Enhancement factors for gas absorption

The chemical method used to estimate the interfacial area is based on the theory of the enhancement factor for gas absorption accompanied with a chemical reaction. It is clear from Equations 6.22-6.24 that, in the range where y > 5, the gas absorption rate per unit area of gas-liquid interface becomes independent of the liquid phase mass transfer coefficient /cp, and is given by Equation 6.24. Such criteria can be met in the case of absorption with... 

Wellek.R.M., Brunson,R.J. and F.H.Law. "Enhancement factors for gas absorption with second order irreversible chemical reaction". Can.J.Chem.Engng. 56 (1978) 181. 

Wellek RM, Brunson RJ, Law FH (1978) Enhancement factors for gas absorption with 2nd-order irreversible chemical-reaction. Can J Chem Eng 56 181-186... 

DP E F f f. Ha He AG Degree of polymerization Activation energy, enhancement factor for gas-liquid mass transfer with reaction, electrochemical cell potential Faraday constant, F statistic Efficiency of initiation in polymerization Ca/CaQ or na/nao, fraction of A remaining unconverted Hatta number Henry constant for absorption of gas in liquid Free energy change kj/kgmol Btu/lb-mol... 

Fig. 87 Enhancement factor E for gas absorption with subsequent chemical conversion as a function of the Hatta number, Hat, and the ratio of the diffusion currents, Z.

Historically, the analysis of gas/liquid systems arose from the problem of gas absorption accompanied by chemical reaction. Since the chemical reaction in this instance tends to increase the rate of absorption (mass transfer), much of the analysis is based on exploring the effects of chemical reaction on a diffusional process. This is just the opposite of the viewpoint in the theory for gas/solid systems, where we have explored the effects of appending a diffusional process to a chemical reaction. The net result of this difference in viewpoints is that most theories of gas/liquid reactions are concerned with determining enhancement factors for the mass-transfer coefficient rather than penalty functions, such as the effectiveness factor for the reaction kinetic constant. This difference in viewpoints can be rather refreshing in pointing out the various contrasts between the two approaches. 

The most severe aberrations cam be observed for the 30H SO, in the gas phase. The 13 C temperature increase for physical absorption reduces the absorption potential by a factor of almost 6, giving an enhancement factor for values of / M < 1.0 of 0.16. As / M increases, the enhancement factor is predicted to fall to am asymptote of 0.13. This is an exaunple of an increase in the reaction rate giving rise to a decrease in the absorption rate due to the adverse impact of release of heat of reaction. That this behaviour is theoretically possible can be seen from a combination of Eqns (32) and (25) whereby... 

As pointed out in Chapter 1, the occurrence of a chemical reaction in the solution has the effect of increasing the liquid phase absorption coefficient over that which would be observed with simple physical absorption. This increase can be quantified in terms of an enhancement factor the ratio of the actual absorption coefficient with reaction to the absorption coefficient which would be expected under the identical conditions if no reaction occurred. The prediction of enhancement factors for various classes of reactions is quite complex (see Astarita et al., 1983) and requires a knowledge of the reaction path and rate as well as liquid phase physical properties. As the reaction rate increases, the enhancement factor, and thus the liquid phase absorption coefficient, also increases. When the reaction rate is extremely fast, die liquid phase absorption coefficient can be high raiough to make the gas phase mass transfer resistance controlling. 

Fermentation broths are suspensions of microbial cells in a culture media. Although we need not consider the enhancement factor E for respiration reactions (as noted above), the physical presence per se of microbial cells in the broth will affect the k a values in bubbling-type fermentors. The rates of oxygen absorption into aqueous suspensions of sterilized yeast cells were measured in (i) an unaerated stirred tank with a known free gas-liquid interfacial area (ii) a bubble column and (iii) an aerated stirred tank [6]. Data acquired with scheme (i) showed that the A l values were only minimally affected by the presence of cells, whereas for schemes (ii) and (iii), the gas holdup and k a values were decreased somewhat with increasing cell concentrations, because of smaller a due to increased bubble sizes. 

It is obvious that re-atomization yields decrease the mean diameter of the liquid droplets and thus an increased interface area at the same time, it results in reduced average transfer coefficients, because heat and mass transfer coefficients between gas flow and particle or droplet are in positive correlation with the diameter of the particle or droplet, while coalescence of droplets yields influences opposite to those described above. In their investigation on the absorption of C02 into NaOH solution, Herskowits et al. [59, 60] determined theoretically the total interface areas and the mass transfer coefficients by comparing the absorption rates with and without reaction in liquid, employing the expression for the enhancement factor due to chemical reaction of second-order kinetics presented by Danckwerts [70],... 

Experimental measurements of absorption fluxes and colour development for the gas-liquid reaction between sulphur trioxide and dodecylbenzene have been carried out in a stirred cell absorber. A model with two parallel reaction paths representing sulphonation and discolouration has been applied to analyse the exothermic absorption accompanying conversions up to 70%. The results show that the two reactions have similar activation energies and that temperature increases greater than 100°C occur at the interface during absorption. The absorption enhancement factor exhibits a maximum value as liquid phase conversion proceeds. 

Transient absorption of gas, followed by irreversible second-order reaction, has been studied extensively by Brian et al. (B26) and Danckwerts (Dl). The average rate of absorption for a contact time d is also given in terms of the enhancement factor... 

In the overall picture, different expressions are proposed for the rate of gas absorption with chemical reaction, depending on the forms of the enhancement factor E corresponding to different kinetic regimes, going from reaction-controlling to mass transfer-controlling. Typical cases are ... 

Gas-to-liquid mass transfer is a transport phenomenon that involves the transfer of a component (or multiple components) between gas and liquid phases. Gas-liquid contactors, such as gas-liquid absorption/ stripping columns, gas-liquid-solid fluidized beds, airlift reactors, gas bubble reactors, and trickle-bed reactors (TBRs) are frequently encountered in chemical industry. Gas-to-liquid mass transfer is also applied in environmental control systems, e.g., aeration in wastewater treatment where oxygen is transferred from air to water, trickle-bed filters, and scrubbers for the removal of volatile organic compounds. In addition, gas-to-liquid mass transfer is an important factor in gas-liquid emulsion polymerization, and the rate of polymerization could, thus, be enhanced significantly by mechanical agitation. 

For a given gas-liquid system, the gas side should either be pure or used at a very high flow rate so that issues related to gas-phase back-mixing are eliminated. Furthermore, the gas-phase impeller speed is varied such that, beyond a particnlar impeller speed, the rate becomes independent of speed, ensnring that the gas-phase resistance is eliminated. For a given gas-liquid system, the specihc rate of absorption, 7 , is measnred, and the enhancement factor is estimated nsing the following equation ... 

Figure 6.3a shows the idealized sketch of concentration profiles near the interface by the Hatta model, for the case of gas absorption with a very rapid second-order reaction. The gas component A, when absorbed at the interface, diffuses to the reaction zone where it reacts with B, which is derived from the bulk of the liquid by diffusion. The reaction is so rapid that it is completed within a very thin reaction zone this can be regarded as a plane parallel to the interface. The reaction product diffuses to the liquid main body. The absorption of C02 into a strong aqueous KOH solution is close to such a case. Equation 6.21 provides the enhancement factor E for such a case, as derived by the Hatta theory ... 

For gas-liquid reactions an enhancement factor is often defined. The enhancement factor is the ratio between the chemical absorption rate and the physical absorption rate. Eq. (9.42) is valid for component A when only physical absorption occurs in the liquid film. The enhancement factor, EA, is in this case defined as... 

For intermediate reaction rates the use of the enhancement factor is not consistent with the standard approach of diffusional limitations in reactor design and may be somewhat confusing. Furthermore, there are cases where there simply is no purely physical mass transfer process to refer to. For example, the chlorination of decane, which is dealt with in the coming Sec. 6.3.f on complex reactions or the oxidation of o-xylene in the liquid phase. Since those processes do not involve a diluent there is no corresponding mass transfer process to be referred to. This contrasts with gas-absorption processes like COj-absorption in aqueous alkaline solutions for which a comparison with C02-absorption in water is possible. The utilization factor approach for pseudo-first-order reactions leads to = tfikC i and, for these cases, refers to known concentrations C., and C . For very fast reactions, however, the utilization factor approach is less convenient, since the reaction rate coefficient frequently is not accurately known. The enhancement factor is based on the readily determined and in this case there is no problem with the driving force, since Cm = 0- Note also that both factors and Fji are closely related. Indeed, from Eqs. 6.3.C-5 and 6.3.C-10 for instantaneous reactions ... 

So far, only pseudo-first-order and instantaneous second-order reactions were discussed. In between there is the range of truly second-order behavior for which the continuity equations for A (Eq. 6.3.a-l) or B (Eq. 6.3.a-2), cannot be solved analytically, only numerically. To obtain an approximate analytical solution. Van Krevelen and Hoftijzer [3] dealt with this situation in a way analogous to that apfdied to pseudo-first-order kinetics, namely by assuming that the concentration of B remains approximately constant close to the interface. They mainly considered very fast reactions encountered in gas absorption so that they could set Cm - 0, that is, the reaction is completed in the film. Their development is in terms of the enhancement factor, F. The approximate equation for is entirely analogous with that obtained for a pseudo-first-order reaction Eq. 

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