Analysis of volume change effects in a fluidized bed catalytic reactor

A 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.     

The clustered dense phase model for group A fluidization: I. Dense phase hydrodynamics

A new hydrodynamic model is proposed to represent the gas flow in the dense phase of fluidized Group A powders. The model views that the particles form clusters under the influence of inter-particle forces, giving rise to the formation of a heterogeneous void structure consisting of clusters of particles and interstitial cavities. The model contains two parameters, one representing the intrinsic void structure of the clusters and the other representing their size.The model predictions have been tested against reported experimental dense phase hydrodynamic data of Group A powders, both in bubble-free beds and in freely bubbling beds. The results show 2-3 particle clusters in bubble-free beds, but considerably larger clusters, containing 100 particles or so, in the dense phase of freely bubbling beds. The model also provides predictions for bubble through-flow, bubble splitting from below, dense-phase solids circulation, and interstitial gas bypassing in freely bubbling beds.     

Novel phenomenological discrete bubble model of freely bubbling dense gas–solid fluidized beds: Application to two‐dimensional beds

A phenomenological discrete bubble model has been developed for freely bubbling dense gas–solid fluidized beds and validated for a pseudo‐two‐dimensional fluidized bed. In this model, bubbles are treated as distinct elements and their trajectories are tracked by integrating Newton's equation of motion. The effect of bubble–bubble interactions was taken into account via a modification of the bubble velocity. The emulsion phase velocity was obtained as a superposition of the motion induced by individual bubbles, taking into account bubble–bubble interaction. This novel model predicts the bubble size evolution and the pattern of emulsion phase circulation satisfactorily. Moreover, the effects of the superficial gas velocity, bubble–bubble interactions, initial bubble diameter, and the bed aspect ratio have been carefully investigated. The simulation results indicate that bubble–bubble interactions have profound influence on both the bubble and emulsion phase characteristics. Furthermore, this novel model may become a valuable tool in the design and optimization of fluidized‐bed reactors. © 2012 American Institute of Chemical Engineers AIChE J, 2012     

A Novel Model for Predicting the Dense Phase Behavior of 3D Gas‐Solid Fluidized Beds

A novel phenomenological discrete bubble model was developed and tested for prediction of the hydrodynamic behavior of the dense phase of a 3D gas‐solid cylindrical fluidized bed. The mirror image technique was applied to take into account the effects of the bed wall. The simulation results were validated against experimental data reported in the literature that were obtained by positron emission particle tracking. The time‐averaged velocity profiles of particles predicted by the developed model were found to agree well with experimental data. The initial bubble diameter had no significant influence on the time‐averaged circulating pattern of solids in the bed. The model predictions clearly indicate that the developed model can fairly predict the hydrodynamic behavior of the dense phase of 3D gas‐solid cylindrical fluidized beds.     

RADIAL DISPERSION AND BUBBLE CHARACTERISTICS IN THREE-PHASE FLUIDIZED BEDS

The effects of gas and liquid velocities, liquid viscosity and particle size on the radial dispersion coefficient of liquid phase (D_r) and the bubble properties in three-phase fluidized beds have been determined. A new flow regime map based on the drift flux theory in three-phase fluidized beds has been proposed.

In three-phase fluidized beds, D, increases with increasing gas velocity in the bubble coalescing and in the slug flow regimes, but it decreases in the bubble disintegrating regime. The coefficient exhibits a maximum value in the bed of small particles with increasing liquid velocity at lower gas velocities. However, it increases with increasing liquid velocity at higher gas velocities. In two and three-phase fluidized beds of larger particles (6,8 mm), D_r exhibits a maximum value with an increase in liquid viscosity at lower gas velocities, but it increases at higher gas velocities. The mean bubble chord length and its rising velocity increase with increasing gas velocity and liquid viscosity. However, the bubble chord length decreases with an increase in liquid velocity and it exhibits a maximum value with increasing particle size in the bed. The radial dispersion coefficients in the bubble coalescing and disintegrating regimes of three-phase fluidized beds in terms of the Peclet number in the present and previous studies have been well represented by the correlations based on the concept of isotropic turbulence theory.     

The effect of pressure on the flow of gas in fluidized beds of fine particles

The division of gas flow between the bubble and dense phases of fluidized beds of six different types of Group A powders has been studied at pressures of up to 20 bar using surface collapse and X-ray absorption measurements. It was found that with these fine powders as pressure increases at constant volumetric gas flowrate so the size and hold-up of bubbles decrease while their frequency increases. Contrary to previous measurements the average bubb velocity appears to decrease with increasing pressure. The dominant mode of bubble break-up in all the powders was found to be division from the rear, contrast to that observed with Group B powders at atmospheric pressure. Interstitial phase voidage was found to increase with increasing pressure.The results are interpreted in terms of a model which assumes a difference between the voidages, and hence the gas flow, of powder in the wakes behind     

Residence times in fluidized beds with secondary gas injection

Experiments were carried out to determine the effects of secondary gas injection on the gas residence time and macromixing characteristics in a bubbling fluidized bed. Primary gas is introduced via a bottom distributor plate, while secondary gas is introduced via a fractal injector submerged in the bed. Results indicate that the average residence time decreases only slightly. Calculated overall reactor Péclet numbers indicate that the gas experiences less back-mixing with secondary gas injection. The bubble size was observed to decrease by up to 70%, indicating improved gas–solid contact. Taking this improved contact and plug flow behavior into account, the conversion in a fluidized bed with secondary gas injection is expected to increase significantly, particularly for mass-transfer limited reactions.     

Effect of secondary gas injection on the particle entrainment rate in a gas fluidized bed

The effect of secondary gas injection on the particle entrainment rate was measured in a cold model fluidized bed (i.d. 0.1 m, height 2.25 m) and discussed. Sand particles below 0.425 mm in screen size were used as bed materials. The particle size (0.128–0.363 mm), the overall superficial gas velocity (0.78–2.76 m/s), the secondary gas fraction (0–0.5), and the static bed height (0.1–0.3 m) were considered as experimental variables. The particle entrainment rate decreased with an increase of the secondary gas fraction. The injection level of the secondary gas was shown to have an important influence on its effect. The effect of the secondary gas was appreciable for over-bed injection; the effect was reduced, however, when the injection level was placed in the splash zone or in the dense phase by means of increasing the bed height.     

High temperature fluidized bed reactor: measurements,hydrodynamics and simulation

This paper was made possible through the development of a novel high temperature optical fiber probe to study the hydrodynamics of a high temperature fluidized bed reactor. The experimental results show that the hydrodynamic parameters considerably change with bed temperature when fluidizing FCC particles. For a given superficial gas velocity, the average local particle concentration, the dense phase fraction and the particle concentration in the dense phase decrease with increasing bed temperature. As a result of an increase in temperature, the fluidized behavior of the FCC particles progressively shifts from typical Geldart A towards B. Consequently, a modified two-phase model, based on the simple two-phase model, integrating the effects of temperature and superficial gas velocity on the hydrodynamics, is proposed. Simulation of a reactive catalytic system using a conventional simple two-phase model and the modified model is achieved. The predicted reactor performances strongly differ for each model. In the present case, the simple two-phase model underestimates the reactor performance by inadequately accounting for the solid fractions in the bubble and dense phases and their dependence on temperature and superficial gas velocity. This suggests that the hydrodynamic models should take into account the effects of temperature and superficial gas velocity when simulating the performance of a high temperature fluidized bed reactor.     

Heat transfer between an isolated bubble and the dense phase in a fluidized bed

Heat transfer between the bubble and dense phases of a bubbling fluidized bed plays a very important role in the system performance, especially for applications involving solids drying and gas‐phase combustion. However, very few experimental data are available on this subject in the literature. An experimental and modelling investigation on the heat transfer behaviour of isolated bubbles injected into an incipiently fluidized bed is reported in this paper. A new single‐thermocouple technique was developed to measure the heat transfer coefficient. The effects of bed particle type and size, and bubble size on the heat transfer coefficient were examined. The heat transfer coefficient was found to exhibit a maximum as the bubble size increased in the bubble size range investigated. The bed particle size had a comparatively small effect on the heat transfer coefficient. A simple mathematical model was developed which provides good agreement with experimental data.     

EXPERIMENTAL OBSERVATIONS OF FLUIDIZED BEDS AT ELEVATED PRESSURES

The object of the work described here was to elucidate the effects of operation under pressure on the physical behaviour of gas fluidized beds. Extensive measurements of various bubble properties such as size, shape and rise velocity in beds of coarse powders (mean particle diameters of 184 μm and 450μm) operated at pressures of up to 81 bar were made by photographing the images created by irradiation of the bed with X-rays, and analysing the bubble silhouettes thereby obtained. Most of the results presented here are averages of some 200 individual measurements.

Experimental evidence to support the following picture of the effect of pressurization on the behaviour of freely bubbling gas fluidized beds is presented. Both bubble interaction (tendency to coalesce) and the incidence of bubble splitting increase with increasing pressure; the two are intimately connected. The nett results are a decrease in bubble size with increasing pressure over most of the pressure range and an increase in the tendency for bubbles to distribute non-uniformly in a radial direction. This latter tendency probably causes gross solids circulation in the bed, and this in turn leads to higher bubble rise velocities than those observed for single bubbles under similar conditions. The splitting mechanism accounting for the decrease in bubble size was found to be intrusion of the wake into the bubble void by the flow of gas through the wake region of a leading bubble during pair coalescence.

An updated review of other published work relating to the subject of experimental observations of the effects of pressure on gas fluidized beds is included in the form of a table.     

高密度浓相流化床中气泡的兼并与分裂特性

利用先进的高速动态分析系统对二维床中气泡的行为进行了研究,通过对所拍摄图象的分析处理．得到了不同介质流化床内形成的气泡形状、大小、聚并及分裂的基本规律和特点．实验研究表明．气泡的兼并主要是两气泡问的合并、被合并气泡总是从气泡的尾涡区曳入气泡;气泡分裂主要发生在操作气速较大或大气泡中,是由于其顶部粒子流(或“剪切流”)的侵入造成的;操作气速较低,粒度、密度较大粒子形成的流化床更易于造成气泡的湮灭。     

Analogous description of the hydrodynamics of gas-solid fluidized beds and bubble columns

In this paper we stress analogies in the hydrodynamic behaviour of gassolid fluidized beds and bubble columns. Using published experimental data, it is demonstrated that the analogous hydrodynamic-behaviour is not only qualitative but also quantitative in nature. Specifically, we show the following.(1) The gas holdup in the homogeneous regimes of bubble columns and fluidized beds can be modelled in a unified way using V_slip = υ_∞(1 − ϵ_d)ⁿ⁻¹, where V_slip refers to the slip velocity between the dispersed (bubbles or particles) and continuous phases and ϵ_d the dispersed phase holdup. The Richardson-Zaki exponent n decreases with increasing gas density.(2) The transition from homogeneous to heterogeneous flow regimes in gasliquid bubble columns and gassolid fluid beds is delayed by increasing system pressure. Extrapolation of the influence of increased gas density allows us to consider liquidliquid dispersions and liquidsolid fluid beds as limiting cases.(3) In the heterogeneous flow regime of operation the classic two-phase theory of fluidized beds can be applied with profit to also describe the hydrodynamics of gasliquid bubble columns provided that the “dilute” phase is identified with the fast-rising large bubbles and the “dense” phase is identified with the liquid phase containing entrained “small” bubbles. Tentative analogies can also be drawn for the interphase mass transfer processes.(4) The “dense” phase backmixing can be modelled in a unified manner.(5) The two-phase theory can be extended to describe slurry reactors.It is argued that, because of cross-fertilization of concepts and information, appreciation of analogies can be invaluable tool in scaling up.     

Gas back-mixing studies in membrane assisted bubbling fluidized beds

Fluidized beds employing fine powders are finding increased application in the chemical and petrochemical industry because of their excellent mass and heat transfer characteristics. However, in fluidized bed chemical reactors axial gas back mixing can strongly decrease the conversion and selectivity. By insertion of membranes in fluidized beds large improvements in conversion and selectivity can be achieved, firstly by optimizing axial concentration profiles via distributive feeding of one of the reactants or selective withdrawal of one of the products, and secondly, by decreasing the effective axial dispersion via compartmentalization of the fluidized bed. Moreover, insertion of membrane bundles in a suitable configuration impedes bubble growth, thereby reducing reactant by-pass via rapidly rising large bubbles. In this work the influence of the presence and configuration of membrane bundles and the effect of gas addition via the membranes on the effective axial dispersion was studied experimentally.Steady state concentration profiles were measured where a CO₂-tracer was injected at different locations through a probe (point injection) or via the membranes (line injection) into a square fluidized bed containing glass particles (75-, 2550 kg/m³) fluidized with nitrogen distributed via a porous plate. Different bed configurations, viz. without internals, with vertical or horizontal membrane bundles were investigated and the effects of overall fluidization velocity and gas flow ratio of gas fed through the membrane bundles and the porous plate distributor were studied.Experimental results revealed that the insertion of vertical and horizontal membrane bundles decreases the effective axial dispersion considerably compared to a bed without internals. The point injection experiments indicated the importance of a non-uniform lateral emulsion phase velocity profile. The line injection experiments clearly pointed out the importance of bubble-to-emulsion phase mass transfer limitations. Gas addition through the membrane bundles decreases the effective axial gas dispersion enormously by almost annihilating the solids down flow along the walls and by decreasing the average bubble size and bubble fraction.     

Minimum stable bubble volumes and bubble collapse rates in gas fluidized beds

Measurements of the collapse rates of small bubbles injected into particulate gas fluidized beds show that the net transfer rate of gas from the bubbles to the continuous phase decreases as the background velocity is increased. The results indicate that the minimum stable bubble volume in a bed fluidized at a velocity equal to twice the minimum fluidizing velocity is 0.08 cc. Evidence of increase in the continuous phase voidage in the path followed by a bubble has been observed; this would explain the formation of stable bubble tracks.     

Effect of bed size on hydrodynamics in 3‐D gas–solid fluidized beds

It is well known that hydrodynamics observed in large scale gas–solid fluidized beds are different from those observed in smaller scale beds. In this article, an efficient two‐fluid model based on kinetic theory of granular flow is applied, with the goal to highlight and investigate hydrodynamics differences between three‐dimensional fluidized beds of diameter 0.10, 0.15, 0.30, 0.60, and 1.0 m, focusing on the bubble and solids flow characteristics in the bubbling regime. Results for the 0.30 m diameter bed are compared with experimental results from the literature. The bubble size evolution closely follows a correlation proposed by Werther for small beds, and a correlation proposed by Darton for sufficiently large beds. The bubble size increases as the bed diameter is increased from 0.10 to 0.30 m, and remains approximately constant for bed diameters from 0.30 to 1.0 m. Concurrently, an increase in bubble rise velocity is observed, with a much high bubble rise velocity in the largest bed of diameter 1.0 m due to gulf stream circulations. The dynamics in shallow and deep beds is predicted to be different, with marked differences in bubble size and solids circulation patterns. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1492–1506, 2015     

Gas transfer from bubbles in a fluidized bed to the dense phase — II. Experiments

An experimental check was made upon the theory given in Part I. Cracking catalyst was used as a solid and differently adsorbed tracer gases were used. In a two-dimensional fluidized bed bubbles were formed underneath a gauze cap, while solid flowed along the bubble at the corresponding bubble velocity. Tracer injections provided the value for the transfer coefficient. In three-dimensional beds of 18 and 90 cm dia. large traced gas bubbles were injected. Tracer concentration was detected at certain heights. From the decrease the transfer coefficient was calculated. In the 90 cm bed the transfer coefficient was also calculated from residence time distribution measurements when the dense phase was perfectly mixed.It shows, that the two-dimensional bubble confirms the theory. For three-dimensional bubbles the transfer is higher than theoretically predicted, especially when the dense phase is expanded.     

RAINING OF PARTICLES FROM AN EMULSION-GAS INTERFACE IN A FLUIDIZED BED

This paper deals with the raining of particles from an interface between a dense fluidized phase and a gas phase with the fluidized phase uppermost. Such interfaces occur at the upper surfaces of gas bubbles and slugs in fluidized beds. Particle rain in these cases would enhance contact between gas and particles within the bubbles and slugs.

The rise velocities of single square-nosed slugs injected in incipiently fluidized beds of different diameters were measured. Relatively small columns of internal diameters of 0.0125, 0.019 and 0.0254 m were employed in the experiments; In such beds, square-nosed slugs are formed which span the entire cross-section of the beds and rise entirely due to raining of particles from their top surfaces. Since the upper surface of such slugs is flat, their motion can be analyzed using the one-dimensional hydrodynamic theory. Glass ballotini and sand of different sizes were used as bed particles. Comparison of theory and experiment has enabled the determination of the dimensionless gradient diffusivity characterizing the motion of particles induced by a gradient in the void fraction. The results confirm the scaling proposed by Batchelor (1988). The use of the calculated gradient diffusivity in the criterion for stability of a gas fluidized bed predicts the systems under consideration to be always unstable.