REACTOR PERIODS AND REACTIVITY

An important quantity in reactor kinetics is neutron lifetime. Fundamentally, the neutron lifetime may be divided into two parts: (a) slowing down time, which is the mean time required for fission neutrons to slow to thermal energies and, (b) diffusion time, which is the average time that thermal neutrons will diffuse before absorption. For the neutron lifetime in water, the sum of these parts is equal to 2.47E-4 sec. The prompt neutron generation time, l_p, which includes the fission time (10E-14 sec) is considered equal to the neutron lifetime. The delayed neutron generation time, l_d , is the weighted average of the mean generation times of the six delayed neutron precursors and is equal to 13.05 sec. The effective decay constant, lambda_eff, for the weighted mean times is 1/ l_d.

Delayed neutrons are a small fraction of all neutrons in the reactor core. Nonetheless, they have dominant effect on the reactor time response. When the weighted average for neutron generation time is calculated, the effective or weighted neutron generation time, l_eff , is approximately equal to 0.085 sec. This value is much greater than the prompt generation time and thereby allows control over reactor response.

The time rate of change of neutron population in a delayed critical reactor is:

dN/dt = (K_eff - 1)N / l_eff = (dK / l_eff)N

When integrating from N(0) to N, this yields:

N(t) = N(0) e^{(dK / leff ) t}

The reciprocal of dK / l_eff is referred to as the reactor period, T.

Thereby, T = l_eff / dK

If we use the approximation rho = dK, the delayed critical period then becomes T = l_eff / rho.

As positive reactivity is added to the critical reactor, the effects, in terms of time response and generation time, for prompt neutrons is enhanced and the effects for delayed neutrons are diminished. The delayed neutron fraction effectively decreases in proportion to the positive reactivity added, while the prompt neutron fraction increases. The effect on the effective neutron generation time can be seen in the following equation:

l_eff= (1-beta_eff + rho)l_p+(beta_eff - rho) l_d

Even for values of reactivity that approach the value of beta-effective, the first portion of the equation is still less than 8% of the total. Therefore, for practical purposes it can be ignored and:

l_eff=(beta_eff - rho)l_d

Substituting 1/lambda_eff for l_d, the period approximation for the delayed critical reactor is then:

T = l_eff/rho = (beta_eff - rho )/(lambda*rho)

To measure the reactor period, and to correlate period with regulating blade reactivity versus blade position.

Regulating Blade

The reactor staff will have the reactor check-out completed and will bring the reactor to critical below 10 watts. The three control blades should be at 30.00" withdrawal. When stable for at least 5 minutes, note the power, water temperature, and the reg blade position. Read the power on CIC 1 and 2.

Have the operator withdraw the reg. blade 2.00", and record successive (power) doubling times after completing rod motion. When a stable doubling time is attained, have the operator drive in the reg blade to establish critical operation. Do not exceed 1 kW.

• Now, with the reactor critical and below 1 kW, note the reg blade position and insert the reg blade 2", taking readings similar to above.
• Establish critical operation near 1 W. Record stable power levels.
• Repeat the above procedures for reg blade changes in two inch increments (i.e., critical position plus or minus 2", 4", 6", etc.).
• Take readings on 15 sec intervals if necessary.
• Do not exceed a 30 sec. period.
• Terminate this portion of the experiment when the time available is insufficient to establish a stable period.

• Have the operator establish a critical power level at 10 kW.
• Allow 5 minutes for the readings to stabilize.
• Note the new reg. blade position and water temperature.

1. Calculate the period for each set of data based upon the observed doubling time.
2. Compile the results and plot the stable period vs. reg blade motion (in and out) from the critical position.
3. Calculate the value of rho as a function of the rod position and plot reactivity vs rod movement.
4. Briefly explain the shapes of the above curves.
5. Calculate the excess reactivity of the reg blade (up to your last measurement)
6. Using your reactivity data, estimate the temperature coefficient for the reactor (reactivity per degree F). How does it compare to the FSAR value?