inverse mass-balance modeling versus “forward modeling” - ndsu.pptVIP

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inverse mass-balance modeling versus “forward modeling” - ndsu.ppt

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inverse mass-balance modeling versus “forward modeling” - ndsu

Inverse Mass-Balance Modeling versus “Forward Modeling” * How much calcite precipitates? 2% CO2 atm CO2 Forward Approach What is the strategy? What data do you need? What assumptions do you need to make? Inverse Approach? Limestone 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 Well 1 Well 2 Inverse modeling is applicable when: Waters are evolutionary! Well 1 Well 2 No mixing. (initial water may be formed by mixing two waters) OK No OK 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) 2% CO2 atm CO2 How much calcite precipitates? Initial Solution? Final Solution ?(mg/kg) ? ?(mg/kg) ? Na 12 4 Ca 49 11 Mg 3 3 Cl 12 17 HCO3- 104 15 Sierra Nevada Spring CompositionsGarrels and Mackenzie (1967) ? ? Halite NaCl Gypsum CaSO4 CO2 gas CO2 Calcite CaCO3 Silica SiO2 Biotite KMg3AlSi3O10(OH)2 Plagioclase An38 Na0.62Ca0.38Al1.38Si2.62 Kaolinite Al2Si2O5(OH)4 Ca-Montmorillonite Ca0.17Al2.33Si3.67O10(OH)2 .016 .015 .427 .115 0 .014 .175 -.033 -.081 mass transfers (mmol/kg water) Sierra Nevada Spring CompositionsGarrels and Mackenzie (1967) Ephemeral Spring Perennial Spring 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