COMSOL 6.4 - Furrow Irrigation — Dual Permeability

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Furrow Irrigation — Dual Permeability

This example shows how to set up a model of furrow irrigation in a nonuniform soil column. It employs the Unsaturated Dual Permeability feature, which links two Richards’ Equations through a fluid transfer function. This scenario can be regarded as a benchmark problem for dual permeability modeling initially suggested by Ref. 1.

Model Definition

In this example model, water infiltrates from a furrow into a 1.5 m deep soil column over a 6-hour period. The water level in the furrow is kept 10 cm above the soil surface, thus resulting in a constant pressure head boundary condition. At the bottom of the soil profile a zero pressure head boundary condition is applied. Zero-flux flow conditions are imposed on all remaining boundaries.

Figure 1: Model setup.

The dual permeability approach is to solve two Richards’ equations, one for the macroscopic soil structures referred to as macropores (index i = M) and one for the microscopic soil structures referred to as micropores (index i = m):

(1)

with θi being the respective volume fraction, Cm,i the moisture capacity, g the gravitational constant, pi the pressure in the respective system, κi the permeability, ρ and μ the fluid density and dynamic viscosity, respectively, and Qip represents the interporosity flow where +Qip indicates flow into the micropores and −Qip the flow out of the macropores.

Results and Discussion

The pressure distribution within the macropores and micropores, following 6 hours of irrigation, is illustrated in Figure 2. Observations reveal that the pressure in the macropores has nearly stabilized uniformly across the entire depth. However, the pressure distribution within the micropores still exhibits a significant gradient near the furrow, indicating that it has not yet reached a state of equilibrium.

Figure 2: Pressure field in the macropores (left) and micropores (right) after six hours of simulated time.

Similarly, for the effective saturation depicted in Figure 3, the saturation level in the macropores has reached a depth of 30 cm below the furrow, whereas in the micropores it has only penetrated to a depth of 5 cm.

Figure 3: Effective saturation in the macropores (left) and micropores (right) after six hours of simulated time.

1. T. Vogel and others, “Modeling flow and transport in a two-dimensional dual-permeability system with spatially variable hydraulic properties,” J. Hydrol., vol. 238, nos. 1–2, pp. 78–89, 2000.

Subsurface_Flow_Module/Verification_Examples/furrow_irrigation_dual_permeability

Modeling Instructions

From the menu, choose .

In the window, click

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In the window, click

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In the tree, select > > .

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In the tree, select > .

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Rectangle 1 (r1)

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In the toolbar, click

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In the window for , locate the section.

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In the text field, type 1.5.

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Polygon 1 (pol1)

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In the toolbar, click

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In the window for , locate the section.

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In the table, enter the following settings:


x (m)	y (m)
0.15	1.5
0.25	1.4
0.35	1.3
0.65	1.3
0.75	1.4
0.85	1.5

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Difference 1 (dif1)

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In the toolbar, click

and choose .

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Select the object only.

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In the window for , locate the section.

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Click to select the

toggle button for .

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Select the object only.

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Form Union (fin)

In the toolbar, click

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Global Definitions

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In the window, under click .

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In the window for , locate the section.

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Browse to the model’s Application Libraries folder and double-click the file furrow_irrigation_dual_permeability_parameters.txt.

Define an interpolation function for the pressure head in the furrows so that it reflects standing water in the furrows.

Applied pressure head

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In the window, expand the > node.

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Right-click and choose > .

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In the window for , type Applied pressure head in the text field.

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Locate the section. In the table, enter the following settings:


t	f(t)
1.4	0
1.3	10

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In the text field, type hp0.

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Locate the section. In the table, enter the following settings:


Function	Unit
hp0	cm

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In the table, enter the following settings:


Argument	Unit
t	m

Richards’ Equation (dl)

Unsaturated Dual Permeability Medium 1

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In the toolbar, click

and choose .

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Select Domain 1 only.

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In the window for , locate the section.

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In the αw text field, type alpha_w.

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In the window, click .

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In the window for , locate the section.

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From the ρ list, choose . In the associated text field, type rho_f.

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From the μ list, choose . In the associated text field, type mu_f.

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In the window, click .

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In the window for , locate the section.

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In the θM text field, type 0.05.

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Locate the section. From the εp,M list, choose . In the associated text field, type epsilon_p_M.

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From the list, choose .

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In the Ks,M text field, type Ks_M.

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Locate the section. In the α text field, type alpha.

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In the n text field, type n.

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In the l text field, type l.

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In the θr text field, type theta_r.

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In the window, click .

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In the window for , locate the section.

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From the εp,m list, choose . In the associated text field, type epsilon_p_m.

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From the list, choose .

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In the Ks,m text field, type Ks_m.

The retention model is the same as in the Macropores.

Initial Values 1

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In the window, under > click .

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In the window for , locate the section.

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Click the button.

Pressure Head 1

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In the toolbar, click

and choose .

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Select Boundaries 5–7 only.

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In the window for , locate the section.

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In the Hp0 text field, type hp0(y).

Pressure Head 2

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In the toolbar, click

and choose .

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Select Boundary 2 only.

Free Triangular 1

In the toolbar, click

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In the window, click .

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In the window for , locate the section.

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From the list, choose .

Free Triangular 1

In the window, right-click and choose .

Step 1: Time Dependent

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In the window, under click .

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In the window for , locate the section.

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From the list, choose .

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In the text field, type range(0,0.5,6).

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In the toolbar, click

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In the window, expand the > node, then click .

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In the window for , type Pressure Head in the text field.

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In the window, click .

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In the window for , click in the upper-right corner of the section. From the menu, choose > > > .

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In the toolbar, click

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Include pressure and saturation plots for the macro- and micropores using the available result templates.

Result Templates

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In the toolbar, click

to open the window.

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Go to the window.

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In the tree, select > > .

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Click the button in the window toolbar.

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In the tree, select > > .

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Click the button in the window toolbar.

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In the toolbar, click

to close the window.

Compare the two images with Figure 2 and Figure 3.