Effect of external mass and heat transfer

EFFECT OF EXTERNAL MASS AND HEAT TRANSFER Uniform and Nonuniform Films... 

Chapter 7 Catalysis by Solids, 2 The Catalyst and Its Microenvironment, 171 Modeling of Solid Catalyzed Reactions, 171 Role of Diffusion in Pellets Catalyst Effectiveness, 183 Effect of External Mass and Heat Transfer, 201 Combined Effects of Internal and External Diffusion, 204 Relative Roles of Mass and Heat Transfer in Internal and External Diffusion, 205 Regimes of Control, 206... 

Combined Influence of External Mass and Heat Transfer on the Effective Rate... 

At this point it is instructive to consider the possible presence of intraparticle and external mass and heat transfer limitations using the methods developed in Chapter 12. In order to evaluate the catalyst effectiveness factor we first need to know the combined diffusivity for use... 

The effects of non-uniform distribution of the catalytic material within the support in the performance of catalyst pellets started receiving attention in the late 60 s (cf 1-4). These, as well as later studies, both theoretical and experimental, demonstrated that non-uniformly distributed catalysts can offer superior conversion, selectivity, durability, and thermal sensitivity characteristics over those wherein the activity is uniform. Work in this area has been reviewed by Gavriilidis et al. (5). Recently, Wu et al. (6) showed that for any catalyst performance index (i.e. conversion, selectivity or yield) and for the most general case of an arbitrary number of reactions, following arbitrary kinetics, occurring in a non-isothermal pellet, with finite external mass and heat transfer resistances, the optimal catalyst distribution remains a Dirac-delta function. 

In this section we have presented and solved the BVPs associated with the diffusion and reaction that take place in the pores of a porous catalyst pellet. The results were expressed graphically in terms of the effectiveness factor rj versus the Thiele modulus d> for two cases One with negligible external mass and heat transfer resistances, i.e., when Sh and Nu —> oo, and another with finite Sh and Nu values. This problem is very important in the design of fixed-bed catalytic reactors. The sample results presented here have shown that for exothermal reactions multiple steady states may occur over a range of Thiele moduli d>. Efficient numerical techniques have been presented as MATLAB programs that solve singular two-point boundary value problems. 

Here we consider a spherical catalyst pellet with negligible intraparticle mass- and negligible heat-transfer resistances. Such a pellet is nonporous with a high thermal conductivity and with external mass and heat transfer resistances only between the surface of the pellet and the bulk fluid. Thus only the external heat- and mass-transfer resistances are considered in developing the pellet equations that calculate the effectiveness factor rj at every point along the length of the reactor. 

The catalyst pellets and the processes taking place on them represent the heart of this important and troublesome reactor. Modem catalysts for this reaction are usually non-porous with active material coating the external surface of the support pellets. Only few steady state cases are presented in order to show the complexity of the behaviour of the catalyst pellets. The behaviour is quite complex although the governing mathematical equations are simple. The only mass and heat transfer resistances in this case are the external mass and heat transfer resistances which are evaluated using J-factor correlations. The effect of the different parameters on the effectiveness factors are shown on the effectiveness factors vs. bulk temperature diagrams. 

The boundary conditions at the external surface of the catalyst are T = Tsurface and Ca = Ca surface, and A effeciive is the effective thermal conductivity of the composite catalyst structure (i.e., 1.6 x 10 J/cm s K for alumina). Initially, the surface temperature and concentration of reactant A in Uie vicinity of a single isolated catalytic peUet are chosen to match the inlet values to the packed reactor. If external mass and heat transfer resistances are minimal, then bulk gas-phase temperature and reactant concentration at each axial position in the reactor represent the characteristic quantities that should be used to calculate the intrapellet Damkohler number for nth-order chemical kinetics ... 

The first step in heterogeneous catalytic processes is the transfer of the reactant from the bulk phase to the external surface of the catalyst pellet. If a nonporous catalyst is used, only external mass and heat transfer can influence the effective rate of reaction. The same situation will occur for very fast reactions, where the reactants are completely exhausted at the external catalyst surface. As no internal mass and heat transfer resistances are considered, the overall catalyst effectiveness factor corresponds to the external effectiveness factor,... 

The external mass and heat transfer resistances are often different on the laboratory scale than on the industrial scale. Therefore, it is inevitable that the mass and heat transfer effects should be taken into account in both reactor models and that the determined kinetic parameters should deseribe the rates of the intrinsic chemical reactions. 

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

There have been many studies of the effect of boundary films on mass and heat transfer to single pellets and in packed beds, including the work of Ranz and Marshall 27 and Dwivedi and Upadhey(28). Other theories of mass and heat transfer are discussed in Volume 1, Chapter 10, although only the steady-state film-theory is considered here. It is assumed that the difference in concentration and temperature between the bulk fluid and the external surface of a pellet is confined to a narrow laminar boundary-layer in which the possibility of accumulation of adsorbate or of heat is neglected. 

Mass and heat transfer between the bulk fluid phase and the external catalyst surface can have an affect on reaction rates, and hence the selectivity, because of modified concentration and temperature driving forces. Such effects are unimportant for porous catalysts, but are significant for catalysis by non-porous metallic gauzes (for example, in NH3 oxidation referred to in Sect. 6.1.1). 

Before we proceed with quantitative illustrations, let us consider the qualitative effect of external resistances on reaction rates and summarize the available information for mass- and heat-transfer coefficients (Sec. 10-2). 

Essentially all of the surface, of porous catalyst pellets is internal (see page 295). Reaction and mass and heat transfer occur simultaneously at any position within the pellet. The resulting intrapellet concentration and temperature gradients cause the rate to vary with position. At steady state the average rate for a whole pellet will be equal to the global rate at the location of the pellet in the reactor. The concentration and temperature of the bulk fluid at this location rhay not be equal to those properties at the outer surface of the pellet. The effect of such external resistances can be accounted for by the procedures outlined in Chap. 10. The objective in the present chapter is to account for internal resistances, that is, to evaluate average rates in terms of the temperature and concentration at the outer surface. Because reaction and transport occur simultaneously, differential... 

In most investigations concerning the reactor modelling, simple pseudohomogeneous (t = 1) reactor models were used. The effect of external and internal mass and heat transfer resistances on the effectiveness factors using realistic complex reaction network has not been widely investigated. The simple linear kinetics proposed by... 

The governing mass and heat balance equations were derived in section 5.1.9 which simulate the concentration and temperature gradient between the bulk fluid and the external surface of the catalyst pellet. The effectiveness factors which represent the ratios of the observed actual rates of reactions to the intrinsic reactions rates where there is no mass and heat transfer resistances are computed for different reactions and different components. 

In the heterogeneous model for the high temperature shift converter, the effectiveness factor accounts for the external and the intraparticle mass and heat transfer resistances (e.g. Satterfield and Roberts, 1968 Hutchings and Carberry, 1966 Petersen et ai, 1970 Chu and Hougen, 1972) and is multiplied by the rate of reaction at bulk conditions to get the actual rate of reaction. 

The rates at which chemical transformations take place are in some circumstances strongly influenced by mass and heat transfer processes (see Sections 12.3 to 12.5). In the design of heterogeneous catalytic reactors, it is essential to utilize a rate expression that takes into account the influence of physical transport processes on the rate at which reactants are converted to products. Smith (94) has popularized the use of the term global reaction rate to characterize the overall rate of transformation of reactants to products in the presence of heat and mass transfer limitations. We shall find this term convenient for use throughout the remainder of the chapter. Global rate expressions then include both external heat and mass transfer effects on the reaction rate and the efficiency with which the internal... 

For reactions that are catalyzed by solid porous catalyst particles, the sequence of elementary steps may include adsorption on the catalyst surface of one or more reactants and/or desorption of one or more products. In that case, a Langmuir-Hinshelwood (LH) kinetic equation is often found to fit the experimental kinetic data more accurately than the power-law expression of Eq. (6.19). The LH formulation is characterized by a denominator term that includes concentrations of certain reactants and/or products that are strongly adsorbed on the catalyst. The LH equation may also include a prefix, ti, called an overall effectiveness factor that accounts for mass and heat transfer resistances, both external and internal, to die catalyst particles. As an example, laboratory kinetic data for the air-oxidation of SO2 to SO are fitted well by the following LH equation ... 

The calculated values of temperature and ammonia concentration in the bulk gas and at the catalyst external surface are reported in Table 6.7 for the first catalyst bed of Fig. 6.2 in both axial and radial centrifugal flow. Since radial flow converters are usually filled with smaller-size catalyst particles than the catalyst considered here, from this point of view they are equivalent to axial converters, which are always filled with large-size catalysts to contain pressure drops. It also appears that the effects of mass and heat transfer at the external surface of the catalyst particle are oppositely directed so that they partly compensate for each other. We may conclude that in industrial converters their combined influence on the reaction rate is negligible compared to the inaccuracies inherent in the experimental determination of the intrinsic activity of the catalyst. In any case, interparticle phenomena can be readily incorporated as boundary conditions in the intraparticle problem ... 

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