Shutdown Margin – SDM

Shutdown margin, SDM, defines safe subcritical condition. Shutdown margin is the instantaneous amount of reactivity by which a reactor is subcritical or would be subcritical from its present condition assuming all control rods are fully inserted except for the single rod with the highest integral worth (so called stuck control rod), which is assumed to be fully withdrawn. However, with all control rods verified fully inserted by two independent means, it is not necessary to account for a stuck rod in the SDM calculation. With any control rod not capable of being fully inserted, the reactivity worth of all control rods must be accounted for in the determination of SDM. SDM is usually defined for PWRs as well as for BWRs.

Shutdown margin is required to exist at all times, even when the reactor is critical. Let assume the SDM is 2%. Reactor can either be critical or safe subcritical (keff < 0.98). Subcriticality of about 0.99 with all rods inserted is not safe subcritical condition.

During power operation, SDM is ensured by operating with the shutdown banks fully withdrawn and the control banks within the so called “rod insertion limits” specified in the technical specifications. If operator wants to shutdown the reactor from Hot Full Power – equilibrium xenon to Hot Zero Power – with xenon, for example, in case of reactor SCRAM, he must insert negative reactivity to compensate the power defect. It is obvious, if the power defect for PWRs is about 2500 pcm (about 4 βeff), the control rods must weigh more than 2500 pcm to achieve the subcritical condition. A shutdown margin in the range of one to five percent reactivity is typically required. Therefore to ensure the safe subcritical condition, the control rods must weigh more than 2500 pcm plus value of SDM. The total weight of control rods is design specific value, but, for example, it may reach about 6000 to 9000 pcm.

When the reactor is in the shutdown and refueling modes, the SDM requirements are met by means of adjustments to the boron concentration.

See also: Iodine Pit

The most spectacular and well known phenomenon associated with xenon 135 is the behaviour of a reactor after a reactor shutdown. Recall, the proportion of 135I (6.6h) and 135Xe (9.2) half-lives is very important and determines these transients, especially those with power reduction, where the xenon buildup rate is higher than xenon decay.

Consider the reactor shutdown from 100% to zero. Consider the reactor that is operated at 100% for a long time (i.e. iodine and xenon equilibria are established). At time t0, reactor power fall from 100% to 0% of rated power (e.g. after SCRAM). After shutdown, xenon 135 is no longer produced by fission and is no longer removed by burnup. The only remaining production mechanism is the decay of the iodine 135 which was in the core at the time of shutdown. The only removal mechanism for xenon 135 is decay. Therefore, when the reactor power is decreased, xenon concentration initially increases because the xenon burnup fall to zero and the 135I decay (6.6 h) is faster than the 135Xe decay (9.2 h).

The rate of the increase depends on the original neutron flux and increases with increasing flux. For large values of the neutron flux, the peak concentration occurs at 11.3 hours after shutdown (ln( λΙXe)/( λI − λXe) ≈ 11.3 hours). The peak is reached when the product of the terms λΙNI is equal to λXeNXe. The amount of additional negative reactivity in the xenon peak is strongly dependent especially on the original neutron flux. For the reactor shutdown (LWRs) from 100% to zero the amount of additional negative reactivity may reach up to 2500 pcm, which has very important consequences. After reaching the xenon peak, the production of xenon from iodine decay is less than the removal of xenon by decay (λΙNI < λXeNXe), and the concentration of xenon 135 decreases. After another ten half-lives (from 11.3 hours to 80 hours), all the xenon undergo a beta decay. The decay of xenon 135 causes a continuous insertion of positive reactivity. This positive reactivity insertion must be taken into account in subcriticality maintenance (i.e. SDM) or when approaching to criticality. For LWRs, the xenon 135 concentration about 20 hours after shutdown from full power will be the same as the equilibrium xenon 135 concentration at full power. About 3 days after shutdown, the xenon 135 concentration will have decreased to a small percentage of its pre-shutdown level, and the reactor can be assumed to be xenon free without a significant error introduced into reactivity calculations.

An important consequence of this ‘xenon peak’ after a reactor shutdown is that, unless sufficient additional reactivity is present, it cannot be possible to restart the reactor again before many hours have passed. This phenomenon is known as the “iodine pit” or “xenon pit” and it is particularly important (LWRs) near or at the end of the cycle (EOC), since there is usually insufficient positive reactivity available from chemical shim. At the end of the cycle, the additional xenon reactivity (up to 2500 pcm) may provide sufficient negative reactivity to make the estimated critical conditions out of the allowed range, because there is insufficient positive reactivity available from control rod removal or chemical shim to counteract it. In another case, when there is sufficient reactivity to make a reactor critical, there need not be enough reactivity to increase reactor power (i.e. to balance power defect).

The inability of the reactor to be started due to the effects of xenon is sometimes referred to as a xenon precluded startup. It is of particular importance for reactors with very small excess reactivity (e.g. Heavy Water Reactors). The period of time where the reactor is unable to “override” the effects of xenon 135 is called “xenon dead time”.

Thermal power reactors are normally limited to flux levels of about 5 x 1013neutrons/cm-2.s-1 so that timely restart can be ensured after shutdown. For reactors with very low thermal flux levels (~5 x 1013 neutrons/cm-2.s-1 or less), most xenon is removed by decay as opposed to xenon burnup. For these cases, reactor shutdown does not cause any xenon 135 peaking effect. Following the peak in xenon 135 concentration about 10 hours after shutdown, the xenon 135 concentration will decrease at a rate controlled by the decay of iodine 135 into xenon 135 and the decay rate of xenon 135.

Xenon pit - Iodine pit

Iodine Pit – Response to Reactor Shutdown

SDM and Safety Analyses (PWRs)

It is obvious, the minimum required SDM is assumed as an initial condition in safety analyses, that are started from subcritical states. For cold shutdown mode, the primary safety analysis that relies on the SDM limits is the analysis of inadvertent decrease in boron concentration in the reactor coolant system (only for PWRs), where unborated water is added to the reactor coolant system (RCS) to increase core reactivity. This may be inadvertent due to operator error or system malfunction, and cause an unwanted increase in reactivity and a decrease in shutdown margin. The required SDM defines the reactivity difference between an initial subcritical boron concentration and the corresponding critical boron concentration.  The operator must stop this unplanned dilution before the shutdown margin is eliminated.

For PWRs, the most limiting accident for the SDM requirements is based on a main steam line break (MSLB) starting from subcritical states. The steamline break causes the steam pressure, the saturation temperature in the steam generators to fall rapidly. As a result of falling saturation temperature in the steam generators the moderator temperature will rapidly decrease. The rapid moderator temperature drop causes a positive reactivity insertion. The amount of reactivity inserted depends also on a magnitude of the MTC and therefore it must be limited. Typical values for lower limit is MTC = -80 pcm/°C, but it is a plant specific value limited in technical specifications. This positive reactivity addition may cause criticality of the core even with all rods inserted. The required SDM defines the reactivity difference between an initial subcritical boron concentration and the corresponding critical boron concentration.

In addition to these accidents, the SDM requirement is also assumed in:

  • Uncontrolled Control Rod Assembly Withdrawal from a Subcritical or Low Power Startup Condition
  • Spectrum of Rod Ejection Accidents
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