Bodenstein numbers

A dimensionless group that frequently occurs in this context is the Bodenstein number expressed as... 

The inverse of the Bodenstein number is eD i/u dp, sometimes referred to as the intensity of dispersion. Himmelblau and Bischoff [5], Levenspiel [3], and Wen and Fan [6] have derived correlations of the Peclet number versus Reynolds number. Wen and Fan [6] have summarized the correlations for straight pipes, fixed and fluidized beds, and bubble towers. The correlations involve the following dimensionless groups ... 

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... 

Figure 3.12 Residence time distribution in a micro reactor which is tightened by different means. ( ) Glued reactor without catalyst coating (X) glued reactor with catalyst coating ( ) reactor with graphite joints. Calculated curves for tubular reactors with the Bodenstein number Bo = 33 (solid line) and Bo = 70 (dashed line).

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... 

Phg modified Bodenstein number for gas phase (dimensionless—see just after Eqn. [49])... 

In order to evaluate the efficacy of the expanded bed technique the plate height (HETP), plate number (N), resolution (Rs), Bodenstein number (Bo), particle Peclet number (Pep) and axial dispersion coefficient (DJ have been calculated and compared with the corresponding values of a traditional HPLC column. N can be expressed by... 

Other factors limiting the overall rate can be external or internal mass transfer, or axial dispersion in a fixed-bed reactor. Pertinent dimensionless numbers are the Biot number Bi, the Damkohler number of the second kind Dan, or the Bodenstein number Bo (Eqs. (5.46)—(5.48)]. 

Characterizing the distribution according to the dispersion model yields a dimensionless number describing the degree of axial mixing within the bed. The Bodenstein number Bo relates convective transport of liquid to dispersion according to Eq. (9). 

In Fig. 5, the liquid phase axial dispersion coefficient Daxi and the Bodenstein number Bo calculated from this relationship according to Eqs. (9), (10) and (13) are plotted for a range of linear velocities used in fluidized bed adsorption. The physical parameters of the commercial Streamline SP adsorbents (average particle size 247 pm, average particle density 1143 kg/m3, terminal settling velocity 0.0044 m/s, n = 4.7 as described by Chang and Chase [37]) were... 

The Ha number (Ham) defined here for the mth sublayer of the membrane layer corresponds to the well-known Thiele modulus defined for catalyst particles, while the Peclet number corresponds to the often used Bodenstein number. 

In Figure 11 the Bodenstein-number is plotted versus superficial gas velocity at different distances between tracer input and detection. The effects of efflux at the top of the column cause the sharp bend at about 5 mm/s of superficial gas velocity. The Reynolds number at this point amounts to about 2000. The Bodenstein number is defined as ... 

---