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One of the major issues with multiparticle reactors is to handle theirmultiscale aspect. For modeling, it usually comes to coupling a reactor model(describing the phenomena at the macroscopic scale) with a so-called grainmodel (simulating the behavior of a single grain or a particle). An interestingapproach proposed by H.Y. Sohn (1978) is to use the law of additive reactiontimes in order to calculate, approximately but analytically, the reaction rateof a particle in the reactor model. Its great advantage, compared to anumerical grain model, is to drastically reduce the computation time,particularly in the case of complex reactor models. This is the approach weretained for modeling the moving bed furnace, a counter-current gas-solidreactor used in the nuclear fuel-making route for producing uraniumtetrafluoride from uranium trioxide. The numerical model we developed is2-dimensional, steady-state and based on the finite volume method. It describessolid and gas flow, convective, conductive and radiative heat transfers, andsix chemical reactions involved in the process. The law of additive reactiontimes is used to calculate analytically the rate of the three principalgas-solid reactions at every discrete point in the reactor. We havedemonstrated the validity of this approach by comparing its results with thosecalculated from a numerical grain model. Also detailed in the paper are themain results of the moving bed furnace model itself and the possibilities ofoptimizing the process revealed by the calculations.

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