Page 257 - Handbook of Energy Engineering Calculations

23
weight = 238.07; Avogadro’s constant = N = 6.023 ×10 atoms/(g · atom).
m
3
With the uranium nuclei per cm known, compute the U 235 nuclei in the
24
6
reactor from N U 235 = 0.007 N V = 0.007(0.0472 ×10 )(2.31 ×10 ) = 7.64
U
fc
26
×10 U 235 nuclei in the reactor.
4. Compute the U 235 fissionable material consumed
Use the relation F U 235 = F G /N , where F U 235 = fissionable U 235 material
m
r m
consumed or burned up for power only, g/s; G g/mol of the fissionable
m
19
material; other symbols as before. Substituting gives F U 235 = (1.5 ×l0 )
−3
(235)/6.023 = 5.85 ×10 g/s.

5. Compute the annual consumption of fissionable material

Use the relation A = F U 235 YL/1000, where A = annual consumption of
c
c
fissionable material, kg; Y = s/year; L = load factor; other symbols as before.
−3
Substituting reveals A = 5.85 ×10 (3600 ×8760)(0.8)/1000 = 147.4
c
kg/year.

6. Compute the U 235 annual consumption
The U 235 is consumed by fissioning for power and is also lost by
absorption. The proportion of these two forms of consumption is expressed
by α = U 235 total capture cross section/U 235 fission cross section. With α =

1.2 for a typical reactor, the total annual U 235 consumption = 1.2(147.4) =
177 kg/year.

7. Compute the maximum allowable atom burnup
Both U 235 and U 238 are regarded as reactor fuel. The allowable percentage
of burnup depends on the total integrated radiation dosage and radiation

energy level, and the effect on fuel material dimensional stability, thermal
conductivity, and reduction in effective multiplication factor. Assuming a
maximum allowable burnup of 20 percent, which is a typical value, compute
3
3
B = (percentage of burnup)(fuel atoms per cm )(total cm of fuel), where
ma
B = maximum allowable atom burnup, atoms. Substituting gives us B =
ma
ma
6
26
24
(0.002)(0.0472 ×10 )(2.31 ×10 ) = 2.18 ×10 atoms.