Surface species specific dissolution of goethite_Kinetics

[Tao]

Dear all Phreeqc users,

Sorry in advance for possible naive questions on kinetic modeling, I'm quite new to kinetics since for long I have been working only in equilibrium reactions.
I built up a model that can successfully describe the sorption of fluoride ions on goethite sites, including singly and doubly coordinated ones. My next step is to simulate the detachment of surface complex for instance Goe_sF-0.5 to FeF+2 into solutions.
The batch data suggests a zero-order (0.35uM h-1) formation of Fe+3 at pH 3 and pF 3. I'm asking for some suggestions that can help incorporate RATE and KINETICS to simulate the dissolution process after the Fluoride binding.

I assume I need to add a reaction that describes the detachment of surface complexes Goe_sF-0.5, and then add a RATE and a KINETICS to predict this process. however, I have no idea where to start with, please help if you know :)

best regards,
TAO

Code: [Select]

PHASES
Fix_H+
    H+ = H+
    log_k     0

SURFACE_MASTER_SPECIES
    Goe_s         Goe_sOH-0.5 
    Goe_d         Goe_dOH     

SURFACE_SPECIES
Goe_sOH-0.5 = Goe_sOH-0.5
    log_k     0
Goe_dOH = Goe_dOH
    log_k     0
Goe_sOH-0.5 + H+ = Goe_sOH2+0.5
    log_k     9.1
Goe_dOH + H+ = Goe_dOH2+
    log_k     9.1
Goe_sOH-0.5 + Na+ = Goe_sOHNa+0.5
    log_k     -1
Goe_dOH + Na+ = Goe_dOHNa+
    log_k     -1
F- + Goe_sOH-0.5 + H+ = Goe_sF-0.5 + H2O
    log_k     9.6
F- + Goe_dOH + H+ = Goe_dF + H2O
    log_k     6.7
Goe_sF-0.5 = FeF+2
    log_k     9.6
    -no_check
    -mole_balance
END

SOLUTION 0
    temp      25
    pH        3
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001 charge
    Na        0.001
    -water    1 # kg
EQUILIBRIUM_PHASES 0
    Fix_H+    -3 HF        10
SURFACE 1
    -equilibrate with solution 0
    -sites DENSITY
    Goe_d      3.55      81        3
        -capacitance 2.3    1.07
    Goe_s      3.55
    -cd_music
SAVE surface 0
END

SOLUTION 1
    temp      25
    pH        3
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001 charge
    Na        0.001
    -water    1 # kg
USE surface 0
EQUILIBRIUM_PHASES 1
    Fix_H+    -3 HF        10
 end

RATES
    FeF_formation
-start
 1 k_L = parm(1)
10 L = mol("Goe_sF-0.5")
20 rate =  k_L * L
30 dS = rate * time
40 save dS
-end

SOLUTION 1
    temp      25
    pH        3
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001 charge
    Na        0.001
    -water    1 # kg
USE surface 1
EQUILIBRIUM_PHASES 1
    Fix_H+    -3 HF        10

KINETICS 1
FeF_formation
    -formula  FeF  1
    -m        0
    -m0       0
    -parms    0.0005
    -tol      1e-08
-steps       800000 in 10 steps # seconds
-step_divide 1
-runge_kutta 3
-bad_step_max 500
INCREMENTAL_REACTIONS true

USER_GRAPH 1
    -headings               time FeF
    -axis_titles            "Time / days" "FeF" ""
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
10 graph_x total_time / 86400
20 graph_y mol("FeF+2")
  -end
    -active                 true
END



[dlparkhurst]

Show me a balanced chemical reaction for what you want to model.

What is driving the reaction? or What is the equilibrium condition that the reaction will reach?

[Tao]

Hi dlparkhurst,

thanks for your reply. here below is the equilibrium code for fluoride sorption. The main surface species are found to be Goe_sF-0.5, and Goe_dF at high loadings, one is mononuclear monodentate and the another binuclear bidentate. my batch data at pH 3 and pF 3 shows a zero order kinetics as said above. however, this dissolution cannot be described as the equilibrium do.

Conventional dissolutions usually use a full formula as 'FeOOH + 3 H+ = Fe+3 + 2 H2O' which doesnt require molecular level information. here in my work, i intends to correlate the dissolution rate R_L to the amount of specific surface species concentration which can be derived from equilibrium model. for instance i guess R_L = k_s * C_Goe_sF-0.5 or  Goe_dF or both with a fraction factor. however it seems hard to write an equation that can describe the dessociation process that produces aqueous FeF+2.

simply are these questions:
1. how to write or where to find these surface dissolution reactions, and what inputs are necessary?
2. how to define the reaction rate as a function of a specific equilibrium species, which i assume is constant in a relatively short reaction time?

I would appreciate it if you could give me some examples or something you know close to the topic.

best regards,
Tao CHEN

Code: [Select]

PHASES
Fix_H+
    H+ = H+
    log_k     0

SURFACE_MASTER_SPECIES
    Goe_s         Goe_sOH-0.5 
    Goe_d         Goe_dOH     

SURFACE_SPECIES
Goe_sOH-0.5 = Goe_sOH-0.5
    log_k     0
Goe_dOH = Goe_dOH
    log_k     0
Goe_sOH-0.5 + H+ = Goe_sOH2+0.5
    log_k     9.1
    -cd_music 1 0 0 0 0
Goe_dOH + H+ = Goe_dOH2+
    log_k     9.1
    -cd_music 1 0 0 0 0
Goe_sOH-0.5 + Na+ = Goe_sOHNa+0.5
    log_k     -1
    -cd_music 0 0 1 0 0
Goe_dOH + Na+ = Goe_dOHNa+
    log_k     -1
    -cd_music 0 0 1 0 0
F- + Goe_sOH2+0.5 = Goe_sF-0.5 + H2O
    log_k     9.6
    -cd_music -1.4 0.4 0 0 0
F- + Goe_dOH2+ = Goe_dF + H2O
    log_k     6.7
    -cd_music -1.4 0.4 0 0 0
F- + Goe_sOH-0.5 + H+ = Goe_sF-0.5 + H2O
    log_k     9.6
    -cd_music 0.4 -0.4 0 0 0
F- + Goe_dOH + H+ = Goe_dF + H2O
    log_k     6.7
    -cd_music 0.4 -0.4 0 0 0
END

SOLUTION 0
    temp      25
    pH        2
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001 charge
    Na        0.001
    -water    1 # kg
EQUILIBRIUM_PHASES 0
    Fix_H+    -2 HF        10
SURFACE 1
    -equilibrate with solution 0
    -sites DENSITY
    Goe_d      3.55      81        3
        -capacitance 2.3    1.07
    Goe_s      3.55
    -cd_music
SAVE surface 1
END

USER_GRAPH 1
#   -headings               pH Fsys Fedissolve F- HF Fsorbed
    -headings               pH Fsorb GoeF Goe2F GoeOH GoeOH2
    -initial_solutions      false
    -connect_simulations    true
    -plot_concentration_vs  x
  -start
 10 graph_x -log10(mol("H+"))
#120 graph_y sys("F")
#122 graph_y TOT("F")
#125 graph_y mol("F-")
#126 graph_y mol("HF")
#130 graph_y surf("F","Goe")
131 graph_y surf("F","Goe")*1e6/(81*3)
140 graph_y mol("Goe_sF-0.5")*1e6/(81*3)
141 graph_y mol("Goe_dF")*1e6/(81*3)
145 graph_y mol("Goe_sOH-0.5")*1e6/(81*3)
150 graph_y mol("Goe_sOH2+0.5")*1e6/(81*3)
  -end
    -active                 true

SOLUTION 1
    temp      25
    pH        2
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001 charge
    Na        0.001
    -water    1 # kg
USE surface 1
EQUILIBRIUM_PHASES 1
    Fix_H+    -2 HF        10
 end

SOLUTION 1
    temp      25
    pH        3
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001 charge
    Na        0.001
    -water    1 # kg
USE surface 1
EQUILIBRIUM_PHASES 1
    Fix_H+    -3 HF        10
 end

SOLUTION 1
    temp      25
    pH        4
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001 charge
    Na        0.001
    -water    1 # kg
USE surface 1
EQUILIBRIUM_PHASES 1
    Fix_H+    -4 HF        10
 end

SOLUTION 1
    temp      25
    pH        5
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001 charge
    Na        0.001
    -water    1 # kg
USE surface 1
EQUILIBRIUM_PHASES 1
    Fix_H+    -5 HF        10
 end

SOLUTION 1
    temp      25
    pH        6
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001 charge
    Na        0.001
    -water    1 # kg
USE surface 1
EQUILIBRIUM_PHASES 1
    Fix_H+    -6 HF        10
 end

SOLUTION 1
    temp      25
    pH        7
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001
    Na        0.001 charge
    -water    1 # kg
USE surface 1
EQUILIBRIUM_PHASES 1
    Fix_H+    -7 HF        10
 end

SOLUTION 1
    temp      25
    pH        8
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001
    Na        0.001 charge
    -water    1 # kg
USE surface 1
EQUILIBRIUM_PHASES 1
    Fix_H+    -8 HF        10
 end

SOLUTION 1
    temp      25
    pH        9
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001
    Na        0.001 charge
    -water    1 # kg
USE surface 1
EQUILIBRIUM_PHASES 1
    Fix_H+    -9 HF        10
 end

SOLUTION 1
    temp      25
    pH        10
    pe        4
    redox     pe
    units     mol/kgw
    density   1
    F         0.001
    Na        0.001 charge
    -water    1 # kg
USE surface 1
EQUILIBRIUM_PHASES 1
    Fix_H+    -10 HF        10
 end


[dlparkhurst]

I will be out of contact for a while.

I will tell you this: you cannot add FeF as a REACTION or a KINETICS formula. The effect will be

Code: [Select]

H2O + FeF = Fe+2 + F- + OH- + 1/2H2(aq)

which will create a reducing environment.

Perhaps you want to link your Goe surface sites to an equilibrium phase Goethite, so that as goethite dissolves and precipitates (perhaps kinetically), the number of surface sites varies. Look at the description of the SURFACE keyword in the user's manual.

I do not know how to remove a single surface species kinetically. I think you would have to treat the entire surface calculation as a KINETIC reaction.

[Tao]

Appreciate your comments, a linking between a single surface complex and dissolution kinetics does not look that easy.

To do so, I presumably think it has to keep a constant site density and meanwhile a constant surface loading, even under kinetic conditions. it will thus make sense that the dissolution rate R_L, a function of surface complex concentration, becomes a zero-order fixed value given that the surface loadings are constant throughout the reaction. but this is only valid in a low ligand-solid ratio scenario, on the presumption that consumption of one surface site will result in the exposure of another equivalent site.

but the above is just theoretical thinking, I do not know how to code this.

appreciate again for your efforts.