233 235 23Q 241

From an engineering viewpoint U, U, and 9Pu (and Pu) are fissile

nuclides and most nuclear reactors in operation or under planning use one of them. Among these fissile nuclides only 235U (0.72 % isotopic abundance in natural uranium) exists as a natural resource and the others are artificially produced in nuclear reactors through conversion of fertile nuclides: Th to U and U to

9Pu (and Pu). A burnup chain (nuclear transmutation and decay chain) includ­

ing those nuclides is shown in Fig. 1.1.

Let us derive the burnup equation of each nuclide from the burnup chain of uranium, presented by characteristic expressions which include terms for: atomic number density at position r and time t, N(r, t); absorption, capture, and (n, 2n)
reaction cross sections, aa, <rc, and <rn,2n respectively; decay constant, 1; and neutron flux, ф(~, t). The absorption cross section is the sum of the cross sections of all neutron absorption reactions such as fission, capture, and (n, 2n). For simplicity of calculation, the one-group neutron energy is assumed.

Recalling the volumetric reaction rate (reaction rate per unit time and volume) expressed by афN (XN in case of decay) and making a balanced relation between the production and destruction rates of a target nuclide, the burnup equations can be given by the following equations, where nuclides are identified by a two-digit superscript indicating the last digit in the atomic number and the last digit in the mass number, respectively.

ПДТ42

(1.11)

ot

,9 TV51

(1.12)

ot

The following approximation can be used for a short-lived nuclide which has a very short half-live relative to fuel burnup period in nuclear reactors. The short­lived nuclide decays immediately after it is produced and it reaches a balanced state between production and destruction like a radioactive equilibrium. If the time differentials of 237U, 239Pu, and 239Np are set to be zero, the burnup equations of

237 239

Np and Pu are represented by the next equations.

ПДГ49

(1.14)

ot

It is considered that the short-lived nuclides decay instantaneously in this burnup chain.