Total volume calculation in the aquifer

[Master Z]

Hi everyone, I have a short question. I have an aquifer where I initially defined initial water levels inside the cell so unconfined situations. Then I implement river package to my aquifer with transient simulation, 1 stress period, multiple time steps.

using the formula:

unconfined volume = water depth (water level - cell bottom) x cell area x specific yield (sy)

I thought I would have my initial volume.

However, at the end of simulation, I am looking for a way to find total volume which is like

initial volume + river in = total volume (at the end)

My volume budget looks like this:

  VOLUME BUDGET FOR ENTIRE MODEL AT END OF TIME STEP   10, STRESS PERIOD   1
  ---------------------------------------------------------------------------------------------------

     CUMULATIVE VOLUME      L**3       RATES FOR THIS TIME STEP      L**3/T          PACKAGE NAME    
     ------------------                 ------------------------                     ----------------

           IN:                                      IN:
           ---                                      ---
              STO-SS =          10.6715                STO-SS =       8.4283E-03     STORAGE                          
              STO-SY =       91679.0637                STO-SY =          76.0940     STORAGE                          
                 RIV =         152.0480                   RIV =           0.1520     RIV-1                            

            TOTAL IN =       91841.7832              TOTAL IN =          76.2545

          OUT:                                     OUT:
          ----                                     ----
              STO-SS =          12.5189                STO-SS =       1.1018E-02     STORAGE                          
              STO-SY =       91829.2644                STO-SY =          76.2434     STORAGE                          
                 RIV =           0.0000                   RIV =           0.0000     RIV-1                            

           TOTAL OUT =       91841.7832             TOTAL OUT =          76.2545

            IN - OUT =      -8.6104E-08              IN - OUT =      -6.4163E-10

 PERCENT DISCREPANCY =          -0.00     PERCENT DISCREPANCY =          -0.00

I tried to calculate by separating unconfined and confined cells but could not reach a value like
river in = total volume - initial volume exactly the same when I checked the inflow from river in volume budget package

I also dont have idea where the river goes to. Is it like balancing by the storage? Technically, if I put some volume from river package to my aquifer, shouldnt I have increased total volume when compared to the initial condition? Does anyone have an idea about this?

Best Regards,

[ashutosh singh]

Hi,

I dont think that it can be done. I think that using the groundwater flow equation, we calculate the fluxes and not the volumes itself.

Someone will have to second my opinion.

The solution you are getting is the flux exchange between the river and the hydrogeological medium.

//Ashutosh Singh

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[Jakab Andras - Gmail]

First of all, for this simple case where you only have three budget terms as reported above, the water from river leakage goes into storage. You may see that the net increase in storage is equal to river leakage (i.e., you have to check both "in" and "out" terms). 

What probably confuses you is that you have both confined and unconfined storage volumes and the fact that you have both storage "in" and storage "out" terms. The latter is because water is both added and removed from storage as it is "transmitted" from cell to cell. The confined storage volume, however, appears either because some of your cells that receive river leakage convert to confined during the time step (I should know your heads relative to the top of the model), or because you also have a second model layer that is most likely confined.

--

[Master Z]

Basically, I have one layer only. At the beginning, I had my aquifer levels as model bot + 2.5 meters. My layer thickness is 5 meters so I have unconfined all the cells at the beginning. I am only looking for a method that gives me aquifer volume, based on water depths for example. Since I have inflow from river to the aquifer, can I assume that this increases total volume of my aquifer and aquifer levels at the end, and I can assume a calculation like

(initial water depths) x cell area + River in cumulative = Total volume

or when the inflow from river goes to storage, it means it increases storage volume but total aquifer volume means something else?

[Ashutosh]

Hi,

I dont think so. 

It would be incorrect to calculate volume based on the likely incorrect assumption that specific yield (Sy) represents porosity.

The flux from the river is lost to the hydrogeological unit, so the corresponding volume can be calculated by multiplying the flux by the time step.

//Ashutosh Singh

On 4 Apr 2025, at 13:08, Master Z <zeyti...@gmail.com> wrote:

Basically, I have one layer only. At the beginning, I had my aquifer levels as model bot + 2.5 meters. My layer thickness is 5 meters so I have unconfined all the cells at the beginning. I am only looking for a method that gives me aquifer volume, based on water depths for example. Since I have inflow from river to the aquifer, can I assume that this increases total volume of my aquifer and aquifer levels at the end, and I can assume a calculation like

To view this discussion visit https://groups.google.com/d/msgid/modflow/f09129c3-3047-450d-9d92-6c6dd3519ea5n%40googlegroups.com.

[Master Z]

Hi,

Thanks a lot for the information. I appreciate if you could show me the formulation of total aquifer volume based on this volume budget. I really need to know how it is calculated. Lets say my volume budget is like:

VOLUME BUDGET FOR ENTIRE MODEL AT END OF TIME STEP   10, STRESS PERIOD   1
  ---------------------------------------------------------------------------------------------------

     CUMULATIVE VOLUME      L**3       RATES FOR THIS TIME STEP      L**3/T          PACKAGE NAME    
     ------------------                 ------------------------                     ----------------

           IN:                                      IN:
           ---                                      ---
              STO-SS =          10.6715                STO-SS =       8.4283E-03     STORAGE                          
              STO-SY =       91679.0637                STO-SY =          76.0940     STORAGE                          
                 RIV =         152.0480                   RIV =           0.1520     RIV-1                            

            TOTAL IN =       91841.7832              TOTAL IN =          76.2545

          OUT:                                     OUT:
          ----                                     ----
              STO-SS =          12.5189                STO-SS =       1.1018E-02     STORAGE                          
              STO-SY =       91829.2644                STO-SY =          76.2434     STORAGE                          
                 RIV =           0.0000                   RIV =           0.0000     RIV-1                            

           TOTAL OUT =       91841.7832             TOTAL OUT =          76.2545

            IN - OUT =      -8.6104E-08              IN - OUT =      -6.4163E-10

 PERCENT DISCREPANCY =          -0.00     PERCENT DISCREPANCY =          -0.00

lets say I have my initial aquifer levels as half of the cell thickness all the cells are unconfined. At the end of this calculation, I have my latest aquifer levels at the end, with some confined, some unconfined. I checked that volume for unconfined cells are calculated like:

water depth x cell area x specific yield (sy)

for confined, how to calculate them? Also for these terms STO-SS IN, STO-SS OUT values, should I use them in my volume calculation?


I would like to check that

initial aquifer volume + River in = last aquifer volume

not the storage. Only the total volume staying in the system. I dont have any outflow condition as well so the system volume should be like that I guess.

Best Regards

[Jakab Andras - Gmail]

Based on the new information that you provided, i.e., that your aquifer remains unconfined and you don't have other layers, I would like to  ammend my previous comment, taking into account that in MODFLOW 6 both storage terms (confined and unconfined) are accounted for under unconfined conditions. In my initial comment I mistakenly was assuming you were using MODFLOW-2005 that has a different storage formulation, although the storage budget term names (i.e., STO) clearly indicate MODFLOW 6 usage. The formulation in MODFLOW 6 is different from previous MODFLOW formulations such as MODFLOW-2005, but consistent with MODFLOW-USG and -NWT, and it is also consistent with the general formula used to calculate unconfined storage (Sy + Ss*bave).

In regards to your question, what you would like to achieve is not possible based on the reported overall budget, as it only reports changes and not total volumes. In fact, MODFLOW itself doesn't even account for the total volume of water in the aquifer.

To view this discussion visit https://groups.google.com/d/msgid/modflow/4a1b6248-d7f6-4c7f-b385-f1d6a2d50796n%40googlegroups.com.

[Master Z]

Yes MODFLOW does not. But I am looking for a way to calculate it manually to see total volume development in my aquifer. Any suggestions, formulations for this total volume calculation you can recommend?

[Jakab Andras - Gmail]

Changes are reported, so that's not a problem. In your case, the change is only coming from the river. If you would like to have an idea about the available volume of water for flow, you can calculate it based on the storage formula presented above in my previous reply by multiplying the unconfined storage by the volume of the aquifer. The total amount of water, however, is more than that.

To view this discussion visit https://groups.google.com/d/msgid/modflow/4c3d447d-0d4f-4db1-9645-9c31725b9c10n%40googlegroups.com.

[Master Z]

What can you recommend for my confined cells? After the simulation at the end, I figured out that some cells become confined cells, some cells unconfined. Therefore, I am looking for calculation to calculate both these total cell volumes and sum them up. In this condition, which formula should I use to calculate their volume so that at the end, I assume that I should have smth like:

initial volume = water depth x cell area x Sy

final volume = initial volume + River in = unconfined volume + confined volume (at the end of simulation, latest time step)

Could you guide me on that as well?

Best Regards