Mass Biot number

The concentration history appears to be a function of three dimensionless parameters, a modified Thiele modulus, y, the mass Biot number, gj, and the dimensionless feed concentration, /3. The set of non-linear equations is uncoupled by introducing an effectiveness factor, r, and numerically solved. In order to reduce computer time, the effectiveness factor has been conveniently expressed as a weighted sum of its value for the zero and first order reaction rate. Different regime conditions are depicted in terms of a dimensionless parameter,... 

A little clearer physical interpretation is obtained, however, if we write equation (7-50) in terms of the ratio of the inter- to intraphase transport coefficients, a quantity called the mass Biot number, Ngj. We define... 

Figure 7.15 Combined inter-intraphase effectiveness factor, rjQ, for a finite external surface area with mass Biot number equal to 10.

As might be expected, the influence of the external area contribution dominates for high values of [Pg.492]

Increasing values of Bi correspond to increasing internal diffusion resistance compared to the external mass transfer. For Bi — oo, the external mass transfer is fast and the reactant concentration on the outer catalyst surface is equal to the bulk-phase concentration the reaction is only influenced by internal transport processes. The influence of internal and external mass transfers on the overall efficiency (Eq. (11.2)) is shown in Figure 11.4 as an example. The catalyst efficiency decreases strongly at small mass Biot numbers. This is because of the reduced... 

Figure 11.4 Overall efficiency factor as a function of Thiele modulus for different mass Biot numbers (isothermal, irreversible first-order reaction in a porous slab).

The catalyst efficiency decreases strongly at small mass Biot numbers as seen in Figure 2.30. This is because of the reduced reactant concentration on the external pellet surface. In contrast, external mass transfer influences can be neglected at > 100. In practice, catalytic particles are in the range of several millimeters and the mass Biot numbers are in the order of 100— 200. Hence, the overall effectiveness factor is almost entirely determined by the intraparticle diffusion. 

Figure 2.30 Overall effectiveness factor as a function of the Weisz modulus for different mass Biot numbers (isothermal, irreversible first order reaction in a porous slab). (Adapted from Ref. [16], Figure 4.17 Copyright 2012, Wiley-VCH GmbH Co. KGaA.)...

Biot number (mass), Biot number (thermal) —... 

Experimental results show that the mass Biot number (B()m> which is sometimes called the modified Sherwood number [17], is much larger than unity, indicating that the major resistance to mass transfer resides in the internal pore diffusion process. 

The same asymptote is shown in Figure 3.4 for the region mainly limited by intraphase diffusion. The regime of strong interphase mass transfer resistance is also depicted in the same representation for two values of the mass Biot number. The asymptotic behavior of the effectiveness factor in this limit 1 and low is obtained from (power-law... 

The ratio of timescales for internal diffusion within the catalyst pellet and for external mass transfer is of the order of the mass Biot number given in (3.43e). Since for many practical conditions Bim is reasonably high (10 -10 as estimated in Ref. [72]), it is expected that the external mass transfer dominates over the internal one. If we extend this consideration to the reactor scale, then a very useful pseudo-homogeneous model [51] is obtained. The scaling condition that expresses fast fluid-solid mass transfer compared with other processes (X) in Equation 3.22 is... 

The basic approximations made in arriving at the reactor point effectiveness are (1) isothermal pellet, (2) negligible external mass transfer resistance, and (3) estimation of the pellet center concentration by a simple relationship when the reaction is not severely diffusion-limited. The first two approximations are quite adequate in view of the fact that the mass Biot number is of the order of hundreds under realistic reaction conditions. Both theoretical and experimental justifications for these approximations have been given in Chapter 4. The first approximation will be relaxed when reactions affected by pore-mouth poisoning are considered since a definite temperature gradient then exists within the pellet. An additional approximation is the representation of the difference between the Arrhenius exponentials evaluated at the pellet surface and the bulk-fluid temperatures by a linear rela-... 

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