NUKEFACT #26

POWER DOUBLING in REACTOR STARTUP

last update June 25, 1997

"Power doubling" is a procedure commonly used in reactor startup, primarily on BWR reactors. Control rods are withdrawn from the fully inserted position until the equilibrium subcritical power level is double the shutdown power. After a time appropriate to ensure equilibrium, control rods are then withdrawn further until the equilibrium power again doubles. Typically, five power doubles are used during the startup. At this point, the reactor is sufficiently near to criticality that the operator can pull rods, while monitoring nuclear instruments, to establish a positive operational stable reactor rate. The reactor is then supercritical and the power increase can proceed to the Point-of-Adding-Heat (POAH).

Some PWR reactors use a single "Factor-of-Eight" increase in power to control the startup. Of course, this is three doubles lumped into one overall increase in equilibrium power. At this point, the reactor is considered sufficiently near to criticality that the operator can pull rods, while monitoring nuclear instruments, to establish a positive operational stable reactor rate.

NUKEFACT # 24 showed that for the subcritical equilibrium power to increase by any factor (F), with a constant non-fission source, the reactivity must decrease by the same factor. In equation form this was expressed as:

26.1

where:
P = core power, watts
S-bar = S/(3.1x10¹⁰x 2.46)
S = non-fission source strength, neutrons/sec
rho = subcritical reactivity
F = the factor of increase in power

POWER DOUBLING

For power doubling, the factor F is numerically equal to two. So that we have:

26.2

This means that each time the power is doubled, the subcritical reactivity status of the core is halved. To illustrate by example, assume that the shutdown power, or Source Range count rate, is 10 counts per second (cps) and the shutdown reactivity is -0.1000. A series of 5 power doubles produces the following:

On the first power doubling, from 10 cps to 20 cps, the subcritical reactivity is reduced from rho = -0.1000 to -0.0500.

On the second power doubling, from 20 cps to 40 cps, the subcritical reactivity is reduced from rho = -0.0500 to -0.0250.

On the third power doubling, from 40 cps to 80 cps, the subcritical reactivity is reduced from rho = -0.0250 to -0.0125.

On the fourth power doubling, from 80 cps to 160 cps, the subcritical reactivity is reduced from rho = -0.0125 to -0.0063.

On the fifth power doubling, from 160 cps to 320 cps, the subcritical reactivity is reduced from rho = -0.0063 to -0.0032.

As can be seen from the "Multiplier" column of the Table, power doubling involves cummulative increases in power, which are: first = 2¹ = 2, second = 2² = 4 , third = 2³ = 8 , fourth = 2⁴ = 16 , fifth = 2⁵ = 32. Thus, five power doubles increases power by a factor-of-32 and reduces shutdown reactivity by the same factor-of-32.

There are four noteworthy features about this process, namely:

• It constitutes a simple procedure, which is desirable operationally.

• If not carried to extremes, e.g. by attempting to use an excessive number of doubles, it affords a very conservative procedure for approaching criticality.

• Five doubles, even when starting at a relatively large shutdown reactivity, places the reactor in close proximity of criticality, fully adequate for the operator to proceed with rod withdrawals at his discretion.

• Power doubling provides a safe procedure for reactor startup.

1. If the Source Range count rate is low and erratic, time must be allowed at each equilibrium condition to obtain an average reading on individual and multiple detectors.

2. Count response on different detectors may differ significantly in the early stages of startup. An average of multiple detectors should be used.

3. If the control rod reactivity rate is high, power double may be inadvertently exceeded. Remember that the delayed neutrons are lagging the power increase and will cause power to continue to rise to equilibrium after termination of rod withdrawal.

4. For each successive power double, as criticality is approached, the power increase after termination of rod withdrawal will be greater and the time to reach equilibrium will be longer.

5. Even though power behavior is being used as a guide for the startup, the operator should always continuously monitor the reactor rate behavior during any rod withdrawal.

FACTOR-of-EIGHT INCREASE in POWER

For a factor-of-eight increase in power, we have:

26.3

This means that after a factor-of-eight increase in power, the subcritical reactivity status of the core is reduced by the same factor-of-eight. Of course, from the previous examples, a factor-of-eight is equivalent to three power doubles. For a shutdown rho = -0.1000, this gives:

SUMMARY

In the early days of nuclear power, both fuel loading and reactor startup employed Inverse Multiplication (1/M) curves. Today, fuel loading still does, and some startup procedures, as well. However, power doubling and factor-of-8 methods for reactor startup have come into widespread usage. We are not aware of who is responsible for developing this technique, but it certainly is a positive contribution to operational procedures and to reactor safety. These startup techniques can be introduced to students, and practiced, on THE REACTOR TRAINER.