In this Nukefact we address the questions under the subsection Neutron Life Cycle. Of the forty-two questions in the INPO Catalog pertaining to the Neutron Life Cycle we find eighteen to be technically incorrect, that's 43% wrong folks. Of the eighteen incorrect questions, six are about keffective, two are about kexcess, three are about reactivity or reactivity change, and seven are about Shutdown Margin (SDM). The remaining twenty four questions treat no other topics. Even though this section of the Catalog is about the Neutron Life Cycle, there are no questions on any of the six factors in the six factor formula! Considering INPO's difficulty in defining keff, it is quite probable that INPO wants no part of the individual factors. And, what do Shutdown Margin and K-excess have to do with the Neutron Life Cycle?
As we have quoted: Josh Billings, in the nineteenth century said, "It ain't so much what we don't know that hurts us, as what we do know that ain't so". Josh must have been a psychic. He saw INPO coming. This 43% is truly disturbing ... and totally unacceptable. Can it be that nobody sees a problem here? We know that there are many trainers out there who have discovered this problem ... and tried to deal on with it through the NRC ... all to no avail. If 43% of the questions are in technical error, then 43% of the subject matter taught in the class room is in error. Do we have to live with this nonsense? If the regulators don't understand nuclear reactors, then why are they regulating? This is just not your normal run-of-the-mill problem; this is a catastrophe!
Let us make one thing clear. Our time is as limited as anyone elses'. In reviewing each question we spend the shortest possible time and mainly identify the glaring error. Our comments are not all inclusive, nor do our recommendations for the revised question necessarily include all changes that would make for the best question. Many trainers have identified and tried to get technically incorrect questions corrected, or removed from the Catalog ... occasionally with some success, but more often with lots of resistence from the NRC. So the problem persists ... big time. What we are trying to do here is to take one section of the INPO Catalog, one that happens to be extremely important, crucial, to the operation of a nuclear plant, and expose the magnitude of the overall problem ... with specifics.
Question 1 : A reactor with an effective multiplication factor (Keff) slightly greater than one is
a. subcritical
b. critical
c. supercritical*
d. prompt critical
Comment: The asterisk indicates the intended correct answer is choice "c". The question is not technically incorrect but it is certainly flawed, and potentially confusing to the student. Is 0.0065 slight? Slight is a very general decriptive term ... not definitive. Restate the question and choices as follows:
Question 1: (revised) A reactor with an effective multiplication factor (Keff) of 1.0013 is
a. subcritical
b. critical
c. supercritical*
d. prompt critical
Question 2: A reactor is classified as subcritical when Keff is _____________ and the reactor does not have a self-supporting _______________ .
a. less than 1, reactor period
b. less than 1, chain-reaction*
c. greater than 1, quantized state
d. greater than 1, thermal neutron supply
Comment: The asterisk indicates the intended correct answer is choice "b". The answer is incorrect. The nuclear status of the reactor is defined by Keff alone, no other qualifications are necessary. What is a self-supporting chain reaction supposed to be? Below prompt critical chain reactions are not selfsustaining. Restate the question as follows:
Question 2: (revised) A reactor is classified as subcritical when Keff is _____________ .
a. negative
b. less than 1*
c. zero
d. greater than 1
Question 5: The effective multiplication factor (Keff) is defined as
a. (no. of neutrons generated by fast fission)/(no. of neutrons generated by thermal fission)
b. (no. of neutrons generated in the source)/(no. of neutrons in active fuel area)
c. (no. of neutrons from fission in one generation)/(no. of neutrons in previous generation)*
d. (no. of neutrons in previous generation)/(no. of neurtons in present generation)
Comment: The asterisk indicates the intended correct answer is choice "c". The answer is incorrect. Keff is a ratio of neutrons in successive generations, taken at a particular point in the life cycle ... not just the ratio of any neutrons in successive generations. The number of neutrons starting a life cycle undergoes continuous decrease as the neutrons proceed through the life cycle. What are the "no. of neutrons in the previous generation ... fast neutrons, thermal neutrons, fission neutrons, total neutrons"? Restate the question as follows:
Question 5: (revised) The effective multiplication factor (Keff) is defined as
a. (no. of neutrons generated by fast fission)/(no. of neutrons generated by thermal fission)
b. (no. of neutrons generated in the source)/(no. of neutrons in active fuel area)
c. (no. of fission neutrons produced in generation-2)/(total no. of neutrons produced in generation-1)*
d. (no. of neutrons in previous generation)/(no. of neurtons in present generation)
Question 6: The "number of neutrons from fission in the present generation compared to the number of neutrons in the previous generation " is the
a. reproduction factor
b. fast fission factor
c. neutron generation factor
d. effective multiplication factor*
Comment: The asterisk indicates the intended correct answer is choice "d". The question is incorrect ... as per comment for question #5. Also, "comparison" does not necessarily require division ... or indicate a ratio. Restate the question as follows:
Question 6: (revised) The ratio of "fission neutrons produced in the present generation" to "total number of neutrons produced in the previous generation" is the
a. reproduction factor
b. fast fission factor
c. neutron generation factor
d. effective multiplication factor*
Question 9: A reactor with a Keff of 1.002 would be considered
a. supercritical*
b. critical
c. subcritical
d. prompt critical
Comment: The asterisk indicates the intended correct answer is choice "a". The question is poorly worded. Restate the question as follows:
Question 9: (revised) A reactor with a Keff of 1.002 is
a. supercritical*
b. critical
c. subcritical
d. prompt critical
Question 10: Keff is not dependent on
a. core dimensions
b. core burnout
c. moderator-to-fuel ratio
d. installed neutron sources*
Comment: The asterisk indicates the intended correct answer is choice "d". The terminology of choice b is poor. Restate the question as follows:
Question 10: (revised) Keff is not dependent on
a. core dimensions
b. fuel depletion
c. moderator-to-fuel ratio
d. installed neutron sources*
Question 11: Which of the following is the multiplication factor of a reactor?
a. shutdown margin
b. Keff*
c. Kinfinity
d. Kexcess
Comment: The asterisk indicates the intended correct answer is choice "b". Since there are multiple versions of the multiplication factor, the question is incorrect. Restate the question as follows:
Question 11: (revised) Which of the following represents the multiplication factor for an operating BWR, having a core geometric shape of a 13 ft diameter by 12 tall cylinder?
a. Kmultiplication
b. Keff*
c. Kinfinity
d. Kexcess
Question 12: Effective multiplication factor is defined as "the number of fission neutrons in the present generation" divided by "the number of neutrons produced in the previous generation" and is represented by the symbol
a. LTH
b. Kex
c. Keff*
d. betaeff
Comment: The asterisk indicates the intended correct answer is choice "c". The question is flawed because it is an obvious gimme. Restate the question as follows:
Question 12: (revised) The ratio of "the number of fission neutrons in the present generation" to "the total neutrons produced in the previous generation" is represented by the symbol
a. LTH
b. Kex
c. Keff*
d. betaeff
Question 16: The term "K-excess" is defined as
a. the fractional change in neutron population per generation
b. the amount by which Keff exceeds 1.0 in a supercritical reactor
c. the amount of reactivity that must be inserted to bring a shutdown reactor to criticality
d. the amount by which the total installed core Keff exceeds 1.0*
Comment: The asterisk indicates the intended correct answer is choice "d". The question is technically incorrect because the terminology is pure invention. What, pray tell, is the "total installed core Keff" ? Restate the question as follows:
Question 16: (revised) The term "K-excess" is defined as
a. the fractional change in neutron population per generation
b. the amount by which Keff exceeds 1.0 in a supercritical reactor
c. the amount of reactivity that must be inserted to bring a shutdown reactor to criticality
d. the amount Keff exceeds 1.0 for the hypothetical condition of all control rods fully withdrawn*
Question 18: Which of the following contribute to the value of a reactor's Kexcess?
a. fuel*
b. control rods
c. fission product poisons
d. burnable poisons
Comment: The asterisk indicates the intended correct answer is choice "a". The question is technically incorrect because there are three correct choices. At any time in core life, fuel, fission product poisons, and burnable poisons effect the value of Keff and hence of Kexcess. The control rods do not effect the value of Kexcess because it is a hypothetical condition which assumes all control rods to be fully withdrawn. Restate the question as follows:
Question 18: (revised) Which of the following does not contribute to the value of a reactor's Kexcess?
a. fuel
b. control rods*
c. fission product poisons
d. burnable poisons
Question 20: Shutdown margin (SDM) is a measure of how much
a. a reactor is subcritical compared to Keff equal to 1.0*
b. reactivity must be inserted to maintain Keff less than 1.0
c. difference exists between Keff at beginning and end of cycle
d. reactivity is inserted when all control rods are fully inserted
Comment: The asterisk indicates the intended correct answer is choice "a". The question is technically incorrect because choice "a" is so general that it can apply to any subcritical condition. Restate the question as follows:
Question 20: (revised) Shutdown margin (SDM) is a measure of how much
a. subcritcality exists in a cold, xe-free reactor with the highest worth control rod fully withdrawn*
b. reactivity must be inserted to maintain Keff less than 1.0
c. difference exists between Keff at beginning and end of cycle
d. reactivity is inserted when all control rods are fully inserted
Question 22: Shutdown margin for an operating reactor is the amount of reactivity by which a xenon-free reactor at 68F would by subcritical if all control rods were:
a. withdrawn, assuming an average worth rod remains fully inserted
b. inserted, assuming an average worth rod remains fully withdrawn
c. withdrawn, assuming the highest worth rod remains fully inserted
d. inserted, assuming the highest worth rod remains fully withdrawn*
Comment: The asterisk indicates the intended correct answer is choice "d". The question is incorrect because the descriptive state of the control rods is deficient. If the rod of highest worth is "fully" withdrawn, then the position of all other rods must be defined as "fully" inserted. Restate the question as follows:
Question 22: (revised) Shutdown margin is the amount of reactivity by which a xenon-free reactor at 68F would by subcritical if all control rods were:
a. fully withdrawn, with an average worth rod remaining fully inserted
b. fully inserted, with an average worth rod remaining fully withdrawn
c. fully withdrawn, with the highest worth rod remaining fully inserted
d. fully inserted, with the highest worth rod remaining fully withdrawn*
Question 23: Shutdown margin (SDM) is defined as the amount a cold, xenon-free reactor at 68F would be subcritical if all control rods were inserted, assuming the control rod of the _____________ worth remains fully withdrawn.
a. lowest reactivity
b. highest reactivity*
c. lowest activity
d. highest activity
Comment: The asterisk indicates the intended correct answer is choice "b". The problem is poorly worded ... cold and 68F are redundant. The comment pertaining to question #22 applies. Restate the question as follows:
Question 23: (revised) Shutdown margin (SDM) is defined as the subcriticality of a xenon-free reactor at 68F with all control rods fully inserted, and with the control rod of _________________ fully withdrawn.
a. lowest reactivity worth
b. highest reactivity worth*
c. lowest B-10 burnup
d. highest B-10 burnup
Question 24: The phrase "the amount a cold, xenon-free reactor at 68F would be subcritical if all control rods were inserted, assuming the control rod of the highest worth remains fully withdrawn" is the definition of shutdown
a. deficit
b. defect
c. margin*
d. coefficient
Comment: The asterisk indicates the intended correct answer is choice "c". The comments pertaining to question #22 and #24 apply. Restate the question as follows:
Question 24: (revised) "The subcriticality of a xenon-free reactor at 68F with all control rods fully inserted, and with the control rod of the highest worth fully withdrawn" is the definition of shutdown
a. deficit
b. defect
c. margin*
d. coefficient
Question 26: Which one of the following is the most accurate definition of the term "reactivity"?
a. the rate of change of reactor power in neutrons per second
b. the ratio of the number of neutrons at some point in a generation to the number of neutrons at the same point in the previous generation
c. the factor by which the neutron population changes per unit time
d. the fractional change in the nearness of the reactor to a critical condition*
Comment: The asterisk indicates the intended correct answer is choice "d". Why is the student instructed to chose the "most accurate" definition? There should be only one correct choice. In this case there is no correct choice. This question is technically incorrect because of the definition given in choice "d". If the "nearness to criticality" means delta-k, then reactivity is not the fractional change in the nearness to criticality. Reactivity is often defined as a measure of the deviation or departure of the reactor from criticality. Restate the question as follows:
Question 26: (revised) Which one of the following is the most accurate definition of the term "reactivity"?
a. the rate of change of reactor power in neutrons per second
b. the ratio of the number of neutrons at some point in a generation to the number of neutrons at the same point in the previous generation
c. the factor by which the neutron population changes per unit time
d. the fractional change in the neutron population in one generation time.*
Question 28: In a subcritical reactor, Keff was increased from 0.85 to 0.95 by rod withdrawal. Which one of the following is closest to the amount of reactivity that was added to the core?
a. 0.099 delta-k/k
b. 0.124 delta-k/k*
c. 0.176 delta-k/k
d. 0.229 delta-k/k
Comment: The asterisk indicates the intended correct answer is choice "b". This question is technically incorrect because there is no correct answer ... the units for all choices (delta-k/k = reactivity) are incorrect. Reactivity is a dimensionless quantity ... it has no units ... it is unitless. Attaching delta-k/k to the numeric value makes it appear as though the units are reactivity. Reactivity itself is not a unit measure of anything. Reactivity is a physical property of the core ... a measure of the nuclear state of one particular reactor condition, in terms of its deviation from criticality. The differece between two nuclear states, as in this question, is delta-rho = rhofinal - rhoinitial, or delta(delta-k/k). Taking temperature as perhaps a more familar example, consider temperature with units of oF. These units apply whether reference is to the temperature of a particular body or to a temperature change in that body. However, in the first case the parameter is temperature, commonly represented by the capital letter "T". In the second case the parameter is temperature change, commonly represented as delta-T = Tfinal - Tinitial. Reactivity is comparable to T and reactivity change is comparable to delta-T, but neither reactivity or T are units identifying the magnitude of change.
Having said all this, we recommend attaching delta(delta-k/k) to the four choices listed, not as units but to indicate what the number represents. Delta-rho give a correct description of what the value represents, delta-k/k does not ... it is incorrect. A question like this always offers a good opportunity to give plus and minus choices of the same magnitude to determine if the student understands how to evaluate reactivity change. The question, as stated, gives away the algebraic sign of the change. In any case, it is always good practice to include the algebraic sign of the reactivity change with the numeric value. The sloppy (and incorrect) terminology of this question raises a particularly concern, because understanding reactivity and reactivity change is essential to understanding reactor behavior. Restate the question as follows:
Question 28: (revised) In a subcritical reactor, Keff was increased from 0.85 to 0.95 by rod withdrawal. To three decimal places, the reactivity change introduced into the core was
a. +0.099 delta-rho
b. +0.124 delta-rho*
c. +0.176 delta-rho
d. +0.229 delta-rho
Question 32: With Keff equal to 0.983, how much reactivity must be added to make the reactor exactly critical?
a. 1.70% delta-k/k
b. 1.73% delta-k/k*
c. 3.40% delta-k/k
d. 3.43% delta-k/k
Comment: The asterisk indicates the intended correct answer is choice "b". Per comments to question #28, this question is technically incorrect because the numeric choices do not represent reactivity, but rather reactivity change. In addition, "exactly critical" is poor terminology, since criticality is a very exact condition. Restate the question as follows:
Question 32: (revised) With Keff equal to 0.983, what reactivity change is required to bring the reactor critical?
a. +1.70% delta-rho
b. +1.73% delta-rho*
c. +3.40% delta-rho
d. +3.43% delta-rho
Question 35: List five parameters or design features whose change would effect a shutdown reactor's criticality condition (margin of shutdown). And explain the reactivity effect of an increase in each one.
Answer: Any five of the following parameters and explanations will satisfy this question:
* moderate temperature - An increase would insert negative reactivity, increasing the shutdown margin.
* fuel temperature - An increase (caused by a decrease in heat removal rate or an increase in moderator temperature) would insert negative reactivity, increasing the shutdown margin.
* control rod position - A withdrawal would add positive reactivity, decreasing the shutdown margin.
* xenon concentration - An increase would add negative reactivity, increasing the shutdown margin.
* number of fuel assemblies in the core - An increase would add positive reactivity, decreasing the shutdown margin.
* exposure/burnup of fuel assemblies in the core - An increase would add negative reactivity, increasing the shutdown margin.
Comment: The terminology of the question is flawed ... what is "a shutdown reactor's criticality condition (margin of shutdown)"? By the listed answers it apparently refers to Shutdown Margin. The student has no way of knowing this. A reactor's Shutdown Margin is a technical specification that must be met under a very specific set of conditions, namely ... reactor temperature is at 68oF, the reactor is xenon-free, and all control rods are fully inserted except the control rod of maximum worth is fully withdrawn. Now let's examine each of the answers that supposedly satisfy the question.
* What is "moderate" temperature"? Since the SDM applies at 68oF, an increase in temperature violates the technical specification. This answer is incorrect.
* Since the SDM applies at 68oF, an increase in fuel temperature violates the technical specification. This answer is incorrect.
* Since the SDM sets the position of all control rods, a change in position of one or more rods violates the technical specification. This answer is incorrect.
* Since the SDM requires that the reactor be xenon-free, an increase in xenon concentration violates the technical specification. This answer is incorrect.
* Perhaps. Increasing the number of fuel assemblies in the core is taken to be a change in a design feature. This is the only answer provided that might possibly be correct.
* Burnup of fuel assemblies depletes both the fuel and the burnable poison. It is well known that in BWRs the Shutdown Margin decreases over the first third of the fuel cycle because burnable poison depletes more rapidly than the fuel. This answer is technically incorrect.
Eliminate the question; it is so bad that it is irrecoverable. The question can be salvaged by requiring a determination of the shutdown reactivity for the conditions given. Shutdown reactivity is not specific to any condition other than that all control rods are fully inserted.
Question 37: The effective multiplication factor (Keff) describes the ratio of the number of fission neutrons at the end of one generation to the number of fission neutrons at the __________ of the __________ generation.
a. end;previous*
b. beginning;previous
c. end; next
d. beginning;next
Comment: The asterisk indicates the intended correct answer is choice "a". The question, as stated is technically incorrect. Restate the question as follows:
Question 37: (revised) The effective multiplication factor (Keff) is the ratio of fission neutrons produced in ____________ to the total neutrons produced in _____________.
a. generation-1;generation-2*
b. prompt lifetime-1;generation-1
c. generation-2; generation-1
d. prompt lifetime-2;delayed neutron lifetime-1
Question 38: One hour ago, the reactor scrammed from 100% steady state power due to an instrument malfunction. All systems operated normally.
Given the following absolute values of reactivities added since the scram, assign a (+) or (-) as appropriate and choose the current value of shutdown margin.
Xenon = ( ) 1.0% delta-k/k
Fuel Temperature = ( ) 2.0% delta-k/k
Control Rods = ( )14.0% delta-k/k
Voids = ( ) 3.0% delta-k/k
a. -8.0% delta-k/k
b. -10.0% delta-k/k*
c. -14.0% delta-k/k
d. -20.0% delta-k/k
Comment: The asterisk indicates the intended correct answer is choice "b". This question is technically incorrect because, as stated in the comment for question #35, a reactor's Shutdown Margin is a technical specification that must be met under a very specific set of conditions, namely ... reactor temperature is at 68oF, the reactor is xenon-free, and all control rods are fully inserted except the control rod of maximum worth is fully withdrawn. The conditions given are irrelevant to determination of the shutdown margin. The question can be salvaged by requiring a determination of the shutdown reactivity for the conditions given. Shutdown reactivity is not specific to any condition other than that all control rods are fully inserted. In addition, the four "reactivity values" listed are not reactivities but reactivity changes, i.e. delta-rho. These delta-rhos must be added or subtracted from the initial reactivity (zero at criticality) to determine final reactivity. Restate the question as follows:
Question 38: (revised) One hour ago, the reactor scrammed from 100% steady state power due to an instrument malfunction. All systems operated normally.
Given the following values of reactivity change since scram, assign a (+) or (-) to each, as appropriate, and determine the current value of shutdown reactivity.
Xenon = ( ) 1.0% delta-rho
Fuel Temperature = ( ) 2.0% delta-rho
Control Rods = ( )14.0% delta-rho
Voids = ( ) 3.0% delta-rho
a. -8.0% rho
b. -10.0% rho*
c. -14.0% rho
d. -20.0% rho
Question 41: Which one of the following will increase the reactivity margin to criticality in a subcritical reactor at 250 oF?
a. decay of SM-149
b. increased core recirculation flow rate
c. reactor coolant heatup*
d. contol rod withdrawal
Comment: The asterisk indicates the intended correct answer is choice "c". This question is technically incorrect because it uses ambiguous terminology ... namely reactivity margin. Does this refer to Shutdown Margin? If so, then two of the choices given violate the conditions of the technical specification, including the so called correct answer. If not then the term "margin" should be avoided in order not to confuse the situation. Restate the question as follows:
Question 41: (revised) With the reactor subcritical at 250 oF, which one of the following will increase the magnitude of subcriticality?
a. decay of SM-149
b. increased core recirculation flow rate
c. reactor coolant heatup*
d. contol rod withdrawal
Question 42: Which one of the following defines K-excess?
a. Keff - 1*
b. Keff + 1
c. (Keff - 1)/Keff
d. (1 - Keff)/Keff
Comment: The asterisk indicates the intended correct answer is choice "a". This question is technically incorrect because (Keff - 1) does not define K-excess. (Keff - 1) defines delta-K, which can be used to determine the departure from criticallity of any off-critical condition. K-excess is a hypothetical reactor condition with all control rods withdrawn. (Keff - 1) can be used to calculate the supercritical delta-K for this condition. Restate the question as follows:
Question 42: (revised) For the hypothetical condition of all control rods fully withdrawn, which one of the following equations can be used to calculate k-excess?
a. keff - 1*
b. keff + 1
c. (keff - 1)/keff
d. (1 - keff)/keff
If you disagree with any of our comments on these questions, or would care to add further enlightenment, we would appreciate hearing from you. Our E-MAIL EXPRESS is just a click away. In the next issued of NUKEFACTS we will address questions dealing with Reactor Kinetics and Neutron Sources.