Radial well freatic benchmark (Water Module) - Revision history

Rudolf@tygron.nl at 11:39, 17 October 2025

2025-10-17T11:39:52Z

← Older revision		Revision as of 11:39, 17 October 2025
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	===Formulas===		===Formulas===
	The lowering of the ground water table in a closed freatic layer, without additional rainfall, can be described by the following formula <ref ~~name="~~verruijt70~~"/>~~		The lowering of the ground water table in a closed freatic layer, without additional rainfall, can be described by the following formula {{ref\|verruijt70}}

	<math>{h(r)}^2 = {h_0}^2 + \frac {Q_0}{\pi\cdot k} \ln{\left ( \frac{r}{R} \right )}</math>		<math>{h(r)}^2 = {h_0}^2 + \frac {Q_0}{\pi\cdot k} \ln{\left ( \frac{r}{R} \right )}</math>
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	[[File:2m_8m3_0_44k.png]]		[[File:2m_8m3_0_44k.png]]

	~~===References==~~=		{{article end
			\|references=
	<references>		<references>
	<ref name=~~"verruijt70>Verruijt, A. (1970).~~ Theory of Groundwater Flow. Macmillan, London.~~</ref>~~		{{ref\|verruijt70
			\|name=Theory of Groundwater Flow. Macmillan, London
			\|author=Verruijt, A. (1970)
			\|page=
			\|source=
			\|link=
			\|lastvisit=
			}}
	</references>		</references>
			}}

	{{Water Module buttons}}		{{Water Module buttons}}

Hedi@tygron.com: /* Test results */

2021-01-13T14:47:28Z

Test results

← Older revision		Revision as of 14:47, 13 January 2021
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	===Test results===		===Test results===
	Important in all these tests in chosen days it was ran, because the formula says nothing on how long it should take until the stable situation is reached. Secondly, the measurements are done relative to the impenetrable soil, which is situated 10 meters below the surface.		Important in all these tests is the amount of chosen days it was ran, because the formula says nothing on how long it should take until the stable situation is reached. Secondly, the measurements are done relative to the impenetrable soil, which is situated 10 meters below the surface.

	====Test case 1====		====Test case 1====

Frank@tygron.nl: /* Setup */

2020-12-18T16:16:24Z

Setup

← Older revision		Revision as of 16:16, 18 December 2020
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	The [[Terrain water storage percentage (Water Overlay)\|water storage fraction]] is set to 0.25.<br>		The [[Terrain water storage percentage (Water Overlay)\|water storage fraction]] is set to 0.25.<br>
	The [[Terrain ground infiltration md (Water Overlay)\| vertical infiltration]] is set to 0.05 m / day. <br>		The [[Terrain ground infiltration md (Water Overlay)\| vertical infiltration]] is set to 0.05 m / day. <br>
	The [[Terrain hydraulic conductivity (Water Overlay)\| hydraulic conductivity]] is set to k m / day.<br>		The [[Terrain hydraulic conductivity md (Water Overlay)\| hydraulic conductivity]] is set to k m / day.<br>

Frank@tygron.nl: /* Test results */

2020-12-18T15:00:08Z

Test results

← Older revision		Revision as of 15:00, 18 December 2020
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	===Test results===		===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.		Important in all these tests in chosen days it was ran, because the formula says nothing on how long it should take until the stable situation is reached. Secondly, the measurements are done relative to the impenetrable soil, which is situated 10 meters below the surface.

	====Test case 1====		====Test case 1====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>k</math>: m/day;		:<math>k</math>: 4.4 m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 50;		:<math>Q_0</math>: 50 m³ /day;
	:Simulation days <math>n</math>: 64 days;		:Simulation days <math>n</math>: 64 days;
	[[File:~~5m_50m3_k~~.png]]		[[File:5m_50m3_4_4k.png]]

	====Test case 2====		====Test case 2====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>k</math>: m/day;		:<math>k</math>: 2.2 m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 50;		:<math>Q_0</math>: 50 m³ /day;
	:Simulation days <math>n</math>: 64 days;		:Simulation days <math>n</math>: 128 days;
	[[File:~~5m_50m3_k~~.png]]		[[File:5m_50m3_2_2k.png]]

	====Test case 3====		====Test case 3====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>k</math>: m/day;		:<math>k</math>: 2.2 m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 50;		:<math>Q_0</math>: 25 m³/day;
	:Simulation days <math>n</math>: 64 days;		:Simulation days <math>n</math>: 128 days;
	[[File:~~5m_50m3_k~~.png]]		[[File:5m_25m3_2_2k.png]]

	====Test case 4====		====Test case 4====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>k</math>: m/day;		:<math>k</math>: 0.44 m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 50;		:<math>Q_0</math>: 4 m³/day;
	:Simulation days <math>n</math>: 64 days;		:Simulation days <math>n</math>: 512 days;
	[[File:~~5m_50m3_k~~.png]]		[[File:5m_4m3_0_44k.png]]

	====Test case 5====		====Test case 5====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>k</math>: m/day;		:<math>k</math>: 0.11 m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 25;		:<math>Q_0</math>: 4 m³/day;
	:Simulation days <math>n</math>: 64 days;		:Simulation days <math>n</math>: 1256 days;
	[[File:~~5m_25m3_k~~.png]]		[[File:5m_4m3_0_11k.png]]

	====Test case 6====		====Test case 6====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>k</math>: m/day;		:<math>k</math>: 2.2 m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: ~~100~~;		:<math>Q_0</math>: 10;
	:Simulation days <math>n</math>: 64 days;		:Simulation days <math>n</math>: 128 days;
	[[File:~~5m_100m3_k~~.png]]		[[File:5m_10m3_2_2k.png]]

	====Test case 7====		====Test case 7====
	:cell size: 2 m;		:cell size: 2 m;
	:<math>k</math>: m/day;		:<math>k</math>: 2_2 m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 1;		:<math>Q_0</math>: 1;
	:Simulation days <math>n</math>: 64 days;		:Simulation days <math>n</math>: 64 days;
	[[File:~~2m_1m3_k~~.png]]		[[File:2m_1m3_2_2k.png]]

	====Test case 8====		====Test case 8====
	:cell size: 2 m;		:cell size: 2 m;
	:<math>k</math>: m/day;		:<math>k</math>: 0.22 m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 16;		:<math>Q_0</math>: 1;
	:Simulation days <math>n</math>: 64 days;		:Simulation days <math>n</math>: 256 days;
	[[File:~~2m_16m3_k~~.png]]		[[File:2m_1m3_0_22k.png]]

	====Test case 9====		====Test case 9====
	:cell size: 2 m;		:cell size: 2 m;
	:<math>k</math>: m/day;		:<math>k</math>: 0.22 m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 4;		:<math>Q_0</math>: 4;
	:Simulation days <math>n</math>: 64 days;		:Simulation days <math>n</math>: 256 days;
	[[File:~~2m_4m3_k~~.png]]		[[File:2m_4m3_0_22k.png]]

	====Test case 10====		====Test case 10====
	:cell size: 2 m;		:cell size: 2 m;
	:<math>k</math>: m/day;		:<math>k</math>: 2.2 m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 4;		:<math>Q_0</math>: 4;
	:Simulation days <math>n</math>: 64 days;		:Simulation days <math>n</math>: 64 days;
	[[File:~~2m_4m3_k~~.png]]		[[File:2m_4m3_2_2k.png]]

	====Test case 11====		====Test case 11====
	:cell size: 2 m;		:cell size: 2 m;
	:<math>k</math>: m/day;		:<math>k</math>: 0.22 m/day;
			:<math>R</math>: 110;
			:<math>Q_0</math>: 6;
			:Simulation days <math>n</math>: 128 days;
			[[File:2m_6m3_0_22k.png]]


			====Test case 12====
			:cell size: 2 m;
			:<math>k</math>: 0.44 m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 4;		:<math>Q_0</math>: 8;
	:Simulation days <math>n</math>: 64 days;		:Simulation days <math>n</math>: 64 days;
	[[File:~~2m_4m3_k~~.png]]		[[File:2m_8m3_0_44k.png]]

	===References===		===References===

Frank@tygron.nl: /* Test results */

2020-12-17T16:55:48Z

Test results

← Older revision		Revision as of 16:55, 17 December 2020
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	====Test case 3====		====Test case 3====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>kD</math>: m/day;		:<math>k</math>: m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 50;		:<math>Q_0</math>: 50;
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	====Test case 4====		====Test case 4====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>kD</math>: m/day;		:<math>k</math>: m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 50;		:<math>Q_0</math>: 50;
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	====Test case 5====		====Test case 5====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>kD</math>: m/day;		:<math>k</math>: m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 25;		:<math>Q_0</math>: 25;
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	====Test case 6====		====Test case 6====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>kD</math>: m/day;		:<math>k</math>: m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 100;		:<math>Q_0</math>: 100;
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	====Test case 7====		====Test case 7====
	:cell size: 2 m;		:cell size: 2 m;
	:<math>kD</math>: m/day;		:<math>k</math>: m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 1;		:<math>Q_0</math>: 1;
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	====Test case 9====		====Test case 9====
	:cell size: 2 m;		:cell size: 2 m;
	:<math>kD</math>: m/day;		:<math>k</math>: m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 4;		:<math>Q_0</math>: 4;

Frank@tygron.nl: /* Test case 2 */

2020-12-17T16:55:21Z

Test case 2

← Older revision		Revision as of 16:55, 17 December 2020
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	====Test case 2====		====Test case 2====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>kD</math>: m/day;		:<math>k</math>: m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 50;		:<math>Q_0</math>: 50;

Frank@tygron.nl: /* Test case 1 */

2020-12-17T16:55:09Z

Test case 1

← Older revision		Revision as of 16:55, 17 December 2020
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	====Test case 1====		====Test case 1====
	:cell size: 5 m;		:cell size: 5 m;
	:<math>kD</math>: m/day;		:<math>k</math>: m/day;
	:<math>R</math>: 110;		:<math>R</math>: 110;
	:<math>Q_0</math>: 50;		:<math>Q_0</math>: 50;

Frank@tygron.nl: /* Formulas */

2020-12-17T16:52:40Z

Formulas

← Older revision		Revision as of 16:52, 17 December 2020
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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

Frank@tygron.nl: /* Setup */

2020-12-17T16:51:19Z

Setup

← Older revision		Revision as of 16:51, 17 December 2020
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	The [[Ground bottom distance m (Water Overlay)\|ground bottom distance]] is configured as 10 meters, which places the bottom at -10 meters (datum).		The [[Ground bottom distance m (Water Overlay)\|ground bottom distance]] is configured as 10 meters, which places the bottom at -10 meters (datum).

	The [[Terrain water storage percentage (Water Overlay)\|water storage fraction]] is set to 0.25.		The [[Terrain water storage percentage (Water Overlay)\|water storage fraction]] is set to 0.25.<br>
			The [[Terrain ground infiltration md (Water Overlay)\| vertical infiltration]] is set to 0.05 m / day. <br>
			The [[Terrain hydraulic conductivity (Water Overlay)\| hydraulic conductivity]] is set to k m / day.<br>

	~~The [[Terrain ground infiltration md (Water Overlay)\| infiltration m / day]] is set to 0.05.~~

	The simulation is run for 64 days with 0 rainfall, which is configured in the weather's [[Weather rain m (Water Overlay)\|rain attribute]] as: <math>[64 \cdot 24 \cdot 3600, 0]</math>		The simulation is run for 64 days with 0 rainfall, which is configured in the weather's [[Weather rain m (Water Overlay)\|rain attribute]] as: <math>[64 \cdot 24 \cdot 3600, 0]</math>

Frank@tygron.nl: /* Setup */

2020-12-17T16:50:23Z

Setup

← Older revision		Revision as of 16:50, 17 December 2020
Line 39:		Line 39:
	The [[Terrain water storage percentage (Water Overlay)\|water storage fraction]] is set to 0.25.		The [[Terrain water storage percentage (Water Overlay)\|water storage fraction]] is set to 0.25.

	The [[Terrain ground infiltration md (Water Overlay) infiltration m / day]] is set to 0.05.		The [[Terrain ground infiltration md (Water Overlay)\| infiltration m / day]] is set to 0.05.

	The simulation is run for 64 days with 0 rainfall, which is configured in the weather's [[Weather rain m (Water Overlay)\|rain attribute]] as: <math>[64 \cdot 24 \cdot 3600, 0]</math>		The simulation is run for 64 days with 0 rainfall, which is configured in the weather's [[Weather rain m (Water Overlay)\|rain attribute]] as: <math>[64 \cdot 24 \cdot 3600, 0]</math>

← Older revision		Revision as of 16:16, 18 December 2020
Line 38:		Line 38:
	The [[Terrain water storage percentage (Water Overlay)\|water storage fraction]] is set to 0.25.<br>		The [[Terrain water storage percentage (Water Overlay)\|water storage fraction]] is set to 0.25.<br>
	The [[Terrain ground infiltration md (Water Overlay)\| vertical infiltration]] is set to 0.05 m / day. <br>		The [[Terrain ground infiltration md (Water Overlay)\| vertical infiltration]] is set to 0.05 m / day. <br>
	The [[Terrain hydraulic conductivity (Water Overlay)\| hydraulic conductivity]] is set to k m / day.<br>		The [[Terrain hydraulic conductivity md (Water Overlay)\| hydraulic conductivity]] is set to k m / day.<br>

← Older revision		Revision as of 16:51, 17 December 2020
Line 37:		Line 37:
	The [[Ground bottom distance m (Water Overlay)\|ground bottom distance]] is configured as 10 meters, which places the bottom at -10 meters (datum).		The [[Ground bottom distance m (Water Overlay)\|ground bottom distance]] is configured as 10 meters, which places the bottom at -10 meters (datum).

	The [[Terrain water storage percentage (Water Overlay)\|water storage fraction]] is set to 0.25.		The [[Terrain water storage percentage (Water Overlay)\|water storage fraction]] is set to 0.25.<br>
			The [[Terrain ground infiltration md (Water Overlay)\| vertical infiltration]] is set to 0.05 m / day. <br>
			The [[Terrain hydraulic conductivity (Water Overlay)\| hydraulic conductivity]] is set to k m / day.<br>

	~~The [[Terrain ground infiltration md (Water Overlay)\| infiltration m / day]] is set to 0.05.~~

	The simulation is run for 64 days with 0 rainfall, which is configured in the weather's [[Weather rain m (Water Overlay)\|rain attribute]] as: <math>[64 \cdot 24 \cdot 3600, 0]</math>		The simulation is run for 64 days with 0 rainfall, which is configured in the weather's [[Weather rain m (Water Overlay)\|rain attribute]] as: <math>[64 \cdot 24 \cdot 3600, 0]</math>