Processes > Mixing

Mixing two solutions

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cevans3098:
I have perhaps a simple question.

I have two solutions which are identical (molalities, temperatures, pH, etc...) and both as expected have the same density.  However, when I mix these two solutions, the resulting density and pH is different.  Why is this so?  I would have expected the same density and pH.

My input file is shown below

SOLUTION 1
    temp      50
    pH        7 charge
    redox     Fe(2)/Fe(3)
    units     mol/kgw
    Cl        4.53
    Fe(2)     0.75
    Fe(3)     1e-05
    K         3
    -water    0.0637 # kg

SOLUTION 2
    temp      50
    pH        7 charge
    redox     Fe(2)/Fe(3)
    units     mol/kgw
    Cl        4.53
    Fe(2)     0.75
    Fe(3)     1e-05
    K         3
    -water    0.004432 # kg
MIX 1
    1    1
    2    1
SELECTED_OUTPUT 1
    -file                 selected_output_1.sel
    -high_precision       true
    -active               true
    -user_punch           true

USER_PUNCH 1
    -headings
    -start
10 PUNCH RHO
    -end

This results in the following

Solution 1 Density: 1.171882065764e+00
Solution 2 Density: 1.171882065764e+00
Mixed Density:       1.171879901476e+00

Solution 1 pH: 1.678781383752e+00
Solution 2 pH: 1.678781383752e+00
Mixed pH:       1.678781383889e+00

I can see where the pH is perhaps numerical error, but the density is quite different.  Any suggestions?

Craig

dlparkhurst:
Curious. I simplified the problem to remove the Fe redox, mimicing Fe(2) with Ca and adding a CaCl+ ion pair equal to the FeCl+ pair (eliminating K as well). I also removed the mixing of two solutions, and simply allowed one of the solutions to mix with a mixing factor of 1.0. The same discrepancy between the calculations remained. My hypothesis is that there are actually two solutions to the problem with different concentrations of CaCl+. The difference causes a difference in ionic strength and consequently a difference in the activity coefficients of the species. The two different sets of activity coefficients and concentrations satisfy the mass action expression for CaCl+ and the mole balance equations.

Considering the Ca-Cl system, the MIX calculation has a different set of equations from the initial solution calculation. The initial solution has charge balance, Ca mole balance, Cl mole balance, and ionic strength equation. Whereas the MIX calculation also has mole balance equations for O and H. However, the mass of H2O (associated with O mole balance) is calculated to be the same in both calculations and the pe (associated with H mole balance) does not make any significant differences.

I ran the Ca-Cl simulation and did not see a discrepancy with pitzer.dat, which has a very different activity coefficient formulation. I got very similar results for initial solution and MIX. The density differed more than I would have expected, but was equal to several more decimal places than the phreeqc.dat simulation.

There are cases where there are multple solutions to the nonlinear equations. I have not seen it before for this activity coefficient/mass-action combination, so I am not positive my hypothesis is right. For now, the differences seem smaller than any experimental resolution. I'll look more closely if there are other cases where the discrepancies are larger.

cevans3098:
David,

Yes, I noticed the mass balance of the solutions was satisfied, so I agree there must be multiple feasible solutions.  Creates a problem for me though because I use the solution volume for other calculations in my model and these differences can add up making for a large error.

I'll look at it further and see if I can find a work around.  If you have any suggestions in the meantime, please let me know.

Thanks again,

Craig

dlparkhurst:
I think you probably have more issues. The ionic strength is near 5, which is well outside the range of reliability for the ion-association model, except perhaps in NaCl solutions. Most of the activity coefficients are Davies, and I am guessing that it is the mix of Davies and Wateq Bdot activity coefficients that causes the multiple feasible solutions. I noticed that if I defined FeCl+ to have the Cl- activity coefficient definition, then, at least the FeCl+ results were more consistent.

Density still varies between the initial and MIX calculation, so I will try to take a look at how it is calculated. It may need to be checked for convergence. There are no volume definitions for the Fe-Cl and Fe-OH species, so the density is really uncertain for these Fe systems anyway.

cevans3098:

Agreed, my solution is relatively concentrated.  I was hoping the Davies equations/ Debye-Huckel theory models would be able to deal with it.  From my early testing PHREEQC was relatively accurate with pH and eH predictions, so I made the assumption the speciation was ok.  There are few models/programs available that can handle my ionic strength. 

I might do some of the preprocessing of the mix in my own code and just send the resulting solution into PHREEQ

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