Mixing characteristics of irregular binaries in a promoted gas–solid fluidized bed: A mathematical model

The vertical as well as horizontal dispersion for the gas–solid fluidization has been analyzed in the present work. The fluidization and solids mixing characteristics of large irregular particles (Geldart‐BD type) for both homogeneous and heterogeneous materials (size‐variant and density‐variant respectively) have been investigated in a 15 × 100 cm² cylindrical column. A theoretical model for concentration of jetsam particles has been developed as a function of height of any layer of particles (measured from the grid) by considering the counterflow of solids and circulation model together with the dispersion model for the vertical and the horizontal displacement of the particles in the fluidized bed. The mixing index at any position in the bed has thereby been expressed as a function of the concentration of the jetsam. The values of mixing index calculated from the above model as well as the experimentally measured ones for both the homogeneous and the heterogeneous systems have been compared with each other. Attempt has also been made to develop correlations for the mixing index using various system parameters based on the dimensional analysis approach for the unpromoted and the promoted beds. The mixing index values thus obtained through the dimensional analysis approach have been compared with those obtained from the developed theoretical model. The values of the mixing index calculated for promoted beds have also been compared with the corresponding values for the unpromoted beds. Segregation effect is found to be stronger for the heterogeneous systems than the homogeneous ones. The density difference is the major factor affecting the segregation.     

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

With 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.     

Prediction of Pressure Drop and Holdup for Homogeneous Ternary Mixtures of Spherical Glass Bead Particles in a Three-Phase Fluidized Bed

Hydrodynamic characteristics, viz. bed pressure drop and gas holdup, have been studied for ternary mixtures of homogeneous regular particles in a co-current three-phase fluidized bed. For this, a series of experiments have been carried out in a 5-cm diameter column with air as the gas phase, water as the liquid phase, and ternary mixtures of glass beads (1.54, 1.3, and 1.1 mm) as the solid phase. The dependence of bed pressure drop on the average particle diameter, superficial gas velocity, and initial static bed height has been discussed. Based on the dimensional and statistical analyses, correlations have been developed with the system parameters, for both bed pressure drop and gas holdup. Experimental values of bed pressure drop and gas holdup have been found to agree well with those calculated from developed correlations.     

Bubbling fluidization of biomass and sand binary mixtures: Minimum fluidization velocity and particle segregation

Understanding the minimum fluidization velocity of biomass and sand mixtures is fundamental to ensuring the optimal performance of fluidized beds in a thermo-conversional process, such as fast pyrolysis. The present work aimed to determine the minimum fluidization velocity of binary mixtures using the characteristic diagram of pressure drop in the bed and to develop an experimental correlation for the minimum fluidization velocity of biomass and sand mixtures. Three types of biomass (sweet sorghum bagasse, waste tobacco and soybean hulls) and four sands with different sizes were investigated. The results showed that the fluid dynamic behavior of binary mixtures is directly related to the biomass size and shape. For sweet sorghum bagasse (more irregular particles), higher biomass percentages led to lower minimum fluidization velocities, which differed from the behaviors observed for waste tobacco and soybean hulls. The diameter ratio inert/biomass effectively influenced the segregation, with a higher ratio causing more pronounced bed segregation. A good fluidization regime (with little segregation) for biomass and sand mixtures was obtained using the smallest sand (d₅₀ = 0.35). Considering the studied operating conditions, the proposed correlation can be used satisfactorily to predict the minimum fluidization velocities for mixtures of biomass and sand in fluidized beds.     

Effect of particle shape on liquid-fluidized beds of binary (and ternary) solids mixtures: segregation vs. mixing

Experiments were carried out in water-fluidized binary (and ternary) mixtures of teflon spheres, discs and rods. All particles had the same volume, while the discs and rods had nearly the same sphericity. It is shown that segregation can occur by shape, with similar segregated and mixed zones as when binary mixtures of different size or density are fluidized. The model of Pruden and Epstein (1964; Stratification by size in particulate fluidisation and in hindered settling. Chemical Engineering Science 19, 696), in which the degree of segregation depends on the bulk density difference(s) of the corresponding monocomponent beds at the same liquid velocity, is vindicated qualitatively for each system, but sphericity is not sufficient as a single shape factor to yield a single quantitative correlation of the transitions between segregation patterns for the different systems. Segregation by shape of non-isometric particles appears to require higher reduced density differences than sizing of spheres, probably because of the greater bed instabilities generated by the non-isometric particles. Overall bed voidage is predicted well by the serial model of Epstein et al. (1981; Liquid fluidisation of binary particle mixture- I.Overall bed expansion. Chemical Engineering Science 36, 1803).     

Prediction of critical fluidization velocity and maximum bed pressure drop for binary mixture of regular particles in gas–solid tapered fluidized beds

The problems associated with conventional (cylindrical) fluidized beds, viz., fluidization of wider size range of particles, entrainment of particles and limitation of fluidization velocity could be overcome by using tapered fluidized beds. Limited work has been carried out to study the hydrodynamics of single materials with uniform size particles in tapered beds. In the present work, an attempt has been made to study the hydrodynamic characteristics of binary mixtures of homogeneous and heterogeneous regular particles (glass bead and sago) in tapered fluidized beds having different tapered angles. Correlations have been developed for critical fluidization velocity and maximum bed pressure drop for gas–solid tapered fluidized beds for binary mixtures of regular particles. Model predictions were compared with experimental data, which were in good agreement.     

Dynamics of segregation and fluidization of binary mixtures in a cylindrical fluidized bed

Dynamics of segregation and fluidization of unary particles and binary mixtures in a cylindrical fluidized bed is investigated using temporally– and spatially–resolved measurements of solids volume fraction (α_s) performed using Electrical Capacitance Tomography (ECT). Through the comparison with high-speed imaging, we have shown that ECT can be used to measure the segregation behavior in cylindrical fluidized beds quantitatively. ECT measurements have been used further to quantify the effects of mixture composition, particle–diameter ratio, and superficial gas velocity on the bed segregation behavior. Dynamics of fluidization behavior is characterized using the time–evolution of local α_s fluctuations, corresponding frequency distribution, and bubble size distribution. Further, a relation between the measured variance of α_s fluctuations at different radial locations and corresponding flow structures under different fluidization conditions is established. The present work helps to understand dynamics of segregation and fluidization of binary mixtures and to provide a database for validation of Eulerian multifluid CFD models.     

Development of a multi-fluid model for poly-disperse dense gas-solid fluidised beds, Part II: Segregation in binary particle mixtures

Particle mixing and segregation rates in a bi-disperse freely bubbling fluidised bed have been studied with a new multi-fluid model (MFM) based on the kinetic theory of granular flow for multi-component systems (see Part I). The MFM simulation results have been compared with digital image analysis experiments obtained by Goldschmidt et al. [2003. Digital image analysis of bed expansion in dense gas-fluidised beds. Powder Technology 138, 135-159] for bi-disperse mixtures of glass beads. In strong contrast to MFMs previously described in the literature, that strongly overestimate the segregation rates, the new MFM seems to underestimate the segregation rates at longer times. This underprediction of the segregation rate is probably related to the neglect of frictional stresses associated with long-term multiple-particle contacts resulting in an overestimation of the mobility of the emulsion phase, which is corroborated by discrete particle simulations without friction between the particles and the particles and the wall. The level of the granular temperature of the segregating system, as computed with the new MFM, compares reasonably well with the granular temperatures found in the DPM simulation.     

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.     

气-固流化床的气泡参数测定——直射式光纤探头在流化床研究中的应用

在鼓泡域中,从直射式光纤探头在二维床的测试与图像分析的结果得到气泡的平均直径与平均刺穿长度的关系为:d_b=1.6E[l]气泡的球形度为0.96。通过反射式和直射式光纤探头信号的比较表明,直射式探头的信号便于处理,并可用来测定气泡内的粒子含量。直射式光纤探头在二维床和三维床的测定结果对比表明,两种塔内的气泡行为规律一致但有明显的差异。     

Cold flow experimental study and computer simulations of a compact spouted bed reactor

Spouted beds are a very interesting class of gas–solid contactors that possess excellent heat transfer and mixing characteristics, while they are particularly suited to process coarse particles. Proper design of such beds requires the prediction of various hydrodynamic characteristics, such as the minimum spouting velocity and maximum spoutable height. Contrary to their typical initial applications, spouted beds have been finding recently more frequent use on the one hand at endothermic processes and on the other hand using much finer particle sizes. In the current work, the hydrodynamic characteristics of a laboratory scale spouted bed of 0.05 m diameter have been investigated via cold flow studies using olivine particles of 3.55–5.00 × 10⁻⁴ m size. Hydrodynamic parameters have been measured at this compact geometry and fine particle size and were compared with common literature correlations. An empirical correlation was derived to predict the fountain height for the studied fine particle spouted bed. Computer simulations have been further used to investigate the heat transfer characteristics of the bed under endothermic reactive conditions, using methane reforming as a case study. Given sufficient external heat supply, a spouted bed operating at a well-mixed regime can efficiently drive even highly endothermic reactions.     

Correlations for critical fluidization velocity and maximum bed pressure drop for heterogeneous binary mixture of irregular particles in gas–solid tapered fluidized beds

The tapered fluidized bed is a remedial measure for certain drawbacks of the gas–solid system, by the fact that a velocity gradient exists along the axial direction of the bed with increase in cross-sectional area. To study the dynamic characteristics of heterogeneous binary mixture of irregular particles, several experiments have been carried out with varying tapered angles and composition of the mixtures with various particles. The tapered angle of the bed has been found to affect the characteristics of the bed. Models based on dimensional analysis have been proposed to predict the critical fluidization velocity and maximum bed pressure drop for gas–solid tapered fluidized beds. Experimental values of critical fluidization velocity and maximum bed pressure drop compare well with that predicted by the proposed models and the average absolute errors are well within 15%.     

The minimum fluidisation velocity,bed expansion and pressure-drop profile of binary particle mixtures

The total bed pressure drop, the pressure-drop profile, bed expansion and bed voidage have been measured for a variety of binary particle mixtures over a wide range of gas velocities.Apparent minimum fluidisation velosities have been defined for segregating systems, and the addition of dense particles of lower minimum fluidisation velocity can cause a decrease in apparent minimum fluidisation velocity of the mixture in a very similar fashion to the addition of finer particles to larger ones of the same density.The measured u_mf s are compared with presently derived simplified theoretical equations and with equations from the literature. It is clearly shown that because of the sensitivity of u_mf determination to voidage, such relationships cannot be used with confidence. However, the empirical equation of Cheung on average follows the shape of the experimental curves well, includig those for binary systems of different density, provided the bed is in a well-mixed condition.Bed pressure-drop profiles are related to the mixing/segregation state and to the amount of fluidisation of the bed and may offer a simple indirect method of determining these conditions in practice.     

The flow of non-Newtonian slurries through fixed and fluidised beds

Measurements have been taken of the flow rate, pressure drop and bed height characteristics when non-Newtonian slurries flow through fixed and fluidised beds of uniformly sized spherical particles.In the case of fixed beds, the pressure drop-flow rate data has been interpreted using the capillary model of a porous medium together with rheological data for the slurries obtained from a tubular viscometer. The resulting friction factor-Reynolds number relationship is

This correlation was used to satisfactorily predict the minimum fluidisation velocity for a given solid/liquid system by equating the pressure drop to the net weight per unit area of particles in the bed. However, the correlation was not adequate for the prediction of bed expansion in the fluidised state. For systems which have a Reynolds number at minimum fluidisation, Re′_mf′ less than 40 an effect of particle diameter to bed diameter was observed. For systems having Re′_mf >40 the velocity, υ, and voidage, ?, were related to their values at minimum fluidisation by

It is therefore clear that, in the fluidised state, the capillary model does not present an adequate basis for the prediction of bed expansion.     

床形结构对气固流化床流化质量和气体返混特性的影响

用实验方法比较了一个二维床和一个大型三维床内FCC颗粒流化床在鼓泡域和湍动域内的流化质量和气体返混特性。实验结果表明,床形对A类颗粒气固流化床具有非常大的影响。二维床和三维床的流动和气固混合行为既具有相似性,如床膨胀随气速的变化趋势;也具有很大的差异性,既包括三维床流化质量差、轴向气体扩散系数大等量上的不同,又包括压力脉动、轴向气体扩散系数的变化趋势以及湾流模式等质上的不同。总之,在本研究中,二维床体现的是一种具有强烈壁效应的小型流化床的特征,而三维床则体现的是静床高度具有很大影响的大型流化床的特征。     

CFD modeling of solid-liquid fluidized beds of mono and binary particle mixtures

CFD simulation of bed expansion of mono size solid-liquid fluidized beds has been performed in creeping, transition and turbulent flow regimes, where Reynolds number (Re_∞=d_pV_S∞ρ_L/μ_L) has been varied from 0.138 to 1718. It has been observed that the predicted values of bed voidage using the drag law of Joshi [1983. Solid-liquid fluidized beds: some design aspects. Chemical Engineering Research and Design 61, 143-161] and Pandit and Joshi [1998. Pressure drop in packed, expanded and fluidized beds, packed columns and static mixers—a unified approach. Reviews in Chemical Engineering 14, 321-371] (which has been derived from the first principals), exhibited an excellent agreement with the Richardson and Zaki equation. CFD simulations have also been performed for the prediction of segregation and/or intermixing of binary particle systems having the ratio of terminal settling velocity over a range from 3.2 to 1.06. The Reynolds number has also been varied over the range of 0.33 to 2080. It has been observed that the present CFD model explains all the qualitative and quantitative observations reported in the published literature (complete segregation, partial segregation, complete intermixing, etc) and these predictions are in good agreement with the experimental results. The present CFD model also predicts successfully the layer inversion phenomena which occur in the binary particle mixtures of different size as well as density. Further, the critical velocity at which the complete mixing of the two particle species occurs has also been predicted.     

Entrance effects at a multi-orifice distributor in gas-fluidised beds

The behaviour of multi-orifice distributors in gas-solids fluidised beds has been studied with particular regard to the height of the entrance effect and the mechanics of gas-solids flow in the region immediately above the distributor plate. A model is proposed to predict the height of the entrance effect for a given distributor and gas-solids system at various fluidising flow-rates, and good agreement has been found with experiment. Experiments have been carried out with (a) a two-dimensional air-fluidised bed using three sizes of sand particles (d_p: 137, 263, and 350 μm) and four distributors (orifice diameters: 0.001 m, 0.002 m; orifice spacings: 0.025 m, 0.05 m); and (b) a three-dimensional air-fluidised bed, 0.3 m square in cross-section, using 350 μm sand particles on a distributor with 0.003 m diameter orifices at a spacing of 0.04 m. The principal factors influencing the height of the entrance effect were found to be the incipient fluidising velocity, mean particle size, orifice spacing and gas flow-rate. The model has been used to estimate the minimum ratio of distributor pressure drop to bed pressure drop to bring about an even distribution of gas at the bottom of the bed.     

Determination of adsorption and diffusion parameters in zeolites through a structured approach

Temporal analysis of products (TAP) is a transient pulse-response technique that allows to extract kinetic information from reacting and adsorbing systems. In a previous work (Chem Eng Sci 57(2002) 1835), a detailed-transport model for the Multitrack set-up, a TAP-like system, was developed, which allows studying systems with a low bed resistance. The use of structured beds, having both a low bed resistance and small sorbent particles, is required to determine adsorption and diffusion parameters when strong adsorption and slow diffusion occurs. A method is presented to extend the range of measurable adsorption and diffusion parameters in zeolitic sorbents in the TAP technique by a structured approach. Small zeolite crystals are coated on larger non-porous glass beads. Adsorption and diffusion parameters for n-butane, SF₆ and 3-methylpentane have been determined in MFI-type zeolites. Absolute diffusivity values in the zeolite coating are estimated by using a well-defined silicalite sample as a reference to determine the effective diffusion length in the coating.Two criteria have been derived, one for the characteristic time for transport through the bed, , and one for the ratio of the latter and the characteristic diffusion time in the zeolite crystal, 0.01<α<200t_bed/(1+t_bed), which should be satisfied both to be able to determine values of the zeolite diffusivity.     

Prediction of minimum velocity and minimum bed pressure drop for gas-solid fluidization in conical conduits

Experimental investigations have been carried out for spherical and non-spherical particles using beds comprised of single-sized particles and mixtures in the size and particle density ranges of 439 to 1524 μm and 1303 to 4948 kg/m³, respectively. Five conical fluidizers with varying apex angles of 8.86, 14.77, 19.60, 32.0 and 43.2 degrees were used. Experimental values of minimum velocity and bed pressure drop with air as the fluidizing medium have been compared with their respective values obtained from different models available in the literature. Deviations for each chosen model have been presented.