Lateral mixing of solids in gas—solid fluidized beds with continuous flow of solids

Lateral mixing of solids in a gas—solid fluidized bed with continuous flow of solids can be adequately expressed by the dispersion model. An expression for estimating the lateral dispersion coefficient in such a bed is proposed.     

Longitudinal dispersion of solid particles in fluid beds with horizontal baffles

The axial pressure profiles, allowable gas velocities and temperature distributions are measured for the fluidization of air—FCC cracking catalyst systems in 12- and 19-cm-diam. eight-stage fluid beds equipped with seven horizontal baffles. From these measurements, gas bubble holdup, apparent longitudinal dispersion and intermixing velocity of solid particles through the baffles are studied as functions of baffle design. It is shown that the gas bubble holdup increases, the operational range of gas flow decreases and the flow pattern of solid particles approaches plug flow with decreasing free area of baffles.     

Mass transfer in liquid fluidized beds of ion exchange particles

Mass transfer rate data in a shallow liquid fluidized bed of ion exchange resin particles have been obtained in the range 2 < Re_s, < 25. At low voidage, ε < 0.55–0.60, the rate of mass transfer is reduced and it is inferred that a fluidized bed tends to maintain an ordered axial structure. This is lost at high voidage due to increased flow perturbation caused by the distributor plate. A generalised correlation is given for fluidized, fixed and distended beds in the range 2 < Re_s, < 25.     

Effect of bubble interaction on interphase mass transfer in gas fluidized beds

A non-interfering technique has been used to measure the concentration of ozone in pairs of bubbles injected into a bed of inactive 390 μm glass beads fluidized by ozone-free air. The transfer of the ozone tracer from the bubble phase to the dense phase is enhanced when compared to the transfer from isolated bubbles in the same particles and the same column. Bubble growth is also greater for the case where pairs of bubbles are introduced than when bubbles are present in isolation. Enhancement of interphase mass transfer for interacting bubbles in the present work and in previous studies incr with particle size and can be explained in terms of enhancement of the throughflow (or convective) component of transfer while the diffusive component unaltered. This mechanism leads to new equations for estimating interphase mass transfer in freely bubbling fluidized beds.     

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     

Heat and mass transfer in monolithic honeycomb catalysts—I.

The body of information presented in this paper is directed to engineers and scientists concerned with control of automobile emissions and exhaust gases from some industrial processes. The differential equations describing heat and mass transfer in a monolithic honeycomb catalyst are developed. Following transport mechanism is considered: convective heat and mass transfer in the holes of the structure, longitudinal thermal conductivity of the honeycomb support and gas-to-solid heat and mass transfer. The magnitudes of governing parameters for monolithic modules in use are discussed. Two methods for the numerical solution of a system of coupled, nonlinear ordinary differential equations with split boundary conditions are proposed. The first method-shooting procedure can be used only for problems with low values of Peclet number. For high values of Peclet number finite-difference approach along with the Newton-Raphson algorithm is suggested. It is shown that two stable steady states exist in certain regions of operation of a particular monolithic structure. The all-metal monolithic supports are more prone to multiplicity of steady states than the ceramic ones. For ceramic supports the two-phase piston-flow model is sufficiently accurate.     

Particle-fluid heat transfer and dispersion in fluidised beds

The dynamic response of a gas fluidised bed has been measured for a range of particle sizes of lead glass ballotini and a range of particle Reynolds numbers. A dispersion model has been formulated that includes the effects of gas and particle mixing, fluid-to-particle heat transfer and intraparticle thermal conductivity, and the dynamic thermal response in theory has been found by solving the partial differential equations in the Laplace transform domain. The coefficient of thermal dispersion, the particle-to-fluid heat transfer coefficient and the intraparticle thermal conductivity have been found for the experimental response by non-linear regression. The coefficient of axial dispersion was found to be large and the particle to fluid heat transfer coefficients agreed with an established correlation for fixed and fluidised beds. The intraparticle thermal conductivity agreed with literature values for lead glass, the estimates showed no trend with flowrate, and the standard deviation of the estimate was three times smaller than the deviation found from similar experiments in fixed beds.     

Mass transfer to large particles in fluidised beds of smaller particles

A theory is proposed for predicting the transfer of a gas through a fluidised bed of small particles to a large particle. It is proposed that non steady-state mass transfer of the gas occurs by two mechanisms: (i) mass transfer of gas in clusters or packets of the smaller particles approaching the large particle; and (ii) gas convection. The theory developed enables prediction of the Sherwood number (N_sh, the dimensionless mass transfer coefficient) for a large particle, diameter d: N_sh=2ε_mf+$\text{4}\text{g3}\text{mfd}\text{(U}\text{mf}\text{ε}\text{mf}\text{+}\text{uinb}$)/π D_A${}^1{}^2$ where U_mf is the minimum fluidising velocity, εmf is the bed voidage at U_mf-0u_b is the mean bubble rise velocity and D_A is the gas diffusivity. This equation is shown to be in excellent agreement with Sherwood numbers determined from combustion experiments in which single large particles of petroleum coke were burned in air fluidised beds over a wide range of operating conditions. It is also shown that predictions using this expression are in close agreement with those from an empirical expression previously proposed by the autho     

Development of a new system for circulating fluidized particles within a single vessel

A new system for circulating fluidized particles within a single vessel has been developed which has the same advantages as the dual-bed systems widely used for the FCC process and the Fluid Coker process. The interior of the vessel was divided into four sections by intersecting two flat vertical plates at right angles. Two sections were used for the upflowing bubbling fluidized beds and the other two sections were used for the downflowing bubble-free fluidized beds. Fluidized particles were circulated between the two upflowing beds, which were to be used as reactors, through the two downflowing beds, which were to be used as downcomers. Solid particles were fluidized by several streams of gas injected at several stages of the bed. The effects of these gas injection rates on the circulation rate of solids were investigated. The circulation rate of solids was measured using both a measuring box, which collected the overflowing particles, and the downward motion of a gauze net induced by the descending particles. The static pressure distribution within the vessel and the residence time distribution for coarse foreign solids in the system were measured. The present research demonstrated that the proposed system potentially had the same advantages as the conventional dual-bed system, and that the system can be applied to the simple gasification of biomass and solid wastes.     

Heat and mass transfer in honeycomb catalysts—II

Heat and mass gas-to-solid coefficients associated with the vaporisation of water and some hydrocarbons from the surface of a porous, monolithic structure were experimentally established. The mass transfer results are correlated using Reynolds and Schmidt number and the length-to-diameter ratio. The data for heat transfer are correlated on the Nu-Re(d/L) plot. The experimental results can be used for design of afterburner reactors utilizing monolithic structures.     

Heat transfer in laminar flow of non-Newtonian fluids

The main objective of this work is the consideration of local heat transfer coefficients for non-Newtonian power-law pseudoplastic liquid in laminar flow in circular conduits. The wall boundary conditions chosen are cases involving uniformly constant heat flux and step change in heat flux.Analytical solutions are developed for the wall temperature profile and compared with experimental data. Additionally, the experimental data have been correlated for comparison with existing relationships, hitherto not verified adequately. The limits of experimental data are:

     

The measurement of emulsion phase voidage in gas fluidized beds of fine powders

The results of two different experimental methods, X-ray absorption and bed collapse, for the determination of the emulsion-phase voidage of gas fluidized beds are compared. It is shown that good agreement exists between them over the range of gas velocities studied, but that possible differences in voidage in an axial direction are only revealed by the X-ray technique. The bed collapse method applied to a Geldart Group A powder confirms that there is little difference between the surface settling rates of a bubbling bed and of a uniformly expanded bed of the same voidage.     

Adsorption of acid dye onto woodmeal by solid diffusional mass transfer

The adsorption of Telon Blue (Acid Blue 25) dye onto wood has been studied using an agitated batch adsorber. The variables studied include agitation, initial dye concentration, wood mass, wood particle size and dye solution temperature. Isotherms were measured and the isotherm parameters were determined.

A mathematical model has been developed using the basis of the model proposed by Mathews and Weber Jr. This model is based on external mass transfer and solid-phase diffusion, and has been used to generate theoretical concentration—time decay curves. The results of the model were adjusted to the experimental data using a ‘best fit’ approach. The external mass transfer coefficient was found to vary with the degree of agitation, and consequently all other variables were considered at a constant agitation speed of 400 rev min⁻¹. A good agreement between the theoretical generated and the experimental concentration—time decay curves was achieved using a constant external mass transfer coefficient, 0.30 × 10⁻³ cm ⁻¹, and a constant solid-phase diffusivity, 0.200 × 10⁻⁸ cm² s⁻¹, for varying initial dye concentrations as well as wood mass. In experiments where the particle diameter was varied, a constant external mass transfer coefficient was sufficient to describe the system, but a decreasing diffusivity was required with increasing particle size. To simulate the effect of varying temperature, both external mass transfer coefficient and diffusivity were varied.     

Effect of fluid dispersion coefficients on particle-to-fluid mass transfer coefficients in packed beds: Correlation of sherwood numbers

Gas-phase and liquid-phase mass transfer data published in the literature are corrected for the axial fluid dispersion coefficient values proposed by WThe corrected Sherwood numbers in the range of Reynolds number from about 3 to 10,000 are correlated by Sh = 2 + 1.1 Sc^1/3Re^0.6.     

Drying granular solids in fluidized bed—I: Description on basis of mass and heat transfer coefficients

In this paper on drying of wet solids in a fluidised bed a model is presented which describes the mass transfer from the solids to a rising bubble for the case that there is no diffusion limitation inside the solids. Two contributions are accounted for: the mass transfer from the dense phase across the cloud boundary and the mass transfer from the solids which are passing the cloud during the rise of the bubble. A similar model is presented for the heat exchange between the bed and the rising bubbles.     

Segregation and mixing in liquid fluidized beds

Segregation and mixing were studied in beds of binary mixtures of lead glass spherical particles (2 mm with 3 mm; and 2 mm with 4 mm diameter) fluidize by paraffin oil. Concentration profiles were obtained both by measuring pressure gradients in the bed and by sampling.A model for solid mixing, based on the combined effects of diffusive and convective mechanisms, has been used in conjunction with the experimental resu     

Heat transfer from a plane sufrace to liquids and to liquids-solid fluidised beds

Heat transfer coefficients have been measured for transfer between a small immersed electrically heated surface and both liquids and liquid-solid fluidised beds. Fluid viscosity, and hence Prandtl number, has been varied approximately 600 fold. Experimental results for liquids have been expressed in terms of Nusselt, Reynolds and Prandtl numbers and for the fluidised systems in terms of Stanton number, particle Reynolds number for free falling conditions, and bed voidage. Maxima in the heat transfer coefficient-voidage relations are satisfactorily predicted.     

A heat transfer study for a partially immersed refractory rod in a plasma

The thermal behavior of a tungsten rod partially immersed in a plasma flame is analyzed. The longitudinal temperature profiles are obtained by numerical solution of the heat balance equation. Results show that a heat transfer model consisting of pure natural convection up to the plasma outer edge and forced convection inside the plasma, fails to predict temperatures at the hot tip of the rod. In order to make the experimental and calculated profiles to converge, one has to consider modifications in the mechanical and thermal conditions of the surrounding medium due to the presence of the rod in the plasma. This leads to the use, in the “cold” gas zone, of particular values of heat transfer coefficient h and of a parameter T_x which is defined only at the immediate boundary of the rod. The latter are given in the form of variations along the axis of the rod. This perturbation effect decreases with the rod diameter. Allowance is made for the variation of the thermal properties of the solid.