Particle growth mechanisms in fluidised bed granulation—II: Comparison of experimental data with growth models

Growth data from batch granulation experiments have been fitted to simple geometrical models. Layered granule growth approximates to concentric coating of core particles with binder, although the actual mechanism of growth is different. In the case of agglomeration, a relationship is established betwee mean granule size and binder content.     

Particle growth mechanisms in fluidised bed granulation—I: The effect of process variables

Two types of product granule have been identified in an experimental study of batch fluidised bed granulation; agglomerates which consist of two or more, and usually several, initial particles; and layered granules, which consist of single primary particles with dried feed material adhering to the surface. Increasing the excess fluidising gas velocity, in the range U-U_mf = 0.15-0.525 m s^?1, resulted in decreased particle growth rates and, depending upon the binder material, a change in product morphology from agglomerates to layered granules. Similar changes resulted from increasing the mean size of the starting material. Thus, a mechanism of particle growth is proposed in which the strength of inter-particle bridges and the extent of fluid drag and inertial forces on particles determine the equilibrium granule form and size. However, if the initial particles are porous this mechanism may break down since liquid may enter intra-particle pores and be unavailable for the initial formation of liquid bonds.     

An automated catalytic system for the sequential optimal discrimination between rival models

An on-line, computer controlled, automatic experimental setup for the determination of reaction kinetics in gas phase heterogeneous catalytic reactions is presented and demonstrated through the sample study of a simple reaction. The system is automatic to the extent of being capable to carry out, with little or no human intervention, an optimal sequence of experimental runs and single out from a set of plausible rate equations the one that fits best the experimental results.Application of the system to the study of Pt-catalyzed ethylene oxidation around 350°K and atmospheric pressure, showed the classic Langmuir-Hinshelw     

A unified model for particulate expansion of fluidised beds and flow in fixed porous media

A model is derived for a fluidised bed that enables its steady state particulate expansion to be predicted as a function of superficial velocity from the initial (packed bed) condition to the final fully expanded (single suspended particle) state. These predictions are in good agreement with the empirical correlations and functional dependencies found by Richardson and Zaki[1,2] over the full range of flow conditions. The derivations incorporat revisions in the form of the pressure drop correlations for flow in porous media that are justified on theoretical and empirical grounds.     

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.     

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.     

Drying granular solids in a fluidised bed—II The influence of diffusion limitation on the gas—solid contacting around bubbles

When diffusion inside the solid particles which are dried in a fluidised bed can not be neglected this internal diffusion can be accounted for by two mechanisms: (a) the long term response which describes the gradual build up of a concentration profile inside the solid particles as function of the total drying time, and (b) the short term response which describes the generation of a thin concentration boundary layer inside the particles during the passage of these particles through the cloud of a rising bubble. Both mechanisms can be analyzed separately and are included in a final model which can be conceived as a further development of the model presented in Part I.     

A model for desulphurisation with limestone in a fluidised coal combustor

Kinetic expressions used to describe the reactions of deactivating catalyst particles are applied here to the sulphation of calcined limestone in a fluidised bed coal combustor where reactivity diminishes as pores fill with sulphate. Following closely the recent work of Fieldes and Davidson it is shown how experiments with batchwise addition of limestone to the combustor may be used to derive the two reaction rate constants of the system, k_s, and k_d, and how these may be incorporated into a two-phase model of a fluidised bed reactor to obtain predictions of desulphurisation efficiency under conditions of continuous operation. The resulting equation for SO₂ retention, η, may be simplified to:η = 1 ? [$\text{1}\text{1 +}\text{K}\text{β}$] where K is a function of limestone type and operating conditions and β is the calcium-to-sulphur mole ratio. The predictions of this equation are shown to be in agreement with experimental results.     

Effect of interfacial resistance on quiescent gas-liquid absorption

Traditional models for gas absorption have considered the gas-liquid interface to be instantaneously saturated with the gas, hence ignoring any interfa     

Theory and experiment on the three-dimensional motion of a freely suspended spherical particle at the entrance to a pore at low Reynolds number

This paper examines the three dimensional approach of a neutrally buoyant sphere of any size to a circular hole in a plane wall at very low Reynolds number. The analysis differs from previous studies, largely applied to the multipore filter, in that the authors investigate the three dimensional hydrodynamic interaction of the sphere with the entrance geometry of the pore in the limit of zero inertia. The problem is first exactly formulated as the linear superposition of fundamental Stokes flows for rotation and translation of the sphere and flow past a stationary sphere. Approximate solutions are then obtained for the deviation of sphere trajectories from fluid stream lines and the results compared with laboratory model experiments in a low Reynolds number settling tank. The theory and experiment show that because of the hydrodynamic interaction sphere trajectories and fluid streamlines deviate significantly as the opening is approached, that all spheres eventually enter the pore regardless of their initial position, but that a non-uniform concentration profile develops with large increases in concentration near the walls of the orifice in the vicinity of the opening. The results provide a basic mechanism to explain the onset of Fahraeus phenomenon for red cells entering small blood vessels and glass tubes.     

Multiple equilibrium shapes of partially constrained menisci: A quasi-static mechanism for instability of a coating bead

The upstream meniscus of an extrusion coating bead operating in the capillary limit is modelled as a cylindrical meniscus that pins to the die and inte     

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.     

A two-parameter model for partial segregation: Application to flow reactors with pre- and unmixed feed

A two-parameter (TP) mixing model for partial segregation has been applied to continuous stirred tank reactors (CSTR) for cases with premixed and unmixed feed. It was found that in the case of perfectly mixed, homogeneous feed the model predicts similar or better results than earlier one-paramete models. However, a significant advantage of the TP model was found in the case of unmixed feed. Its two parameters are suitable for representing two se situations existing in the case of unmixed feed, namely, imperfect mixing of the feed and partial segregation of the reacting mixture. The single-param models cannot be used to represent both phenomena. Reversible and irreversible reactions were studied, and deviations from a perfectly mixed CSTR were into account by considering the RTD expression of Wolf and Resnick. The parameters of the model were determined from experimental data, when available, from arbitrary values within their permissible range, otherwise. Good agreement was found between experimental and predicted conversions.     

Effectiveness factor and selectivity estimation for a parallel reaction system

The case of double parallel reaction scheme taking place in a porous catalytic pellet is analyzed. Effectiveness factor expressions for both reactions are derived after matching asymptotic solutions strictly valid for small and large values of the Thiele moduli.It is assumed that the kinetics of both reactions follow a general irreversible power law model, that isothermal conditions prevail and that external mApproximate results in terms of effectiveness factors compare fairly well with exact results obtained by numerical integration of the differential equa     

Useful representations of series solutions for transport problems

Simple techniques are presented for rearrangement of an infinite series in a systematic way such that the convergence of the resulting expression is accelerated. These procedures also allow calculation of required boundary derivatives. Several examples of conduction and diffusion-reaction problems illustrate the methods.     

Global simulation of countercurrent separation processes via one-parameter imbedding techniques

A new computational strategy for simulation of countercurrent separation processes based on the one-parameter imbedding method, is developed. The one-parameter imbedding technique is formulated in a general form, for a separation column problem, the resulting procedures are classified as the one-through and multi-loop methods. The proposed procedures are of the global type, i.e. all equations are solved simultaneously. The method is capable of taking advantage of the concept of the generalized Newton-Raphson approach to construct a general computer code for solution of rectification and absorption problems. The important point is that the one-parameter imbedding method makes it possible (similar to the Newton-Raphson approach) to calculate the design problems or problems of controlled simulation in a straightforward way. The advantage of the one-parameter imbedding technique over the Newton-Raphson method is better convergence, i.e. the one-parameter imbedding method may force to convergence such problems where the Newton-Raphson approach fails.     

Micro-macropore model for sorption of water on silica gel in a dehumidifier

A mathematical model for laminar flow through a duct of an isothermally maintained dehumidifier and for simultaneous diffusion and absorption of water vapor into a desiccant was formulated as an integral equation. The macro-micro pore model for the desiccant was fitted to transient experimental data for isothermal adsorption of water on a silica gel sheet with an average deviation of four percent. The data could not be explained by the conventional Rosen model which considers diffusion in the macropores only.A Graetz type analysis of experimental data showed that the mass transfer in the channel could be approximated by constant mass transfer coefficients which agreed with the asymptotic Nusselt numbers for the laminar Graetz problems. However, the corresponding mass transfer coefficients for the desiccant are highly time dependent. Hence a more complicated model is required.