Input file: ../examples/ex17 Output file: ex17.out Database file: ../database/pitzer.dat ------------------ Reading data base. ------------------ SOLUTION_MASTER_SPECIES SOLUTION_SPECIES PHASES PITZER EXCHANGE_MASTER_SPECIES EXCHANGE_SPECIES SURFACE_MASTER_SPECIES SURFACE_SPECIES END ------------------------------------ Reading input data for simulation 1. ------------------------------------ TITLE Example 17.--Inverse modeling of Black Sea water evaporation SOLUTION 1 Black Sea water units mg/L density 1.014 pH 8.0 # estimated Ca 233 Mg 679 Na 5820 K 193 S(6) 1460 Cl 10340 Br 35 C 1 CO2(g) -3.5 SOLUTION 2 Composition during halite precipitation units mg/L density 1.271 pH 5.0 # estimated Ca 0.0 Mg 50500 Na 55200 K 15800 S(6) 76200 Cl 187900 Br 2670 C 1 CO2(g) -3.5 INVERSE_MODELING solutions 1 2 uncertainties .025 range balances Br K Mg phases H2O(g) pre Calcite pre CO2(g) pre Gypsum pre Halite pre Glauberite pre Polyhalite pre END ----- TITLE ----- Example 17.--Inverse modeling of Black Sea water evaporation ------------------------------------------- Beginning of initial solution calculations. ------------------------------------------- Initial solution 1. Black Sea water -----------------------------Solution composition------------------------------ Elements Molality Moles Br 4.401e-04 4.401e-04 C 8.425e-04 8.425e-04 Equilibrium with CO2(g) Ca 5.841e-03 5.841e-03 Cl 2.930e-01 2.930e-01 K 4.960e-03 4.960e-03 Mg 2.807e-02 2.807e-02 Na 2.544e-01 2.544e-01 S(6) 1.527e-02 1.527e-02 ----------------------------Description of solution---------------------------- pH = 8.000 pe = 4.000 Specific Conductance (uS/cm, 25 oC) = 31377 Density (g/cm3) = 1.01094 Volume (L) = 1.00889 Activity of water = 0.990 Ionic strength = 3.752e-01 Mass of water (kg) = 1.000e+00 Total alkalinity (eq/kg) = 8.655e-04 Total CO2 (mol/kg) = 8.425e-04 Temperature (deg C) = 25.00 Electrical balance (eq) = 2.253e-03 Percent error, 100*(Cat-|An|)/(Cat+|An|) = 0.35 Iterations = 9 Gamma iterations = 3 Osmotic coefficient = 0.89876 Density of water = 0.99704 Total H = 1.110132e+02 Total O = 5.556982e+01 ----------------------------Distribution of species---------------------------- MacInnes MacInnes MacInnes Log Log Log mole V Species Molality Activity Molality Activity Gamma cm3/mol OH- 1.670e-06 1.002e-06 -5.777 -5.999 -0.222 -3.15 H+ 1.289e-08 1.000e-08 -7.890 -8.000 -0.110 0.00 H2O 5.551e+01 9.903e-01 1.744 -0.004 0.000 18.07 Br 4.401e-04 Br- 4.401e-04 3.006e-04 -3.356 -3.522 -0.166 25.36 C(4) 8.425e-04 HCO3- 8.017e-04 4.931e-04 -3.096 -3.307 -0.211 25.95 CO3-2 1.603e-05 2.258e-06 -4.795 -5.646 -0.851 -1.27 MgCO3 1.441e-05 1.441e-05 -4.841 -4.841 0.000 -17.09 CO2 1.033e-05 1.093e-05 -4.986 -4.961 0.024 29.09 Ca 5.841e-03 Ca+2 5.841e-03 1.477e-03 -2.233 -2.831 -0.597 -16.97 Cl 2.930e-01 Cl- 2.930e-01 1.962e-01 -0.533 -0.707 -0.174 18.61 K 4.960e-03 K+ 4.960e-03 3.421e-03 -2.305 -2.466 -0.161 9.48 Mg 2.807e-02 Mg+2 2.805e-02 7.533e-03 -1.552 -2.123 -0.571 -20.69 MgCO3 1.441e-05 1.441e-05 -4.841 -4.841 0.000 -17.09 MgOH+ 1.246e-06 1.158e-06 -5.904 -5.936 -0.032 (0) Na 2.544e-01 Na+ 2.544e-01 1.837e-01 -0.595 -0.736 -0.141 -0.79 S(6) 1.527e-02 SO4-2 1.527e-02 2.124e-03 -1.816 -2.673 -0.857 17.27 HSO4- 2.958e-09 2.023e-09 -8.529 -8.694 -0.165 40.79 ------------------------------Saturation indices------------------------------- Phase SI** log IAP log K(298 K, 1 atm) Anhydrite -1.28 -5.50 -4.22 CaSO4 Aragonite -0.26 -8.48 -8.22 CaCO3 Arcanite -5.83 -7.60 -1.78 K2SO4 Bischofite -8.02 -3.56 4.46 MgCl2:6H2O Bloedite -6.61 -8.96 -2.35 Na2Mg(SO4)2:4H2O Brucite -3.24 -14.12 -10.88 Mg(OH)2 Burkeite -14.64 -15.41 -0.77 Na6CO3(SO4)2 Calcite -0.07 -8.48 -8.41 CaCO3 Carnallite -11.07 -6.74 4.33 KMgCl3:6H2O CO2(g) -3.50 -4.96 -1.46 CO2 Pressure 0.0 atm, phi 1.000 Dolomite 0.84 -16.25 -17.08 CaMg(CO3)2 Epsomite -2.94 -4.83 -1.88 MgSO4:7H2O Gaylussite -6.20 -15.62 -9.42 CaNa2(CO3)2:5H2O Glaserite -9.68 -13.48 -3.80 NaK3(SO4)2 Glauberite -4.40 -9.65 -5.25 Na2Ca(SO4)2 Gypsum -0.93 -5.51 -4.58 CaSO4:2H2O H2O(g) -1.51 -0.00 1.50 H2O Halite -3.01 -1.44 1.57 NaCl Hexahydrite -3.19 -4.82 -1.63 MgSO4:6H2O Kainite -7.79 -7.98 -0.19 KMgClSO4:3H2O Kalicinite -6.05 -16.11 -10.06 KHCO3 Kieserite -4.68 -4.80 -0.12 MgSO4:H2O Labile_S -8.13 -13.80 -5.67 Na4Ca(SO4)3:2H2O Leonhardite -3.93 -4.81 -0.89 MgSO4:4H2O Leonite -8.44 -12.42 -3.98 K2Mg(SO4)2:4H2O Magnesite 0.06 -7.77 -7.83 MgCO3 Mirabilite -2.97 -4.19 -1.21 Na2SO4:10H2O Misenite -75.63 -86.44 -10.81 K8H6(SO4)7 Nahcolite -3.64 -14.38 -10.74 NaHCO3 Natron -6.34 -7.16 -0.82 Na2CO3:10H2O Nesquehonite -2.62 -7.78 -5.17 MgCO3:3H2O Pentahydrite -3.53 -4.82 -1.28 MgSO4:5H2O Pirssonite -6.37 -15.60 -9.23 Na2Ca(CO3)2:2H2O Polyhalite -9.67 -23.42 -13.74 K2MgCa2(SO4)4:2H2O Portlandite -9.64 -14.83 -5.19 Ca(OH)2 Schoenite -8.10 -12.43 -4.33 K2Mg(SO4)2:6H2O Sylvite -4.07 -3.17 0.90 KCl Syngenite -5.66 -13.11 -7.45 K2Ca(SO4)2:H2O Thenardite -3.79 -4.14 -0.35 Na2SO4 Trona -10.12 -21.51 -11.38 Na3H(CO3)2:2H2O **For a gas, SI = log10(fugacity). For ideal gases, fugacity = pressure / 1 atm. For a Peng-Robinson gas, fugacity = pressure * phi / 1 atm Initial solution 2. Composition during halite precipitation -----------------------------Solution composition------------------------------ Elements Molality Moles Br 3.785e-02 3.785e-02 C 7.178e-06 7.178e-06 Equilibrium with CO2(g) Cl 6.004e+00 6.004e+00 K 4.578e-01 4.578e-01 Mg 2.354e+00 2.354e+00 Na 2.720e+00 2.720e+00 S(6) 8.986e-01 8.986e-01 ----------------------------Description of solution---------------------------- pH = 5.000 pe = 4.000 Specific Conductance (uS/cm, 25 oC) = 599384 Density (g/cm3) = 1.26987 Volume (L) = 1.17915 Activity of water = 0.680 Ionic strength = 1.111e+01 Mass of water (kg) = 1.000e+00 Total alkalinity (eq/kg) = 7.757e-06 Total CO2 (mol/kg) = 7.178e-06 Temperature (deg C) = 25.00 Electrical balance (eq) = 4.629e-02 Percent error, 100*(Cat-|An|)/(Cat+|An|) = 0.29 Iterations = 16 Gamma iterations = 7 Osmotic coefficient = 1.71320 Density of water = 0.99704 Total H = 1.110124e+02 Total O = 5.910065e+01 ----------------------------Distribution of species---------------------------- MacInnes MacInnes MacInnes Log Log Log mole V Species Molality Activity Molality Activity Gamma cm3/mol H+ 5.590e-07 1.000e-05 -6.253 -5.000 1.253 0.00 OH- 1.209e-08 6.888e-10 -7.918 -9.162 -1.244 11.12 H2O 5.551e+01 6.805e-01 1.744 -0.167 0.000 18.07 Br 3.785e-02 Br- 3.785e-02 4.959e-02 -1.422 -1.305 0.117 27.92 C(4) 7.178e-06 HCO3- 4.537e-06 3.388e-07 -5.343 -6.470 -1.127 47.51 CO2 2.568e-06 1.093e-05 -5.590 -4.961 0.629 29.09 MgCO3 6.745e-08 6.745e-08 -7.171 -7.171 0.000 -17.09 CO3-2 5.816e-09 1.551e-12 -8.235 -11.809 -3.574 14.84 Cl 6.004e+00 Cl- 6.004e+00 4.520e+00 0.778 0.655 -0.123 20.71 K 4.578e-01 K+ 4.578e-01 4.795e-01 -0.339 -0.319 0.020 14.34 Mg 2.354e+00 Mg+2 2.354e+00 5.130e+01 0.372 1.710 1.338 -15.59 MgOH+ 6.305e-06 5.420e-06 -5.200 -5.266 -0.066 (0) MgCO3 6.745e-08 6.745e-08 -7.171 -7.171 0.000 -17.09 Na 2.720e+00 Na+ 2.720e+00 8.690e+00 0.435 0.939 0.504 2.74 S(6) 8.986e-01 SO4-2 8.986e-01 2.278e-03 -0.046 -2.643 -2.596 31.36 HSO4- 2.684e-06 2.170e-06 -5.571 -5.664 -0.092 42.44 ------------------------------Saturation indices------------------------------- Phase SI** log IAP log K(298 K, 1 atm) Arcanite -1.50 -3.28 -1.78 K2SO4 Bischofite -2.44 2.02 4.46 MgCl2:6H2O Bloedite -0.02 -2.37 -2.35 Na2Mg(SO4)2:4H2O Brucite -5.73 -16.61 -10.88 Mg(OH)2 Burkeite -10.69 -11.46 -0.77 Na6CO3(SO4)2 Carnallite -1.98 2.35 4.33 KMgCl3:6H2O CO2(g) -3.50 -4.96 -1.46 CO2 Pressure 0.0 atm, phi 1.000 Epsomite -0.22 -2.10 -1.88 MgSO4:7H2O Glaserite -1.50 -5.30 -3.80 NaK3(SO4)2 H2O(g) -1.67 -0.17 1.50 H2O Halite 0.02 1.59 1.57 NaCl Hexahydrite -0.30 -1.94 -1.63 MgSO4:6H2O Kainite -0.90 -1.10 -0.19 KMgClSO4:3H2O Kalicinite -7.07 -17.13 -10.06 KHCO3 Kieserite -0.98 -1.10 -0.12 MgSO4:H2O Leonhardite -0.71 -1.60 -0.89 MgSO4:4H2O Leonite -0.90 -4.88 -3.98 K2Mg(SO4)2:4H2O Magnesite -2.27 -10.10 -7.83 MgCO3 Mirabilite -1.22 -2.44 -1.21 Na2SO4:10H2O Misenite -40.25 -51.05 -10.81 K8H6(SO4)7 Nahcolite -5.13 -15.87 -10.74 NaHCO3 Natron -10.78 -11.60 -0.82 Na2CO3:10H2O Nesquehonite -5.43 -10.60 -5.17 MgCO3:3H2O Pentahydrite -0.48 -1.77 -1.28 MgSO4:5H2O Schoenite -0.89 -5.22 -4.33 K2Mg(SO4)2:6H2O Sylvite -0.56 0.34 0.90 KCl Thenardite -0.41 -0.76 -0.35 Na2SO4 Trona -14.75 -26.14 -11.38 Na3H(CO3)2:2H2O **For a gas, SI = log10(fugacity). For ideal gases, fugacity = pressure / 1 atm. For a Peng-Robinson gas, fugacity = pressure * phi / 1 atm --------------------------------------------- Beginning of inverse modeling 1 calculations. --------------------------------------------- Using Cl1 standard precision optimization routine. Solution 1: Black Sea water Input Delta Input+Delta pH 8.000e+00 + 0.000e+00 = 8.000e+00 Alkalinity 8.655e-04 + 0.000e+00 = 8.655e-04 Br 4.401e-04 + 0.000e+00 = 4.401e-04 C(4) 8.425e-04 + 0.000e+00 = 8.425e-04 Ca 5.841e-03 + 0.000e+00 = 5.841e-03 Cl 2.930e-01 + 8.006e-04 = 2.938e-01 K 4.960e-03 + 1.034e-04 = 5.063e-03 Mg 2.807e-02 + -7.018e-04 = 2.737e-02 Na 2.544e-01 + 0.000e+00 = 2.544e-01 S(6) 1.527e-02 + 7.631e-05 = 1.535e-02 Solution 2: Composition during halite precipitation Input Delta Input+Delta pH 5.000e+00 + 0.000e+00 = 5.000e+00 Alkalinity 7.757e-06 + -1.939e-07 = 7.563e-06 Br 3.785e-02 + 9.440e-04 = 3.880e-02 C(4) 7.178e-06 + 1.795e-07 = 7.358e-06 Ca 0.000e+00 + 0.000e+00 = 0.000e+00 Cl 6.004e+00 + 1.501e-01 = 6.154e+00 K 4.578e-01 + -1.144e-02 = 4.464e-01 Mg 2.354e+00 + 5.884e-02 = 2.413e+00 Na 2.720e+00 + -4.642e-02 = 2.674e+00 S(6) 8.986e-01 + -2.247e-02 = 8.761e-01 Solution fractions: Minimum Maximum Solution 1 8.815e+01 8.780e+01 8.815e+01 Solution 2 1.000e+00 1.000e+00 1.000e+00 Phase mole transfers: Minimum Maximum H2O(g) -4.837e+03 -4.817e+03 -4.817e+03 H2O Calcite -3.814e-02 -3.910e-02 -3.704e-02 CaCO3 CO2(g) -3.612e-02 -3.893e-02 -3.317e-02 CO2 Gypsum -4.768e-01 -4.906e-01 -4.611e-01 CaSO4:2H2O Halite -1.975e+01 -2.033e+01 -1.901e+01 NaCl Redox mole transfers: Sum of residuals (epsilons in documentation): 1.926e+02 Sum of delta/uncertainty limit: 9.823e+00 Maximum fractional error in element concentration: 2.500e-02 Model contains minimum number of phases. =============================================================================== Summary of inverse modeling: Number of models found: 1 Number of minimal models found: 1 Number of infeasible sets of phases saved: 11 Number of calls to cl1: 29 ------------------ End of simulation. ------------------ ------------------------------------ Reading input data for simulation 2. ------------------------------------ ------------------------------ End of Run after 0.03 Seconds. ------------------------------