Chapter 9 - Anomalous diffusion exponent in nuclear reactors

Abstract

The anomalous diffusion exponent is the fractional order of the differential operators of the mathematical model between differential equations for nuclear reactor analysis. When the anomalous diffusion exponent takes values greater than zero and less than one, it is established that the phenomenon is subdiffusive, which is a characteristic of the heterogeneous system. Besides, from a mathematical point of view, the differential operators of fractional order are nonlocal, which translates into memory effects in space if the neutron current vector is of fractional order, and memory effects in time if the differential operator is fractional respect to time, but the existence of double memory in space and time is another approach. The fractional nuclear reactor analysis constitutes the study of anomalous diffusion in nuclear reactors. However, in previous chapters, we have studied the advantages through numerical experiments that a fractional neutron diffusion model produces results like the neutron transport theory, with Monte Carlo type numerical codes and in reactor dynamics, and new results are generated in the domain of time and frequency. So far, subdiffusive phenomena have been analyzed in nuclear reactors with tests of the anomalous diffusion coefficient and comparing the results with normal diffusion, or with transport theory. The objective of this chapter is to present two possible methods to determine the anomaly diffusion coefficient using nuclear power plant data from power monitors (LPRM and APRM). In addition, the impact of the annual diffusion coefficient is analyzed through a sensitivity and uncertainty analysis.