Time stepping in dry-out zones
Hello all,
I know it is a general question, but any hint will be appreciated.
I am running a 3D model of CO2 injection into a layered aquifer using the ECO2N module. The aquifer depth is 1000 m and I inject the CO2 into the bottom 100 m.
I first ran a homogeneous model with a permeability that was a little larger than the value of the permeability of the sand-stone formation I inject the CO2 to (100 md vs. 60 md) .The simulation ran fine and there was no dry-out zone.
Then I modeled each layer with a formation-specific parameters. The aquifer structure is such that on top of the bottom layer there is a carbonate layer with a relatively low permeability which delays CO2 migration. I first ran radial simulation. In this simulation I got a dry-out zone around the well.
In the layered simulation time steps were very small (a few seconds) and it seems that TOUGH2 has difficult time when a cell goes from 2 phase to a single phase co2. It is important to note that pressure and temperature were in the limits of the model.
I tried to run a 3D model for the layered aquifer (I need 3D simulation since I include groundwater flow), but time steps decreased to a fraction of a second after 11 hrs, making it unfeasible to run.
I wonder if anyone encountered such a behavior and if there are any suggestions to overcome such difficulties?
Thank you very much,
Ravid
4 replies
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Dear Ravid,
Unfortunately, this reply is not going to resolve your issue. I just want to take the opportunity to explain why this kind of problems are difficult to resolve in a TOUGH User Forum post.
Yes, convergence problems are encountered quite frequently - I'm tempted to say that overcoming convergence issues is a main part of modeling. The problem is that there are no general solutions to such problems, as they may be caused by a very large number of potential issues. While I appreciate your description of the problem, one has to dig several layers deeper to even begin making suggestions (I don't know what properties you chose and what the property contrasts are; how many elements you have and how the discretization looks like; what weighting scheme, convergence criteria, and solver options you selected; all of these factors (and mode) impact convergence behavior).
So, here is the only advice I can give:
(1) Set MOP(1) = 1
(2) Look at the last few time steps before the convergence failure occurs (in case TOUGH2 does not stop by itself, but just goes on with very small time steps, set MCYC to a number when time steps became small and rerun your simulation, making sure you get a full output).
(3) Identify the element(s) that have the largest residuals during the Newton-Raphson iterations or at convergence. Check which equation causes the problem.
(4) Go to the full output after convergence failure, search for these elements, and try to find out what the conditions are. It seems you already identified that the transition to single-phase gas conditions seems difficult. Look at all the primary variables and secondary parameters in those elements and try to find discontinuities or strong non-linearities, unphysical states (e.g., very large capillary pressure, very high or low temperatures or pressures).
(5) Try to fix unphysical behavior or make it easier to transition (very often by making changes to the relative permeability or capillary pressure functions).
(6) Check out "Tips & Tricks" (https://tough.forumbee.com/t/19pkq) specifically Karsten Pruess's post "0=0"
(7) If you get desperate (but only then!), start playing around with solvers, convergence criteria, and solver options (first try MOP(21)=2). Don't get your hopes up too much, though...
Steps (3) provides you the key information needed to start debugging your model; and Step (5) is the main process you have to go through to fix the issue; it requires understanding of the underlying physics and your specific system.
I realize I just punted the ball back to you...but maybe you get lucky and somebody from the TOUGH User Community picks it up and has some specific advice.
Cheers,
Stefan
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Hello Stefan,
Thank you very much for your reply. Really appreciate it.
Although you didn't give me the answer, you gave me the tools to find it.
Apparently, the value of Pmax of van Genuchten's capillary curve model was too large for one of the layers and caused large capillary pressure near the injection well. When I decreased it, the simulation ran smoothly.
By the way, are there guidelines to choose the value of Pmax?
Thank you very much for your help,
Ravid
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Ravid,
No general guidelines; depends, among other things, on what you do with the relative permeability curve (hope you saw the note for CP(2) under ICP=7 in the TOUGH2 manual), whether you expect liquid saturation to go below residual (e.g., by evaporation), and other considerations.
I'm glad you resolved the issue!
Stefan
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Saw the note. Thanks.
Ravid