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Lesson 1: Groundwater Divide

Acknowledgement: This lesson and the accompanying tutorial were originally written by Carmen Nale in 2004 as part of her Master's Project in Environmental Engineering.

1.1 Introduction

A groundwater divide generally forms a barrier to groundwater movement. Groundwater divides have noticeably divergent groundwater flow directions on either side of the divide with the water table sloping away from the divide.

Darcy's Law is the most basic equation used to describe groundwater movement. It is used to derive the Dupuit equation, an analytical solution used for unconfined groundwater flow, with the following assumptions:

  1. the water table is only slightly inclined;
  2. streamlines are horizontal and equipotential lines are considered vertical;
  3. the free surface and hydraulic gradient slopes are equal.

The following analytical solutions are used to determine the flow and head values within the groundwater divide, which is located between two bodies of water. Equation 1.2 is the analytical solution used to calculate flow at a certain location, x. Equation 1.3 is an analytical solution to Equation 1.2 that describes the head distribution of a water table aquifer and is used in this lesson to compare with the simulation’s head distribution (Bedient et al., 1999).

Equation 1.1: Darcy's Law
Equation 1.2: Dupuit Equation, flow
Equation 1.3: Dupuit Parabola, head

Where:
 
vx = Darcy velocity
A = Area of the cross section
Q = discharge
K = hydraulic conductivity
dh/dx = hydraulic gradient
q = one dimensional flow per unit width
L = Distance between the two rivers
x = location from the water body
h = actual water table
ho = water elevation in left river
hL = water elevation in right river
W = recharge

1.2 Simulation in IGW

For this simulation, the model was setup as having a parent zone that describes the aquifer properties (i.e., recharge rate, conductivity, porosity, thickness, etc.), and two groundwater receptors (one on each side of the aquifer) given values of constant head. For details on the model setup and analysis, refer to the instructions and calculations available in section 1.3 Groundwater Divide Tutorial. These instructions will allow the reader to re-create the model and determine the ‘varies’ values by pointing the curser at the working area screen at any point. (The Model Setup section of this website also contains a basic description of the IGW interface. )

Figure 1.1. (A) Shows a plan and profile view of IGW output data and (B) shows the numerical vs. the analytical head profile.

Figure 1.1 (A) displays the graphical output data from the IGW model. The blue arrows represent streamline flow and the red lines represent constant head. The thick straight horizontal red line represents the location of the cross-section with the side view shown above the line. The bottom of the aquifer is represented as solid brown with a black diagonal line going to the right. Notice the parabolic shape of the water table aquifer caused by the recharge of water percolating into the aquifer system then eventually reaching one of the receptors, the lake or creek. The decreasing space between the head contours (red lines) from the divide towards a receptor and the increasing size of the velocity vectors (blue arrows) show that the groundwater velocity increases going towards the receptors. The model's output data (i.e., numerical solution) was then compared to the Dupuit Equation (i.e., analytical solution) as shown in Figure 1.1(B). The head distribution determined by the model is in good agreement with the analytical solution, therefore, the model is able to accurately simulate the groundwater divide equations.

1.3 Step-by-Step Tutorial

Click below to download a pdf document with step-by-step instructions to complete this simulation in IGW. You can also download the IGW file that will result from successful completion of the tutorial. The IGW file is compressed as a ZIP file. To open it, you will need to save the ZIP file to your local computer and uncompress it with a program such as Winzip or Windows Explorer.

 

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