Chernobyl Incident

 

 The Chernobyl accident was occurred in 1986. Two Chernobyl plant workers died immediately and a further 28 people died within a few weeks due to acute radiation poisoning. The peoples around the case area were relocated. The April 1986 disaster at the Chernobyl nuclear power plant in the Ukraine was the product of  a not good design reactor and the also mistake made by  reactor operator in terms of safety culture. The accident destroyed the Chernobyl 4 reactor, killing 30 operators within three months and several further deaths later. Two people were killed immediately at the site. The Chernobyl disaster was the only accident in the history of commercial nuclear power where radiation-related fatalities occurred .However, the design of the reactor is unique and the accident is thus of little relevance to the rest of the nuclear industry outside the then Eastern Bloc.

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, k_eff. Multiplication factor k_eff 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 k_eff 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 (α_x) is introduced. Actually, the reactivity coefficient (α_x) is the amount of change in reactivity per unit change in parameter and is given by

Where Δρ = reactivity defects and Δx = change in variable parameter that effects reactivity. We can further observe the relationship of each variable in above equation. The Table 1 below shows the relationship of each variable

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 (α_x) 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 α_x listed below 

1)      Moderator temperature coefficient of ρ, α_Tmod                       (moderator/coolant) 
2)      Fuel temperature coefficient of ρ, α_Tfuel                                     (fuel) 
3)      Pressure coefficient of ρ, α_P                                                             (moderator/coolant) 
4)      Void coefficient of ρ, α_void                                                               (moderator/coolant)

Figure 1 : Variation of k_eff and its factors with the fuel-to-moderator ratio

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 N^m/N^u ratio and also called moderator to fuel ratio. The amount of neutron will increase as we increase the amount of moderator N^m 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 N^m/N^u 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 N^m/N^u so that it can operated under moderated condition as shown in Figure 1. From Figure 1, when the temperature increases, the N^m/N^u 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 N^m/N^u and the density of water become decrease, the negative reactivity will be occurred. The effective multiplication factor k_eff 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 N^m/N^u ration in their design and put their design in under moderated region to make sure their reactor becomes more self-regulating.

References : 

1. Lecture Notes (Reactor Theory II) ; by COE, Uniten
2. http://library.thinkquest.org/3426/ 
3. http://en.wikipedia.org/wiki/Chernobyl_disaster