Defluidized zones in liquid–solid fluidized beds

Defluidized zones often appear on the distributor plates of liquid–solid fluidized beds. They can lead to hot spots, the formation of undesirable side products or the degradation of products or reactants. In some cases, a solid residue forms and plugs the distributor.Two different techniques were developed to detect defluidized zones. The first technique uses a specially designed collision probe to monitor local particle motion. The second technique is aimed at the on-line detection of defluidized zones in industrial bioreactors. It uses local bed conductivity fluctuations.Defluidized zones were measured in beds of 3 or 5 mm diameter glass beads fluidized by an aqueous saline solution. Special experiments established the importance of horizontal liquid flow and distributor plate roughness on the formation of defluidized zones.A model describes how a defluidized zone can be eliminated. It considers that a defluidized zone is broken by the drag force on its particles of downward and sideways liquid flow. This liquid flow is induced by suction from the liquid jets issuing from the distributor holes. The resulting drag force is resisted by friction between particles or between particles and the distributor surface.     

Local solid mixing in gas–solid fluidized beds

Diffusivity of the solid particles in a 152-mm ID gas–solid fluidized bed was determined at different regimes of fluidization. The gas was air at room temperature and atmospheric pressure and the solids were 385 μm sand or 70 μm FCC particles. The experiments were done at superficial gas velocities from 0.5 to 2.8 m/s for sand and 0.44 to 0.9 m/s for FCC (in both bubbling and turbulent regimes). Movement of a tracer was monitored by radioactive particle tracking (RPT) technique. Once the time-position data became available, local axial and radial diffusivity of solids were calculated from these data. Calculated diffusivities are in the range of 3.3×10⁻³ to 5.6×10⁻² m²/s for axial and 2.6×10⁻⁴ to 1.5×10⁻³ m²/s for radial direction. The results show that the diffusivities, both axial and radial, increase with superficial gas velocity and are linearly correlated to the axial solid velocity gradient. Solid diffusivity in a bed of FCC was found to be higher than that of a bed of sand at the same excess superficial gas velocity.     

Gas–solid fluidized beds in vortex chambers

This review deals with gas–solid fluidized beds in vortex chambers. High-G fluidization can be achieved in a static geometry and allows significant process intensification. Thin, dense and more uniform particle beds can be obtained at high gas–solid slip velocities, intensifying interfacial transfer of mass, heat and momentum and reducing the gas–solid contact time. Existing fluidized bed processes can be carried out more efficiently and novel processing routes can be developed, e.g., involving cohesive particles or a dispersed liquid phase in relatively high concentrations.The first section of the review discusses the unique hydrodynamic characteristics of gas–solid fluidized beds in vortex chambers. The flow pattern, flexibility in the operating conditions and stability conditions are explained.The design of vortex chambers is dealt with in the second section and is critical for processing both larger and fine particles. The influence of the gas and solids in- and outlet design is focused on and insight is gained from recent theoretical, experimental and CFD studies.In the third section (potential) applications are discussed and process intensification and novel processing routes demonstrated. The fourth and last section presents extensions of the concept. Multi-zone operation and the integration of other technologies in vortex chambers are considered.     

Supersonic attrition nozzles in gas–solid fluidized beds

Gas–solid fluidized beds are used in both catalytic and non-catalytic processes, and some of the industrial applications are fluid catalytic cracking, polyethylene production, drying and classification, coating, and granulation. In some applications, the size distribution of the bed particles must be controlled in order to maintain good fluidization, and attrition nozzles can be used for this purpose. Supersonic attrition nozzles are more efficient than subsonic nozzles, and, in this study, different geometries of the Laval nozzle, a convergent–divergent (C–D) nozzle, have been investigated. The geometry of this type of nozzles gives supersonic velocities under the right operating conditions.     

Phase holdup and liquid dispersion in gas-liquid-solid circulating fluidized beds

Axial and radial profiles of gas and solids holdups have been studied in agas-liquid-solid circulating fluidized bed at 140mm i.d..Experimental results indicate that the axialand radial profiles of gas and solids holdups are more uniform than those in a conventionalfluidized bed.Axial and radial liquid dispersion coefficients in the gas-liquid-solid circulating fluidizedbed are investigated for the first time.It is found that axial and radial liquid dispersioncoefficients increases with increaes in gas velocity and solids holdup.The liquid velocity has littleinfluence on the axial liquid dispersion coefficient,but would adversely affect the redial liquiddispersion coefficient.It can be concluded that the gas-liquid-solid circulating fluidized bed hasadvantages such as better interphase contact and lower liquid dispersion along the axial directionover the expanded bed.     

Investigation of electrostatic charge distribution in gas–solid fluidized beds

Over the past few decades there have been numerous attempts to measure electrostatic charges in gas–solid fluidized bed reactors; these charges have been prone to cause reactor downtime from electrostatic phenomena. In this study, a new system was developed that aimed to quantifying the electrostatic charge generation in three key areas within a gas–solid fluidized bed simultaneously: the bed particles, the particles that adhered to the column wall, and the particles that were entrained from the column. A unique online Faraday cup method was used to measure the electrostatic charge of the particles. The system was operated with dry air at two fluidizing gas velocities, one in the bubbling and the other in the slugging flow regime. An industrial polyethylene resin with a wide particle size range was utilized in all experiments. Results showed the occurrence of bi-polar charging in both flow regimes with entrained fines being mainly positively charged, whereas the bed particles and those attached to the column wall carrying a net negative charge. The charge-to-mass ratio (q/m) of the entrained fines in the bubbling regime was significantly higher than in the slugging regime. It was discovered that particles with a certain size range were predominantly adhering to the column wall with a significantly higher q/m than the other bed particles. These findings led to a proposed mechanism for the migration of particles within the fluidization column due to the effect of electrostatic charge generation.     

On-line detection of bed fluidity in gas–solid fluidized beds with liquid injection by passive acoustic and vibrometric methods

Passive acoustic and vibrometric methods were investigated for the detection and monitoring of changes in bed fluidity in a large scale gas–solid fluidized bed after liquid injection. Water was injected into a 9 tonne air-fluidized bed of silica sand using an industrial nozzle and pre-mixer assembly. Acoustic signals were recorded using non-intrusive and externally mounted microphones. Vibration data was recorded using an accelerometer mounted to a rod inserted into the bed. The signals were analyzed offline using Fourier and wavelet analysis techniques. The average frequency of the acoustic and vibration measurements decreased as the bed solids dried while the standard deviation of the coefficients in the 10–20 kHz band characterized from wavelet analysis increased during drying. Samples from the bed were taken and evaluated for flowability by measuring the median avalanche time with a Revolution Powder analyzer. Linear and power law regressions of the wavelet and Fourier analyzed vibration measurements provided a reliable correlation of the flowability of the bed solids and thus could be successfully used as a passive and real-time monitoring method of bed fluidity.     

A critical evaluation of literature correlations for predicting bubble size and velocity in gas–solid fluidized beds

Twenty-five different correlations for bubble size and seven different correlations for bubble rise velocity have been evaluated by comparing their predictions with data available from the open literature. The performance of these correlations has been quantified by calculating the squared difference between the correlation predictions and the experimental data in seven categories for bubble size (Geldart A, B, and D particles, low (less than 10 U_mf) and high (greater than 10 U_mf) excess gas velocity, and perforated and porous plate distributers) and three categories for bubble rise velocity (Geldart A, B, and D particles). The results indicate that the correlations of Cai et al. [Powder Technol. 80 (1994) 99–109] and Werther [Ger. Chem. Eng. 1 (1978) 166–174] are the best choices for calculating the bubble size and bubble rise velocity, respectively.     

Development of a model for thin-film stability and spreading in solid–liquid–liquid systems

The presence of thin aqueous films and their stability has a profound effect on reservoir rock–fluids interactions involved in spreading and adhesion. The stability of thin wetting aqueous films on rock surfaces is governed by several variables including pH, brine and crude oil compositions, and capillary pressure. These variables govern the wetting states in the solid–liquid–liquid systems. The wetting states influence the residual oil saturation and the oil-water relative permeabilities and, consequently, the oil recovery. The objective of this study was to deduce a functional dependence of thin-film stability on the above parameters by considering intermolecular and surface interactions in rock–crude oil–brine systems. The surface forces are manifested as disjoining pressure in thin films. The disjoining pressure isotherms for the selected solid–liquid–liquid systems have been computed in terms of the bulk properties of the media. The equilibrium contact angles have also been computed from the integration of the Young–Laplace equation, which relates contact angle to the capillary pressure and disjoining pressure isotherm of the system. The contact-angle data obtained from sessile-drop experiments have been compared with the calculated results, as well as with other published results. Adhesion maps, which relate the film stability to brine pH and molarity, have been developed. The rock–fluids systems considered for this study consisted of smooth glass, quartz and Yates reservoir fluids. The DLVO theory has been used to model the intermolecular forces. The structural forces are incorporated to overcome the limitations of the DLVO theory. A charge regulation model has been used to analyze the crude oil–brine and glass–brine interfaces. The effects of multivalent ions have been incorporated using an equivalent molarity concept. The overall computational model developed in this study is aimed at providing a priori prediction capability of rock-fluids interactions in petroleum reservoirs for inclusion in reservoir simulators.     

A new model in correlating and calculating the solid–liquid equilibrium of salt–water systems

In this work, a new activity coefficient model was deduced for the correlation of solid–liquid equilibrium(SLE) in electrolyte solutions. The new excess Gibbs energy equation for SLE contains two parts: the single electrolyte item and the mixed electrolyte item. Then a new hypothesis for the reference state of activity coefficients was proposed in the work. Literature data for single electrolyte solution and mixed electrolyte solution systems,with temperature spanning from 273.15 to 373.15 K, were successfully correlated using the developed model.     

A machine learning approach for electrical capacitance tomography measurement of gas–solid fluidized beds

Electrical capacitance tomography has been widely used to obtain key hydrodynamic parameters of gas–solid fluidized beds, which is normally realized by first reconstructing images and then by analyzing these images. This indirect approach is time-consuming and hence difficult for on-line monitoring. Meanwhile, considering recurrence of similar flow patterns in fluidized beds, most of these calculations are repetitive and should be avoided. Here, we develop a machine learning approach to address these problems. First, superficial gas velocity linear-increasing strategy is used to perform high-throughput experiments to collect a large amount of training samples. These samples are used to train the map from normalized capacitance measurements to key parameters that obtained by an iterative image reconstruction algorithm off-line. The trained model can then be used for on-line monitoring. Preliminary tests revealed that the trained models show good prediction and generality for the estimation of the overall solid concentration and the equivalent bubble diameter.     

Models for prediction of hydrodynamic characteristics of gas–solid tapered and mini-tapered fluidized beds

Prediction of hydrodynamic characteristics is a prerequisite in the design and operation of tapered and mini-tapered fluidized beds. This paper has been focused on the development of generalized models for prediction of minimum fluidization velocity and maximum pressure drop in gas–solid tapered and mini-tapered fluidized beds. The empirical correlations were developed based on dimensionless analysis of empirical data. These correlations have the ability to predict the minimum fluidization velocity and maximum pressure drop in both tapered and cylindrical beds (the beds with tapered angle of zero). The empirical data were collected from tapered beds with different cone angles for various particles. The predicting capability of correlations has been discussed. Predicted values of minimum fluidization velocity and maximum pressure drop by the proposed models compared well with the empirical data. The effects of tapered angle are also discussed.     

Experimental studies and empirical models for the prediction of bed expansion in gas–solid tapered fluidized beds

Studies in the expansion behaviour of tapered fluidized bed systems are important for specifying the height of the bed. Data have been obtained on the expanded heights of tapered fluidized beds and bed expansion ratios for spherical and non-spherical particles have been calculated. Based on dimensional analysis, models have been developed as a function of geometry of tapered bed, static bed height, particle diameter, density of solid and gas and superficial velocity of the fluidizing medium. The data used to derive the models cover a wide range of operating conditions, with varying fluidization velocities. Effects of static bed height, particle diameter, density, tapered angle and superficial gas velocity over minimum fluidization velocity on bed expansion ratios have been investigated experimentally. A comparison has been made between the calculated values of bed expansion ratios using proposed models and the experimental data. It has been seen that calculated values by models agree well with the experimental values. Models have also been compared with literature data of conventional bed and found its applicability at higher gas velocities with good accuracy.     

Computational fluid dynamics for dense gas–solid fluidized beds: a multi-scale modeling strategy

Dense gas–particle flows are encountered in a variety of industrially important processes for large scale production of fuels, fertilizers and base chemicals. The scale-up of these processes is often problematic, which can be related to the intrinsic complexities of these flows which are unfortunately not yet fully understood despite significant efforts made in both academic and industrial research laboratories. In dense gas–particle flows both (effective) fluid–particle and (dissipative) particle–particle interactions need to be accounted for because these phenomena, to a large extent, govern the prevailing flow phenomena, i.e. the formation and evolution of heterogeneous structures. These structures have significant impact on the quality of the gas–solid contact and as a direct consequence thereof strongly affect the performance of the process.Due to the inherent complexity of dense gas-particles flows, we have adopted a multi-scale modeling approach in which both fluid–particle and particle–particle interactions can be properly accounted for. The idea is essentially that fundamental models, taking into account the relevant details of fluid–particle (lattice Boltzmann model (LBM)) and particle–particle (discrete particle model (DPM)) interactions, are used to develop closure laws to feed continuum models which can be used to compute the flow structures on a much larger (industrial) scale. Our multi-scale approach (see Fig. 1) involves the LBM, the DPM, the continuum model based on the kinetic theory of granular flow, and the discrete bubble model. In this paper we give an overview of the multi-scale modeling strategy, accompanied by illustrative computational results for bubble formation. In addition, areas which need substantial further attention will be highlighted.     

A semi-empirical model for the drag force and fluid–particle interaction in polydisperse suspensions

Fluid flow through stationary or moving particle beds is a common process in industrial units. The two-phase hydrodynamics strongly influences the performances and characteristics of reactors and contactors in general, but the possibility to model comprehensively the details of the two-phase field of motion still lacks. Computational methods and multi-scale modeling are capable of providing essential information at the microscopic scale. In the present paper, recently published data on the fluid–particle interaction obtained at the sub-particle scale are used to propose a semi-empirical model for the calculation of the fluid–particle interaction, named the basis of computer simulations of fluid–solid flows. The proposed approach starts from flow through monodisperse particle beds and leads to a general expression valid over a very wide range of Reynolds’ number and porosity and, most notably, accounts for polydispersion in a consistent and general way. Available actual drag force data from lattice-Boltzmann simulations for mono- and bi-disperse systems are fitted by a physically consistent and computationally efficient model, obtaining a very good agreement over a broad range of conditions. The resulting model is validated both against lattice-Boltzmann simulations involving ten different species and against experimental measurements in real two-component beds fluidized by a liquid exhibiting the layer inversion phenomenon. The model is shown to predict well the correct values under a significant variability of operating conditions. Finally a discussion of the application of the model in the context of numerical simulations is presented.     

A fundamental CFD study of the gas–solid flow field in fluidized bed polymerization reactors

A Eulerian–Eulerian model incorporating the kinetic theory of granular flow was applied to describe the gas–solid two-phase flow in fluidized bed polymerization reactors. The model parameters were examined, and the model was validated by comparing the simulation result with the classical calculated data. The effects of distributor shape, solid particle size, operational gas velocity and feed manner on the flow behavior in the reactor were also investigated numerically. The results show that with the increase of solid particle diameter, the bubble numbers decrease and the bubble size increases, resulting in a smaller bed expansion ratio. Bed expansion ratio increases with increasing the gas inlet velocity. Moreover, the final fluidized qualities are almost the same for the plane distributor case and the triangle distributor case. There exists a tempestuous wiggle from side to side in the bed at the continuous feed manner, which could not be obtained at a batch feed manner.     

Hydrodynamics of an inverse liquid–solid circulating conventional fluidized bed

An inverse liquid–solid circulating conventional fluidized bed (I-CCFB) is realized by injecting particles from the top of a conventional liquid–solid fluidized bed (0.076 m ID and 5.4 m height) that is operated in a newly developed circulating conventional fluidization regime located between the conventional and circulating fluidization regimes. The I-CCFB can achieve a higher solids holdup compared to both conventional and circulating liquid–solid fluidized beds. A new parameter, the bed intensification factor, is defined to quantify the increased solids holdup observed with external solids circulation. The Richardson–Zaki equation is shown to be applicable to the I-CCFB regime and can be used to correlate the slip velocity and solids holdup, both of which increase with the solids circulation rate. A new flow regime map is presented, including the I-CCFB and a variety of other liquid–solid fluidized beds.     

The onset velocity of a liquid–solid circulating fluidized bed

The critical transition velocity, U_cr, previously defined by Liang et al. [W.-G. Liang, S.-L. Zhang, J.-X. Zhu, Y. Jin, Z.-Q. Yu and Z.-W. Wang, Flow characteristics of the liquid–solid circulating fluidized bed, Powder Technol., 90 (1997) 95–102.] to demarcate the liquid–solid conventional and circulating fluidization regimes, was found to vary with the total solids inventory and the solids feeding system. In this work, an onset velocity for circulating fluidization regime, U_cf, is proposed to give the lowest U_cr value and to provide a convenient demarcation velocity that is independent of system geometry. This liquid velocity is obtained by measuring the time required to empty all particles in a batch operated fluidized bed under different liquid velocities. This method can be used for a wide range of particles and involves less influence of the operating conditions such as the solids inventory and the solids feeding system. Compared to the critical transition velocity, this newly defined onset velocity is a more intrinsic parameter, only dependent on the liquid and particle properties. Based on the experimental results obtained in this work and other published results, the influence of particle properties and equipment setup on the onset velocity is also discussed.     

Euler multiphase-CFD simulation on a bubble-driven gas–liquid–solid fluidized bed

An integrated flow model was developed to simulate the fluidization hydrodynamics in a new bubble-driven gas–liquid–solid fluidized bed using the computational fluid dynamic (CFD) method. The results showed that axial solids holdup is affected by grid size, bubble diameter, and the interphase drag models used in the simulation. Good agreements with experimental data could be obtained by adopting the following parameters: 5 mm grid, 1.2 mm bubble diameter, the Tomiyama gas–liquid model, the Schiller–Naumann liquid–solid model, and the Gidaspow gas–solid model. At full fluidization state, an internal circulation of particles flowing upward near the wall and downward in the centre is observed, which is in the opposite direction compared with the traditional core-annular flow structure in a gas–solid fluidized bed. The simulated results are very sensitive to bubble diameters. Using smaller bubble diameters would lead to excessive liquid bed expansions and more solid accumulated at the bottom due to a bigger gas–liquid drag force, while bigger bubble diameters would result in a higher solid bed height caused by a smaller gas–solid drag force. Considering the actual bubble distribution, population balance model (PBM) is employed to characterize the coalescence and break up of bubbles. The calculated bubble diameters grow up from 2–4 mm at the bottom to 5–10 mm at the upper section of the bed, which are comparable to those observed in experiments. The simulation results could provide valuable information for the design and optimization of this new type of fluidized system.     

Experimental study and hydrodynamic modeling of countercurrent liquid–solid system with batch liquid

It is known that a transient effluent outlet concentration is obtained with a batch of adsorbent solids in any operation. A preferred steady state outlet concentration can be achieved with a continuous flow of solids. In the present work, information on pressure profiles, the total pressure drop across the column and holdup of solids are experimentally obtained for various solid flow rates, particle sizes and densities in a countercurrent liquid–solid system. These experimental results are compared with the prediction obtained using a phenomenological model containing continuity and momentum balance equations. The dominant drag force term was expressed in terms of various drag equations. The drag expression developed by Foscolo et al. (1983 Foscolo, P. U., Gibilaro, L. G., and Waldram, S. P. (1983). A unified model for particulate expansion of fluidized beds and flow in fixed porous media, Chem. Eng. Sci., 38(8), 1251–1260.[Crossref], [Web of Science ®] , [Google Scholar]) could predict the axial profiles of pressure drop and holdup, and the effect of various parameters on total pressure drop and solid holdup most satisfactorily.