In your January 10th and February 28th letters you included the following equation, drawn from the INPO Catalog, which you stated is incorrect.

(1)

The Generic Fundamentals Examination Equation Sheet contains two equations (the second, an inverted form of the above) which relate stable reactor period, Tau, to reactivity, rho, viz.:

	(1)
	(2)

where Tau = stable reactor period (seconds)

Beta = average delayed neutron fraction (approx. = 0.007)

Lambda = average precursor decay constant (approx. = 0.1 sec.^-1)

l^*= prompt neutron generation time (approx. = 0.0001 sec.)

Rho = reactivity

These equations are developed in all of the standard texts (Glasstone and Sesonske, Nuclear Reactor Engineering, 3rd. ed., 1981 and Lamarsh, Introduction to Nuclear Engineering, 2nd. Edition, 1983).

In the usual case where reactivity insertions are small, and hence periods are long, the first term on the right-hand side of equation (2) is negligibly small and may be dropped from the equation. In that case, equations (1) and (2) become identical.

The stable reactor period given by equation (1) strictly applies to the situation where power is constant, a step change in positive reactivity is inserted, and the power increases on a constant period, all other effects (such as temperature changes) being neglected. There is another form of the equation which includes a rate of reactivity insertion. This form applies to situations where reactivity is changing at the same time that power is changing, such as continuously withdrawing a control rod, viz.:

(3)

where delta-rho/delta-t = the rate at which reactivity is inserted. Equation (3) is referred to as the transient period equation.

ATTACHMENT

Insofar as the GFES is concerned, questions which require calculations of reactor period are usually phrased so that equation (1) or (2) applies. 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). Commercial reactors have many control rods (e.g. Limerick, with 185 rods), each having a small worth by design. In such cases, it is not possible to add positive reactivity with control rods at an appreciable rate since rod worths are small and rod withdrawal rates are low. This is different from a research or naval reactor, where rapid insertions of positive reactivity are routine.

As an example, the total rod worth of the Limerick reactor is about 12% delta-k/k, or about 0.00065 delta-k/k per rod. If the reactivity of a single rod was added as a step change, then equation (1) is applicable and would result in a period of about 100 seconds. In an actual plant, the withdraw speed is about 3 inches per second and requires about 48 seconds to fully withdraw a rod. In this case, the rate of reactivity addition (delta-rho/delta-t) is about 0.000014 delta-k/k/second. In accordance with equation (3) the period will continually change as reactivity is added, but can never be shorter than 100 seconds. One hundred seconds is a long period, easily controllable by an operator.

Finally, as you know, 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. The operator has available either a rate meter, a period meter, or a power meter to assess the rate of change of the neutron population. We conclude that the combination of training, procedures, and instrumentation is adequate for reactor plant operations in typical commercial nuclear reactors.

Issue 2: Identification of certain problematic generic fundamentals test items.

Question: Reactor operational Physics, number 10

If Keff = 1.0, what is the subcritical Multiplication factor?

A. zero
B. 0. 5
C. 1.0
D. infinite

Answer: D

Comment:

Subject Area: REACTOR OPERATIONAL PHYSICS Question Number: 10

Explanation of problem:

If the question is intended to be one of identifying the equation for the subcritical multiplication factor and then correctly plugging in a Keff value to evaluate a particular condition, then the value chosen for Keff is not appropriate for two reasons:

1. Mathematically, the subcritical multiplication factor representation is invalid at Keff = 1.0000. The algebraic sign of (Keff - 1) must be negative for the subcritical multiplication factor to be valid. Or put another way, Keff must be less than 1.0000 for the subcritical multiplication factor to be a valid expression.

2. From the practical operational standpoint, it is impossible for the subcritical multiplication factor to be infinite, because this would make the power level infinite.

Proposed resolution

Use a value such as Keff = 0.9999. Then the subcritical multiplication factor would be

M = 1/1-K = 1/1-0.9999 = 10,000

NRC Response:

1. Merit: Concur with both points in the comment. The key issue concerning the applicability of the subcritical multiplication factor is that it only applies when the reactor is subcritical. According to Glasstone and Sesonske, Nuclear Reactor Engineering, 1981, p. 191, the subcritical multiplication factor is valid "provided K < 1, i.e., the [reactor] is subcritical." Westinghouse, Fundamentals of Nuclear Reactor Physics, 1983, p. 8-14, states,

"If the reactor becomes critical ... the subcritical multiplication factor is undefined." Since the question references a reactor with a Keff of 1.0, the reactor is critical and, therefore, subcritical multiplication does not apply.

2. Resolution: Concur with the comment. Do not use the question in its present form.

3. Presence in NRC examination question bank: Not present.

4. Presence in 9/94 INPO BWR catalog: Not present.

5. Presence in 9/94 INPO PWR catalog: Question #28 is nearly the same.

Question: Reactor Kinetics and Neutron Sources, number 20

The graph in Figure 14 shows how reactor period would respond to a notch withdrawal of a control rod. Which of the following statements best interprets the graph from points 4 to 5?

A. The period is controlled by prompt neutron production.

B. The period is controlled by prompt and delayed neutron production.

C. The period is controlled by the production of delayed neutrons only.

D. This line depicts the existence of a period equal to zero.

Answer: B

Comment:

Subject Area: REACTOR KINETICS AND NEUTRON SOURCES Question Number: 20

Explanation of problem: There are two weaknesses with this question.

1. The question is poorly worded because there is a second way that the reactor period can respond to a notch withdrawal of the control rod ... namely, when the notch withdrawal is from an initial condition of equilibrium multiplication and the final reactivity remains subcritical.

2. The specified correct answer (B), is not the best answer choice for the situation intended. The reactor period is constant from Point 4 to 5 because the delayed neutron emissions are increasing exponentially with time. The prompt neutrons are also increasing exponentially, but would not be doing so if it were not for the increasing delayed neutrons. It is the delayed neutrons that are controlling the period from point 4 to point 5

Proposed resolution:

1. Reword the question to read as follows:

"The graph in Figure 14 shows how reactor period responds to a notch withdrawal of a control rod from criticality. Which of the following statements best interprets the graph from point 4 to point 5?

2. Make (B) the correct answer to read:

"B. The period is controlled by the production of delayed neutrons."

and change (C) to read:

"C. The period is controlled by the production of non-fission source neutrons."

NRC Response:

1. Merit: Do not concur with point 1. The reactor period shown in the figure cannot represent the reactor period response when the reactor remains subcritical. If a reactor remains subcritical after a notch withdrawal, reactor period will become negative and approach infinity. The figure shows a final reactor period that is positive and steady state. With rod movement stopped, this could be achieved only by a critical reactor with neutron level below the point of adding heat (POAH). Therefore, the contention that the reactor may remain subcritical is incorrect.

Concur with point 2. According to Glasstone and Sesonske, Nuclear Reactor Engineering, 1981, p. 242 and 243, and General Electric, BWR Academic Series, Reactor Theory, 1984, p. 3-33a, the steady state reactor period following a small positive reactivity addition to a critical reactor is determined by the amount of positive reactivity in the core and the value of the average delayed neutron fraction (Beta). Beta is determined by the fraction of fission neutrons that are born delayed. Without delayed neutrons in the core, the reactor period would be determined by prompt neutrons alone, resulting in an uncontrollably short reactor period for even a small addition of positive reactivity--this is what happens in a prompt critical reactor. However, if the reactor does not become prompt critical, the fraction of fission neutrons that are born delayed will control the reactor period.

It also appears that there is a problem with word choice in this question. The stem asks which option "best" interprets the graph. NRC examination policy discourages use of the word "best" since it may require a subjective evaluation of the options, yielding the possibility that there is more than one correct answer. Additionally, three of the four options begin, "The period is controlled..." In these options, the word "controlled" can be interpreted to mean "determined," in which case options A and B would be correct answers.

2. Resolution: Do not concur. Although some of the problems with the question have been corrected, the use of the word "controlled" will still cause some interpretation problems. In addition, the use of the word "best" in the stem should also be avoided. Do not use the question in its present form. Do not use the proposed solution.

3. Presence in NRC examination question bank: Not present.

4. Presence in 9/94 INPO BWR catalog: Not present.

5. Presence in 9/94 INPO PWR catalog : Not present.

Question: Reactor Kinetics and Neutron Sources, number 21

The graph in Figure 14 (refer to p. 5) shows how reactor period would respond to a notch withdrawal of a control rod. Which of the following statements best interprets the graph from points 2 to 3?

A. The change in period is controlled by neutron production.

B. This portion of the curve depicts the existence of an infinite period.

C. The change in period is controlled by the production of delayed neutrons.

D. This portion of the curve depicts the existence of a period equal to zero.

Answer C

Comment:

Subject Area: REACTOR KINETICS AND NEUTRON SOURCES Question Number: 21

Explanation of problem: There are two weaknesses with this question.

1. The question is poorly worded because there is a second way that the reactor period can respond to a notch withdrawal of the control rod .:. namely, when the notch withdrawal is from an initial condition of equilibrium multiplication and the final reactivity remains subcritical.

2. The specified correct answer (C), is not the best answer choice for the situation intended. The reactor period response from point 2 to 3 is due to combination of increasing prompt neutrons and increasing delayed neutrons. The prompt neutrons are increasing because ongoing rod withdrawal from point 2 to point 3 produces an ongoing increase in source multiplication, and power. The delayed neutrons are increasing because the power increase from greater multiplication causes precursor production to exceed precursor losses, increasing the precursor inventory.

Proposed resolution:

1. Reword the question to read as follows:

"The graph in Figure 14 shows how reactor period responds to a notch withdrawal of a control rod from criticality. Which of the following statements best interprets the graph from point 2 to point 3?"

2. Make (C) the correct answer to read:

"B. The change in period is controlled by the production of both prompt and delayed neutrons."

NRC Response:

1. Merit: Do not concur with point 1. The reactor period shown in the figure cannot represent the reactor period response when the reactor remains subcritical. The figure shows a final reactor period that is positive and steady state. With rod movement stopped, this could be achieved only by a critical reactor with neutron level below the point of adding heat (POAH). Therefore, the contention that the reactor may remain subcritical is incorrect.

Do not concur with point 2. The comment describes what causes changes in reactor period but the question asks what controls the reactor period. According to Glasstone and Sesonske, Nuclear Reactor Engineering, 1981, p. 242 and 243, and General Electric, BWR Academic Series, Reactor Theory, 1984, p. 3-33a, the steady state reactor period following a small positive reactivity addition to a critical reactor is determined by the amount of positive reactivity in the core as well as the value of the average delayed neutron fraction (Beta). Beta is determined by the fraction of fission neutrons that are born delayed. Without delayed neutrons in the core, the reactor period would be determined by prompt neutrons alone, resulting in an uncontrollably short reactor period for even a small addition of positive reactivity--this is what happens in a prompt critical reactor. However, if the reactor does not become prompt critical, the fraction of fission neutrons that are born delayed will control the reactor period.

It also appears that there is a problem with word choice in this question. The stem asks which option "best" interprets the graph. As stated in the previous question, the word "best" should be avoided as it requires a subjective evaluation of the options, yielding the possibility that there is more than one correct answer. In options A and C, the word "controlled" can be interpreted to mean "determined," in which case, options A and C would be correct answers.

2. Resolution: Do not concur. Although some of the problems with the question have been corrected, the use of the word "controlled" will still cause some interpretation problems. In addition, the use of the word "best" in the stem should-be avoided. Do not use the question in its present form and do not use the proposed solution.

3. Presence in NRC examination Question bank: Not present.

4. Presence in 9194 INPO BWR catalog: Not present.

5. Presence in 9/94 INPO PWR catalog: Not present.

Question: Reactor Kinetics and Neutron Sources, number 22

(Note: Although you did not comment on this question, it contains the same problems as numbers 20 and 21 and, therefore, will not be used in its present form.)

The graph in Figure 14 shows how reactor period responds to a notch withdrawal of a control rod. Which of the following statements best describes the slope of the graph from point 1 to 2?

A. The change in period is controlled by prompt neutron production rate.

B. This portion of the graph depicts the existence of an infinite period.

C. The change in period is controlled by the production of delayed neutrons.

D. This portion of the graph depicts the existence of a period equal to 0 (zero).

Answer A

attachment continued - pp 11-19

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