Hydrostatic Pressure Conditions in PetraSim/TOUGH

This is the first in a series of posts discussing the initialization of a TOUGH model to represent realistic natural state conditions.  In almost all cases, it is beneficial to run a model to steady state before adding transient boundary conditions, injection or pumping wells, etc.  We’ll give a very simple example first, where we’ve used EOS3 to establish a hydrostatic pressure gradient in a single phase model.

We’ve created a simple three dimensional model with dimensions of 1000x1000x100 meters.  We use a rectangular grid with spacing of 100m x 100m x 10m in the x, y and z directions.  The top of the model is 900 meters below ground surface. We’ll assume that all of the material above the top of the model is saturated with fluid of a constant density, so the top boundary of the model will be at a hydrostatic pressure based on a water column that is 900 feet thick.

The equation to calculate hydrostatic pressure is:

P = gρh,

where:

P = Hydrostatic Pressure (Pa)
g = Gravity (m/s2)
ρ = Density of Water (kg/m3)
h = height (m)

The hydrostatic pressure calculated at the center of the top layer of cells in the model (a depth of 905 meters below ground surface) is 8.97E6 Pa.  We’ve also estimated a temperature of 47.625 °C based on a geothermal gradient of 25 °C/km with a surface temperature of 25 °C.  The global initial conditions for this model look like this:

Hydrostatic Pressure Global Initial Conditions

Figure 1: Global Initial Conditions based on Pressure and Temperature at a saturated depth of 905 meters.

We’ve made the top cell layer in the model “Fixed State”. By setting the top layer to “Fixed State”, these cells will remain at the pressure and temperature conditions defined in the Initial Conditions Dialog. The cells below the top layer will be at a higher pressure which will be calculated by TOUGH. Since this water will compress, the top layer of cells will act as a source to supply the required water.

Hydrostatic Pressure "Fixed State" cells

Figure 2: The top layer of cells are set as “Fixed State” cells and colored in red. These cells will have a constant pressure and temperature equal to the global initial conditions throughout the simulation.

We set the end time of the model to 100K years with a maximum time step of 100 years. TOUGH does a transient calculation. By setting a long time, the transient will reach steady state.

Hydrostatic Pressure Solution Controls

Figure 3: Solution Controls accessible through the Analysis menu.

The model reaches steady state conditions after around 1400 years and the resulting pressure gradient looks like the figure below.  Note that the resulting minimum pressure in the model is equal to the pressure at the top of the model.  The model cells below the top cell layer have equilibrated to higher pressure values based on hydrostatic pressure.

Hydrostatic pressure final pressure iso-surfaces

Figure 4: Final pressure iso-surfaces show a linear pressure gradient.

To load this pressure gradient as initial conditions in a new model, follow these steps:

  1. On the File menu, click Save and save a new .sim file in a different directory.
  2. With the new .sim file open, on the File menu, click Load Initial Conditions and choose the SAVE file created by the original simulation (stored in the same directory as the original SIM file).

Send comments or suggestions on this post to Alison Alcott at RockWare.

Download the PetraSim input files here:

A Trick for Modeling Lithologic Unconformities

If you are trying to create a lithology model composed of horizontal beds that have been eroded and then overlain by a layer of soil, fill or even material such as concrete, you’ll often find that the horizontal lithoblending algorithm incorrectly places this upper layer of material below the sediments in some places.

One solution is to use some newer tools in the Lithology menu to create two separate Lithology models that can then be combined.  Here is an explanation of how this works.

Let’s start with the “Soil” layer at the top of the model.  First, it is important to assign a G-value to the Soil Lithology Type that is lower or higher than all the other material types.  In this case, the Soil material has been assigned a G-Value of 2.  All of the other material types have been assigned values between 3 and 8.

In the Lithology modeling tree menu, choose to create a model titled “Lithology Warped”.  Warp the model based on a grid that represents ground surface elevations, and turned off the “Randomize Blending” option to avoid interfingering of the soil and sand below.

While the representation of the sediments is probably not reasonable, I think that the soil layer at the top of the model looks much better in the diagram below than it does in the diagram above.

Next, create a model of just the flat lying sediments (in this example, the model is called “Lithology Sediments.mod”).  When creating this model, turn the Randomize Blending option back on, the warping option OFF, and tell the program to limit the model to just materials with G-Values between 3 and 8.

 As you can see in the diagram below, RockWorks has included everything except for Soil in this model.

Finally, use the Solid à Filter à Replacement Filter tool in the RockWorks Utilities, to insert the Soil in the warped model into the sediments model.

The diagram below displays this final model in a cross-section.

     

Tips for Creating Contour Maps of Sparse Groundwater Elevation Data

Contouring sparse data in any mapping program can be challenging.  We’ve found a few tools in the RockWorks15 to be particularly helpful when creating contour maps of sparse groundwater elevation data.

First, let’s take a look at a contour map created using the EZ-Map tool in the RockWorks Utilities.

The EZ-Map tool uses simple triangulation to create contours.  For some data sets, this may be all you need to create a reasonable looking map.  However, it will often be necessary to create grid-based maps with smoother contour lines that extend to the edge of the project.  Note the increase in the groundwater elevation on the eastern edge of the map.  This is something that can be resolved by switching to a grid-based map.  We’ll explore grid-based mapping tools next.

Here is a map created using the default Inverse Distance Weighting settings.  I should note that I had both the “Smoothing” and “High-Fidelity” options turned on during grid creation.

The “bull’s eyes” that you see around the high and low points in the map are typical of the Inverse Distance interpolation method.  One way to resolve this is to decrease the number of points used during interpolation.

To do this, change the Number of Points used for the Inverse Distance Algorithm from 8 (the default setting) to 4 (which is more appropriate for a data set of this size).

Here is a map created with the modified “Number of Points” value:

The bull’s eye effect has been muted somewhat, but notice that the contours don’t honor the data extremely well.  Let’s move on to Kriging.

In the map below, I let the RockWorks program choose the appropriate variogram settings.  With Kriging especially, which can create fairly blocky models, I highly recommend that you turn on both the grid “Smoothing” and “High-Fidelity” options when
creating a contour map. 

This may be a little bit more to your liking, but the general groundwater flow direction could still be better represented along the borders of the map.  Just to cover all of our
bases, here is another map created using Triangulation gridding.  Unfortunately, there are some problems with edge effects in the resulting map as well.

None of these are really doing it for me.  At this point, I think that a lot of people would probably resort to hand drawing their contour maps, or adding additional control points to the data set to force the contours into the shape they have in mind.  Before you resort to these tedious and time-consuming options, I would recommend you look at the Densify and Polyenhancement options available in RockWorks15.

Here is a diagram showing the contour maps created with the Inverse Distance interpolation algorithm, with and without Densify turned on.  As you can see, the densification process (which adds additional control points to the data set before
interpolation using triangulation) straightens out the contour lines quite a bit.

I did the same test using the Kriging algorithm and got the following results.

Last but not least, here is a contour map created with the Polyenhancement option turned on.  When this option is activated, the program fits the data to a polynomial surface and then warps that surface to honor the data points (in this case, I choose a 2nd order polynomial surface).  I think I have my map!

 

In real life, I’ve found first, second and third order polynomials useful when creating groundwater contour maps.  If the groundwater flow direction is fairly constant through the area, go with a 1st order polynomial (which is a planar surface).  If it is variable because of topography or a feature such as a river or stream, then a 2nd or 3rd order polynomial is the way to go.

 

 

RockWorks “Triangle Map” Illustrates Water Quality in Eastern Virginia Aquifer

Thanks to David Buss at aquaFUSION, Inc. for allowing us to post this map created using RockWorks15 and ArcGIS.

The triangle map (created through the Map -> Multivariate Maps -> Spider Map menu in the RockWorks Utilities and imported into ArcMap as a DXF)  illustrates the relative percentages of Filtered Residue, Fluoride and Sodium in well water as triangles with variable shapes and sizes.  Each triangle “axis” is scaled independently based on the minimum and maximum measured value of that constituent normalized to values ranging from 0 to 100.

The triangle map shows a general increase in constituents in well water in the in the southern portion of the watershed, as illustrated by larger triangles in Northumberland and Lancaster Counties.  A more subtle trend can be seen when comparing triangles located along the groundwater divide (which generally follows the eastern border of Richmond County) to those closer to the rivers.  There appears to be a correlation between proximity to a river and the amount of TDS, Sodium and Fluoride in well water.