# Learning Module: Groundwater Flow and Wells G & H

## Student Assignment

## Overview

This assignment utilizes the Thiem equation (see image below) in an EXCEL worksheet to create a two-dimensional groundwater flow model that computes drawdown relative to steady-state pumping from wells. The worksheet is based on the dimensions and locations of wells G and H. The model assumes the aquifer is isotropic, homogeneous, flat lying, infinite, flow is steady-state, wells discharge at the uniform rate, and the wells have no borehole storage. The solution to the Thiem equation assumes the the drawdown (s_{2}) at the distance (r

_{2}) is zero. The Thiem equation is embedded into the cells of the worksheet and automatically calculates drawdown at specified distances based on cell dimensions.

In this exercise, we will explore different well pumping rates and how they would affect groundwater flow in the aquifer underlying Aberjona River Valley. It should be noted the yellow and white curved lines on the EXCEL worksheet represent the Aberjona River. Wells G and H are to the right of the river line and the Riley well is on the left. The lower graphic represents a cross section along column 14 on the map in the upper left corner of the spreadsheet. Although there are multiple tabs on the spreadsheet, the tab labeled 'Summary' is the only one required to complete this exercise. A link to the EXCEL spreadsheet occurs below.

Theim equation used for the EXCEL spreadsheet calculator. Note the assumptions used to simplify the equation

Thiem Equation Calculator (Excel 280kB Aug13 09)

## Assignment

For this exercise we will assume the permeability (K) of the aquifer is 400 feet per day (ft/d), the Riley well (Q_{R}) pumps at an average rate of 200 gallons per minute (gpm), Well G (Q

_{G}) pumps at an average rate of 700 gpm, and Well H (Q

_{H}) pumps at an average rate of 400 gpm. After opening the Thiem Equation Calculator file (above), insert these values in the highlighted blue cells. Notice that after entering each value, the map in the upper portion of the spreadsheet changes, the upper left image populates with numbers in the grid and the upper right map exhibits a series of semicircular shapes that are concentric around the three pumping wells. The image on the upper left represents the drawdown relative to non-pumping conditions, the value in each cell is the composite amount of drawdown related to pumping from each well (drawdowns are additive). Note how the values increase in the cells immediately around the wells and decrease toward the margins of the graph. The map in the upper right shows contours of the composite values. Drawdown values of the given range (say the 20-25 feet drawdown range) are given a similar color (purple), a separate color then is given to cells that occur between the 25-30 feet interval (orange), and so on. The cells with values between the upper and lower limit of the range appear as rings or areas of like colored cells.

The cross section shown on the lower left portion of the spreadsheet shows the drawdown associated with the north-south line of section between wells G and H. The curved black line on the cross section represents the water table surface at steady-state conditions with respect to the pumping stresses. At this point, the data entered into the light blue highlighted cells represents steady-state pumping conditions with all three wells (G, H, and Riley) operating. Using the Thiem Equation Calculator spreadsheet, you will evaluate this pumping condition to answer the questions below.

### Questions

- Referring to the cross section, which well G or H has the greatest drawdown? (Well H is located north of Well G.) Why does this well have a larger drawdown?
- How does pumping from the Riley well and Well H affect the shape of the drawdown contours? Why does the contour shape for the 20-25 feet interval (purple) become uniformly round?

- Place a zero (0) in the highlighted cells for both wells G and H (Q
_{G}and Q_{H}). How does this change the shape of drawdowns on the map and the contours? Would this pumping condition affect the direction and rate of movement of a contaminant plume? - Now place a 700 in the highlighted cell for Q
_{G}and keep the Riley well value at 200. How does this pumping configuration change the shape of drawdowns on the cross section and contour map? What is the net change in drawdown in well G when the value used in question 3 (0 GPM) is compared to that used for question 4 (700 gpm)? Could the new pumping conditions (well G = 700 gpm) pull TCE-contaminated water from the Riley property to well G? Explain why.

- Although this calculator can be an effective tool for examining hypothetical pumping rates and groundwater conditions, there are some severe limitations to using this simplistic treatment in a mock trial. What are these limitations? Hint: review the assumptions of the Thiem equation and your knowledge of the geology and hydrology of the wells G and H area. Refer to the geologic cross-section assignment in Module 3 and the induced infiltration assignment in Module 7 and consider about how aquifer boundaries and recharge from the Aberjona River would affect the Thiem Equation Calculator.

- Numerical groundwater flow models commonly are used today to address many of the limitations assumptions of Thiem Equation as applied to the flow system at Woburn (see MODFLOW information). Why would a numerical groundwater flow model, such as the USGS model, MODFLOW, which was in development during the trial, have been advantageous to the experts?