Inverse modeling using Cl and 18O only

[MichaelZ20]

Hello!
I have several (2-3) water bodies that mix without evaporation and give the final water. For every one I have only Cl and 18O data. I have calculated mixing fractions manually. Is it possible to perform inverse modeling for detection of possible ranges of change of mixing fractions basing on data of the supposed uncertainties in Cl and 18O? I tried to balance Cl by Na, but this gives their molar ratio of 1, and actually it is close to 0.7 in the studied area. In addition, if I don't set H2O as a phase, I have a problem with H(O). The program proposes to change initial data of Cl and 18O, and as a result I have received one nil mixing fraction instead of the not-nil obtained by manual calculation.
I"ll very appreciate the colleagues' help.
Sincerely,
Michael

[dlparkhurst]

It may not be worth the trouble to do this with Phreeqc. The manual calculations are probably sufficient.

You can't really complain about the Na:Cl ratio if you only have data for Cl and 18O. I think you had the right idea, just balance with Na and do the calculations. Because both Cl and 18O are conservative, one set of mixing fractions will have to account for both conservative species. PHREEQC will possibly adjust the concentrations of Cl and (or) 18O in the endmembers, but it will be within the tolerances that you specify. If the mixing fraction is nil and the tolerances are reasonable, then you have to consider the possibility that the water is not involved. I suspect there will be other models where the mixing fraction is not nil.

PHREEQC will include several mole-balance equations, including alkalinity. You can specify uncertainties of 1.0 for everything but Cl and 18O.

[MichaelZ20]

Dear David,
Thank you for your fast help!
Sincerely,
Michael

[MichaelZ20]

I received the solution when disabled the "-minimal" option. It was irrelevant in my case.
I paid attention that in several received models the "main" mixing fraction lays out of the range of minimum and maximum. Why may this take place?

Solution fractions:                   Minimum        Maximum
   Solution   1      8.487e-02      3.566e-02      2.903e-01
   Solution   2      8.458e-01      9.662e-01      1.041e+00
   Solution   3      6.930e-02     -3.314e-01     -1.822e-03
   Solution   4      1.000e+00      1.000e+00      1.000e+00

[dlparkhurst]

Got me. Could you attach the file?

[MichaelZ20]

I attach the input file.

[dlparkhurst]

Sometimes the numerical method has issues. In these cases there is an attempt to catch the problems, and say something about "CL1 errors". The results of this particular input file tends to have these errors, and I suspect that is the reason why the mixing fraction sometimes fell outside the range.

On reconsideration, it may be better not to charge balance with Na because that adds another element which could affect the results. Instead, I defined a new uncharged chloride in the file below. It seems to result in much more robust results, and without the CL1 errors.

It is possible to do the range calculation, while forcing consideration of specified minerals and solutions. If you force all minerals and solutions into the range calculation, you should get the same set of ranges for each model.

A minor point, for isotope calculations, the isotopic composition of the phase may be defined; however, each phase must be specified to either dissolve or precipitate. You can define the same phase twice, once to dissolve and once to precipitate. In your case, H2O(g) is required to precipitate, but no isotopic composition is specified. You could check on the effects of selecting an isotopic composition for the water that enters the solution. If you both add and remove water, I suspect the problem is unconstrained.

SOLUTION_MASTER_SPECIES
    [Cl]          [Cl]             0     35.5            35.5
SOLUTION_SPECIES
[Cl] = [Cl]
    log_k     0
END
TITLE
SOLUTION_SPREAD
    -units    mg/l
 Number    Temp    [Cl]     18O
      1      25    1978    -1.8
      2      25    1976    -4.6
      3      25    3925    -3.7
      4      25    2111    -4.3
INVERSE_MODELING 1
    -solutions      1        2        3        4
    -uncertainty    1        1        1        1
    -phases
        H2O(g)         force  pre   # 18O -2   2
        #H2O(g)         force  dis  18O -2   2
    -balances
        [Cl]        0.05     0.05     0.1      0.05
    -isotopes
        18O         0.15     0.1      0.1      0.1
    -range             1000
    -mineral_water     true
    -force_solutions   true  true true true
END

[MichaelZ20]

Dear David,
Thank you for solving my problem and for your detailed explanation!
Why do you think that it is important to consider mineral water in this case?
Sincerely,
Michael

[dlparkhurst]

I only considered it because you did. It was just a teaching point about the definition of the isotopic composition of the reactive phases.

[MichaelZ20]

Actually, I did not expect any change in water mass in my mix. I was forced to consider H2O(g) in "-phases", because without it I received warnings about H(0). I hoped that some models with nil H2O(g) transfer will be obtained. Will it be correct in my case to set H(0) in "-balances" and to disable "-phases" at all?

[dlparkhurst]

Three models are found if no water phase is included in -phases.

[MichaelZ20]

Thank you very much for your help!