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.     

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.     

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     

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     

Solids mixing in fluidized beds—a hydrodynamic approach

Solids mixing in fluidized beds has traditionally been treated using empirical transfer or diffusion coefficients. This study presents a new approach. A hyperbolic diffusion equation is derived by linearizing two phase flow equations of motion obtained previously by minimizing the rate of entropy production.Analytical solutions to the hyperbolic diffusion equation for a tracer concentration are obtained using Laplace transforms and the method of images. The solutions compare well with solids mixing experiments. The solutions involve a propagation velocity, which is determined by two phase mass balances, and a diffusion coefficient which is a ratio of kinetic energy to interphase friction or drag, as in Einstein's diffusion coefficient. Least square curve fits of data to the theory produced reasonable values of the drag coefficients.     

Interpretation of mass transfer measurements in bubble columns considering dispersion of both phases

Mass transfer measurements in two bubble columns with an inner diameter of 100 resp. 140 mm with the systems air/water/carbon dioxide and nitrogen/n-propanol/carbon dioxide have been evaluated with the axial dispersion model. The dispersion coefficients of both phases have been determined in separate investigations. As the results revealed a strong influence of the liquid viscosity, additional dispersion coefficient measurements have been carried out with the system air/glycol. It could be shown that the liquid phase dispersion coefficient decreases with increasing viscosity while the gas phase dispersion coefficient increases with increasing liquid viscosity. Both coefficients are strongly dependent on the gas throughput and the column diameter. Using these coefficients, the mass transfer coefficients have been calculated by fitting the calculated concentration profile to the measured values and by splitting the volumetric mass transfer coefficient with the experimental value of the interfacial are a. The results agree best with a correlation of Calderbank and Moo-Young.     

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.     

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.     

Measurements of bubble properties in continuously operated fluidized bed reactors at elevated temperatures

In a fluidized bed reactor the thermal decomposition of sodium hydrogen carbonate into sodium carbonate, carbon dioxide and water was carried out in continuous operation. The fluid dynamical structure of the bed was characterized by measurements with capacitance probes. Signal processing was carried out by a process computer.Data for bubble volume fraction, bubble rising velocity and bubble diameter have been obtained in the presence and absence of a chemical reaction. The influence of the reaction on the fluid-dynamical structure is significant.     

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     

A dynamic response technique for the estimation of gas—liquid mass transfer coefficients in a stirred vessel

A method is described for evaluating mass transfer coefficients, k_La, in gas sparged stirred vessels. It involves measurement of both liquid and gas concentration responses following a step change in inlet gas concentration, and differs from previously published methods in that the k_La evaluation is independent of the gasresidence time distribution. Results are presented that demonstrate the suitability and consistency of the method for a range of gas mixing levels.A modification, that involves only a knowledge of the early liquid concentration response, is suggested as worthy of further consideration.     

Measurements of particle-to-gas heat transfer coefficients from one-shot thermal responses in packed beds

By applying the technique of one-shot thermal input, particle-to-gas heat transfer coefficients have been obtained for glass beads-air system in the range of Reynolds number from 5 to 229. The obtained heat transfer coefficients are well represented by a correlation, eqn (14), proposed by Wakao et al. Sensitivity test on the experimental results shows that at low flow rates the particle-to-gas heat transfer cannot be a controlling step in the overall heat transfer process.     

Errors in the determination of mass transfer in gas-liquid dispersions

Mass transfer behaviour of gas-liquid dispersions is usually characterized by the volumetric mass transfer coefficient β_La. For its experimental determination various methods exist which can be grouped into stationary and instationary (dynamic) methods. Very often volumetric mass transfer coefficients published in literature show surprisingly large scattering and divergence which cannot be explained by differences in properties of the systems. In order to find possible causes for these inconsistencies in experimental results, the two types of methods have been subjected to an analysis of errors. It is shown that deviations of real from assumed mixing behaviour in both phases as well as rather small errors in the concentration of the liquid phase may result in deviations up to a factor of 5–10. This may also be the case in the evaluation of results obtained by the dynamic method, if the approximations used are too rigorous. The limits of applicability of the two methods are discussed.     

Natural convection mass transfer at cylinders in different positions

Rates of natural convection mass transfer between an electrolyte and horizontal, vertical and inclined cylinders have been determined using an electrochemical technique involving the measurement of limiting currents for the deposition of copper on copper cylinders from acidified cupric sulphate solutions. The data were correlated for different cylinder positions using dimensional analysis. For horizontal cylinders, a single correlation covered both laminar and turbulent conditions, along with existing literature data for the turbulent regime. For vertical cylinders the new correlation agrees closely with the classical vertical plate correlation, and is also compared to heat transfer equations. For inclined cylinders, the new correlation is also compared to existing equations for inclined plates.     

Turbulent heat and mass transfer in dilute polymer solutions

A new model based on Levich's three-zone model is developed to discuss the turbulent heat and mass transfer in drag-reducing solutions. The proposed model, which has no adjustable parameters and is represented in an explicit form, provides satisfactory predictions of the maximum heat and mass transfer reduction in smooth and rough pipes. The mass transfer to a disk rotating in drag-reducing solutions is also discussed using the proposed model.     

Wall heat/mass transfer in pulsatile flow

Heat/mass transfer is considered from a solid surface to a fluid undergoing pulsatile flow, consisting of sinusoidal pulsations superimposed on a mean flow. Mass transfer was measured from small strips using the diffusion-controlled electrode method for both non-reversing and reversing flows, corresponding to small and large pulsation amplitudes, respectively. Heat/mass transfer rates from the surface consist of a mean component, with a superimposed oscillatory component that is dependent on the amplitude, α, of the fluctuating wall shear rate, and the dimensionless frequency parameter, F_p. For small α, the amplitude and phase of the first harmonic of the measured transfer rates agree well with the theory of Mizush for all values of F_p. The same is true for larger α (< 1), only when F_p is also large; for large α and small F_p, there is significant deviation from theory. In the latter case, the experimentally measured amplitudes of the second harmonic become large, and the assumptions the theory are no longer valid. For α > 1, flow reversal occurs, and the theory again does not apply. For α < 1, the shapes of the mass transfe time curve are almost sinusoidal, and space-and-time-averaged transfer rates decrease slightly compared to steady flow as α increases. For a > 1, f takes place, and as α increases to about 1.5–2, the average transfer rates increase and become equal to those in steady flow. For α > 2 the tra become greater than the steady flow values and the second harmonic of the fluctuating transfer rate is as significant as the first harmonic. The change of the transfer rate vs time curves is quite significant, with two maxima and minima appearing in a period compared to the single maximum and minimum w characteristic of small α. These changes in average transfer rates and in the shapes of the transfer rate vs time curves are substantial for small va frequency parameter, F_p. As F_p is increased, the changes become less pronounced, and the trend of the data indicates that for F_p large enough, there is no increase in the transfer rate in pulsatile flow, and this appears to be independent of the value of α.     

Monte carlo simulation of mass transfer in liquid-liquid dispersions

A simulation technique is developed to predict the performance of a two phase liquid-liquid continuous flow stirred tank reactor as an extractor. The dynamics of the dispersed phase droplet interactions and the microscopic interphase mass transfer in the turbulent flow field are digitally simulated using the interval of quiescence method. The use of realistic breakage and coalescence functions together with the natural evolution of the interactive drop population has made it possible to predict the dispersed phase drop size distribution and mass transfer efficiency in a rational manner from the known physicochemical properties of the dispersion and the operating conditions of the extractor.