Gas film resistance

In situations where the gas film resistance is predominant (gas film-controlled situation), k Pis much smaller than and the tie line is very steep. approachesjy so that the overall gas-phase driving force and the gas-film driving force become approximately equal, whereas the Hquid-film driving force becomes negligible. From equation 7 it also follows that in such cases. The reverse is tme if the Hquid film resistance is controlling. Since the... 

In the case of a less soluble gas such as oxygen, diffusion occurs so slowly through the Hquid film that only a small concentration difference is required to overcome the resistance of the gas film. Thus the Hquid film at the interface is considered to be very close to oxygen saturation and it is not necessary to consider gas film resistance in the calculation (14). 

E] Ammonia absorption into water from air at 70 F. Gas-film resistance controls. Thin-waUed polyethylene Raschig rings and 1-inch Intalox saddles. Fit 25%. See Reiss for fit. Terms defined as above. 

Liquid-Film Coefficients (Physical) and (Reactive) The gas-side resistance can be eliminated by employing a pure gas, thus leaving the liquid film as the only resistance. Alternatively, after the gas-film resistance has been found experimentally or from corre-... 

Note that H is simply Henry s constant corrected for units. When the solute gas is readily soluble in the liquid solvent, Henry s law constant (H or H ) is small and Kj approximately equals k, and the absorption process is controlled by the gas film resistance. For systems where the solute is relatively insoluble in the liquid, H is large and K( approximately equals k, and the absorption rate is controlled by the liquid phase resistance. In most systems, the solute has a high solubility in the solvent selected, resulting in the system being gas film resistance controlled. 

Later publications have been concerned with mass transfer in systems containing no suspended solids. Calderbank measured and correlated gas-liquid interfacial areas (Cl), and evaluated the gas and liquid mass-transfer coefficients for gas-liquid contacting equipment with and without mechanical agitation (C2). It was found that gas film resistance was negligible compared to liquid film resistance, and that the latter was largely independent of bubble size and bubble velocity. He concluded that the effect of mechanical agitation on absorber performance is due to an increase of interfacial gas-liquid area corresponding to a decrease of bubble size. 

Carbon dioxide is absorbed in water from a 25 per cent mixture in nitrogen. How will its absorption rate compare with that from a mixture containing 35 per cent carbon dioxide, 40 per cent hydrogen and 25 per cent nitrogen It may be assumed that the gas-film resistance is controlling, that the partial pressure of carbon dioxide, at the gas-liquid interface is negligible and that the two-lilm theory is applicable, with the gan film thickness the same in the two cases. 

The solubility of gases varies widely. Gases with a low solubility (e.g. N2, O2) have large values of the Henry s Law coefficient. This means that the liquid-film resistance in Equation 7.6 is large relative to the gas-film resistance. On the other hand, if the gas is highly soluble (e.g. CO2, NH3), the Henry s Law coefficient is small. This leads to the gas-film resistance being large relative to the liquid-film resistance in Equation 7.6. Thus,... 

To eliminate cAi and take gas-film resistance into account, we again use 9.2-3 and 9.2-8. Thus, eliminating cAi,pAl, and NA(z = 0) from 9.2-3, -8, -44a, and -45, we obtain the following rather cumbersome expression ... 

The overall absorption coefficient KGa may be taken as 1.5 x 10 4 kmol/[m3s (kN/m2) partial pressure difference] and the gas film resistance controls the process. 

Combining the liquid- and gas-film resistances and replacing kl by k L since the mass transfer is enhanced by the reaction, then ... 

The complexity of eqn. (58) arises because it was not assumed that any one of the three rate processes identified is rate determining. The relation between time and conversion is considerably simplified one of the rate processes dominates the overall process. When reactant gas flows through a fixed bed of solid particles, the gas film resistance to conversion is... 

If the two terms are of the same order of magnitude we may suspect that the gas film resistance affects the rate. On the other hand, if k J p is much smaller than kgS we may ignore the resistance to mass transport through the film. Example 18.1 illustrate this type of calculation. The results of that example confirm our earlier statement that film mass transfer resistance is unlikely to play a role with porous catalyst. 

Nonisothermal Effects. We may expect temperature gradients to occur either across the gas film or within the particle. However, the previous discussion indicates that for gas-solid systems the most likely effect to intrude on the rate will be the temperature gradient across the gas film. Consequently, if experiment shows that gas film resistance is absent then we may expect the particle to be at the temperature of its surrounding fluid hence, isothermal conditions may be assumed to prevail. Again see Example 18.1. 

Gas film resistance controls for highly soluble gases. 

Combination of Resistances. The above conversion-time expressions assume that a single resistance controls throughout reaction of the particle. However, the relative importance of the gas film, ash layer, and reaction steps will vary as particle conversion progresses. For example, for a constant size particle the gas film resistance remains unchanged, the resistance to reaction increases as the surface of unreacted core decreases, while the ash layer resistance is nonexistent at the start because no ash is present, but becomes progressively more and more important as the ash layer builds up. In general, then, it may not be reasonable to consider that just one step controls throughout reaction. 

As described previously, the reactant has to first reach the external surface of the catalyst. For simplicity, we take into consideration the case of a gas reacting on a solid catalytic surface. Owing to gas film resistance, the concentration of the reactant at the catalytic surface (Cs) is lower than that in the bulk of the fluid (Cb). This difference depends on... 

Furthermore, a temperature gradient may also be developed due to gas film resistance. This means that the temperature of the bulk of the fluid (7b) is also different from the temperature of the exterior surface of the catalyst (Tj. As before, this difference depends on... 

Consider a second order reaction in the liquid phase between a substance A which is transferred from the gas phase and reactant B which is in the liquid phase only. The gas will be taken as consisting of pure A so that complications arising from gas film resistance are avoided. The stoichiometry of the reaction is represented by ... 

The individual mass transfer and reaction steps occurring in a gas-liquid-solid reactor may be distinguished as shown in Fig. 4.15. As in the case of gas-liquid reactors, the description will be based on the film theory of mass transfer. For simplicity, the gas phase will be considered to consist of just the pure reactant A, with a second reactant B present in the liquid phase only. The case of hydro-desulphurisation by hydrogen (reactant A) reacting with an involatile sulphur compound (reactant B) can be taken as an illustration, applicable up to the stage where the product H2S starts to build up in the gas phase. (If the gas phase were not pure reactant, an additional gas-film resistance would need to be introduced, but for most three-phase reactors gas-film resistance, if not negligible, is likely to be small compared with the other resistances involved.) The reaction proceeds as follows ... 

In general, small/light particles can enhance heat transfer. The cluster formation in small/light particle systems contributes to the enhancement of hpc. Also the gas film resistance can be reduced by fluidizing with small particles [Wu et al., 1987]. When the temperature is lower than 400°C, the effect of bed temperature on the heat transfer coefficient is due to the change of gas properties, while hr is negligible. At higher temperatures, h increases with temperature, mainly because of the sharp increase of radiative heat transfer. 

This form is particularly appropriate when the gas is of low solubility in the liquid and "liquid film resistance" controls the rate of transfer. More complex forms which use an overall mass transfer coefficient which includes the effects of gas film resistance must be used otherwise. Also, if chemical reactions are involved, they are not rate limiting. The approach given here, however, illustrates the required calculation steps. The nature of the mixing or agitation primarily affects the interfacial area per unit volume, a. The liquid phase mass transfer coefficient, kL, is primarily a function of the physical properties of the fluid. The interfacial area is determined by the size of the gas bubbles formed and how long they remain in the mixing vessel. The size of the bubbles is normally expressed in terms of their Sauter mean diameter, dSM, which is defined below. How long the bubbles remain is expressed in terms of gas hold-up, H, the fraction of the total fluid volume (gas plus liquid) which is occupied by gas bubbles. 

In this equation, it is assumed that Hg is constant over the height of the packed bed and can therefore be removed from the integral. The remaining integral function of y is the number of transfer units based on the gas film resistance Ng. 

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