Three mass transfer

Heterogeneously catalyzed hydrogenation is a three-phase gas-liquid-solid reaction. Hydrogen from the gas phase dissolves in the liquid phase and reacts with the substrate on the external and internal surfaces of the solid catalyst Mass transfer can influence the observed reaction rate, depending on the rate of the surface reaction [15]. Three mass transfer resistances may be present in this system (Fig. 42.1) ... 

If one wants to take into account all three mass-transfer resistances, the mass-balance equation [Equation 14.16] should be given for every layer. From that one can obtain the solution for every layer (i = m for membrane layer, i = g for gel layer, the concentration-polarization layer has no index according to Figure 14.4) ... 

In the most general situation, all three mass transfer modes cooperate algebraically thus the number of moles crossing a surface of unit area per unit of time is given in Eq. (133), which constitutes an extension of the Pick s first law. 

In the baffled design, the shell-side fluid is fed through a central perforated distributor. It flows radially through the fiber bundle, around a baffle located in the middle of the module, and leaves the module through the central distributor. As in conventional extraction, the mass transfer of solute occurs across a liquid-liquid interface. However, unlike in conventional extraction, the interface is maintained at micrometer-size pores, and three mass-transfer resistances are present tube-side (k,), shell-side (k,), and pore or membrane-side (k ). The overall mass-transfer coefficient based on the tube-side liquid k is given by... 

Therefore, the scaling rules for these three mass transfer models are Liquid-gas diffusive... 

The rates of the three mass-transfer processes may be expressed as r = kgdgiCg gas to bubble interface (10-41)... 

The global transformation rate of a gas-liquid reaction catalyzed by a solid material is influenced by the mass transfer at the gas-liquid boundary and the liquid-solid boundary. Mass transfer and surface reaction occur in sequence, and for fast chemical reactions, mass transfer may affect the reactant concentration on the catalyst surface and, as a result, the reactor performance and the product selectivity. For a gaseous reactant, three mass transfer steps can be identified [113] (1) the direct transfer from the bubble through the thin liquid film near the wall to the catalyst surface (characterized by k aQg), (2) the transfer from the caps (i.e., front and back end) of the gas bubbles to a dissolved state in the liquid slug (characterized by and (3) the transfer of dissolved gas... 

For the gaseous reactant three mass transfer steps can be identified [14] (i) the transfer from the bubble through the liquid film to the catalyst (/tgs gs)> ( ) the transfer from the caps of the gas bubbles to the liquid slug (/cgl gl)> (hi) the transfer of dissolved gas to the catalytic surface (/cls ls)- Steps (ii) and (iii) are in series and in parallel with respect to step (i) (Figure 8.8). 

Comparison of the Three Mass Transfer Resistances The resistances of the various steps estimated through the reciprocals of the transfer coefficients are as follows ... 

The three mass transfer processes can be combined in an overall mass transfer coefficient ... 

A heterogeneous model is being developed by taking three mass transfer resistances in series for both ethanol and sugar these are as follows ... 

The model equations are developed for the floes with three mass transfer resistances in series for sugar and ethanol. The present floe model is more... 

Balance of mass requires that all three mass transfer rates are equal ... 

The mass transfer rate in monolith reactors is mainly controlled by four mechanisms - gas/solid, gas/liquid, liquid/solid, and pore diflhsion. The reaction takes place on the surface and in the pores of the wash coat layer at the channel wall. The reactants are transferred from the bulk liquid and gas phases to the solid surface, and the reactants from the gas phase are also transferred from bulk gas phase to bulk liquid phase and from there to the solid surface. The three mass transfer coefficients involved are gas-liquid, liquid-solid and gas-solid. In addition to these factors, diffusion of the reactants into the pores and products out of the pores also influences the overall mass transfer rate. The correlations for liquid-solid and gas-liquid mass transfer have been reported by Roy et.al. [24], where Sherwood number is expressed... 

One-dimensional mass transfer is operative once the geometries of WE and of the cell are suitable, as described below for pure diffusion. In the case that all three mass transfer processes are operative, it is accounted for by the Nemst—Planck equation. The first term accounts for diffusion, the second one for migration, and the third one for convection ... 

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