Dense phase convection

The lean/gas phase convection contribution has received the least attention in the literature. Many models in fact assume it to be negligible in comparison to dense phase convection and set hl to be zero. Compared to experimental data, such an approach appears to be approximately valid for fast fluidized beds where average solid concentration is above 8% by volume. Measurements obtained by Ebert, Glicksman and Lints (1993) indicate that the lean phase convection can contribute up to 20% of total... 

Assuming that the Fourier number is sufficiently large to take C = 1.0 from Eq. (33), the coefficient for dense phase convection is then obtained from Eq. (67) as... 

Some researchers have noted that this approach tends to underestimate the lean phase convection since solid particles dispersed in the up-flowing gas would cause enhancement of the lean phase convective heat transfer coefficient. Lints (1992) suggest that this enhancement can be partially taken into account by increasing the gas thermal conductivity by a factor of 1.1. It should also be noted that in accordance with Eq. (3), the lean phase heat transfer coefficient (h,) should only be applied to that fraction of the wall surface, or fraction of time at a given spot on the wall, which is not submerged in the dense/particle phase. This approach, therefore, requires an additional determination of the parameter fh to be discussed below. 

An alternate to the concept of cluster renewal discussed above is the concept of two-phase convection. This second approach disregards the separate behavior of lean and dense phases, instead models the time average heat transfer process as if it were convective from a pseudo-homogeneous particle-gas medium. Thus h hcl, hh and hd are not... 

Development of a mechanistic model is essential to quantification of the heat transfer phenomena in a fluidized system. Most models that are originally developed for dense-phase fluidized systems are also applicable to other fluidization systems. Figure 12.2 provides basic heat transfer characteristics in dense-phase fluidization systems that must be taken into account by a mechanistic model. The figure shows the variation of heat transfer coefficient with the gas velocity. It is seen that at a low gas velocity where the bed is in a fixed bed state, the heat transfer coefficient is low with increasing gas velocity, it increases sharply to a maximum value and then decreases. This increasing and decreasing behavior is a result of interplay between the particle convective and gas convective heat transfer which can be explained by mechanistic models given in 12.2.2, 12.2.3, and 12.2.4. 

A unique feature of the dense-phase fluidized bed is the existence of a maximum convective heat transfer coefficient /zmax when the radiative heat transfer is negligible. This feature is distinct for fluidized beds with small particles. For beds with coarse particles, the heat transfer coefficient is relatively insensitive to the gas flow rate once the maximum value is reached. 

The bubble-to-emulsion phase mass transfer can be described with a convection term and a diffusion term. The convection term describes the flow pattern of the fluidization gas from the emulsion phase inside the bubble which is dominant for the first part of our experiments. The molecular dif fusion of CO2 from the bubble phase (especially from the vortices) to the dense phase also influences the mass transfer process as discussed by Kunii and Levenspiel. 

An explanation of why convection occurred when brine formed in the TRS system can be given by interface stability analysis (18). During the experiments, slight tipping of the sample cells indicated that the intermediate brine phases were more dense than the mixtures of liquid crystal and brine below them. This adverse density difference caused a gravitational instability for which the smallest unstable wavelength X is given by... 

When symmetric membranes are used or when enzymes are fed to the spongy part of asymmetric membranes, enzyme immobilization results in either a uniform fixation of enzymes throughout the membrane wall, or in the formation of a carrier-enzyme insoluble network in the sponge of the membrane. Mass transfer through this solid phase must therefore be taken into account. A theoretical model neglecting radial convective transport and the dense layer in asymmetric membranes is available in the literature.81 The reacting solution is still assumed to be fed to the core of the hollow fibers. Steady state, laminar flow, and isothermal conditions are assumed. Moreover, the enzymes are assumed to be uniformly distributed and the membrane wall curvature is neglected. Differential dimensionless mass balance equations can be written as follows ... 

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