X2t discharge units

[Lucek]

Hi ! . I am looking at X2t and I can't get my head around the discharge units. For example meters per day (or m3/m2/day). I went through the manual and cannot find a sensible answer. I am sure it is quite simple to explain, and as I am new to flow modelling, I just don’t get it. Anyone can help understand? but please in layman's terms

[Jia Wang]

Hello,

The reactive transport model applications in the GWB carry flow in terms of specific discharge, which is also known as the volumetric flux. The volumetric flux is written in units of volume of fluid per area of your domain cross section per time. Because the units for volume are length cubed (cm^3) and area is length square (e.g. cm^2) , the simplification reduces the unit to length per time (e.g. cm/day).

In the GWB, you can prescribe discharge as a constant value or allow the program to calculate it according to Darcy's law. In the latter option, you would have to provide the program with the hydraulic potential across the domain, permeability, and the fluid viscosity. For more information on how flow rate is carried in the software, please see section 3.2 Setting flow rate in the Reactive Transport Modeling Guide. If you would like even more information, please refer to Chapter 20, Transport in flowing groundwater, in the Geochemical and Biogeochemical Reaction Modeling textbook. The text provides a more detailed explanation on the theory and application of reactive transport modeling along with many examples setup in the GWB. 

Hope this helps,
Jia Wang
Aqueous Solutions LLC

[Lucek]

So will that be correct? my domain = x 1 km, y 1 km and z 2 m

discharge rate of the model from left is 25 m/year.

Therefore:

2e3 m area x 25 m/year = 5e4 m3/year = 5e7 k/year     

 

5e7 kg/year/3.1e7 sec = 1.61 kg/s? 

 

so my discharge in that domain would be 1.61 kg/sec or 5e7 kg/year 

 

cheers

L

[Jia Wang]

Hello L,

You math looks correct to me. I am assuming that you're using 1000kg / m3 for the conversion from volume to mass. The GWB will display discharge in volume units, but you can most certainly do the conversion outside of the application. The model will also calculate the density of the solution as well if you would like to use that for your conversion. 

If you like, you can set up a very simple system in X2t to test your calculation. I think this may be a good exercise for you to familiarize yourself with the software before incorporating geochemical reactions.

In a new X2t instance:

• set your discharge on the left boundary to 25 m/yr (Flow pane)
• your domain to the dimensions as you described above (Domain pane)
• add Na+ and Cl- as your solutes in the Initial pane and set small amounts of Na+ (e.g. 10 mmol/kg) and leave Cl- as the charge balancing ion. I just want to set some dilute fluid here that is basically non-reacting
• in Fluids pane, click add and if you configured the Initial pane, the fluid will copy over what you have included there. 
• in the Intervals Pane, set the left boundary as the fluid you just added in the Fluids. Set simulation to end at 1 year
• go to the Run tab and select Go to trigger the calculation

Once the run is finished, you can select Plot Results on the Results pane to render your run in Xtplot. You can display the result as a map of the 2D domain or examine the result for each row or column in the domain. You can plot the pore volume displaced along each time step of the simulation in either plot format. In a map plot, you would select the Variable type to map as Physical parameters and the Pore volume displaced as the variable. If you select the time level at the end of the simulation (1 year), you can see that the pore volume displaced is 0.025 everywhere in the domain. If you multiple the pore volume displaced by the total volume of the domain (0.025 * 2E6 m3), that would give 5E4 m3/year, your answer from above. You can play around with different variables to see how each affects the model outcome. 

You can find more details on configuring plots in Xtplot in Chapter 6 of the Reactive Transport Modeling User Guide. Additionally, I think you may also find the GWB Command Reference very helpful for learning about configurations in X2t and other GWB apps. 

Hope this helps,
Jia 

 

[Kirkoff Xn]

Hi Jia,

Just a follow-up to this question. Let's say an injection well has a capacity of 0.26 m3/s and you want to  run a 2D model in GWB with the same domain dimension above (1Kmx 1kmx 2m). How would you input the volumetric flux? Am not sure if considering the domain area cross section as unit (1m2) is accurate so that the flux would be 0.26 m/s(?).

Thanks

[Kirkoff Xn]

I understand that the domain area cross-section in this case is 2,000 m^2 and that the volumetric flux is dependent on the length of the domain (considering that cell lengths are all the same).  My question here is how to set up an accurate vol. flux value so that one can further be able to calibrate observed and simulated values of solutes (in a 3D). 

 

[Jia Wang]

Hello,

To clarify, the discussion was originally regarding boundary flow conditions. Specific discharges set at the boundary are volumetric fluxes but that's not the same for wells. Injection well units are in volumetric flow, which is in volume per time. It sounds like you should be able to use the measured value directly as is.

Hope this helps,
Jia