Surface reactions internal mass transfer

If diffusion of reactants to the active sites in pores is slower than the chemical reaction, internal mass transfer is at least partly limiting and the reactant concentration decreases along the pores. This reduces the reaction rate compared to the rate at external surface conditions. A measure of the reaction rate decrease is the effectiveness factor, r, which has been defined as ... 

A final, obvious but important, caution about catalyst film preparation Its thickness and surface area Ac must be low enough, so that the catalytic reaction under study is not subject to external or internal mass transfer limitations within the desired operating temperature range. Direct impingement of the reactant stream on the catalyst surface1,19 is advisable in order to diminish the external mass transfer resistance. 

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. 

First-order reactions without internal mass transfer limitations A number of reactions carried out at high temperatures are potentially mass-transfer limited. The surface reaction is so fast that the global rate is limited by the transfer of the reactants from the bulk to the exterior surface of the catalyst. Moreover, the reactants do not have the chance to travel within catalyst particles due to the use of nonporous catalysts or veiy fast reaction on the exterior surface of catalyst pellets. Consider a first-order reaction A - B or a general reaction of the form a A - bB - products, which is of first order with respect to A. For the following analysis, a zero expansion factor and an effectiveness factor equal to 1 are considered. 

At catalytically active centers in the center of carrier particles, external mass transfer (film diffusion) and/or internal mass transfer (pore diffusion) can alter or even dominate the observed reaction rate. External mass transfer limitations occur if the rate of diffusive transport of relevant solutes through the stagnating layer at a macroscopic surface becomes rate-limiting. Internal mass transfer limitations in porous carriers indicate that transport of solutes from the surface of the particle towards the active site in the interior is the slowest step. 

In many industrial reactions, the overall rate of reaction is limited by the rate of mass transfer of reactants and products between the bulk fluid and the catalytic surface. In the rate laws and cztalytic reaction steps (i.e., dilfusion, adsorption, surface reaction, desorption, and diffusion) presented in Chapter 10, we neglected the effects of mass transfer on the overall rate of reaction. In this chapter and the next we discuss the effects of diffusion (mass transfer) resistance on the overall reaction rate in processes that include both chemical reaction and mass transfer. The two types of diffusion resistance on which we focus attention are (1) external resistance diffusion of the reactants or products between the bulk fluid and the external smface of the catalyst, and (2) internal resistance diffusion of the reactants or products from the external pellet sm-face (pore mouth) to the interior of the pellet. In this chapter we focus on external resistance and in Chapter 12 we describe models for internal diffusional resistance with chemical reaction. After a brief presentation of the fundamentals of diffusion, including Pick s first law, we discuss representative correlations of mass transfer rates in terms of mass transfer coefficients for catalyst beds in which the external resistance is limiting. Qualitative observations will bd made about the effects of fluid flow rate, pellet size, and pressure drop on reactor performance. 

Phenyl-1,2-propanedione (Aldrich, 99%) was hydrogenated in a pressurized reactor (Parr 4560, V=300 cm ) in the absence of external and internal mass transfer limitation (verified experimentally). The reactor was equipped with an propeller type stirrer (four blades, propeller diameter 35 mm) operating at stirring rate of 1950 rpm. The hydrogen (AGA, 99.999%) pressure was 6.5 bar and teii ierature was 15 - 35°C. Pt/Al203 (Strem Chemicals, 78-1660) was used as a catalyst. The catalyst mass and liquid volume were 0.15 g and 150 cm, respectively The metal content was 5 wt.%, BET specific surface area 95 m / g, the mean metal particle size 8.3 nm (XRD), dispersion 40% (H2 chemisorption), the mean catalyst particle size 18.2 pm (Malvern). Catalysts were activated under hydrogen flow (100 cm / min) for 2 h at 400°C prior to the reaction. 

When the reaction rates in the monolith channels are sufficiently high, a significant gradient will develop between the concentration at the channel center and that at the catalyst surfaces. This external mass transfer effect must be considered in addition to internal diffusion effects. The rate of external mass transfer at a given value of z is equal to the reaction rate inside the catalyst at steady state ... 

Two types of mass- transfer can be distinguished for catalysis with heterogeneous catalyst particles. External mass transfer refers to molecular transport between the bulk reaction mixture and the surface of the enzyme particle through a boundary layer. Internal mass transfer is the molecular transport inside the solid enzyme phase. Internal mass transfer occurs within the pores of the catalyst particle to and from the particle surface. Figure 4.9-4 illustrates the definitions of external and internal mass transfer. 

Chemical vapor deposition (CVD) of tetraethoxysilane on HZSM5 was performed stepwise under well-controlled, mild conditions. Several test reactions were performed over the series of modified samples. Under mild conditions, CVD follows first order kinetics with respect to uncovered external sites on the zeolite crystals. The external surface is homogeneous with regard to both CVD and catalytic activity. Reactions, which are controlled by strong internal mass transfer restrictions, do respond in a way, which indicates that CVD causes pore mouth plugging rather than pore mouth narrowing. 

In general, the thickness of the catalytic layer is kept sufficiently small to avoid the influence of internal mass transfer on the kinetics. In this way, only the transfer of the reactants from the bulk of the fluid to the catalytic wall and the reaction rate per unit of the outer surface of the catalytic layer must be considered. 

In fluid-solid systems, the reaction takes place on the catalyst surface. Prior to this, the reactant molecules have first to reach the catalyst surface and, therefore, the rate of mass transfer is an important operational parameter (Figure 15.3). Two types of mass transfer need to be considered in fluid-solid reactions external and internal mass transfer. In particular, internal mass transfer limitations should be avoided, since they more often limit the performance of the reactor and more strongly influence the product selectivity. The internal mass transfer is characterized by an effectiveness factor, q, defined as the ratio of the observed reaction rate to that at constant concentration throughout the catalyst layer. To ensure an effectiveness factor of q > 0.95 in an isothermal catalyst layer, the following criterion must be fulfilled [16] ... 

Transport phenomena often accompany processes conducted in reactors with a catalyst bed. Included are internal and external diffusion, and internal and external energy transfer. Chemical reactions taking place on the surface of non-porous catalyst grains usually meet a resistance in a form of an external mass or energy transfer, whereas the internal mass transfer and an external energy transfer most often accompany non-isodiermal processes in porous grains. 

Since the reactant concentrations along the pores and within the particles are lower than the external surface concentrations, the overall effect of internal mass transfer resistances is to reduce the actually observed global rate below that measured at exterior surface conditions. It can be stated for isothermal effectiveness factors that r]concentration profile showing the pore diffusion-affected surface reaction is labeled as II in Figure 2.3. 

Although the reaction rate is nth order in the absence of internal mass transfer limitations, the order determined from global rate data affected by pore diffusion will be ((n -t l)/2] instead of the true order of the surface reaction, for example, 3/2 instead of 2. The intrinsic reaction order will be observed only when n = 1. 

Coupling of surface reaction rate and internal mass transfer 53... 

A detailed surface-reaction mechanism was used for the example system presented here, the partial oxidation of methane over rhodium (Deutschmann et al., 2001). The mechanism includes 20 species and 38 reactions. It can be imported into FLUENT in the format of the CHEMKIN database. The mean-field approximation was applied for modeling the surface chemistry (Section 2). In these simulations, the influence of the internal mass transfer—in contrast to the SFR models discussed above— was not directly covered by the employed CFD code but estimated by adapting the active catalytic surface area by an effectiveness factor. No gas-phase reaction mechanism was employed, as it was already shown in the literature that reactions in the gas phase can be neglected for the given operational conditions (Beretta et al., 2011 Bitsch-Larsen et al., 2008 Deutschmann and Schmidt, 1998 Veser and Frauhammer, 2000). 

Single Cylindrical Pore In contrast to the interplay of chemical reaction with interfacial mass transfer, a reaction at the walls of the pores of a solid catalyst and the internal mass transfer by pore diffusion are not consecutive processes. For a single cylindrical pore of length L and a reactant A diffusing into the pore, where a first-order reaction takes place at the pore surface, we obtain ... 

A catalytic gas-liquid reaction is carried out in a slurry reactor with small catalyst particles, for which the internal mass transfer resistance is negligible. Mixing in the reactor is inefficient, and thus some external mass transfer resistance remains at the outer surfaces of the catalyst particles. The overall stoichiometry is given by... 

To determine if internal mass transfer is important, one performs the reaction using several different sized catalyst pellets, all with the same surface area per unit volume. As the catalyst particle size increases, the importance of internal mass transfer also increases. If the particles are small enough, internal mass transfer will become unimportant. As shown in Figure 6.14, a graph is obtained which is similar to that obtained for external mass transfer, except the kinetic regime is now found to occur at small catalyst particles. 

This BVP introduces several new issues (1) nonCartesian (spherical) coordinates, (2) more than one coupled PDE, and (3) a BC at r = 0 that specifies the local value of the gradient (a von Neumann-type boundary condition). Also, experience tells us that when internal mass transfer resistance is strong, reaction only occurs within a thin layer near the surface over which the local concenUation of A drops rapidly to zero. Thus, we use a computational... 

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