Conceptual Models > Design of conceptual models

Modeling a batch experiment of CO2-rich water with CaCO3

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lrossi:
Hello all,
I try to reproduce by modeling an experiment that I made in the laboratory. In this experiment, I placed a volume of CaCO3 powder (98% +/- 1%, according to the analyzes of the samples) in a beaker which I filled with a volume of water enriched with CO2. This beaker is closed and there is no headspace. I see over time a gradual increase in pH until the equilibrium, and an increase and decrease in major and traces ions concentrations.

First, I modeled this taking into account only the major ions. I obtain a correct stabilization of the pH  but the HCO3- and Ca2 + ions concentrations increase until reaching a high threshold and they do not decrease.

Here is the script:

--- Code: ---SOLUTION 1
temp      17.89
pH        7.89
pe        4
redox     pe
units     mg/l
density   1
Alkalinity 247 as HCO3
Ca        102
Cl        23
F         3
Mg        39
N(5)      48
Na        14
S(6)      53
water    1 # kg
K         16

EQUILIBRIUM_PHASES 1
CO2(g)    -0.1

Save solution 1
end

use solution 1
RATE 1
Calcite
KINETICS 1
Calcite
-formula  Calcite  8
-m        0.003
-m0       0.003
-parms    15380 0.6
-tol      1e-08
-steps       3024000 in 105 steps # seconds
-step_divide 1
-runge_kutta 3
save solution 1
end

--- End code ---

I feel that the way I am modeling the batch is wrong.
Do you have a solution to my problem?

Regards,
L. Rossi

dlparkhurst:

--- Code: ---RATE 1
Calcite

--- End code ---

This section has no effect. The keyword RATES (with an S) is used to define the rate expression for kinetic reactions. The word RATE is not interpreted correctly, an is ignored. So, the rate expression used in the calculation is the RATES definition for Calcite in the database that you are using.

The coefficient of 8 in the -formula definition is odd. You define -m 0.003 in the KINETICS definition. Each mole of reactant has 8 moles of calcite, so effectively you have defined 0.024 moles of calcite available to react kinetically. With the 8 coefficient, there is enough calcite to react to equilibrium; about 8.7e- x 8 ~ 0.007 moles of calcite react to reach equilibrium. If you use a coefficient of 1, only 0.003 moles are available, and all the calcite dissolves to reach a saturation index of -0.7. Perhaps this is why you have higher concentrations than you expected. Note your initial solution has a P(CO2) of 10^-0.1, or a partial pressure of about 0.8 atm; hopefully that is what you wanted.

If you add the keyword INCREMENTAL_REACTIONS true, the calculation will proceed faster. The default (INCREMENTAL_REACTIONS false) is a little brain dead in that it runs the kinetic reaction for 1/105 of the total time, then goes back to the start and runs for 2/105 of the total time, etc. With INCREMENTAL_REACTIONS true, it runs 1/105 of the time, stores the result, and runs for the next 1/105 of the time; so, it does not keep repeating the early parts of the integration.

lrossi:
Hello,
Thank you for your response and your helpful advice. I can correctly model the pH and the increase in Ca concentration is similar to what I get experimentally.
However, I experimentally observe a reprecipitation of Ca over time as the pH increases, but not with the model.
Is it possible to also model this reprecipitation at the same time?

Regards,
L. Rossi

dlparkhurst:
Theoretically, a closed system at constant temperature would not reprecipitate calcite.

If CO2 escapes, or temperature rises, then you could model those effects.

I suppose there could be an effect from fine grain size, where small grains are more soluble than larger grains because of surface energies. You could look at the literature about recrystallization. You could force the effect by changing the log K with time in the RATES definition, but without some mechanistic basis, you may be simply data fitting.

lrossi:
Hello

I am coming back to you for advice concerning a new carbonate dissolution model on which I am working on the same experiment (putting a carbonate rock (98% CaCO3 + 2% SiO2 and amorphous iron oxides) in contact with water gasified with CO2).
I observed an increase in the concentrations of most of the major and trace elements correlated with the decrease of the pH. I also observed a decrease in the concentration of SO4, NO3 ions correlated with the decrease in pH.

I was able to model the increase in concentrations of all trace elements using this script with SOLID_SOLUTIONS:

--- Code: ---REACTION 1

CO2(g)     1
4 moles in 2000 steps
INCREMENTAL_REACTIONS True

SOLUTION 1
temp      15
pH        7.8
pe        4
redox     pe
units     mg/l
density   1
Alkalinity 300 as HCO3
As        0.0009
Ba        0.023
Ca        139.6
Cl        54.1
Co        0.0003
Cr        0.0036
Cu        0.0028
F         4.55
Fe        0.01
K         3
Mg        4
Mn        0.005
N(5)      20
Na        10
Ni        0.0008
Pb        0.0002
S(6)      59.65
Sr        0.1
Zn        0.021
Sb        0.0003
Sn        0.0001
Cd        0.0001
V         0.0013
Se        0.0002
Li        0.0008
Si        0.0046
Al        0.0048
Mo        0.0018
-water    1 # kg

SOLID_SOLUTIONS 1
CaSrBaCO3
-comp Calcite 1
-comp Witherite 0.0005
-comp Magnesite 0.005
-comp Celestite 0.01
-comp K-Jarosite 0.005
-comp CuCO3 0.0009
-comp CoCO3 0.0003
-comp Rhodochrosite 0.0001
-comp Cerussite 0.0001
-comp Smithsonite 0.0002
-comp Natron 0.0003
-comp CaCrO4 3e-05
-comp NiCO3 0.0003
-comp Otavite 0.0003
-comp Ca(VO3)2 2e-07
-comp Quartz 0.002
-comp NiCO3 0.0002
-comp Li2MoO4 2e-07
-comp Fe2(SeO3)3:2H2O 0.0001
-comp Ca3(AsO4)2:4H2O 1e-08
-comp Na-Jarosite 0.0002

end

--- End code ---

However I am unable to model the increase in Na, K , Cl concentrations and the decrease in SO4 and NO3 concentrations with this method.

I have a doubt about this model, because for me I don't take into account the sorption on iron oxides or on the surface of calcite.
Do you think I am doing wrong? Also, do you know how I could model the decrease of NO3 and SO4?