the halfway point down the river, which is the north-south position of the well in all cases. However, upstream from the halfway point, streamflow is lowest for the case of the closer well and highest for the case of the further well. The area upstream of the halfway point is where the river is losing water because of natural seepage losses as well as induced infiltration because of the drawdown caused by pumping. Downstream of the halfway point, the opposite is true—with higher streamflow when the well is located further from the river. In the downstream reach of the river, the streamflow is increasing because of groundwater discharge into the river. At a distance of about 40 km downstream (just past the midpoint), the difference in streamflow between the case with the well closer to the river and the case with the well further from the river after 200 years of pumping is the largest, at about 535 m3/d, which is large relative to the magnitude of the well pumpage (Q = 2,026 m3/d).

Graph showing effect of well location on streamflow
Figure ExSol 1-1 – Effect of well location on streamflow after 200 years. For comparison, streamflow is shown under steady-state predevelopment conditions (Konikow and Bredehoeft, 2020).

The stream gage at the outlet of the model represents surface water outflow from the system being simulated. Comparison of these data for the three well locations (Figure ExSol 1-2) show that most of the capture (and stream depletion) occurs during the early times. As might be expected, the fastest effect occurs when the well is located closest to the river. In this case, half the total depletion occurs in the first 15 years of pumping. But in the long run, the total depletion of streamflow is the same regardless of well location—it is a function of the overall water budget.

Graph showing effect of pumping on streamflow
Figure ExSol 1-2 – Effect of pumping on streamflow as recorded at the stream gage at the outlet of the model during 200 years of pumping for three different well locations (Konikow and Bredehoeft, 2020).

It is also worth looking at the gains and losses in streamflow along the river, and how they change due to pumping from wells at different locations. The changes in streamflow gains and losses are determined by the differences between streamflow gains and losses during the steady-state predevelopment period and those during the transient pumping period. We evaluate those after 200 years of pumping; detailed steps are described in Box 3.

The streamflow loss is greatest in the first cell of the river (i.e., the most upstream reach) (Figure ExSol 1-3). For the predevelopment case, streamflow is diminished in the first reach of the river by 836 m3/d out of an inflow of 20,000 m3/d; the losses then decrease consistently in a downstream direction until they reach a minimum near the middle reach of the river. Then the streamflow starts to increase in reach 37 (about 30 km downstream), increasing exponentially to a maximum gain of 883 m3/d in the most downstream reach of the river. Differences between predevelopment streamflow gains and losses and those after 200 years of pumping appear to be relatively small and only evident in the middle third of the river—closest to the pumping well. This indicates that most of the streamflow gains and losses are related to the natural predevelopment boundary conditions of the problem and that the changes caused by sustained pumping are small relative to that. Even though these changes are small, they still need to be considered as a real effect by water managers.

Graph showing changes in streamflow along the length of the river
Figure ExSol 1-3 – Changes in streamflow along the length of the river for predevelopment conditions and after 200 years of pumping at three different well locations (Konikow and Bredehoeft, 2020).

The difference between the predevelopment values and those after 200 years for the three well locations represent the effects of pumping on streamflow (Figure ExSol 1-4). These results show that when the well is closest to the river, it will have the greatest magnitude of reducing streamflow per unit length of river (in this case, at a river location 32 km downstream from where it enters the valley). When the well is furthest from the river, its effects are smoothed out (or dampened) over a longer reach of the river.

Graph showing changes in streamflow gains and losses attributable to pumping
Figure ExSol 1-4 – Changes in streamflow gains and losses attributable to pumping for 200 years at three different well locations (Konikow and Bredehoeft, 2020).

Even for the well location that is closest to the river, the reduction in streamflow in the central reaches of the river never reach 1 percent of the streamflow. Thus, one can conclude that the effects of pumping on streamflow are small and tolerable given the benefits of the groundwater supply. However, one must also be cognizant that streamflow is variable in time and that droughts may cause low-flow periods in which streamflow is substantially less than the long-term steady rate assumed in this exercise. At those times, the impact of the well on streamflow would be proportionately greater.

Sources of Water to the Well:

As should be expected, the closer the well is to the river, the sooner the system becomes capture dominated and the greater are the near-term impacts on streamflow (and streamflow depletion). The aquifer’s transition from storage-depletion dominated to capture-dominated, reflected in Figure ExSol 1-5 by the time location of the crossover of the two curves for each distance, increased from about 5 years for a distance of 4 km, to 18 years for a distance of 8 km, to 74 years for a distance of 20 km. Thus, where the well is positioned makes a substantial difference in the response of the system (and on the timing of its effect on surface water).

Graph showing annual storage depletion and capture fractions
Figure ExSol 1-5 – Annual storage depletion and capture fractions for simulations of variants of the base case (Figure 17) in which the distance from the well to the stream is varied by placing it at a distance (x) of 4 km, 8 km (the base case), and 20 km from the river. Storage depletion fractions are shown in red and capture fractions are shown in blue (Konikow and Bredehoeft, 2020).

Sustainability:

The simulation model for all three well locations indicates that the pumping is sustainable for at least 200 years (at least from a strictly hydraulic perspective; in general, there may be other environmental considerations that render this too damaging to the environment to be considered “sustainable”). That is, as pumping continues over time, stream capture continues to increase. This means reduced streamflow, which may have unacceptable consequences from the perspective of downstream water users or ecological considerations. However, in this particular idealized case, that would not appear to be a major concern. However, these results also demonstrate that even “sustainable” groundwater development can cause streamflow depletion. Declining water tables also may impact the extent and duration of wetlands. During droughts or low-flow periods, the central reach of the river may dry up. Thus, “sustainability” must be evaluated from a broader perspective than just the physical ability to withdraw groundwater from the aquifer. These factors were not considered or evaluated in this simplified example.

If the pumping rate can be maintained until the system reaches a new equilibrium, then no further system changes will occur and the pumping can be sustained indefinitely based on hydraulic factors and processes. We can infer from the plots in Figure ExSol 1-5 that the system has not yet reached equilibrium in any of the three cases. That is, groundwater storage is still being depleted after 200 years of pumping, which means that water levels are still declining, which in turn means that the system has not reached a steady-state condition. To assess whether the system can eventually reach equilibrium (steady-state) conditions, additional simulations were run for longer periods of time. The results of these extended simulations yield water budget data indicating that a new hydraulic equilibrium can be reached in all three cases, although the time to equilibrium varies with the distance of the well to the stream (Figure ExSol 1-6). Equilibrium is reached soonest (in about 884 years) for the case where the pumping well is closest to the river (4 km), and the longest (in about 1,140 years) when the well is furthest from the river (20 km).

Graph showing time for model to reach a new steady-state condition
Figure ExSol 1-6 – Relation between time for model to reach a new steady-state condition and the distance from the pumping well to the river (Konikow and Bredehoeft, 2020).

Drawdown:

The drawdown in the pumping wells would be expected to vary for the three different well locations because each has a different distance to nearby barrier boundaries and recharge boundaries. These differences are seen in Figure ExSol 1-7, which compares calculated drawdowns in the pumping wells at the three different locations. Even though a new equilibrium condition has not strictly been achieved in 200 years for any of the three locations, the rates of change in head are very small at that time for all cases. The annual additional drawdown is less than 0.001 m/yr after just 16 years in the closer well, after 30 years in the base case, and after 94 years for the well location furthest from the river. These rates are very small compared to the average saturated thickness of the aquifer (150 m), so additional long-term drawdown would not be a major concern to water managers. The maximum difference in drawdown among the three cases is less than 0.3 m. Although pumping costs might be somewhat greater for the furthest well, which has the largest drawdown, the magnitude of this difference is quite small and would not likely be a major concern to water managers.

Graph showing calculated drawdown in the pumping well
Figure ExSol 1-7 – Calculated drawdown in the pumping well for three different well locations (Konikow and Bredehoeft, 2020).

The drawdown in the aquifer can be mapped at various times to show how water levels change in time and space, or as a function of well location. The drawdown map for the base case after 200 years of pumping (Figure ExSol 1-8) indicates that the drawdown near the stream is only about 0.01 m or less, with the greatest drawdown in the middle reach of the river (which is also the closest point on the river to the well) and smaller drawdowns in either direction along the river away from the well location. However, even these small drawdowns are enough to affect the exchange of water between the river and the aquifer (as seen in Figure ExSol 1-3).

Contour map of drawdown in the aquifer
Figure ExSol1-8. Contour map of drawdown (in m) in the aquifer after 200 years of pumping for the Base Case (Konikow and Bredehoeft, 2020).

Water Management Perspective:

The results indicate that the further the well is from the river, the greater the drawdown in the well. A lower water level increases the lift and energy costs to deliver the water. On the other hand, the further the well is from the river, the more the effect on streamflow is delayed and dampened. In this particular simplified hypothetical case, the streamflow is large relative to the well pumpage, and the pumpage is small relative to the transmissivity of the aquifer. Thus, the tradeoffs between well efficiency and streamflow capture are not dramatic and a water manager’s decision is not clear or obvious. That is, in this particular case, it would not make a big difference whichever well location was selected. However, if all else were the same, and if seasonal streamflow variability were high, then preserving downstream water rights and protecting ecosystem water needs would indicate a preference for selecting the further well location. On the other hand, if hydraulic properties of the aquifer were less favorable and resulted in much greater drawdown for the same pumping rate, then the closer well location would seem preferable.

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