Wakao-Smith random pore model

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]. 

Accordingly, in addition to rate parameters and reaction conditions, the model requires the physicochemical, geometric and morphological characteristics (porosity, pore size distribution) of the monolith catalyst as input data. Effective diffusivities, Deffj, are then evaluated from the morphological data according to a modified Wakao-Smith random pore model, as specifically recommended in ref. [63[. 

IS a modified Damkohler number = A nhsCno ts the dimensionless NH3 adsoiption constant, D, is the molecular diffusivity of species 1 is the effective intraporous diffusivity of species i evaluated according to the Wakao-Smith random pore model [411. Equation (4) is taken from Ref. 39. Equations (6)-(8) provide an approximate analytical solution of the intraporous diffusion-reaction equations under the assumption of large Thiele moduli (i.e., the concentration of the limiting reactant is zero at the centerline of the catalytic wall) the same equations are solved numencally in Ref. 36. 

Computed from the random pore model of Wakao and Smith (22) and given here at 101.3 kPa and 723 K. 

Wakao and Smith [20] originally developed the random pore model to account for the behaviour of bidisperse systems which contain both micro- and macro-pores. Many industrial catalysts, for example, when prepared in pellet form, contain not only the smaller intraparticle pores, but also larger pores consisting of the voids between compressed particles. Transport within the pellet is assumed to occur through void regions... 

Different theoretical models applied to this pore size distribution can give relatively large variations of the calculated effective diffusivity value (DelT). The most commonly used approximations are (i) random-pore model (Wakao and Smith, 1962) using two characteristic transport pores (micropores ji and macropores M)... 

If data are available on the catalyst pore- structure, a geometrical model can be applied to calculate the effective diffusivity and the tortuosity factor. Wakao and Smith [36] applied a successful model to calculate the effective diffusivity using the concept of the random pore model. According to this, they established that ... 

For the actual pore-size distribution to be taken into account, the above relations for single pore sizes are usually assumed to remain true, and they are combined with the pore size distribution information. The random pore" model, or micromacro pore model, of Wakao and Smith [57,58]) is useful for compressed particle type pellets. The pellet pore-size distribution is, somewhat arbitrarily, broken up into macro (M) and micro (g) values for the pore volume and average pore radius / m and s. (often a pore radius of 1(X) A is used as the dividing point). Based on random placement of the microparticles within the macropellet pores. 

The following correlation for the tortuosity factor is proposed by Wakao and Smith (1962) using a random pore model ... 

The two major pore models that have been used extensively over the years for practical purposes are the parallel-pore model proposed by Wheeler in 1955 [5, 9] and the random-pore model proposed by Wakao and Smith in 1962 [34]. Among the more recent advanced models are the parallel cross-linked pore model [35] and pore-network models [36, 37]. 

The random pore model, or macro- micro-pore model, of Wakao and Smith [1962, 1964] is intended for application to pellets manufactured by compression of small particles. The void fraction and pore radius distributions are each replaced by two averaged values 8m, I m for the macro and for the micro distribution (often a pore radius of -100 A is used as the dividing point between macro and micro). The particles which contain the micro-pores are randomly positioned in the pellet space. The interstices are the macro-pores of the pellet (see Fig. 3.5.2.1-1). The diffusion flux consists of three parallel contributions the first through the macro-pores, the second through the micro-pores and the third through interconnected macro-micro-pores in which the dominant resistance lies in the latter. The contributions to the diffusivity are added up to yield ... 

Figure 14.1 Random-pore model. (Wakao and Smith 1962 reprinted with permission from Chemical Engineering Science. Copyright by Pergamon Press, Inc.)...

The random pore model of Wakao and Smith (1962) for a bidisperse pore structure may also be applied in order to estimate De. It was supposed that the porous solid is composed of stacked layers of microporous particles with voids between the particles forming a macroporous network. The magnitude of the micropores and macropores becomes evident from an experimental pore size distribution analysis. If Dm and Dp are the macropore and micropore diffusivities calculated from equations (4.9) and (4.10), respectively, the random pore model gives the effective diffusivity as... 

A less detailed model led Wheeler [1955] to a value of 2. Wakao and Smith [1962] obtained values between 2.5 and 3.5 for macro-micro pore networks. Feng and Stewart [1973] and also Dullien [1975] obtained a value of 3 for perfectly interconnecting pores with completely random orientation. Experimental values reported by Feng and Stewart [1973] for alumina pellets are 4.6 by Dumez and Froment [1976] for a chromia/alumina catalyst, 5 by De Deken et al. [1982] for a Ni/AhOs steam reforming catalyst, 4.4 to 5.0 by Satterfield and Caddie [1968], from 2.8 to 7.3 and by Patel and Butt [1974] from 4 to 7 for a nickel/molbydate catalyst. Note that the above calculation does not account for dead end pores and that the pores are considered to be strictly... 

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