Simplified mass transfer Peclet number

The following strategy should be used to calculate the interpellet axial dispersion coefficient and the mass transfer Peclet number in packed catalytic tubular reactors (see Dullien, 1992, Chap. 6). Initially, one should calculate a simplified mass transfer Peclet number (i.e., Pesimpie) based on the equivalent diameter of the catalytic pellets, equivalent, the average interstitial fluid velocity through the packed bed, (Uj>intetstitiai, and the ordinary molecular diffusion coefficient of reactant A, a, ordinary-... 

Empirical and theoretical correlations for T are summarized in Table 22-6, and documented for the following range of simplified mass transfer Peclet numbers 10 < Pcsimpie < 3 X 10 . Theoretical correlation (4) in Table 22-6, which has been developed in detail by Been (1998, pp. 398-404) and Bird et al. (2002,... 

When the simplified mass transfer Peclet number is very small (i.e., <1), T 0.67 instead of unity because the numerator of T (i.e., lSA.eff. axial disp.) is based on unsteady-state pore diffusion without convection, whereas the denominator of T (i.e., a, ordinary) is measured in an unrestricted bulk fluid phase. In other words, the diffusivity in the numerator of T is reduced by porosity and tortuosity factors. 

The solution to this laminar boundary layer problem must satisfy conservation of species mass via the mass transfer equation and conservation of overall mass via the equation of continuity. The two equations have been simplified for (1) two-dimensional axisymmetric flow in spherical coordinates, (2) negligible tangential diffusion at high-mass-transfer Peclet numbers, and (3) negligible curvature for mass flux in the radial direction at high Schmidt numbers, where the mass transfer... 

If there is only one chemical reaction on the internal catalytic surface, then vai = — 1 and subscript j is not required for all quantities that are specific to the yth chemical reaction. When the mass transfer Peclet number which accounts for interpellet axial dispersion in packed beds is large, residence-time distribution effects are insignificant and axial diffusion can be neglected in the plug-flow mass balance given by equation (22-11). Under these conditions, reactor performance can be predicted from a simplified one-dimensional model. The differential design equation is... 

Step 5. Use your results from step 4 together with the following assumptions the mass transfer Peclet number is large, and the tube diameter is much smaller than the overall length of the reactor to simplify the mass transfer equation. 

Order-of-magnitude analysis indicates that diffusion is neghgible relative to convective mass transfer in the primary flow direction within the concentration boundary layer at large values of the Peclet number. Typically, liquid-phase Schmidt numbers are at least 10 because momentum diffusivities (i.e., i/p) are on the order of 10 cm /s and the Stokes-Einstein equation predicts diffusion coefficients on the order of 10 cm /s. Hence, the Peclet number should be large for liquids even under slow-flow conditions. Now, the partial differential mass balance for Cji,(r,0) is simplified for axisynunetric flow (i.e., = 0), angu-... 

Hlavacek and Hofmann also defined necessary and sufficient conditions for multiplicity, for a simplified rate law of the type Barkelew used (Eq. 11.5-c) and equality of the Peclet numbers for heat and mass transfer. The necessary and sufficient conditions for multiplicity, which have to be fulfilled simultaneously are... 

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