Parallel-path pore model

Desig- nation Nominal Size Surface Area (m /g) Total Void Fraction Dt X 10s (cm2/sec) Average Tortuosity Factor t, Parallel-Path Pore Model r = 2K./5. (A) r Based on Average Pore Radius... 

The literature data on the tortuosity factor r show a large spread, with values ranging from 1.5 to 11. Model predictions lead to values of 1/e s (8), of 2 (parallel-path pore model)(9), of 3 (parallel-cross-linked pore model)(IQ), or 4 as recently calculated by Beeckman and Froment (11) for a random pore model. Therefore, it was decided to determine r experimentally through the measurement of the effective diffusivity by means of a dynamic gas chromatographic technique using a column of 163.5 cm length,... 

For the case of pellet, the presence of uneven pore size as well as the interconnection of pores and tortuous path of diffusion, the flux expression for the pellet case has to be derived from that for a cylindrical capillary (eq. 13.2-1) through some model about the structure of the pellet. One such model is the parallel path pore model and in this model the effective flux is calculated by summing the combined Knudsen and molecular binary diffusions over each increment of pore volume. The expression for the steady state effective flux is ... 

An effective diffusivity can now be predicted by combining Eq. (1 l-l) for a single pore with this parallel-pore model. To convert D, which is based on the cross-sectional area of the pore, to a diffusivity based upon the total area perpendicular to the direction of diffusion, D should be multiplied by the porosity. In Eq. (11-1), x is the length of a single, straight cylindrical pore. To convert this length to the diffusion path in a porous pellet, X , from Eq. (11-22) should be substituted for x. With these modifications the diffusive flux in the porous pellet will be... 

Satterfield and Cadle [48, 49] and Brown, Haynes, and Manogue [50] have tested the various models against experimental data from several types of solids, pressures, and the like. Both the macro-micro and the parallel path models are often superior to the simple mean pore-size model, as might be expected the former two are more or less equivalent, where applicable, but the parallel path model seems to be slightly more general in its predictive abilities. These theoretical models do not completely describe all aspects of pore diffusion, and some complex interactions have recently been described by Brown et al. [61, 62] and by Abed and Rinker [63]. 

In summary, a fairly narrow unimodal pore-size distribution can be adequately described by the simple mean pore-size model. A broad pore-size distribution, /(r), requires a more extensive treatment, such as the parallel path model. A bimodal pore-size distribution can also be described by the micro-macro random pore model. 

Kenjo et al. [1991] have described composite electrodes using the finite length pore model shown in Figure 4.1.15. The electronic and ionic conductor paths run in parallel, with pores providing access to the gas phase via the electrolyte, which is unrealistic, but may not be of any great consequence. Essentially, the composite... 

The only other variable required for predicting D is the length of the diffusion path, which is the thickness of the particle multiplied also by the adjustable tortuosity factor, S, that accounts for distorted diffusion pathways and also for varying pore cross sections in interconnections and constrictions the value of 5 varies between V2 and 10 but is typically 3 or 4 in most industrial catalysts. The simplest geometric model which is still commonly used in practical applications for estimating is the parallel-pore model ... 

These observations have been explained from a simple electric model of the resistive paths implied (see Figure 9.25) and the total impedance for such a membrane with N identical pores is the impedance of the tip, in series with N parallel porous ionic pathways, which can be decomposed into a pore exit, internal and entrance resistances in series, respectively, 7 exit> internal and /Gentry It is then considered that, when the tip rasters a pore region, only the resistances of the tip, and of the rastered pore exit, are changed. In order to be observed, a pore needs to induce a significant... 

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