E.U Schlünder

On the mechanism of the constant drying rate period and its relevance to diffusion controlled catalytic gas phase reactions

Abstract The fact that the drying rate does not depend on the moisture content during the constant rate period gives rise to analyse the diffusion process near solid surfaces, which are partially wetted. It is shown that under certain conditions partially wetted surfaces yield practically the same drying rate such as entirely wetted ones. This result is applied to diffusion controlled catalytic gas phase reactions at partially activated surfaces. It is shown again that less than 1% of the surface needs to be activated in order to give the same reaction rate such as an entirely activated one. This effect depends on the magnitude of two dimensionless groups; the so-called molecular Sherwood number Shmol = Λβ/δ and the microscopic Sherwood number Shmic = rβ/δ, where Λ = mean free path of the gas molecules, r = radius of the active centers, δ = diffusion coefficient, β = mass transfer coefficient.

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.

Heat transfer to packed and stirred beds from the surface of immersed bodies

Abstract The heat transfer between packed and stirred beds and immersed surfaces is controlled by the contact resistance at the surface followed by the heat penetration resistance of the bulk. Both resistances can be predicted from model equations with sufficient accuracy. The contact resistance and the bulk penetration resistance for packed beds follow from physical properties, while the prediction of the bulk penetration resistance for stirred beds requires the introduction of an empirical parameter, the so-called mixing number in order to describe the random particle motion. The mixing number was found to lie between 2 and 25, depending on the design of the stirrer.

Vacuum contact drying of free flowing mechanically agitated particulate material

In vacuum contact drying of particulate material heat is supplied from a hot surface to adjacent layers of mechanically agitated material. The drying rate curves can be predicted from physical properties alone provided that the actual contact time of the material at the hot surface is known. For mechanically agitated particulate material the actual contact time has been correlated to the time scale of the agitator by the “penetration model”. Only one empirical parameter, the so called mixing number Nmix is necessary in order to predict drying rates for bench scale as well as for industrial dryers.

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.

Diffusion coefficients of naphthalene and caffeine in supercritical carbon dioxide

Abstract An experimental set-up is presented with which the diffusion coefficients of naphthalene and caffeine in supercritical carbon dioxide may be determined. The experimental conditions range from 118 to 226 bar and from 35 to 60 °C. The method consists in evaporating the component to be analyzed out of capillaries into supercritical carbon dioxide. The diffusion coefficient can be calculated from the amount of evaporated material during an experimental run. The method is of the pseudo-steady-state type, whereas diffusion coefficients of naphthalene in carbon dioxide given in the literature were obtained with an unsteady-state method. Depending on experimental conditions, the unsteady method yields slightly lower values than the pseudo-steady method. It can be shown that the strongly non-ideal behavior of the gaseous phase restricts the range of application of the unsteady method.

Contact drying of mechanically agitated particulate material in the presence of inert gas

Abstract A model permitting the calculation of drying rates during contact drying of mechanically agitated particulate material in the presence of inert gas is introduced. The so-called penetration theory is used to calculate the heat transfer from the heating surface to the bed. The mixing intensity is described with an empirical parameter, the mixing number N mix . Calculated drying rate curves are compared with drying rates measured in three different disc dryers.

Heat and mass transfer in non-isothermal absorption of gases in falling liquid films: Part I: Experimental determination of heat and mass transfer coefficients

Abstract In non-isothermal absorption of steam in falling films of aqueous LiBr solutions local heat and mass transfer coefficients were determined independently of each other by measuring the film surface temperature with an infrared pyrometer. The experimentally determined mass transfer coefficients (Sherwood numbers) confirm well-known correlations, as well as the statements of the Levich-type description of falling film heat and mass transfer, that is, the damping of the turbulence not only near the wall but also in the vicinity of the film surface. So, the assumption that the bulk and the surface temperatures of the film are equal, owing to undamped eddy transport, is not correct. The experimentally determined heat transfer coefficients deviate from the experimental data of Blangetti, the latter determined in film condensation of 1-methoxy-2-propanol-water azeotrope (MWA). This discrepancy is due to the thermal entrance effects in the experiments of Blangetti and will be discussed in Part II.

Diffusion distillation - A new separation process for azeotropic mixtures Part 1: Selectivity and transfer efficiency

Abstract A new separation process for azeotropic mixtures3diffusion distillation—is proposed. A liquid mixture is evaporated below the boiling temperature, diffuses through an inert gas gap and is recondensed. Hence the separation effect is not only based on the relative volatility of the components concerned but also on their diffusivity in the inert gas. In a wetted-wall column consisting of two concentric tubes, a significant separation effect can be achieved. Several experiments were carried out with a binary isopropanol-water mixture and a ternary isopropanol-water-methanol mixture at different evaporation and condensation temperatures, with different inert gases and annular widths in the wetted-wall column. The experimental results were well described by the vapour-liquid equilibrium and the Stefan-Maxwell equations, that is, by steady-state molecular diffusion.

Measurements of mass transfer between particles and gas in packed tubes at very low tube to particle diameter ratios

Experimental results for the mass transfer between spherical naphthalene particles and air in packed tubes of very low tube to particle diameter ratio (D/d=1.41, 1.98, and 3.77) are presented. During the experiments the Reynolds number (2.4<Re0<1500), the bed length, and the test temperature have been varied. Data reduction has been carried out with and without accounting for axial dispersion in the model. The measured Sherwood numbers are compared with the predictions according to the correlation of Gnielinski and of Wakao/Funazkri, originally developed for large packed beds. The porosity of packings at smallD/d-ratios is discussed.ZusammenfassungEs werden Versuchsergebnisse über die Stoffübertragung zwischen kugelförmigen Naphthalinpartikeln und Luft in Festbetten mit sehr kleinem Verhältnis zwischen dem Rohr- und dem Partikeldurchmesser (D/d=1,41, 1,98 und 3,77) mitgeteilt. Während der Experimente wurden die Reynoldszahl (2,4<Re0<1500), die Bettlänge und die Temperatur variiert. Die Versuchsauswertung erfolgte sowohl mit als auch ohne Berücksichtigung der axialen Dispersion. Die experimentell ermittelten Sherwoodzahlen werden mit den Voraussagen der Korrelationen von Gnielinski und von Wakao/Funazkri verglichen; beide Korrelationen wurden für Betten mit einem großenD/d-Verhältnis entwickelt. Außerdem wird die Porosität von Betten im Bereich kleinerD/d-Quotienten behandelt.