Fluidized Bed Model Research Articles

Derivation and validation of a binary multi-fluid Eulerian model for fluidized beds

The paper presents a multi-fluid Eulerian model derived from binary kinetic theory of granular flows, free path theory and an empirical friction theory. The effects of the inter- and inner-particle collisions, particle translational motions and particle–particle friction are included. As the effects due to fluiddynamic particle velocity differences and particle–particle friction are considered, some unconventional terms are produced compared with the previous models. Model validation using the data from Mathiesen et al. (2000) shows that the coupling terms give a stronger and more realistic particle–particle coupling because the effects due to the fluiddynamic velocity differences are considered. The model gives reasonable predictions of the particle volume fraction, particle velocities and velocity fluctuations. The model analysis reveals that the basic particle velocity fluctuations constitute 2 terms: the velocity fluctuations of the discrete particles, and the velocity fluctuations of the continuous fluid flow. Furthermore, the simulation results show that the velocity fluctuations of the continuous fluid flow are dominant in a binary riser flow.

Validation of a DEM Modeling of Gas-Solid Fluidized Bed using the S-statistic in the State-Space Domain

A reliable method was developed to validate results of a gas-solid bubble fluidized bed model with discrete element method (DEM) through comparison of corresponding pressure fluctuations experimental data. Attractors of two independent pressure signals, evaluation series of DEM model and reference time series of measured pressure signals, were compared in the state-space domain using the S-statistic. Comparison between two reconstructed attractors of evaluation and reference series was performed based on the null hypothesis. The null hypothesis that the evaluation and reference time series originate from the same dynamic sources is rejected if the two series significantly differ. To prove the power of the method, the S-statistic was estimated for obtained experimental data under the same operating conditions. In addition, experimental and model pressure fluctuations were decomposed into 9 levels using wavelet transform to study the validity of the model in a broad range of frequencies. Results indicated that the model results were consistent with experiments.

Carbonate looping process simulation using a 1D fluidized bed model for the carbonator

The carbonate looping process is an efficient post-combustion technology for CO2 capture using limestone based sorbents. The absorption of CO2 by CaO occurs in the carbonator that is realized as a circulating fluidized bed reactor. An accurate prediction of the CO2 absorption efficiency is crucial for the design of a carbonate looping plant. In this study, a 1D fluidized bed model for the carbonator is implemented into a process model of a full-scale plant. A net electrical efficiency penalty of less than 2.9% points is determined for a CO2 absorption efficiency of 80% in the carbonator, leading to 88% CO2 capture of the entire carbonate looping process. Furthermore, the effect of various operational and model parameters on the results is assessed by parameter variations and sensitivity analyses.

Methanation in a fluidized bed reactor with high initial CO partial pressure: Part II— Modeling and sensitivity study

A model of a bench-scale methanation reactor was set-up by modifying the classical two-phase model approach and introducing an additional bulk flow from bubble to dense phase to consider the volume contraction of the methanation reaction. The model uses experimentally determined kinetics and hydrodynamic correlations from literature. It was satisfyingly validated by comparing the calculated gas concentration profiles with the experimental data, especially with respect to initial reaction rates and reactor exit concentrations. A sensitivity study with respect to different bubble size correlations, mass transfer rates and considering or neglecting the bulk flow (influence of volume contraction caused by the methanation reaction) was carried out. It showed that the bubble size correlation by Werther and the resulting gas concentration profiles fit the measured data better than the computed gas concentration profiles using the bubble size correlation by Rowe. Neither a variation of the mass transfer coefficient nor neglecting the bulk flow in the fluidized bed model did yield further improvement of the calculated concentration profiles.

Bed expansion and fluctuation in cylindrical gas solid fluidized beds with stirred promoters

A profound and fundamental understanding of bed dynamics such as bed expansion ratio and bed fluctuation ratio of irregular particles of binary mixtures has been made in a cylindrical fluidized column for gas solid systems, resulting in a predictive model for fluidized beds. In the present work attempt has been made to study the effect of various system parameters (viz. rotational speed of the promoter, initial static bed height, superficial velocity of the fluidizing medium, particle size and density) on the bed dynamics through experimentation. The correlations for the bed dynamics have been developed on the basis of dimensional analysis. It was observed that the calculated values of bed dynamics agree well with the experimental values in most of the cases.

SIMULATION OF SULFUR DIOXIDE REMOVAL FROM A GAS STREAM IN A FLUIDIZED-BED REACTOR

The object of this work is to model and simulate a fluidized bed desulfurization reactor by coupling a reactor kinetic model with a fluidized bed model based on two –phase theory(bubbling-bed model) proposed by Kunni and Levenspiel(1968).This model is useful for analysis of a reaction involving gas and solid. It generates the conversion data with respect to reaction time of both reacting gas and solids in a continuous flow(for both gas and solids) in fluidized bed. The flue gas or stack gas from a combustor which normally contains sulfur dioxide mixed with excess air is used as the fluidizing gas with calcium oxide as the fluidized solids . Calcium oxide is quite capable of reacting with 2 SO to effect its removal from the gas phase according to the exothermic reaction :s  CaO + g  SO2 + 2 1g  O2 s  CaSO4 + HeatThe effects of the solid feed rate, SO2 concentration in the flue gas, bed height, bed diameter, particle size, fluidizing velocity and operating temperature on the extent of conversion of both gas and solid were investigated, for a fixed feed rate of flue gas and SO2concentration (50.000 cm3/sec ,3-5% by volume)at temperature range of (950-1000oC)and pressure 1 atm.

Three-dimensional simulation of the particle distribution in a downer using CFD–DEM and comparison with the results of ECT experiments

A three-dimensional numerical model of the down-flow fluidized bed (Downer) with a newly designed distributor was applied to investigate the particle distribution profiles using combined computational fluid dynamics (CFD) and the discrete element method (DEM). A realistic model of DEM, which calculates the contact force acting on the individual particles, is used to monitor the movement of individual particles in the bed. The contact force is calculated using the concepts of the spring, dash-pot, and friction slider. The flow field of gas is predicted by the Navier–Stokes equation. This CFD–DEM model provides information regarding the particle movement and distribution, the particle velocity, and the gas velocity in the bed under different air-particle mixture conditions. The results demonstrate that the air supply conditions directly influence the particle distribution uniformity. Furthermore, the numerical predictions for the axial and radial profiles of the particle distribution were found to agree well with the experimental results obtained by electrical capacitance tomography (ECT).

Fluorination of UF 4 in a mini-tapered fluidized bed and mathematical modeling

A mini-tapered fluidized bed reactor can be used for fluorination reaction of UF 4 to produce uranium hexafluoride. By adopting the mini-tapered bed the problems associated with fluidization in a cylindrical bed such as entrainment of particles and the limitation of operating velocity can be overcome, consequently the performance of the reactor can be enhanced. Simulation of the reactor was performed employing two-phase models, bubble phase with piston flow and emulsion phase with piston (D.P-P model) or perfectly mixed flow (D.P-M model). The voidage of the emulsion and bubble phases were estimated from the distribution two-phase structure hydrodynamic model. The model predictions have been compared with the results from a pilot-scale experiment. The D.P-P model gives good agreement between computed and empirical results. The effects of various parameters on the reactor performance are discussed using the model.

Fluidized-Bed Methanation: Interaction between Kinetics and Mass Transfer

In the present work, the influence of reaction and mass transfer on the fluidized-bed methanation have been investigated by both experiments and modeling. By applying spatially resolved gas concentration and temperature measurements in a bench-scale fluidized-bed reactor, it was shown that most of the reaction proceeds in the first 20 mm while the temperature increases by 74 K in the first 2 mm of the bed. A CO conversion of practically 100% is achieved. The experimental data indicate that the measured gas composition represents mainly the dense phase and that mass transfer between bubble and dense phase is the dominant effect in the upper part of the bed. A fluidized-bed model is proposed based on the two-phase model approach, hydrodynamic correlations from the literature and kinetic parameters previously determined. Although it was not possible to reproduce all measured phenomena within the methanation reactor, this first attempt to model the fluidized bed provides a better understanding of the behavior...

CFD Modeling and X-Ray Imaging of Biomass in a Fluidized Bed

Computational modeling of fluidized beds can be used to predict the operation of biomass gasifiers after extensive validation with experimental data. The present work focused on validating computational simulations of a fluidized bed using a multifluid Eulerian–Eulerian model to represent the gas and solid phases as interpenetrating continua. Simulations of a cold-flow glass bead fluidized bed, using two different drag models, were compared with experimental results for model validation. The validated numerical model was then used to complete a parametric study for the coefficient of restitution and particle sphericity, which are unknown properties of biomass. Biomass is not well characterized, and so this study attempts to demonstrate how particle properties affect the hydrodynamics of a fluidized bed. Hydrodynamic results from the simulations were compared with X-ray flow visualization computed tomography studies of a similar bed. It was found that the Gidaspow (blending) model can accurately predict the hydrodynamics of a biomass fluidized bed. The coefficient of restitution of biomass did not affect the hydrodynamics of the bed for the conditions of this study; however, the bed hydrodynamics were more sensitive to particle sphericity variation.

Effects of the plenum chamber volume and distributor geometry on fluidized bed hydrodynamics

Most hydrodynamic fluidized bed models, including CFD codes, neglect any effects of the plenum chamber volume. Experiments were performed in a 0.13 m ID fluidization column to determine plenum chamber volume effects on fluidized bed hydrodynamics for FCC and glass particles. Two low-pressure-drop distributors were used, one with a single orifice, and the other with 33 orifices and the same total open area as the single orifice. The results show two peaks in the frequency spectra for the single-orifice distributor, one representing bubble eruption at the bed surface and the other of higher frequency corresponding to the bubbling frequency at the distributor. The latter decreased slightly with increasing plenum volume and with increasing bed depth. For the multi-orifice distributor, broad frequency spectra from pressure measurements became narrower and moved towards higher frequency with decreasing plenum volume.

Numerical and Experimental Analysis of a Fluidized Bed for IFE Target Layering

A fluidized bed is being studied as a very promising method for mass production of IFE targets. Large beds could be filled with many targets to provide large-scale production, while a near-isothermal environment could be maintained in principle around each target (as required for smooth layering to meet the physics requirements on the ice characteristics) through the random movement and spin of individual targets within a precisely controlled gas stream. Concerns exist, however, including the effect of unbalanced spheres on the bed behavior and ultimately on the target thermal environment, as well as the possible damage of the target surface (in particular the thin high-Z coating).This effort includes developing a numerical fluidized bed model and conducting laboratory-scale companion experiments to help understand the cryogenic fluidized bed behavior. Key challenges in developing the model include the relative size of the spherical targets (˜4.0 mm) compared to the size of the prototypic fluidized bed container (˜26 mm in diameter), which is much larger than those found in conventional fluidized bed models and which calls for a different modeling approach. In addition, the behavior of unbalanced targets, which results from the initial D-T filling and freezing in the target production process, needs to be accounted for.This paper summarizes the development of this model, including the validation performed by comparing the model results to controlled lab-scale experiments. The goal is to use the model for parametric analysis to help determine the most promising state of operation to deliver large quantities of uniformly layered target shells. This will provide key pre-operational input to the prototypical experimental set-up, which is currently being built and which includes a high-pressure deuterium filling station in addition to the cryogenic fluidized bed operating at temperatures around 18 K.

Multi-scale modeling and control of fluidized beds for the production of solar grade silicon

In this paper we develop a multi-scale model to describe the growth of silicon particles due to chemical vapor deposition (CVD) in a fluidized bed reactor (FBR). The reactor system is designed to make poly-silicon for solar cell applications by thermal decomposition of silane. The complex interplay between the continuous and the disperse phases and CVD onto the silicon particles in the FBR is modeled using three modules — Computational Fluid Dynamics (CFD), Reaction Module and Population Balance Module (PBM). The Computational Fluid Dynamics (CFD) module describes the hydrodynamics via momentum, mass and heat transfer between different phases. The reaction module describes the homogeneous gas phase reactions and deposition on polycrystalline silicon particles. The population balance represents the dynamic evolution of the particle size distribution. By coupling together the modules, we provide a complete multi-scale model for the particulate CVD process. The resulting nonlinear, multi-scale model is solved using COMSOL Multi-physics and MATLAB. The results from the proposed model match the experimental data obtained from a pilot scale reactor. An inventory controller maintains the void fraction and in turn the average diameter of the silicon particles at the exit.

CFD modeling and validation of the turbulent fluidized bed of FCC particles

AbstractAn experimental and computational study is presented on the hydrodynamic characteristics of FCC particles in a turbulent fluidized bed. Based on the Eulerian/Eulerian model, a computational fluid dynamics (CFD) model incorporating a modified gas‐solid drag model has been presented, and the model parameters are examined by using a commercial CFD software package (FLUENT 6.2.16). Relative to other drag models, the modified one gives a reasonable hydrodynamic prediction in comparison with experimental data. The hydrodynamics show more sensitive to the coefficient of restitution than to the flow models and kinetics theories. Experimental and numerical results indicate that there exist two different coexisting regions in the turbulent fluidized bed: a bottom dense, bubbling region and a dilute, dispersed flow region. At low‐gas velocity, solid‐volume fractions show high near the wall region, and low in the center of the bed. Increasing gas velocity aggravates the turbulent disorder in the turbulent fluidized bed, resulting in an irregularity of the radial particle concentration profile. © 2009 American Institute of Chemical Engineers AIChE J, 2009

Gas–solid packed and fluidized bed models for bioremediation of volatile organic compounds in air

A steady state, one-dimensional model is developed to describe biodegradation of a volatile organic compound (VOC) in a gas–solid fluidized bioreactor. For comparison purposes, biodegradation in a packed bed bioreactor is also modelled. The models are used to predict outlet concentrations of a VOC substrate (ethanol) and the estimates are compared to experimental data. The fluidized bioreactor model includes properties of the bubbles such as rise velocity, bubble size and gas exchange rate with the emulsion phase surrounding the bubbles. The overall rate of biodegradation is modelled with the two limiting cases of zero and first order kinetics with respect to the substrate, which depend on whether the overall resistance is limited by microbial growth or mass transport. The models highlight how maximum elimination capacity and removal efficiency are influenced by bubble properties, residence time, maximum specific growth rate of the microorganisms, and microbial population.

Experimental and computational study of the bed dynamics of semi‐cylindrical gas–solid fluidized bed

AbstractWith computational fluid dynamics (CFD) it is possible to get a detailed view of the flow behaviour of the fluidized beds. A profound and fundamental understanding of bed dynamics such as bed pressure drop, bed expansion ratio, bed fluctuation ratio, and minimum fluidization velocity of homogeneous binary mixtures has been made in a semi‐cylindrical fluidized column for gas–solid systems, resulting in a predictive model for fluidized beds. In the present work attempt has been made to study the effect of different system parameters (viz., size and density of the bed materials and initial static bed height) on the bed dynamics. The correlations for the bed expansion and bed fluctuations have been developed on the basis of dimensional analysis using these system parameters. Computational study has also been carried out using a commercial CFD package Fluent (Fluent, Inc.). A multifluid Eulerian model incorporating the kinetic theory for solid particles was applied in order to simulate the gas–solid flow. CFD simulated bed pressure drop has been compared with the experimental bed pressure drops under different conditions for which the results show good agreements.

CFD simulations of expanding/contracting homogeneous fluidized beds and their transition to bubbling

This work presents a new Eulerian–Eulerian fluid dynamic model for monodisperse suspensions of solid particles fluidized by Newtonian incompressible fluids. The closure relationships for the fluid–particle interaction force distinguish the proposed equations of motion. The force consists of buoyancy, local fluid acceleration, drag and elastic forces. The closures of Mazzei and Lettieri [2007. A drag force closure for uniformly-dispersed fluidized suspensions. Chemical Engineering Science 62, 6142] based on the Richardson and Zaki [1954. Sedimentation and fluidization: part I. Transactions of the Institution of Chemical Engineers 32, 35] empirical correlation, and Mazzei et al. [2006. A revised mono-dimensional particle bed model for fluidized beds. Chemical Engineering Science 61, 1958], generalized for multidimensional applications, model the drag and elastic forces, respectively. For the first time these relations are solved in a computational fluid dynamic code. To test the drag force closure, we evaluate the steady-state expansion profiles of liquid-fluidized systems computationally, and compare them with those obtained using the closures of Wen and Yu [1966. Mechanics of fluidization. Chemical Engineering Progress Symposium Series 62, 100] and Ergun [1952. Fluid flow through packed columns. Chemical Engineering Progress 48, 89] and with experimental data. We successively analyze the behavior of uniform systems subjected to sudden changes in fluid flux, and compare the computational results with the theoretical predictions of the mechanistic one-dimensional model of Gibilaro et al. [1984. A simple mechanistic description of the unsteady-state expansion of liquid-fluidized beds. Chemical Engineering Science 39, 607]. To conclude the work, we investigate the stability of homogeneous gas-fluidized suspensions and the transition from the particulate to the aggregative state. Analytical and computational results (obtained by linear stability analysis and by integration of the equations of motion, respectively) are compared with experimental findings. The dynamics predicted are described and discussed; considerations on the meaning of fluid dynamic stability are debated.

Modeling and Characterization of Air Emissions from Laboratory and Industrial Fluidized Beds

AbstractA fluidized bed model using several elutriation correlations was developed and tested against an operating fluidized bed used in a Fluidized Catalytic Cracker Unit (FCCU) and a 1:8.5 scale laboratory system. It was found that there was little variation between the emission rates predicted using different elutriation correlations, although the newly developed equations were slightly more accurate for the laboratory‐scale system. Although total emission rates were predicted with reasonable accuracy, the actual volatility and fluctuations seen in real fluidized beds emissions were not predicted. When the model was used to predict particle emission from the industrial FCCU, they preformed poorly, grossly overestimating the actual levels. It was determined that the attrition terms used in emission modeling were inappropriate and that the model preformed better without them, but still overestimated the actual emissions. This overestimation was greater in the industrial system compared with the smaller laboratory system. It was also found that the older elutriation terms were better for predicting industrial emissions compared with those of the smaller scale units.

Influence of Hydrodynamic Models on Dynamic Response of the Fluidized Bed Polyethylene Reactor

In this study, the influence of hydrodynamic models on dynamics of the fluidized bed polyethylene production process has been investigated via modeling. The overall fluidized bed model consists of two integrated sub-models. The hydrodynamic sub-models, which are the simple and dynamic two-phase, well mixed and tanks in series models, were used in the study along with the reaction sub-model from the literature. The hydrodynamic sub-models differ from each other in terms of flow structure and the presence of solids in the disperse phase. The conventional PID controllers were used to control the reactor conditions for these different hydrodynamic conditions. The results of this study showed that a choice of a hydrodynamic model for the fluidized bed polyethylene reactor has a minor effect on the dynamic response and the grade transition of the polyethylene production process and a simple hydrodynamic sub-model can be used for the proper dynamic modeling and control of the process.

Acceleration techniques for reduced-order models based on proper orthogonal decomposition

This paper presents several acceleration techniques for reduced-order models based on the proper orthogonal decomposition (POD) method. The techniques proposed herein are: (i) an algorithm for splitting the database of snapshots generated by the full-order model; (ii) a method for solving quasi-symmetrical matrices; (iii) a strategy for reducing the frequency of the projection. The acceleration techniques were applied to a POD-based reduced-order model of the two-phase flows in fluidized beds. This reduced-order model was developed using numerical results from a full-order computational fluid dynamics model of a two-dimensional fluidized bed. Using these acceleration techniques the computational time of the POD model was two orders of magnitude shorter than the full-order model.