[Paper Review] 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

Fabrice Patisson, B. Dussoubs+1 more|ArXiv.org|Mar 19, 2008

Iron and Steelmaking Processes19 references3 citations

TL;DR

This paper presents a computationally efficient analytical model for simulating gas-solid reactions in a moving bed furnace converting UO3 to UF4, using Sohn's law of additive reaction times to approximate particle-scale kinetics within a 2D steady-state finite volume reactor model. The approach reduces simulation time significantly while maintaining accuracy, validated against a detailed numerical grain model, and enables process optimization for nuclear fuel production.

ABSTRACT

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.

Motivation & Objective

• To address the multiscale challenge in modeling multiparticle reactors, particularly in nuclear fuel processing.
• To reduce computational cost in simulating complex gas-solid reactions in a moving bed furnace.
• To validate Sohn's law of additive reaction times as an analytical alternative to numerical grain models.
• To enable process optimization for uranium tetrafluoride production from uranium trioxide.
• To develop a 2D steady-state finite volume model integrating heat transfer, flow dynamics, and multiple chemical reactions.

Proposed method

• Application of Sohn's law of additive reaction times to analytically compute reaction rates at the particle scale within the reactor model.
• Development of a 2D steady-state finite volume numerical model for the moving bed furnace.
• Incorporation of convective, conductive, and radiative heat transfer mechanisms in the reactor model.
• Modeling of six chemical reactions, with the three main gas-solid reactions calculated using Sohn's law.
• Coupling of macroscopic reactor behavior with particle-scale kinetics via additive reaction time approximation.
• Validation of the analytical approach by comparison with results from a detailed numerical grain model.

Experimental results

Research questions

• RQ1 Can Sohn's law of additive reaction times provide an accurate and computationally efficient alternative to numerical grain models in multiparticle reactor simulations?
• RQ2 How does the use of additive reaction times impact the prediction of conversion rates in a moving bed furnace for UO3 to UF4 conversion?
• RQ3 What are the key thermal and flow parameters influencing the efficiency of the UO3 to UF4 conversion process in a counter-current reactor?
• RQ4 To what extent can the analytical model replicate the results of a full numerical grain model?
• RQ5 What process optimization strategies emerge from the simulation results of the reactor model?

Key findings

• The analytical model based on Sohn's law produced results in close agreement with those from a detailed numerical grain model, validating its accuracy.
• The use of additive reaction times reduced computation time significantly compared to full numerical grain simulations, enabling faster reactor-scale analysis.
• The 2D finite volume model successfully captured the coupled effects of solid and gas flow, heat transfer, and multiple chemical reactions in the furnace.
• The model revealed critical operating conditions and parameter sensitivities that influence the conversion efficiency of UO3 to UF4.
• Process optimization studies identified key variables such as temperature profiles, gas flow rates, and residence time distributions for improved yield and energy efficiency.
• The model demonstrated the feasibility of using analytical particle kinetics in complex, multiscale reactor simulations without sacrificing predictive capability.