Mass and Heat Transfer in Porous Catalysts

The porosimetry method permits the study of porous structures in a wider pore-size range than does the method of capillary condensation. The two methods do not always agree but porosimetry is better for sizes of 10 nm and higher, whereas the capillary condensation method is more suitable for sizes below 10 nm. A more direct overview of the pore structure of catalysts is obtained by using the stereoscan electron microscope [16]. 

When a chemical reaction takes place inside a porous catalyst, all reactants and products must find their way to and from the internal catalytically active surfaces. This transport can strongly influence the apparent reaction rates and selectivity, hence various mass transport models have been developed. Some of the best known and used models and the basic principles behind these models are described in this chapter. Since only little systematic information is available about transport in liquids, the discussion is mainly concerned gaseous mixtures. 

Transport of molecules of any gaseous species in pores can be hindered by encounters with the wall of the pores and is influenced by collisions between molecules (also of other species). 

The relative frequency of the intermolecular collisions and collisions between molecules and the pore wall can be characterized by the ratio of the length of the mean free path A and the equivalent pore diameter dt = 2rf This ratio determines the flow regime and is called the Knudsen number Kn  

The mean free path A is the average distance traveled by a molecule between successive collisions [17]. For a single gas and assuming the molecules are rigid spheres of diameter d, A is given by 

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Most of the actual reactions involve a three-phase process gas, liquid, and solid catalysts are present. Internal and external mass transfer limitations in porous catalyst layers play a central role in three-phase processes. The governing phenomena are well known since the days of Thiele [43] and Frank-Kamenetskii [44], but transport phenomena coupled to chemical reactions are not frequently used for complex organic systems, but simple - often too simple - tests based on the use of first-order Thiele modulus and Biot number are used. Instead, complete numerical simulations are preferable to reveal the role of mass and heat transfer at the phase boundaries and inside the porous catalyst particles. 

The ratio of the observed reaction rate to the rate in the absence of intraparticle mass and heat transfer resistance is defined as the elFectiveness factor. When the effectiveness factor is ignored, simulation results for catalytic reactors can be inaccurate. Since it is used extensively for simulation of large reaction systems, its fast computation is required to accelerate the simulation time and enhance the simulation accuracy. This problem is to solve the dimensionless equation describing the mass transport of the key component in a porous catalyst[l,2]... 

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... 

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). 

The existence of radial temperature and concentration gradients means that, in principle, one should include terms to account for these effects in the mass and heat conservation equations describing the reactor. Furthermore, there should be a distinction between the porous catalyst particles (within which reaction occurs) and the bulk gas phase. Thus, conservation equations should be written for the catalyst particles as well as for the bulk gas phase and coupled by boundary condition statements to the effect that the mass and heat fluxes at the periphery of particles are balanced by mass and heat transfer between catalyst particles and bulk gas phase. A full account of these principles may be found in a number of texts [23, 35, 36]. 

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. 

Two other crucial factors are mass transfer and heat transfer. In Chapter 3 we assumed that the reactions were homogeneous and well stirred, so that every substrate molecule had an equal chance of getting to the catalytic intermediates. Here the situation is different. When a molecule reaches the macroscopic catalyst particle, there is no guarantee that it will react further. In porous materials, the reactant must first diffuse into the pores. Once adsorbed, the molecule may need to travel on the surface, in order to reach the active site. The same holds for the exit of the product molecule, as well as for the transfer of heat to and from the reaction site. In many gas/solid systems, the product is hot as it leaves the catalyst, and carries the excess energy out with it. This energy must dissipate through the catalyst particles and the reactor wall. Uneven heat transfer can lead to hotspots, sintering, and runaway reactions. 

The quantity (RA) can be further elaborated if interface mass and heat transfer coefficients are known, and with the theory of mass transfer with reaction inside porous catalysts as treated in Chapters 6 and 7 ... 

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... 

The lumped parameter approximation for porous catalyst pellets represents, in the majority of cases, a gross simplification that needs to be justified thoroughly before being used in simulating industrial gas solid catalytic systems. Usually when intraparticle mass and heat transfer resistances are not large this approximation can be used in two ways ... 

The heart of the catalytic reactor is the catalyst pellet itself. This in quantitative terms involves the rates of mass and heat transfer between the bulk of the fluid and the surface of the catalyst pellet, the intraparticle mass and heat transfer within the tortuous structure of the pellet (in the case of the porous catalyst pellet) as well as the heart of the catalyst pellet behaviour itself which is the intrinsic rate of reaction (i.e. the rate of reaction in terms of the local concentration and temperature after these variables have been modified from the bulk conditions values through the mass and heat transfer resistances). The reaction kinetics include the effect of both the surface reaction and the chemisorption in an integrated form as explained earlier. 

Chapter 3 dealt with the problem of the reaction kinetics for different gas-solid reactions, while chapter 5 dealt with the mass and heat transfer problems for porous as well as non-porous catalyst pellets. In chapter 5 different degrees of complexities and rigor were used. In chapter 5, the analysis started with the simplest case of non-porous catalyst pellets where the only mass and heat transfer Coefficients are those at the external surface which depend mainly on the flow conditions around the catalyst pellet and the properties of the reaction mixture. It was shown clearly that j-factor correlations are adequate for the estimation of the external mass and heat transfer coefficients (k, h) associated with these resistances. For the porous catalyst pellets different models with different degrees of rigor have been used, starting from the simplest case of Fickian diffusion with constant diffusivity, to the rigorous dusty gas model based on the Stefan-Maxwell equations for multicomp>onent diffusion. 

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. 

Even though most solid catalysts are porous bodies, few research reports have been concerned with the relationships between catalytic activity and pore structure. Chemical engineers are now studying the relationships between mass and heat transfer and the pore structure of catalysts used in reactor devices. The usual models of pore structure, however, are too simple to provide fundamental knowledge of the catalyst. The pore structure of a catalyst is related not only to the dispersion state of the solid but also to its surface structure, and so we believe that a study of the porous structure of a solid catalyst is an important fundamentgil research. 

In any catalytic system not only chemical reactions per se but mass and heat transfer effects should be considered. For example, mass and heat transfer effects are present inside the porous catalyst particles as well as at the surrounding fluid films. In addition, heat transfer from and to the catalytic reactor gives an essential contribution to the energy balance. The core of modelling a two-phase catalytic reactor is the catalyst particle, namely simultaneous reaction and diffusion in the pores of the particle should be accounted for. These effects are completely analogous to reaction-diffusion effects in liquid films appearing in gas-liquid systems. Thus, the formulae presented in the next section are valid for both catalytic reactions and gas-liquid processes. 

THERMAL ENERGY BALANCE IN MULTICOMPONENT MIXTURES AND NONISOTHERMAL EFFECTIVENESS FACTORS VIA COUPLED HEAT AND MASS TRANSFER IN POROUS CATALYSTS... 

Explain very briefly the following trends that are predicted for coupled heat and mass transfer in porous catalysts when the chemical reaction is first-order and exothermic. 

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 ... 

In the previous chapters tve discussed the influence of internal mass and heat transfer by neglecting external transport phenomena. Hence, we assumed that concentrations and temperature at the outer surface of the catalyst particle and the bulk of the fluid are the same. But this assumption is not justified under certain conditions and concentration and temperature profiles inside and outside the porous catalyst must be considered. 

Application of the pressure-based solver via the SIMPLE algorithm can be explained in the context of transport equations that quantify hydrodynamics, mass, and heat transfer inside a single porous catalyst-coated channel of a monolith reactor shown in Figure 11.3 [17]. The relevant transport equations are given in their generalized form as follows ... 

Chemical engineers have to consider a wide range of scale-up dimensions (e.g., for solid catalysts). Starting with molecules and active sites of a catalyst with dimensions in the nanometer range, one has to consider the porous structure of particles and the mass and heat transfer processes involved on the micro- to millimeter range. Finally, the design of a reactor up to several hundred m in size has to be realized. 

The catalytic oxidation of ammonia is one of the rare cases where a non-porous solid catalyst is used. To calculate the ammonia conversion and the temperature of the wire we have to recall the equations for the interaction of external mass and heat transfer and a chemical reaction derived in Section 4.5.3. Initially, we consider the ammonia oxidation on a single Pt wire for cross-flow of the gas. 

For purposes of kinetic modeling, it is important to collect reaction rate data that are free from experimental artifacts. Various types of reactors can be used to acquire these data, and the first portion of this chapter discusses these reactors. The second half of the chapter describes models which introduce the effect of mass and heat transfer gradients on the observed reaction rate, and it then provides different methods to evaluate the presence or absence of such artifacts in both gas-phase and liquid-phase reactions involving porous catalysts. 

For the reactions catalyzed by porous heterogeneous catalysts, the phase state of the reaction mixtures confined within the pores of the catalysts can be significantly different from that of the bulk, and this is poorly understood. Therefore, many factors that control the reactions, such as the mass and heat transfer and the interaction between the reactants or products with the catalysts in the pores, are insufficiently known. 

The influence which the simultaneous transfer of heat and mass in porous catalysts has on the selectivity of first-order concurrent catalytic reactions has recently been investigated by 0stergaard(27). As shown previously, selectivity is not affected by any limitations due to mass transfer when the process corresponds to two concurrent first-order reactions ... 

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