Conceptual Models > Equilibrium assumptions

Solubility Modeling in open system adjusted to high pH

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bschroth:
I've been asked to examine solubility of several minerals over a very large pH range, up to pH 13, in both open and closed systems.  I have been simulating this by using pure water with a series of EQUILIBRIUM_PHASES expressions containing the mineral in question with SI set to 0.0 and excess moles available, along with a pH_fix phase adjusted to the target pH using either HCl or NaOH.  For the open system, I also include CO2(g) SI set to -3.5 with excess moles.  The trouble is that the simulation does not converge at pH above 10, I suspect because I'm asking PHREEQC to keep adding NaOH to get to a very high pH but at the same time keeping CO2(g) at levels that the solution would not have at this pH.  How do I honor the open system at pH>10 in this type of simulation?  Is there a better way to run this solubility simulation in an open system so that I get correct results at very high pH?

dlparkhurst:
It is not physically reasonable to be in equilibrium with the atmosphere at pH much greater than 10. Concentrations of C and Na become infeasibly large. PHREEQC cannot make the calculation, but other programs like minteq probably could. They allow setting activities without regard to feasibility, like moles of base or charge balance.

I would say that you are getting the correct results at very high pH; you can't do it.

Note the Y axis is a log scale.


--- Code: ---SOLUTION 1
pH 7 charge
END
USE solution 1
REACTION 1
NaOH 1
1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1 10
EQUILIBRIUM_PHASES 1
CO2(g) -3.4
INCREMENTAL_REACTIONS true
USER_GRAPH 1
    -headings               pH TOT(C(4)) TOT(Na)
    -axis_titles            "pH" "Molality" ""
    -axis_scale y_axis      auto auto auto auto log
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 GRAPH_X -LA("H+")
20 GRAPH_Y TOT("C(4)"), TOT("Na")
  -end
    -active                 true
END

--- End code ---

bschroth:
Thank you for the response.  I had another question on this.  After noting that imposing the "CO2(g) -3.4" condition is fine up until about pH 8 or 8.5, the C(4) buildup in solution becomes huge, reaching 0.1M at pH 10.  This seemed ridiculous, so I looked up the solubility of CO2 in water and got a value of 1.449 g/L (0.0329 M) from a source at Harvard (please let me know if you think this is accurate).  Using 0.0329 instead of the usual "10.0" default in EQUILIBRIUM_PHASES, I found that between pH 9.5 and 10 there is simply not enough CO2(g) in the "atmosphere" above the 1L of water and the SI for CO2(g) simply drops below -3.5, as would be expected.  With this condition applied throughout the solubility curve, the model converges all the way up to pH 13, flattening out around 0.3 mg Ca/L (but not totally flat, as CO3-2 speciation continues to change).  Does this make sense as an approach to modeling an open system?

dlparkhurst:
The solubility of CO2 only makes sense if you specify a partial pressure of CO2(g). The number you give is probably the solubility at 1 atm partial pressure.


--- Code: ---SOLUTION
REACTION
CO2(g) 1
1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 1
USER_GRAPH 1
    -axis_titles            "log CO2 parital pressure" "CO2(g), grams" ""
    -axis_scale y_axis      auto auto auto auto log
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 GRAPH_X SI("CO2(g)")
20 GRAPH_Y RXN * GFW("CO2")
  -end
    -active                 true
END

--- End code ---

By fixing the amount of CO2 you are really specifying a closed system. 0.03 moles seems a bit arbitrary. An open system to pH 10, and then a closed system to higher pH adjusted with NaOH would make a little more sense.

bschroth:
I agree that the system is essentially closed above pH 9.5 or 10, as far as CO2(g) is concerned.  Below that pH, the solubility of calcite is significantly different between open and closed systems, with the presence of CO2 interaction in the open system effectively limiting the concentration of dissolved calcium by a factor of 10 or more between pH 8.5 and 10.  By your suggestion of a closed system above pH 10, do you assume that whatever C(4) concentration there is in solution at pH 10 remains in solution when adjusting pH upward with NaOH, or do you assume a completely closed system with C(4) coming only from calcite equilibration?  In the latter case, there would be a big jump in calcium concentration for the closed system simulation.  In the former case, there is a continuity in calcium results between the open and closed system transition.  For that former case, I think the approach I am taking is producing essentially the same results, though admittedly I agree that using the indicated solubility may be arbitrary. 

I was surprised, however, to see that this molar solubility of 0.0329 is able to maintain a CO2(g) SI of -3.5 at each 0.5 pH step up to pH 10, which was exactly where convergence became an issue with an infinite amount of CO2 available.  When running this pH profile as a series of batch reactions of 1L water each, it made me wonder whether using that solubility is a reasonable approach.  Or was it simply a coincidence that it becomes insufficient to maintain an SI of -3.5 at pH 10?

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