Problems often arise that require the use of MCNP to simulate a small response change caused by a variation in system parameters. The direct computation approach for such problems often leads to a too large statistical uncertainty for the predicted response change to be acceptable when the response change is small, unless extremely large number of particle histories is used in the MCNP simulations. Consequently, correlated sampling and the differential operator perturbation technique have been developed for MCNP to simulate small response changes with an acceptable uncertainty at reasonable number of particle histories. A thorough investigation is conducted on the theory, performance, and applicability of the two methods in this dissertation research and it consists of three components.
First, the performance of correlated sampling is investigated. It is found that under certain conditions using the default output format of MCNP5 and the original practice of batch statistics developed for correlated sampling may overestimate the uncertainty of the change in system response. The cause of the overestimation is analyzed; correspondingly two new improved procedures are proposed for correlated sampling to ensure correct estimation of the uncertainty. The performances of the improved procedures of correlated sampling are also compared with that of direct, uncorrelated computation. Results show that the improved correlated sampling method may yield a standard deviation that is up to one magnitude smaller than that predicted by the direct simulation at the same number of particle histories.
Secondly, the performances of improved correlated sampling method and the differential operator perturbation technique of MCNP are compared for different types of fixed source problems. In terms of precision of response changes, it is found that the MCNP perturbation technique significantly outperforms correlated sampling for one type of problems but performs comparably with or even underperforms correlated sampling for the other two types of problems. In terms of accuracy of changes in system response, it is found that the MCNP normal perturbation calculations may produce biased results for two types of problems. The magnitude of the bias is problem-dependent and can be quite significant even when response changes are very small. However, accurate results can be obtained for all the test problems if the MCNP perturbation calculations are done by the midpoint correction technique that takes into account the effect of second order cross-differential terms.
Thirdly, the two methods are applied to the pin diversion analysis of PWR spent fuel assemblies, for which the small change in neutron flux needs to be estimated when some of the spent fuel pins are missing or replaced with dummy pins. Since the pin diversion analysis involves variation in particle source, the current MCNP perturbation technique cannot be directly applied to such problems. The correlate sampling method in theory can be applied to the pin diversion problem, but it cannot reduce the uncertainty of response change significantly. Some kind of source treatment must be introduced in order for the two methods to work effectively. Two different source treatment strategies are proposed for the pin diversion analysis in this work. It is demonstrated that when coupled with an appropriate source treatment strategy, the MCNP perturbation technique may still produce inaccurate results thus it is not recommended to be used in the pin diversion analysis; however, the MCNP correlated sampling method works well for all the pin diversion problems.