Page 256 - Handbook of Energy Engineering Calculations

of a nuclear cycle are important, the cost of the plant must also be considered
before a final choice of a cycle is made. The method presented is the work of
Henry C. Schwenk and Robert H. Shannon, as reported in Power magazine.

FUEL CONSUMPTION OF NUCLEAR REACTORS

Determine the amount of fissionable material used in a 500-mW reactor
10
having 3 × 10 fissions per watt-second. The reactor core has a volume of
3
3
1360 ft (38.5 m ) and the fuel (99.3 percent U 238 plus 0.7 percent U 235)
occupies 6 percent of the reactor volume. How much fissionable material is
consumed if the plant operates 8760 h/year at an 80 percent load factor and
the capture cross-section/fission cross-section ratio = 1.2? What are the

maximum allowable atom burnup, the average fuel-cycle time, and the
reactor neutron flux?

Calculation Procedure:

1. Compute the reactor fission rate

Use the relation F = P C, where F = reactor fission rate, fissions/(W · s); P T
r
T
r
6
10
= total reactor power, W; C = fissions (W · s). So F = 500 × 10 (3 × 10 ) =
r
19
1.5 × 10 fissions/s.
2. Compute the total volume of the fuel
Since the fuel occupies 6 percent of the reactor volume, the fuel volume V =
f
3
3
0.06 ×1360 = 81.6 ft (2.3 m ). Since reactor fuel quantities are often
expressed in cubic centimeters, convert the fuel volume in cubic feet by
4
4
multiplying by the conversion factor 2.832 ×10 , or V = 2.832 ×10 (81.6) =
fc
6
3
2.31 ×10 cm .
3. Compute the U 235 nuclei in the reactor
3
First determine the uranium nuclei per cm N , using the relation N =
U
U
3
[(uranium density, g/cm )/uranium atomic weight] (Avogadro’s constant) =
24
3
23
(18.68/238.07)(6.023 ×10 ) = 0.0472 ×10 nuclei/cm . In this relation the
3
following constants are used: uranium density = 18.68 g/cm , uranium atomic