Mass transfer equilibrium considerations

These considerations can be extended to reversible processes. They also apply to single phase, liquid systems. For the case, rather common in heterogeneous catalysts, in which one reactant is in a gas phase and the others and the products are in a liquid phase, application of the principles given above is straightforward provided that there is mass transfer equilibrium between gas phase and liquid phase, i.e., the fugacity of the reactant in the gas phase is identical with its fugacity in the liquid phase. In such case, a power rate law for an irreversible reaction of the form... 

The separation of components by liquid-liquid extraction depends primarily on the thermodynamic equilibrium partition of those components between the two liquid phases. Knowledge of these partition relationships is essential for selecting the ratio or extraction solvent to feed that enters an extraction process and for evaluating the mass-transfer rates or theoretical stage efficiencies achieved in process equipment. Since two liquid phases that are immiscible are used, the thermodynamic equilibrium involves considerable evaluation of nonideal solutions. In the simplest case a feed solvent F contains a solute that is to be transferred into an extraction solvent S. 

Equilibrium Considerations - Most of the adsorption data available from the literature are equilibrium data. Equilibrium data are useful in determining the maximum adsorbent loading which can be obtained for a specific adsorbate-adsorbent system under given operating conditions. However, equilibrium data by themselves are insufficient for design of an adsorption system. Overall mass transfer rate data are also necessary. 

This expression insures that the heat-transfer considerations of the second law of thermodynamics are satisfied. For a given pair of corresponding temperatures (T, t) it is thermodynamically and practically feasible to transfer heat from any hot stream whose temperature is greater than or equal to T to any cold stream whose temperature is less than or equal to t. It is worth noting the analogy between Eqs. (9.2) and (3.5). Thermal equilibrium is a special case of mass-exchange equilibrium with T,t and AT " corresponding to yi,Xj and ej, respectively, while the values of rrij and bj arc one and zero, respectively. 

Distillation design is based on the theoretical consideration that heat and mass transfer from stage to stage (theoretical) are in equilibrium [225-229]. Actual columns with actual trays are designed by establishing column tray efficiencies, and applying these to the theoretical trays or stages determined by the calculation methods to be presented in later sections. 

In this type of apparatus, the two phases do not come to equilibrium, at any point in the contactor and the simulation approach is based, therefore, not on a number of equilibrium stages, but rather on a consideration of the relative rates of transport of material through the contactor by flow and the rate of interfacial mass transfer between the phases. For this, a consideration of mass transfer rate theory becomes necessary. 

At low temperatures, the nonenzymatic reaction is reduced to a larger extent than the enzymatic reaction. The mass transfer rate is reduced to a smaller extent. Mass transfer limitation is required for high enantiomeric excess and determines the conversion rate. Therefore, the volumetric productivity decreases at lower temperatures. The equilibrium constant is considerably higher at low temperatures, resulting in a higher extent of conversion or a lower HCN requirement. Both the volumetric productivity and the required enzyme concentration increase by increasing the reaction temperature and aqueous-phase volume while meeting the required conversion and enantiomeric excess [44]. The influence of the reaction medium (solvent and water activity) is much more difficult to rationalize and predict [45],... 

Many industrial processes involve mass transfer processes between a gas/vapour and a liquid. Usually, these transfer processes are described on the basis of Pick s law, but the Maxwell-Stefan theory finds increasing application. Especially for reactive distillation it can be anticipated that the Maxwell-Stefan theory should be used for describing the mass transfer processes. Moreover, with reactive distillation there is a need to take heat transfer and chemical reaction into account. The model developed in this study will be formulated on a generalized basis and as a consequence it can be used for many other gas-liquid and vapour-liquid transfer processes. However, reactive distillation has recently received considerable attention in literature. With reactive distillation reaction and separation are carried out simultaneously in one apparatus, usually a distillation column. This kind of processing can be advantageous for equilibrium reactions. By removing one of the products from the reactive zone by evaporation, the equilibrium is shifted to the product side and consequently higher conversions can be obtained. Commercial applications of reactive distillation are the production of methyl-... 

Certainly the condition in Eq. (74) is valid since there must be no accumulation of solute at the interface. But the condition for equilibrium at the interface in Eq. (75) may not be adequate for the description of many mass transfer processes. It is not, for example, difficult to imagine that in the evaporation of a liquid, the vaporization may take place so rapidly that the concentration of vapor just above the liquid surface is considerably less than the concentration corresponding to the equilibrium vapor pressure. The problem of obtaining a quantitative theoretical description of this process has been attacked by Schrage (S4), who has suggested several molecular theories for describing gas-liquid and gas-solid systems. 

Source Considerations. Many CVD sources, especially sources for or-ganometallic CVD, such as Ga(CH3)3 and Ga(C2H5)3, are liquids at near room temperatures, and they can be introduced readily into the reactor by bubbling a carrier gas through the liquid. In the absence of mass-transfer limitations, the partial pressure of the reactant in the gas stream leaving the bubbler is equal to the vapor pressure of the liquid source. Thus, liquid-vapor equilibrium calculations become necessary in estimating the inlet concentrations. For the MOCVD of compound-semiconductor alloys, the computations have also been used to establish limits on the control of bubbler temperature to maintain a constant inlet composition and, implicitly, a constant film composition (79). Similar gas-solid equilibrium considerations govern the use of solid sources such as In(CH3)3. 

For all of the general techniques of Figure 2, the separations are achieved by enhancing the rate of mass transfer by diffusion of certain species relative to mass transfer of all species by bulk movement within a particular phase. The driving force and direction of mass transfer by diffusion is governed by thermodynamics, with the usual limitations of equilibrium. Thus, both transport and thermodynamic considerations are crucial in separation operations. The rate of separation is governed by mass transfer, while the extent of separation is limited by thermodynamic equilibrium. Fluid mechanics also plays an important role, and applicable principles are included in other chapters. 

To design large scale supercritical desorption processes is necessary to understand in which way dynamic desorption is influenced by process variables as mass transfer effects and equilibrium considerations. The governing equilibrium in all desorption processes is the adsorption equilibrium and a description of this equilibrium is essential in all desorption models and design equations [3]. 

Equations for describing ammonia synthesis under industrial operating conditions must represent the influence of the temperature, the pressure, the gas composition, and the equilibrium composition. Moreover, they must also take into consideration the dependence of the ammonia formation rate on the concentration of catalyst poisons and the influence of mass-transfer resistances, which are significant in industrial ammonia synthesis. 

With donor-controlled conditions, typically, a considerably higher mass transfer rate can be obtained. It is then limited by the diffusion in the donor phase and thus depends on the diffusion coefficient in the donor phase, Dq, and on the donor convection (flow, stirring, etc.) conditions. As a mle of thumb, the donor-controlled extraction conditions prevail when Kq is larger than about 10, while the mass transfer is mainly membrane-controlled when Kx, < 1. It is found that the value of the partition coefficient has no large influence on the efficiency of extraction or the enrichment factors that can be obtained, as long as it is reasonably large. On the other hand, the rate at which equilibrium is reached will be influenced by the partition coefficients. Further, there are observations that too large partition coefficients are not favorable, as the transfer of analyte out of the membrane into the acceptor phase in those cases may become less efficient. 

In designing a preconcentration scheme to operate in real time, consideration must be given to kinetic factors involved in the preconcentration step. In general, any preconcentration step will alter the trace metal s chemical equilibrium and will involve a time-dependent reaction or mass-transfer step. Of those species likely to be affected during preconcentration, the most thermodynamically and kinetically stable are typically the organically bound forms. Organically bound copper has been carefully studied and provides the best example. 

The absorption of ozone by cyanide solutions in stirred reactors is complicated by mass transfer considerations. The presence of ozone gas in the exhaust from such a reactor does not indicate that equilibrium has been obtained between ozone gas bubbles and ozone in solution, but rather that the mass transfer through the individual bubbles is not complete, because of the resistance on the gas side. In other words, mass transfer controls the reaction, as the ozone will react almost instantaneously with the cyanide ion in solution. The presence of some metals, particularly copper, appears to speed up the absorption by acting as oxygen carriers. A solution of ozone in dilute acid decomposes somewhat more quickly when a trace of cupric ion is added. The presence of these metal catalysts, if this be their function, does not appear to be a necessary condition to ozone oxidation. What is important is that adequate mass transfer time and surface be available, as would be found in a countercurrent packed tower. 

By contrast, when the mass transfer resistances and/or axial dispersion are considered, there is no analytical solution for an SMB operated under nonlinear isotherm conditions. A numerical solution of the applicable mathematical model must be used instead to calculate the performance of the SMB, to simulate the influence of the various design and operating parameters, and to search for the optimum flow rates and switching time that give the desired results. In this quest, the selection as a starting point of the optimum set of flow rates and switching time derived from the equilibrium theory permits a considerable reduction of the number of calculations. As discussed earlier by Ruthven and Ching [27], four... 

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