Samarium Equilibrium – Promethium Equilibrium
When the rate of production of promethium equals the rate of removal of promethium equilibrium exists. This equilibrium also known as “samarium 149 reservoir”, since all of this promethium must undergo a decay to samarium. In equilibrium, the promethium concentration remains constant and is designated NPm(eq). The following equation for the promethium equilibrium concentration can be determined from the preceding equation by setting the dNPm/dt =0.
Since the equilibrium promethium concentration is proportional to the fission reaction rate, it is also proportional to reactor power level.
When the rate of production of samarium equals the rate of removal, equilibrium exists also for samarium. The samarium concentration remains constant and is designated NSm(eq). The following equation for the samarium equilibrium concentration can be determined from the preceding equation by setting the dNSm/dt =0. For samarium to be in equilibrium, promethium must also be in equilibrium. Substituting the expression for equilibrium promethium concentration into the equation for equilibrium samarium results in the following equation:
This expression for equilibrium samarium 149 concentration during reactor operation illustrates that equilibrium samarium 149 concentration is independent of neutron flux and power level. It follows the time of saturation is dependent upon the neutron flux level. The equilibrium concentration usually produces negative reactivity (samarium worth) of about -600 pcm.