The objective of the assignment is to use the spreadsheet package Microsoft Excel to investigate the effect of changing boundary conditions on a simple rectangular isotropic and homogeneous confined aquifer, firstly without pumping and then including a groundwater pumping bore abstracting or injecting water. The assignment is based on the analysis of Frank and Reilly (1987).
You should set up a model for your unique aquifer. Figure 1 is an example and does not necessarily match your aquifer dimensions. Your aquifer has an area X m wide (AB and CD) by Y m long (BC and DA). Use a finite difference discretisation where ∆x = ∆y = 100 m. Your model will then be X’ nodes wide in the x‐direction along boundaries AB and CD and Y’ nodes long in the y-direction along boundaries BC and DA.
In the example, the aquifer is X = 800 m wide by Y = 1500 m long and ∆x = ∆y = 100 m. This model, therefore, has X’ = 9 nodes in the x‐direction (from node 0 to node 8 along boundaries AB and CD) and Y’ = 16 nodes in the y‐direction (from node 0 to node 15 along boundaries BC and DA). See Figure 1.
Each student will have a unique set of data for the transmissivity, Pumping rate, initial head conditions (h [m]), and an x‐y coordinate pair representing the bore location. Find your data in the excel sheet on Moodle. Figure 1 shows how the bore location x‐y coordinate corresponds to a node in the numerical scheme.
For the spreadsheet to successfully iterate, circular references should be enabled. In Microsoft Excel 2010+ this is done under the menus: ”File” ‐ ”Options” ‐ ”Formulas”: Here you need to tick ”Enable iterative calculation”, set ”Maximum iterations” to 30,000, and ”Maximum change” to 0.0001.
Model the following two sets of aquifer conditions:
Model 1: The problem domain (aquifer) is surrounded by Dirichlet (fixed head) boundary conditions. Use a linear decrease in the head from hm to 0 m along with BC and AD, a fixed head of 0m along boundary CD, and a fixed head of h m along with boundary AB.
Model 2: The problem domain (aquifer) is surrounded by a mix of Dirichlet and Neumann (no flow) boundary conditions. Use a no‐flow boundary condition (with ∂h/∂x = 0) across BC and AD, a fixed head of 0 m along boundary CD, and a fixed head of h m along with boundary AB.
