Mass transfer and reaction

We have covered a body of material in this chapter that deals with movement of mass along gradients and between phases. We have examined the commonalities and differences between linear driving forces, net rates of adsorption, and permeation. Each has the common feature that reaction is not involved but does involve transport between apparently well-defined regions. We move now to chemically reactive systems in anticipation of eventually analyzing problems that involve mass transfer and reaction. 

Example 11.8 With highly reactive absorbents, the mass transfer resistance in the gas phase can be controlling. Determine the number of trays needed to reduce the CO2 concentration in a methane stream from 5% to 100 ppm (by volume), assuming the liquid mass transfer and reaction steps are fast. A 0.9-m diameter column is to be operated at 8 atm and 50°C with a gas feed rate of 0.2m /s. The trays are bubble caps operated with a 0.1-m liquid level. Literature correlations suggest = 0.002 m/s and A, = 20m per square meter of tray area. 

Reaction, diffusion, and catalyst deactivation in a porous catalyst layer are considered. A general model for mass transfer and reaction in a porous particle with an arbitrary geometry can be written as follows ... 

The selection of reactor type in the traditionally continuous bulk chemicals industry has always been dominated by considering the number and type of phases present, the relative importance of transport processes (both heat and mass transfer) and reaction kinetics plus the reaction network relating to required and undesired reactions and any aspects of catalyst deactivation. The opportunity for economic... 

The combined fiuld fiow, heat transfer, mass transfer and reaction problem, described by Equations 2-7, lead to three-dimensional, nonlinear, time dependent partial differential equations. The general numerical solution of these goes beyond the memory and speed capabilities of the current generation of supercomputers. Therefore, we consider appropriate physical assumptions to reduce the computations. 

Losey, M. W, Schmidt, M. A., Jensen, K. F., Microfabricated multiphase packed-bed reactors characterization of mass transfer and reactions, Ind. Chem. Res. 

The reaction (Eqn. 5.4-65) takes place in the liquid phase. The molecules are transferred away from the interface to the bulk of the liquid, while reaction takes place simultaneously. Two limiting cases can be envisaged (1) reaction is very fast compared to mass transfer, which means that reaction only takes place in the film, and (2) reaction is very slow compared to mass transfer, and reaction only takes place in the liquid bulk. A convenient dimensionless group, the Hatta number, has been defined, which characterizes the situation compared to the limiting cases. For a reaction that is first order in the gaseous reactant and zero order in the liquid reactant (cm = 1, as = 0), Hatta is ... 

Although the Lewis cell was introduced over 50 years ago, and has several drawbacks, it is still used widely to study liquid-liquid interfacial kinetics, due to its simplicity and the adaptable nature of the experimental setup. For example, it was used recently to study the hydrolysis kinetics of -butyl acetate in the presence of a phase transfer catalyst [21]. Modeling of the system involved solving mass balance equations for coupled mass transfer and reactions for all of the species involved. Further recent applications of modified Lewis cells have focused on stripping-extraction kinetics [22-24], uncatalyzed hydrolysis [25,26], and partitioning kinetics [27]. 

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... 

We treat each of these three cases in turn to obtain, as far as possible, analytical or approximate analytical rate expressions, taking both mass transfer and reaction into account. Each of these cases gives rise to important subcases, some of which are developed further, and some of which are left to problems at the end of the chapter. In treating the cases in the order above, we are proceeding from special, relatively simple, situations to more general ones, the reverse of the approach taken in Section 9.1 for gas-solid systems. 

Describe the various mass transfer and reaction steps involved in a three-phase gas-liquid-solid reactor. Derive an expression for the overall rate of a catalytic hydrogenation process where the reaction is pseudo first-order with respect to the hydrogen with a rate constant k (based on unit volume of catalyst particles). 

Jannasch, H. W., Honeyman, B. D. and Murray, J. W. (1996). Marine scavenging the relative importance of mass transfer and reaction rates, Limnol. Oceanogr. 41, 82-88. 

Now put all the mass transfer and reaction steps into the same rate form and then combine. Thus... 

Comments. The five terms in brackets of the performance equation, Eq. 21, represent the complex series-parallel resistances to mass transfer and reaction or... 

The reaction rate expressed in terms of surface concentrations provides the relationship between Cs and CL. From the definition of the effectiveness factor, we may express the required equality of mass transfer and reaction rates as... 

Note that internal mass transfer and reaction are dealt with simultaneously, in contrast to external mass transfer, which is considered to be in series with the reaction at the catalyst external surface. 

Before examining internal mass transfer and reaction, let us consider the diffusion of fluids within solid particles, which is expressed by means of the effective diffusivity. 

Managing all complexity Calculation of the overall reaction rate combining external mass transfer, internal mass transfer, and reaction... 

Mass transfer and reaction of the liquid species limiting For a first-order reaction in both A and B and provided that the liquid phase is entirely saturated with A throughout the bed, i.e. CAS is constant,... 

The resistance to mass transfer of reactants within catalyst particles results in lower apparent reaction rates, due to a slower supply of reactants to the catalytic reaction sites. Ihe long diffusional paths inside large catalyst particles, often through tortuous pores, result in a high resistance to mass transfer of the reactants and products. The overall effects of these factors involving mass transfer and reaction rates are expressed by the so-called (internal) effectiveness factor f, which is defined by the following equation, excluding the mass transfer resistance of the liquid film on the particle surface [1, 2] ... 

The general mass balance for each phase at nonsteady state, considering convection, mass transfer and reaction (e. g. ozone decay), can be written ... 

Since we know the mass of ozone transferred has to have reacted or left the system, it is relatively easy to determine the reaction rate for slow reactions, which are controlled by chemical kinetics with this method. For kinetic regimes with mass transfer enhancement, the two rates, mass transfer and reaction rate are interdependent. Whether kLa or kD can be determined in such a system and how depends on the regime. Possible methods are similar to those described below in Section B 3.3.3 (see Levenspiel and Godfrey, 1974). 

Rather than proceed by trying to read a reaction factor fA from Fig. 4.3, it is better to set out the basic material balance for mass transfer and reaction as below. Locating the position of 0 on Fig. 4.3 does however confirm that reaction will be occurring in the main bulk of the liquid and that an agitated tank is a suitable type of reactor. 

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 ... 

Flo. 4.IS. Mass transfer and reaction steps in gas-liquid-solids reactors (solids completely wetted by liquid), showing concentration gradients for reactant A being transferred from the gas phase... 

The individual mass transfer and reaction steps outlined in Fig. 4.15 will now be described quantitatively. The aim will be firstly to obtain an expression for the overall rate of transformation of the reactant, and then to examine each term in this expression to see whether any one step contributes a disproportionate resistance to the overall rate. For simplicity we shall consider the gas to consist of just a pure reactant A, typically hydrogen, and assume the reaction which takes place on the interior surface of the catalyst particles to be first order with respect to this reactant only, i.e. the reaction is pseudo first-order with rate constant A ,. In an agitated tank suspended-bed reactor, as shown in Fig. 4.20, the gas is dispersed as bubbles, and it will be assumed that the liquid phase is well-mixed , i.e. the concentration CAL of dissolved A is uniform throughout, except in the liquid films immediately surrounding the bubbles and the particles. (It will be assumed also that the particles are not so extremely small that some are present just beneath the surface of the liquid within the diffusion film and are thus able to catalyse the reaction before A reaches the bulk of the liquid.)... 

Fig. 4.20. Suspended-bed agitated-tank teactor Combination of mass transfer and reaction steps. Impeller used would typically be a pitched-blade turbine, pumping downwards as shown, serving both to suspend particles and to disperse gas...

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