Simple Mixing Chemistry Equilibria using LookupTables and PHREEQC
One of most common application of geochemical models is prediction of the effects of mixing solutions of different chemical compositions. This model is an example of how to incorporate PHREEQC geochemical calculations into a GoldSim model through the use of a "Lookup Table" element. In this approach, the Lookup Table element is constructed using water quality results from a series of PHREEQC model runs that encompass the range of compositions that might occur in the system.
The approach is applied to a scenario in which there is a combined surface and small amount of base flow from an acid rock drainage (ARD) source that mixes with a neutral pH water with moderate alkalinity in a pond.
The ARD surface flow is highly variable because it is a function of precipitation runoff whereas the neutral pH flow is constant representing a stream or pipe flow. The two solutions are mixed with Cell Pathway element producing a bulk solution composition. The bulk composition is out of equilibrium with various geochemical reactions. Hence, PHREEQC is used to mix and equilibrate the mixture. However, this mixing process is done outside of GoldSim by making a PHREEQC model run using PHREEQC's "Mix" keyword that calculates the effects of mixing two solutions and applying specific set of chemical equilibria. In this case, the Mix keyword is run 100 times such that each mixture represents 1% increments of the ARD flow mixed with the neutral pH flow. The following excerpt from the PHREEQC input file illustrates the approach for the Mix keyword block:
MIX 1
1 0.00
2 1.00
EQUILIBRIUM_PHASES
Gypsum 0 0
Calcite 0 0
CO2(g) -2.5 1
O2(g) -0.7 1
Fe(OH)3(a) 0 0
Jarosite(ss) 0 0
Gibbsite 0 0
USE Surface 1
END
MIX 2
1 0.01
2 0.99
EQUILIBRIUM_PHASES
Gypsum 0 0
Calcite 0 0
CO2(g) -2.5 1
O2(g) -0.7 1
Fe(OH)3(a) 0 0
Jarosite(ss) 0 0
Gibbsite 0 0
USE Surface 1
END
MIX 3
1 0.02
2 0.98
EQUILIBRIUM_PHASES
Gypsum 0 0
Calcite 0 0
CO2(g) -2.5 1
O2(g) -0.7 1
Fe(OH)3(a) 0 0
Jarosite(ss) 0 0
Gibbsite 0 0
USE Surface 1
END
MIX 4
1 0.03
2 0.97
EQUILIBRIUM_PHASES
Gypsum 0 0
Calcite 0 0
CO2(g) -2.5 1
O2(g) -0.7 1
Fe(OH)3(a) 0 0
Jarosite(ss) 0 0
Gibbsite 0 0
USE Surface 1
END
---
etc.
---
MIX 100
1 1.00
2 0.00
EQUILIBRIUM_PHASES
Gypsum 0 0
Calcite 0 0
CO2(g) -2.5 1
O2(g) -0.7 1
Fe(OH)3(a) 0 0
Jarosite(ss) 0 0
Gibbsite 0 0
USE Surface 1
END
This PHREEQC simulation will produce 100 equilibrated solution compositions that represent from 0 to 100% ARD flow. These solution compositions are imported in an Excel spreadsheet file named "phreec_mixfractions_table.xlsx", which is referenced in 2-D Lookup Table element in this GoldSim model called "TableOfMixFractionChemistries."
To determine the appropriate proportions to mix in the GoldSim simulation, an artificial species called "ARD_Tracer" is added to the species list. The ARD_Tracer concentration is set at 100 mg/L for the ARD flow and 0 mg/L for the neutral pH flow. This combination of concentrations allows the ARD_Tracer concentration to be used as index to retrieve the appropriate equilibrated mixture of ARD and neutral pH flows from the Lookup Table ("TableOfMixFractionChemistries").
This approach utilizes PHREEQC outside of GoldSim but provides a means to take into account chemical reactions as needed. The approach mixes two solutions with a 2-D Lookup table. Three solutions could be mixed with a 3-D Lookup Table in the same manner. Because the model relies on Lookup Tables, it results in GoldSim model that have very fast execution times, allowing analysis of the effects of uncertainties in flow rates on water chemistry to be examined. The disadvantage of the approach is that examination of the effects of different combinations of mineral-water and gas-water equilibria requires re-running PHREEQC and re-importing the results back in to the Lookup Table.
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