KINETICS and REACTION in the context of pyrite oxidation

[emkau]

Dear Mr. Parkhurst,
I do have a question regarding KINETICS and REACTION in the context of pyrite oxidation.

I have code simulating pyrite oxidation and O2 consumption with a rates equation after Williamson and Rimstidt (1994) in a simple batch model (partially adopted from Battistel et al. 2019).

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SOLUTION 1     
   temp   20
   pH   6                 
   units   mmol/l
   O(0)   0.52
   Na   5   
   Cl   5
   -water  0.02

GAS_PHASE 1         
   -fixed_volume
   -equilibrate with solution 1
   -pressure    1
   -volume 0.0068   
   -temperature   20
   O2(g)

KINETICS 1
Pyrite
   -formula   FeS2
   -m0      0.008   
   -parms      47
   -steps      720000 in 200 steps
INCREMENTAL_REACTIONS True   

RATES
Pyrite
-start
 10 A=parm(1) * m0
 20 if SI("Pyrite") > 0 then goto 100
 30 fH = mol("H+")
 50 rO2 = 10^-8.19 * mol("O2")^0.5 * fH^-0.11
 90 rate = A * (m/m0)^0.67 * (rO2) * (1 - SR("Pyrite"))
 100 save rate * time
 -end
END
Now IŽd like to receive the result (chemical composition after last rate step) with a simple model without kinetics, using REACTION or EQUILIBRIUM_PHASES.
Therefore i used the following code:

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SOLUTION 1         
   temp   20
   pH   6                 
   units   mmol/l
   O(0)   0.52
   Na   5   
   Cl   5
   -water  0.02

GAS_PHASE 1     
   -fixed_volume
   -equilibrate with solution 1
   -pressure    1   
   -volume 0.0068     
   -temperature   20
   O2(g)

REACTION
   FeS2      1   
   0.008
However, the results are quite different. In the second model, more pyrite is being oxidized, although the amount of available oxygen should be the same. Probably its my lack of knowledge about the KINETICS and RATES mechanism and iŽd like to understand what I did wrong here.Thank you for your time.

GreetingsE. Kau

[dlparkhurst]

In the first calculation, SOLUTION 1 has 0.02 kg water and 1.040e-05 mole of O(0), and the total number of moles of O2(aq) is 5.2e-6 [1.04e-5/2, where 2 is the number of moles of O(0) in O2(aq)]. That corresponds to a molality of 2.6e-4 of O2(aq) [1.04e-5/0.2/2, ]  The GAS_PHASE is required to be in equilibrium with that molality/activity of O2(aq). (Note that when you equilibrate the gas phase with the solution, the initial partial pressure makes no difference; it is the activity of O2 in the solution that determines the amount of O2(g) in the gas phase.) The result of that calculation is in this part of the output:

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--------------------------------------------------------
Beginning of initial gas_phase-composition calculations.
--------------------------------------------------------

Gas_Phase 1.

-----------------------------------Gas phase-----------------------------------

Total pressure:  0.19      atmospheres
    Gas volume:   6.80e-03 liters
  Molar volume:   1.29e+02 liters/mole

                                                        Moles in gas
                                            ----------------------------------
Component                log P           P     Initial       Final       Delta

O2(g)                    -0.73   1.862e-01   5.263e-05   5.263e-05   0.000e+00


So the partial pressure of O2 in the gas phase is set to 0.19 to be in equilibrium with the solution. In turn, you have 5.263e-5 moles of O2(g) in the gas phase (gas volume was set to 6.8e-3). So, the total number of moles of O2 in your system is the sum of the dissolved (5.2e-6) plus the gas (5.2e-5) equals 5.3e-5 moles.

The KINETIC reaction stops when O2 in the water becomes small according to the rate expression. I'm not going to work out the stoichiometry of oxygen to pyrite, but it ends up dissolving 5.2e-5 moles of pyrite. The saturation index of pyrite is still undersaturated, even with only a small amount of oxygen present.

Your second calculation has the same number of moles of O2(aq) and O2(g), but you force 0.008 moles of pyrite to dissolve. That consumes all of the O2 and generates a lot of S(-2), so the solution is way supersaturated with pyrite.

I'd suggest you add EQUILIBRIUM_PHASES with pyrite in place of KINETICS or REACTION to see where the equilibrium with pyrite would be.