Need help in modeling of corrosion of carbon steel bar in concrete by PHREEQC

[Sidol]

Dear Colleagues!

I am working on a long term geochemical degradation modeling of concrete. I use geochemical transport model built in PHREEQC in order to reach the goal. I need to modeling the corrosion of steel reinforcement bars of the concrete too, in order to predict possible corrosion induced cracking of concrete body. In the modelled volume I use a 6 mm diameter and 200 mm long cylindrical rebar. The only possibility is the kinetic way to model steel corrosion. I need help with the following questions:

1.: Does anyone have any data on specific surface area (A0) of carbon steel, or the cylindrical surface of the reinforcement can be used?

2.: I have to use to calculate the volume factor (A/V) in order to modeling corrosion of steel bar in kinetic way. What volume of solution should I use for this? Is this the volume of input solution (solution 0) or volume of pore solution (solution 1-n)?

3.: What is the appropriate method to calculate the changing of surface area of reinforcement during corrosion? I have found a formula: area = (m/m0)^2/3*A0 in Zhu & Anderson (2002, p. 240) which have been used for albite kinetic dissolution but the cylindrical reinforcement bar is not built up by small spherical or cubic particles. Can I use the corrosion rate and the geometry data of the cylindrical rebar during the calculation or is it too simple approximation?

Here is my code for corrosion kinetics of carbon steel. I use this currently:

Code: [Select]

KINETICS 2-9
Fe(cr,alpha)
    -formula  Fe  1
    -m        0.7968
    -m0       0.7968
    -parms    2.45e-011 4.9e-011 6.5e-011
    -tol      1e-008
-steps       1 in 0 steps # seconds
-step_divide 1
-runge_kutta 3
-bad_step_max 500
-cvode true
-cvode_steps 100
-cvode_order 5
INCREMENTAL_REACTIONS True
RATES
    Fe(cr,alpha)
-start
  1 REM a0 is surface area (cm2), simple surface of cylindrical rebar 6 mm diameter 200 mm long
  2 REM v is solution volume (cm3) (pore solution -> solution 1-10)
 10 a0 = 37.68
 20 v = 78.15
 30 sr_iron = SR("Fe(cr,alpha)")
 40 IF(M <= 0) THEN GOTO 90
 50 area = (M/M0)^(2/3)*a0
 60 IF (-LA("H+") >= 14) THEN rate_const = PARM(1)
 70 IF (-LA("H+") < 14) AND (-LA("H+") > 12) THEN rate_const = PARM(2)
 80 IF (-LA("H+") < 12) THEN rate_const = PARM(3)
 90 rate = (area/v)*rate_const*(1-sr_iron)
100 moles = rate*TIME
110 SAVE moles
-end

Thank You for Your help.

[dlparkhurst]

You will have to decide on surface area and rates of reaction.

My only comment is that if you are using TRANSPORT, the volume of solutions 0-ncells should be the same. They will be equal to the volume of solution 0 after "ncells" shifts in any event.

[Sidol]

Thank you for your answer.  The role of solution volume during transport is clearer now.
Could you clarify in more detail what do you mean about decide on surface area and rate of reaction?

[dlparkhurst]

I meant that I do not know the best rate expression or how you want to calculate or adjust the surface area(s) of the reactant(s). You will have to decide.

[John Mahoney]

In many acid rock drainage situations where pyrite is oxidized and if the pH remains near neutral there is significant evidence that rinds of ferric hydroxide armor the pyrite.  Then oxidation is controlled by diffusion of oxygen through the rind.  This is an alternative oxidation process, and in acid rock situations the theory is that it will slow the process. (There are some details I am skipping here as they are not germane to your issue.)    You need to think about the alternative oxidation reactions of your steel bars, and that the process may change as things develop.   What does the literature say?  Ferric hydroxides are apt to show some increase in volume around your cylinder. 

Unless you are dissolving a large amount of the phase I think the (m/m0)^0.67 term really will not matter.  I would just adjust the area of the cylinder as things proceed.  But again you probably will need to dissolve quite bit of the steel cylinder for this to really matter.   

[Sidol]

Thank You for Your answers, they are very useful.