When designing a nuclear reactor core, a channel ‘rating’ can be related to the reactor power and weight of uranium in a particular channel. This channel ‘rating’ can be related to a rate of change in the graphite properties. The channel rating is given in MW/Atu and over time the channel burnup as mega­watt days per adjacent tonne of uranium (MWd/Atu). Note that this unit is literally the (power in a particular channel) x (number of days) x (weight of uranium in that channel). No account is taken of refueling. However, fuel burnup is a function of reactor design and therefore, the equivalence concept was used and damage was related to a standard position.

In the United Kingdom, the change in graphite property was defined at a standard position in a Calder Hall reactor to give Calder equivalent dose. This was defined as the dose at a position on the wall of a fuel channel in a Calder Hall reactor. In the Calder Hall design, the lattice pitch is 8 in. The stan­dard position was chosen to be in a 3.55-in.-diameter fuel channel at a point on the shortest line between the centers of two fuel channels. The fuel is assumed to be 1.15-in.-diameter natural uranium metal rods. Calder equivalent dose was then used as a function to relate graphite property change to fuel burnup.

Kinchin14 had measured the change in graphite electric resistivity as a function of distance into the BEPO reflector. By normalizing this change, he defined a ‘graphite damage function’; see also Bell eta/.15

Thus, graphite damage at some position in a reac­tor core graphite component could be defined as a function of the following:

• source strength

• distance between position and source

• attenuation in damage with distance through the intervening graphite

The damage function is a measure of the last two bullet points. The source strength is related to fuel burnup. The graphite damage function df is defined as fRg)

R where f(Rg) is the damage absorption curve for an equivalent distance through BEPO graphite ‘Rg’ of density 1.6 gcm~3, and R is the distance through graphite between the source and position of interest. Note that nonattenuating geometric features, that is, holes, need to be accounted for.

Calder equivalent rating Pe can now be defined as

AdfP

ACalder dfCalder

where ‘ACalder’ and ‘A’ are the uranium fuel cross­sectional areas in Calder (1.04 in.2) and in the reactor under consideration, respectively; ‘d/Calder’ and ‘df ’ are the values of the damage at the Calder standard position (1.395) and in the reactor under consider­ation, respectively, and ‘P is the fuel rating in the reactor under consideration.

Thus, a graphite property change in a reactor under assessment can be related to the equivalent graphite property change at the Calder standard position.

However, in a real reactor there is more than one fuel channel. There may also be absorbers or empty interstitial holes, the fuel rating will change with burnup, and the fuel will be replaced from time to time. Therefore, a more complex, multiple source cal­culation is required to take account of the actual chan­nel rating and the geometric features of the core. This is normally done by considering a 5 x 5 lattice array:

[4]

where Bj and B are the accumulated fuel burnup at the jth and reference source, respectively, f(Rg); is the damage absorption function corresponding to thickness Rg for jth source, and Rg is the distance between the jth source and target.

This method was successfully used to design the Magnox reactors. However, because of the higher enriched oxide fuel and more complex fuel design in the AGRs, this approach became less satisfactory and new ‘damage functions’ that accounted for the new fuel and geometry were calculated using Monte Carlo methods (made possible by the introduction of the digital computer). This method was until recently still used in industry codes such as ‘Fairy’ (National Nuclear Company) and ‘GRAFDAM’ (UKAEA).

4.11.5.2.1 Calder effective dose

When only low-dose irradiation graphite property data were available, it was assumed that irradiation damage could be obtained at one temperature and that the property change versus dose (fluence) curves could be adjusted for all other temperatures using the so called R(0) curve: