NUKEFACT #65 Continued

last update July 4, 2001

p 1: EO 1.3 - reactivity is not added.

p 5: Second paragraph - the qualification that the neutron level can be determined "provided the values of k_eff or reactivity for both times are known" is misleading because operationally k_eff values are never known to any great accuracy. What is the value of being able to determine the neutron level?

p 5: Fourth paragraph - First sentence - the referral to "shutdown operation" is misleading; better defined as startup operation. Positive reactivity is not added. The same comment as for the second paragraph applies. The equation is not useful because the k-effective values are not known.

p 5: Example - reactivity is not inserted by control rods; units for reactivity change are delta-pcm, not pcm.

p 6: Last paragraph - The fourth sentence, "The closer the reactor is to criticality, the faster M will increase for equal step insertions of positive reactivity," is incomprehensible. In the fifth sentence, the subcritical multiplication factor (M) does not apply at criticality. If the multiplication were infinite, then power would be infinite.

p 7: Second paragraph - The statement that "For a critical reactor, 1/M is equal to zero" is incorrect. The first equation on this page is only applicable for values of k_effective that are less-than-one.

p 7: Third paragraph - reactivity is not inserted.

pp 1 to p 9: Subcritical Multiplication Factor - the use of inverse multiplication to monitor the loading of fuel assemblies into a reactor seems to have been omitted.

p 9: Fourth bullet - reactivity is not added. It is not possible to apply this equation as indicated.

p 11: Equation (4-7) - is incorrect. In addition, ell-star (l^*) is not the prompt generation time. It is the prompt neutron lifetime/k_eff. (see KEY CONCEPT #5)

p 12: Last paragraph - the statement that beta_effective is defined as the fraction of neutrons at thermal energies which were born delayed is misleading. Although beta has historically been labeled as the "delayed neutron fraction", it is actually the "precursor yield fraction." Beta does not represent the fraction of the neutron population that consists of delayed neutrons, and multiplying beta by an "importaince factor" does not make it so. (Beta - rho) is the real measure of the fraction of delayed neutrons in the total population. (see KEY CONCEPT #1)

p 13: Last paragraph - the three values quoted for lambda_eff are more appropriately referred to as rule-of-thumb values, rather than approximate values.

p 14: Period equation - same comment as p 11, the period equation is incorrect.

p 14: Paragraph after the period equation - this entire paragraph is garbled nonsense. No reactivity is added. The increasing neutron level for a constant positive reactivity value occurs because the delayed neutron source strength is increasing with time and being multiplied by the prompt neutrons. The delayed neutron source increase occurs because with positive reactivity the production of delayed neutrons exceeds the loss of delayed neutrons. See KEY CONCEPT #2.

The equation, though incorrect, is intended to give the period for a specific reactivity condition. Even if reactivity is positive, the period can still be negative if rho-dot is negative and of greater magnitude than (lambda_eff x rho). The period equation has nothing to do with prompt jump. A prompt jump in power is not caused by a reactivity insertion, which unless specified may be by a slow ramp. Rather, a prompt jump results from a step change in reactivity. The prompt jump equation, which is not included in this Module, defines the prompt jump in power caused by a step change in reactivity. There is no such thing as a prompt neutron generation time and its value was not previously given as 10^-13 seconds.

p 14: Figure 2 - the figure should show a separate trace of reactivity with time. The reactivity is constant before time zero. A step change in reactivity occurs at time zero. And, the reactivity is constant after time zero. For potential reactor operators, a trace of reactor period versus time would also be helpful. The title should indicate that the power behavior illustrated is for a step change in reactivity from an initial condition of criticality.

p 15: First paragraph and Figure 3 - same comment as p 14 for Figure 2.

p 15: Prompt Criticality - what can be readily seen from Equation (4-7) is irrelevant because Equation (4-7) is incorrect. The equation shown for reactor period at prompt criticality is wrong.

p 16: First paragraph - There is no such thing as a prompt neutron generation lifetime. If one plugs numbers into Equation (4-7), the result will not show that period changes in a regular manner. That's because Equation (4-7) is incorrect.

p 16: Paragraph following Equation (4-8) - if the core is undergoing a reactivity change, then the rho-dot term accounts for the effect of an ongoing reactivity change with time on the reactor period. Ell-star/rho is not the prompt period.

p 19: Example 2 - reactivity is not added; a -130 delta-pcm reactivity change is introduced.

p 19: Step 3 - the calculation of power change is incorrect because it does not account for the power decrease that occurs due to the reactivity change, e.g. the prompt drop for a step change in reactivity. Without specifying how the reactivity change occurred, by ramp or by step change, it is not possible to calculate the power change.

p 21: Seventh bullet - the equation for reactor period is incorrect. Ell-star is not the prompt generation lifetime.

p 22: Third bullet - these equations can determine power change once a stable reactor period (startup rate) has been established.

p 22: Fourth bullet - prompt jump occurs only for a step change in reactivity. Practically, a step change in reactivity must occur in a short interval of time, e.g. one to two seconds maximum. A reactor scram can be considered as a step change in reactivity. Reactivity is not inserted.

p 22: Fifth bullet - same comment as for prompt jump.

p 22: Seventh bullet - there is no such thing as a prompt neutron generation time.

p 22: Eighth bullet - one dollar of reactivity is not equivalent to lambda_eff.

p 24: Last sentence of second paragraph - During reactor startup this process can ...

p 24: Third paragraph - xenon does not introduce negative reactivity.

p 25: Direct Xenon Reactivity - the reactivity "change" associated with xenon present at shutdown, corrected for decay.

p 25: Indirect Xenon Reactivity - the reactivity "change" associated with xenon produced by iodine decay ...

p 25: Temperature Reactivity - the reactivity "change" related to the difference ...

p 25: Paragraph after Temperature Reactivity - A graph of "integral" control rod worth versus ... .

p 28: Shutdown Margin - the shutdown margin is usually only of concern for the most reactive condition of the core, typically cold and xenon-free. Negative reactivity is not inserted.

p 28: Temperature: First paragraph - temperature does not add negative reactivity. It is the ongoing change in negative rho-dot, which is opposite in sign to the existing positive reactivity, which causes power turning, not the reactivity value itself. The reactor is typically still supercritical when power is turned.

p 29: First paragraph - if the reactor uses low enriched uranium, the Doppler effect from the U-238 as the fuel temperature increases will cause a Tav droop which must be compensated by control rod withdrawal to maintain a constant Tav.

p 30: Flow: Second paragraph - When the flow rate is varied "at high power", however, the change in temperature ...

p 30: Core Burnup: Second paragraph - use burnup rather than burnout to be consistent. Besides, burnout is sometimes used in reference to fuel damage.

p 31: Shutdown: Second paragraph - negative reactivity is not added. The prompt drop only occurs if the reactor is scrammed. The level of delayed neutrons does not change during prompt drop. It is the source multiplication that is reduced. The source is delayed neutrons. The final power level is at "equilibrium" subcritical multiplication as determined by the strength of the non-fission neutron source.

p 33: Third bullet last sentence - Positive reactivity is not added. A graph of "integral" rod worth is used?

p 34: Third bullet - same comment as p 28, most reactive condition?