Mass transfer effect, simple

Discussion of the concepts and procedures involved in designing packed gas absorption systems shall first be confined to simple gas absorption processes without compHcations isothermal absorption of a solute from a mixture containing an inert gas into a nonvolatile solvent without chemical reaction. Gas and Hquid are assumed to move through the packing in a plug-flow fashion. Deviations such as nonisotherma1 operation, multicomponent mass transfer effects, and departure from plug flow are treated in later sections. 

In assessing whether a reactor is influenced by intraparticle mass transfer effects WeiSZ and Prater 24 developed a criterion for isothermal reactions based upon the observation that the effectiveness factor approaches unity when the generalised Thiele modulus is of the order of unity. It has been showneffectiveness factor for all catalyst geometries and reaction orders (except zero order) tends to unity when the generalised Thiele modulus falls below a value of one. Since tj is about unity when 0 < ll for zero-order reactions, a quite general criterion for diffusion control of simple isothermal reactions not affected by product inhibition is < 1. Since the Thiele modulus (see equation 3.19) contains the specific rate constant for chemical reaction, which is often unknown, a more useful criterion is obtained by substituting l v/CAm (for a first-order reaction) for k to give ... 

This paper has provided a framework for further application of Second Law based design methodology to separation systems. It has done so by providing a relationship that gives the available-energy destruction for a binary separation as a function of the process variables for the case in which the entropy production is primarily due to mass transfer effects. The Second Law methodology has been described and applied to a simple binary separation system. The method yields results identical to those obtained from a traditional direct search technique, and accurately indicates the respective trade-offs between fuel costs and capital investment. 

The contents of the present contribution may be outlined as follows. Section 6.2.2 introduces the basic principles of coupled heat and mass transfer and chemical reaction. Section 6.2.3 covers the classical mathematical treatment of the problem by example of simple reactions and some of the analytical solutions which can be derived for different experimental situations. Section 6.2.4 is devoted to the point that heat and mass transfer may alter the characteristic dependence of the overall reaction rate on the operating conditions. Section 6.2.S contains a collection of useful diagnostic criteria available to estimate the influence of transport effects on the apparent kinetics of single reactions. Section 6.2.6 deals with the effects of heat and mass transfer on the selectivity of basic types of multiple reactions. Finally, Section 6.2.7 focuses on a practical example, namely the control of selectivity by utilizing mass transfer effects in zeolite catalyzed reactions. 

Table 2 lists most of the available experimental criteria for intraparticle heat and mass transfer. These criteria apply to single reactions only, where it is additionally supposed that the kinetics may be described by a simple nth order power rate law. The most general of the criteria, 5 and 8 in Table 2, ensure the absence of any net effects (combined) of intraparticle temperature and concentration gradients on the observable reaction rate. However, these criteria do not guarantee that this may not be due to a compensation of heat and mass transfer effects (this point has been discussed in the previous section). In fact, this happens when y/J n [12]. 

The role of mass transfer effects, whether occurring accidentally or by design, is ambivalent, causing Trevan to ask the question Diffusion limitation - friend or foe [115]. Lower activity as a result of low efficiency indicates that only a minor portion of enzyme is active during operation. The other unused portion may, in simple terms, replace the enzyme as it is inactivated step by step. In other words, mass transfer controlled reactions appear to be much less sensitive to decay of enzyme activity, thus falsely creating an impression of stabilization. Under harsh reaction conditions it may be advantageous to operate under these conditions to keep the reaction rate constant until the diffusion limitation disappears [82,115,116]. 

Proportional pattern or disperse front— usually a gradual and asymmetric transition during regeneration or uptake under unfavorable (Type II) equilibrium. The physical limit (without mass transfer effects) is a simple wave. 

A good reactor to use for laboratory experiments is a batch reactor with a qiescent interface. This is particularly useful in obtaining rate data under different controlled conditions of mass transfer. A simple way of varying the mass transfer. A simple way of varying the mass transfer effect is to float various sizes of plastic balls at the liquid-liquid interface, thus controlling the area of mass transfer. Reactors in which droplets of one liquid are introduced into the other can also be used. 

The same group further developed the model to include mass transfer effects, where mass is transferred from the gas phase to a reacting wall [84]. Given a solution for the bubble shape, it is a simple matter to include mass transfer, as this involves only the addition of a scalar equation with the flow-field kept frozen . The entire approach represents a clever use of CFD both to determine the bubble hydrodynamics and then to explore the influence of the flow on mass transfer, enabling them to generate useful data for the design of multi-phase monolith reactors. 

Simple Electron Transfer Reaction Without Mass Transfer Effects... 

In the case of a simple one-electron transfer reaction in Tafel conditions (i.e., irreversible electrochemical process without mass transfer effects), the faradaic current is described as... 

However, as during corrosion no net current will pass the interface, the theory of electrochemical reaction kinetics will have to be applied in order to calculate the current density under free corrosion conditions. This current density is called the corrosion current density. For a corroding surface under simple electrochemical conditions (no mass transfer effect), the relation between the current density and its driving force, the potential drop across the interface (electrode potential), is given by the Butler-Volmer equation... 

Trickle-bed reactors, wherein gas and liquid reactants are contacted in a co-current down flow mode in the presence of heterogeneous catalysts, are used in a large number of industrial chemical processes. Being a multiphase catalytic reactor with complex hydrodynamics and mass transfer characteristics, the development of a generalized model for predicting the performance of such reactors is still a difficult task. However, due to its direct relevance to industrial-scale processes, several important aspects with respect to the influence of external and intraparticle mass transfer effects, partial wetting of catalyst particles and heat effects have been studied previously (Satterfield and Way (1972) Hanika et. al., (1975,1977,1981) Herskowitz and Mosseri (1983)). The previous work has mainly addressed the question of catalyst effectiveness under isothermal conditions and for simple kinetics. It is well known that most of the industrially important reactions represent complex reaction kinetics and very often multistep reactions. Very few attempts have been made on experimental verification of trickle-bed reactor models for multistep catalytic reactions in the previous work. 

A simple system is shown in Figure 5.10a to depict heterogeneous polymerization. A gaseous monomer is continuously fed into a glass vessel. The vessel (serving as a reactor) has a suitable solvent (usually hexane for propylene) in which the catalyst-cocatalyst system is xmiformly dispersed. In Figure 5.10b, the effect of stirring speed on the rate of propylene polymerization is shown schematically. These results clearly demonstrate the external mass transfer effect. 

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

Most studies on heat- and mass-transfer to or from bubbles in continuous media have primarily been limited to the transfer mechanism for a single moving bubble. Transfer to or from swarms of bubbles moving in an arbitrary fluid field is complex and has only been analyzed theoretically for certain simple cases. To achieve a useful analysis, the assumption is commonly made that the bubbles are of uniform size. This permits calculation of the total interfacial area of the dispersion, the contact time of the bubble, and the transfer coefficient based on the average size. However, it is well known that the bubble-size distribution is not uniform, and the assumption of uniformity may lead to error. Of particular importance is the effect of the coalescence and breakup of bubbles and the effect of these phenomena on the bubble-size distribution. In addition, the interaction between adjacent bubbles in the dispersion should be taken into account in the estimation of the transfer rates... 

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