The methodologies used to predict the oxidation rate in Magnox reactors are based on work by Standring28 as discussed below:

Weight of TO2 in the = /273

pores of 1g of graphite P0 14.7 T [

where P (psi) is the gas pressure, T (K) the tem­perature, and p0 is the density of CO2 at standard conditions for temperature and pressure (STP) (gcm— ). The dose rate to the graphite can then be given in watts as follows:

P 273

Dose rate to graphite = eDp0 — — t W [19]

 

Ct A

 

[24]

 

g0t

 

This equation yields higher weight loss than the constant dose rate equation. This approach was used to design the early Magnox stations. However, as higher weight loss data became available from the operating Magnox stations, it was found necessary to modify the rela­tionship to account for the pore distribution with increasing oxidation.

 

4.11.7.7 Weight Loss Prediction in Inhibited Coolant It had not been possible to regularly add CH4 as an inhibitor to the coolant in the Magnox reactors because of concerns regarding the metallic compo­nents in the coolant circuit. However, the higher rated AGRs were designed with this in mind by selecting denser graphite and adding CH4 gas as an oxidation inhibitor. The addition of an inhibitor causes the process of radiolytic weight loss to be more complex than that for Magnox reactors as the oxidation rate becomes a com­plex function of the coolant gas composition. This is because gas composition, and hence, graphite oxidation rate, is not uniform within the moderator bricks and keys as CH4 is destroyed by radiolysis and may thus be depleted in the brick interior. In addition, methane destruction gives rise to the formation of carbon

 

where D (W g—1 s—1) is the ‘energy deposition rate’ or ‘dose rate’ and e is the OPV (cm3 g—1). This reasoning can be taken further to give

 

Percentage initial oxidation rate, g0

 

% per year [20

 

145

 

Standring and Ashton29 measured the OPV and CPV in PGA as a function of weight loss (Figure 11). In the specimens they examined, there appeared to be a small amount of pores which opened rapidly before the pore volume increased linearly as a func­tion of weight loss over the range of the data. To account for this behavior, they modified eqn [20] by defining an effective OPV as ‘ee’:

 

g0 = 145 % per year [21 ]

monoxide and moisture which may be higher in the brick interior. Graphite oxidation forms carbon mon­oxide, thereby further increasing CO levels in the brick interior. These destruction and formation processes are gas composition dependent and the flow rates of these gases within the porous structure are dependent upon graphite diffusivity and permeability values which change with graphite weight loss.

The exact mechanism of radiolysis in a CH4- inhibited coolant is complex and the radicals are disputed. However, from a practical point of view the mechanisms for oxidation and inhibition can be considered as given below:

In the gas phase

ionizing radiation

CO2 ———————- CO + O* [IV]

CO + O* ! CO2 [V]

CH4 ! P [vi]

where O* is the activated oxidizing species formed by radiolysis of CO2 and P is a protective species formed from CH4 oxidation.

At the graphite surface (mainly internal porosity),

O* + C! CO [VII]

O* + P! OP [VIII]

where OP is the deactivated gaseous product of CH4 destruction.

An altogether more satisfactory explanation and model for the effect of pore structure on corrosion in gas mixtures containing carbon monoxide, CH4, and

water was developed by Best and Wood30 and Best et a/.,26 who gave a relationship for G_c with respect to a pore structure parameter F and to P, the proba­bility of graphite gasification resulting from species which reach the pore surface:

G-C = 2.5 FP [25]

The inhibited-coolant radiolytic oxidation rate is usually referred to as the graphite attack rate. Data on initial graphite attack rate have been obtained in experiments carried out in various materials test reactors (MTRs)3 for Gilsocarbon and to some extent other types of graphite (Figure 12). From Figure 12, it can be seen that the oxidation rate does not go on exponentially increasing as predicted by earlier low-dose work, but the increasing rate saturates at about 3 times the initial oxidation rate.

The approach to predicting temporal and spatial weight loss in graphite components irradiated in inhibited coolant is to use numerical analysis to solve the diffusion equations given below:

Methane concentrations

VT(A0V(CO — V(v • C1)) — K1 = 0

Moisture concentrations

VT(D20V(C2) — V(v • C2)) + K1STOX = 0

Carbon monoxide concentrations

VT(D30V(C3) — V(v • C3))

+ K1STOX + K2STOX2 = 0 [26]

The basic unknowns are the CH4, C1, moisture, C2, carbon monoxide, C3, and gas concentration profiles.

In the CH4 part of eqn [26], the first term is the pure diffusion contribution, and D10 is the effective diffusion coefficient in graphite of CH4 in CO2. The second term is the contribution from porous flow due to permeation, and v is the velocity vector for CO2 flow through the graphite pores, and K1 is the sink term for CH4 destruction.

In the moisture part of eqn [26], the first term is again the pure diffusion contribution, and D20 is the effective diffusion coefficient in graphite of moisture in CO2. The second term is the contribu­tion from porous flow. K1STOX is the source term for moisture formation from CH4 destruction in accordance with

CH4 + 3CO2 ! 4CO + 2H2O [IX]

In the carbon monoxide part of eqn [26], the first term is the pure diffusion contribution, and D30 is the effective diffusion coefficient in graphite of car­bon monoxide in CO2. The second term is the contribution from porous flow. K1STOX is defined above and K2STOX2 is the source term of carbon monoxide formation from graphite oxidation.

The various terms in the diffusion equations must be updated at each time-step for changes in coolant composition, dose rate, attack rate, and all parameters controlling graphite pore structure, diffusivity, and permeability which change with oxidation. These equations can be solved numerically using finite dif­ference or finite element techniques to give point wise, temporal distributions of weight loss in a graph­ite component.

10	20 30 40	50	60

Fluence (MWh kg-1)