Processes > Inverse modelling

Combination of INVERSE_MODELING and MIX

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ViktoriaRfq:
Hello everyone,

I'm working on a quite simple problem but cannot get to model it correctly in PHREEQC.

I want to find out the composition of a water x that turns the defined solution 1 into solution 2. So to say 1 + x = 2.
I also know, that solution 1 accounts to around 40% of solution 2. So to say 0.4 Sol 1 + 0.6 Sol x = Sol 2.

I'm not getting the input right. Here's what I wrote:

TITLE   composition of the seeped water between Gesenk 2. Sohle and Mundloch  TSS
#wateq4f.dat

units mmol/L

Number   temp   pH   pe   Al   Ca   Fe   K   Mg   Na   S(-2)   C(4)   S(6)   As   description

1   10.8   6.94   7.6   0.008895478   1.848802395   0.006803939   0.104859335   0.662278898   0.701609395   7.79788E-05   1.606994172   1.509479531   0.003336893   #ED-U-3_Ge2_unf_Nov22
2   11.1   6.83   8.8   0.002965159   0.696107784   0.003043868   0.062148338   0.246400658   0.678990866   7.79788E-05   0.782681099   0.499689776   0.004271223   #ED-O-5-STO-TSS_unf_Nov22

INVERSE_MODELING   1
-solutions   1   2
-uncertainty
-balances
Al
Ca
Fe
K
Mg
Na
C(4)
S(6)
As

-phases
Fe(OH)3(a)
Scorodite
Magnesite
Calcite
Dolomite
Gypsum
Al(OH)3(a)
Gibbsite
Siderite
Jarosite(ss)
Jarosite-K
-range

SAVE   solution    3
END

TITLE   adjustment of the ratio 40:60
MIX   1
1   0.4
3   0.6
SAVE   solution   4

SELECTED_OUTPUT
-file IM und MIX.xls
-reset false
-percent_error
-solution   4
-pH
-pe
-molalities   CO2   HCO3-
-totals   As   As(5)   As(3)   Fe   Fe(3)   Fe(2)   Al   Ca   Mg   Na   K   C(+4)   Cl   S(+6)
-saturation_indices   Fe(OH)3(a)             Scorodite   Magnesite   Calcite   Dolomite   Gypsum   Al(OH)3(a)   Gibbsite   Siderite   Jarosite(ss)   Jarosite-K
END

dlparkhurst:
First, the charge balances on your solutions are not great 10 to 17 percent error, so you are starting out with a lot of uncertainty.

Second, unless you have more constraints, there is no way to sort out unknown solution composition from mineral reaction.

Here is a calculation that uses solution 1, the unknown solution 2, to make solution 3, with mixing fractions approximately 0.4 and 0.6. Br was added to produce the mixing fractions. Solution 2 was given the composition of solution 3, but was given 100% uncertainties. Thus, concentrations could range anywhere from twice solution 3 to zero. Inverse modeling will then pick concentrations for solution 2 that allow for mixing of solution 1 with solution 2, while producing charge balance in solution 2.

I am not sure if this calculation is helpful, but maybe it gives you some ideas on how to proceed. There are too many degrees of freedom to make any definitive statements.

-units    mmol/l
Number temp    pH   pe           Al           Ca           Fe            K           Mg           Na     S(-2)         C(4)         S(6)           As   Br
1 10.8 6.94 7.6 0.008895478 1.848802395 0.006803939 0.104859335 0.662278898 0.701609395 7.80E-05 1.606994172 1.509479531 0.003336893    0
2 11.1 6.83 8.8 0.002965159 0.696107784 0.003043868 0.062148338 0.246400658 0.678990866 7.80E-05 0.782681099 0.499689776 0.004271223 1.0
3 11.1 6.83 8.8 0.002965159 0.696107784 0.003043868 0.062148338 0.246400658 0.678990866 7.80E-05 0.782681099 0.499689776 0.004271223 0.6
END

INVERSE_MODELING   1
-solutions   1   2   3
-uncertainty  0.2 1.0 0.2
-balances
Al
Ca
Fe
K
Mg
Na
C
S
As
Br 0.05 0.05 0.05
pH 0.05 1 0.05

-phases
Fe(OH)3(a)
Scorodite
Magnesite
Calcite
Dolomite
Gypsum
Al(OH)3(a)
Gibbsite
Siderite
Jarosite(ss)
Jarosite-K
-minimal
END

--- End code ---

ViktoriaRfq:
Thank you for that brilliant idea.

Later on yesterday, I managed to model on my own (without the mixing) after adjusting the uncertainty to 0.2 for solution 1 and 0.3 for solution 2 (due to the high CBE... these are mine waters so higher CBEs are not unusual). PHREEQC offered 160 possible scenarios :-D

Greetings from Freiberg.

--- Quote from: dlparkhurst on June 07, 2023, 07:24:29 PM ---First, the charge balances on your solutions are not great 10 to 17 percent error, so you are starting out with a lot of uncertainty.

Second, unless you have more constraints, there is no way to sort out unknown solution composition from mineral reaction.

Here is a calculation that uses solution 1, the unknown solution 2, to make solution 3, with mixing fractions approximately 0.4 and 0.6. Br was added to produce the mixing fractions. Solution 2 was given the composition of solution 3, but was given 100% uncertainties. Thus, concentrations could range anywhere from twice solution 3 to zero. Inverse modeling will then pick concentrations for solution 2 that allow for mixing of solution 1 with solution 2, while producing charge balance in solution 2.

I am not sure if this calculation is helpful, but maybe it gives you some ideas on how to proceed. There are too many degrees of freedom to make any definitive statements.

-units    mmol/l
Number temp    pH   pe           Al           Ca           Fe            K           Mg           Na     S(-2)         C(4)         S(6)           As   Br
1 10.8 6.94 7.6 0.008895478 1.848802395 0.006803939 0.104859335 0.662278898 0.701609395 7.80E-05 1.606994172 1.509479531 0.003336893    0
2 11.1 6.83 8.8 0.002965159 0.696107784 0.003043868 0.062148338 0.246400658 0.678990866 7.80E-05 0.782681099 0.499689776 0.004271223 1.0
3 11.1 6.83 8.8 0.002965159 0.696107784 0.003043868 0.062148338 0.246400658 0.678990866 7.80E-05 0.782681099 0.499689776 0.004271223 0.6
END

INVERSE_MODELING   1
-solutions   1   2   3
-uncertainty  0.2 1.0 0.2
-balances
Al
Ca
Fe
K
Mg
Na
C
S
As
Br 0.05 0.05 0.05
pH 0.05 1 0.05

-phases
Fe(OH)3(a)
Scorodite
Magnesite
Calcite
Dolomite
Gypsum
Al(OH)3(a)
Gibbsite
Siderite
Jarosite(ss)
Jarosite-K
-minimal
END

--- End code ---

--- End quote ---

ViktoriaRfq:
Dear David,
is there some other way to include the mixing fractions? If I use the Br, PHREEQC does not output any simulation. If I remove it, I get 66 simulations. Among these, the most "suitable" are simulations suggesting 15% of solution 1 or 18% of solution 2 - so not really close to the 40%.

My updated code:

--- Code: ---TITLE composition of the seeped water between Gesenk 2. Sohle and Mundloch TSS
#wateq4f.dat

#KNOBS
#solution 1, unknown solution 2 and solution 3 with mixing fractions app. 0.4 and 0.6 (Br added to produce the fractions). Solution 2 given the composition od solution 3 but with 1.0 uncertainty (concentrations could range anywhere from twice solution 3 to zero. inverse modeling will pick the concentration for solution 2 that allow for mixing of solution 1 with solution 2 while producing charge balance in solution 2.
#-uncertainity default (0.05) wenn charge balance error um die 10%, uncertainty 0.1 wählen
# the "minimal" indicator gives fewer mnodels at the cost of greater "sums of residuals" … sums of residuals - how much the data has been fudged; residual 1.0 means that one analytical datum has been changed by ist maximum uncertainty
#alle Werte von AG BBW gemessen
#<LOD-Werte =0.5 LOD gesetzt
#TIC als C(4)
#S(6) aus Photometrie
#Fluorwerte mit Fit-Funktion berechnet
#Cu, Ni, S(-2) aus dem Input gelöscht

units mmol/L
Number temp pH pe Al Ba Ca Fe K Li Mg Mn Na Si Sr Zn Cl C(4) S(6) N(5) As F

1 10.80 6.94 7.60 0.00889548 0.00014565 1.85 0.00680394 0.10485934 0.01008646 0.6622789 0.0076447 0.7016094 0.22961908 0.00182607 0.00290609 0.79541929 1.61 1.51 0.01784822 0.00333689 0.48952521
2 11.10 6.83 8.80 0.00296516 0.00021847 0.69610778 0.00304387 0.06214834 0.00288184 0.24640066 0.00091008 0.67899087 0.17230331 0.00102716 0.00038238 0.75028912 0.7826811 0.49968978 0.17348469 0.00427122 0.10527424
3 11.10 6.83 8.80 0.00296516 0.00021847 0.69610778 0.00304387 0.06214834 0.00288184 0.24640066 0.00091008 0.67899087 0.17230331 0.00102716 0.00038238 0.75028912 0.7826811 0.49968978 0.17348469 0.00427122 0.10527424

INVERSE_MODELING 1
-solutions 1 2 3
-uncertainty 0.2 1 0.2
-balances Al
Ba
Ca
Fe
K
Li
Mg
Mn
Na
Si
Sr
Zn
Cl
C(4)
S(6)
N(5)
As
F
Br 0.05 0.05 0.05
pH 0.05 1 0.05

-phases
Fe(OH)3(a)
Scorodite
Magnesite
Calcite
Dolomite
Gypsum
Al(OH)3(a)
Gibbsite
Siderite
Jarosite(ss)
Jarosite-K
CaX2
MgX2
NaX

SELECTED_OUTPUT
-file zusitzendes wasser inverse modeling.xls
-inverse_modeling true

END

--- End code ---

dlparkhurst:
You can change the Br concentration in solution 3, or increase the Be uncertainty. But it sounds like you already know what you want.