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6.1 MSBR PHYSICS ANALYSIS
0. L. Smith
Optimization of Reactor Parameters
H. T. Kerr
The two principal indices by which the perfor-
mance of the Molten-Salt Breeder Reactor is cus-
tomarily evaluated are the cost of power and the
annual fuel yield, that is, the annual fractional in-
crease in the inventory of fissionable material.
These are used as figures of merit in assessing the
influence of various design parameters or the effect
of design changes that may be contemplated, and,
in fact, we customarily combine them into a com-
posite figurc of merit,
F = y i lOO(C +~ x>-1 ,
in which 17 is the annual fuel yield in percent per
year, C is that part of the power cost which de.-
pends on any of the parameters considered, and X
is an adjustable constant, having i10 physical sig-
nificance, whose value merely determines the rela-
tive sensitivity of F to y and C. Since a large num-
ber of reactor parameters are usually involved, we
make use of an automatic search procedure, carried
out on an IBM 7090 computer, which finds that com-
bination of the variable desigu parameters that rnax-
imizes the figure of merit, F, subject to whatever
constraints may be imposed by the fixed values of
other design parameters not allowed to vary. This
procedure, called OPTIhfERC, incorporates a mul-
tigroup diffusion calculation (synthesizing a two-
space-dimensional description of the flux by al-
ternating one-dimensional flux calculations), a
determination of the fissile, fertile, and fission
product concentrations consistent with the proc-
A. M Perry
82
essing rates of the fuel and fertile salt streams,
and a method of steepest gradients for optiiiiizing
the values of the variabies. By choosing different
values for the constant X in the figure of merit, F,
we can generate a curve showing the minimum cost
associated with any attainable value of the fuel
yield, and by carrying out the optimization proce-
dure for different, successive fixed values of se-
lected design parameters, we can generate families
of such curves of C vs y. (In OPTIMEKC any of
some 20 parameters may either be assigned fixed
values or be allowed to vary within specified limits
subject to the optimization procedure.)
One of the design parameters which has a sig-
nificant influence on both yield and power cost is
the power density in the core. (Actually, the core
dimensions for a given total power are the param-
eters used.) The performance of the reactor is
better at high power densities. At the same time,
the useful life of the graphite moderator, which is
dependent on the total exposure to fast neutrons,
is inversely proportional to the power density (see
next section). It is necessary, therefore, to de-
termine the effect of power density on performance
with considerable care.
In Fig. 5.1 the fuel-cycle cost is used because
it contains, in fact, most of the variation of power
cost with the parameters being varied. It may be
seen from Fig. 6.1 that a reduction ii1 power density
from 80 to 20 w/cm3 involves a fuel-cycle cost
penalty of about 0.1 mill/kwhr (electrical) and a
reduction in annual fuel yield of perhaps 1.5%.
,,
Ihere is, of course, also an increase in capital
cost (cf. Chap. 5), but this is essentially offset by
a reduction in the cost of replacing the graphite
and reactor vessel at intervals determined by radiation
damage to the graphite. The combined
penalty for having to replace the graphite, compared
with a high-power-density core not requiring
replacement, is about 0.2 mill/kwhr (electrical),