  One of the major issues with multiparticle reactors is to handle their
multiscale aspect. For modeling, it usually comes to coupling a reactor model
(describing the phenomena at the macroscopic scale) with a so-called grain
model (simulating the behavior of a single grain or a particle). An interesting
approach proposed by H.Y. Sohn (1978) is to use the law of additive reaction
times in order to calculate, approximately but analytically, the reaction rate
of a particle in the reactor model. Its great advantage, compared to a
numerical grain model, is to drastically reduce the computation time,
particularly in the case of complex reactor models. This is the approach we
retained for modeling the moving bed furnace, a counter-current gas-solid
reactor used in the nuclear fuel-making route for producing uranium
tetrafluoride from uranium trioxide. The numerical model we developed is
2-dimensional, steady-state and based on the finite volume method. It describes
solid and gas flow, convective, conductive and radiative heat transfers, and
six chemical reactions involved in the process. The law of additive reaction
times is used to calculate analytically the rate of the three principal
gas-solid reactions at every discrete point in the reactor. We have
demonstrated the validity of this approach by comparing its results with those
calculated from a numerical grain model. Also detailed in the paper are the
main results of the moving bed furnace model itself and the possibilities of
optimizing the process revealed by the calculations.
