{"id":13795,"date":"2017-02-08T20:34:29","date_gmt":"2017-02-08T20:34:29","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=13795"},"modified":"2022-10-21T07:39:59","modified_gmt":"2022-10-21T07:39:59","slug":"operational-factors","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-power\/reactor-physics\/nuclear-fission-chain-reaction\/operational-factors\/","title":{"rendered":"Operational factors that affect the multiplication in PWRs"},"content":{"rendered":"
<\/div>\n

Detailed knowledge of all possible operational factors that may affect the multiplication factor of the system is of importance in reactor control<\/strong>. It was stated the keff<\/sub> <\/strong>is during reactor operation kept as near to the value of 1.0 as possible<\/strong>. Many factors influence the criticality of the reactor<\/b>. For illustration, in an extreme case, the presence of humans (due to the water, carbon, which are good neutron moderators<\/a>) near fresh uranium fuel assembly influences the multiplication properties of the assembly.<\/p>\n

If any operational factor changes one of the contributing factors to keff<\/sub><\/strong>\u00a0(keff<\/sub> = \u03b7.\u03b5.p.f.Pf<\/sub>.Pt<\/sub><\/strong>), the ratio of 1.0 is not maintained, and this change in keff<\/sub><\/strong>\u00a0makes the reactor either subcritical<\/strong> or supercritical<\/strong>. In most cases, each operational change influences all coefficients in the six-factor formula, but there is always a dominant effect that can be separated. For illustration, here are some examples of these operational changes and their impacts on keff<\/sub><\/strong>\u00a0that may take place in PWRs<\/a>.<\/p><\/div><\/div>

\u00a0
<\/span>Change in the control rods position<\/div>
\u2193control rods\u00a0\u21d2\u00a0\u2193keff<\/sub> = \u03b7.\u03b5.p. \u00a0\u2193f \u00a0.Pf<\/sub>.Pt<\/sub><\/span><\/strong>\n

The thermal\u00a0utilization factor for heterogeneous reactor cores must be calculated in terms of reaction rates<\/a> and volumes<\/strong>, for example, by the following equation:<\/p>\n

\"thermal<\/a><\/p>\n

where \u03a3a<\/sub><\/strong> is the macroscopic absorption cross-section, which is the sum of the capture cross-section<\/a> and the fission cross-section, \u03a3a<\/sub> = \u03a3c<\/sub> + \u03a3f<\/sub><\/strong>. The superscripts U, M, P, CR, B, BA, and O,<\/strong>\u00a0refer to uranium fuel, moderator<\/a>, poisons, control rods<\/a>, boric acid<\/a>, burnable absorbers, etc<\/strong>. The presence of control rods<\/strong>, boric acid,<\/strong> or poisons causes a decrease in neutron utilization<\/strong>, which, in turn, causes a decrease in the multiplication factor<\/strong>.<\/p>\n

Compared with the chemical shim<\/a>, which offset positive reactivity excess in the entire core, with control rods, the unevenness of neutron-flux density<\/a> in the reactor core may arise because they act locally.<\/p><\/div><\/div>

<\/span>Change in the boron concentration<\/div>
\n

\u2191boron \u21d2\u00a0\u2193keff<\/sub> = \u03b7.\u03b5.p. \u00a0\u2193f \u00a0.Pf<\/sub>.Pt<\/sub><\/span><\/strong><\/p>\n

The concentration of boric acid diluted in the primary coolant\u00a0influences the thermal utilization factor<\/strong>. For example, an increase in the concentration of\u00a0boric acid (chemical shim)<\/a> causes the addition of new absorbing material<\/strong> into the core, and this causes a decrease in the thermal utilization factor.<\/span><\/strong><\/span><\/strong>\u00a0<\/span><\/p>\n

The thermal\u00a0utilization factor for heterogeneous reactor cores must be calculated in terms of reaction rates<\/a> and volumes<\/strong>, for example, by the following equation:<\/p>\n

\"thermal<\/a><\/p>\n

where \u03a3a<\/sub><\/strong> is the macroscopic absorption cross-section, which is the sum of the capture cross-section<\/a> and the fission cross-section, \u03a3a<\/sub> = \u03a3c<\/sub> + \u03a3f<\/sub><\/strong>. The superscripts U, M, P, CR, B, BA, and O,<\/strong>\u00a0refer to uranium fuel, moderator<\/a>, poisons, control rods<\/a>, boric acid<\/a>, burnable absorbers, etc<\/strong>. The presence of control rods<\/strong>, boric acid,<\/strong> or poisons causes a decrease in neutron utilization<\/strong>, which, in turn, causes a decrease in the multiplication factor<\/strong>.<\/p>\n

Compared with burnable absorbers<\/strong> (long-term reactivity control) or control rods<\/strong> (rapid reactivity control), the boric acid avoids the unevenness of neutron-flux density<\/a> in the reactor core because it is dissolved coolant homogeneously in the entire reactor core. On the other hand, high concentrations of boric acid may lead to a positive moderator temperature coefficient, which is undesirable. In this case, more burnable absorbers must be used.<\/p>\n

Moreover, this method is slow in controlling reactivity. Normally, it takes several minutes to change the boric acid concentration (dilute or borate) in the primary loop. For rapid changes of reactivity, control rods<\/a> must be used.<\/p><\/div><\/div>

<\/span>Change in the moderator temperature<\/div>
\u2191TM<\/sub>\u00a0\u21d2\u00a0\u2193keff<\/sub> = \u03b7.\u03b5. \u00a0\u2193p \u00a0. \u2191f . \u00a0\u2193Pf \u00a0<\/sub>. \u00a0\u2193Pt\u00a0<\/sub> (BOC)<\/span><\/strong>\n

\u2191TM<\/sub>\u00a0\u21d2\u00a0\u2193keff<\/sub> = \u03b7.\u03b5. \u00a0\u2193p \u00a0.f. \u00a0\u2193Pf \u00a0<\/sub>. \u00a0\u2193Pt\u00a0<\/sub> (EOC)<\/span><\/strong><\/p>\n

This operational change is very difficult to describe because changes in moderator temperature<\/strong> lead to almost all the coefficients. Major impacts<\/strong> on the multiplication of the system arise from the change of the resonance escape probability <\/a>and the change of total neutron leakage (see thermal non-leakage probability<\/a>\u00a0and fast non-leakage probability<\/a>).<\/p>\n

Control rods<\/strong><\/a>\u00a0(<\/span><\/strong>insertion\/withdrawal)<\/span> influence the thermal utilization factor<\/strong>. For example, control rods insertion causes the addition of new absorbing material<\/strong> into the core, and this causes a decrease in thermal utilization<\/strong><\/span><\/strong>.<\/span><\/strong><\/p>\n