Mass transport, in porous catalyst

Surface diffusion is yet another mechanism that is often 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... 

Several experimental techniques have been developed for the investigation of the mass transport in porous catalysts. Most of them have been employed to determine the effective diffusivities in binary gas mixtures and at isothermal conditions. In some investigations, the experimental data are treated with the more refined dusty gas model (DGM) and its modifications. The diffusion cell and gas chromatographic methods are the most widely used when investigating mass transport in porous catalysts and for the measurement of the effective diffusivities. These methods, with examples of their application in simple situations, are briefly outlined in the following discussion. A review on the methods for experimental evaluation of the effective diffusivity by Haynes [1] and a comprehensive description of the diffusion cell method by Park and Do [2] contain many useful details and additional information. 

This tutorial paper begins with a short introduction to multicomponent mass transport in porous media. A theoretical development for application to single and multiple reaction systems is presented. Two example problems are solved. The first example is an effectiveness factor calculation for the water-gas shift reaction over a chromia-promoted iron oxide catalyst. The methods applicable to multiple reaction problems are illustrated by solving a steam reformer problem. The need to develop asymptotic methods for application to multiple reaction problems is apparent in this example. 

The described treatment of mass transport presumes a simple, relatively uniform (monomodal) pore size distribution. As previously mentioned, many catalyst particles are formed by tableting or extruding finely powdered microporous materials and have a bidisperse porous structure. Mass transport in such catalysts is usually described in terms of two coefficients, a effective macropore diffusivity and an effective micropore diffusivity. 

Due to short diffusion pathways in the microsystem, the overall mass transport in the phases or the transfer via phase boundaries is often magnitudes higher than in conventional reactor systems. However, with regard to the desired high loadings with catalyst and low cost for fluid compression or pumping, the mass transfer to the catalyst and the mass transport within porous catalyst still has to be effective. As for the heat transport the differentiation between packed bed and wall-coated microreactor is necessary for mass transport considerations. The mass transport in packed bed microreactors is not significantly different to normal tubular packed bed reactors, so that equations like the Mears criteria (Eq. 6) can be used. 

Rates and selectivities of soHd catalyzed reactions can also be influenced by mass transport resistance in the external fluid phase. Most reactions are not influenced by external-phase transport, but the rates of some very fast reactions, eg, ammonia oxidation, are deterrnined solely by the resistance to this transport. As the resistance to mass transport within the catalyst pores is larger than that in the external fluid phase, the effectiveness factor of a porous catalyst is expected to be less than unity whenever the external-phase mass transport resistance is significant, A practical catalyst that is used under such circumstances is the ammonia oxidation catalyst. It is a nonporous metal and consists of layers of wire woven into a mesh. 

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. 

Whitaker, S, Transport Processes with Heterogeneous Reaction. In Concepts and Design of Chemical Reactors Whitaker, S Cassano, AE, eds. Gordon and Breach Newark, NJ 1986 1. Whitaker, S, Mass Transport and Reaction in Catalyst Pellets, Transport in Porous Media 2, 269, 1987. 

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. 

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... 

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. 

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). 

However, if convective transport of heat and species mass in porous catalyst pellets have to be taken into account simulating catal3dic reactor processes, either the Maxwell-Stefan mass flux equations (2.394) or dusty gas model for the mass fluxes (2.427) have to be used with a variable pressure driving force expressed in terms of mass fractions (2.426). The reason for this demand is that any viscous flow in the catalyst pores is driven by a pressure gradient induced by the potential non-uniform spatial species composition and temperature evolution created by the chemical reactions. The pressure gradient in porous media is usually related to the consistent viscous gas velocity through a correlation inspired by the Darcy s law [21] (see e.g., [5] [49] [89], p 197) ... 

Whitaker S (1987) Mass Transport and Reaction in Catalyst Pellets. Transport in Porous Media 2 269-299... 

Fig. 6 shows the activities of the sulfated zirconium hydroxide and the sulfated calcined zirconia catalyst. In contrast to the activities displayed in the gas-phase reaction, the calcined zirconia catalyst now shows the higher activity. Since the mass transport in the liquid is much slower, the rate of the reaction is now more strongly transport-limited with the catalyst prepared from the more porous zirconium hydroxide. Upon removal of the solid catalyst by filtration the reaction continues also with these two catalysts. 

The overall rate of reaction is equal to the rate of the slowest step in the mechanism. When the diffusion steps (1.2. 6. and 7 in Table 10-2) are very fast compared with the reaction steps (14. and 5), the concentrations in the immediate vicinity of the active sites are indistinguishable from those in the bulk Ouid. In this situation, the transport or diffusion steps do not affect the overall rate of the reaction. In other situations, if the reaction. steps are very fast compared with the diffusion steps, mass transport does affect the reaction rate. In systems where diffusion from the bulk gas or liquid to the catalyst surface or to the mouths of catalyst pores affects the rate, changing the flow conditions past the catalyst should change the overall reaction rate. In porous catalysts, on the other hand, diffusion within the catalyst pores may limit the rate of reaction. Under these circumstances, the overall rate will be unaffected by external flow conditions even though diffusion affects the overall reaction rate. 

Some of the first considerations of the problem of diffusion and reaction in porous catalysts were reported independently by Thiele [E.W. Thiele, Ind. Eng. Chem., 31, 916 (1939)] Damkohler [G. Damkohler, Der Chemie-Ingenieur, 3, 430 (1937)] and Zeldovich [Ya.B. Zeldovich, Acta Phys.-Chim. USSR, 10, 583 (1939)] although the first solution to the mathematical problem was given by Jiittner in 1909 [F. Jiittner, Z. Phys. Chem., 65, 595 (1909)]. Consider the porous catalyst in the form of a flat slab of semi-infinite dimension on the surface, and of half-thickness W as shown in Figure 7.3. The first-order, irreversible reaction A B is catalyzed within the porous matrix with an intrinsic rate (—r). We assume that the mass-transport process is in one direction though the porous structure and may be represented by a normal diffusion-type expression, that there is no net eonveetive transport eontribution, and that the medium is isotropic. For this case, a steady-state mass balance over the differential volume element dz (for unit surface area) (Figure 7.3), yields... 

Besides the physical concepts leading to eqs. (15) to (18), we need one more concept, and that is the law of conservation of mass. Applied to porous catalyst in a steady state of reaction, this law says that the total mass of matter which flows into a pellet or pore (or any region thereof) must equal the mass that flows out. For example, in Fig. 4 the mass of reactants plus products which flows across the plane at M must equal the mass of these which flows across the plane at N. The most important special case is the usual one encountered for catalysts of small pore size in reactors operating at low pressure drops across the reactor. For such catalysts the Poiseuille flow forced through the pellet by the reactor pressure drop will be negligible so that there will be no net transport of mass... 

The concentration and temperature gradients in porous catalyst particles are given by the equations describing the simultaneous mass, heat transport, and reaction within the catalyst particles considering that the reactants diffusion occurs in the liquid phase by virtue of completely internally wetted catalysts ... 

Fig. 15.25 Pathways for future electrocatalyst development for automotive PEMFCs. (a) Thick films or bulk single crystal and polycrystalline catalysts that are ideal for fundamental studies on surface structure and mechanisms these materials need to be modified into (c) and (d) to be applicable to fuel cells, (b) Typical commercial nanoparticles (2-4 nm) on a high-surface-area carbon support used in fuel cells at this time (c) Thin continuous films of catalyst on a support such as carbon nanotubes that may provide a physical porous structure for mass transport in a fuel cell (d) Core-shell catalysts where only the shell eonsists of precious metals and are supported on a typical high-surface-area support [72, 77, 89]...

A dynamic mathematical model of the three-phase reactor system with catalyst particles in static elements was derived, which consists of the following ingredients simultaneous reaction and diffusion in porous catalyst particles plug flow and axial dispersion in the bulk gas and liquid phases effective mass transport and turbulence at the boundary domain of the metal network and a mass transfer model for the gas-liquid interface. 

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