Effect of mass transfer

In considering the effect of mass transfer on the boiling of a multicomponent mixture, both the boiling mechanism and the driving force for transport must be examined (17—20). Moreover, the process is strongly influenced by the effects of convective flow on the boundary layer. In Reference 20 both effects have been taken into consideration to obtain a general correlation based on mechanistic reasoning that fits all available data within 15%. 

Zabor et al. (Zl) have described studies of the catalytic hydration of propylene under such conditions (temperature 279°C, pressure 3675 psig) that both liquid and vapor phases are present in the packed catalyst bed. Conversions are reported for cocurrent upflow and cocurrent downflow, it being assumed in that paper that the former mode corresponds to bubble flow and the latter to trickle-flow conditions. Trickle flow resulted in the higher conversions, and conversion was influenced by changes in bed height (for unchanged space velocity), in contrast to the case for bubble-flow operation. The differences are assumed to be effects of mass transfer or liquid distribution. 

In general, the concentration of the reactant will decrease from CAo in the bulk of the fluid to CAi at the surface of the particle, to give a concentration driving force of CAo - CAi)-Thus, within the pellet, the concentration will fall progressively from CAi with distance from the surface. This presupposes that no distinct adsorbed phase is formed in the pores. In this section the combined effects of mass transfer and chemical reaction within the particle are considered, and the effects of external mass transfer are discussed in Section J 0.8.4. 

When the resistance to mass transfer to the external surface of the pellet is significant compared with that within the particle, part of the concentration driving force is required to overcome this external resistance, and the concentration of reacting material at the surface of the pellet Cm is less than that in the bulk of the fluid phase Cao- In Sections 10.7.1-10.7.3, the effect of mass transfer resistance within a porous particle... 

A hydrocarbon is cracked using a silica-alumina catalyst in the form of spherical pellets of mean diameter 2.0 mm. When the reactant concentration is 0.011 kmol/m3, the reaction rate is 8.2 x 10"2 kmol/(m3 catalyst) s. If the reaction is of first-order and the effective diffusivity De is 7.5 x 10 s m2/s, calculate the value of the effectiveness factor r). It may be assumed that the effect of mass transfer resistance in the. fluid external Lo the particles may be neglected. 

Quantitative analytical treatments of the effects of mass transfer and reaction within a porous structure were apparently first carried out by Thiele (20) in the United States, Dam-kohler (21) in Germany, and Zeldovitch (22) in Russia, all working independently and reporting their results between 1937 and 1939. Since these early publications, a number of different research groups have extended and further developed the analysis. Of particular note are the efforts of Wheeler (23-24), Weisz (25-28), Wicke (29-32), and Aris (33-36). In recent years, several individuals have also extended the treatment to include enzymes immobilized in porous media or within permselective membranes. The important consequence of these analyses is the development of a technique that can be used to analyze quantitatively the factors that determine the effectiveness with which the surface area of a porous catalyst is used. For this purpose we define an effectiveness factor rj for a catalyst particle as... 

It has been shown that when the intracolumn effect of mass transfer and diffusion is the main factor controlling band broadening, the column efficiency decreases with the increase of the viscosity of the meth-anol/water mixture on the other hand, when the extra-column effect is the main factor, an increase in viscosity of the eluents will help in improving column efficiency. Column efficiency is also related to the properties of the sample [86]. 

The mass transfer coefficient describes the effect of mass transfer resistance of the reactants flowing from the gas phase to the surface of the individual particles in the bed. The mass transfer coefficient can be obtained from a correlation for the Sherwood number (or dimensionless mass transfer coefficient) given by Eq. (7) ... 

Dekker et al. [170] studied the extraction process of a-amylase in a TOMAC/isooctane reverse micellar system in terms of the distribution coefficients, mass transfer coefficient, inactivation rate constants, phase ratio, and residence time during the forward and backward extractions. They derived different equations for the concentration of active enzyme in all phases as a function of time. It was also shown that the inactivation took place predominantly in the first aqueous phase due to complex formation between enzyme and surfactant. In order to minimize the extent of enzyme inactivation, the steady state enzyme concentration should be kept as low as possible in the first aqueous phase. This can be achieved by a high mass transfer rate and a high distribution coefficient of the enzyme between reverse micellar and aqueous phases. The effect of mass transfer coefficient during forward extraction on the recovery of a-amylase was simulated for two values of the distribution coefficient. These model predictions were verified experimentally by changing the distribution coefficient (by adding... 

Effects of Mass Transfer on the Performance of Immobilized-biocatalyst Reactors... 

It is obvious that to have high conversion, the reaction should be fast enough and the term Zf /wbub should be high. Hence, uhuh should be small or, in other words, t/bub should be small. The effect of mass transfer resistance is shown in Figures 5.20 and 5.21 for the cases of a fast (kvs = 1 s-1) and a slow reaction (kvs = 0.01 s-1), respectively. 

Figure 5.20 The effect of mass transfer resistance for a slow reaction ( vs = 0.01 s r).

Effects of Mass Transfer Around and within Catalyst or Enzymatic Particles on the Apparent Reaction Rates... 

Consider an idealized simple case of a Michaelis-Menten type bioreaction taking place in a vertical cylindrical packed-bed bioreactor containing immobilized enzyme particles. The effects of mass transfer within and outside the enzyme particles are assumed to be negligible. The reaction rate per dilfcrential packed height (m) and per unit horizontal cross-sectional area of the bed (m ) is given as (cf. Equation 3.28) ... 

Some components in a gas or liquid interact with sites, termed adsorption sites, on a solid surface by virtue of van der Waals forces, electrostatic interactions, or chemical binding forces. The interaction may be selective to specific components in the fluids, depending on the characteristics of both the solid and the components, and thus the specific components are concentrated on the solid surface. It is assumed that adsorbates are reversibly adsorbed at adsorption sites with homogeneous adsorption energy, and that adsorption is under equilibrium at the fluid- adsorbent interface. Let (m" ) be the number of adsorption sites and (m 2) the number of molecules of A adsorbed at equilibrium, both per unit surface area of the adsorbent. Then, the rate of adsorption r (kmol m s ) should be proportional to the concentration of adsorbate A in the fluid phase and the number of unoccupied adsorption sites. Moreover, the rate of desorption should be proportional to the number of occupied sites per unit surface area. Here, we need not consider the effects of mass transfer, as we are discussing equilibrium conditions at the interface. At equilibrium, these two rates should balance. Thus,... 

Use of reaction kinetic data from the literature Are kinetic data (e. g. kn(M)) from the literature useful for comparisons with my own data and may they be used for predictions of my own results Yes, if all data necessary to describe the entire process have been assessed and reported comparisons are only possible on this basis. Consider that mass transfer might influence the (apparent) disappearance kinetics of M in the specific system. Keep in mind, that the kD (and kR) values do not take into account the effect of mass transfer enhancement on the removal rate of M (r(M)). B 1 B 4 B 3.2... 

In deriving eqn. (80), limitations due to mass transport at the interface were not considered. Strictly speaking, this is not realistic and as the reaction rate increases with overpotential in each direction a variation of the concentrations of reactant and product at the surface operates and concentration polarization becomes more important. Each exponential expression in eqn. (80) must be multiplied by the ratio of surface to bulk concentrations, ci s/ci b. The effect of mass transfer in electrode kinetics has been discussed in Sect. 2.4. 

In this section the effect of mass transfer limitation on the drop conversion rate and the order of drop conversion will be treated, and it will be shown that a process for which the real chemical reaction is of first order in the reactant A (which is dissolved in the dispersed phase) can still be influenced by the effect of segregation when the chemical conversion rate is limited by mass transfer of the reactants. 

Although the transfer unit concept allows for the effects of mass transfer rate, in the simplified form given here it... 

Paraffin to olefin molar ratios for the C3 and Cy fractions are reported in Table I for two sets of runs in which the degree of mass transfer was varied by changing RPM. Even with a CSTR, data on the effect of mass transfer must be Interpreted carefully. An Increase in mass transfer resistance, caused by decreased agitation, causes a drop in conversion. Usually the consumption ratio of H2/CO is different than the feed ratio and hence a drop in conversion is accompanied by a change in the H2/CO ratio in... 

The orthogonal collocation polynomial approximation using a single parameter trial function was employed to solve equations (l)-(3), In addition to the solution for time concentration and activity profiles, effectiveness factors representing the combined effect of mass transfer resistance and poisoning in terms of pellet surface conditions were computed according to... 

Pignatello, J.J. (1992) Dark and photoassisted iron (3+)-catalyzed degradation of chlorophenoxy herbicides by hydrogen peroxide. Environ. Sci. Technol. 26, 944-951 Polcaro, A.M., Mascia, M, Palmas, S. and Vacca, A. (2002) Electrochemical oxidation of phenolic and other organic compounds at boron doped diamond electrodes for wastewater treatment Effect of mass transfer. Ann. Chim. 93, 967-976... 

X. EFFECT OF MASS TRANSFER RESISTANCES IN PREPARATIVE HPLC OF POLYPEPTIDES AND PROTEINS... 

Novel and effective bioseparation techniques must be continuously researched and developed for profitable removal of proteins and other bioproducts of interest from very dilute solutions (A. Ramakrishnan and A. Sadana, personal communication, 1999). There appear to be two techniques that have tremendous potential for commercial applications the reverse micelle technique and aqueous two-phase extraction. Before these techniques achieve their potential, it will be necessary to further delineate the effect of mass transfer, interactions at the interfaces, and other parameters that affect both the quality and quantity of proteins separated by these techniques. It is also necessary to have a large data bank of a wide variety of proteins and bioproducts with regard to their characteristics and stability to assist future improvements in bioseparations. 

X. Effect of Mass Transfer Resistances in Preparative HPLC of Polypeptides and Proteins 178... 

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