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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-9 838 4.02 -1.836 0.415 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 tracer diffusion.
# For SC, Dw(TK) *= (viscos_0_tc / viscos)^visc (visc = 0.415 for H+)
# a3 > 5 or a3 = 0 or not defined ? ka = DH_B * a * (1 + (vm - v0))^a2 * mu^0.5, in Onsager-Falkenhagen eqn. (For H+, the reference ion, vm = v0 = 0, a *= (1 + mu)^a2.)
# 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-9 149 0.805 1.961 1e-9 0.7876
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 -6.98e-2 -0.141 1.78e-2 0.159 7.76e-3 6.25e-2 0.859
-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 -2.26e-2 0.106 2.184e-2 -3.2e-3 0 0.4082 -1.634 # < 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
-viscosity 1.15e-2 9.82e-2 3.59e-2 0 0 0 0.266
-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 -40.0
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
-LAMBDA
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
GAS_BINARY_PARAMETERS
H2O(g) CO2(g) 0.19
H2O(g) H2S(g) 0.19
H2O(g) H2Sg(g) 0.19
H2O(g) CH4(g) 0.49
H2O(g) Mtg(g) 0.49
H2O(g) Methane(g) 0.49
H2O(g) N2(g) 0.49
H2O(g) Ntg(g) 0.49
H2O(g) Ethane(g) 0.49
H2O(g) Propane(g) 0.55
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.
# These 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
# but are overwritten by the data block GAS_BINARY_PARAMETERS of this file.
# =============================================================================================
# 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 * Sum(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 = (I^d3 * (1 + fI) + ((z_i^2 + z_i) / 2 <20> m_i)^d3) / (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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