Bubbling Bed Model Research Articles

Nickel carbonyl formation in a fluidized bed reactor: experimental investigation and modeling

AbstractBACKGROUNDThe Mond process has been used in the industry for nickel purification over a century. However, theoretical studies on this process are few and primarily based on empirical models. In this article, experimental and theoretical modeling of nickel tetracarbonyl formation through the Mond process under different conditions in a fluidized bed reactor is presented. Nickel tetracarbonyl, known primarily as nickel carbonyl gas, is formed through the reaction between nickel powder and carbon monoxide. The apparent reaction rate is modeled as a function of reaction temperature, inlet gas pressure, and carbon monoxide flow rate. Experimental results were obtained using a fluidized bed reactor. A diffusion‐kinetics and a two‐phase bubbling bed model were developed to compare with experimental results. The reactor is considered as a differential flow reactor for the theoretical modeling.RESULTSRate of reaction is measured in a fluidized bed and used for the verification of the studied models. The best performing model is a kinetic‐diffusion model with a rate of reaction that obeys rem = Kem([CO])n, in which Kem is a function of mass transfer as well as kinetic variables, but is primarily temperature dependent. Also, n for low‐pressure and high‐pressures regions is −1 and −3, respectively.CONCLUSIONSThe reaction rate is strongly dependent on carbon monoxide gas pressure. The models developed are rather simple yet provide significant improvement in predictions of the reaction rate compared to the existing models in the literature. © 2020 Society of Chemical Industry

Dynamical and technological consequences of multiple isolas of steady states in a catalytic fluidised-bed reactor

Abstract Steady-state characteristics of a catalytic fluidised bed reactor and its dynamical consequences are analyzed. The occurrence of an untypical steady-state structure manifesting in a form of multiple isolas is described. A two-phase bubbling bed model is used for a quantitative description of the bed of catalyst. The influence of heat exchange intensity and a fluidisation ratio onto the generation of isolated solution branches is presented for two kinetic schemes. Dynamical consequences of the coexistence of such untypical branches of steady states are presented. The impact of linear growth of the fluidisation ratio and step change of the cooling medium temperature onto the desired product yield is analyzed. The results presented in this study confirm that the identification of a region of the occurrence of multiple isolas is important due to their strong impact both on the process start-up and its control.

Steady-state characteristics of autothermal structures with fluidized-bed catalytic reactors

The paper focuses on the analysis of steady-state properties of autothermal structures with a fluidized bed. The concept of autothermicity is discussed, and typical autothermal structures are presented. A method for the determination of the steady-states of such systems is described. Quantitative analysis of steady-states multiplicity is presented for two autothermal structures, that is a fluidized-bed reactor with an external heat exchanger, and with a partial recirculation of hot gases. A two-phase bubbling bed model is employed to describe quantitatively the behavior of the catalytic fluidized bed. The influence of selected design and operating parameters on steady-state characteristics is analyzed for two simple kinetic models. The effect of these parameter on the desired product yield is evaluated for the multiple-reaction process. The results obtained have both scientific and practical importance.

Continuous CaO/Ca(OH)2 Fluidized Bed Reactor for Energy Storage: First Experimental Results and Reactor Model Validation

Novel thermochemical energy storage systems that employ fluidized beds of CaO/Ca(OH)2 for hydration/dehydration reactions are under development because of the inherent advantages of the low cost of the materials and their relatively high temperature operation windows (450 °C–550 °C). We report in this work the results of the first steady state experiments conducted in a new pilot plant designed to test the concept under realistic reactor conditions. The pilot has a fluidized bed reactor with an internal diameter of 0.108 m and a height of 780 mm fed continuously with gas and solids as well as heat exchangers to supply/extract the required reaction heat. The experimental results during dynamic and steady state periods were fitted to a KL reactor bubbling bed model, using kinetic parameters from thermogravimetric studies and a single crossflow factor. The resulting continuous reactor model will serve as useful tool for the continued scaling up of this technology.

Autothermicity, multiplicity, yield and selectivity of catalytic processes in a polytropic fluidized bed reactor

The work covers some basic issues related to stationary properties of a catalytic fluidized bed reactor. A bubbling bed model has been employed for the quantitative description of a catalyst. Autothermicity, yield and selectivity of catalytic processes described by three selected kinetic models have been discussed in terms of multiplicity and stability of steady states. The steady states structure has been illustrated graphically in selected planes of the model parameters by means of two-parameter bifurcation diagrams. The results obtained have both scientific and practical importance.

Confined fluidised bed porosity in the light of bubbling-bed models

Abstract Based on hydrodynamic data, Kato-Wen and Kunii-Levenspiel bubbling-bed model parameters, supplemented with assumptions characteristic for tested confined fluidised bed, were analysed. The calculated bubble diameters and the bed composition proved essential influence of inter-particle space of packed compacted component onto fluidisation character. The usability of the conducted model analysis was also confirmed. Finally, it can be concluded that Kunii-Levenspiel and Kato- Wen models with characteristic assumptions (for the tested bed) can be applied for calculation of the confined fluidised bed layer porosity. Discrepancies of ε f value, determined on the basis of the above mentioned bubbling-bed models do not exceed 8% of the error. The model parameters obtained from the matching the model relations to experimental data εf = f(u0) allow an analysis of the fluidisation character as well as gas velocity regime and the fluidised bed structural composition identification. A description of the regime of the process in which confined fluidised bed is characterised with an increase of mass and heat transfer rate is also possible using relation (17) derived in the present study.

Comparison between fluidised bed and packed bed reactors: non-catalytic gas–solid reactions

Mathematical modelling of both fluidised and packed bed reactors has been carried out. In the fluidised bed reactor, a two-phase bubbling bed model has been used in order to estimate the interaction between gas bubbles and the dense phase in the bed. Modelling in the packed bed reactor was carried out based on that used by Ranade and Evans. The reduction behaviour of solid reactants has been expressed by the grain model, and computerised programs were developed in MATLAB software for solving the governing equations at conditions of different temperatures and pressures. The behaviour of both types of reactors for variations in temperatures, size of the pellets and inlet gas compositions has been studied, and a comparison between the reactors has been carried out. Excellent mixing of reactants in the fluidised bed helps to minimise temperature variations and renders this system attractive for carrying out gas–solid reactions. The fluidised bed reactors show better conversion of reactants in comparison with packed beds when solid reactants are used in the form of small pellets.

Combined resistance bubbling bed model for drying of solids in fluidized beds

Fluidized bed drying kinetics of highly porous material which offers free flow of moisture to surface of the material is modeled utilizing the simplified bubbling bed model. The simplification step utilizes estimation of the overall transfer resistance, by summing all the resistances from the bubble phase to the emulsion phase. The model predictions are compared with the published experimental data covering the operating variables such as the inlet air temperature, the air flow rate, material characteristics and are found to match satisfactorily. The model highlights the importance of bubble size estimation, as it largely dictates the drying kinetics.

Mathematical modelling of fluidized‐bed reactors for non‐catalytic gas–solid reactions

AbstractMathematical modelling of a continuous fluidized‐bed reactor has been carried out for non‐catalytic gas–solid reactions. The two‐phase bubbling bed model has been used and the elutriation phenomenon for the fine particles has been investigated. The feed stream consisting particles with size distribution and reversible or irreversible first‐order kinetics can be treated by the model. The reduction behaviour of solid reactants was described by the grain model. A program was developed in MATLAB software for solving the governing equations at conditions of different temperatures and pressures. The model was validated using experimental data and simulation results available in the literature for the iron ore reduction with a gas mixture containing hydrogen [Srinivasan and Staffansson, Chem. Eng. Sci. 45(5), 1253–1265 (1990)]. The mathematical modelling was also used for predicting the extent of reaction for reduction of cobalt oxide by methane.

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.

Analysis of Fluidized Bed Drying Kinetics on the Basis of Interphase Mass Transfer Coefficient

A particular way to define fluidized bed drying kinetics on the basis of interphase mass transfer coefficient and the conception of general kinetic curve has been described. The presented method, which allows for minimization of laboratory tests, has been checked experimentally. The method for calculating of mass transfer interphase coefficient in the constant rate period of fluidized bed drying based on Kunii and Levenspiel bubbling bed model is shown.

Modeling of Sorption-Enhanced Steam Reforming in a Dual Fluidized Bubbling Bed Reactor

This paper highlights the use of a dual fluidized bed reactor system for producing hydrogen by sorption-enhanced steam methane reforming. Hydrogen concentrations of >98% are predicted for temperatures of ∼600 °C and a superficial gas velocity of 0.1 m/s, using a simple two-phase bubbling bed model for the reformer. The kinetics of the steam methane reforming and water-gas shift reactions are based on literature values, whereas experimentally derived carbonation kinetics are used for the carbonation of a dolomite. It is shown that the reformer temperature should not be <540 °C or >630 °C for carbon capture efficiencies to exceed 90%. Operating at relatively high solids circulation rates to reduce the need for fresh sorbent is predicted to give higher system efficiencies than for the case where fresh solid is added. This finding is attributed to the additional energy required to decompose both CaCO3 and MgCO3 in fresh dolomite.

Development of an inverse method to identify the kinetics of heavy metal release during waste incineration in fluidized bed

This paper deals with the emission of heavy metals (HM) during the incineration of municipal solid waste in a fluidized bed reactor. This study focused on the development of a general method to identify the kinetics of vaporization of heavy metals from the on-line analysis of exhaust gas. This method is an inverse method, which requires only the time evolution of the HM concentration in exhaust gases (experimental data) and a global bubbling bed model developed for transient conditions at the reactor scale. First, a lab-scale fluidized bed incinerator was set-up to simulate the HM release during the thermal treatment of metal-spiked model wastes. A specific on-line analysis system based on ICP-OES was developed to measure in real time the variation of the relative concentration of HM in exhaust gases. Then, a two-phase flow bubbling bed model was developed and validated to calculate the kinetics of vaporization of HM from its measured concentration time profile in the outlet gas. The technique was first validated with model waste (metal-spiked mineral matrices), thus enabling at each time both solid sampling for measuring the HM vaporization kinetic and on-line analysis for measuring the HM concentration in the outlet gas. The inverse method was then applied to realistic artificial wastes (derived from real wastes) to identify the HM vaporization kinetics from the on-line analysis results.

Spanning the flow regimes: Generic fluidized‐bed reactor model

AbstractProbabilistic averaging is used to model fluidized‐bed reactors across the three fluidlization flow regimes most commonly encountered in industry (bubbling, turbulent, and fast fluidization), extending earlier work, which introduced this approach to bridge the bubbling and turbulent regimes of fluidization. In extending this concept to the fast fluidization regime, the probabilities of being in each of the three regimes are represented as probability density functions derived from regime boundary transition data. The three regime‐specific models—a generalized version of a two‐phase bubbling bed model at low gas velocities, a dispersed flow model for turbulent beds at intermediate velocities, and a generalized version of a core‐annulus model at higher velocities—are employed, leading to improved predictions compared with any of the individual models, while avoiding discontinuities at the regime boundaries. Predictions from the new integrated model are in good agreement with available ozone decomposition data over the full range of applicability covered elsewhere.

The kinetics of vaporization of a heavy metal from a fluidized waste by an inverse method

This study addresses the emission of heavy metals during the incineration of municipal solid waste. A global method was developed to determine the vaporization rate of the metal from the on-line analysis of exhaust gas. This method differs from direct models, which predict the time course of the metal concentration in the gas from the vaporization rate profile, but which are not practicable because this vaporization rate cannot be measured in real incinerators burning real wastes. The method is based on the determination of the global rate of release of heavy metal from the combustion of model wastes in a fluidized bed. It is an inverse method, which involves only the measured concentration of heavy metal in the exhaust gases and a model developed at the reactor scale. The thermal treatment of model wastes spiked with a metal was performed in a laboratory- scale fluidized bed. In fact, a solid matrix derived from real waste was dosed with Cd, Pb, or Zn and burned to simulate the metal’s release during the incineration of municipal solid waste. An on-line analysis system was linked to the gas outlet of the reactor, and the metal’s vaporization was tracked successfully by continuously measuring by inductively coupled plasma optical emission spectroscopy (ICP-OES) the relative concentration of the metal in exhaust gases. On the theoretical front, a bubbling bed model was developed and validated to calculate the metal’s vaporization rate from its concentration-time profile in the outlet gas. The inverse method consists in identifying these vaporization rates at the particle level from only the on-line diagnostic results and using the model, whatever the waste considered. The data obtained may be used in any process, in which wastes are heated rapidly (several hundreds of degrees per second), as in fluidized beds.

Implementation of mathematical and computer modelling to investigate the characteristics of isothermal ammonia fluidized bed catalytic reactors

The potential of a fluidized bed catalytic reactor to improve the ammonia conversion under isothermal conditions has been studied. Mathematical and computer modelling have been utilized in this investigation. The mathematical model is based on the two phase bubbling bed model. It is shown that a substantial increase in the overall ammonia conversion is possible by implementation of the fluidized bed technology. The effect of mass transfer, hydrodynamics, and thermodynamic equilibrium on the ammonia conversion are presented. The investigation reveals that the bubble phase can play an important role in enhancing the conversion by removing ammonia from the emulsion phase and resulted in a shift of the thermodynamic equilibrium. It is also shown that the freeboard has a significant effect in increasing the overall ammonia conversion. Ammonia fixed-bed reactor is used for comparison.

A generalized bubbling/turbulent fluidized-bed reactor model

A new reactor model is proposed as a means of representing fluidized-bed reactors which are subject to high enough gas velocities that they operate, or may operate, in the turbulent flow regime of fluidization. The model views the turbulent regime as filling the interval between fully two-phase behavior, represented by a generalized version of the two-phase bubbling bed model of Grace (1984), and a homogeneous (single-phase) structure, subject to axially dispersed plug flow. The two limiting models are merged into each other by allowing key parameters to vary continuously with the superficial velocity, U, using probabilistic averaging. The resulting model is shown to give good predictions in comparison with experimental data from the literature. In addition, it predicts a smooth transition from dense to dilute-phase fluidization, consistent with experimental trends.

Fluidized bed catalytic reactor modeling across the flow regimes

AbstractFluidized bed reactor models are generally specific to a single flow regime resulting in ambiguities and discontinuities at the regime boundaries. In practice, only the bubbling, turbulent and fast fluidization regimes are of industrial significance for catalytic reactions. The turbulent fluidization regime is especially advantageous because of improved interphase mass transfer, resulting in improved selectivities and conversions. It is shown that some of the difficulties in modeling can be resolved by means of the probabilistic‐averaging model, recently published by Thompson et al. (1999). This model interpolates between the Grace (1984) two‐phase bubbling bed model at low velocities and single phase axially dispersed flow for fully established turbulent fluidization conditions, leading to improved predictions of conversion and selectivity for catalytic fluidized bed reactors operated at flow rates covering the full range between bubbling and fully turbulent fluidization. An analogous approach should be useful for beds operated at higher gas velocities as fast fluidization conditions are approached.

The fluidized-bed membrane reactor for steam methane reforming: model verification and parametric study

A new approach is presented for the modelling of a fluidized-bed membrane reactor (FBMR). The model considers the two-phase nature of the fluidized-bed reactor system and the parallel reactions taking place in stream methane reforming, as well as selective permeation through the walls of membrane tubes immersed in the bed. The model is based on the two-phase bubbling bed model with allowance for some gas flow in the dense phase. Plug flow is assumed for the combined sweep gas and permeating hydrogen flowing through the membrane tubes. Freeboard non-isothermal effects and reactions are also taken into account. The coupled differential equations for the fluidized bed and membrane tubes are solved numerically. The model is in very good agreement with experimental data, both with and without permeation, obtained in a pilot-scale reactor system. Parametric investigations demonstrate the effect of key operating variables and design parameters over a wide range. The model is also tested for its sensitivity to changes in hydrodynamic parameters. Increasing the permeation of hydrogen through the membrane tubes is of key importance in achieving high methane conversions and in minimizing adverse reactions in the freeboard region. Hydrodynamic and kinetic properties have limited influence for the conditions studied.

Reaction engineering simulations of a fluidized‐bed reactor for selective oxidation of fluorene to 9‐fluorenone

AbstractThe catalytic oxidation of fluorene to 9‐fluorenone in a fluidized‐bed reactor was investigated by modeling of the reactor and simulation of its performance. The “Bubble Assemblage Model” of Kato and Wen, the “Bubbling Bed Model” of Kunii and Levenspiel and the “Countercurrent Backmixing Model” of Potter were applied. From a comparison of simulation results obtained by the various fluidized‐bed models and a fixed‐bed model conclusions were drawn about the influence of interphase mass transfer and gas backmixing on the conversion of fluorene and slectivity of 9‐fluorenone formation. Furthermore, the dependence of conversion and selectivity on temperature and hydrodynamic conditions was investigated. In particular, the implications of a change of hydrodynamic conditions for scale‐up were analysed. The highest yield of 9‐fluorenone predicted for a bench‐scale fluidized bed amounted to 88% (XF = 97%, SNON = 91%). This yield was lower than in a fixed‐bed reactor (YNON = 92%, XF = 99%, SNON = 93%). A further drop of the yield was predicted when scaling‐up from a bench‐scale reactor to a commercial size unit (YNON = 54%, XF = 86%, SNON = 63%).