Hydrology.nl

Start MicroFEM and load the "Lesson 1" model by clicking the project file "Lesson 1.fpr"

To make sure that all heads are computed, we will run the model first.

Menu bar: Calculate / Go calculate

Step 10: Water balance

[Walking mode] / [Draw grid (Ins)]

Make the centre node the current node.

[Waterbalance node (F2)]

An area around the current node is shaded. This area intersects the nodal connections of the current node exactly in the middle. This area is also exactly one third of each neighbouring element of the current node. It is called the "Nodal area".

Also a pop-up window with a water balance is displayed. The size of the shaded area appears to be 21650650 m². The outflow (by the well) is 1000 m³/d and the lateral inflow is the same. The well outflow was given (we entered a well discharge of 1000 m³/d). The lateral inflow is computed, based on the location of the nodes, the transmissivity and the nodal heads.

[Water balance node (F2)] or Close the Water Balance pop-up window.

Step 11: Head computation based on water balance of nodal area

Table: Make the "head [m]" cell (4th cell from the top) the active cell.

From now on we will use codes for all cells in the table. From top to bottom the codes of these cells are: H0, C1, T1, H1, Q1. The "C" and "Q" are the often used notations for "vertical resistance (days)" and "well discharge (m³/day)" respectively. The "1" is used here because these codes refer to the uppermost aquifer (aquifers are numbered top-down).
H0 and C1 are used in MicroFEM to specify the top boundary condition.
H0 and C1 are zero for all nodes in this model. This implies that the aquifer is fully confined.
Other top boundary conditions will be discussed in another lesson.

Toolbar [Drawing mode] / [Blue] / [Draw grid] / [Yellow] / [Draw contours (F7)] / Maket Interval = 0.072 / [OK]

In this way we created a yellow six-sided polygon around the centre node. This polygon connects the middles of the nodal connections.

Make the centre node the current node.

[Walking mode] / [Water balance node (F2)]

The lateral inflow into the shaded area is the same as the flow over the yellow polygon. The net lateral inflow (inflow minus outflow) of the shaded areas outside the yellow polygon is zero for each element (because these are closed areas within an area with uniform flow). The length of each side of the polygon is 2500 m. The gradient is perpendicular to these sides (in this model).

Using Darcy the inflow over each side = Length of the side * Transmissivity * Gradient. Total inflow of the nodal area = 6 * 2500 * 2000 * delta_h/(2500*√3).
delta_h is the head difference between the model boundary and the centre node.

Total outflow = Well discharge = 1000 m³/d.
Total inflow = totale outflow, so delta_h = (√3)/12.
Since all boundary heads are equal to zero, the head in the well node = –(√3)/12 = –0.144337567 m.

With a higher head (less negative) the gradient in all elements would be lower and the lateral inflow would be less that the well discharge. Similarly, a more negative head and associated higher gradient would produce more lateral inflow than the well discharges. There is only one head for the centre node that makes the total inflow equal to the outflow.

Please note:
1 For this simple 6-elements grid, the computed head in the well is independent of the element size!
2 In reality the drawdown in a well is dependent on the well radius.

We will continue with this in the next lesson.

Menu bar: Files / Save all

This last command is routine only. Actually we did not have to save the model, because we did not change the model data.

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