The Chernobyl accident was occurred in 1986.
The Chernobyl incident had experienced positive (+ve) reactivity feedback effect. We need to know first what the reactivity is. Reactivity is a measure of the departure of a reactor from criticality. Actually the criticality is related to the effective multiplication factor, keff. Multiplication factor keff is the ratio of number of fission in one generation to the number of fission in preceeding generation as shown below.
In diffusion theory when k < 1, the condition of reactor is subcritical. Subcritical mean the neutron population is keep decreasing in each generation. If we have k =1, the condition of reactor is called critical. Critical means the neutron population in the reactor is neither decreasing nor increasing. It is also called self-sustaining for the neutron chain reaction. When we have k > 1, the population neutron is supercritical. We know that the neutron population is increasing to each generation. The k value is important to determine the criticality. Actually the reactivity, ρ is related with keff with the equation below:
Once we know the amount of reactivity, ρ in reactor core, the population of neutron can be determined. Hence we can predict the reactor power at any given time. We should noted that there are many factor that effect the power level in reactor such as fuel depletion, temperature of reactor, pressure of reactor and poisons. Because there are many parameters to consider, the reactivity coefficient (αx) is introduced. Actually, the reactivity coefficient (αx) is the amount of change in reactivity per unit change in parameter and is given by
Δx | Δρ | αx |
↑ | +ve | +ve |
↑ | -ve | -ve |
Table 1 : Relationship between each variable
Changes in the physical properties materials in reactor will results in change of reactivity. Hence the reactivity coefficient (αx) is very crucial in indentifying the reactivity change (Δρ) given the change in physical properties (Δx). In nuclear physics, there are four most important reacticity coefficient αx listed below
1) Moderator temperature coefficient of ρ, αTmod (moderator/coolant)
2) Fuel temperature coefficient of ρ, αTfuel (fuel)
3) Pressure coefficient of ρ, αP (moderator/coolant)
4) Void coefficient of ρ, αvoid (moderator/coolant)
2) Fuel temperature coefficient of ρ, αTfuel (fuel)
3) Pressure coefficient of ρ, αP (moderator/coolant)
4) Void coefficient of ρ, αvoid (moderator/coolant)
Graph in Figure 1 is applicable to a large core fuelled with low-enriched fuel which is been used in nuclear industry today. We have been introduced with another ratio which is Nm/Nu ratio and also called moderator to fuel ratio. The amount of neutron will increase as we increase the amount of moderator Nm because the high amount moderator will make the leakage of neutron decreases. Then the absorption of neutron will be high and the thermal utilization factor will decrease and also resonance escape probability will increase. All of this trend can be seen in Figure 1. As we decrease the amount of moderator from the right to the left graph, the Nm/Nu ratio will decrease, then increase in slowing down time. This will increase the loss in neutrons by the resonance absorption thus increase the neutron in leakage. In practice, water-moderated reactor is designed with a Nm/Nu so that it can operated under moderated condition as shown in Figure 1. From Figure 1, when the temperature increases, the Nm/Nu decreases and because the water density becomes less, it’s creating the positive reactivity addition. The positive reactivity addition ρ will increase the effective multiplication factor and further increase the power and temperature in a dangerous cycle. This state called over moderated region. However when the same temperature increases would decreases the Nm/Nu and the density of water become decrease, the negative reactivity will be occurred. The effective multiplication factor keff will decrease and further decrease the power and the temperature in safe cycle. All of this can be explained in Figure 1. The Chernorbyl reactor power plan used the Boiling Water Reactor (BWR). It is uses water-moderated reactor. The disaster incident happened because there was no negative reactivity feedback effect in this reactor to lower down the reactor power as temperature. We hope that for the future, the engineer must take consideration of Nm/Nu ration in their design and put their design in under moderated region to make sure their reactor becomes more self-regulating.
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