Using Sohn's law of additive reaction times for modeling a multiparticle reactor. The case of the moving bed furnace converting uranium trioxide into tetrafluoride

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.