Supplementary Material – Benchmark definition
Benchmark Problems for Reactive Transport Modeling of the Generation and Attenuation of Acid Rock Drainage
K. Ulrich Mayer1,*, Peter Alt-Epping2, Diederik Jacques3, Bhavna Arora4 and Carl I. Steefel4
1University of British Columbia, Dept. of Earth, Ocean and Atmospheric Sciences, 2207 Main Mall., Vancouver, BC, V6T 1Z4, Canada.
2Rock-Water Interaction Group, University of Bern, Institute of Geological Sciences, Baltzerstrasse 3, 3012 Bern, Switzerland
3Belgian Nuclear Research Centre SCK.CEN, Boeretang 200, Mol Belgium B-2400
4Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA
*Corresponding author: e-mail: , ph: ++1-604-822-1539
S.1. Boundary and Initial Conditions for Benchmarks ARD-B1 – ARD-B3
Table S.1: Boundary and initial conditions – Benchmark ARD-B1 - ARD-B3, total component concentrations in units of [mol L-1], unless otherwise noted
Components / Recharge / InitialAl3+ / 1.28 x 10-8 / 2.59 x 10-8
Ca2+ / 1.90 x 10-3 / 1.43 x 10-2
K+ / 8.70 x 10-3 / 9.00 x 10-3
CO32- / a3.17 x 10-4 / 2.49 x 10-3
Cl- / 1.14 x 10-4 / 1.14 x 10-3
H4SiO4 / 1.99 x 10-4 / 1.93 x 10-3
H+ (as pH) / 5.0 / 7.0
O2(aq) / b0.21 / c-2.5
SO42- (S(VI) + S(-II)) / charge / charge
Fe (Fe(II) + Fe(III)) / 5.0 x 10-7 / 1.45 x 10-4
a as pCO2 [atm]
b as pO2 [atm]
c as pe
Table S.2: Initial mineral volume fractions – Benchmark ARD-B1 – ARD-B3
Volume fraction [-]Primary Mineral / ARD-B1 / ARD-B2 / ARD-B3
Pyrite / 2 x 10-3 / 2 x 10-3 / 2 x 10-3
Calcite / - / 1.77 x 10-3 / 1.77 x 10-3
Gibbsite / - / 8.3 x 10-4 / -
K-feldspar / - / 2.68 x 10-2
Muscovite / - / 7.31 x 10-2
S.2: Geochemical database
Table S.3: Thermodynamic parameters for components
Component / Charge / Debye-Hückel constants / Molar weight[g mol-1] / Alkalinity factor
a / b
O2(aq) / 0.0 / 3.0 / 0.0 / 31.9998 / 0
Al3+ / 3.0 / 9.0 / 0.0 / 26.9815 / 0
CO32- / -2.0 / 5.4 / 0.0 / 60.0094 / 2
Ca2+ / 2.0 / 6.0 / 0.17 / 40.0800 / 0
Cl- / -1.0 / 3.0 / 0.01 / 35.4530 / 0
Fe2+ / 2.0 / 6.0 / 0.0 / 55.8470 / 0
H+ / 1.0 / 9.0 / 0.0 / 1.0080 / -1
K+ / 1.0 / 3.0 / 0.01 / 39.1020 / 0
SO42- / -2.0 / 4.0 / -0.04 / 96.0616 / 0
H4SiO4 / 0.0 / 0.0 / 0.0 / 96.1155 / 0
Table S.4: Thermodynamic parameters for complexed species
Aqueous complexation reaction / Log K / Charge / Debye-Hückel constants / Molar weight[g mol-1] / Alka-linity factor
a / b
OH- ↔ H2O – H+ / -13.9980 / -1.0 / 3.5 / 0.0 / 17.0074 / 1
CaHCO3+ ↔ Ca2+ + CO32- + H+ / 11.4400 / 1.0 / 6.0 / 0.0 / 101.0970 / 1
CaCO3(aq) ↔ Ca2+ + CO32- / 3.2200 / 0.0 / 0.0 / 0.0 / 100.0890 / 2
CaSO4(aq) ↔ Ca2+ + SO42- / 2.3090 / 0.0 / 0.0 / 0.0 / 136.1410 / 0
KSO4- ↔ K+ + SO42- / 0.8500 / -1.0 / 5.4 / 0.0 / 135.1630 / 0
AlOH2+ ↔ 3 Al3+ + H2O – H+ / -4.9900 / 2.0 / 5.4 / 0.0 / 43.9880 / 0
Al(OH)2+ ↔ 3 Al3+ + 2 H2O – 2 H+ / -10.1000 / 1.0 / 5.4 / 0.0 / 60.9960 / 0
Al(OH)4- ↔ 3 Al3+ + 4 H2O – 4 H+ / -22.7000 / -1.0 / 4.5 / 0.0 / 95.0110 / 0
AlSO4+ ↔ Al3+ + SO42- / 3.5000 / 1.0 / 4.5 / 0.0 / 123.0430 / 0
Al(SO4)2- ↔ Al3+ + 2 SO42- / 5.0000 / -1.0 / 4.5 / 0.0 / 219.1040 / 0
Al(OH)3(aq) ↔ Al3+ + 3 H2O – 3 H+ / -16.9000 / 0.0 / 0.0 / 0.0 / 78.0030 / 0
FeOH+ ↔ Fe2+ + H2O – H+ / -9.5000 / 1.0 / 5.0 / 0.0 / 72.8540 / 0
FeSO4(aq) ↔ Fe2+ + SO42- / 2.2500 / 0.0 / 0.0 / 0.0 / 151.9080 / 0
FeOH2+ ↔ Fe3+ + H2O – H+ / -2.1900 / 2.0 / 5.0 / 1.0 / 72.8540 / 0
FeSO4+ ↔ Fe3+ + SO42- / 4.0400 / 1.0 / 5.0 / 0.0 / 151.9080 / 0
Fe(OH)2+ ↔ Fe3+ + 2 H2O – 2 H+ / -5.6700 / 2.0 / 5.4 / 0.0 / 89.8610 / 0
FeOH3(aq) ↔ Fe3+ + 3 H2O – 3 H+ / -12.5600 / 0.0 / 0.0 / 0.0 / 106.8690 / 0
HCO3- ↔ CO32- + H+ / 10.3300 / -1.0 / 5.4 / 0.0 / 61.0170 / 1.0
H2CO3(aq) ↔ CO32- + 2 H+ / 16.6810 / 0.0 / 0.0 / 0.0 / 62.0250 / 0.0
HSO4- ↔ SO42- + H+ / 1.9870 / -1.0 / 4.5 / 0.0 / 97.0690 / 0.0
H3SiO4- ↔ H4SiO4 – H+ / -9.8300 / -1.0 / 4.0 / 0.0 / 95.1070 / 0.0
Table S.5: Mineral dissolution precipitation reactions and thermodynamic parameters
Primary minerals / Density[g cm-3] / Molar volume
[cm3 mol-1] / log Ksp
aPyrite / / 5.02 / 23.90 / 215.3
bCalcite / / 2.71 / 36.93 / -8.48
bGibbsite / / 2.35 / 33.19 / 8.11
cK-feldspar / / 2.57 / 108.30 / 0.08
cMuscovite / / 2.82 / 141.25 / 12.99
Secondary minerals / Density
[g cm-3] / Molar volume
[cm3 mol-1] / log Ksp
bFerrihydrite / / 4.37 / 23.99 / 4.89
bJarosite / / 3.20 / 154.63 / -9.21
bGypsum / / 2.32 / 74.21 / -4.58
cSilica (am) / / 2.65 / 22.67 / -2.71
a considered for ARD-B1 - ARD-B3
b considered for ARD-B2 and ARD-B3
c considered for ARD-B3
Table S.6: Kinetic parameters for mineral dissolution-precipitation reactions
Primary minerals / keff[mol dm-3 s-1] / Update of reaction rate
aPyrite / 3x10-10 / dEquation 15
bCalcite / 1x10-8 / dEquation 15
bGibbsite / 1x10-8 / Constant
cK-feldspar / dEquation 16 / dEquation 15
cMuscovite / dEquation 17 / dEquation 15
Secondary minerals / keff
[mol dm-3 s-1] / Update of reaction rate
bFerrihydrite / 1x10-8 / Constant
bJarosite / 1x10-8 / Constant
bGypsum / 1x10-8 / Constant
cSiO2(am) / 1x10-8 / Constant
a considered for ARD-B1 - ARD-B3
b considered for ARD-B2 and ARD-B3
c considered for ARD-B3
d refers to equations in manuscript
Table S.7: Thermodynamic parameters for gas exchange reactions
Gas exchange reaction / Log K[L atm mol-1] / Molar weight
[g mol-1]
CO2(g) ↔ CO32- + 2H+ - H2O / 18.1600 / 41.0100
O2(g) ↔ O2(aq) / 2.8980 / 101.0970
Table S.8: Thermodynamic parameters for redox equilibrium reactions
Redox equilibrium reaction / Log K / Charge / Debye-Hückel constants / Molar weight[g mol-1] / Alka-linity factor
a / b
Fe3+ ↔ Fe2+ + ¼ O2(aq) + H+ - ½ H2O / -8.4725 / 3.0 / 9.0 / 0.0 / 55.8470 / 0
HS- ↔ SO42- - 2O2(aq) + H+ / -138.3760 / -1.0 / 3.5 / 0.0 / 33.0720 / 0
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