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Tutorial 3

Correlated Random Hydraulic Conductivity Field

Table of Contents

Objective …………………………………………………………………………………. 1

Step-by-Step Procedure ……………………………………………………………….... 2

Section 1 – Generation of Correlated Random Hydraulic Conductivity Field …………… 2

Step 1: Open Adaptive Groundwater Input (.agw) File ………………………………… 2

Step 2: Change Porous Media Type to “Correlated Random K Region” ………………. 3

Step 3: Open Random K Field Dialog ………………………………………………….. 4

Step 4: Define Random K Field Parameter Values ……………………………………... 5

Step 5: Generate Random K Field and View Plan-View Contour Map ………………… 6

Step 6: Generate Cross-Section Flood Map of K Values ……………………………….. 8

Step 7: 3D Volume Plot of Random K ………………………………………………….. 9

Step 8: 3D Surface Plot …………………………………………………………………. 11

Section 2 – Simulation Results Visualization …………………………………………….. 12

Step 1: Generate Plan-View Map of Simulated Solute Concentrations ………………… 12

Step 2: Plot Groundwater Pathline ………………………………………………………. 16

Step 3: Cross-Section View of Plume …………………………………………………… 16

Step 4: 3D Volume Plot of Plume ………………………………………………………. 20

Step 5: 3D Fence Diagram of Plume ……………………………………………………. 23

Step 6: Define Fence Diagram Type and Slice Locations ………………………………. 23

Step 7: Add Concentration Blanking to Fence Diagram ………………………………… 24

Objective

Illustrate the generation of a three-dimensional, correlated random hydraulic conductivity field

(K). The completed Adaptive Groundwater input files for this tutorial are included in the

Tutorial_3 subdirectory of the tutorials directory under the Adaptive_Groundwater program

folder:

C:\Adaptive_Groundwater\Tutorials\Tutorial_3\Tutorial_3_Completed.agw

Because Tutorial 3 builds upon the input data and boundary conditions for Tutorial 1, you can

refer to this first tutorial for illustrations of basic input data preparation (e.g., grid design, basic

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boundary condition specification, time step control, etc.). The completed Tutorial 3 project files

are provided to you as a reference (you can check the completed input data if you have questions

while working through the tutorial). Many output times are also provided so that you can view

the variations of hydraulic heads and solute concentrations over a long time period. As discussed

below, you will work with a separate set of project files.

This tutorial is divided into two sections. The first part covers the random K field generation.

The second section shows how to create two- and three-dimensional visualizations of the

simulation results.

Step-by-Step Procedure

Section 1 – Generation of Correlated Random Hydraulic Conductivity Field

Step 1 - Open Adaptive Groundwater Input (.agw) File

Go to File > Open in the main menu to open the file Tutorial_3_Start.agw that is stored in the

following subdirectory:

C:\Adaptive_Groundwater\Tutorials\Tutorial_3

The Base Grid is initially displayed on the screen (Figure 1).

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Figure 1

Step 2 – Change Porous Media Type to “Correlated Random K Region”

On the main menu select Simulation > Simulation Control Parameters and in the Simulation

Control Parameters dialog select the “Media” tab (Figure 2). Observe that the hydraulic

conductivity type has been changed to “Correlated Random K Region.” The Porous Media

Zones > Correlated Random K Field menu selection is inactive unless this media tab is changed

to “Correlated Random K Region.” Note that you still must define material property zones for

the solute transport solution, as illustrated in Tutorial 1.

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Figure 2

Step 3 – Open Random K Field Dialog

On the main menu select Porous Media Zones > Correlated Random K Field (Figure 1).

Because you have not yet generated a random permeability field, you will receive the message in

Figure 3. Click “OK” in this dialog and the Assign Random Hydraulic Conductivity Field dialog

pops up (Figure 4). Note that the initial parameter values in the various fields of this dialog will

be different than those shown in Figure 4.

Figure 3

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Figure 4

Step 4 -Define Random K Field Parameter Values

Enter the parameter values from Figure 4 in the various fields of your “random K field” dialog.

The following is an overview of the four key parameters groups (color boxes) in the random K

dialog (Figure 4). You can read a full discussion of the parameters and options in this dialog by

clicking the “Help” button.

In this example, the average K of the lognormal distribution (the geometric mean; red box) is

equal to 8.64 m/day (0.01 cm/sec). A ln(K) variance of 1.0 (purple box), which is representative

of coarse-grained sediments, is used (see “Help” discussion). Because random field generators

approximate the target input parameters, the dialog shows the actual computed ln(K) variance.

Therefore, if necessary, you can adjust your target value so that the computed variance satisfies

your objectives.

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For this hypothetical example (and to illustrate macrodispersivity) we have selected correlation

lengths (green box) that create several thin (z-dir.) high- and low-K lenses that are elongated in

the flow (x) direction.

Note: To generate different random K field realizations (i.e., same statistical parameters but

different values from cell to cell) you must vary the “Random Seed” integer number (light blue

box).

The Random K Region (blue box) is the portion of the model domain where the hydraulic

conductivity is randomly distributed. This region is delineated by the Base Grid column, row,

and layer ranges. Any cells that lie outside of this region are assigned the geometric mean K. In

this example, the three columns at both ends of the grid are not included because the random

field generator requires that the mesh spacing is uniform in each coordinate direction (but cell

dimensions may vary with direction). (The random K distribution in this area is shown in Step

5).

As explained in the “Help” discussion, the random K field is generated using the finest cell size

(i.e., highest level Subgrid cell sizes) in the AMR mesh. Therefore, field generation can be

computationally intensive when many levels of AMR refinement are used. One approach to

lowering this computational overhead is to limit the random K region to the plume area.

Step 5 – Generate Random K Field and View Plan-View Contour Map

To generate a random K field select the “Compute K Field” button (orange box in Figure 4) to

start the computation of the random hydraulic conductivity distribution for all levels of the AMR

mesh. This computation may take a few minutes for larger grids. The progress dialog in Figure

5 provides updates on the computational effort.

You can use the Figure 4 parameter values or perform your own sensitivity analyses [e.g., vary

the ln(K) variance and/or the correlation length scales]. To reduce the computational time for

sensitivity analyses you can limit the size of the Random K Region (e.g., only use one Base

Grid layer).

Figure 5

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When the computation is complete a horizontal slice through the random permeability field is

shown (Figure 6). You can change the slice location by varying the “layer number” (corresponds

to the Base Grid layers) or entering a coordinate (“View Plane Coord.”); refer to Figure 4.

Figure 6

Figure 7 is a plan view of the grid near the left-hand boundary showing the assigned geometric

mean K to the first three columns.

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Figure 7

Step 6 – Generate Cross-Section Flood Map of K Values

Figure 8 is an x-z cross-section through the aquifer. To create this view, click on the Switch to

XZ view button (circled in Figure 6) and then use your mouse to select a model slice (any row).

You can also change the view by selecting View > Change View Plane on the main menu. When

you first switch to the cross-section view, you will want to add vertical exaggeration (e.g., VE =

10-20) by going to View > Vertical Exaggeration in the main menu.

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Figure 8

Step 7 – 3D Volume Plot of Random K

To create a three-dimensional Volume Plot of the computed random K field simply (i) click the

“Contour Options” button (Figure 4) and (ii) in the Contour Parameters dialog select the “3D

Volume” radio button next to Contour Type (Figure 9). As a result, the volume plot in Figure 10

is generated.

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Figure 9

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Figure 10

Step 8 – 3D Surface Plot

To create a three-dimensional Surface Plot of the computed random K field select the “3D

Surface” radio button (Figure 9) next to Contour Type, and Figure 11 is automatically generated

for an x-y slice through the mid-depth of the aquifer. Vary the slice plane coordinate by using

either the “+/-“ layer selection buttons or directly entering a coordinate (see bottom Random K

Field dialog; Figure 4).

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Figure 11

Section 2 – Simulation Results Visualization

In this section we show how to create various two- and three-dimensional plots of the simulation

results for Tutorial 3. You can use either the supplied Tutorial_3_Completed project files or

your working copy of the Adaptive Groundwater files for this tutorial: Tutorial_3_Start.agw. It

does not matter if you have made new runs with shorter simulation times than those shown here;

select whatever output time that you want.

Step 1 – Generate Plan-View Map of Simulated Solute Concentrations

In the main menu select Output > Solute Concentration and the View Simulation Results dialog

appears (Figure 12). Click the “Go To” button at the top of the dialog to pop up a child dialog

with available output times; click on any output time you want and select “OK” in the “Go to

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Output Time” dialog. You may also use the “+” / “-“ buttons to toggle through the output times.

Under Plot and Contour Types you see that “2D” (i.e., two-dimensional) plots are the default.

Figure 12

A plan-view flood map through the middle of the aquifer is automatically generated (Figure 13).

The AMR mesh is also shown as an overlay. The mesh overlay can be turned off by un-

checking the “Mesh” box in the Contour Options dialog (under the “Overlays” tab; Figure 14).

Figure 15 is the same x-y slice through the plume without the grid overlay.

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Figure 13

Figure 14

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Figure 15

You can change the slice coordinate by selecting the “Go To” button or the Layer no. “+/-“

buttons (Figure 12). Further, you can view an animation of the different plan-view slices by

changing the “Animation Type” to Layer (K-plane) and clicking the “Start Animation” button.

Note: the layer number refers to the Adaptive Mesh Refinement (AMR) mesh associated with

the multi-level AMR grid created during the simulation. In highly-refined mesh areas the

vertical discretization is equal to the grid spacing in the highest-level subgrid (e.g, Level 5 in this

example which utilizes five AMR levels). In less-refined areas the grid layer thickness for the

output is equal to the grid spacing in the most-refined subgrid (e.g., Level 1, 2, 3, or 4).

For any of these illustrations, you can save the plot format (and import it later) by clicking on the

“Save Plot Format” button at the bottom of the View Simulation Results dialog. You can also

print or export drawings in various graphics formats using the File > Print/Export option in the

main menu.

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Step 2 – Plot Groundwater Pathline

If groundwater pathline starting locations are defined in the input data (Pathlines > Assign in the

main menu) their computed trajectories can be shown in the output by checking the “Show

Pathlines” box in the Contour Options dialog (under the Pathlines tab; Figure 16). Check the

“with Time Markers” box to add specified travel-time symbols. If the “Include Retardation” box

is checked the pathline length and travel-time markers are based on the pore velocity divided by

the retardation factor.

Figure 16

Step 3 – Cross-Section View of Plume

To display the cross-sectional view of the plume in Figure 17, click on the X-Z Slice (Row)

button in the lower left hand corner (red circle), and then select a row of cells going through the

center of the plume (or select View > Change View Plane in the main menu). When you first

switch to the cross-section view, you will want to add vertical exaggeration (e.g., VE = 10-20) by

going to View > Vertical Exaggeration in the main menu.

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Figure 17

Figures 18 (no grid overlay; see travel-time marker specification in red box) and 19 (with AMR

mesh overlay) are vertical (x-z) cross-section views of the plume, including a groundwater

pathline with 5-year travel time markers.

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Figure 18

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Figure 19

Figure 20 is a close-up view of the plume and the pore velocity vectors (activate under the

“Vectors” tab in the Contour Options dialog). You can change the vector length [“V

Length(%)”] and spacing (“Vector Indices Skip”) under the Vectors tab.

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Figure 20

As usual, you can “Zoom In”, “Zoom Last”, or “Translate” the view by clicking one of the icons

in the upper-left corner of the display (Figure 17) or by making the appropriate selection under

View in the main menu.

Step 4 – 3D Volume Plot of Plume

Create a three-dimensional volume plot of the plume by selecting the “3D Volume” radio button

in the View Simulation Results dialog. Click on the “Contour Options” button to load the

Contour Parameters and Overlays dialog (Figure 21). Click on the “Contour Options” tab and

change the concentration contour range to 0-0.025 mg/L.

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Figure 21

Select the “3D Option” tab in the Contour Parameters and Overlays dialog (Figure 21). Activate

the first blanking parameter (click checkbox) and select “C (mg/L)” as the blanking parameter.

Select the “.LE.” operator and enter a value of 0.001 mg/L to blank all cells with C .LE. 0.001

mg/L. Click the “Redraw Contours” button to view an isosurface of the central core of the

plume.

Now add a second blanking parameter to also view a slice through the plume. Click the “+”

button and activate “Y (m)” (y-coordinate) as a blanking variable and enter y .LE. 880 m. Click

the “-“ button to return to the first blanking variable (C) and select “.OR.” as the logical operator.

Click the “Redraw Contours” button to view a drawing similar to Figure 22.

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Figure 22

Note: the two blanking variables and logical operator are now:

C .LE. 0.001 mg/L .or. y .LE. 880 m

Zoom in by increasing the “Magnification” to 1.5 and reduce the vertical exaggeration by

increasing the “Aspect Ratio” to 2.0. Translate the drawing to the left by changing the “x

Translation” to -10. Click “Redraw Contours”.

Finally, show the computed groundwater pathline (activate under the “Pathlines” tab).

You may also generate a higher resolution plot by changing to the “High” Graphics Resolution

under the “Contour Options” tab (click “Redraw Contours” to generate).

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Step 5 – 3D Fence Diagram of Plume

Under Plot and Contour Types, choose the “3D Fence Diagram” radio button (Figure 23).

Click the “Set Fence Type” button, and in the “Fence Diagram Type” child dialog change

(scroll) the fence diagram type to “I- & K-planes”. Click “OK” in the Fence Diagram Type child

dialog.

NOTE: you can increase the plot resolution to “high resolution” for final hardcopy output by

selecting the “Contour Options” button, but the screen redraw times are longer.

Figure 23

Step 6 – Define Fence Diagram Type and Slice Locations

Click on the “Set Fence Location” button, and choose the following locations (Figure 24; you

can also vary the values as you wish):

• y-z planes: x =1617 m, x = 2001 m, x = 2348 m, x = 2610 m, and x = 2995 m (hold

down the ctrl key to select multiple planes);

• x-y plane: z = 26.4 m.

When you are finished, click the “OK” button and the plot is automatically regenerated (C

blanking is added in the next step).

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Figure 24

Step 7 – Add Concentration Blanking to Fence Diagram

Concentration blanking is also used to generate the fence diagram. Click on the Contour Options

button and make the following changes in the 3D Options tab (Figure 25). The C blanking

option renders any model areas with concentrations less than 0.0001 mg/L transparent. Click the

“Redraw Contours” button to refresh the screen. Figure 26 is the final plot.

Figure 25

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In Figure 26 you could also blank parts of the plot based different combinations of x-, y-, and z-

coordinates. For example, you could activate “x .GE. 1,000 m” as the second blanking variable

and use “.or.” as the logical operator. In this case, any portion of the 3D model domain in which

either C .LE. 0.0001 mg/L or x .GE. 1,000 m would be blanked. Conversely, selecting “.and.” as

the logical operator would only blank regions where both C .LE. 0.0001 mg/L and x .GE. 1,000

m. Similarly, you could blank portions of the model domain in the y- and/or z-directions by

adding third or fourth blanking variables.

Figure 26

The 3D Graphics Viewing options include: view angle [“Rotation” (around z-axis) and

“Elevation” (tilt about horizontal axes)]; translations of the plot in any of the three coordinate

directions; changes in the overall plot size (“Magnification”; increasing the magnification is

similar to zooming in); and the plot aspect ratio (increasing the “Aspect Ratio” reduces the

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vertical size of the plot; decreasing the Aspect Ratio is analogous to vertical exaggeration in

cross-section diagrams). Selecting the “Fit to Full Size” button restores the default view

parameter values and fits the simulation domain to the axes.