Conductivities

At this point anisotropic conductivities can be assigned differentiated according to their spatial direction.

In a 3D model the input conductivities k1, k2, k3 are stored together with the angles a1, a2 and a3 at the end of the *.3d model file after confirming with OK and saving the model. They are stored for each zone automatically. The attribute Z-KA will automatically be assigned to the deeper layers, if it is not assigned there.

In a horizontal model the input conductivities k1 and k2 are stored together with the angle a1 automatically as attribute MATE in the *.net file after confirming with OK and saving the model.

Angles

In addition to the direction-dependent conductivities the angles a1 (horizontal and 3D model), a2 and a3 (3D model only) can be defined, if the conductivity-ellipsoid differs from the Cartesian coordinate system.

By taking into account these angles, the conductivities are corrected in accordance with the following general rotation algorithm:

k_korr = H* k_orig* H^T

with:

k_korr = Tensor of the (layer-)corrected conductivities

k_orig = Tensor of the conductivities of the model data

H = Rotation matrix based on the angles a1, a2, a3

H^T = transposed rotation matrix

Angle a1: Rotation in the XY-plane, counter clockwise from the X-axis (looking down the Z-axis toward the origin)

Angle a2: Rotation in the new XZ-plane, counter clockwise from the new X-axis (looking down the Y-axis toward the origin)

Angle a3: Rotation in the new YZ-plane, counter clockwise from the new Y-axis (looking down the new X-axis toward the origin)

Preview diagram

The dashed axes in the preview (3D example) indicate the Cartesian coordinate system x, y, and z. The angle a1 = 45 ° means that the maximum conductivity is applied in the direction of 45 ° relative to the x-axis. In the example it can be seen that this information results in a rotation of the xy-plane by 45° (the solid red axis is the new x-axis). The diagram can be saved as an image at any location.

It is possible to change the filled shader model in a line graph with the key "f" (after activating the preview window with the left mouse button). Similarly, the model can be illuminated with the key "l".

For this illustration, k1 = k2 = k3 and a1 = 45 ° were set.

Automatic layer correction (3D only)

The permeability values (attribute KWER) defined in SPRING are generally for isotropic flow conditions. That means the resulting flow direction is given by the pure potential gradient of the aquifer without considering the geometric discretization.

By activating this button an optional (and automatic) layer correction takes place in which the conductivities are automatically adjusted to the element or layer geometry. Since the element geometry adapts typically the geological stratification of the model area, a geometric correction of the permeabilities takes place without giving angles.

For the internal calculation the average level between the upper and lower "element surface" is generated, and its normal is calculated. The deviations of the normal to the respective coordinate plane result in the angles a1, a2, a3, with which the conductivities are corrected in accordance to the general rotation algorithm described above.

If the conductivities should be corrected for ALL layers, an assignment of the attribute Z-KA is not required. For this purpose, it is enough, to add the following line at the end of the batch file sitra.bsi:

ROTATION KWER

The following figure shows the result of the flow calculation with (red potential lines) and without (blue potential lines) consideration of the layer-corrected conductivities for all layers:

Comparison of the potential lines with (red) and without (blue) layer corrected conductivities for all layers

The yellow layer is impermeable against the green layers by a factor of 100.

If the conductivities should be corrected only for selected layers, this is done by zoning the layers with the attribute Z-KA.

For this purpose, the appropriate zone is selected in the dialog and the button "Automatic layer correction" is enabled.

The following figure shows a model in which only the layers 9 to 11 were defined as Zone 2. The conductivities are the same for all layers (horizontal 0.0001, 0.0001 vertically), as shown by the associated element attributes:

Due to the automatic assignment of deeper layers the attribute Z-KA must be reassigned from the layer 12 on, because zone 2 shall apply only to the layers 9 to 11.

Then an automatic layer correction was carried out for Zone 2. The following figure shows the result of the flow calculation:

Comparison of the potential lines with (red) and without (blue) layer corrected conductivities in zone 2

Zone 2 includes the layers 9 to 11, which are colored in turquoise. Zone 1are all other layers (green).