Modelling of a moving bed furnace for the production of uranium tetrafluoride Part 1: formulation of the model

Reduction, followed by hydrofluorination of uranium trioxide UO₃ to produce uranium tetrafluoride UF₄ is one of the stages of the French nuclear fuel making route. This dual operation is carried out in a specific reactor known as a moving bed furnace, consisting of a series of steel cylinders that form an L. In this first part of a two-part paper, the mathematical modelling of the furnace is presented in detail. The model describes solid and gas flow, heat transfer by convection, conduction and radiation in the moving bed and in the walls of the furnace, and chemical reactions. In the vertical part of the reactor, mass, momentum and energy balances are solved using the finite volume method. The horizontal part is modelled by a cascade of stirred gas and solid reactors. The assumptions and equations of the model, as well as the boundary conditions and numerical solution techniques are detailed. An example of calculated results is presented and found to agree satisfactorily with available measurements. Application of the model is discussed in Part 2.     

Particle segregation of binary mixture in a moving bed by penetration model

Segregation patterns of particles of different sizes in a moving bed were theoretically analyzed by a penetration model. Flow experiments with a two-dimensional hopper verified the derived equations in combination with those in the filling of the hopper. The segregating component was revealed to be more unevenly distributed inside the moving bed of wider cone angle at lower feed rate and lower initial mixing ratio as a result of prevalent segregation during heaping on the top of the moving bed. The steeper velocity profile inside the moving bed resulted in a bit more uneven distribution of the segregating component in the angular direction. In general, the segregation profile gradually became smooth during descent of the particle mixture inside the hopper due to particle penetration in the gravitational direction.     

Modeling and simulation of a small-scale trickle bed reactor for sugar hydrogenation

Laboratory-scale trickle bed reactor was modeled and simulated, taking into account axial dispersion, gas–liquid, liquid–solid and internal mass transfer as well as catalyst deactivation under isothermal conditions. For catalyst particles dynamic and steady state models were developed, including both mass and heat balances. Catalyst deactivation was included in the model by using the final activity concept for the catalyst particles. A well-working numerical algorithm (method of lines) was applied for solving the reactor model with Matlab 7.1 and the results followed experimental trends very well. The steady-state reactor model was based on simultaneous solution of mass balances. The aim was to illustrate how these parabolic partial differential equations could be solved with a step-by-step calculation for a selected geometry. The final model verification was done against experimental data from the hydrogenation of arabinose to arabitol on a ruthenium catalyst.     

Temperature distribution within the moving bed of rotary kilns: Measurement and analysis

Inadequacies in the temperature measurement within the moving bed have hindered a thorough understanding of the processes occurring within rotary kilns. A new measuring system, consisting of thermocouple arrays, a radio-transmitter, a radio-receiver and a computer monitor is introduced in this paper. With it, the 3D temperatures within the moving bed, as well as the temperatures of the freeboard gas and the kiln wall, can be measured and saved automatically. Experiments with sand on a co-current pilot kiln demonstrated that, in the passive layer of the moving bed, the temperatures were approximately constant in the circumferential direction. In the radial direction, however, large temperature difference was observed within the bed near the feed end of the kiln, and the difference became smaller as the bed went progressed through the kiln. This temperature measuring system can be used to obtain data over a wide range of operating conditions for use in engineering design. The obtained results may give new thoughts in theoretical modeling of heat transfer within the moving bed of rotary kilns.     

Vapor recovery reactor in carbothermic aluminum production: model verification and sensitivity study for a fixed bed column

In this paper we develop a distributed parameter model for a fixed bed vapor recovery reactor (VRR) in a carbothermic aluminum process. The model we develop for the reaction mechanism is based on the mass transfer limited (shrinking core) reaction scheme. This model is combined with the partial differential equations (PDEs) describing the component mass and energy balances. The system of PDEs is converted to a large system of differential algebraic equations (DAEs) using the method of lines. The large scale system of DAEs is solved using a DAE solver. The theoretical results have been compared to experiments, showing that the model predicts the reactor's behavior. Sensitivity analysis has been applied to the model using two important variables, gas superficial velocity and gas composition.     

Numerical analysis of interphase heat and mass transfer of cluster in a circulating fluidized bed

Interphase heat and mass transfer characteristics of a naphthalene particle cluster in a circulating fluidized riser are numerically analyzed using a three-dimensional CFD model. Heat and mass transfer characteristics of gas over an in-line array of three naphthalene particles and an isolated naphthalene particle are analyzed. Distributions of gas concentration, temperature and velocity are obtained. The heat and mass transfer rates of gas-to-cluster increase with the increase of the cluster porosity and Reynolds number. Present simulations indicate that the small cluster gives higher heat and mass transfer coefficients than those of the large cluster. The heat and mass transfer rates of individual particles in the cluster are lower than that of an isolated particle and particles in an in-line array under a given cluster porosity.     

Fluidized bed spray granulation: Analysis of the system behaviour by means of dynamic flowsheet simulation

Nowadays, software tools for the flowsheet simulation of industrial processes are commonly used for design, simulation, balancing, troubleshooting and optimization purposes. Most of the tools are applicable to fluid processes only and cannot be effectively used for processes which involve solids.In this contribution we want to present the conceptual design of a new system applicable for the dynamic flowsheet simulation of complex solids processes. This system is developed as an enhancement to the existing simulation program.The novel software is able to simulate the unsteady behaviour of complex circuits of granulation processes. The transient behaviour during the start-up and changing of the process or material parameters can also be examined.As flowsheet examples, a typical spray granulation process with different schemes consisting of fluidized bed granulators, screens, mill and splitters was used. The mathematical model of the fluidized bed granulator is described by a one-dimensional population balance equation and coupled with heat and mass transfer and simple fluid dynamics.Received simulation results have shown that the proposed concept of the dynamic flowsheet simulation of granulation processes can be used effectively and has the potential to be generalized for other types of solids processes.     

Modelling the liquid-phase adsorption in packed beds at low Reynolds numbers: An improved hydrodynamic model

A hydrodynamic model including only one parameter (λ_O) for the prediction of both axial dispersion and external mass transfer in fixed-bed adsorbers at low Reynolds numbers (creeping flow regime) has been developed. The theoretical analysis is based on the application of the (two-dimensional) uniform dispersion model originally proposed by Bischoff and Levenspiel [1962a. Fluid dispersion—generalization and comparison of mathematical models—I. Generalization of models. Chemical Engineering Science 17, 245-255] to the representative capillary of a tube bundle model for describing the flow and mixing behaviour in packed beds. The combination of this model with the relationship between longitudinal and radial dispersion leads to the definition of the sole hydrodynamic parameter λ_O (one-parameter hydrodynamic model). Furthermore, the detailed investigation reveals that the one-parameter concept may be utilized for the application of the (one-dimensional) axial dispersed plug flow model as well. The functional dependence of the parameter λ_O on the flow conditions is elaborated from axial dispersion measurements. Both the new (one-parameter) hydrodynamic model and the classical model including axial dispersion and external mass transfer coefficients (two-parameter model) are utilized to simulate the breakthrough curves for the adsorption of naphthalene onto silica gel. This simulation study reveals that only the one-parameter hydrodynamic model is able to predict the adsorber dynamics over a large range of flow rates.     

CFD modelling of the fast pyrolysis of biomass in fluidised bed reactors. Part B: Heat, momentum and mass transport in bubbling fluidised beds

The fluid-particle interaction inside a 150 g/h fluidised bed reactor is modelled. The biomass particle is injected into the fluidised bed and the heat, momentum and mass transport from the fluidising gas and fluidised sand is modelled. The Eulerian approach is used to model the bubbling behaviour of the sand, which is treated as a continuum. Heat transfer from the bubbling bed to the discrete biomass particle, as well as biomass reaction kinetics are modelled according to the literature. The particle motion inside the reactor is computed using drag laws, dependent on the local volume fraction of each phase. FLUENT 6.2 has been used as the modelling framework of the simulations with the whole pyrolysis model incorporated in the form of user-defined function (UDF). The study completes the fast pyrolysis modelling in bubbling fluidised bed reactors.     

Modelling of a continuous kneader reactor for the polymerization of partially neutralized acrylic acid

A mathematical model and analysis of the continuous polymerization of partially neutralized acrylic acid (AA) in a continuous kneader reactor is presented here as an initial attempt to simulate the synthesis of a superabsorbent polymer. A detailed kinetic model has been used to describe the copolymerization of AA and sodium acrylate (NaA) in aqueous medium. This model is used to describe batch and continuous operations. The polymerization is initiated by a mixture of potassium persulphate (K₂S₂O₈, KPS) and hydrogen peroxide (H₂O₂) as oxidizing agent and ascorbic acid (AsA) as reducing agent. A novel set of kinetic parameters has been estimated by fitting experimental data from different literature sources. The operation of a continuous kneader reactor modelled as a plug-flow reactor with axial dispersion is theoretically investigated to predict temperature profile, total and individual monomer conversion, consumption of KPS, H₂O₂, and AsA, and polymer average molecular weights. The simulation results show the presence of a hot spot close to the reactor entrance that could be potentially severe during startup and could have a detrimental impact on polymer quality. This model is a first step in the direction of achieving optimal operating protocols and exploring improved polymerization reactor designs.     

DEM-LES of coal combustion in a bubbling fluidized bed. Part I: gas-particle turbulent flow structure

The gas and particle motions in a bubbling fluidized bed both with and without chemical reactions are numerically simulated. The solid phase is modelled as Discrete Element Method (DEM) and the gas phase is modelled as 2-D Navier-Stokes equations for 2-phase flow with fluid turbulence calculated by large Eddy simulation (LES), in which the effect of particles on subgrid scale gas flow is taken into account. The gas/particle flow structure, the mean velocities and turbulent intensities can be predicted as a function of several operating parameters (particle size, bed temperature, and inlet gas velocity). The lower the inlet gas velocity, the higher the ratio of particle collision. The distributions of the particle anisotropic velocity show that the particles have no local equilibrium, and the distribution of gas kinetic energy corresponds to the distribution of gas-particle coupling moment in the fluidized bed. An intensive particle turbulent region exists near the wall, and the gas Reynolds stress is always much higher than the particle stress. The presence of the large reactive particles in the fluidized bed may affect significantly the gas and particle velocities and turbulent intensities. The effects of the bed temperature and inlet gas velocity on the gas particle flow structure, velocity, and turbulent intensity are also studied.     

DEM-LES simulation of coal combustion in a bubbling fluidized bed Part II: coal combustion at the particle level

The discrete element method-large eddy simulation (DEM-LES) is used to model coal combustion at the particle level in a bubbling fluidized bed. The gas phase is modelled as a continuum and the solid phase is modeled by DEM. Chemical reactions consist in the heterogeneous reactions of char with O₂, CO, CO₂, NO, and N₂O, and in the homogeneous reactions involving CO, O₂, NO, and N₂O. The colliding particle-particle heat transfer is based on the analysis of the elastic deformation of the spheres during their contact. The model predicts the effects of the particle heterogeneous flow structure on the thermal characteristics of coal particles when heating and burning, and the gaseous emissions from a fluidized sand-coal binary mixture. The heating rates are 1627 and for, respectively, 0.8 and diameter coal particles fed into the fluidized bed. The instantaneous contribution of the collision heat transfer is weak, less than 5.0% of the total power exchanges (coal combustion, radiation, convection and collision) during the heating and 1.5% during the combustion. The temperature of the coal particles exceeds the bed temperature, which is in qualitative agreement with experimental data from literature. The effects of the diameter of coal particles, of the bed temperature, and of the inlet gas velocity on the thermal characteristics are also studied.     

Numerical study of heat and mass transfer in the microwave-assisted and conventional packed bed reactors with an irreversible first-order endothermic chemical reaction

This paper presents a numerical study on heat and mass transfer in the microwave-assisted and conventional packed bed reactors with an irreversible first-order endothermic chemical reaction. The numerical simulations have been carried out using one-dimensional heterogeneous reactor models for the both reactors. The obtained results have been compared applying the criterion of the same electrical powers utilized in the reactors. The effects of the inlet gas temperature and microwave power, gas velocity, bed porosity and the heat of reaction on performance of the packed bed reactors have been presented.     

Freeze concentration of milk and saline solutions in a liquid–solid fluidized bed: Part I. Experimental

Fluidized bed freeze concentration is a novel technique that uses a fluidized bed heat exchanger (FBHE) to concentrate liquids through the process of freeze concentration. Ice formed on the cooled surface of the vertical heat exchanger is removed by particles fluidized inside the FBHE. In this paper, the operating conditions are reported for freeze concentration of saline solutions and milk in FBHE. The operation was tested with equilateral 4 mm and then 5 mm particles at different bed porosities, cooling rates and NaCl and milk concentrations. Experiments with NaCl solutions showed that the 5 mm particles were more aggressive than 4 mm in removing ice from the heat exchanger wall. Whilst particle size was considered responsible for this, the particle shape could have played a major role. A theoretical analysis on effect of FBHE parameters showed the size of particles to exert influence on FBHE performance. The result from experiments with skim milk and whole milk maintained the conclusions formed previously with NaCl experiments with regard to the effect of tested parameters on operational stability. However, the ice formed from milk was more difficult to remove than the ice formed from NaCl solutions. Whole milk showed even more resistance to ice removal. Skim milk was freeze concentrated from 13% to 27% TS content in these experiments. Installing a wash screen further improved the purity of separated ice.     

A discrete model for non-wetting liquid flow from a point source in a packed bed under the influence of gas flow

A study of non-wetting flow in a packed bed under the influence of gas flow has been carried out. Departing from the usual continuum models, a discrete and deterministic model for liquid flow has been presented to model the liquid flow from single and multiple point sources. Liquid flow is modelled based on force balance approach considering gas drag, bed resistance and gravity forces. Gas flow is modelled using k-ε model for turbulent flow. An X-ray flow visualization technique, developed by our group, is used to study the liquid flow paths in the packed bed. Liquid flow path and velocity has been obtained for various liquid and gas flow rate. Flow paths obtained from the simulation results are in good agreement to those obtained from flow visualization procedure under various conditions. Also, liquid distribution at the bed bottom is reported and compared with the experimental results.     

Coupling CFD and Diffusion Models for Analyzing the Convective Drying Behavior of a Single Rice Kernel

The drying behavior of a single rice kernel subjected to convective drying was analyzed numerically by solving heat and moisture transfer equations using a coupled computational fluid dynamics (CFD) and diffusion model. The transfer coefficients were computed simultaneously with the external flow field and the internal diffusive field of the grain. The model was validated using results of a thin-layer drying experiments from the literature. The effects of velocity and temperature of the drying air on the rice kernel were analyzed. It was found that the air temperature was the major variable that affected the drying rate of the rice kernel. The initial drying rates (in first 20 min) were 7, 12, and 19% per hour at inlet air temperatures of 30, 45, and 60 ^° C, respectively. Important temperature gradients within the grain existed only in the first few minutes of the drying process. The moisture content gradients reached a maximum value of 11.7% (db) mm ^?1 at approximately 45 min along the short axis in the thickness direction. The variation in the inlet air velocity showed a minor effect on the drying rate of the rice kernel. The heat and mass transfer coefficients varied from 16.57 to 203.46 W·m ^?2·K ^?1 and from 0.0160 to 0.1959 m·s ^?1, respectively. The importance of the computation of the transfer coefficients with the heat and mass transfer model is demonstrated.     

A Reynolds mass flux model for gas separation process simulation:II. Application to adsorption on activated carbon in a packed column☆

Simulations of adsorption process using the Reynolds mass flux model described in Part I of these serial articles are presented. The object of the simulation is the methylene chloride adsorption in a packed column (0.041 m id, packed with spherical activated carbon up to a length of 0.2 m). With the Reynolds mass flux model, breakthrough/regeneration curves, concentration and temperature as well as the velocity distributions can be obtained. The simulated results are compared with the experimental data reported in the literature and satisfactory agreement is found both in breakthrough/regeneration curves and temperature curves. Moreover, the anisotropic turbulent mass diffusion is characterized and discussed.     

Numerical simulation of the combustion of hydrogen-air mixture in micro-scaled chambers Part II: CFD analysis for a micro-combustor

Understanding of the flow dynamics, chemical kinetics and heat transfer mechanism within micro-combustors is essential for the development of combustion-based power MEMS devices. In Part I, CFD based numerical simulation has been proven to be an effective approach to analyse the performance of the micro-combustor under various conditions. In this paper, numerical simulations are performed to analyse the combustion behaviour in a three-dimensional micro-combustor based on the prototype used in the MIT micro-gas turbine engine. The CFD model of the micro-combustor includes fuel/air flow path, combustion chamber as well as solid walls used to construct the combustor. The simulation analysis includes not only the detailed chemical reactions occurred in the combustion chamber, but also the fluid flow dynamics, heat transfer within the combustor and heat loss to the ambient. The performance of the combustor is evaluated under various fuel/air ratio, flow rate and heat loss conditions. Through such systematic numerical analysis, a proper operation space for the micro-combustor is suggested, which may be used as the guideline for micro-combustor design. In addition, the results reported in this paper illustrate that the numerical simulation can be one of the most powerful and beneficial tools for the micro-combustor design, optimisation and performance analysis.     

Cross-Flow Drying of Wheat. A Simulation Program with a Diffusion-Based Deep-Bed Model and a Kinetic Equation for Viability Loss Estimations.

ABSTRACT

A mathematical model of heat and mass transfer for fixed beds was developed according to the modern theory of process simulation and standard laws of thermodynamics and transport phenomena. The mass transfer grain-air was predicted with simplified diffusional expressions together with an equation for the static equilibrium moisture content. Four differential equations were obtained for a grain layer and they were integrated along the bed depth and time with second and a fourth-order methods, respectively. The model was validated by comparing drying time predictions with experimental values, being the average error of 6%. The model was extended into a program for continuous cross-flow drying-cooling