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iphreeqc/database/pitzer.dat

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# File 1 = C:\GitPrograms\phreeqc3-1\database\pitzer.dat, 22/05/2024 19:46, 1033 lines, 38088 bytes, md5=d70476773ed110a269ebbcaf334f1133
# Created 22 May 2024 19:49:25
# C:\3rdParty\lsp\lsp.exe -f2 -k=asis -ts pitzer.dat
# Pitzer.DAT for calculating temperature and pressure dependence of reactions, and the specific conductance and viscosity of the solution, using
# diffusion coefficients of species, molal volumina of aqueous species and minerals, and critical temperatures and pressures of gases used in Peng-Robinson's EOS.
# Details are given at the end of this file.
SOLUTION_MASTER_SPECIES
Alkalinity CO3-2 1 Ca0.5(CO3)0.5 50.05
B B(OH)3 0 B 10.81
Ba Ba+2 0 Ba 137.33
Br Br- 0 Br 79.904
C CO3-2 2 HCO3 12.0111
C(4) CO3-2 2 HCO3 12.0111
Ca Ca+2 0 Ca 40.08
Cl Cl- 0 Cl 35.453
E e- 1 0.0 0.0
Fe Fe+2 0 Fe 55.847
H H+ -1 H 1.008
H(1) H+ -1 0.0
K K+ 0 K 39.0983
Li Li+ 0 Li 6.941
Mg Mg+2 0 Mg 24.305
Mn Mn+2 0 Mn 54.938
Na Na+ 0 Na 22.9898
O H2O 0 O 16.00
O(-2) H2O 0 0.0
S SO4-2 0 SO4 32.064
S(6) SO4-2 0 SO4
Si H4SiO4 0 SiO2 28.0843
Sr Sr+2 0 Sr 87.62
# redox-uncoupled gases
Hdg Hdg 0 Hdg 2.016 # H2 gas
Oxg Oxg 0 Oxg 32 # Oxygen gas
Mtg Mtg 0 Mtg 16.032 # CH4 gas
Sg H2Sg 0 H2Sg 32.064 # H2S gas
Ntg Ntg 0 Ntg 28.0134 # N2 gas
SOLUTION_SPECIES
H+ = H+
-viscosity 9.35e-2 -8.31e-2 2.487e-2 4.49e-4 2.01e-2 1.57 # for viscosity parameters see ref. 4
-dw 9.31e-9 823 5.55 0 3.07 24.01 0
# Dw(25 C) dw_T a a2 visc a3 a_v_dif
# Dw(TK) = 9.31e-9 * exp(823 / TK - 823 / 298.15) * viscos_0_25 / viscos_0_tc
# a = DH ion size, a2 = exponent, visc = viscosity exponent, a3(H+) = 24.01 = new dw calculation from A.D. 2024, a_v_dif = exponent in (viscos_0_tc / viscos)^a_v_dif
# For SC, Dw(TK) *= (viscos_0_tc / viscos)^visc (visc = 3.07 for H+)
# a3 > 5 or a3 = 0 or not defined ? ka = DH_B * a * (1 + (vm - v0))^a2 * mu^0.5, in Debye-Onsager eqn. (a2 = Vm = 0 for H+, the reference for Vm)
# a3 = -10 ? ka = DH_B * a * mu^a2 in DHO. (Define a3 = -10.)
# -5 < a3 < 5 ? ka = DH_B * a2 * mu^0.5 / (1 + mu^a3), Appelo, 2017: Dw(I) = Dw(TK) * exp(-a * DH_A * z * sqrt_mu / (1 + ka))
# If a_v_dif <> 0, Dw(TK) *= (viscos_0_tc / viscos)^a_v_dif in TRANSPORT.
e- = e-
H2O = H2O
-dw 2.299e-9 -254
Li+ = Li+
-Vm -0.419 -0.069 13.16 -2.78 0.416 0 0.296 -12.4 -2.74e-3 1.26 # The apparent volume parameters are defined in ref. 1 & 2 For Li+ additional data from Ellis, 1968, J. Chem. Soc. A, 1138
-viscosity 0.162 -2.45e-2 3.73e-2 9.7e-4 8.1e-4 2.087 # < 10 M LiCl
-dw 1.03e-9 -14 4.03 0.8341 1.679
Na+ = Na+
-Vm 2.28 -4.38 -4.1 -0.586 0.09 4 0.3 52 -3.33e-3 0.566
# for calculating densities (rho) when I > 3...
# -Vm 2.28 -4.38 -4.1 -0.586 0.09 4 0.3 52 -3.33e-3 0.45
-viscosity 0.1387 -8.66e-2 1.25e-2 1.45e-2 7.5e-3 1.062
-dw 1.33e-9 75 3.627 0 0.7037
K+ = K+
-Vm 3.322 -1.473 6.534 -2.712 9.06e-2 3.5 0 29.7 0 1
-viscosity 0.116 -0.191 1.52e-2 1.4e-2 2.59e-2 0.9028
-dw 1.96e-9 254 3.484 0 0.1964
Mg+2 = Mg+2
-Vm -1.41 -8.6 11.13 -2.39 1.332 5.5 1.29 -32.9 -5.86e-3 1
-viscosity 0.426 0 0 1.66e-3 4.32e-3 2.461
-dw 0.705e-9 -4 5.569 0 1.047
Ca+2 = Ca+2
-Vm -0.3456 -7.252 6.149 -2.479 1.239 5 1.6 -57.1 -6.12e-3 1 # The apparent volume parameters are defined in ref. 1 & 2
-viscosity 0.359 -0.158 4.2e-2 1.5e-3 8.04e-3 2.3 # ref. 4, CaCl2 < 6 M
-dw 0.792e-9 34 5.411 0 1.046
Sr+2 = Sr+2
-Vm -1.57e-2 -10.15 10.18 -2.36 0.86 5.26 0.859 -27 -4.1e-3 1.97
-viscosity 0.472 -0.252 5.51e-3 3.67e-3 0 1.876
-dw 0.794e-9 160 0.68 0.767 1e-9 0.912
Ba+2 = Ba+2
-Vm 2.063 -10.06 1.9534 -2.36 0.4218 5 1.58 -12.03 -8.35e-3 1
-viscosity 0.338 -0.227 1.39e-2 3.07e-2 0 0.768
-dw 0.848e-9 174 10.53 0 3
Mn+2 = Mn+2
-Vm -1.1 -8.03 4.08 -2.45 1.4 6 8.07 0 -1.51e-2 0.118 # ref. 2
-dw 0.688e-9
Fe+2 = Fe+2
-Vm -0.3255 -9.687 1.536 -2.379 0.3033 6 -4.21e-2 39.7 0 1
-dw 0.719e-9
Cl- = Cl-
-Vm 4.465 4.801 4.325 -2.847 1.748 0 -0.331 20.16 0 1
-viscosity 0 0 0 0 0 0 1 # the reference solute
-dw 2.033e-9 216 3.16 0.2071 0.7432
CO3-2 = CO3-2
-Vm 8.569 -10.4 -19.38 3e-4 4.61 0 2.99 0 -3.23e-2 0.872
-viscosity 0 0.296 3.63e-2 2e-4 -1.9e-2 1.881 -1.754
-dw 0.955e-9 -60 2.257 0.1022 0.4136
SO4-2 = SO4-2
-Vm -7.77 43.17 176 -51.45 3.794 0 4.97 20.5 -5.77e-2 0.45
-viscosity -4.1e-2 0.1735 1.308e-2 2.16e-4 2.83e-2 3.375 0.21
-dw 1.07e-9 -63 0.397 0.982 1.01
B(OH)3 = B(OH)3
-Vm 7.0643 8.8547 3.5844 -3.1451 -.2 # supcrt
-dw 1.1e-9
Br- = Br-
-Vm 6.72 2.85 4.21 -3.14 1.38 0 -9.56e-2 7.08 -1.56e-3 1
-viscosity -1.16e-2 -5.23e-2 5.54e-2 1.22e-2 0.119 0.9969 0.818
-dw 2.09e-9 208 3.5 0 0.5737
H4SiO4 = H4SiO4
-Vm 10.5 1.7 20 -2.7 0.1291 # supcrt 2*H2O in a1
-dw 1.1e-9
# redox-uncoupled gases
Hdg = Hdg # H2
-Vm 6.52 0.78 0.12 # supcrt
-dw 5.13e-9
Oxg = Oxg # O2
-Vm 5.7889 6.3536 3.2528 -3.0417 -0.3943 # supcrt
-dw 2.35e-9
Mtg = Mtg # CH4
-Vm 9.01 -1.11 0 -1.85 -1.5 # Hnedkovsky et al., 1996, JCT 28, 125
-dw 1.85e-9
Ntg = Ntg # N2
-Vm 7 # Pray et al., 1952, IEC 44 1146
-dw 1.96e-9 -90 # Cadogan et al. 2014, JCED 59, 519
H2Sg = H2Sg # H2S
-Vm 1.39 28.3 0 -7.22 -0.59 # Hnedkovsky et al., 1996, JCT 28, 125
-dw 2.1e-9
# aqueous species
H2O = OH- + H+
-analytic 293.29227 0.1360833 -10576.913 -123.73158 0 -6.996455e-5
-Vm -9.66 28.5 80 -22.9 1.89 0 1.09 0 0 1
-viscosity -5.45e-2 0.142 1.45e-2 -3e-5 0 3.231 -1.791 # < 5 M Li,Na,KOH
-dw 5.27e-9 491 1.851 0 0.3256
CO3-2 + H+ = HCO3-
log_k 10.3393; delta_h -3.561 kcal
-analytic 107.8975 0.03252849 -5151.79 -38.92561 563713.9
-Vm 9.463 -2.49 -11.92 0 1.63 0 0 130 0 0.691
-viscosity 0 0.633 7.2e-3 0 0 0 1.087
-dw 1.18e-9 -108 9.955 0 1.4928
CO3-2 + 2 H+ = CO2 + H2O
log_k 16.6767
delta_h -5.738 kcal
-analytic 464.1965 0.09344813 -26986.16 -165.75951 2248628.9
-Vm 7.29 0.92 2.07 -1.23 -1.6 # McBride et al. 2015, JCED 60, 171
-dw 1.92e-9 -120 # TK dependence from Cadogan et al. 2014, , JCED 59, 519
SO4-2 + H+ = HSO4-
-log_k 1.988; -delta_h 3.85 kcal
-analytic -56.889 0.006473 2307.9 19.8858
-Vm 8.2 9.259 2.1108 -3.1618 1.1748 0 -0.3 15 0 1
-viscosity 3.29e-2 -4.86e-2 0.409 1e-5 4.23e-2 1.069 0.7371
-dw 0.731e-9 1e3 7.082 3 0.86
H2Sg = HSg- + H+
log_k -6.994
delta_h 5.3 kcal
-analytical 11.17 -0.02386 -3279
-Vm 5.0119 4.9799 3.4765 -2.9849 1.441 # supcrt
-dw 1.73e-9
2 H2Sg = (H2Sg)2 # activity correction for H2S solubility at high P, T
-analytical 10.227 -0.01384 -2200
-Vm 36.41 -71.95 0 0 2.58
-dw 2.1e-9
B(OH)3 + H2O = B(OH)4- + H+
log_k -9.239
delta_h 0 kcal
3 B(OH)3 = B3O3(OH)4- + 2 H2O + H+
log_k -7.528
delta_h 0 kcal
4 B(OH)3 = B4O5(OH)4-2 + 3 H2O + 2 H+
log_k -16.134
delta_h 0 kcal
Ca+2 + B(OH)3 + H2O = CaB(OH)4+ + H+
log_k -7.589
delta_h 0 kcal
Mg+2 + B(OH)3 + H2O = MgB(OH)4+ + H+
log_k -7.84
delta_h 0 kcal
# Ca+2 + CO3-2 = CaCO3
# log_k 3.151
# delta_h 3.547 kcal
# -analytic -1228.806 -0.299440 35512.75 485.818
# -dw 4.46e-10 # complexes: calc'd with the Pikal formula
# -Vm -.2430 -8.3748 9.0417 -2.4328 -.0300 # supcrt
Mg+2 + H2O = MgOH+ + H+
log_k -11.809
delta_h 15.419 kcal
Mg+2 + CO3-2 = MgCO3
log_k 2.928
delta_h 2.535 kcal
-analytic -32.225 0 1093.486 12.72433
-dw 4.21e-10
-Vm -.5837 -9.2067 9.3687 -2.3984 -.03 # supcrt
H4SiO4 = H3SiO4- + H+
-log_k -9.83; -delta_h 6.12 kcal
-analytic -302.3724 -0.050698 15669.69 108.18466 -1119669
-Vm 7.94 1.0881 5.3224 -2.824 1.4767 # supcrt H2O in a1
H4SiO4 = H2SiO4-2 + 2 H+
-log_k -23; -delta_h 17.6 kcal
-analytic -294.0184 -0.07265 11204.49 108.18466 -1119669
PHASES
Akermanite
Ca2MgSi2O7 + 6 H+ = Mg+2 + 2 Ca+2 + 2 H4SiO4 - H2O # llnl.dat
log_k 45.23
-delta_H -289 kJ/mol
Vm 92.6
Anhydrite
CaSO4 = Ca+2 + SO4-2
log_k -4.362
-analytical_expression 5.009 -2.21e-2 -796.4 # ref. 3
-Vm 46.1 # 136.14 / 2.95
Anthophyllite
Mg7Si8O22(OH)2 + 14 H+ = 7 Mg+2 - 8 H2O + 8 H4SiO4 # llnl.dat
log_k 66.8
-delta_H -483 kJ/mol
Vm 269
Antigorite
Mg48Si34O85(OH)62 + 96 H+ = 34 H4SiO4 + 48 Mg+2 + 11 H2O # llnl.dat
log_k 477.19
-delta_H -3364 kJ/mol
Vm 1745
Aragonite
CaCO3 = CO3-2 + Ca+2
log_k -8.336
delta_h -2.589 kcal
-analytic -171.8607 -.077993 2903.293 71.595
-Vm 34.04
Arcanite
K2SO4 = SO4-2 + 2 K+
log_k -1.776; -delta_h 5 kcal
-analytical_expression 674.142 0.30423 -18037 -280.236 0 -1.44055e-4 # ref. 3
# Note, the Linke and Seidell data may give subsaturation in other xpt's, SI = -0.06
-Vm 65.5
Artinite
Mg2CO3(OH)2:3H2O + 3 H+ = HCO3- + 2 Mg+2 + 5 H2O # llnl.dat
log_k 19.66
-delta_H -130 kJ/mol
Vm 97.4
Barite
BaSO4 = Ba+2 + SO4-2
log_k -9.97; delta_h 6.35 kcal
-analytical_expression -282.43 -8.972e-2 5822 113.08 # ref. 3
-Vm 52.9
Bischofite
MgCl2:6H2O = Mg+2 + 2 Cl- + 6 H2O
log_k 4.455
-analytical_expression 7.526 -1.114e-2 115.7 # ref. 3
Vm 127.1
Bloedite
Na2Mg(SO4)2:4H2O = Mg+2 + 2 Na+ + 2 SO4-2 + 4 H2O
log_k -2.347
-delta_H 0 # Not possible to calculate enthalpy of reaction Bloedite
Vm 147
Brucite
Mg(OH)2 = Mg+2 + 2 OH-
log_k -10.88
-delta_H 4.85 kcal/mol
Vm 24.6
Burkeite
Na6CO3(SO4)2 = CO3-2 + 2 SO4-2 + 6 Na+
log_k -0.772
Vm 152
Calcite
CaCO3 = CO3-2 + Ca+2
log_k -8.406
delta_h -2.297 kcal
-analytic 8.481 -0.032644 -2133 # ref. 3 with data from Ellis, 1959, Plummer and Busenberg, 1982
-Vm 36.9
Carnallite
KMgCl3:6H2O = K+ + Mg+2 + 3 Cl- + 6 H2O
log_k 4.35; -delta_h 1.17
-analytical_expression 24.06 -3.11e-2 -3.09e3 # ref. 3
Vm 173.7
Celestite
SrSO4 = Sr+2 + SO4-2
log_k -6.63
-analytic -7.14 6.11E-3 75 0 0 -1.79E-5 # ref. 3
-Vm 46.4
Chalcedony
SiO2 + 2 H2O = H4SiO4
-log_k -3.55; -delta_h 4.72 kcal
-Vm 23.1
Chrysotile
Mg3Si2O5(OH)4 + 6 H+ = H2O + 2 H4SiO4 + 3 Mg+2 # phreeqc.dat
-log_k 32.2
-delta_h -46.8 kcal
-analytic 13.248 0 10217.1 -6.1894
-Vm 110
Diopside
CaMgSi2O6 + 4 H+ = Ca+2 + Mg+2 - 2 H2O + 2 H4SiO4 # llnl.dat
log_k 20.96
-delta_H -134 kJ/mol
Vm 67.2
Dolomite
CaMg(CO3)2 = Ca+2 + Mg+2 + 2 CO3-2
log_k -17.09
delta_h -9.436 kcal
-analytic -120.63 -0.1051 0 54.509 # 50<35>175<37>C, B<>n<EFBFBD>zeth et al., 2018, GCA 224, 262-275
-Vm 64.5
Enstatite
MgSiO3 + 2 H+ = - H2O + Mg+2 + H4SiO4 # llnl.dat
log_k 11.33
-delta_H -83 kJ/mol
Vm 31.3
Epsomite
MgSO4:7H2O = Mg+2 + SO4-2 + 7 H2O
log_k -1.881
-analytical_expression 4.479 -6.99e-3 -1.265e3 # ref. 3
Vm 147
Forsterite
Mg2SiO4 + 4 H+ = H4SiO4 + 2 Mg+2 # llnl.dat
log_k 27.86
-delta_H -206 kJ/mol
Vm 43.7
Gaylussite
CaNa2(CO3)2:5H2O = Ca+2 + 2 CO3-2 + 2 Na+ + 5 H2O
log_k -9.421
Glaserite
NaK3(SO4)2 = Na+ + 3 K+ + 2 SO4-2
log_k -3.803; -delta_h 25
-Vm 123
Glauberite
Na2Ca(SO4)2 = Ca+2 + 2 Na+ + 2 SO4-2
log_k -5.31
-analytical_expression 218.142 0 -9285 -77.735 # ref. 3
Vm 100.4
Goergeyite
K2Ca5(SO4)6H2O = 2 K+ + 5 Ca+2 + 6 SO4-2 + H2O
log_k -29.5
-analytical_expression 1056.787 0 -52300 -368.06 # ref. 3
-Vm 295.9
Gypsum
CaSO4:2H2O = Ca+2 + SO4-2 + 2 H2O
-log_k -4.58; -delta_h -0.109 kcal
-analytical_expression 82.381 0 -3804.5 -29.9952 # ref. 3
-Vm 73.9
Halite
NaCl = Cl- + Na+
log_k 1.57
-analytical_expression 159.605 8.4294e-2 -3975.6 -66.857 0 -4.9364e-5 # ref. 3
-Vm 27.1
Hexahydrite
MgSO4:6H2O = Mg+2 + SO4-2 + 6 H2O
log_k -1.635
-analytical_expression -0.733 -2.8e-3 -8.57e-3 # ref. 3
Vm 132
Huntite
CaMg3(CO3)4 + 4 H+ = Ca+2 + 3 Mg+2 + 4 HCO3- # llnl.dat
log_k 10.3
-analytical_expression -1.145e3 -3.249e-1 3.941e4 4.526e2
Vm 130.8
Kainite
KMgClSO4:3H2O = Cl- + K+ + Mg+2 + SO4-2 + 3 H2O
log_k -0.193
Kalicinite
KHCO3 = K+ + H+ + CO3-2
log_k -9.94 # Harvie et al., 1984
Kieserite
MgSO4:H2O = Mg+2 + SO4-2 + H2O
log_k -0.123
-analytical_expression 47.24 -0.12077 -5.356e3 0 0 7.272e-5 # ref. 3
Vm 53.8
Labile_S
Na4Ca(SO4)3:2H2O = 4 Na+ + Ca+2 + 3 SO4-2 + 2 H2O
log_k -5.672
Leonhardite
MgSO4:4H2O = Mg+2 + SO4-2 + 4 H2O
log_k -0.887
Leonite
K2Mg(SO4)2:4H2O = Mg+2 + 2 K+ + 2 SO4-2 + 4 H2O
log_k -3.979
Magnesite
MgCO3 = CO3-2 + Mg+2
log_k -7.834
delta_h -6.169
Vm 28.3
MgCl2_2H2O
MgCl2:2H2O = Mg+2 + 2 Cl- + 2 H2O
-analytical_expression -10.273 0 7.403e3 # ref. 3
MgCl2_4H2O
MgCl2:4H2O = Mg+2 + 2 Cl- + 4 H2O
-analytical_expression 12.98 -2.013e-2 # ref. 3
Mirabilite
Na2SO4:10H2O = SO4-2 + 2 Na+ + 10 H2O
-analytical_expression -301.9326 -0.16232 0 141.078 # ref. 3
Vm 216
Misenite
K8H6(SO4)7 = 6 H+ + 7 SO4-2 + 8 K+
log_k -10.806
Nahcolite
NaHCO3 = CO3-2 + H+ + Na+
log_k -10.742
Vm 38
Natron
Na2CO3:10H2O = CO3-2 + 2 Na+ + 10 H2O
log_k -0.825
Nesquehonite
MgCO3:3H2O = CO3-2 + Mg+2 + 3 H2O
log_k -5.167
Pentahydrite
MgSO4:5H2O = Mg+2 + SO4-2 + 5 H2O
log_k -1.285
Pirssonite
Na2Ca(CO3)2:2H2O = 2 Na+ + Ca+2 + 2 CO3-2 + 2 H2O
log_k -9.234
Polyhalite
K2MgCa2(SO4)4:2H2O = 2 K+ + Mg+2 + 2 Ca+2 + 4 SO4-2 + 2 H2O
log_k -13.744
Vm 218
Portlandite
Ca(OH)2 = Ca+2 + 2 OH-
log_k -5.19
Quartz
SiO2 + 2 H2O = H4SiO4
-log_k -3.98; -delta_h 5.99 kcal
-Vm 22.67
Schoenite
K2Mg(SO4)2:6H2O = 2 K+ + Mg+2 + 2 SO4-2 + 6 H2O
log_k -4.328
Sepiolite(d)
Mg2Si3O7.5OH:3H2O + 4 H+ + 0.5 H2O = 2 Mg+2 + 3 H4SiO4 # phreeqc.dat
-log_k 18.66
-Vm 162
Sepiolite
Mg2Si3O7.5OH:3H2O + 4 H+ + 0.5 H2O = 2 Mg+2 + 3 H4SiO4 # phreeqc.dat
-log_k 15.76
-delta_h -10.7 kcal
-Vm 154
SiO2(a)
SiO2 + 2 H2O = H4SiO4
-log_k -2.71; -delta_h 3.34 kcal
-analytic 20.42 3.107e-3 -1492 -7.68 # ref. 3
-Vm 25.7
Sylvite
KCl = K+ + Cl-
log_k 0.9; -delta_h 8
-analytical_expression -50.571 9.8815e-2 1.3135e4 0 -1.3754e6 -7.393e-5 # ref. 3
Vm 37.5
Syngenite
K2Ca(SO4)2:H2O = 2 K+ + Ca+2 + 2 SO4-2 + H2O
log_k -6.43; -delta_h -32.65 # ref. 3
-Vm 127.3
Talc
Mg3Si4O10(OH)2 + 4 H2O + 6 H+ = 3 Mg+2 + 4 H4SiO4 # phreeqc.dat
-log_k 21.399
-delta_h -46.352 kcal
-Vm 140
Thenardite
Na2SO4 = 2 Na+ + SO4-2
-analytical_expression 57.185 8.6024e-2 0 -30.8341 0 -7.6905e-5 # ref. 3
-Vm 52.9
Trona
Na3H(CO3)2:2H2O = 3 Na+ + H+ + 2 CO3-2 + 2 H2O
log_k -11.384
Vm 106
Borax
Na2(B4O5(OH)4):8H2O + 2 H+ = 4 B(OH)3 + 2 Na+ + 5 H2O
log_k 12.464
Vm 223
Boric_acid,s
B(OH)3 = B(OH)3
log_k -0.03
KB5O8:4H2O
KB5O8:4H2O + 3 H2O + H+ = 5 B(OH)3 + K+
log_k 4.671
K2B4O7:4H2O
K2B4O7:4H2O + H2O + 2 H+ = 4 B(OH)3 + 2 K+
log_k 13.906
NaBO2:4H2O
NaBO2:4H2O + H+ = B(OH)3 + Na+ + 3 H2O
log_k 9.568
NaB5O8:5H2O
NaB5O8:5H2O + 2 H2O + H+ = 5 B(OH)3 + Na+
log_k 5.895
Teepleite
Na2B(OH)4Cl + H+ = B(OH)3 + 2 Na+ + Cl- + H2O
log_k 10.84
CO2(g)
CO2 = CO2
log_k -1.468
delta_h -4.776 kcal
-analytic 10.5624 -2.3547e-2 -3972.8 0 5.8746e5 1.9194e-5
-T_c 304.2 # critical T, K
-P_c 72.8 # critical P, atm
-Omega 0.225 # acentric factor
H2O(g)
H2O = H2O
log_k 1.506; delta_h -44.03 kJ
-T_c 647.3 # critical T, K
-P_c 217.6 # critical P, atm
-Omega 0.344 # acentric factor
-analytic -16.5066 -2.0013E-3 2710.7 3.7646 0 2.24E-6
# redox-uncoupled gases
Oxg(g)
Oxg = Oxg
-analytic -7.5001 7.8981e-3 0 0 2.0027e+5
T_c 154.6; -P_c 49.8; -Omega 0.021
Hdg(g)
Hdg = Hdg
-analytic -9.3114e+0 4.6473e-3 -4.9335e+1 1.4341e+0 1.2815e+5
-T_c 33.2; -P_c 12.8; -Omega -0.225
Ntg(g)
Ntg = Ntg
-analytic -58.453 1.818E-3 3199 17.909 -27460
T_c 126.2; -P_c 33.5; -Omega 0.039
Mtg(g)
Mtg = Mtg
-analytic 10.44 -7.65e-3 -6669 0 1.014e6 # CH4 solubilities 25 - 100<30>C
T_c 190.6; -P_c 45.4; -Omega 0.008
H2Sg(g)
H2Sg = H+ + HSg-
-analytic -45.07 -0.02418 0 17.9205 # H2S solubilities, 0 - 300<30>C, 1 - 987 atm, Jiang et al., 2020, CG 555, 119816
T_c 373.2; -P_c 88.2; -Omega 0.1
PITZER
-B0
B(OH)4- K+ 0.035
B(OH)4- Na+ -0.0427
B3O3(OH)4- K+ -0.13
B3O3(OH)4- Na+ -0.056
B4O5(OH)4-2 K+ -0.022
B4O5(OH)4-2 Na+ -0.11
Ba+2 Br- 0.31455 0 0 -0.33825E-3
Ba+2 Cl- 0.5268 0 0 0 0 4.75e4 # ref. 3
Ba+2 OH- 0.17175
Br- H+ 0.196 0 0 -2.049E-4
Br- K+ 0.0569 0 0 7.39E-4
Br- Li+ 0.1748 0 0 -1.819E-4
Br- Mg+2 0.4327 0 0 -5.625E-5
Br- Na+ 0.0973 0 0 7.692E-4
Br- Sr+2 0.331125 0 0 -0.32775E-3
Ca+2 Br- 0.3816 0 0 -5.2275E-4
Ca+2 Cl- 0.3159 0 0 -3.27e-4 1.4e-7 # ref. 3
Ca+2 HCO3- 0.4
Ca+2 HSO4- 0.2145
Ca+2 OH- -0.1747
Ca+2 SO4-2 0 # ref. 3
CaB(OH)4+ Cl- 0.12
Cl- Fe+2 0.335925
Cl- H+ 0.1775 0 0 -3.081E-4
Cl- K+ 0.04808 -758.48 -4.7062 0.010072 -3.7599e-6 # ref. 3
Cl- Li+ 0.1494 0 0 -1.685E-4
Cl- Mg+2 0.351 0 0 -9.32e-4 5.94e-7 # ref. 3
Cl- MgB(OH)4+ 0.16
Cl- MgOH+ -0.1
Cl- Mn+2 0.327225
Cl- Na+ 7.534e-2 9598.4 35.48 -5.8731e-2 1.798e-5 -5e5 # ref. 3
Cl- Sr+2 0.2858 0 0 0.717E-3
CO3-2 K+ 0.1488 0 0 1.788E-3
CO3-2 Na+ 0.0399 0 0 1.79E-3
Fe+2 HSO4- 0.4273
Fe+2 SO4-2 0.2568
H+ HSO4- 0.2065
H+ SO4-2 0.0298
HCO3- K+ 0.0296 0 0 0.996E-3
HCO3- Mg+2 0.329
HCO3- Na+ -0.018 # ref. 3 new -analytic for calcite
HCO3- Sr+2 0.12
HSO4- K+ -0.0003
HSO4- Mg+2 0.4746
HSO4- Na+ 0.0454
K+ OH- 0.1298
K+ SO4-2 3.17e-2 0 0 9.28e-4 # ref. 3
Li+ OH- 0.015
Li+ SO4-2 0.136275 0 0 0.5055E-3
Mg+2 SO4-2 0.2135 -951 0 -2.34e-2 2.28e-5 # ref. 3
Mn+2 SO4-2 0.2065
Na+ OH- 0.0864 0 0 7E-4
Na+ SO4-2 2.73e-2 0 -5.8 9.89e-3 0 -1.563e5 # ref. 3
SO4-2 Sr+2 0.2 0 0 -2.9E-3
-B1
B(OH)4- K+ 0.14
B(OH)4- Na+ 0.089
B3O3(OH)4- Na+ -0.91
B4O5(OH)4-2 Na+ -0.4
Ba+2 Br- 1.56975 0 0 6.78E-3
Ba+2 Cl- 0.687 0 0 1.417e-2 # ref. 3
Ba+2 OH- 1.2
Br- H+ 0.3564 0 0 4.467E-4
Br- K+ 0.2212 0 0 17.4E-4
Br- Li+ 0.2547 0 0 6.636E-4
Br- Mg+2 1.753 0 0 3.8625E-3
Br- Na+ 0.2791 0 0 10.79E-4
Br- Sr+2 1.7115 0 0 6.5325E-3
Ca+2 Br- 1.613 0 0 6.0375E-3
Ca+2 Cl- 1.614 0 0 7.63e-3 -8.19e-7 # ref. 3
Ca+2 HCO3- 2.977 # ref. 3 new -analytic for calcite
Ca+2 HSO4- 2.53
Ca+2 OH- -0.2303
Ca+2 SO4-2 3.546 0 0 5.77e-3 # ref. 3
Cl- Fe+2 1.53225
Cl- H+ 0.2945 0 0 1.419E-4
Cl- K+ 0.2168 0 -6.895 2.262e-2 -9.293e-6 -1e5 # ref. 3
Cl- Li+ 0.3074 0 0 5.366E-4
Cl- Mg+2 1.65 0 0 -1.09e-2 2.6e-5 # ref. 3
Cl- MgOH+ 1.658
Cl- Mn+2 1.55025
Cl- Na+ 0.2769 1.377e4 46.8 -6.9512e-2 2e-5 -7.4823e5 # ref. 3
Cl- Sr+2 1.667 0 0 2.8425E-3
CO3-2 K+ 1.43 0 0 2.051E-3
CO3-2 Na+ 1.389 0 0 2.05E-3
Fe+2 HSO4- 3.48
Fe+2 SO4-2 3.063
H+ HSO4- 0.5556
HCO3- K+ 0.25 0 0 1.104E-3 # ref. 3
HCO3- Mg+2 0.6072
HCO3- Na+ 0 # ref. 3 new -analytic for calcite
HSO4- K+ 0.1735
HSO4- Mg+2 1.729
HSO4- Na+ 0.398
K+ OH- 0.32
K+ SO4-2 0.756 -1.514e4 -80.3 0.1091 # ref. 3
Li+ OH- 0.14
Li+ SO4-2 1.2705 0 0 1.41E-3
Mg+2 SO4-2 3.367 -5.78e3 0 -1.48e-1 1.576e-4 # ref. 3
Mn+2 SO4-2 2.9511
Na+ OH- 0.253 0 0 1.34E-4
Na+ SO4-2 0.956 2.663e3 0 1.158e-2 0 -3.194e5 # ref. 3
SO4-2 Sr+2 3.1973 0 0 27e-3
-B2
Ca+2 Cl- -1.13 0 0 -0.0476 # ref. 3
Ca+2 OH- -5.72
Ca+2 SO4-2 -59.3 0 0 -0.443 -3.96e-6 # ref. 3
Fe+2 SO4-2 -42
HCO3- Na+ 8.22 0 0 -0.049 # ref. 3 new -analytic for calcite
Mg+2 SO4-2 -32.45 0 -3.236e3 21.812 -1.8859e-2 # ref. 3
Mn+2 SO4-2 -40
SO4-2 Sr+2 -54.24 0 0 -0.42
-C0
B(OH)4- Na+ 0.0114
Ba+2 Br- -0.0159576
Ba+2 Cl- -0.143 -114.5 # ref. 3
Br- Ca+2 -0.00257
Br- H+ 0.00827 0 0 -5.685E-5
Br- K+ -0.0018 0 0 -7.004E-5
Br- Li+ 0.0053 0 0 -2.813E-5
Br- Mg+2 0.00312
Br- Na+ 0.00116 0 0 -9.3E-5
Br- Sr+2 0.00122506
Ca+2 Cl- 1.4e-4 -57 -0.098 -7.83e-4 7.18e-7 # ref. 3
Ca+2 SO4-2 0.114 # ref. 3
Cl- Fe+2 -0.00860725
Cl- H+ 0.0008 0 0 6.213E-5
Cl- K+ -7.88e-4 91.27 0.58643 -1.298e-3 4.9567e-7 # ref. 3
Cl- Li+ 0.00359 0 0 -4.52E-5
Cl- Mg+2 0.00651 0 0 -2.5e-4 2.418e-7 # ref. 3
Cl- Mn+2 -0.0204972
Cl- Na+ 1.48e-3 -120.5 -0.2081 0 1.166e-7 11121 # ref. 3
Cl- Sr+2 -0.0013
CO3-2 K+ -0.0015
CO3-2 Na+ 0.0044
Fe+2 SO4-2 0.0209
H+ SO4-2 0.0438
HCO3- K+ -0.008
K+ OH- 0.0041
K+ SO4-2 8.18e-3 -625 -3.3 4.06e-3 # ref. 3
Li+ SO4-2 -0.00399338 0 0 -2.33345e-4
Mg+2 SO4-2 2.875e-2 0 -2.084 1.1428e-2 -8.228e-6 # ref. 3
Mn+2 SO4-2 0.01636
Na+ OH- 0.0044 0 0 -18.94E-5
Na+ SO4-2 3.418e-3 -384 0 -8.451e-4 0 5.177e4 # ref. 3
-THETA
B(OH)4- Cl- -0.065
B(OH)4- SO4-2 -0.012
B3O3(OH)4- Cl- 0.12
B3O3(OH)4- HCO3- -0.1
B3O3(OH)4- SO4-2 0.1
B4O5(OH)4-2 Cl- 0.074
B4O5(OH)4-2 HCO3- -0.087
B4O5(OH)4-2 SO4-2 0.12
Ba+2 Na+ 0.07 # ref. 3
Br- OH- -0.065
Ca+2 H+ 0.092
Ca+2 K+ -5.35e-3 0 0 3.08e-4 # ref. 3
Ca+2 Mg+2 0.007
Ca+2 Na+ 9.22e-2 0 0 -4.29e-4 1.21e-6 # ref. 3
Cl- CO3-2 -0.02
Cl- HCO3- 0.03
Cl- HSO4- -0.006
Cl- OH- -0.05
Cl- SO4-2 0.03 # ref. 3
CO3-2 OH- 0.1
CO3-2 SO4-2 0.02
H+ K+ 0.005
H+ Mg+2 0.1
H+ Na+ 0.036
HCO3- CO3-2 -0.04
HCO3- SO4-2 0.01
K+ Na+ -0.012
Mg+2 Na+ 0.07
Na+ Sr+2 0.051
OH- SO4-2 -0.013
-LAMDA
B(OH)3 Cl- 0.091
B(OH)3 K+ -0.14
B(OH)3 Na+ -0.097
B(OH)3 SO4-2 0.018
B3O3(OH)4- B(OH)3 -0.2
Ca+2 CO2 0.183
Ca+2 H4SiO4 0.238 # ref. 3
Cl- CO2 -0.005
Cl- H2Sg -0.005
Cl- (H2Sg)2 -0.005
CO2 CO2 -1.34e-2 348 0.803 # new VM("CO2"), CO2 solubilities at high P, 0 - 150<35>C
CO2 HSO4- -0.003
CO2 K+ 0.051
CO2 Mg+2 0.183
CO2 Na+ 0.085
CO2 SO4-2 0.075 # Rumpf and Maurer, 1993
H2Sg Na+ 0.1047 0 -0.0413 # Xia et al., 2000, Ind. Eng. Chem. Res. 39, 1064
H2Sg SO4-2 0 0 0.679
(H2Sg)2 Na+ 0.0123 0 0.256
H4SiO4 K+ 0.0298 # ref. 3
H4SiO4 Li+ 0.143 # ref. 3
H4SiO4 Mg+2 0.238 -1788 -9.023 0.0103 # ref. 3
H4SiO4 Na+ 0.0566 75.3 0.115 # ref. 3
H4SiO4 SO4-2 -0.085 0 0.28 -8.25e-4 # ref. 3
-ZETA
B(OH)3 Cl- H+ -0.0102
B(OH)3 Na+ SO4-2 0.046
Cl- H4SiO4 K+ -0.0153 # ref. 3
Cl- H4SiO4 Li+ -0.0196 # ref. 3
CO2 Na+ SO4-2 -0.015
H2Sg Cl- Na+ -0.0123 # Xia et al., 2000, Ind. Eng. Chem. Res. 39, 1064
H2Sg Na+ SO4-2 0.157
(H2Sg)2 Cl- Na+ 0.0119
(H2Sg)2 Na+ SO4-2 -0.167
-PSI
B(OH)4- Cl- Na+ -0.0073
B3O3(OH)4- Cl- Na+ -0.024
B4O5(OH)4-2 Cl- Na+ 0.026
Br- K+ Na+ -0.0022
Br- K+ OH- -0.014
Br- Na+ H+ -0.012
Br- Na+ OH- -0.018
Ca+2 Cl- H+ -0.015
Ca+2 Cl- K+ -0.025
Ca+2 Cl- Mg+2 -0.012
Ca+2 Cl- Na+ -1.48e-2 0 0 -5.2e-6 # ref. 3
Ca+2 Cl- OH- -0.025
Ca+2 Cl- SO4-2 -0.122 0 0 -1.21e-3 # ref. 3
Ca+2 K+ SO4-2 -0.0365 # ref. 3
Ca+2 Mg+2 SO4-2 0.024
Ca+2 Na+ SO4-2 -0.055 17.2 # ref. 3
Cl- Br- K+ 0
Cl- CO3-2 K+ 0.004
Cl- CO3-2 Na+ 0.0085
Cl- H+ K+ -0.011
Cl- H+ Mg+2 -0.011
Cl- H+ Na+ -0.004
Cl- HCO3- Mg+2 -0.096
Cl- HCO3- Na+ 0 # ref. 3 new -analytic for calcite
Cl- HSO4- H+ 0.013
Cl- HSO4- Na+ -0.006
Cl- K+ Mg+2 -0.022 -14.27 # ref. 3
Cl- K+ Na+ -0.0015 0 0 1.8e-5 # ref. 3
Cl- K+ OH- -0.006
Cl- K+ SO4-2 -1e-3 # ref. 3
Cl- Mg+2 MgOH+ 0.028
Cl- Mg+2 Na+ -0.012 -9.51 # ref. 3
Cl- Mg+2 SO4-2 -0.008 32.63 # ref. 3
Cl- Na+ OH- -0.006
Cl- Na+ SO4-2 0 # ref. 3
Cl- Na+ Sr+2 -0.0021
CO3-2 HCO3- K+ 0.012
CO3-2 HCO3- Na+ 0.002
CO3-2 K+ Na+ 0.003
CO3-2 K+ OH- -0.01
CO3-2 K+ SO4-2 -0.009
CO3-2 Na+ OH- -0.017
CO3-2 Na+ SO4-2 -0.005
H+ HSO4- K+ -0.0265
H+ HSO4- Mg+2 -0.0178
H+ HSO4- Na+ -0.0129
H+ K+ Br- -0.021
H+ K+ SO4-2 0.197
HCO3- K+ Na+ -0.003
HCO3- Mg+2 SO4-2 -0.161
HCO3- Na+ SO4-2 -0.005
HSO4- K+ SO4-2 -0.0677
HSO4- Mg+2 SO4-2 -0.0425
HSO4- Na+ SO4-2 -0.0094
K+ Mg+2 SO4-2 -0.048
K+ Na+ SO4-2 -0.01
K+ OH- SO4-2 -0.05
Mg+2 Na+ SO4-2 -0.015
Na+ OH- SO4-2 -0.009
EXCHANGE_MASTER_SPECIES
X X-
EXCHANGE_SPECIES
X- = X-
log_k 0
Na+ + X- = NaX
log_k 0
K+ + X- = KX
log_k 0.7
delta_h -4.3 # Jardine & Sparks, 1984
Li+ + X- = LiX
log_k -0.08
delta_h 1.4 # Merriam & Thomas, 1956
Ca+2 + 2 X- = CaX2
log_k 0.8
delta_h 7.2 # Van Bladel & Gheyl, 1980
Mg+2 + 2 X- = MgX2
log_k 0.6
delta_h 7.4 # Laudelout et al., 1968
Sr+2 + 2 X- = SrX2
log_k 0.91
delta_h 5.5 # Laudelout et al., 1968
Ba+2 + 2 X- = BaX2
log_k 0.91
delta_h 4.5 # Laudelout et al., 1968
Mn+2 + 2 X- = MnX2
log_k 0.52
Fe+2 + 2 X- = FeX2
log_k 0.44
SURFACE_MASTER_SPECIES
Hfo_s Hfo_sOH
Hfo_w Hfo_wOH
SURFACE_SPECIES
# All surface data from
# Dzombak and Morel, 1990
#
#
# Acid-base data from table 5.7
#
# strong binding site--Hfo_s,
Hfo_sOH = Hfo_sOH
log_k 0
Hfo_sOH + H+ = Hfo_sOH2+
log_k 7.29 # = pKa1,int
Hfo_sOH = Hfo_sO- + H+
log_k -8.93 # = -pKa2,int
# weak binding site--Hfo_w
Hfo_wOH = Hfo_wOH
log_k 0
Hfo_wOH + H+ = Hfo_wOH2+
log_k 7.29 # = pKa1,int
Hfo_wOH = Hfo_wO- + H+
log_k -8.93 # = -pKa2,int
###############################################
# CATIONS #
###############################################
#
# Cations from table 10.1 or 10.5
#
# Calcium
Hfo_sOH + Ca+2 = Hfo_sOHCa+2
log_k 4.97
Hfo_wOH + Ca+2 = Hfo_wOCa+ + H+
log_k -5.85
# Strontium
Hfo_sOH + Sr+2 = Hfo_sOHSr+2
log_k 5.01
Hfo_wOH + Sr+2 = Hfo_wOSr+ + H+
log_k -6.58
Hfo_wOH + Sr+2 + H2O = Hfo_wOSrOH + 2 H+
log_k -17.6
# Barium
Hfo_sOH + Ba+2 = Hfo_sOHBa+2
log_k 5.46
Hfo_wOH + Ba+2 = Hfo_wOBa+ + H+
log_k -7.2 # table 10.5
#
# Derived constants table 10.5
#
# Magnesium
Hfo_wOH + Mg+2 = Hfo_wOMg+ + H+
log_k -4.6
# Manganese
Hfo_sOH + Mn+2 = Hfo_sOMn+ + H+
log_k -0.4 # table 10.5
Hfo_wOH + Mn+2 = Hfo_wOMn+ + H+
log_k -3.5 # table 10.5
# Iron
# Hfo_sOH + Fe+2 = Hfo_sOFe+ + H+
# log_k 0.7 # LFER using table 10.5
# Hfo_wOH + Fe+2 = Hfo_wOFe+ + H+
# log_k -2.5 # LFER using table 10.5
# Iron, strong site: Appelo, Van der Weiden, Tournassat & Charlet, subm.
Hfo_sOH + Fe+2 = Hfo_sOFe+ + H+
log_k -0.95
# Iron, weak site: Liger et al., GCA 63, 2939, re-optimized for D&M
Hfo_wOH + Fe+2 = Hfo_wOFe+ + H+
log_k -2.98
Hfo_wOH + Fe+2 + H2O = Hfo_wOFeOH + 2 H+
log_k -11.55
###############################################
# ANIONS #
###############################################
#
# Anions from table 10.6
#
#
# Anions from table 10.7
#
# Borate
Hfo_wOH + B(OH)3 = Hfo_wH2BO3 + H2O
log_k 0.62
#
# Anions from table 10.8
#
# Sulfate
Hfo_wOH + SO4-2 + H+ = Hfo_wSO4- + H2O
log_k 7.78
Hfo_wOH + SO4-2 = Hfo_wOHSO4-2
log_k 0.79
#
# Carbonate: Van Geen et al., 1994 reoptimized for HFO
# 0.15 g HFO/L has 0.344 mM sites == 2 g of Van Geen's Goethite/L
#
Hfo_wOH + CO3-2 + H+ = Hfo_wCO3- + H2O
log_k 12.56
Hfo_wOH + CO3-2 + 2 H+ = Hfo_wHCO3 + H2O
log_k 20.62
#
# Silicate: Swedlund, P.J. and Webster, J.G., 1999. Water Research 33, 3413-3422.
#
Hfo_wOH + H4SiO4 = Hfo_wH3SiO4 + H2O; log_K 4.28
Hfo_wOH + H4SiO4 = Hfo_wH2SiO4- + H+ + H2O; log_K -3.22
Hfo_wOH + H4SiO4 = Hfo_wHSiO4-2 + 2 H+ + H2O; log_K -11.69
MEAN_GAMMAS
CaCl2 Ca+2 1 Cl- 2
CaSO4 Ca+2 1 SO4-2 1
CaCO3 Ca+2 1 CO3-2 1
Ca(OH)2 Ca+2 1 OH- 2
MgCl2 Mg+2 1 Cl- 2
MgSO4 Mg+2 1 SO4-2 1
MgCO3 Mg+2 1 CO3-2 1
Mg(OH)2 Mg+2 1 OH- 2
NaCl Na+ 1 Cl- 1
Na2SO4 Na+ 2 SO4-2 1
NaHCO3 Na+ 1 HCO3- 1
Na2CO3 Na+ 2 CO3-2 1
NaOH Na+ 1 OH- 1
KCl K+ 1 Cl- 1
K2SO4 K+ 2 SO4-2 1
HCO3 K+ 1 HCO3- 1
K2CO3 K+ 2 CO3-2 1
KOH K+ 1 OH- 1
HCl H+ 1 Cl- 1
H2SO4 H+ 2 SO4-2 1
HBr H+ 1 Br- 1
END
# For the reaction aA + bB = cC + dD,
# with delta_v = c*Vm(C) + d*Vm(D) - a*Vm(A) - b*Vm(B),
# PHREEQC adds the pressure term to log_k: -= delta_v * (P - 1) / (2.3RT).
# Vm(A) is volume of A, cm3/mol, P is pressure, atm, R is the gas constant, T is Kelvin.
# Gas-pressures and fugacity coefficients are calculated with Peng-Robinson's EOS.
# Binary interaction coefficients from Soreide and Whitson, 1992, FPE 77, 217 are
# hard-coded in calc_PR():
# kij CH4 CO2 H2S N2
# H2O 0.49 0.19 0.19 0.49
# =============================================================================================
# The molar volumes of solids are entered with
# -Vm vm cm3/mol
# vm is the molar volume, cm3/mol (default), but dm3/mol and m3/mol are permitted.
# Data for minerals' vm (= MW (g/mol) / rho (g/cm3)) are defined using rho from
# Deer, Howie and Zussman, The rock-forming minerals, Longman.
# --------------------
# Temperature- and pressure-dependent volumina of aqueous species are calculated with a Redlich-
# type equation (cf. Redlich and Meyer, Chem. Rev. 64, 221), from parameters entered with
# -Vm a1 a2 a3 a4 W a0 i1 i2 i3 i4
# The volume (cm3/mol) is
# Vm(T, pb, I) = 41.84 * (a1 * 0.1 + a2 * 100 / (2600 + pb) + a3 / (T - 228) +
# a4 * 1e4 / (2600 + pb) / (T - 228) - W * QBrn)
# + z^2 / 2 * Av * f(I^0.5)
# + (i1 + i2 / (T - 228) + i3 * (T - 228)) * I^i4
# Volumina at I = 0 are obtained using supcrt92 formulas (Johnson et al., 1992, CG 18, 899).
# 41.84 transforms cal/bar/mol into cm3/mol.
# pb is pressure in bar.
# W * QBrn is the energy of solvation, QBrn is the pressure dependence of the Born equation,
# W is fitted on measured solution densities.
# z is charge of the solute species.
# Av is the Debye-H<>ckel limiting slope (DH_AV in PHREEQC basic).
# a0 is the ion-size parameter in the extended Debye-H<>ckel equation:
# f(I^0.5) = I^0.5 / (1 + a0 * DH_B * I^0.5),
# a0 = -gamma x for cations, = 0 for anions.
# For details, consult ref. 1.
# =============================================================================================
# The viscosity is calculated with a (modified) Jones-Dole equation:
# viscos / viscos_0 = 1 + A Sum(0.5 z_i m_i) + fan (B_i m_i + D_i m_i n_i)
# Parameters are for calculating the B and D terms:
# -viscosity 9.35e-2 -8.31e-2 2.487e-2 4.49e-4 2.01e-2 1.570 0
# # b0 b1 b2 d1 d2 d3 tan
# z_i is absolute charge number, m_i is molality of i
# B_i = b0 + b1 exp(-b2 * tc)
# fan = (2 - tan V_i / V_Cl-), corrects for the volume of anions
# D_i = d1 + exp(-d2 tc)
# n_i = ((1 + fI)^d3 + ((z_i^2 + z_i) / 2 <20> m_i)d^3 / (2 + fI), fI is an ionic strength term.
# For details, consult ref. 5.
#
# ref. 1: Appelo, Parkhurst and Post, 2014. Geochim. Cosmochim. Acta 125, 49<34>67.
# ref. 2: Procedures from ref. 1 using data compiled by Lalibert<72>, 2009, J. Chem. Eng. Data 54, 1725.
# ref. 3: Appelo, 2015, Appl. Geochem. 55, 62<36>71.
# http://www.hydrochemistry.eu/pub/pitzer_db/appendix.zip contains example files
# for the high P,T Pitzer model and improvements for Calcite.
# ref. 4: Appelo, 2017, Cem. Concr. Res. 101, 102-113.
# ref. 5: Appelo and Parkhurst in prep., for parameters see subroutine viscosity in transport.cpp
#
# =============================================================================================
# It remains the responsibility of the user to check the calculated results, for example with
# measured solubilities as a function of (P, T).
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