NUKEFACT #32

POWER REVERSAL in the DELAYED-CRITICAL REGION

last update September 11, 1998
Power reversal, sometimes referred to as power turning, is a common operational condition in both the Sub-Critical (S-C) and Delayed-Critical (D-C) regions. Herein, we address power reversal in the Delayed-Critical region. D-C power reversal is a transient condition that occurs whenever an ongoing reactivity change, i.e. a rho-dot, causes an ongoing power change to reverse direction. The unusual feature of a power reversal is that it does not require a reversal in reactivity itself. This means that power can be decreasing while the reactor is supercritical, and likewise, power can be increasing while the reactor is subcritical. Power reversal is important for two reasons:

Operational: power reversal demonstrates that the reactivity condition in the D-C Region, i.e. the determinant of power behavior with time, is completely defined only when both rho and rho-dot are specified. (See NUKEFACT #5, REACTIVITY, and NUKEFACT #9, AGAIN: TWO CONTRIBUTORS). Most importantly, the reactor operator should be cognizant of the fact that the direction of power change is not necessarily indicative of whether reactivity is positive or negative, of whether the reactor is subcritical or supercritical, in the Delayed-Critical region.

Safety: power reversal is crucial factor in certain aspects of reactor safety. For example, in a supercritical accident type power excursion, a negative rho-dot of sufficient magnitude, as in a reactor scram, can provide instantaneous power reversal while still supercritical, and thereby terminate the transient without core damage. Reactor scram will be the topic of the next essay, Nukefact #33.

The Physical Process Underlying Power Reversal:

Explanation of the physical process causing power reversal is found in the D-C transient reactor rate equation.

32.1

D-C TRANSIENT REACTOR RATE

where:
SUR(t) = the reactor startup rate at time t, decades-per-minute (DPM)
T(t) = the reactor period at time t, seconds
rho-dot = reactivity rate, delta-rho/sec
rho(t) = reactivity at time t
beta = precursor yield fraction
Lambda = effective precursor decay constant, sec-1

Previously, we have seen that constant power exists at criticality, with the reactor startup rate (SUR) = 0 DPM and the reactor period (T) = infinite seconds, because reactivity = 0 and reactivity rate = 0 delta-rho/second. However, there is another condition whereby zero reactor rate can be attained, albeit it momentarily in a transient condition. This is during a power reversal, e.g. as increasing power decelerates until reaching a maximum value and then decreasing. For power reversal to occur, rho and rho-dot must be of opposing algebraic sign, i.e. the reactivity ramp must be in a direction that reduces the magnitude of existing reactivity. For example a positive stable rate can be reversed by ramp-in to a negative transient rate while the reactivity, though being reduced, remains positive. At the instant of power reversal, reactor power is momentarily level, i.e. the startup rate = 0 DPM and the period = infinite seconds. The two terms in the numerator of the startup rate equation (denominator of the period equation), Equation 32.1, are equal in magnitude and opposite in sign, they sum to zero as (rho-dot + rho(t)) = 0, making the startup rate = 0 DPM and the period = infinite seconds.

As to the underlying physical process during power reversal, the prompt neutron population and the delayed neutron source strength are moving in opposite directions, one increasing while the other decreases. The prompt neutron population as determined by source multiplication, always changes in the same direction as rho-dot. Positive rho-dot causes the prompt neutrons to increase. Negative rho-dot causes the prompt neutrons to decrease. But the delayed neutron source strength changes in the same direction as the precursor inventory, which as a general rule depends on the algebraic sign of reactivity. Even though a complex power history can sometimes alter this dependence, we assume that an initial constant reactivity has set the direction of precursor change. Recall that a precursor imbalance exists at any time that the reactor is off-critical. Positive reactivity causes a mismatch such that precursor production in a life cycle exceeds precursor loss and the precursor inventory increases. Negative reactivity causes a mismatch such that precursor inventory decreases. If the rate of change of prompt neutrons from rho-dot is equal and opposite to that of the rate of change of delayed neutrons (precursor atoms), then the power reversal condition is met.

32.2

D-C POWER REVERSAL CONDITION

This condition applies to both subcritical and supercritical reversals in the D-C region. Beyond prompt criticality, with both delayed neutrons and prompt neutrons increasing from life cycle to life cycle, the condition does not apply.

Power Reversal on the D-C Reactor Rate Diagram

In practice, with rho and rho-dot of opposite algebraic sign, the reversal condition occurs in one of two ways, either as a reversal at some time after the ramp is initiated or as an immediate reversal:

1. Ramp Reversal (rho-dot < initial (lambda x rho)): Power change continues in the direction prior to ramp but at decelerating rate, until rho-dot = lambda x rho, at which point the ongoing ramp causes power reversal.

An example of a ramp reversal, as it appears on the reactor rate diagram, is shown in Figure 32.1.


FIGURE 32.1 - RAMP POWER REVERSAL on the D-C REACTOR RATE DIAGRAM

The sequence of events in ramp power reversal is as follows:

A. A stable positive rate exists (A). Reactivity is positive and constant.
B. As ramp-in initiates the reactor rate immediately moves downscale to a positive transient rate (B).
C. Continuation of ramp-in moves the transient rate to the left along the ramp-in curve. The positive rate is reduced as the power increase decelerates until the reactor rate crosses the horizontal (reactivity) axis (C). At this instant SUR = 0 DPM and T = infinite seconds. Power is momentarily constant as the power increase reverses to become a power decrease. Note that at this power turning point (C) reactivity is still well to the right of the origin, meaning that reactivity remains positive. The reactor is supercritical.
D. Further ramp-in continues to move the transient rate to the left along the ramp-in curve. The negative rate increases as the power decrease accelerates until the reactor rate crosses the vertical (reactor rate) axis (D). At this instant reactivity = 0 and continued ramp-in brings the reactor subcritical.
E. Ramp-in continues to introduce negative reactivity until the ramp is terminated at negative transient rate (E).
F. With constant reactivity, the reactor rate immediately moves upscale to the stable rate curve, at negative stable rate (F).

2. Immediate Reversal (rho-dot > initial (lambda x rho)): Power Change reverses direction at the instant ramp action is initiated and continues during ramp interval.


FIGURE 32.2 - IMMEDIATE POWER REVERSAL on the D-C RATE DIAGRAM

The sequence of events in an immediate power reversal is as follows:

A. A stable positive rate exists (A). Reactivity is positive and constant.
B. As ramp-in initiates the reactor rate immediately moves downscale, across the horizontal reactivity axis (B). At this instant SUR = 0 DPM and T = infinite seconds. The power increase is terminated. Note that at this power turning point (B) reactivity is still well to the right of the origin, meaning that reactivity remains positive.
C. The immediate rate move continues to a negative transient rate (C) as the reactor remains supercritical. Continuation of ramp-in moves the transient rate to the left along the ramp-in curve.
D. The negative rate increases as the power decrease accelerates until the reactor rate crosses the vertical (reactor rate) axis (D). At this instant reactivity = 0 and continued ramp-in brings the reactor subcritical.
E. Ramp-in continues to introduce negative reactivity until the ramp is terminated at negative transient rate (E).
F. With constant reactivity, the reactor rate immediately moves upscale to the stable rate curve, at negative stable rate (F).

Note that in both ramp reversal and immediate reversal of a positive stable rate, it is the ramp-in curve in the fourth quadrant of the reactor rate diagram where power decreases with positive reactivity. Correspondingly, in reversal of a negative stable rate, it is the ramp-out curve in the third quadrant of the reactor rate diagram where power increases with negative reactivity.

Example Calculation of Power Reversal

Suppose we have the following condition: the reactor is supercritical on a stable rate. A ramp-in is initiated and power reversal occurs with reactivity = +0.0015. Assuming the rule-of-thumb lambdaeffective = 0.1 seconds-1, what is the rho-dot value of the ramp-in ... and for what time interval does power decrease while reactivity is positive?

SOLUTION -- Using Equation 32.2 to solve for rho-dot gives:


The relationship between rho-dot and reactivity is:

Thus, the time interval until positive reactivity is reduced to zero is 10 seconds. Operationally, this interval, from power reversal to reactivity reversal, usually ranges from a few to several seconds, depending on the specific conditions. However, it is possible for the interval to extend for severval minutes under certain circumstances. Note that in the operational supercritical region, the lambda-effective establishes the magnitude of the negative rho-dot as a fraction of the existing reactivity, or typically about one-tenth of the reactivity value for power reversal.

Real Time Power Reversal Transients

Power reversal in real time reflects the behavior shown on the reactor rate diagram. The two real time transients shown below correspond to the transients illustrated on the reactor rate diagram. The same sequence of events, A through F, is shown on the real time transients. The initial positive reactivity is introduced by a step change in reactivity, from criticality. How the initial positive reactivity occurs is irrelevant to the power reversal.

1. Ramp Reversal (rho-dot < initial (lambda x rho)):


FIGURE 32.3 - RAMP POWER REVERSAL in the D-C REGION

The slope of the reduction in positive reactivity is a measure of rho-dot. During the time lapse between power reversal (C) and reactivity reversal (D), power is decreasing while the reactor is supercritical.

2. Immediate Reversal (rho-dot > initial (lambda x rho)):


FIGURE 32.4 - IMMEDIATE POWER REVERSAL in the D-C REGION

Immediate power reversal in Figure 32.4 is from the same initial positive reactivity, and the same positive stable rate, as in Figure 32.3. On initiation of ramp-in, the reactor rate immediately moves negative, as the power peaks and begins to decrease. Note the greater slope in reduction of positive reactivity than in Figure 32.3, indicative of a larger negative rho-dot. The time interval of power decrease while in a supercritical condition is shorter because the larger negative rho-dot reduces reactivity to zero in less time than in Figure 32.3.

SUMMARY

The Reactor Operator will not be aware of the majority of power reversal transients because there is no indication of reactivity in the Control Room. Nevertheless, power reversal is an important behavioral characteristic of the reactor, and one that the reactor operator should understand.

  1. Power reversal is a common operational occurrence, important to operator understanding of reactor behavior and important to reactor safety.

  2. Power reversal does not require a reversal in reactivity.

  3. Power reversal requires an ongoing reactivity change in a direction that reduces the existing reactivity.

  4. Power reversal means that power can be decreasing while the reactor is supercritical.

  5. Power reversal occurs as either a ramp reversal or an immediate reversal.

  6. Power reversal alway precedes reactivity reversal.

  7. Power reversal results from an ongoing change in prompt neutron population that is opposite to an ongoing change in delayed neutron source strength.

HomePage | NukeFacts | ExamBank | PopQuiz | Visuals | NRC | Rx TRN | Xe TRN | FeedBack | E-mailXpress |