Diffusion effects internal

Weisz, P. B. and Hicks, J. S., The behaviour of porous catalyst particles in view of internal mass and heat diffusion effects, Chem. Eng. Sci., 17, 265-275 (1962). 

Riber, H. H. and Wetzel, R. G. (1987). Boundary layer and internal diffusion effects on phosphorus fluxes in lake periphyton, Limnol. Oceanogr., 32, 1181-1194. 

J. H. Nam and M. Kaviany. Effective diffusivity and water-saturation distribution in single- and two-layer PEMEC diffusion medium. International Journal of Heat Mass Transfer 46 (2003) 4595-4611. 

J. Ramousse, S. Didierjean, O. Lottin, and D. MaUlet. Estimation of the effective thermal conductivity of carbon felts used as PEMFC gas diffusion layers. International Journal of Thermal Science 47 (2008) 1-6. 

No experiments with variation in particle size of the silica gel have been done to study intraparticle diffusion effects. In silica gel such diffusion would be only through the pores (analogous to the macropores of a polystyrene) since the active sites lie on the internal surface. The silica gel used by Tundo had a surface area of 500 m2/g and average pore diameter of 60 A.116). Phosphonium ion catalyst 28 gave rates of iodide displacements that decreased as the 1-bromoalkane chain length increased from C4 to Cg to C16, The selectivity of 28 was slightly less than that observed with soluble catalyst hexadecyltri-n-butylphosphonium bromide U8). Consequently the selectivity cannot be attributed to intraparticle diffusional limitations. 

Here, we consider the general case of a porous catalyst, where the internal diffusion effect is included in the effectiveness factor (//,). 

In the spatially ID model of the monolith channel, no transverse concentration gradients inside the catalytic washcoat layer are considered, i.e. the influence of internal diffusion is neglected or included in the employed reaction-kinetic parameters. It may lead to the over-prediction of the achieved conversions, particularly with the increasing thickness of the washcoat layer (cfi, e.g., Aris, 1975 Kryl et al., 2005 Tronconi and Beretta, 1999 Zygourakis and Aris, 1983). To overcome this limitation, the effectiveness-factor concept can be used in a limited extent (cf. Section III.D). Despite the drawbacks coming from the fact that internal diffusion effects are implicitly included in the reaction kinetics, the ID plug-flow model is extensively used in automotive industry, thanks to the reasonable combination of physical reliability and short computation times. 

The internal diffusion effects cannot be simply included into the reaction kinetics particularly in the case of parametric studies on the varying washcoat thickness. 

When the internal diffusion effects are considered explicitly, concentration variations in the catalytic washcoat layer are modeled both in the axial (z) and the transverse (radial, r) directions. Simple slab geometry is chosen for the washcoat layer, since the ratio of the washcoat thickness to the channel diameter is low. The layer is characterized by its external surface density a and the mean thickness <5. It can be assumed that there are no temperature gradients in the transverse direction within the washcoat layer and in the wall of the channel because of the sufficiently high heat conductivity, cf., e.g. Wanker et al. 

In the laboratory experiments, DOC monolith samples (length 7.5 cm, diameter 1.4 cm) with rather thin catalyst layer coating ( 25 pm) were employed to minimize the internal diffusion effects. The samples were placed into a thermostat to suppress the formation of temperature-gradients along the channels. In the course of each experiment, the temperature of the inlet gas and the monolith sample was increased at a constant rate of /min within the range of 300-800 K. The exhaust gases at the inlet of the converter were simulated by synthetic gas mixtures with defined compositions and flow rates (cf. individual figure captions all gas mixtures contained 6% C02 and 6% H20). 

Applied forces can also induce mass flow between interfaces. When tensile forces are applied, atoms from an unloaded free surface will tend to diffuse toward internal interfaces that are normal to the loading direction this redistribution of mass causes the system to expand in the tensile direction. Applied compressive forces can superpose with capillary forces to cause shrinkage. In this chapter, we introduce a framework to treat the combined effects of capillary and applied mechanical forces on mass redistribution between surfaces and internal interfaces. 

There is an international standard, ISO 691455 which covers both the continuous and intermittent procedures plus the simplified intermittent method. Strip test pieces are used, 1 mm thick to minimise oxygen diffusion effects. Measurement at a series of temperatures is recommended and results are presented in graphical form but no consideration is given to interpretation. British Standards did not accept this revision of ISO 6914 and BS 903 Part A5256 is identical to the 1985 ISO method. The revision was not accepted in the UK because mistakes in handling comments resulted in inconsistencies. As an example, the title is now stress relaxation but a note says that this term is avoided ... 

Ma et al. [104] attributed a decrease in diffusivity with an increase in initial concentration to pore diffusion effects. Because zeolites are bi-dispersed sorbents, both surface and pore diffusions may dominate different regions. In micropores, surface diffusion may be dominant, while pore diffusion may be dominant in macropores. This, therefore, supports the use of a lumped parameter (De). To explore further the relative importance of external mass transfer vis-a-vis internal diffusion, Biot number (NBl — kf r0/De) was considered. Table 9 summarizes the NBi values for the four initial concentrations. The NBi values are significantly larger than 100 indicating that film diffusion resistance was negligible. 

The molecular diffusivity D must be replaced by an effective diffusivity De because of the complex internal structure of the catalyst particle which consists of a multiplicity of interconnected pores, and the molecules must take a tortuous path. The effective distance the molecules must travel is consequently increases. Furthermore, because the pores are very small, their dimensions may be less than the mean free path of the molecules and Knudsen diffusion effects may arise Equation 10.170 is solved in Volume 1 to give equation 10.199 for a catalyst particle in the form of a flat platelet... 

The above kinetics is valid for small particles when the process rate is controlled by the chemical reaction at the surface. Diffusion effects should be accounted for large-size particles. Table 5.8 presents the calculation of the effectiveness factor [24] for spherical particles of 6 mm diameter and a mixture 1 3 phenol/hydrogen at 2 bar and 423 K. Other data are BET internal surface S = 40m2/g, mean pore radius 150 A, catalyst density pp = 1000kg/m3, particle void fraction = 0.3,... 

In fixed bed reactors, however, the catalyst pellet diameter has to be at least 0.1 mm in order to avoid an excessive pressure drop over the bed. With such a diameter internal diffusion effects can be important. 

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 problem of the optimal particle shape and size is crucial for packed bed reactor design. Generally, the larger the particle diameter, the cheaper the catalyst. This is not usually a significant factor in process design - more important are the internal and external diffusion effects, the pressure drop, the heat transfer to the reactor walls and a uniform fluid flow. 

Effectiveness factors for a first-order reaction in a spherical, nonisothermal catalysts pellet. (Reprinted from R B. Weisz and J. S. Hicks, The Behavior of Porous Catalyst Particles in View of Internal Mass and Heat Diffusion Effects, Chem. Eng. Sci., 17 (1962) 265, copyright 1962, with permission from Elsevier Science.)... 

Teramoto M and Matsuyama H. Effect of facilitated diffusion in internal aqueous droplets on effective diffusivity and extraction rate of phenol in emulsion liquid membranes. J Chem Eng Jpn 1986 19 469 72. 

First, let us examine the criteria applicable to diffusion effects in the gas phase, i.e., the spaces and channels over or between catalyst particles. When the catalyst solids are not porous but have all their active surfaces located in their geometric contours, diffusion in the outside gas space will be the only existing diffusion problem. However, even when the catalyst particles are subject to internal diffusion effects, the external gas space conditions need still be examined separately. The criteria will be examined assuming the reaction to be of first order, keeping in mind that deviation from exact first-order kinetics does not alter the diffusion picture by considerable magnitudes, as was seen above. 

An experimental test to verify the absence of significant concentration gradients inside the catalyst particle is based on the inverse proportional relation between the effectiveness factor and the particle diameter for strong internal diffusion limitations. Hence, a measured rate that is independent of the particle size indicates that internal diffusion limitations can be neglected. Care should be taken to avoid artefacts. External heat transfer effects also depend on particle size and for exothermic reactions might balance the internal diffusion effects. Furthermore, if the catalyst particle consists of a support with a non-uniformly distributed active phase, crushing and sieving to obtain smaller particles is hazardous. 

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