Calculation of the eigenfunctions of the two-group neutron diffusion equation and application to modal decomposition of BWR instabilities

In this thesis, numerical methods aiming at determining the eigenfunctions, their adjoint and the corresponding eigenvalues of the two-group neutron diffusion equations representing any heterogeneous system are investigated. First, the classical power iteration method is modified so that the calculation of modes higher than the fundamental mode is possible. Thereafter, the Explicitly-Restarted Arnoldi method, belonging to the class of Krylov subspace methods, is touched upon. Although the modified power iteration method is a computationally-expensive algorithm, its main advantage is its robustness, i.e. the method always converges to the desired eigenfunctions without any need from the user to set up any parameter in the algorithm. On the other hand, the Arnoldi method, which requires some parameters to be defined by the user, is a very efficient method for calculating eigenfunctions of large sparse system of equations with a minimum computational effort. These methods are thereafter used for off-line analysis of the stability of Boiling Water Reactors. Since several oscillation modes are usually excited (global and regional oscillations) when unstable conditions are encountered, the characterization of the stability of the reactor using for instance the Decay Ratio as a stability indicator might be difficult if the contribution from each of the modes are not separated from each other. Such a modal decomposition is applied to a stability test performed at the Swedish Ringhals-1 unit in September 2002, after the use of the Arnoldi method for pre-calculating the different eigenmodes of the neutron flux throughout the reactor. The modal decomposition clearly demonstrates the excitation of both the global and regional oscillations. Furthermore, such oscillations are found to be intermittent with a time-varying phase shift between the first and second azimuthal modes.

Biogas and bio-hydrogen: production and uses. A review

The first part of this essay aims at investigating the already available and promising technologies for the biogas and bio-hydrogen production from anaerobic digestion of different organic substrates. One strives to show all the peculiarities of this complicate process, such as continuity, number of stages, moisture, biomass preservation and rate of feeding. The main outcome of this part is the awareness of the huge amount of reactor configurations, each of which suitable for a few types of substrate and circumstance. Among the most remarkable results, one may consider first of all the wet continuous stirred tank reactors (CSTR), right to face the high waste production rate in urbanised and industrialised areas. Then, there is the up-flow anaerobic sludge blanket reactor (UASB), aimed at the biomass preservation in case of highly heterogeneous feedstock, which can also be treated in a wise co-digestion scheme. On the other hand, smaller and scattered rural realities can be served by either wet low-rate digesters for homogeneous agricultural by-products (e.g. fixed-dome) or the cheap dry batch reactors for lignocellulose waste and energy crops (e.g. hybrid batch-UASB). The biological and technical aspects raised during the first chapters are later supported with bibliographic research on the important and multifarious large-scale applications the products of the anaerobic digestion may have. After the upgrading techniques, particular care was devoted to their importance as biofuels, highlighting a further and more flexible solution consisting in the reforming to syngas. Then, one shows the electricity generation and the associated heat conversion, stressing on the high potential of fuel cells (FC) as electricity converters. Last but not least, both the use as vehicle fuel and the injection into the gas pipes are considered as promising applications. The consideration of the still important issues of the bio-hydrogen management (e.g. storage and delivery) may lead to the conclusion that it would be far more challenging to implement than bio-methane, which can potentially “inherit” the assets of the similar fossil natural gas. Thanks to the gathered knowledge, one devotes a chapter to the energetic and financial study of a hybrid power system supplied by biogas and made of different pieces of equipment (natural gas thermocatalitic unit, molten carbonate fuel cell and combined-cycle gas turbine structure). A parallel analysis on a bio-methane-fed CCGT system is carried out in order to compare the two solutions. Both studies show that the apparent inconvenience of the hybrid system actually emphasises the importance of extending the computations to a broader reality, i.e. the upstream processes for the biofuel production and the environmental/social drawbacks due to fossil-derived emissions. Thanks to this “boundary widening”, one can realise the hidden benefits of the hybrid over the CCGT system.