Innacurate water table near abrupt change in K

Angelo Breda

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Dec 22, 2021, 6:09:15 AM12/22/21

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Hello everybody!

I am working on a project to simulate the water table in waste rock piles from coal mining. Therefore, I have a highly fractured material dumped over a sandstone base. See the image below (or attached) of the front view.

The sandstone base uses the default values from ModelMuse of Kx = 0.0001 [m/day] and Kz = Kx / 10. For the waste rock pile, I used different values of K (Kx = Ky = Kz), but I am having problems when K = 0.2 m/day. So the change in the conductivity is huge.

My boundary conditions are:

CHD = Model_Top on both sides (first and last columns)

RCH (recharge) = 5 mm/year (of course I converted to m/day in ModelMuse) applied to "Top Active Cell"

DRN (drainage) with drains at Model_Top Level, applied only in the upper layer, with a big conductance to assure that any water above Model_Top is drained out.

I am using MODFLOW 6.

In the figure, the light blue line is for the first day (transient simulation of 356 days), the green line for the 5th day and the dark blue for the 365th day. As you can see, the water table quickly moves from the Model_Top (initial head condition) to a flat table at cells under the pile, followed by a quick jump back to Model_Top outside the pile.

The issue is that the table is crossing through the sandstone as if it was also the waste rock.

I have tried many things already. From different spatial discretization to other ways to compute vertical conductivity, but I always get the same results.

Any other idea!?

Thank you!

Richard B. Winston

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Dec 22, 2021, 9:00:53 AM12/22/21

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The most likely explanation is that the high hydraulic conductivity is being applied to the sandstone. Try coloring the grid with Kx and Kz to check that they are being applied the way you want. If not, the explanation shown in the Grid or Mesh Values dialog box can help you diagnose the cause of the problem.

Angelo Breda

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Dec 22, 2021, 11:04:07 PM12/22/21

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Hi Richard! Thank you very much for sharing your thoughts about this issue.

Yes, Kx and Kz are distributed as expected. I checked with the colour visualisation, checked with the information tool and also have a looked in the .npf file. They all have the correct data.

I was trying random things and something that apparently worked was to set the cells within the waste rock pile as Convertible. In the image below, light blue = 5 days, dark blue = 1 year, light green = 2 years, black = 5 years and dark green = 10 years.

I understand that setting a cell to Convertible means that the conductivity (or transmissivity) will be calculated based on the thickness of the saturated part of the cell, instead of the entire cell thickness. So, anyway, it is still doing something wrong in the transition near x = 1500 m.

Kind regards,

Angelo.

Richard B. Winston

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Dec 23, 2021, 2:06:33 AM12/23/21

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In a confined layer, MODFLOW allows the head to drop below the bottom of the layer without going dry. I suspect that what you are seeing is the computed head in waste rock rather than the head of the cells intersected by the computed water table. Because of the high hydraulic conductivity of the waste rock, the heads in it can quickly reach a state in which all the heads in it are nearly equal. To check this, try plotting the flow vectors from the flow (.cbc) file. I would expect upward flow into the waste rock at the upstream end and downward flow out of the waste rock at the downstream end.

Angelo Breda

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Dec 23, 2021, 8:30:17 AM12/23/21

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Hi Richard, you are right, the vector plot shows the water moving upwards in the unmined layer and laterally in the waste rock. The image below shows another section of the mining pit and the profile was coloured based on Kz. The "vectors" (I haven't found a way to put arrowheads in ModelMuse) are in log scale as the flux in the waste rock is two orders of magnitude higher than the flux in the sandstone. Moreover, I checked the heads for each layer, and indeed the head for the sandstone layers are higher than the head in the waste rock one.

So, I believe the right way to define the water table in such cases is to use the bottom of the waste rock layer when the head is below it (or the head of the layer below when it is higher than the waste rock's head, but lower than the waste rock's bottom elevation.

Thank you for such enlightenment about Modflow!

Kind regards,

Angelo.

Boyce, Scott E

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Dec 23, 2021, 11:13:13 PM12/23/21

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I'm not an expert on MF6, but one thing you may need to do is add more layers (I mostly work with the MF-2005 family of products).

Here are a bunch of random thoughts that hopefully are helpful.

In MODFLOW the properties are assigned by the cell and then the flow between the cells uses an averaged value between the two cells.

For flow between layers the conductance (CV) is calculated as the harmonic mean between the two layers vertical hydraulic conductivity.

This does bias towards smaller VK values between layers, but its not a true separation of high VK with low VK.

Given no recharge and enough time, if there is any permeability between layers the water table will eventually drain downward into the lower layers.

I pulled this from pdf page 60 of the MF-2005 report:

Another thing to look is if CV may be held at the saturated valued compared to horizontal Conductance (CC and CR).

For MODFLOW-NWT or MODFLOW-OWHM, when using the NWT solver and UPW flow package the calculation of CV uses the confined formulation for both CONFINE and CONVERTIBLE layers

(that is, it does not vary with saturated thickness and uses the cell thicknesses).

I don't know if that same method is done for MF6, but that is also a common misunderstanding when using the NWT solver.

With the layering there seems to be a pretty dramatic size difference.

I can't remember the rule of thumb but generally huge transitions is cell cells can leave to mass errors.

That bump that represents the waste rock might be swallowed up by the larger lower layers due to the harmonic averaging.

For example, in the California Central Valley model there is a thin clay layer in the center of the model layers (call it layer 5 of a 10 layer model) that we simulate as three numerical layers (that is layer 4, 5, and 6).

The ideas is that layer 5 represents the true clay formation and layers 4 and 6 are washed out through the vertical averaging with layers 3 and 7 (that is the dummy layer 4 is averaged with layer 3, and dummy layer 6 is averaged with layer 7, but the conductance between 4/5 and 5/6 are preserved.

My last thought is what is your Sy for the waste rock and lower confine layer? If you increase Sy for the waste rock and lower Ss/Sy for the confine layers will keep the head higher in the confine layers.

This is because the waste rock will resist changing its head value as it drains, but increase significantly the head in the lower layer as it receives water.

Hopefully that will give you some ideas to work with.

Scott

P.S.

I whipped up a quick Excel workbook with the LPF CV formulation for you to play with properties to see how the conductance is calculated.

– –

Scott Elliott Boyce [USGS Profile]

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California Water Science Center
U.S. Geological Survey

Adjunct Professor [TUM Profile]
Hydrology and River Basin Management
Department of Civil, Geo and Environmental Engineering
Technical University of Munich

Google Scholar Link

4165 Spruance Rd. Suite 200
San Diego, CA 92101-0812
cell: 805-459-0077

seb...@usgs.gov

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CV_Calculator.xlsx

Angelo Breda

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Dec 26, 2021, 8:11:43 AM12/26/21

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Hi Scott, I appreciated your observations a lot as well. Thank you very much!

I did a run including more layers in the domain, even trying with a thin one (10 cm deep) between the pile and the sandstone with an intermediate K, but I got the same result.

As Richard exposed, what ModelMuse plot as the water table is actually the head elevation in the first layer. In the attached image you can see that the line representing the head for layer 1 (waste rock) matches with what was shown as water table previously. Meanwhile, the head for the two sandstone layers are almost the same and above that one is for the overlaying waste rock. So, in sum, the MF6 is doing okay. Just maybe, the way the water table is computed for cases like these is what should be reworked.