Deviation from ideal flow,”244------Difference equations

Such an assumption of cylindrical pores oriented along the flow is so ideal because pores can be randomly oriented and pores can have different shape and size. This deviation from ideal condition can be allowed for by the introduction of the tortuosity factor. In general, this tortuosity factor is a function of pore radius, and the following equation can be used (Brown and Travis, 1983) ... 

For a basic understanding of chemical reactor design, start with Sections 4.10.1 and 4.10.2, where different ideal and isothermal reactor types are introduced and the respective performance equations are derived. You should then study the behavior of real reactors (non-ideal flow and residence time distribution, Section 4.10.4) and the simplest model to account for deviations of real systems from ideal reactors, the tanks-in-series model (Section 4.10.5). 

The two equations for the mass and heat balance, Eqs. (4.10.125) and (4.10.126) or the dimensionless forms represented by Eqs. (4.10.127), (4.10.128) and (4.10.130), consider that the flow in a packed bed deviates from the ideal pattern because of radial variations in velocity and mixing effects due to the presence of the packing. To avoid the difficulties involved in a rigorous and complicated hydrodynamic treatment, these mixing effects as well as the (in most cases negligible contributions of) molecular diffusion and heat conduction in the solid and fluid phase are combined by effective dispersion coefficients for mass and heat transport in the radial and axial direction (D x, Drad. rad. and X x)- Thus, the fluxes are expressed by formulas analogous to Pick s law for mass transfer by diffusion and Fourier s law for heat transfer by conduction, and Eqs. (4.10.125) and (4.10.126) superimpose these fluxes upon those resulting from convection. These different dispersion processes can be described as follows (see also the Sections 4.10.6.4 and 4.10.7.3) ... 

The difference between these equations and those for the ideal piston-flow model is the inclusion of the first term on the left side in each of them. These terms represent the rate of accumulation of ammonia and heat in the bed element, due to mass dispersion and heat conduction, respectively. For small deviations from the ideal piston-flow model, these terms can be omitted in obtaining the second-order derivatives ... 

Comparison of experimental pass duration distribution curves, with the curves calculated using Equations 2.104 and 2.106, results in obtaining the numerical values Bo and n and therefore, an opportunity for the quantitative estimation of the flow structure deviation in reaction zones with different geometry from an ideal model. 

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