The accuracy of HTR calculations has been tested with the above discussed experiments. Starting from the informations available about the uncertainty of the fundamental data and calculational methods it is also possible to have an independent assessment of this accuracy.

Some calculations have been performed in the past in this direction/54’55’ The data used for these calculations were not the best sets now available, so that the errors obtained are somewhat pessimistic. Figure 15.1 gives the relative effects of different uncertainties obtained by a General Atomic study of 1968.<54) The error in space-time depletion effects is here assessed supposing the use of one — and two-dimensional burn-up codes instead of three-dimensional calculations, and the error on space — temperature effects supposes that in the data preparation for the burn-up calculations the effect of local temperature differences in the core have been neglected.

The conclusion of this report is that the total uncertainty arising from cross-sections is of the order of 3% of the fuel cycle cost, or 1% of the total power cost. The estimated cost uncertainties associated with physics data and calculational methods are less than 3% of the total power cost.

A similar study was performed in 1969 for the THTR reactor/55’ analysing the effect of the uncertainties in microscopic nuclear data and in calculational methods on the attainable burn-up. The microscopic nuclear data analysed in this investigation are: absorption and fission cross-sections (including resonance data) and fission product yields. The analysis has been performed with a zero-dimensional burn-up code (BO)<56> and refers to the THTR reference fuel cycle. The reactor is supposed to be in equilibrium so that the average core composition determining keft is the average over all burn-up stages of a fuel element. The quantity Xi (cross-section or yield) being investigated is changed by an amount AXt corresponding to its uncertainty. Using the same residence time as in the reference case the new average composition and are

calculated. In this way is obtained the AkefT due to the change ДХ. Then the burn-up calculation is repeated changing the fuel residence time until reaches again the value of the reference case. In this way Д fifa is obtained. The total inaccuracy in kcff or in fifa is then calculated as square root of the summation of the square of each contribution.

This supposes a normal Gaussian distribution for every single uncertainty. The assumed uncertainties and the single contributions to the total errors are given in Tables 15.1, 15.2, 15.3 and 15.4. It must be remembered that better data are now available in many cases.

The total effect of ke« and burn-up is shown in Fig. 15.2.

+An increase of the absorption cross-section of 232Th causes also an increase in conversion ratio, so that the loss in does not correspond to a full loss in fifa. The opposite is true for 2”Pa.

The uncertainties in the calculation methods include some points characteristic of pebble-bed reactors like burn-up measurement, effect of fuel element flow, streaming in pebble bed, empty space above the core. The errors in space-temperature effects are of little importance in this type of reactor because of the continuous fuel-element movement.

Other errors considered are the inaccuracies of the representation of the reactor geometry by the mesh structure of diffusion theory codes (Akefr = 1.5%c), and the uncertainty of the order of %c in the fresh fuel composition (A= 1.0%o).

A particular treatment is required by the uncertainty in the energy per fission e released in the reactor (Де ~ 3%). This uncertainty has no effect on the burn-up measured in fifa, but on the burn-up measured in MW d/t and then on the fuel cycle cost. For a given reactor power the flux level is affected by an uncertainty equal to Де. In this case of continuous refuelling the change in flux level causes a change in equilibrium composition (average over all burn-up stages) and then on kcfs (Aksf! = 4%o in the case of ref. 55).