Evangelos Tsotsas

Thermal conductivity of packed beds: A review

Abstract The voluminous literature available on thermal conductivities of packed beds without fluid flow is reviewed. The discussion includes experimental methods as well as theoretical approaches. A classification of predictive models is attempted. One of these models is analysed in detail and recommended for practical use. The predictions of the model are compared with a large amount of experimental data. In the course of this comparison phenomena of physical interest and of technical significance are discussed. Most of the methods presented in this review retain validity for dispersed systems other than gas-filled packed beds and for properties other than the thermal conductivity.

A simple and coherent set of coefficients for modelling of heat and mass transport with and without chemical reaction in tubes filled with spheres

Abstract Temperature and concentration profiles are commonly modelled in wall-cooled or -heated packed beds by quasi-homogeneous models. The model coefficients depend on the kind of assumptions with respect to the flow profile and to the wall heat transfer mechanism. The coefficients presently available in literature and handbooks are based on plug flow and a wall heat transfer model which generates a temperature jump at the wall. In this paper we have conducted a comprehensive reevaluation of available experimental work with spherical particles and present a simple and consistent set of coefficients based on an uneven flow distribution and on a wall heat conduction model (Λr(r)-model). All coefficients have been found to be invariable upon bed-to-particle diameter ratio or bed length and applicable without additional adaptation to situations with and without an exothermic chemical reaction. The introduction of a wall heat transfer coefficient is not necessary.

Heat transfer in packed beds with fluid flow: remarks on the meaning and the calculation of a heat transfer coefficient at the wall

Abstract In order to describe heat transfer in diabatic packed tubes a heat transfer coefficient at the wall is usually used. The present work shows that this approach is adequate only for large values of the molecular Peclet number. In this region heat transfer at the wall is inhibited by a layer of unmixed fluid. For small values of the molecular Peclet number no resistance at the rigid wall exists. In this region experimental results should be plotted in the Nusselt-Graetz diagram, using the effective properties of the bed in the definitions of the dimensionless numbers. In the course of the analysis theoretical arguments and numerical calculations, as well as experimental data from the literature, are discussed. The influence of lateral maldistribution of fluid velocity and/or thermal conductivity, of axial dispersion of heat, and of small, systematic errors in measurement is investigated. Finally, recommendations for practical use are given.

METHODS FOR PROCESSING EXPERIMENTAL DRYING KINETICS DATA

This paper provides a review of methods for processing the data obtained from drying kinetics rigs and pilot-plant trials. Different methods for fitting and smoothing drying curves are compared, aiming to generate curves that are usable in industrial design without losing vital information by oversmoothing. Generally, plots of drying rate need more smoothing than moisture content data. Special care is needed at low drying rates and moisture contents. It is shown that some popular methods of processing data, including use of smoothing programs or fitting to equations, may generate drying curves which are seriously in error. Recommendations are made for reliable methods of processing data; cubic splines have been found to be effective for moisture–time curves. It is important to retain the original raw experimental data as a cross-check, as smoothing can conceal valuable information.

Influence of Pore Size Distribution on Drying Kinetics: A Simple Capillary Model

Abstract In this article, convection drying of a porous medium is described by a capillary model. The simplest form of this model was introduced by Krischer for two parallel capillaries to describe fundamental phenomena of drying kinetics such as the existence of a constant rate period and a falling rate period. The model accounts for capillary pressure, mass transfer is described by liquid water convection and vapor diffusion in the capillaries and at the surface, and isothermal conditions are assumed. This theoretical model is extended to a larger (arbitrary) number of capillaries with a size distribution in order to better represent the situation in a real porous medium. Drying curves as well as moisture profiles in the solid are presented for different pore size distributions. In a second step, the isothermal condition is abandoned and heat transfer into the porous medium is included into the theoretical description for the case of two capillaries. Drying curves and the time-dependent temperature profile in the solid are shown.

On axial dispersion in packed beds with fluid flow

Abstract In the present work a theoretical analysis of the dependence between the axial dispersion of mass and the flow nonuniformity in packed beds is given. Three types of flow nonuniformity are defined: micro-, meso- and macroscopical. In order to describe the influence of microscopical flow nonuniformity on axial dispersion in packed beds the flow channels are approximated by equal-sized cylindrical capillaries. A step function is used for the velocity profile and the fluid in the outer region of each capillary is assumed to be stagnant. The relationship derived in this manner can describe most results of tracer experiments well; above all, it helps in understanding the differences observed between dispersion of gases and dispersion of liquids. Anomalously high dispersion coefficients, obtained during dispersion of gases through beds of fine-grained particles, are attributed to the mesoscopical flow nonuniformity and are described in a model. Finally, the dependence between macroscopical flow nonuniformity and axial dispersion in packed beds is discussed. It turns out that the influence of channelling on axial dispersion is rather insignificant. In this manner, the results of tracer experiments can be brought into accordance with velocity profiles proposed in the literature. The essential differences between the present analysis and previous works are pointed out.

Experimental investigation and modelling of continuous fluidized bed drying under steady-state and dynamic conditions

In a lab-scale device, continuous fluidized bed drying has been investigated experimentally under both steady-state and dynamic conditions. The mixing behaviour and residence time distribution of particles in the dryer have been shown to be that of a continuous stirred tank reactor. Particle mass flow rate and inlet moisture content, gas mass flow rate, air heater capacity and gas inlet temperature have been varied systematically. The average moisture content of outlet solids has been determined by means of microwave absorption. In the course of the work, close reference to a previous investigation of batch fluidized bed drying has been kept by using an adapted version of the same equipment and the same material (water-moist γ-Al2O3 with an average particle diameter of ). Furthermore, the model previously developed and successfully validated for batch operation has been the starting point of the actual theoretical analysis. This model has been extended in order to account for continuous and dynamic conditions. Additionally, population balances have been introduced. In spite of the fact that no other adaptations have been undertaken, and though the extended model does not contain adjustable parameters, a very satisfactory agreement between calculated and measured results could be achieved. In this way, it could be demonstrated that it is possible to treat all different modi of fluidized bed drying (batch, steady continuous, dynamic continuous) in a unified, successful and applicable manner. Two aspects are considered essential for the good final performance: The use of separately determined, product-specific single-particle drying kinetics as a basis for every scale-up duty, and a stepwise methodology of model development with detailed experimental validation of every individual step.

Isothermal Drying of Pore Networks: Influence of Friction for Different Pore Structures

An existing network model for isothermal drying of capillary porous media is extended to account for viscosity in the liquid phase so that it is no longer restricted to structures with large pores. Modeling challenges and solution methods are presented in detail. The model is compared with a bundle of capillaries model of drying. Finally, simulation results for two-dimensional pore networks with mono-modal and bimodal pore structure are shown and discussed.

Correlations for effective heat transport coefficients in beds packed with cylindrical particles

A wall heat conduction model (Λ(r)-model by Winderberg et al. (2000) for packed beds of spheres) has been extended to beds of cylindrically shaped particles with almost equal diameter and length (d≃l). Very satisfactory accuracy could be attained in the description of measured temperature profiles for a total of 85 experiments from literature. These cover a range of tube to (equivalent) particle diameter ratios from D/d p =4.1 to D/d p =34.9 and Reynolds numbers from Re 0 =7.4-1786 for particles of relatively low thermal conductivity like catalyst pellets. In all cases the fluid flowing through the bed has been air. Model parameters have been shown to be independent from the thermal boundary condition at the tube wall. The latter is implemented directly in the model, without introduction of an artificial wall heat transfer coefficient. Mass transport and chemical reaction have not been investigated.

A NEW MODEL FOR FLUID BED DRYING

ABSTRACT A new model is proposed which calculates fluid bed drying curves without any adaptation of the Sherwood number between panicles and gas. Even the fine-structure of experimental data, i.e. the influence of bed height and gas flow rate, is predicted reliably. This is achieved by considering backmixing of the suspension gas in the kinetic parameter and not in the driving potential. A traditional derivation with reduced driving potential fails in the comparison with experimental results.