Effect of diffusion resistance

Various reports can be found in the literature in connection with catalyst deactivation kinetics (Wojchiechowsky, 1968), some of them also taking into account the effects of diffusion resistance (Beeckman and Froment, 1980). 

Figure 9.2 shows the concentration profile for various values of Ly/kv/De. This solution shows that the diffusion resistance causes a concentration profile to exist in the pellet when the reactant cannot diffuse in from the bulk sufficiently rapidly. If the resistance is small due to a large value of De, then the concentration profile becomes flat, while it will behave conversely for a large diffusion resistance. In practice, however, the possible adverse effect of diffusion resistance on the rate of reaction is highly compensated by the enormous increase in surface area of the pores. 

Comparison with Eq. (10-26) shows that the effect of diffusion resistance is to reduce y. 

There is also the possibility to calculate the effect of diffusion resistance directly. 

Pachovsky, R.A. and Wojciechowski, B.W., "Effects of diffusion resistance on gasoline selectivity in Catalytic Cracking", AIChE J., 19, 1121 (1973). 

A microelectrode has been used by Uchida et al. to study lithium deposition in order to minimize the effect of solution resistance [41], They used a Pt electrode (10-30 jum in diameter) to measure the lithium-ion diffusion coefficient in 1 mol L 1 LiC104/PC electrolyte. The diffusion coefficient was 4.7 x 10-6 cm2 s at 25 °C. 

Van Deemter considered peak dispersion results from four spreading processes that take place in a column, namely, the Multi-Path Effect, Longitudinal Diffusion, Resistance to Mass Transfer in the Mobile Phase and Resistance to Mass Transfer in the Stationary Phase. Each one of these dispersion processes will now be considered separately... 

Figure 13 shows the potential and concentration distributions for different values of dimensionless potential under conditions when internal pore diffusion (s = 0.1) and local mass transport (y = 10) are a factor. As expected the concentration and relative overpotential decrease further away from the free electrolyte (or membrane) due to the combined effect of diffusion mass transport and the poor penetration of current into the electrode due to ionic conductivity limitations. The major difference in the data is with respect to the variation in reactant concentrations. In the case when an internal mass transport resistance occurs (y = 10) the fall in concentration, at a fixed value of electrode overpotential, is not as great as the case when no internal mass transport resistance occurs. This is due to the resistance causing a reduction in the consumption of reactant locally, and thereby increasing available reactant concentration the effect of which is more significant at higher electrode overpotentials. 

A gas-solid reaction usually involves heat and mass transfer processes and chemical kinetics. One important factor which complicates the analysis of these processes is the variations in the pore structure of the solid during the reaction. Increase or decrease of porosity during the reaction and variations in pore sizes would effect the diffusion resistance and also change the active surface area. These facts indicate that the real mechanism of gas-solid noncatalytic reactions can be understood better by following the variations in pore structure during the reaction. 

The position of the water table determines the oxygen transport and hence the corrosion rate. The moisture content of soil greater than 20% is deemed to be corrosive (general corrosion of carbon steel) and the value of less than 20% was conducive to pitting corrosion.15 This observation is thought to be related to the diffusion rate of oxygen.16 The general effect of soil resistivity on the corrosivity may be denoted as ... 

The network thermodynamics model has been applied to understand the effects of diffusion coupling in the membrane transport of binary flows. In the formalism of network thermodynamics, a membrane is treated as a sequence of discrete elements called lumps, where both dissipation and storage of energy may occur. These lumps are joined in the bond graphs, and have a resistance R, and capacitance (volume) C, which are defined by... 

The question remains as to when the various diffusion effects really influence the conversion rate in fluid-solid reactions. Many criteria have been developed in the past for the determination of the absence of diffusion resistance. In using the many criteria no more information is required than the diffusion coefficient DA for fluid phase diffusion and for internal diffusion in a porous pellet, the heat of reaction and the physical properties of the gas and the solid or catalyst, together with an experimental value of the observed global reaction rate (R ) per unit volume or weight of solid or catalyst. For the time being the following criteria are recommended. Note that intraparticle criteria are discussed in much greater detail in Chapter 6. 

The classical method of investigation of effects of diffusion on reactions is typically to run a reaction with catalyst particles of various sizes. For zeolites, the resistance of intracrystalline diffusion is normally much larger than that characteristic of molecular diffusion or Knudsen diffusion that could occur in the spaces between the zeolite crystals in a catalyst particle. Thus, the crystal size of the zeolite has to be varied instead of the particle size to determine the effects of diffusion on zeolite-catalyzed reactions. Kinetics of the MTO reaction has been measured with SAPO-34 crystals with identical compositions and sizes of 0.25 and 2.5 pm 89). The methanol conversion was measured as a function of the coke content of the two SAPO-34 crystals in the TEOM reactor. 

This case study clearly illustrates the usefulness of the ZLD-TEOM technique in determining intracrystalline diffusivities in zeolites, provided that effects of other transport resistances such as the surface barrier are eliminated by varying the crystal size of the zeolites. The measured steady-state diffusivity can be directly used for predicting effects of diffusion in reactions catalyzed by zeolites. More important, the TEOM makes it possible to distinguish the deactivation caused by blockage of the active sites and by increased diffusion resistance caused by blockage of cavities or channels by coke. 

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. 

From the assumptions and approximations presented, it is clear that, surface diffusion js Jiot jvell junderstoad. lt is. hope.d that impro.V d -interpretations of surface migration will permit a more accurate assessment of its effect on global rates of reaction. When we consider the effect of intraparticle resistances in Secs. 11-6 to 11-11 we shall suppose that the used is the most appropriate value and includes, if necessary, a surface contribution. 

Three liquids, having bulk solute i concentration [CJp, [C,]e, and [C,]r, constant volumes l-p, and Fr, respectively, are separated by two membranes with the same working area. S. Stirring of bulk liquids is effective in such a way that the aqueous (Zzfe, Zz e) and the organic her) boundary layers become sufficiently thin and constant. Concentration profiles with hydrophobic membranes are demonstrated in Fig. 5.2, while those containing hydrophilic or ion-exchange membranes are in Fig. 5.3. Using the concept of the one-dimensional series of diffusion resistances, and... 

The general definition of the effectiveness factor states that the factor describes the ratio between the real molar flux (A)) and the molar flux (AT) that would be obtained if the reaction proceeded in the absence of diffusion resistance. This ratio is equal to the ratio of observed rate and the rate if the diffusion resistance does not have an influence on reaction rate. 

The deactivating effect of coke can become great if coking is very fast [31]. This is the case with all the porous catalysts, the deactivating effect being more pronounced in the case of diffusion resistance for the desired reaction [32]. Again the effect of coke is... 

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