October 23, 1996
Mr. Stewart Richards
Washington, DC 20555
This submittal responds to your letter dated May 14, 1996, pertaining to an incorrect equation used in the INPO Generic Fundamentals Catalog and to seven flawed questions in the same document. I am pleased to find that you concur with even one-half the issues raised. In the attachment to this letter, I extend and clarify my original comments on the issues to which you do not concur.
It is reassuring that these flawed test items do not appear in the NRC examination question bank and that you have recommended to INPO that they be removed from their catalog. However, if as you indicate, the contractor formulates an NRC/GFE by selecting questions from the INPO Catalog, this seems to be a suspect resource and a questionable starting point ... one that always presents the possibility of flawed questions slipping through to the NRC/GFE, in spite of any careful review. But, even more disturbing, the Training Centers use the INPO Generic Fundamentals Catalog in a number of ways, including: for creation of practice exams, as a source of Class Room examples, as exam questions on courses being taught, and even as a basis for subject matter in the course. Here, there is no review to filter flawed questions. When the students encounter the contradictions and errors contained in these INPO questions, it leads to confusion and doubt about their understanding of the subject matter. It has direct and significant impact on lowering the quality of the training and can adversely influence the students attitude toward the program.
In summary, and after review of the original submittal, I still find that all of the questions originally identified are flawed. And, as previously noted, the few questions submitted are just a sampling that represent the tip of the iceberg. I believe that your letter provides verification of this point by identifying 14 INPO questions that were found to be flawed, as identified, but in addition, contained other deficiencies that you discovered in the process of review. In the subject area of Reactor Theory, I estimate that, at a minimum, twenty-five percent of the questions in the INPO Generic Fundamentals Catalog are flawed. By any reasonable standard, this is totally unsatisfactory and in need of serious attention.
I reiterate that I am pleased with your initial response, it certainly differs from that experienced in dealing directly with INPO, and I look forward to mutually resolving the remaining issues.
Issue 1: Erroneous equation
In your letter you identify three equations, as follows:
Equation (2), is a version of the in-hour equation relating constant reactivity to stable period. However, it is not an inverted form of the equation identified as incorrect, namely:
Equation 4 is not equivalent to Equation 2. Specifically, it is the first term on the right-hand-side of this equation that is wrong. Even so, this term is negligible until near to prompt criticality. But it is here that the problem arises, and it is as much related to mathematical chicanery as to outright error. Once at prompt criticality, the numerator of the second term on the right-hand-side of this equation is zero, but beyond prompt criticality it becomes negative so that the equation no longer works. Typically, resolution is simply to drop the second term of Equation 4, to ignore it, and use the first as representative of reactor period at prompt criticality and beyond. Now I happen to believe that Class Room training places too much emphasis on the condition of prompt criticality to begin with. But to treat prompt criticality in this manner is pure voodoo mathematics, as well as bad example and poor training. Equation (2), being correct, does not require such malpractice.
This incorrect period equation, Equation 4, was included on the INPO equation sheet in the INPO Generic Fundamentals Catalog. It is incorrect, it is not accurate, and it is not appropriate. If still in use by INPO, it should be corrected. Both equations (1) and (2), in your letter, are applicable to a constant reactivity condition. It matters not how that constant reactivity condition was attained, i.e. whether preceded by a step reactivity change or a ramp reactivity change. Equation (1), in particular, has no unique relationship to a step change in reactivity. No caveats are necessary in the test item.
You state that "Insofar as actual reactor operation in a commercial power plant is concerned, there is very little difference in using equation (1) or (2) and equation (3)." This assertion, besides being contradicted by what occurs on Control Room period meters every day, is a generalization that cannot withstand scrutiny, first because of the variety of commercial reactors in existence, secondly because of the possible variety of transients that may occur, and thirdly because you selectively focus on only one particular aspect of operation that supports your thesis. The period meter is the most sensitive meter available to the Reactor Operator during reactor startup for indicating the proximity to criticality, and the behavior represented by the delta-rho/dt term in Equation (3) is an invaluable part of such response.
You use the withdrawal of average control rods during startup, with a reactivity rate of 0.000015 delta-rho/second, to support the lack of difference between Equation (2) and Equation (3). Consider the following :
1. While far subcritical, as with the 12% dk/k shutdown value chosen, you are correct, the delta-rho/dt term contribution to the reactor period will be insignificant in Equation (3) and not visible on the Control Room period meter. But, even at this relatively slow reactivity rate, the contribution of the delta-rho/dt term does become significant, quite visible, a key indicator, and very helpful to the Reactor Operator, as criticality is approached and surpassed. The so called 100 second (stable period) limit is shortened to 78 seconds using Equation (3) for an average delta-rho/dt and to 56 seconds for a rod worth three times the average.
2. In actuality, all control rods are not average. Core spatial power distributions cause certain rods to be worth more, i.e. have greater reactivity rates when moving, commonly by factors-of-three or four greater than the average rod. And, situations have actually occurred where the worth of individual rods was even much greater.
3. Rod withdrawal is not the only reactivity change to be considered. To offer just one example, where substantial difference in reactor period derived by equations (1) and (2) versus equation (3) exists, one need only consider a reactor scram. During scram all rods are moving inward simultaneously at a speed considerably in excess of 3 inches/second. Here, the delta-rho/dt contribution is a major component of reactor period until the rods are fully inserted.
Finally, in your concluding paragraph on this matter you state that " ... operation outside of limits is typically precluded by automatic trip features and if operators are faced with unforeseen circumstances, operators will trip the reactor. ... An operator may or may not know about equation (3), however, it is difficult to see how a lack of knowledge of equation (3) could result in a safety problem, or cause an operator to take an unsafe action." With this rationale, most operator training in fundamentals can be eliminated. Equation (3) is the general equation for reactor period, whether it be a transient period or a stable period. It happens to be a rare part of Class Room fundamentals training that relates directly to the behavior of an important meter in the Control Room. It is the most important equation available for describing reactor transient behavior in a practical manner. It is invaluable for student understanding of transient reactor behavior and is not difficult to use. In fact, it is widely used in Training Centers without difficulty.
Question: Reactor Operational Physics, number 10 ... you concur - no further comment.
Question: Reactor Kinetics and Neutron Sources, number 20
You do not concur with point 1. Perhaps my explanation of the flaw was deficient. The first sentence of the problem states that Figure 14 shows how a reactor would respond to a notch withdrawal of a control rod. "Would" is the operative word; it implies that this is the only possible response. My point was that the response shown in the Figure is not the only possible response. The response is dependent on the initial and final reactivity condition. The problem statement does not specifically identify the reactor conditions for which the Figure 14 behavior applies. If a notch withdrawal is made from a subcritical condition of equilibrium multiplication to a lesser subcritical condition, Figure 14 does not represent the response. And, remaining subcritical does not result in a negative reactor period.
You concur with point 2 - no further comment.
Question: Reactor Kinetics and Neutron Sources, number 21
You do not concur for same reason as number 20 - see comment for point 1, number 20.
You do not concur with point 2. You reference the same reasoning to explain the behavior between points 2 and 3 as used in number 20 between points 4 and 5. The two situations differ, such that the same explanation is not applicable to both. In problem 20 the response was correctly qualified as being "after a small positive reactivity addition". The reactivity was constant. The behavior exhibited between points 2 and 3 occurs during reactivity addition. Here there are two contributors to the reactor period, namely an increase in the prompt neutron population due to an ongoing increase in reactivity and an increase in the delayed neutron population because the reactor is supercritical. In Equation (3) the prompt neutron contribution is represented by the delta-rho/dt term, while the delayed neutron increase is represented by the (lambda x rho) term.
Question: Reactor Kinetics and Neutron Sources, number 22
Although I did not comment on this question, you indicate that it contains the same problems as numbers 20 and 21. No comment was made because the answer, describing the slope of the graph from point 1 to 2, was correct.
Question: Reactor Kinetics and Neutron Sources, number 27 ... you concur - no further comment.
Question: Neutron Life Cycle, number 2
You do not concur. You state that "Although not necessary to classify a reactor as supercritical, an increasing neutron population is an important related knowledge and is not irrelevant nor potentially incorrect as stated in the comment." The reference section in the BWR document deals with a primitive model where keff is constant. I do not disagree with this presentation, but a constant keff was not a stated condition in the INPO question. Although I do not have access to Glasstone and Sesonske, I suspect that reference is for the same, constant keff , situation. In any case your statement is incorrect. This is a fundamental concept so paramount to the study of reactor physics and reactor behavior that, if the definition of keff is muddled in this manner, then the entire subject of reactor behavior is corrupted.
The phenomenon of Power turning occurs while the reactor is supercritical and requires no "momentary decrease in keff below 1.0, thereby making the reactor subcritical for an instant". Operators are not required to know the effect of rho-dot, as prompt jump or prompt drop (rho-dot = delta-rho/dt). Prompt jump and prompt drop are related to power behavior. Rho-dot relates to the behavior of reactor period.
Question: Neutron Life Cycle, number 11
You concur in part with the comment. You indicate that there are two contradictory definitions of Shutdown Margin in existence, one in a 12 year old BWR reference and the other in standard Technical Specifications. Receipt of your letter prompted another look at the BWR reference. The section on Shutdown Margin, approximately two-thirds of a page in length, is not particularly well written. It does not specify the conditions to which the shutdown margin applies, although it does state that ... "If plant capability and design are maintained such that some limit less than keff = 1 can always be met, then assurance exists that the reactor can always be made subcritical." In a BWR, the most reactive condition, that must always be met, is cold, xenon free, with the most reactive control rod fully withdrawn. The last paragraph reads as follows:
"In order to meet the tech spec requirements, the shutdown margin is usually calculated with all control rods inserted in the core. Sufficient rods can then be withdrawn to equal the SDM requirements (again calculated), and through use of nuclear instrumentation the core can be shown to be still be subcritical."
It appears that the wording choice in the first line, i.e. shutdown margin, is unfortunate and unnecessarily confusing. I believe that the shutdown reactivity was being calculated for the condition of all control rods inserted. Both shutdown margin and shutdown reactivity can be expressed in terms of 1 - keff. Note that the SDM notation was not used in this instance. The following sentence then speaks of withdrawing control rods to demonstrate the SDM requirements are met as the reactor remains subcritical. Thus, I do not believe there are, in fact, two contradictory definitions of SDM. The standard Technical Specification definition should be used, exclusively.
Question: Reactor Operational Physics, number 24
You concur but do not find corrective action necessary because "the terms step increase and prompt jump are equivalent and are not expected to cause any confusion." No references are given to support this position. The term prompt jump derives from the fact that the observed change power is associated with prompt neutrons. The term step increase defines a geometric shape and lacks the descriptive connotation of prompt jump. Therefore, the two terms are not equivalent. In fact a step change is conventionally understood to be just that, an instantaneous, sharp cornered step. Prompt jump neutron response is technically not a step. Even the prompt neutrons take several thousand life cycles to reach the final equilibrium of the jump. Hence, the prompt neutron response results in a rounded corner instead of the sharp corner on the step. Allowing unnecessary multiple terminology, or using terminology interchangeably where not really appropriate, is not at all helpful to the student.
Robert G. Stater