Since the fuel temperature must be kept below the limit throughout the burnup period, it is expected that the optimized power distribution is maintained. As shown in Fig. 4.24, high effective multiplication factor at the beginning of burnup period requires deep insertion of the control rods for compensating the excess reactivity. In such a case, the peak of power distribution like Fig. 4.21 (“No optimization” case) appears in core bottom and the fuel temperature there exceeds the limit. Thus, the control rod insertion, as illustrated in Fig. 4.21 (“Optimization” case), should be kept shallow throughout the burnup period. To do that, the effective multiplication factor should be made as small as possible while keeping the necessary reactivity for burnup like kexp in Fig. 4.24. The reactivity which should be compensated by burnable poison (4kexp) is given by Eq. (4.21).

4keXp = k — keXp (4.21)

The multiplication factor is expressed as below by one-group theory:

(4.22)

"a

where

v : Neutron yied per fission Df: Macroscopic fission cross section (1/cm)

Da : Macroscopic absorption cross section (1/cm) excluding burnable poison

The multiplication factor kexp which is made as small as possible by loading burnable poison is expressed as the next equation.

(4.23)

Eexp is the adequate absorption cross section of burnable poison for achieving kexp. From Eqs. (4.21), (4.22) and (4.23), £exp is expressed as Eq. (4.24).

^kexp

kcx,

Burnable poison is a strong absorber and hence has a self-shielding effect. Thus, its effective absorption cross section £aBP is expressed as:

^aBP — f ON

where

f : Self-shieldingfactor

a : Microscopic absorption cross section of nuclide of burnable poison(barn) N : Number of densityof nuclides of burnable poison homogenized into fuel block (1/barn/cm)

f can be obtained by the empirical correlation below:

(4.26)

where

C : Fitting factor

I : Factor depending on geometry of burnable poison (1/cm)(the radius is used for a rod type geometry)

NBP : Number density of nuclides having absorption effect in burnable poison (1/barn/cm)

The change in the effective absorption cross section XaBP can be obtained from Eqs. (4.25) and (4.26) by considering the change in the number density of nuclides NBP. Among the changes in XaBP for several burnable poisons with different geometries and nuclide number densities, that which is closest to the change in Eexp is the optimum one. Figure 4.25 shows the comparison of Eexp and several EaBP which were considered in the design of burnable poison of the HTTR. From this figure, the optimum diameter (r) of the burnable poison rods was set as 0.7 cm. This optimization of burnable poison allows operation with shallow insertion of the control rods, as shown in Fig. 4.21, throughout the burnup period. Reference [35] describes details on optimization of the burnable poison.