Peclet number for

Peclet number for dispersion Pe = uUD where t/ is a Bnear velocity, L is a hnear dimension, and is the dispersion coefficient. In packed beds, Pe = udp/De, where u is the interstitial velocity and dp is the pellet diameter. 

The value of n is the only parameter in this equation. Several procedures can be used to find its value when the RTD is known experiment or calculation from the variance, as in /i = 1/C (t ) = 1/ t C t), or from a suitable loglog plot or the peak of the curve as explained for the CSTR battery model. The Peclet number for dispersion is also related to n, and may be obtainable from correlations of operating variables. 

Naturally, there are two more Peclet numbers defined for the transverse direction dispersions. In these ranges of Reynolds number, the Peclet number for transverse mass transfer is 11, but the Peclet number for transverse heat transfer is not well agreed upon (121, 122). None of these dispersions numbers is known in the metal screen bed. A special problem is created in the monolith where transverse dispersion of mass must be zero, and the parallel dispersion of mass can be estimated by the Taylor axial dispersion theory (123). The dispersion of heat would depend principally on the properties of the monolith substrate. Often, these Peclet numbers for individual pellets are replaced by the Bodenstein numbers for the entire bed... 

Fig. 2. Peclet number for gas phase in trickle-flow operation.

The figure shows the ratio of the widths of initially delta-like concentration tracers at the reactor exits as a function of the micro-channel Peclet number for different values of the porosity. Taking a value of = 0.4 as standard, it becomes apparent that the dispersion in the micro-channel reactor is smaller than that in the fixed-bed reactor in a Peclet number range from 3 to 100. Minimum dispersion is achieved at a Peclet number of about 14, where the tracer width in the micro-channel reactor is reduced by about 40% compared with its fixed-bed counterpart. Hence the conclusion may be drawn that micro-channel reactors bear the potential of a narrower residence time than fixed-bed reactors, where again it should be stressed that reactors with equivalent chemical conversion were chosen for the comparison. 

Because the term r(CA T) is exponentially dependent on T and can be nonlinear as well, a numerical solution or piecewise linearization must be used. To simplify the numerical manipulations, equations in Table IX are normalized by = z/L, r = ut/L, and jc = 1 - C,/(C,)0, where i is normally S02. y also is a normalized quantity. The Peclet numbers for mass and heat are written PeM = 2Rpu/D) and PeH = 2Rpcpul t for a spherical particle. They are also written in terms of bed length as Bodenstein numbers. It is... 

At high Reynolds numbers where molecular diffusion effects are negligible, experimental evidence confirms the general validity of equation 12.7.5. Figure 12.15 indicates how the Peclet number for radial mixing varies with the fluid Reynolds number. Above a Reynolds number of 40, the radial Peclet number is approximately 10. 

The Peclet number for axial dispersion is defined in a manner similar to the radial parameter... 

Rough correlations of Peclet numbers for dispersion are given by Wen (in Petho Noble, Residence Time Distribution in Chemical Engineering, 1982)... 

The Peclet number for closed ends is found with the equation from problem P5.08.04,... 

Gravitational constant. Pe = 2aVJa Peclet number for heat... 

Figure 3.38 Comparison of axial (Hiby) and radial (Gunn) Peclet numbers for gases (for e < 0.45, Sc = 1). The minimum value corresponds to 0.05 < Rep and Rev > 80 and is given by Gunn (1968).

For the evaluation of the particle Peclet number and the liquid holdup, the correlations proposed by Inglezakis et al. are used, i.e. eqs. (3.313) and (3.332), respectively. The Biot number, liquid holdup, and bed Peclet number for downflow operation versus relative volumetric flow rate are presented in Figure 4.35. 

Figure 4.35 Biot number, liquid holdup, and bed Peclet number for downflow operation versus relative volumetric flow rate.

The next parameter of importance is the Peclet number of the liquid and the gas phase. For the specified Reynolds number, the Peclet number for the liquid phase using the Michell-Furzer correlation (eq. (3.417)) is 0.74. The minimum value of Z/dp for ethanol conversion between 0.1 and 0.9, evaluated using the Mears criterion (eq. (3.421)), is 2.84 and 62.11 respectively, much lower than the value used in the example, which is about 2500. Thus, the operation can be assumed to follow the plug-flow model. 

Concerning packed bubble bed reactors, the evaluation of the Peclet number of the liquid phase is important in order to decide if we have to use a plug- or backmixed-flow model. For the specified Reynolds number, the Peclet number for the liquid phase using the Stiegel-Shah correlation (eq. (3.422)) is 0.15, much lower than in the trickle bed, which was expected as the backmixing in the liquid phase in packed bubble bed reactors is relatively high. The liquid phase can be considered to be well mixed if (Ramachandran, and Chaudhari, 1980) (eq. (3.423))... 

Fig. 18. Utilized capacity of the filter wall vs. the Peclet number for all the loading cases in study.

What is the Deborah number What is its physical significance What is the Peclet number Describe at least two ways of defining the Peclet number for flow of dispersions. 

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