Mass transfer General remarks

Let us now consider the mass transfer from the gas phase into the droplet or onto an AP according to the scheme presented in Fig. 4.7. The process includes the 

Distinguishing between 7 and 7, (introduced by Poschl et al. (2006) but not used by other authors) is meaningful because it reflects the transport from the bulk gas phase close to the particle surface (0 - g) which might have limitations, expressed by the actual surface collision flux Fcou and the average gas kinetic flux Fcoii From equations (4.257) and (4.258) it follows that  

The gas uptake by liquid droplets is widely described by the so-called resistance model, where substance A must overwhelm layers with a specific resistance (Fig. 4.19). The idea of this model is to describe the single processes (transport, adsorption, dissolution and reaction) as decoupled processes. The dimensionless parameter / (0 y 1 ) is called the net uptake coefficient, which describes the total process including all physical and/or chemical partial processes, here given by the gas phase diffusion ( resistance HFg or conductance Fg) and net uptake (resistance l/y)  

when the gas phase diffusion has a low resistance, it becomes y = Yeff or, 

The most common formula used to calculate the gas transport coefficient is (Poschl et al. 2005)  

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Altogether, Hanratty s investigations represent a remarkable example of the versatility of the electrochemical mass-transfer technique. The method is considered so reliable that generalized correlations, for example, Eq. (33), can be used to measure convection profiles at a reacting surface. 

This section starts with some general remarks concerning scale-up of chemical reactors. Then the influence of chemical kinetics, heat transfer, and mass transfer on scale-up of reactive systems is discussed. Finally, scale-up from the results of calorimetric equipment, such as the ARC and VSP, is reviewed. 

Generally, this text has a dual orientation. On the one hand, it is addressed to persons whose research interests are directly related to electrodiffusion, i.e., chemical engineers, membranologists, electrochemists, and electrophysiologists, with certain parts of this book possibly of interest to semiconductor device engineers. On the other hand, it aims to attract applied mathematicians to a practically relevant and remarkably underdeveloped classical branch of nonlinear mass-transfer. 

Remark Comparing the estimation based on the widely used empirical Equations 7.14 and the semi-empirical Equation 7.27, the latter predicts a roughly two times higher volumetric mass transfer coefficient. This may be because of the fact that Equation 7.14 does not include the capillary diameter. In general, predictions must be taken with caution because the two-phase systems are complex and none of the models include all practical experimental conditions. 

In general, slurry-phase hydroconversion can be advantageous for the upgrading of heaviest feedstocks due to the remarkably high levels of conversion (>90vol%) achieved as well as the low costs associated with the catalyst stock and the simple design of the reactor vessel. The slurry phase is characterized by improved mass transfer and is thermally more stable. The main drawback, however, is the extremely poor quality of the unconverted fraction with very high contents of sulfur and metals. 

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