Bubble Assemblage Model Research Articles

A new model for bubbling fluidized bed reactors

Various mathematical models have been proposed in the past for estimating the conversions of reactant gases in fluidized bed reactors. A new mathematical model is being proposed in this paper that gives relatively better results compared to the prevailing models for bubbling fluidized bed reactors utilizing Geldart B particles. The new model is named as JSR (Jain, Sathiyamoorthy, Rao) model and it is a modified version of bubble assemblage model of Kato and Wen (1969). This paper discusses the development of JSR model and its verification by using data from chemical engineering literature on fluidization and also experimental data from hydrochlorination of silicon in a fluidized bed reactor. The new model is tested for five processes having operating temperatures from 130°C to 450°C, operating velocities from 0.019ms−1 to 0.19ms−1 and solid particle sizes from 65 to 325 mesh.

Development of a Membrane-Assisted Fluidized Bed Reactor. 1. Gas Phase Back-Mixing and Bubble-to-Emulsion Phase Mass Transfer Using Tracer Injection and Ultrasound Experiments

A small laboratory-scale membrane-assisted fluidized bed reactor (MAFBR) was constructed in order to experimentally demonstrate the benefits of this reactor concept, especially the enhanced bubble-to-emulsion phase mass transfer and the reduced overall axial gas phase back-mixing, due to the presence of the membranes and permeation of gas through the membranes. With steady-state tracer gas injection experiments, it was demonstrated that the experimental reactor exhibited approximately plug flow behavior for all the operating conditions investigated in this work as a result of the elimination of macroscale circulation patterns due to the presence of the membranes and, even more importantly, the permeation of gas through the membranes. With an ultrasound technique, the gas residence time distribution (RTD) of the MAFBR was measured over a wide range of fluidization velocities for two different bed heights. Interpretation of the RTD measurements with a phenomenological two-phase reactor model extending the bubble assemblage model proposed by Kato and Wen (Kato, K.; Wen, C. Chem. Eng. Sci. 1969, 24, 1351) showed that the average bubble diameter is significantly decreased for higher ratios of gas permeated through the membranes relative to the total gas flow rate.

Catalytic partial oxidation of ethane to acetic acid over Mo 1V 0.25Nb 0.12Pd 0.0005O x: reactor operation

The operation of a fixed-bed and fluidized-bed reactor for the partial oxidation of ethane to acetic acid was simulated. For the fixed-bed reactor a two-dimensional homogenous model and for fluidized-bed reactor the bubble assemblage model was applied. A kinetic model was used for reactor simulation, which describes the primary oxidative dehydrogenation of ethane to ethylene, the formation of acetic acid via ethylene, as an intermediate as well as a direct formation of acetic acid from ethane. Carbon dioxide formation results from combustion of ethane, ethylene and acetic acid. Furthermore, the influence of water on the reaction pathway was taken into account in the kinetic model. For the fixed-bed reactor, the influence of inlet temperature was investigated in a temperature range from 500 to 525 K and at a total pressure of 16 bar . The range of temperature where the danger of run-away occurs depends on gas velocities and reactor diameters. Accordingly, for a reactor diameter of 0.025 m and a gas velocity of u STP =0.0045 m s −1 runaway must be expected above a temperature of the inlet feed of 520 K . In a fluidized-bed reactor, significant lower selectivities and space-time yields of acetic acid are achieved compared to the fixed-bed due to the slow mass transfer of oxygen between bubble and emulsion phase. However, yield and selectivity of acetic acid can be increased by applying small sized catalyst particles.

Study on natural gas combustion in fluidized beds: modelling and experimental validation

A simulation model of homogeneous combustion of air–methane mixture in a fluidized bed composed of inert particles was established. This model, based on the assumptions of the bubble assemblage model, accounts for the thermal exchanges between phases and the radiating exchange with the wall. The experimental study was performed on a pilot fluidized-bed reactor 180 mm in diameter, fitted axially with sampling probes for analysing the gas composition. For bed temperature ranging between 850 and 950 °C, the comparison of the measured gas compositions and the theoretical results showed a good agreement as regards the methane conversion rate along the bed.

Mathematical modeling of fluidized‐bed chlorination of rutile

AbstractA mathematical model was formulated to describe the reaction rate and the particle size distribution of solids in a fluidized bed for the chlorination of rutile by a CO/Cl2 mixture. The bubble assemblage model was applied to describe the gas behavior in the bed. The particle‐size distribution in the bed was determined by a population balance. Predictions of the model gave satisfactory agreement with experimental results. The effects of important variables such as superficial gas velocity, exchange rate between the phases, and the reaction‐rate constant were evaluated.

Comprehensive model of oxidative coupling of methane in a fluidized-bed reactor

A comprehensive reactor model of the oxidative coupling of methane to higher hydrocarbons (OCM) in a fluidized-bed reactor was developed. Bed hydrodynamics was described according to a modified version of the “bubble assemblage model” of Kato and Wen (1969, Chem. Engng Sci. 24, 1351–1368). The chemical reactions were characterized by two separate kinetic models for heterogeneous and homogeneous networks. The model was validated on the basis of experimental results obtained over a La 2O 3 CaO catalyst in laboratory-scale fluidized-bed reactors (ID = 5 and 7 cm). Conversion of methane and C 2+ selectivity were predicted with accuracy ±20% in a wide range of reaction conditions ( X CH 4 = 8–39% and S C 2+ = 25–74%). The simulation results confirmed the importance of consecutive reactions and gas-phase reactions which are in a fluidized-bed reactor promoted by the bed hydrodynamics.

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%).

An improved bubble assemblage model for fluidized-bed catalytic reactors

A mathematical model based on bubble assemblage concepts for fluidized-bed catalytic reactors is presented. The bed is divided into three phases, namely, bubble, cloud-wake, and emulsion phases. The concept of axial gas mixing in the emulsion phase is incorporated. Hence, upflow and downflow gas streams in the emulsion phase are simultaneously considered in the model. The model developed contains no adjustable parameters. Newly developed correlation equations for the predictions of bubble diameter and superficial bubble-phase gas velocity are also selected and tested for the model. Model predictions are shown to compare quite well with the various published experimental data on both axial concentration profiles and overall conversions.

Analysis of volume change effects in a fluidized bed catalytic reactor

AbstractA mathematical model based on the concept of an improved bubble assemblage model is developed for calculating the conversion of a reaction system involving a volume change in fluidized beds. The influence of volume change on the hydrodynamic behavior of gas in the bed, such as bubble size variation, superficial gas velocity change, and volume fraction occupied by each phase, is also investigated. It is found that increasing stoichiometric coefficient values results in larger bubble size, higher superficial gas velocities, higher crossflow rate between emulsion phase and bubble phase, and greater volume fraction of bubble phase, but smaller volume fraction occupied by the emulsion phase as well as lower conversions.

Modelling and Simulation of Acrylonitrile Synthesis from Propylene Using Fluidized Bed Technology

The synthesis of acrylonitrile by the ammoxidation of propylene was modelled and simulated in a fluidized bed reactor based upon the two phase theory of fluidization. The conversion as obtained from two other models (the bubbling bed model and the bubble assemblage model) was calculated for comparison. The impact of the variation of each of four system parameters upon reactor performance was explored. A preliminary optimization search was initiated and it was shown that the model predicts a 76.6% conversion for a particular combinatioin of the four system parameters which compares favorably with the typical 60-65% conversion reported for actual industrial applications.

Simulation of fluidized‐bed reactors for catalytic oxidative coupling of methane to C2‐hydrocarbons

AbstractThe “bubble assemblage model” of Kato and Wen was applied to simulate the catalytic oxidative coupling of methane to C2‐hydrocarbons in a fluidized bed reactor. Simulation results were compared to experimental data obtained in a laboratory‐scale fluidized bed reactor. To improve the accuracy of predictions, the influence of fluid bed hydrodynamic and kinetic submodels was investigated by applying a sensitivity analysis. It was shown that the most important element in the model is the applied reaction scheme; the consecutive reactions of C2 hydrocarbons occurring most probably in the gas phase should be considered.

Modeling of fluidized bed chlorination of rutile

A model has been developed for fluidized bed chlorination of rutile in the presence of coke to produce titanium tetrachloride. At various reaction conditions, the model can predict the conversion of chlorine, particle size distribution in the bed, composition of the product gas, and reaction temperature. The bubble assemblage model is used to calculate the reactant gas mass transfer rate from the bubble phase to the emulsion phase. The population balance is employed to determine the size distribution of particles in the bed. The reaction in the freeboard zone is neglected. The model predictions have been compared with the results from a pilot-scale experiment, and the model gives good agreement between computed and experimental results. The effects of various reaction parameters on the reaction rate are discussed using the model.

Modelling a two-stage countercurrent fluidized bed reactor for removing SO 2from gases by active soda

The problem of high desulphurization efficiency of flue gases at high conversion in the solid phase has been investigated. Crystalline NaHCO 3 is fed to a reactor and by its thermal decomposition and highly reactive soda (active soda) is formed. To achieve both high process efficiency (over 95%) and high conversion of the solid (nearly 95%), we took to the two-stage countercurrent flow and to the cyclic operation of the reactor. For this purpose, the bubble assemblage model of Kato and Wen (1969) had been modified for a batch process in the solid phase including the kinetics of the chemical process taking place and the enthalpy balance. Effects of various parameters on the process have been examined by simulation. The model obtained and the results may be applied to the control of the reactor.

Mathematical modelling of a fluidised-bed charcoal gasifier

A mathematical model for the behaviour of a fluidised-bed charcoal gasifier was developed, taking into account fluidised-bed hydrodynamic conditions, chemical reaction rates, mass diffusion rates, and the conservation of mass and energy. In the course of the model's development, the modified ‘bubble assemblage model’ developed by Kato & Wen 1 was assumed. Kinetic data for major combustion and gasification reactions were taken from Goldman et al. 2 for anthracite char with a necessary temperature correction as suggested by Rensfelt et al. 3 The model was solved numerically using an IBM 3083 mainframe computer. Results obtained for the simulation show qualitative resemblance to the limited amount of experimental data generated in our laboratory.

Kinetic modelling of a fluidized bed claus plant

AbstractA kinetic model of a fluidized bed Claus reactor was developed using the Modified Bubble Assemblage Model (MBAM) to establish the practical implications of fluid bed technology for this new application. Simulations predicted that a two stage sub‐dewpoint fluidized bed Claus plant is capable of achieving a recovery efficiency of 97.1%, which is comparable to a conventional three stage fixed bed plant, but considerably less than the overall equilibrium conversion of 99.5%. Conversion is limited by gas‐bypassing, particularly in the downstream sub‐dewpoint reactor. In the fluidized bed process, about half the catalyst is required and the pressure drop is significantly lower compared with a conventional plant of equivalent capacity. Moreover, the capital cost estimate for a two reactor fluid bed Claus plant (200 t/d sulphur) was estimated to be $20 million (Can) which is within 10% of a conventional plant.

Statistical assessment of a fluidized bed wood gasifier model

AbstractSensitivity analyses were carried out to assess the behaviour of a fluidized bed wood gasifier simulation model in response to changes in the values of design variables, operating variables, and model coefficients. The model was originally developed using the modified Bubble Assemblage Model. Physical design specifications of the fluidized bed were found to have little influence on the quality of the product gas; in fact the composition of the gas was found to depend almost exclusively on the degree of approach to equilibrium. Overall thermal efficiency could be improved only by increasing the dry wood to oxygen ratio and reducing the moisture content in the wood feed. Because wood gasifiers produce volatiles that greatly enhance the chance of slugging, the influences of the design and operating variables on the occurrence of slugging were also investigated. The onset of slugging was found to be related most strongly to the dynamic bed height.

The reaction characteristics of parallel consecutive reactions in a fluidized bed.

The reaction characteristics (the reactant conversion and the yield of the intermediate product) of a parallel consecutive reaction in a fluidized bed were analyzed on the basis of the Bubble Assemblage Model. The effects of rate constants, particle size and bed diameter upon the reaction characteristics were investigated theoretically. When the rate constants and the size of particles were small, the reaction characteristics for a fluidized-bed reactor closely approached those for a plug-flow reactor and scale-up of the fluidized bed reactor became easy.

A new similarity rule for fluidized bed scale‐up

AbstractA rule of hydrodynamic similarity for a scale change of fluidized beds has been developed based on the governing equations of bubble and interstitial gas dynamics. When geometrically similar scale‐up is to be carried out maintaining hydrodynamic similarity, the proposed similarity rule requires that two conditions be satisfied. The first condition assures a similarity in bubble coalescence. The second assures the similarities in bubble splitting and in the interstitial flow pattern. The present work proves theoretically that these two conditions are the necessary, and almost sufficient, conditions for hydrodynamic similarity. They consider not only bubble coalescence but also bubble splitting. The theory proposed was first tested by previous correlations for bubble diameter and grid zone structure, and second by experiment. It has been proved that as long as the present rule is satisfied, the longitudinal distribution of the average bubble diameter, stochastic variation around it, and the radial distribution of superficial bubble velocity can be maintained similar for a scale change.Application of the present rule to predict the bubbling and solid circulation characteristics in a large‐scale unit by a small‐scale experiment has thus proved promising, at least for Geldart group B particles. In order to further study the possibility of a similarity in mass transfer and chemical reactions, computation was carried out using the three‐phase bubble assemblage model. If the effect of molecular diffusion is negligible, as in the case of fluidized bed combustion, even a chemical similarity is found to be possible.

MODELING OF THE TRANSIENT AND STEADY STATE OPERATION OF A FLUIDIZED BED REACTOR WITH ADAPTIVE CONTROL OF TEMPERATURE

This paper concerns modeling of the transient and the steady state operation of a fluidized bed reactor for the catalytic ammoxidation of propylene to acrylonitrile. To maintain constant the temperature of the reaction in order to facilitate the phenomenological study as well as to avoid risks of destruction of the catalyst, a self tuning P.I.D. controller has been used. The controller derived from a discrete P.I.D. regulator is based on pole assignment. It uses a recursive parameter estimator based on the least square method. The reactor has been interfaced with an Apple II micro-computer. The results obtained illustrates the inherent capability of self adaptive control to adapt the change of the environment where conventional control fails Modeling of the reactor is based on the Kato and Wen bubble assemblage model corrected by including the wake of the bubbles with their clouds, as proposed hy Stergiou. This modified model gives good predictions of the operation of the reactor for steady as well as tra...

高圧流動層による鉄鉱石の水素還元解析

An analytical procedure was developed for reduction in fluidized beds with batch-wise iron ore feed based on the bubble assemblage model and the three-interface reaction model with solid-state diffusion. The experimental results of hydrogen reduction in the high pressure fluidized bed were analyzed according to the proposed procedure. The simulated results were able to describe the experimental data up to the final stage in which the reduction rate became extremely low. Effects of pressure, temperature, gas velocity, bed height, and fractional reduction on the reduction rate and the utilization factor for hydrogen were elucidated quantitatively by the proposed analytical procedure.