Ground Water 2d Model Instructions
From GeoMod
Steady state, 2d model of groundwater flow.
- All boundaries are set as NO FLOW by default.
- Confined and unconfined aquifer versions.
Contents |
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Model/software
Below are two versions of the model, one for confined flow and the other for unconfined flow. The only difference between these models is that the cross-sectional areas for cells (A_x and A_y) use are calculated using head in the unconfined model and aquifer thickness (b) in the confined model.
- Media:2d-model-conf.xls : MS Excel model of a confined aquifer (with no macros but you may need to enable the iterative solver for model to work.
- Media:2d-model-unconf.xls Unconfined aquifer version of MS Excel model. (assumes bottom of aquifer is at 0)
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Instructions
Enable the iterative solver if not already enabled.
- PC (pre-Excel 2007): Tools -> Options -> Calculation (Tab) -> Iteration (checkbox)
- Mac: Excel -> Preferences -> Calculation (Tab) -> Iteration (checkbox)
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Boundaries
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Constant Head
To make a cell a constant head.
- Simply overwrite the equation in the 'h' worksheet cell with the head value.
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No Flow
- All boundaries are by default NO FLOW boundaries.
- To make internal cells NO FLOW you need to use a high K value ('Kx' and 'Ky' sheets).
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Recharge/discharge
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Wells
- Enter values in the 'Q' worksheet cells.
- A value of -500 creates a nice cone of depression in the figure with constant head boundaries.
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Recharge
- Enter the recharge values in the 'R' worksheet cells. These values will be multiplied by the surface area of the cell (dx × dy).
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Confined vs. Unconfined aquifer
There are two versions of the model for confined and unconfined aquifers. The only difference between the two is that in the unconfined version the cross-sectional area for each cell (in 'A' worksheet) is set equal to the head. This makes the implicit assumption that each cell is 1x1 in dimension and the bottom of the aquifer is at 0 elevation.
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Model details
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Worksheets
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Main sheet
- h - hydraulic heads. [L]
- The cells in this sheet have the conservation of mass equations. The boundary cells (cells on the edges of the model) are set up to allow no flow into the model (you'll notice the difference by looking at the equations in the cells).
- Modify the values in these cells to adjust the boundary conditions.
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Input parameters
- Q-well: Recharge or discharge wells [L3/T]
- Enter the groundwater discharge/recharge rates from wells (negative for discharge wells
- R: Recharge [L/T]
- Groundwater recharge.
- dx: cell length in x direction [L]
- dy: cell width in y direction [L]
- Kx: hydraulic conductivity in x direction [L/T]
- Ky: hydraulic conductivity in y direction [L/T]
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Working sheets: For internal calculations
- a_sum: Source term (a_h)
- a_h = a_{i-1} + a_{i+1} + a_{j-1} + a_{j+1}
- a_i+1: a_{i-1} = (K_x A_x / dx)_{i-1}
- a_i+1: a_{i+1} = (K_x A_x / dx)_{i+1}
- a_j-1: a_{j-1} = (K_y A_y / dy)_{j-1}
- a_j+1: a_{j+1} = (K_y A_y / dy)_{j-1}
- Ax: cross-sectional area
- A_x = dy * b ;
- where b = thickness of the aquifer
- where b = h; for unconfined model.
- A_x = dy * b ;
- Ay: cross-sectional area
- A_y = dx * b ;
- where b = thickness of the aquifer
- where b = h; for unconfined model.
- A_y = dx * b ;
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Applications
- The unconfined model has been used instead of Visual Modflow in Timothy Callahan's groundwater modeling exercise that is part of the SERC hydrogeology activities collection.
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Multimedia
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Animation where the upper right cell is set to 10 and the pressure propagates through the model.
