Mass transfer in porous catalysts

Reaction and Mass Transfer in Porous Catalyst Structures... 

If the total pressure p is 1 atm and absolute temperature T is in the vicinity of 298 K, then kinetic theory predicts ordinary molecular diffusivities on the order of 0.1 cm /s, which are comparable to Knudsen diffusivities if the average pore radius is 0.1 xm (i.e., 10 A) and molecular weights are about 50 Da. When pore radii are larger than 1 xm, ordinary molecular diffusion provides the dominant resistance to mass transfer in porous catalysts at standard temperature... 

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. 

This section is concerned with analyses of simultaneous reaction and mass transfer within porous catalysts under isothermal conditions. Several factors that influence the final equation for the catalyst effectiveness factor are discussed in the various subsections. The factors considered include different mathematical models of the catalyst pore structure, the gross catalyst geometry (i.e., its apparent shape), and the rate expression for the surface reaction. 

Surface diffusion is yet another mechanism that is invoked to explain mass transport in porous catalysts. An adsorbed species may be transported either by desorption into the gas phase or by migration to an adjacent site on the surface. It is this latter phenomenon that is referred to as surface diffusion. This phenomenon is poorly understood and the rate of mass transfer by this process cannot be predicted with a reasonable degree of accuracy. Classic discussions of this subject are presented by Satterfield (14) and Barrer (15), while modem animations are contained in Wikipedia (16). 

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 reactions are still most often carried out in batch and semi-batch reactors, which implies that time-dependent, dynamic models are required to obtain a realistic description of the process. Diffusion and reaction in porous catalyst layers play a central role. The ultimate goal of the modehng based on the principles of chemical reaction engineering is the intensification of the process by maximizing the yields and selectivities of the desired products and optimizing the conditions for mass transfer. 

Bulk or forced flow of the Hagan-Poiseuille type does not in general contribute significantly to the mass transport process in porous catalysts. For fast reactions where there is a change in the number of moles on reaction, significant pressure differentials can arise between the interior and the exterior of the catalyst pellets. This phenomenon occurs because there is insufficient driving force for effective mass transfer by forced flow. Molecular diffusion occurs much more rapidly than forced flow in most porous catalysts. 

The Effectiveness Factor Analysis in Terms of Effective Diffusivities First-Order Reactions on Spherical Pellets. Useful expressions for catalyst effectiveness factors may also be developed in terms of the concept of effective diffusivities. This approach permits one to write an expression for the mass transfer within the pellet in terms of a form of Fick s first law based on the superficial cross-sectional area of a porous medium. We thereby circumvent the necessity of developing a detailed mathematical model of the pore geometry and size distribution. This subsection is devoted to an analysis of simultaneous mass transfer and chemical reaction in porous catalyst pellets in terms of the effective diffusivity. In order to use the analysis with confidence, the effective diffusivity should be determined experimentally, since it is difficult to obtain accurate estimates of this parameter on an a priori basis. 

Mass transfer (continued) in monolith, 27 89 in porous catalyst, 27 60-63, 68 in tubular reactor, 27 79, 82, 87 Mass transport processes, 30 312-318 convective, 30 312-313 diffusive, 30 313-315 selectivity, 30 316... 

The study of the intra-phase mass transfer in SCR reactors has been addressed by combining the equations for the external field with the differential equations for diffusion and reaction of NO and N H 3 in the intra-porous region and by adopting the Wakao-Smith random pore model to describe the diffusion of NO and NH3 inside the pores [30, 44]. The solution of the model equations confirmed that steep reactant concentration gradients are present near the external catalyst surface under typical industrial conditions so that the internal catalyst effectiveness factor is low [27]. 

As with the falling film reactor, the rate of mass transfer to the catalyst goes as R, while the size of the reactor goes as R, so this reactor becomes very inefficient except for very small-diameter tubes. However, we can overcome this problem, not by using many small tubes in parallel, but by allowing the gas and liquid to flow (trickle) over porous catalyst pellets in a trickle bed reactor rather than down a vertical wall, as in the catalytic wall reactor. 

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 (1) and Frank-Kamenetskii (2). Transport phenomena coupled to chemical reactions is not frequently used for complex organic systems. A systematic approach to the problem is presented. 

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 ... 

The starting point of a number of theoretical studies of packed catalytic reactors, where an exothermic reaction is carried out, is an analysis of heat and mass transfer in a single porous catalyst since such system is obviously more conductive to reasonable, analytical or numerical treatment. As can be expected the mutual interaction of transport effects and chemical kinetics may give rise to multiple steady states and oscillatory behavior as well. Research on multiplicity in catalysis has been strongly influenced by the classic paper by Weisz and Hicks (5) predicting occurrence of multiple steady states caused by intrapellet heat and mass intrusions alone. The literature abounds with theoretical analysis of various aspects of this phenomenon however, there is a dearth of reported experiments in this area. Later the possiblity of oscillatory activity has been reported (6). 

While we have for heat and mass transfer in a porous catalyst explicit relations for parameters giving rise to multiple steady states, there is nothing similar developed for the monolithic catalysts so far. Hence we are forced to investigate, for particular conditions, the region of multiple steady states numerically. 

Internal diffusion in porous catalysts, if dominant, also reduces the observed activity of the biocatalyst. The decisive coefficient for mass transfer is the effective diffusion coefficient De((, which is defined in Eq. (5.56), where D0is the diffusion coefficient in solution, e the porosity of the carrier, and t the tortuosity factor. 

The mass-transfer coefficient with a reactive solvent can be represented by multiplying the purely physical mass-transfer coefficient by an enhancement factor E that depends on a parameter called the Hatta number (analogous to the Thiele modulus in porous catalyst particles). 

Heat and mass transfer processes always proceed with finite rates. Thus, even when operating under steady state conditions, more or less pronounced concentration and temperature profiles may exist across the phase boundary and within the porous catalyst pellet as well (Fig. 2). As a consequence, the observable reaction rate may differ substantially from the intrinsic rate of the chemical transformation under bulk fluid phase conditions. Moreover, the transport of heat or mass inside the porous catalyst pellet and across the external boundary layer is governed by mechanisms other than the chemical reaction, a fact that suggests a change in the dependence of the effective rate on the operating conditions (i.e concentration and temperature). 

This chapter is concerned with the mathematical modeling of coupled chemical reaction and heat and mass transfer processes occurring in porous catalysts. It focuses primarily on steady state catalyst operation which is the preferred industrial practice. Stationary operation may be important for the startup and shutdown of an industrial reactor, or with respect to dynamic process control. However, these effects are not discussed here in great detail because of the limited space available. Instead, the interested reader is referred to the various related monographs and articles available in the literature [6, 31, 46-49]. 

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