How kinetics works

[luicho]

Hi everyone,

I'm trying to understand how kinetics works in phreeqc, how it does the calculation.

Below is my code for the redox process of  Cr(VI) + Fe(0) -- Cr(III) + Fe(III), and in the literature said that it has a kinetics equation for the Cr(VI) reduction in the form of:

   dC/dt = -k * C^0.5 * H^0.5 * A,     where,
 
   k: is the overall reaction rate, (constant)
   C: is the concentration of Cr(VI),
   H: is the activity of the ion H+,
   A: is the superficial àrea of the iron. (constant)
 
 

 

SELECTED_OUTPUT
    -file                 selec4.out
    -reset                false
    -ph                   true
    -pe                   true
    -totals               Cr(6)  Fe
    -activities           H+
    -kinetic_reactants    Cromato



USER_GRAPH
   -axis_titles Horas "moles"
#   #-axis_scale x_axis 0 5
 -initial_solutions  true
-headings Cr(VI) Total_Cr(VI)
   -start
   10 graph_x total_time/3600
   20 graph_y  1000*tot("Cr(6)")
      30 graph_sy tot("Cr(3)")
      #20 graph_y  tot("Fe")
   -end
END


SOLUTION 1
    temp      25
    pH        7
    pe        4
    redox     pe
    units     mmol/kgw
    density   1
    Cr(6)     1
    Na        0 charge
    -water    1 # kg


SAVE solution 1
END
USE solution 1

RATES
   Cromato
-start
10 k = parm(1)      # overall reaction rate
20 A0 = parm(2)     # size of the grain of  Fe(0)
30 C = TOT("Cr(6)")  # concentration of Cr(VI)
40 rate= k * C^0.5 * act("H+")^0.5 * A0 
50 moles =  rate*time
60 save moles
-end




KINETICS 1
Cromato
    -formula  Fe  1
    -m        10
    -m0       1
    -parms    9.0833e-007 1
    -tol      1e-008
-steps       86400 in 10 steps # seconds
-step_divide 1
-runge_kutta 3
-bad_step_max 500

END


So, i don't understand how this mathematically works, I generate a output-file where I saw a "k_Cromato" and a "dk_Cromato", what's exactly are this values?

Thanks all for read this, any comments will be welcome!

Luis

[dlparkhurst]

The reaction in the KINETICS definition is the addition of Fe. As Fe is added, it is oxidized the iron is oxidized and Cr(6) is reduced, which is not defined explicitly; it follows from thermodynamic equilibrium between the Fe and Cr systems. So the increments of Fe are defined kinetically, but after each addition, PHREEQC calculates redox equilibrium.

K_cromato is the amount of the kinetic reactant the is present. Initially, it is set by the -m parameter in KINETICS. As the reaction proceeds, the amount of reactant may increase or decrease depending on the sign of the SAVEd quantity in RATES A negative save quantity (frequently "SAVE moles") causes K_cromato to increase and a positive save quantity causes K_cromato to decrease. dk_cromato is the change for the current reaction step.

[luicho]

Thanks Mr. Parkhurst, I finally understand how it works. Thanks so much!

[luicho]

Can "equilibrium_phases" work together with "kinetics" in a way that providing information about the precipitation as well as the kinetics reaction is taking along?

Because if I just add this part of code to the model posted above,

EQUILIBRIUM_PHASES 1
    Cr_hydroxide 0 0

It seems that just ignore that part and I want to know at what time it will form a precipitate.

[dlparkhurst]

Perhaps the solution never becomes supersaturated with Cr_hydroxide. Check the saturation indices for Cr_hydroxide through the course of the kinetic reaction.

[luicho]

Hello David,

I see, I'll look at the SI of the elements with which I have interest.

Thanks.

[luicho]

So, If I want to modificate the stoichiometric equation, perhaps this:

If I would like to simulate this stoichiometry equations, like:

- Cr2O7-2 + 2Fe0 + 14H+ ---> 2Cr3+ + 2Fe3+ + 7H2O ... (1)

and the kinetics equation is:

-- dC/dt = -K* C* (H^0.31); where C is the concentration of Cr+6
                                                    H is the concentration of H+,
                                                    K is a constant,
So, Is this code fine to do this job?.
------------------------------------------------------------------------
RATES
Cromato
-start
10 k = parm(1) # Constant reaction,
20 C = TOT("Cr(6)")
40 rate= k * C * act("H+")^0.31
50 moles = rate*time
60 save moles
-end

KINETICS 1
Cromato
-formula Fe 2 # I think the number "2" is the stoichiometry of eq (1)
-parms 9.0833e-007 # The value of K
-tol 1e-008
-steps 86400 in 10 steps # seconds
-step_divide 1
-runge_kutta 3
-bad_step_max 500

---------------------------

Thanks,

Luis

[dlparkhurst]

Depends, if C is the total concentration of Cr in valence 6 state (TOT("Cr(6"))), then the Fe coefficient should be 1 in -formula. If C is the concentration of Cr2O7-2 (MOL("Cr2O7-2")), then I think it should be -formula Fe 2.

[luicho]

Hello Mr. Parkhurst,

C is the Tot("Cr(6)"), so in the coefficient should be 1, right? Even though the stoichiometric formula says 2Fe(0)?

That because I need two moles of Cr(VI) ( because is Cr2O7-2) to reduce 2 moles of Fe(0)?

[dlparkhurst]

If C is total Cr(6), then dC/dt is the change of Cr(6) per time. You are saying it is dCr2O7-2/dt = -K* Cr(6) * (H^0.31), but suit yourself.