Although the equations written up to now are valid in general for most reactor types, the approximations made for their solution should take into account the characteristics of HTRs. As has already been mentioned, more than one fuel element type will have to be considered in order to represent the different burn-up stages. Space-dependent heat-transfer calculations are necessary, while zero-dimensional neutron kinetics calculations are, in many cases, sufficient. Besides, the coefficients appearing in the kinetics equation in one or more energy groups will have to be calculated by codes able to treat properly the neutron spectrum of HTRs (see Chapter 8). The approximation often used in the past, which consisted in performing one thermal group calculations, representing all epithermal events by a resonance escape probability, is not valid for HTRs (more than 10% of all fissions occur above thermal energy).

In comparison to reactors having metal of oxide fuel, HTRs have a very high thermal capacity. This is due to the very high specific heat of graphite, and to the fact that a great amount of graphite is mixed with the fuel. The high thermal capacity gives more time to the control system to intervene. On the other hand, if the temperature coefficient is negative, a higher thermal capacity will eventually cause higher tempera­tures if no scram occurs.

Figure 12.2 shows the time dependence of the total power Q as well as the maximum fuel and gas outlet temperatures for a 3% Ak step. The full line shows a calculation performed with the normal heat capacity of an HTR. In the case of the broken line the heat capacity has been reduced by a factor of 4. In reactors with a very low thermal capacity the maximum temperatures occur so soon that the control system has no possibility of limiting them. By the time the scram comes the temperature coefficient has already stabilized the reactor to a lower power.

In HTRs the temperature increase is relatively slow. As a consequence the temperature coefficient feedback comes also relatively late, so that higher power level, and eventually higher temperatures can be reached, if a scram does not occur.