Lecture 27 Reactor Kinetics-III

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1 Objectives In this lecture you will learn the following In this lecture we will understand some general concepts on control. We will learn about reactivity coefficients and their general nature. Finally, we will learn about Xenon poisoning.

2 Control Rods We have understood the response of a reactor for a change in reactivity. Such planned reactivity insertions are accomplished by operating control rods (neutron absorbers) provided in the reactor. Typically, compounds of B, Cd, Gd, etc. are used. As the rods are discrete entities, their partial insertion or withdrawal changes the homogeneous character of the core composition. Consequently, the analysis of their influence is complex and is beyond the scope of an introductory course. However, to appreciate the qualitative behaviour, it is enough to consider a reactor as a point system. As a control rod is inserted or withdrawn, it affects the fuel utilization factor f. As and Thus an insertion of rod increases neutron absorption in the absorber material and hence the fraction of neutrons absorbed in the fuel, viz., f, decreases. This implies ρ is negative as f 0 > f. In the last lecture we understood that insertion of ρ = β results in prompt criticality. Hence, care has to be taken that an accidental removal of one control rod should not add large enough ρ. At the same time, over the life of the fuel residence time in the core of a reactor, there is a large depletion of fissile material. This implies we need to have a large inventory of the control material. This leads to a conflict that the reactor may not have space to accommodate all of the control rods.

3 Burnable Control Materials This issue is solved by employing burnable control material, at times called burnable poisons (owing to their very large absorption cross section) or by chemically dissolving control material in moderator and coolant (called chemical shim control)). In solid burnable poisons like Gadolinium, once it absorbs a neutron, the cross section of the product nuclei is much smaller and therefore Gadolinium said to have been burnt. Similarly the concentration of dissolved Boron in the form of Boric acid can be controlled to control the reactivity of the core. Thus by using one of the two or both schemes described above the control rod inventory and its movement can be minimised.

4 Reactivity Coefficients When a reactor is operated, change of its operating state can induce reactivity changes. These can be due to changes in: Temperature of the fuel, Temperature of the moderator, Voids in the coolant. Many different reactivity coefficients are used during specific analysis. They are expressed as In the above expression α is the volume fraction of void. Larger the reactivity coefficient, larger will be the influence of that parameter on the power. A positive value for a reactivity coefficient will increase reactivity change in that parameter and therefore would increase the reactor power. A negative value for a reactivity coefficient will decrease reactivity for a positive change in that parameter and therefore would decrease the reactor power. As the changes in reactivity induced are often small, the unit of %mk ( ) is commonly used. Examples of units for reactivity coefficients are, %mk/c (for the temp coefficient),%mk/(g/cm 3 ) (for the density coefficient), %mk/%fp (for the power coefficient; note FP stands for full power).

5 The Fuel Temperature Reactivity Coefficient This coefficient is determined by the influence of temperature on the neutron absorption cross section. Of particular importance is the resonance absorption cross section. We had discussed in our lecture on variation of cross section with energy of neutron that if the neutron has a speed which exactly matches with the resonance energy, then there is a high probability of absorption (shown below). Ideally, this would be a sharp line, but due to the statistical variation of energy introduced by temperature, neutrons having energy nearby the resonance energy will also be absorbed and hence the spread. The net effect of increasing temperature is to broaden the resonance, while at the same time reduce the peak. This is called Doppler Effect or Doppler Broadening as shown below. It has been shown using detailed theoretical arguments that area under the curve increases with temperature and hence the absorptions increase.

6 The overall effect on reactivity will be dictated by the changes in fission and capture resonance. In general, the increase in capture is more than that of fission and hence this reactivity coefficient is generally negative. As fuel responds immediately to power changes, this coefficient plays a crucial role in compensating for accidental insertion of positive reactivity. This effect makes the power increase to be self limiting.

7 The Moderator Temperature Reactivity Coefficient The sign of moderator or coolant temperature coefficient depends on many factors. For water reactors, increase in temperature results in decreased density. This implies less collision leading to less moderation and hence increase in resonance absorption, leading to negative coefficient. However, reduction in density leads to reduction in direct absorption of neutrons, leading to positive coefficient. Particularly if chemical absorbers are added, the net effect is positive. This is often the case in PHWRs.

8 The Void Reactivity Coefficient This is of particular relevance to the BWRs, where voids are present in the core. An increase in void decreases the density of the moderator. This results in decrease of moderation leading to large reduction in thermal neutrons as well as increase in resonance absorption leading to negative coefficient. Though reduction of moderator density leads to reduction in direct absorption of neutrons, leading to increase in reactivity, this effect is small. Hence moderator void coefficient is negative.

9 The Power Reactivity Coefficient As the power of the reactor is increased, all of the effects described comes into play and decides the overall power coefficient of the reactivity. This reactivity coefficient is useful in characterising whether the reactor is load following. Let the reactor have a positive power coefficient of reactivity. Consider a case that due to reduction in grid load, the heat removed from the reactor is decreased. This will lead to increase in temperature of the system leading to an overall negative reactivity and reduction in neutron power. The opposite will be for an increase in power. Such systems that have positive overall power coefficient are said to be load following.

10 Xenon Poisoning Some of the fission products or daughter products of the fission products are highly neutron absorbing and are denoted as poisons. The most important of them are 135 Xe and 149 Sm. In both these cases the nuclides are directly born as fission products as well as produced by the β-decay of other parent fission products. The Chain for Xenon is shown below: The large absorption cross section of 135 Xe plays a crucial role and affects the system reactivity. Usually as the half life of Tellurium is very small, its yield is also added to the yield of Iodine. We will not worry about the chain after Cesium as it is not of our interest. The governing equation for Iodine (I) and Xenon (X) concentration can be represented as In the above equations the symbols represent the following: φ - nuetron flux γ I - yield of Iodine nuclei γ X - yield of Xenon nuclei λ I - decay constant of Iodine λ X - decay constant of Xenon σ X - absorption cross section of Xenon Σ f - macroscopic fission cross section t - time

11 At steady state, the time derivatives are 0 and hence we can write, From above we can write It may be noted that While I ss is directly proportional to flux, X ss saturates at higher fluxes. The reactivity equivalent of these poisons can be estimated as follows: We had derived in the early part of the lecture that As and For the reactor to be steady before poison build up Thus we can write Since and For γ I = and γ x = , ν = 2.42

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