Convergence error in simulation

[Sol-Chan Han]

Hello, Dr. David L Parkhurst and users of Phreeqc.
This is Sol-Chan Han who uses Phreeqc for cement hydration reaction modeling.
By your help on my last post, I could develop the model. However, there is some convergence error in the simulation.

Here is the input data for my model.

---------------------------------------------------------------------------
SOLUTION 1
-units g/l
redox   pe
Temp   25
O(0)   0.02
-water 0.058 # kg


EQUILIBRIUM_PHASES 1

Portlandite   0   0
Calcite   0   0
Gypsum   0   0
Anhydrite   0   0
Hematite   0   0
Brucite   0   0
Fe(OH)3mic   0   0
Al(OH)3am   0   0
CAH10   0   0
hydrotalciteC   0   0
SiO2am   0   0
Fe-ettringite   0   0
SOLID_SOLUTIONS 1
Jennite-Tob-II
   -comp   CSHjen   0   
   -comp   CSHtob2   0
Monocarboaluminate-Fe-monocarbonate
   -comp   monocarboaluminate   0   
   -comp   Fe-monocarbonate   0
hemicarboaluminate-Fe-hemicarbonate
   -comp   hemicarboaluminate   0   
   -comp   Fe-hemicarbonate   0
stratlingite-Fe-stratlingite
   -comp   stratlingite   0   
   -comp   Fe-stratlingite   0
C2AH8-C2FH8
   -comp   C2AH8   0   
   -comp   C2FH8   0
C4AH13-monosulfoaluminate
   -comp1   monosulfoaluminate      0
   -comp2   C4AH13      0
   -Gugg_nondim   0.188   2.49
   #-miscibility_gap   0.50   0.97
OH-hydrotalcite-Fe-hydrotalcite
   -comp   hydrotaliceOH   0   
   -comp   hydrotalciteFe   0
C3AH6-C3FH6
   -comp   hydrogarnetOH   0   
   -comp   hydrogarnetFe   0
(Al-)ettringite-tricarboaluminate
   -comp1   Ettringite   0   
   -comp2   tricarboaluminate   0
   -Gugg_nondim   -0.823   2.82   
(Al-)ettringite-Fe-ettringite
   -comp1   Ettringite   0   
   -comp2   Fe-ettringite   0
   -Gugg_nondim   2.10   -0.169
REACTION 1
CaO   1.112755675
SiO2   0.314562234
Al2O3   0.043154601
Fe2O3   0.015655626
MgO   0.034736006
CO2   0.047717838
SO3   0.0374733
1
END

------------------------------------------------------------------------------------------------------------

To guarantee the oxidizing condition, I manually added some amount of O(0) to a solution.
However, there are some errors occurred in this system.

1. If I change the concentration of O(0) in solution, sometimes it does not converge.
  1.1 The concentration of O(0) in the solution is changed from 0.02 to 0.06 or 0.09, then, the model is not converged.
  1.2 However, this model converges when the concentration of O(0) in the solution is 0.07 or even 0.2.

2. If I change the solution temperature to 50oC the model is not converged.
  2.1 However, it converges when I change the concentration of O(0) in solution from 0.02 to 8. (at 50oC)
  2.2 The model does not converge when the input concentration of O(0) in the solution is 9 but it converges when 10. (at 50oC)

I guess this convergence problem is may related to both the redox equilibrium of Fe and S element. But I cannot find either the exact reason or any tendency of convergence problems.
Could you give me any advice?

Thank you.

[dlparkhurst]

You are generating very high concentrations by having only 0.058 L of water and a REACTION with moles of elements. You are probably well outside the range of the ion-association model. I suggest you add the REACTION incrementally in multiple steps and use INCREMENTAL_REACTIONS.

You need to include your database file for me to look at your simulation.

[Sol-Chan Han]

Hello sir, I attach the database file.
This database is CEMDATA 07.

Thank you.

[dlparkhurst]

Your units are g/l for O(0). Typical oxygen concentrations in equilibrium with air are about 8 mg/L. 0.09 and 8 g/L (90 and 8000 mg/L) are very large concentrations corresponding up to several atm partial pressure of O2(g).

You have a small mass of water to start (0.058 kg). The equilibrium phases and solid solutions take up water, so at the end of the calculation you have only about 0.025 kg. I think PHREEQC is probably having trouble distributing the water between the solution and the solids. Adding the reaction incrementally seems to help. I also used KNOBS to take smaller steps for the iterative solver.

Code: [Select]

SOLUTION 1
-units g/l
redox   pe
Temp   25
O(0)   0.09
-water 0.058 # kg


EQUILIBRIUM_PHASES 1

Portlandite   0   0
Calcite   0   0
Gypsum   0   0
Anhydrite   0   0
Hematite   0   0
Brucite   0   0
Fe(OH)3mic   0   0
Al(OH)3am   0   0
CAH10   0   0
hydrotalciteC   0   0
SiO2am   0   0
Fe-ettringite   0   0
SOLID_SOLUTIONS 1
Jennite-Tob-II
   -comp   CSHjen   0   
   -comp   CSHtob2   0
Monocarboaluminate-Fe-monocarbonate
   -comp   monocarboaluminate   0   
   -comp   Fe-monocarbonate   0
hemicarboaluminate-Fe-hemicarbonate
   -comp   hemicarboaluminate   0   
   -comp   Fe-hemicarbonate   0
stratlingite-Fe-stratlingite
   -comp   stratlingite   0   
   -comp   Fe-stratlingite   0
C2AH8-C2FH8
   -comp   C2AH8   0   
   -comp   C2FH8   0
C4AH13-monosulfoaluminate
   -comp1   monosulfoaluminate      0
   -comp2   C4AH13      0
   -Gugg_nondim   0.188   2.49
   #-miscibility_gap   0.50   0.97
OH-hydrotalcite-Fe-hydrotalcite
   -comp   hydrotaliceOH   0   
   -comp   hydrotalciteFe   0
C3AH6-C3FH6
   -comp   hydrogarnetOH   0   
   -comp   hydrogarnetFe   0
(Al-)ettringite-tricarboaluminate
   -comp1   Ettringite   0   
   -comp2   tricarboaluminate   0
   -Gugg_nondim   -0.823   2.82   
(Al-)ettringite-Fe-ettringite
   -comp1   Ettringite   0   
   -comp2   Fe-ettringite   0
   -Gugg_nondim   2.10   -0.169
KNOBS
-pe 5
-step 10
INCREMENTAL_REACTIONS
REACTION 1
CaO   1.112755675
SiO2   0.314562234
Al2O3   0.043154601
Fe2O3   0.015655626
MgO   0.034736006
CO2   0.047717838
SO3   0.0374733
1 in 100 steps
END


[Sol-Chan Han]

Thank you, sir.
I really appreciate your help.

Based on your comment and the input file you made, I tried some cases.
However, the model still gives me some convergence error when the concentration of O(0) is changed.

Therefore, I am very confused about
1. How to evaluate the reliability of my model.
2. Is it okay that I manually changes the concentration of O(0) in a solution to solve a convergence problem?

[dlparkhurst]

I don't know your system, but adding grams of oxygen is probably not physically reasonable. Even 0.02 g seems odd to me. On the other hand, it probably does not affect the results too much.

As far as trusting the results, if the program does not issue an "ERROR", then the set of equations should be solved accurately.

I suspect the problem is not with oxygen, but with the solid solutions. The numerical method of PHREEQC can have trouble deciding when a solid solution should be present or not. Having several solid solutions (some non-ideal) and several equilibrium phases produces a complicated set of equations. My preference for solving the problem that you gave is to increase the number of steps in the REACTION. You are initially adding moles of reaction to a small volume of solution, even though the final answer increases solution concentrations very little. I would try many (1000, 10000) steps to try to approach the final result gradually, possibly adjusting other convergence parameters, although I did not find any particular approach that worked. I also would keep to a reasonable concentration for O2(aq). If that doesn't work, I think you are beyond the range of PHREEQC capabilities. 

BTW, I do not think it is a good idea to include a phase (ettringite) in two different solid solutions.

[Sol-Chan Han]

Thank you, Dr. David L Parkhurst.

I tried some simulations.
The model seems to be more stable if I did not use a non-ideal solid solution.
However, it does not mean that the model is always stable.
Anyway, I could get some meaning results in some conditions.

Really thank you for your help.