Processes > Inverse modelling
How to solve "inequality not satisfied for Mg eps+"
(1/1)
Doyoung:
Hello.
I want to know how groundwater flowing along the fracture zone is formed through water-rock interactions. I wanted to determine which mineral phase was the main influence on the chemical composition of the groundwater through inverse modeling in phreeqc, so I entered the following
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SOLUTION 1
temp 15
pH 7
units mmol/kgw
density 1
Na 0.613
K 0.007
Ca 0.402
Mg 0.011
Si 0.293
Cl 0.071
S(6) 0.086
N(5) 0.002
F 0.188
Alkalinity 1.16
-water 1 # kg
SOLUTION 2
temp 15
pH 7
units mmol/kgw
density 1
Na 0.487
K 0.007
Ca 0.459
Mg 0.016
Si 0.353
Cl 0.094
S(6) 0.085
N(5) 0.098
F 0.134
Alkalinity 0.96
-water 1 # kg
INVERSE_MODELING 1
-solutions 1 2
-uncertainty 0.05 0.05
-phases
CO2(g)
Calcite
Gypsum
Albite
Anorthite
Kaolinite
Illite pre
CaX2
NaX
Montmorillonite-Ca pre
-balances
Cl 0.05 0.05
F 0.05 0.05
N(5) 0.05 0.05
-tolerance 1e-010
-mineral_water true
END
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The result is shown below
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Database file: C:\Program Files (x86)\USGS\Phreeqc Interactive 3.7.3-15968\database\wateq4f.dat
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Reading data base.
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SOLUTION_MASTER_SPECIES
SOLUTION_SPECIES
PHASES
EXCHANGE_MASTER_SPECIES
EXCHANGE_SPECIES
SURFACE_MASTER_SPECIES
SURFACE_SPECIES
RATES
END
------------------------------------
Reading input data for simulation 1.
------------------------------------
DATABASE C:\Program Files (x86)\USGS\Phreeqc Interactive 3.7.3-15968\database\wateq4f.dat
SOLUTION 1
temp 15
pH 7
units mmol/kgw
density 1
Na 0.613
K 0.007
Ca 0.402
Mg 0.011
Si 0.293
Cl 0.071
S(6) 0.086
N(5) 0.002
F 0.188
Alkalinity 1.16
water 1 # kg
SOLUTION 2
temp 15
pH 7
units mmol/kgw
density 1
Na 0.487
K 0.007
Ca 0.459
Mg 0.016
Si 0.353
Cl 0.094
S(6) 0.085
N(5) 0.098
F 0.134
Alkalinity 0.96
water 1 # kg
INVERSE_MODELING 1
solutions 1 2
uncertainty 0.05 0.05
phases
CO2(g)
Calcite
Gypsum
Albite
Anorthite
Kaolinite
Illite pre
CaX2
NaX
Montmorillonite-Ca pre
balances
Cl 0.05 0.05
F 0.05 0.05
N(5) 0.05 0.05
tolerance 1e-010
mineral_water true
END
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Beginning of initial solution calculations.
-------------------------------------------
Initial solution 1.
-----------------------------Solution composition------------------------------
Elements Molality Moles
Alkalinity 1.160e-03 1.160e-03
Ca 4.020e-04 4.020e-04
Cl 7.100e-05 7.100e-05
F 1.880e-04 1.880e-04
K 7.000e-06 7.000e-06
Mg 1.100e-05 1.100e-05
N(5) 2.000e-06 2.000e-06
Na 6.130e-04 6.130e-04
S(6) 8.600e-05 8.600e-05
Si 2.930e-04 2.930e-04
----------------------------Description of solution----------------------------
pH = 7.000
pe = 4.000
Activity of water = 1.000
Ionic strength (mol/kgw) = 1.992e-03
Mass of water (kg) = 1.000e+00
Total carbon (mol/kg) = 1.448e-03
Total CO2 (mol/kg) = 1.448e-03
Temperature (캜) = 15.00
Electrical balance (eq) = -1.470e-04
Percent error, 100*(Cat-|An|)/(Cat+|An|) = -4.88
Iterations = 6
Total H = 1.110148e+02
Total O = 5.551179e+01
----------------------------Distribution of species----------------------------
Log Log Log mole V
Species Molality Activity Molality Activity Gamma cm?mol
H+ 1.047e-07 1.000e-07 -6.980 -7.000 -0.020 0.00
OH- 4.734e-08 4.507e-08 -7.325 -7.346 -0.021 (0)
H2O 5.551e+01 9.999e-01 1.744 -0.000 0.000 18.03
C(4) 1.448e-03
HCO3- 1.154e-03 1.100e-03 -2.938 -2.959 -0.021 (0)
CO2 2.884e-04 2.886e-04 -3.540 -3.540 0.000 (0)
CaHCO3+ 3.955e-06 3.772e-06 -5.403 -5.423 -0.021 (0)
CO3-2 4.966e-07 4.102e-07 -6.304 -6.387 -0.083 (0)
NaHCO3 3.608e-07 3.609e-07 -6.443 -6.443 0.000 (0)
CaCO3 1.900e-07 1.901e-07 -6.721 -6.721 0.000 (0)
MgHCO3+ 1.154e-07 1.100e-07 -6.938 -6.959 -0.021 (0)
MgCO3 2.965e-09 2.966e-09 -8.528 -8.528 0.000 (0)
NaCO3- 2.774e-09 2.645e-09 -8.557 -8.578 -0.021 (0)
Ca 4.020e-04
Ca+2 3.935e-04 3.249e-04 -3.405 -3.488 -0.083 (0)
CaSO4 3.966e-06 3.968e-06 -5.402 -5.401 0.000 (0)
CaHCO3+ 3.955e-06 3.772e-06 -5.403 -5.423 -0.021 (0)
CaF+ 4.161e-07 3.967e-07 -6.381 -6.402 -0.021 (0)
CaCO3 1.900e-07 1.901e-07 -6.721 -6.721 0.000 (0)
CaOH+ 5.654e-10 5.392e-10 -9.248 -9.268 -0.021 (0)
CaHSO4+ 2.182e-12 2.078e-12 -11.661 -11.682 -0.021 (0)
Cl 7.100e-05
Cl- 7.100e-05 6.761e-05 -4.149 -4.170 -0.021 (0)
F 1.880e-04
F- 1.874e-04 1.784e-04 -3.727 -3.749 -0.021 (0)
CaF+ 4.161e-07 3.967e-07 -6.381 -6.402 -0.021 (0)
MgF+ 9.064e-08 8.636e-08 -7.043 -7.064 -0.021 (0)
NaF 5.988e-08 5.991e-08 -7.223 -7.222 0.000 (0)
HF 2.243e-08 2.244e-08 -7.649 -7.649 0.000 (0)
HF2- 1.474e-11 1.404e-11 -10.831 -10.853 -0.021 (0)
H2F2 1.865e-15 1.866e-15 -14.729 -14.729 0.000 (0)
SiF6-2 4.495e-24 3.709e-24 -23.347 -23.431 -0.083 (0)
H(0) 1.569e-25
H2 7.844e-26 7.848e-26 -25.105 -25.105 0.000 (0)
K 7.000e-06
K+ 6.997e-06 6.663e-06 -5.155 -5.176 -0.021 (0)
KSO4- 2.764e-09 2.635e-09 -8.558 -8.579 -0.021 (0)
Mg 1.100e-05
Mg+2 1.068e-05 8.835e-06 -4.971 -5.054 -0.083 (0)
MgHCO3+ 1.154e-07 1.100e-07 -6.938 -6.959 -0.021 (0)
MgSO4 1.069e-07 1.070e-07 -6.971 -6.971 0.000 (0)
MgF+ 9.064e-08 8.636e-08 -7.043 -7.064 -0.021 (0)
MgCO3 2.965e-09 2.966e-09 -8.528 -8.528 0.000 (0)
MgOH+ 1.321e-10 1.260e-10 -9.879 -9.900 -0.020 (0)
N(5) 2.000e-06
NO3- 2.000e-06 1.904e-06 -5.699 -5.720 -0.021 (0)
Na 6.130e-04
Na+ 6.124e-04 5.835e-04 -3.213 -3.234 -0.021 (0)
NaHCO3 3.608e-07 3.609e-07 -6.443 -6.443 0.000 (0)
NaSO4- 1.937e-07 1.846e-07 -6.713 -6.734 -0.021 (0)
NaF 5.988e-08 5.991e-08 -7.223 -7.222 0.000 (0)
NaCO3- 2.774e-09 2.645e-09 -8.557 -8.578 -0.021 (0)
O(0) 0.000e+00
O2 0.000e+00 0.000e+00 -45.509 -45.509 0.000 (0)
S(6) 8.600e-05
SO4-2 8.173e-05 6.742e-05 -4.088 -4.171 -0.084 (0)
CaSO4 3.966e-06 3.968e-06 -5.402 -5.401 0.000 (0)
NaSO4- 1.937e-07 1.846e-07 -6.713 -6.734 -0.021 (0)
MgSO4 1.069e-07 1.070e-07 -6.971 -6.971 0.000 (0)
KSO4- 2.764e-09 2.635e-09 -8.558 -8.579 -0.021 (0)
HSO4- 5.583e-10 5.319e-10 -9.253 -9.274 -0.021 (0)
CaHSO4+ 2.182e-12 2.078e-12 -11.661 -11.682 -0.021 (0)
Si 2.930e-04
H4SiO4 2.927e-04 2.928e-04 -3.534 -3.533 0.000 (0)
H3SiO4- 3.126e-07 2.978e-07 -6.505 -6.526 -0.021 (0)
H2SiO4-2 1.228e-13 1.015e-13 -12.911 -12.994 -0.083 (0)
SiF6-2 4.495e-24 3.709e-24 -23.347 -23.431 -0.083 (0)
------------------------------Saturation indices-------------------------------
Phase SI** log IAP log K(288 K, 1 atm)
Anhydrite -3.32 -7.66 -4.34 CaSO4
Aragonite -1.60 -9.88 -8.28 CaCO3
Artinite -12.83 -2.49 10.33 MgCO3:Mg(OH)2:3H2O
Brucite -8.58 8.95 17.53 Mg(OH)2
Calcite -1.45 -9.88 -8.43 CaCO3
Chalcedony 0.14 -3.53 -3.67 SiO2
Chrysotile -13.71 19.77 33.48 Mg3Si2O5(OH)4
Clinoenstatite -6.44 5.41 11.85 MgSiO3
CO2(g) -2.20 -3.54 -1.34 CO2
Cristobalite 0.19 -3.53 -3.73 SiO2
Diopside -8.33 12.39 20.72 CaMgSi2O6
Dolomite -4.47 -21.32 -16.85 CaMg(CO3)2
Dolomite(d) -5.06 -21.32 -16.26 CaMg(CO3)2
Epsomite -7.01 -9.23 -2.21 MgSO4:7H2O
Fluorite -0.26 -10.99 -10.73 CaF2
Forsterite -15.18 14.36 29.54 Mg2SiO4
Gypsum -3.07 -7.66 -4.58 CaSO4:2H2O
H2(g) -22.00 -25.11 -3.11 H2
H2O(g) -1.78 -0.00 1.78 H2O
Halite -8.96 -7.40 1.56 NaCl
Huntite -14.88 -44.20 -29.31 CaMg3(CO3)4
Hydromagnesite -29.38 -36.82 -7.43 Mg5(CO3)4(OH)2:4H2O
Magadiite -6.67 -20.97 -14.30 NaSi7O13(OH)3:3H2O
Magnesite -3.57 -11.44 -7.87 MgCO3
Mirabilite -9.04 -10.64 -1.60 Na2SO4:10H2O
Nahcolite -5.55 -6.19 -0.64 NaHCO3
Natron -11.14 -12.86 -1.71 Na2CO3:10H2O
Nesquehonite -5.97 -11.44 -5.47 MgCO3:3H2O
O2(g) -42.70 -45.51 -2.81 O2
Portlandite -13.08 10.51 23.59 Ca(OH)2
Quartz 0.60 -3.53 -4.13 SiO2
Sepiolite -8.74 7.29 16.03 Mg2Si3O7.5OH:3H2O
Sepiolite(d) -11.37 7.29 18.66 Mg2Si3O7.5OH:3H2O
Silicagel -0.40 -3.53 -3.13 SiO2
SiO2(a) -0.74 -3.53 -2.80 SiO2
Talc -9.87 12.71 22.58 Mg3Si4O10(OH)2
Thenardite -10.47 -10.64 -0.16 Na2SO4
Thermonatrite -13.05 -12.85 0.20 Na2CO3:H2O
Tremolite -21.55 37.49 59.04 Ca2Mg5Si8O22(OH)2
Trona -18.71 -19.05 -0.34 NaHCO3:Na2CO3:2H2O
**For a gas, SI = log10(fugacity). Fugacity = pressure * phi / 1 atm.
For ideal gases, phi = 1.
Initial solution 2.
-----------------------------Solution composition------------------------------
Elements Molality Moles
Alkalinity 9.600e-04 9.600e-04
Ca 4.590e-04 4.590e-04
Cl 9.400e-05 9.400e-05
F 1.340e-04 1.340e-04
K 7.000e-06 7.000e-06
Mg 1.600e-05 1.600e-05
N(5) 9.800e-05 9.800e-05
Na 4.870e-04 4.870e-04
S(6) 8.500e-05 8.500e-05
Si 3.530e-04 3.530e-04
----------------------------Description of solution----------------------------
pH = 7.000
pe = 4.000
Activity of water = 1.000
Ionic strength (mol/kgw) = 1.982e-03
Mass of water (kg) = 1.000e+00
Total carbon (mol/kg) = 1.198e-03
Total CO2 (mol/kg) = 1.198e-03
Temperature (캜) = 15.00
Electrical balance (eq) = -1.200e-05
Percent error, 100*(Cat-|An|)/(Cat+|An|) = -0.42
Iterations = 6 (12 overall)
Total H = 1.110148e+02
Total O = 5.551162e+01
----------------------------Distribution of species----------------------------
Log Log Log mole V
Species Molality Activity Molality Activity Gamma cm?mol
H+ 1.047e-07 1.000e-07 -6.980 -7.000 -0.020 0.00
OH- 4.733e-08 4.507e-08 -7.325 -7.346 -0.021 (0)
H2O 5.551e+01 1.000e+00 1.744 -0.000 0.000 18.03
C(4) 1.198e-03
HCO3- 9.544e-04 9.099e-04 -3.020 -3.041 -0.021 (0)
CO2 2.386e-04 2.387e-04 -3.622 -3.622 0.000 (0)
CaHCO3+ 3.745e-06 3.572e-06 -5.427 -5.447 -0.021 (0)
CO3-2 4.106e-07 3.393e-07 -6.387 -6.469 -0.083 (0)
NaHCO3 2.371e-07 2.372e-07 -6.625 -6.625 0.000 (0)
CaCO3 1.799e-07 1.800e-07 -6.745 -6.745 0.000 (0)
MgHCO3+ 1.396e-07 1.329e-07 -6.855 -6.876 -0.021 (0)
MgCO3 3.584e-09 3.586e-09 -8.446 -8.445 0.000 (0)
NaCO3- 1.823e-09 1.738e-09 -8.739 -8.760 -0.021 (0)
Ca 4.590e-04
Ca+2 4.503e-04 3.720e-04 -3.347 -3.429 -0.083 (0)
CaSO4 4.460e-06 4.462e-06 -5.351 -5.350 0.000 (0)
CaHCO3+ 3.745e-06 3.572e-06 -5.427 -5.447 -0.021 (0)
CaF+ 3.394e-07 3.236e-07 -6.469 -6.490 -0.021 (0)
CaCO3 1.799e-07 1.800e-07 -6.745 -6.745 0.000 (0)
CaOH+ 6.472e-10 6.173e-10 -9.189 -9.210 -0.021 (0)
CaHSO4+ 2.453e-12 2.336e-12 -11.610 -11.631 -0.021 (0)
Cl 9.400e-05
Cl- 9.400e-05 8.952e-05 -4.027 -4.048 -0.021 (0)
F 1.340e-04
F- 1.335e-04 1.271e-04 -3.874 -3.896 -0.021 (0)
CaF+ 3.394e-07 3.236e-07 -6.469 -6.490 -0.021 (0)
MgF+ 9.438e-08 8.993e-08 -7.025 -7.046 -0.021 (0)
NaF 3.391e-08 3.392e-08 -7.470 -7.470 0.000 (0)
HF 1.598e-08 1.599e-08 -7.796 -7.796 0.000 (0)
HF2- 7.483e-12 7.126e-12 -11.126 -11.147 -0.021 (0)
H2F2 9.470e-16 9.475e-16 -15.024 -15.023 0.000 (0)
SiF6-2 7.082e-25 5.846e-25 -24.150 -24.233 -0.083 (0)
H(0) 1.569e-25
H2 7.844e-26 7.848e-26 -25.105 -25.105 0.000 (0)
K 7.000e-06
K+ 6.997e-06 6.664e-06 -5.155 -5.176 -0.021 (0)
KSO4- 2.715e-09 2.588e-09 -8.566 -8.587 -0.021 (0)
Mg 1.600e-05
Mg+2 1.561e-05 1.291e-05 -4.807 -4.889 -0.082 (0)
MgSO4 1.535e-07 1.536e-07 -6.814 -6.814 0.000 (0)
MgHCO3+ 1.396e-07 1.329e-07 -6.855 -6.876 -0.021 (0)
MgF+ 9.438e-08 8.993e-08 -7.025 -7.046 -0.021 (0)
MgCO3 3.584e-09 3.586e-09 -8.446 -8.445 0.000 (0)
MgOH+ 1.930e-10 1.842e-10 -9.714 -9.735 -0.020 (0)
N(5) 9.800e-05
NO3- 9.800e-05 9.329e-05 -4.009 -4.030 -0.021 (0)
Na 4.870e-04
Na+ 4.866e-04 4.637e-04 -3.313 -3.334 -0.021 (0)
NaHCO3 2.371e-07 2.372e-07 -6.625 -6.625 0.000 (0)
NaSO4- 1.511e-07 1.441e-07 -6.821 -6.841 -0.021 (0)
NaF 3.391e-08 3.392e-08 -7.470 -7.470 0.000 (0)
NaCO3- 1.823e-09 1.738e-09 -8.739 -8.760 -0.021 (0)
O(0) 0.000e+00
O2 0.000e+00 0.000e+00 -45.509 -45.509 0.000 (0)
S(6) 8.500e-05
SO4-2 8.023e-05 6.622e-05 -4.096 -4.179 -0.083 (0)
CaSO4 4.460e-06 4.462e-06 -5.351 -5.350 0.000 (0)
MgSO4 1.535e-07 1.536e-07 -6.814 -6.814 0.000 (0)
NaSO4- 1.511e-07 1.441e-07 -6.821 -6.841 -0.021 (0)
KSO4- 2.715e-09 2.588e-09 -8.566 -8.587 -0.021 (0)
HSO4- 5.483e-10 5.224e-10 -9.261 -9.282 -0.021 (0)
CaHSO4+ 2.453e-12 2.336e-12 -11.610 -11.631 -0.021 (0)
Si 3.530e-04
H4SiO4 3.526e-04 3.528e-04 -3.453 -3.452 0.000 (0)
H3SiO4- 3.766e-07 3.587e-07 -6.424 -6.445 -0.021 (0)
H2SiO4-2 1.479e-13 1.222e-13 -12.830 -12.913 -0.083 (0)
SiF6-2 7.082e-25 5.846e-25 -24.150 -24.233 -0.083 (0)
------------------------------Saturation indices-------------------------------
Phase SI** log IAP log K(288 K, 1 atm)
Anhydrite -3.27 -7.61 -4.34 CaSO4
Aragonite -1.62 -9.90 -8.28 CaCO3
Artinite -12.58 -2.25 10.33 MgCO3:Mg(OH)2:3H2O
Brucite -8.42 9.11 17.53 Mg(OH)2
Calcite -1.47 -9.90 -8.43 CaCO3
Chalcedony 0.22 -3.45 -3.67 SiO2
Chrysotile -13.05 20.43 33.48 Mg3Si2O5(OH)4
Clinoenstatite -6.19 5.66 11.85 MgSiO3
CO2(g) -2.28 -3.62 -1.34 CO2
Cristobalite 0.27 -3.45 -3.73 SiO2
Diopside -7.94 12.78 20.72 CaMgSi2O6
Dolomite -4.41 -21.26 -16.85 CaMg(CO3)2
Dolomite(d) -5.00 -21.26 -16.26 CaMg(CO3)2
Epsomite -6.86 -9.07 -2.21 MgSO4:7H2O
Fluorite -0.50 -11.22 -10.73 CaF2
Forsterite -14.77 14.77 29.54 Mg2SiO4
Gypsum -3.02 -7.61 -4.58 CaSO4:2H2O
H2(g) -22.00 -25.11 -3.11 H2
H2O(g) -1.78 -0.00 1.78 H2O
Halite -8.94 -7.38 1.56 NaCl
Huntite -14.66 -43.97 -29.31 CaMg3(CO3)4
Hydromagnesite -28.89 -36.32 -7.43 Mg5(CO3)4(OH)2:4H2O
Magadiite -6.20 -20.50 -14.30 NaSi7O13(OH)3:3H2O
Magnesite -3.49 -11.36 -7.87 MgCO3
Mirabilite -9.25 -10.85 -1.60 Na2SO4:10H2O
Nahcolite -5.73 -6.37 -0.64 NaHCO3
Natron -11.43 -13.14 -1.71 Na2CO3:10H2O
Nesquehonite -5.88 -11.36 -5.47 MgCO3:3H2O
O2(g) -42.70 -45.51 -2.81 O2
Portlandite -13.02 10.57 23.59 Ca(OH)2
Quartz 0.68 -3.45 -4.13 SiO2
Sepiolite -8.17 7.86 16.03 Mg2Si3O7.5OH:3H2O
Sepiolite(d) -10.80 7.86 18.66 Mg2Si3O7.5OH:3H2O
Silicagel -0.32 -3.45 -3.13 SiO2
SiO2(a) -0.66 -3.45 -2.80 SiO2
Talc -9.05 13.52 22.58 Mg3Si4O10(OH)2
Thenardite -10.68 -10.85 -0.16 Na2SO4
Thermonatrite -13.33 -13.14 0.20 Na2CO3:H2O
Tremolite -19.96 39.08 59.04 Ca2Mg5Si8O22(OH)2
Trona -19.17 -19.51 -0.34 NaHCO3:Na2CO3:2H2O
**For a gas, SI = log10(fugacity). Fugacity = pressure * phi / 1 atm.
For ideal gases, phi = 1.
---------------------------------------------
Beginning of inverse modeling 1 calculations.
---------------------------------------------
Using Cl1 standard precision optimization routine.
Post_mortem examination of inverse modeling:
ERROR: inequality not satisfied for N(5) eps+, 9.144563e-05
ERROR: inequality not satisfied for S(6) eps-, 4.664847e-05
ERROR: inequality not satisfied for Cl eps-, 3.056996e-05
ERROR: inequality not satisfied for K eps-, 8.597144e-07
ERROR: inequality not satisfied for Mg eps-, 6.100980e-06
Summary of inverse modeling:
Number of models found: 0
Number of minimal models found: 0
Number of infeasible sets of phases saved: 1
Number of calls to cl1: 3
------------------
End of simulation.
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Reading input data for simulation 2.
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End of Run after 0.214 Seconds.
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I don't know why I keep getting an error that says "ERROR: inequality not satisfied for".
I'm new to phreeqc, so there's a lot I don't know yet.
Any help would be greatly appreciated.
dlparkhurst:
Please use the # button (above the text entry box) to insert code and output. It makes your post much more readable.
The point of inverse modeling is to make you consider the sources and sinks for each major constituent in your waters. Generally, skip the trace elements, which can sorb or be minor, uncertain constituents of the major reactants.
So think about your two waters. First they are not that different; so, the question is whether they represent a significant trend in water composition. I'd like to see multiple analyses that show similar changes in composition before putting too much stock in inverse modeling.
Assuming this is a trend, then you must consider a source and (or) sink for each major element in solution. With your waters, I ask what is the source for the increase in nitrate, decrease in fluoride, and increase in chloride? Again the question is whether these are significant trends or simply spatial or temporal variability. With nitrate, is it oxidation of reduced nitrogen in organic matter, addition of fertilizer, or mixing with a nitrate-rich water? An increase in chloride could be evaporation, or random variability, for which you could add halite as a way to account for the change. There are not many ways to account for a decrease in fluoride, so is the change real?
Your other minerals may account for the remaining major elements in water and rock--Ca, Mg, Na, K, C, S(6), Si, and Al.
Finally, if you continue inverse modeling, I would set -minimal if you start getting tens or hundreds of models.
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