Abstract
Typically, reactor safety analyses utilize a deterministic approach where uncertainty is accommodated by assuming pessimistic values for input parameters that are important to safety. This paper considers a stochastic approach for explicitly including uncertainty in safety parameters by applying Monte Carlo sampling coupled with established deterministic reactor safety analysis tools. Similar analyses have been proposed in the past, but in these analyses a limited number of deterministic calculations were used to determine response surfaces for the outputs of interest and the response surfaces coupled to the Monte Carlo sampling. The Monte Carlo approach yields frequency distributions for reactor safety metrics (e.g., peak fuel temperature) that can be compared to performance limits, allowing for an improved determination of safety margin and a clear determination of which safety parameters affect the transient response. Example analyses have been carried out for an 840 MWth, sodium cooled, advanced burner reactor to demonstrate the effect of uncertainty in selected input parameters on the uncertainty of various outputs for calculations of unprotected (failure of reactor shutdown mechanisms) combined loss-of-heat-sink and loss-of-flow, loss-of-flow, and transient overpower events. The reactor has metallic fuel and a conversion ratio (transuranic production rate/transuranic destruction rate) of approximately 0.5 and is similar
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Citation Formats
Morris, E E, and Nutt, W.M. , E-mail: eemorris@anl.gov.
Uncertainty analysis for unprotected loss-of-heat-sink, loss-of- flow, and transient-overpower events in sodium-cooled fast reactors.
IAEA: N. p.,
2009.
Web.
Morris, E E, & Nutt, W.M. , E-mail: eemorris@anl.gov.
Uncertainty analysis for unprotected loss-of-heat-sink, loss-of- flow, and transient-overpower events in sodium-cooled fast reactors.
IAEA.
Morris, E E, and Nutt, W.M. , E-mail: eemorris@anl.gov.
2009.
"Uncertainty analysis for unprotected loss-of-heat-sink, loss-of- flow, and transient-overpower events in sodium-cooled fast reactors."
IAEA.
@misc{etde_21334050,
title = {Uncertainty analysis for unprotected loss-of-heat-sink, loss-of- flow, and transient-overpower events in sodium-cooled fast reactors}
author = {Morris, E E, and Nutt, W.M. , E-mail: eemorris@anl.gov}
abstractNote = {Typically, reactor safety analyses utilize a deterministic approach where uncertainty is accommodated by assuming pessimistic values for input parameters that are important to safety. This paper considers a stochastic approach for explicitly including uncertainty in safety parameters by applying Monte Carlo sampling coupled with established deterministic reactor safety analysis tools. Similar analyses have been proposed in the past, but in these analyses a limited number of deterministic calculations were used to determine response surfaces for the outputs of interest and the response surfaces coupled to the Monte Carlo sampling. The Monte Carlo approach yields frequency distributions for reactor safety metrics (e.g., peak fuel temperature) that can be compared to performance limits, allowing for an improved determination of safety margin and a clear determination of which safety parameters affect the transient response. Example analyses have been carried out for an 840 MWth, sodium cooled, advanced burner reactor to demonstrate the effect of uncertainty in selected input parameters on the uncertainty of various outputs for calculations of unprotected (failure of reactor shutdown mechanisms) combined loss-of-heat-sink and loss-of-flow, loss-of-flow, and transient overpower events. The reactor has metallic fuel and a conversion ratio (transuranic production rate/transuranic destruction rate) of approximately 0.5 and is similar in design to the reactor having a conversion ratio of 0.25 considered by Cahalan, et al. Mean values for the stochastic input parameters were taken to be best estimate values and standard deviations in the range of 10% to 20% of the mean values were assumed. The specific stochastic reactivity coefficients considered are the coolant temperature reactivity feedback, the Doppler coefficient, fuel axial expansion feedback, core radial expansion feedback, and control rod drive line expansion feedback. In addition to the reactivity coefficients, the loss-of-heat-sink calculations assume that the temperature at which a flow coast down initiates and the rate at which heat removal decreases are stochastic. All stochastic parameters were assumed to have normal probability distributions and to be uncorrelated. All the results considered in the present analysis are based calculations for each of 10,000 independent samples of the stochastic input parameters. The number of samples required in a more complete analysis would depend on the purpose of the analysis. For example, initial calculations might consider many more stochastic input parameters and use fewer samples to identify the most important parameters. Then calculations with a larger number of samples might be carried out using a smaller set of stochastic input parameters. Rather than go through a more detailed screening process, the choice of stochastic parameters used in the current analysis was based on previous experience. Frequency distributions for several output parameters were obtained. The frequency distribution for the peak fuel temperature in an unprotected loss-of-flow transient is shown in Fig. 1. 99% confidence limits were estimated based on binomial probability distributions and are shown in the figure. Also shown is the estimated frequency based on a log-normal distribution having the same mean and standard deviation as the results shown by the histogram. It is of interest to note that even though the input parameters were assumed to be independent of one another and to have normal probability distributions, the distribution for the peak fuel temperature does not resemble a normal distribution. In this case, even a log-normal distribution provides a poor approximation to the observed frequency distribution. Similar plots have been made for the peak fuel temperature for loss-of-heat-sink and transient overpower transients and for the peak coolant outlet temperature for each of the three considered transients. In some of these other cases, a log-normal distribution provides a better approximation to the observed frequency distribution, but in no case does the log-normal distribution fall within the 99% confidence limits over the entire range of temperatures. Scatter plots of the peak fuel temperature against the various stochastic input parameters show that for the loss-of-heat-sink and loss-of-flow transients, the most important parameter is the core radial expansion feedback coefficient. For the transient overpower case, the peak fuel temperature depends most heavily on the total worth of the moving control rod and on the fuel axial expansion feedback coefficient. The approach to uncertainty described provides for the estimation of probabilities for violating safety boundaries and should be useful in a risk based regulatory environment. It has the advantage of not requiring any substantial rewriting of existing the safety analysis computer codes. Future work should consider a larger set of input parameters and give more attention to appropriate probability distributions and possible correlations.}
place = {IAEA}
year = {2009}
month = {Jul}
}
title = {Uncertainty analysis for unprotected loss-of-heat-sink, loss-of- flow, and transient-overpower events in sodium-cooled fast reactors}
author = {Morris, E E, and Nutt, W.M. , E-mail: eemorris@anl.gov}
abstractNote = {Typically, reactor safety analyses utilize a deterministic approach where uncertainty is accommodated by assuming pessimistic values for input parameters that are important to safety. This paper considers a stochastic approach for explicitly including uncertainty in safety parameters by applying Monte Carlo sampling coupled with established deterministic reactor safety analysis tools. Similar analyses have been proposed in the past, but in these analyses a limited number of deterministic calculations were used to determine response surfaces for the outputs of interest and the response surfaces coupled to the Monte Carlo sampling. The Monte Carlo approach yields frequency distributions for reactor safety metrics (e.g., peak fuel temperature) that can be compared to performance limits, allowing for an improved determination of safety margin and a clear determination of which safety parameters affect the transient response. Example analyses have been carried out for an 840 MWth, sodium cooled, advanced burner reactor to demonstrate the effect of uncertainty in selected input parameters on the uncertainty of various outputs for calculations of unprotected (failure of reactor shutdown mechanisms) combined loss-of-heat-sink and loss-of-flow, loss-of-flow, and transient overpower events. The reactor has metallic fuel and a conversion ratio (transuranic production rate/transuranic destruction rate) of approximately 0.5 and is similar in design to the reactor having a conversion ratio of 0.25 considered by Cahalan, et al. Mean values for the stochastic input parameters were taken to be best estimate values and standard deviations in the range of 10% to 20% of the mean values were assumed. The specific stochastic reactivity coefficients considered are the coolant temperature reactivity feedback, the Doppler coefficient, fuel axial expansion feedback, core radial expansion feedback, and control rod drive line expansion feedback. In addition to the reactivity coefficients, the loss-of-heat-sink calculations assume that the temperature at which a flow coast down initiates and the rate at which heat removal decreases are stochastic. All stochastic parameters were assumed to have normal probability distributions and to be uncorrelated. All the results considered in the present analysis are based calculations for each of 10,000 independent samples of the stochastic input parameters. The number of samples required in a more complete analysis would depend on the purpose of the analysis. For example, initial calculations might consider many more stochastic input parameters and use fewer samples to identify the most important parameters. Then calculations with a larger number of samples might be carried out using a smaller set of stochastic input parameters. Rather than go through a more detailed screening process, the choice of stochastic parameters used in the current analysis was based on previous experience. Frequency distributions for several output parameters were obtained. The frequency distribution for the peak fuel temperature in an unprotected loss-of-flow transient is shown in Fig. 1. 99% confidence limits were estimated based on binomial probability distributions and are shown in the figure. Also shown is the estimated frequency based on a log-normal distribution having the same mean and standard deviation as the results shown by the histogram. It is of interest to note that even though the input parameters were assumed to be independent of one another and to have normal probability distributions, the distribution for the peak fuel temperature does not resemble a normal distribution. In this case, even a log-normal distribution provides a poor approximation to the observed frequency distribution. Similar plots have been made for the peak fuel temperature for loss-of-heat-sink and transient overpower transients and for the peak coolant outlet temperature for each of the three considered transients. In some of these other cases, a log-normal distribution provides a better approximation to the observed frequency distribution, but in no case does the log-normal distribution fall within the 99% confidence limits over the entire range of temperatures. Scatter plots of the peak fuel temperature against the various stochastic input parameters show that for the loss-of-heat-sink and loss-of-flow transients, the most important parameter is the core radial expansion feedback coefficient. For the transient overpower case, the peak fuel temperature depends most heavily on the total worth of the moving control rod and on the fuel axial expansion feedback coefficient. The approach to uncertainty described provides for the estimation of probabilities for violating safety boundaries and should be useful in a risk based regulatory environment. It has the advantage of not requiring any substantial rewriting of existing the safety analysis computer codes. Future work should consider a larger set of input parameters and give more attention to appropriate probability distributions and possible correlations.}
place = {IAEA}
year = {2009}
month = {Jul}
}