1. Inverse Mass-Balance Modeling versus “Forward Modeling” How much calcite precipitates? 2% CO 2 atm CO 2 Forward Approach What is the strategy? What data do you need? What assumptions do you need to make? Inverse Approach? Limestone

2. Solution to Solid (precipitation, exchange) Solid to Solution (dissolution, exchange) gases, water Final Solution Initial Solution Need to Know Initial Solution Final Solution Reacting Phases

3. Well 1 Well 2 Inverse modeling is applicable when: Waters are evolutionary!

4. Well 1 Well 2 No mixing. (initial water may be formed by mixing two waters) OK No OK

5. 2x + 3y -2z = 3 x + 3y - z = 2 3x + 2y + 5z = 7 high school algebra always looking for n equations with n unknowns Variables = Constraints (elements, electrons, isotopes) Equations are the mineral reactions. How we do the mass balance (the very short version)

6. 2% CO 2 atm CO 2 How much calcite precipitates? Initial Solution Final Solution (mg/kg) Na124 Ca4911 Mg33 Cl1217 HCO 3 - 10415

7. Sierra Nevada Spring Compositions Garrels and Mackenzie (1967) "Halite"NaCl "Gypsum"CaSO 4 CO2 gasCO 2 CalciteCaCO 3 SilicaSiO 2 BiotiteKMg 3 AlSi 3 O 10 (OH) 2 Plagioclase An 38 Na 0.62 Ca 0.38 Al 1.38 Si 2.62 KaoliniteAl 2 Si 2 O 5 (OH) 4 Ca-MontmorilloniteCa 0.17 Al 2.33 Si 3.67 O 10 (OH) 2.016.015.427.115 0.014.175 -.033 -.081 mass transfers (mmol/kg water)

8. Sierra Nevada Spring Compositions Garrels and Mackenzie (1967) Ephemeral Spring Perennial Spring

9. SOLUTION 1 Ephemeral Springs temp 25 pH 6.2 pe 4 redox pe units mmol/kgw density 1 Ca 0.078 Cl 0.014 K 0.028 Mg 0.029 Na 0.134 S(6) 0.01 Si 0.273 Alkalinity 0.328 -water 1 # kg SOLUTION 2 Perennial Springs temp 25 pH 6.8 pe 4 redox pe units mmol/kgw density 1 Ca 0.41 Cl 0.03 K 0.04 Mg 0.071 Na 0.259 S(6) 0.025 Si 0.41 Alkalinity 0.895 -water 1 # kg

13. Always as dissolution Thermo data

15. Na 0.62 Ca 0.38 Al 1.38 Si 2.62 O 8 + 5.52H + + 2.48H 2 O = 1.38Al +3 + 0.38Ca +2 + 2.62H 4 SiO 4 + 0.62Na + Plagioclase (An 38 ) KMg 3 AlSi 3 O 10 (OH) 2 Biotite ?

17. Phase mole transfers: Minimum Maximum Halite 1.600e-005 1.490e-005 1.710e-005 NaCl Gypsum 1.500e-005 1.412e-005 1.587e-005 CaSO4:2H2O Kaolinite -3.316e-005 -5.381e-005 -1.223e-005 Al2Si2O5(OH)4 Ca-Montmorillon -8.269e-005 -1.099e-004 -5.618e-005 Ca0.165Al2.33Si3.67O10(OH)2 CO2(g) 2.951e-004 2.392e-004 3.563e-004 CO2 Calcite 1.216e-004 1.007e-004 1.279e-004 CaCO3 Biotite 1.370e-005 1.317e-005 1.370e-005 KMg3AlSi3O10(OH)2 Plag(An38) 1.777e-004 1.629e-004 1.934e-004 Na0.62Ca0.38Al1.38Si2.62O8 Phase mole transfers: Minimum Maximum Halite 1.600e-005 1.490e-005 1.710e-005 NaCl Gypsum 1.500e-005 1.412e-005 1.587e-005 CaSO4:2H2O Ca-Montmorillon -1.112e-004 -1.204e-004 -1.024e-004 Ca0.165Al2.33Si3.67O10(OH)2 CO2(g) 2.904e-004 2.358e-004 3.503e-004 CO2 Calcite 1.262e-004 1.067e-004 1.313e-004 CaCO3 Chalcedony 3.814e-005 1.407e-005 6.189e-005 SiO2 Biotite 1.370e-005 1.317e-005 1.370e-005 KMg3AlSi3O10(OH)2 Plag(An38) 1.777e-004 1.629e-004 1.934e-004 Na0.62Ca0.38Al1.38Si2.62O8 Phase mole transfers: Minimum Maximum Halite 1.600e-005 1.490e-005 1.710e-005 NaCl Gypsum 1.500e-005 1.412e-005 1.587e-005 CaSO4:2H2O Kaolinite -1.295e-004 -1.403e-004 -1.193e-004 Al2Si2O5(OH)4 CO2(g) 3.088e-004 2.527e-004 3.702e-004 CO2 Calcite 1.079e-004 8.680e-005 1.144e-004 CaCO3 Chalcedony -1.108e-004 -1.473e-004 -7.528e-005 SiO2 Biotite 1.370e-005 1.317e-005 1.370e-005 KMg3AlSi3O10(OH)2 Plag(An38) 1.777e-004 1.629e-004 1.934e-004 Na0.62Ca0.38Al1.38Si2.62O8 #1 #2 #3

18. SOLOUTION 2 Perennial Spring FINAL Phase SI log IAP log KT Anhydrite -3.99 -8.35 -4.36 CaSO4 Aragonite -1.92 -10.26 -8.34 CaCO3 Calcite -1.78 -10.26 -8.48 CaCO3 Chalcedony 0.16 -3.39 -3.55 SiO2 Chrysotile -10.85 21.35 32.20 Mg3Si2O5(OH)4 CO2(g) -2.05 -20.20 -18.15 CO2 Dolomite -3.99 -21.08 -17.09 CaMg(CO3)2 Gypsum -3.77 -8.35 -4.58 CaSO4:2H2O H2(g) -21.60 -21.60 0.00 H2 H2O(g) -1.51 -0.00 1.51 H2O Halite -9.73 -8.15 1.58 NaCl O2(g) -39.92 43.20 83.12 O2 Quartz 0.59 -3.39 -3.98 SiO2 Sepiolite -7.17 8.59 15.76 Mg2Si3O7.5OH:3H2O Sepiolite(d) -10.07 8.59 18.66 Mg2Si3O7.5OH:3H2O SiO2(a) -0.68 -3.39 -2.71 SiO2 Talc -6.82 14.58 21.40 Mg3Si4O10(OH)2

19. Phase mole transfers: Minimum Maximum Halite 1.600e-005 1.490e-005 1.710e-005 NaCl Gypsum 1.500e-005 1.412e-005 1.587e-005 CaSO4:2H2O Kaolinite -3.316e-005 -5.381e-005 -1.223e-005 Al2Si2O5(OH)4 Ca-Montmorillon -8.269e-005 -1.099e-004 -5.618e-005 Ca0.165Al2.33Si3.67O10(OH)2 CO2(g) 2.951e-004 2.392e-004 3.563e-004 CO2 Calcite 1.216e-004 1.007e-004 1.279e-004 CaCO3 Biotite 1.370e-005 1.317e-005 1.370e-005 KMg3AlSi3O10(OH)2 Plag(An38) 1.777e-004 1.629e-004 1.934e-004 Na0.62Ca0.38Al1.38Si2.62O8 Phase mole transfers: Minimum Maximum Halite 1.600e-005 1.490e-005 1.710e-005 NaCl Gypsum 1.500e-005 1.412e-005 1.587e-005 CaSO4:2H2O Ca-Montmorillon -1.112e-004 -1.204e-004 -1.024e-004 Ca0.165Al2.33Si3.67O10(OH)2 CO2(g) 2.904e-004 2.358e-004 3.503e-004 CO2 Calcite 1.262e-004 1.067e-004 1.313e-004 CaCO3 Chalcedony 3.814e-005 1.407e-005 6.189e-005 SiO2 Biotite 1.370e-005 1.317e-005 1.370e-005 KMg3AlSi3O10(OH)2 Plag(An38) 1.777e-004 1.629e-004 1.934e-004 Na0.62Ca0.38Al1.38Si2.62O8 Phase mole transfers: Minimum Maximum Halite 1.600e-005 1.490e-005 1.710e-005 NaCl Gypsum 1.500e-005 1.412e-005 1.587e-005 CaSO4:2H2O Kaolinite -1.295e-004 -1.403e-004 -1.193e-004 Al2Si2O5(OH)4 CO2(g) 3.088e-004 2.527e-004 3.702e-004 CO2 Calcite 1.079e-004 8.680e-005 1.144e-004 CaCO3 Chalcedony -1.108e-004 -1.473e-004 -7.528e-005 SiO2 Biotite 1.370e-005 1.317e-005 1.370e-005 KMg3AlSi3O10(OH)2 Plag(An38) 1.777e-004 1.629e-004 1.934e-004 Na0.62Ca0.38Al1.38Si2.62O8 #1 #2 #3

20. "Halite"NaCl "Gypsum"CaSO 4 CO2 gasCO 2 CalciteCaCO 3 SilicaSiO 2 BiotiteKMg 3 AlSi 3 O 10 (OH) 2 Plagioclase An 38 Na 0.62 Ca 0.38 Al 1.38 Si 2.62 KaoliniteAl 2 Si 2 O 5 (OH) 4 Ca-MontmorilloniteCa 0.17 Al 2.33 Si 3.67 O 10 (OH) 2 biotite dissolution vermiculite precipitation This would allow for K + release by Fe2+ oxidation in the biotite albite NaAlSi 3 O 8 anorthite CaAl 2 Si 2 O 8 This would allow variable plagioclase composition, but needs to be near An 25 Evaporative Concentration? Deep Brine?

22. How do you determine the mineralogy? Thin Section and use an ion probe or a SEM with EDX Mineralogy and composition of specific minerals. Poor job of fine grained secondary phases such as clays and oxy-hydroxides X-ray diffraction Gives mineralogy, including fine grained phases and clays. Does not give the specific mineral compositions. Geologic/Hydrologic Information A good guess.

23. Snowmelt Perennial Spring Ephemeral Spring

24. 24Sierra Nevada Spring Compositions Garrels and Mackenzie (1967) "Halite"NaCl "Gypsum"CaSO 4 CO2 gasCO 2 CalciteCaCO 3 SilicaSiO 2 BiotiteKMg 3 AlSi 3 O 10 (OH) 2 Plagioclase An 38 Na 0.62 Ca 0.38 Al 1.38 Si 2.62 KaoliniteAl 2 Si 2 O 5 (OH) 4 Ca-MontmorilloniteCa 0.17 Al 2.33 Si 3.67 O 10 (OH) 2 Problem: Can the Ephemeral Springs be the result of weathering in the soil zone?

25. INVERSE_MODELING 1 -solutions 3 1 -uncertainty 0.05 0.05 -phases Kaolinite Ca-Montmorillonite CO2(g) Plag(An38) SiO2(a) Gypsum K-feldspar Biotite -tolerance 1e-010 -mineral_water true PHASES Plag(An38) Na0.62Ca0.38Al1.38Si2.62O8 + 5.52H+ + 2.48H2O = 1.38Al+3 + 0.38Ca+2 + 2.62H4SiO4 + 0.62Na+ log_k 0 Biotite KMg3AlSi3O10(OH)2 + 6H+ + 4H2O = Al(OH)4- + 3H4SiO4 + K+ + 3Mg+2log_k 0 END SOLUTION 1 Ephemeral Springs temp 25 pH 6.2 pe 4 redox pe units mmol/kgw density 1 Ca 0.078 Cl 0.014 K 0.028 Mg 0.029 Na 0.134 S(6) 0.01 Si 0.273 Alkalinity 0.328 -water 1 # kg SOLUTION 3 Precipitation temp 25 pH 5.8 pe 4 redox pe units umol/l density 1 Na 0.11 Ca 0.068 Mg 0.022 K 0.02 S(6) 0.01 Cl 0.013 Si 0.27 Alkalinity 0.314 -water 1 # kg No halite or calcite. Add K-feldspar.

26. Phase mole transfers: Minimum Maximum Kaolinite -4.796e-005 0.000e+000 0.000e+000 Al2Si2O5(OH)4 Ca-Montmorillon -9.511e-005 0.000e+000 0.000e+000 Ca0.165Al2.33Si3.67O10(OH)2 CO2(g) 7.739e-004 0.000e+000 0.000e+000 CO2 Plag(An38) 2.098e-004 0.000e+000 0.000e+000 Na0.62Ca0.38Al1.38Si2.62O8 SiO2(a) 8.404e-005 0.000e+000 0.000e+000 SiO2 Gypsum 9.990e-006 0.000e+000 0.000e+000 CaSO4:2H2O K-feldspar 1.832e-005 0.000e+000 0.000e+000 KAlSi3O8 Biotite 9.659e-006 0.000e+000 0.000e+000 KMg3AlSi3O10(OH)2 No halite or calcite. How would you get these in the soil? Add K-feldspar. That makes sense. But….Gypsum? There is something we are missing with SO 4

27. Isotopes -isotopes 13C 34S PHREEQC treats each isotope as a separate component. Calcite is no longer CaCO 3 it is now: CaC 12.999 C 13.001 O 3 PHREEQC does NOT handle fractionation processes. NETPATH handles fractionations, but does not allow uncertainty in the concentrations measurements.

28. Mixing Use -Mix to make a starting solution, and use this as the initial solution.

29. -balancesused to force balancing of an element not in the solid phases For example, Cl - to quantify evaporation in a soil. Evaporation - include H 2 O as a heterogeneous phase “precipitation” of H 2 O = evaporation solid solutions -use a mixture of the end members individually Olivine MgSiO 4 FeSiO 4 Mg-calciteMgCO 3 CaCO 3

33. No Way

35. Suggestions: Try to only change one thing at a time. The solid phases are important. It helps to look at the solids! Many minerals are messy, but the variations in composition can be important. The model results will only be as reliable as your understanding of the hydrochemical system.