Radial well freatic benchmark (Water Module): Difference between revisions

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where:
where:
: <math>phi(0)</math>: stable water level at the considered stable water table edge
: <math>h_0</math>: stable water level at the considered stable water table edge
: <math>phi(r)</math>: water level between the considered stable water table edge and the well
: <math>h(r)</math>: water level between the considered stable water table edge and the well
: <math>phi(rw)</math>: water level in the well
: <math>k</math>: hydraulic conductivity of the freatic layer in m / day
: <math>k</math>: hydraulic conductivity of the freatic layer in m / day
: <math>r</math>: distance to the well
: <math>r</math>: distance to the well

Revision as of 16:52, 17 December 2020

This testcase demonstrates a situation where a well is extracting ground water in a confined freatic layer. There is no aquifer present. A characteristic ground water level curve will form over time.

Drainage freatic benchmark.gif

Formulas

The lowering of the ground water table in a closed freatic layer, without additional rainfall, can be described by the following formula [1]

where:

: stable water level at the considered stable water table edge
: water level between the considered stable water table edge and the well
: hydraulic conductivity of the freatic layer in m / day
: distance to the well
: distance of the considered stable water table edge to the well
: amount of water pumped out in m³ / day

Setup

We use the following setup in our tests. The grid size used is 51 by 51, with a configurable cell size of in meters. There is one underground outlet, which pumps water away continuously with a default amount per second.

The terrain height is set to 0 meters (datum).

The outlet is placed on the cells x = 25 and y = 25 as an inlet with a negative inlet.

INLET Q is set to
UNDERGROUND is set to true (1.0) to place the outlet below the surface.

To stabilized the water levels on the edges of the test case , an additional underground inlet is used. It is located on all cells equal to or further away than the chosen R. This inlet is configured as followed:

Inlet Q set to 0, such that is unlimited.
UNDERGROUND is set to true (1.0) to place the outlet below the surface.
UPPER_THRESHOLD set to -2 m.
LOWER_THRESHOLD set to -2 m.

The ground bottom distance is configured as 10 meters, which places the bottom at -10 meters (datum).

The water storage fraction is set to 0.25.
The vertical infiltration is set to 0.05 m / day.
The hydraulic conductivity is set to k m / day.


The simulation is run for 64 days with 0 rainfall, which is configured in the weather's rain attribute as:

Test results

Important in all these tests in the chosen R, which is the distance to the well that is considered a stable water level. Additionally, the measurements are done relative to the impenetrable soil, which is situated 10 meters below the surface.

Test case 1

cell size: 5 m;
: m/day;
: 110;
: 50;
Simulation days : 64 days;

File:5m 50m3 k.png

Test case 2

cell size: 5 m;
: m/day;
: 110;
: 50;
Simulation days : 64 days;

File:5m 50m3 k.png

Test case 3

cell size: 5 m;
: m/day;
: 110;
: 50;
Simulation days : 64 days;

File:5m 50m3 k.png

Test case 4

cell size: 5 m;
: m/day;
: 110;
: 50;
Simulation days : 64 days;

File:5m 50m3 k.png

Test case 5

cell size: 5 m;
: m/day;
: 110;
: 25;
Simulation days : 64 days;

File:5m 25m3 k.png

Test case 6

cell size: 5 m;
: m/day;
: 110;
: 100;
Simulation days : 64 days;

File:5m 100m3 k.png

Test case 7

cell size: 2 m;
: m/day;
: 110;
: 1;
Simulation days : 64 days;

File:2m 1m3 k.png

Test case 8

cell size: 2 m;
: m/day;
: 110;
: 16;
Simulation days : 64 days;

File:2m 16m3 k.png

Test case 9

cell size: 2 m;
: m/day;
: 110;
: 4;
Simulation days : 64 days;

File:2m 4m3 k.png

Test case 10

cell size: 2 m;
: m/day;
: 110;
: 4;
Simulation days : 64 days;

File:2m 4m3 k.png

Test case 11

cell size: 2 m;
: m/day;
: 110;
: 4;
Simulation days : 64 days;

File:2m 4m3 k.png

References

  1. Verruijt, A. (1970). Theory of Groundwater Flow. Macmillan, London.