REACTIVITY

REACTIVITY 

•  Reactivity is a measure of departure of a reactor from critically. The reactivity is related to the value of Keff  and it is a useful concepts to predict how the neutron population of a reactor will change over time.
• Reactivity is a dimensionless number.  It does not have dimensions of time, length, mass, or any combination of these dimensions.   It is simply a ratio of two quantities that are dimensionless.

1. Reactivity  Coefficients 

•  A reactivity coefficient is defined as the derivative of the system reactivity with respect to the change in a lattice parameter.
  
• For instance, we can define:

•             It is important to know, for any given reactor design, the sign and magnitude of the various reactivity coefficients, as these coefficients suggest the consequences of sudden changes in the operating parameters:

•             A positive value for a reactivity coefficient means that a positive change in that parameter will increase reactivity and tend to increase power.

•              A negative value for a reactivity coefficient means that a positive change in that parameter will decrease reactivity and tend to increase power

•             In both cases, a larger absolute value of the reactivity coefficient Þ greater sensitivity to changes in that parameter. 

2. Moderator effects

                Figure 1    Effects of Over and Under Moderation on k_eff

Because the moderator-to-fuel ratio affects the thermal utilization factor and the resonance escape Figure 2   Effects of Over and Under Moderation on k_eff probability, it also affects k_eff.   The remaining factors in the six factor formula are also affected by the moderator-to-fuel ratio, but to a lesser extent than f and p.   As illustrated in Figure 1, which  is  applicable  to  a  large  core  fueled  with  low-enriched  fuel,  there  is  an

optimum  point above which increasing the  moderator-to-fuel ratio decreases  k_eff  due to  the dominance of the decreasing thermal utilization factor.  Below this point, a decrease in the moderator-to-fuel ratio decreases k_eff due to the dominance of the increased resonance absorption in the fuel.  If the ratio is above this point, the core is said to be over moderated, and if the ratio is below this point, the core is said to be under moderated.

In  practice,  

•  water-moderated  reactors  are  designed  with  a  moderator-to-fuel  ratio  so  that  the reactor is operated in an under moderated condition.  

• The reason that some reactors are designed to be under moderated is if the reactor were over moderated, an increase in temperature would decrease the N^m/N^u due to the expansion of the water as its density became lower.  This decrease in N^m/N^u would be a positive reactivity addition, increasing k_eff  and further raising power and temperature  in  a  dangerous  cycle.    

• If  the  reactor  is  under  moderated,  the  same  increase  in temperature  results  in  the  addition of negative  reactivity,  and  the  reactor  becomes  more self-regulating.

 

3. Moderator Temperature Effects

• The change in reactivity per degree change in temperature is called the temperature  coefficient of reactivity.   Because different materials in the reactor have different reactivity changes  with temperature and  the  various  materials  are  at  different  temperatures  during  reactor  operation, several  different temperature  coefficients  are  used.

•  Usually,  the  two  dominant  temperature coefficients are the moderator temperature coefficient and   the fuel temperature coefficient. The change in  reactivity  per  degree  change in  moderator temperature  is  called  the  moderator temperature  coefficient  of  reactivity.

• The  magnitude  and  sign  (+  or  -)  of  the  moderator temperature  coefficient  is  primarily  a function  of  the  moderator-to-fuel  ratio.  

•  If  a  reactor  is under moderated, it will have a negative moderator temperature coefficient.   

• If a reactor is over moderated,  it  will  have  a  positive  moderator  temperature  coefficient. A negative  moderator temperature  coefficient  is  desirable  because  of  its  self-regulating  effect.    For example,  an increase in reactivity causes the reactor to produce more power.  This raises the temperature of the core and adds negative reactivity, which slows down, or turns, the power rise.
  
  

4. Fuel Temperatue Coefficients

•  The fuel temperature coefficient is the change in reactivity per degree change in fuel temperature. This coefficient is also called the "prompt" temperature coefficient because an increase in reactor power causes an immediate change in fuel temperature.

•  A negative fuel temperature coefficient is generally considered to be even   more important  than   a  negative   moderator   temperature coefficient  because   fuel temperature immediately increases following an increase in reactor power.  The time for heat to be transferred to the moderator is measured in seconds.

• In the event of a large positive reactivity insertion, the moderator temperature cannot turn the power rise for several seconds, whereas the fuel temperature coefficient starts adding negative reactivity immediately.

• Another  name  applied  to  the  fuel  temperature  coefficient  of  reactivity  is  the  fuel  doppler reactivity  coefficient.    This  name  is  applied  because  in  typical  low  enrichment,  light  water- moderated, thermal reactors the fuel temperature coefficient of reactivity is negative and is the result  of the  doppler effect, also  called doppler  broadening.  

•  The phenomenon of  the doppler effect is caused by an apparent broadening of the resonances due to thermal motion of nuclei as illustrated in Figure 3.   Stationary nuclei absorb only neutrons of energy E_o.  If the nucleus is moving away from the neutron, the velocity (and energy) of the neutron must be greater than E_o to undergo resonance absorption.   Likewise, if the nucleus  is  moving toward the neutron, the neutron needs less energy than E_o to be absorbed.   Raising the temperature causes the nuclei to vibrate more rapidly within their lattice structures, effectively broadening the energy range of neutrons that may be resonantly absorbed in the fuel.  Two nuclides present in large amounts in the  fuel of  some  reactors  with  large  resonant  peaks  that  dominate  the  doppler  effect  are uranium-238 and plutonium-240.

Figure 2: Effects of fuel temperature on absorptions resonance Peaks

 

5. Pressure  Coefficient 

• Peaks The reactivity in a reactor core can be affected by the system pressure.  The pressure coefficient of reactivity  is  defined as  the  change in  reactivity per  unit  change in  pressure.   The pressure coefficient of reactivity for the reactor is the result of the effect of pressure on the density of the moderator. For  this  reason,  it  is  sometimes  referred  to  as  the  moderator density reactivity coefficient. As  pressure  increases,  density  correspondingly  increases,  which  increases the moderator-to-fuel  ratio in the  core. In  the  typical  under  moderated  core  the  increase  in  the moderator-to-fuel ratio will result in a positive reactivity addition.  In reactors that use water as a moderator, the absolute value of the pressure reactivity coefficient is  seldom a major factor because it is very small compared to the moderator temperature coefficient of reactivity.
  

6. Void  Coefficient

• In  systems   with  boiling  conditions,  such  as   boiling  water  reactors  (BWR),  the  pressure coefficient becomes an important factor due to the larger density changes that occur when the vapor phase of water undergoes  a pressure change. Of prime importance during operation of a BWR, and a factor in some other water-moderated reactors, is the void coefficient. The void coefficient is caused by the formation of steam voids in the moderator.

• The void coefficient of reactivity  is  defined  as  the  change  in  reactivity  per  percent  change in void volume. As  the reactor power is raised to the point where the steam voids start to form, voids displace moderator from  the  coolant  channels  within  the  core.  This  displacement  reduces  the moderator-to-fuel ratio, and in an under moderated core, results in a negative reactivity addition, thereby limiting reactor power rise. The void coefficient is significant in water-moderated reactors that operate at or near saturated conditions.