External Mass Transfer and Intraparticle Diffusion Control

External Mass Transfer and Intraparticle Diffusion Control With a linear isotherm, the solution for combined external mass transfer and pore diffusion control with an infinite fluid volume is (Crank, Mathematics of Diffusion, 2d ed., Clarendon Press, 1975) ... 

External Mass Transfer and Intraparticle Diffusion Control... 16-29... 

Finally, Rosen [J.B. Rosen, J. Chem. Phys., 20, 387 (1952) Ind. Eng. Chem., 46, 1590 (1954)] presented the solution for linear equilibrium and intraparticle diffusion-controlled adsorption (no external mass-transfer resistance). In this case... 

Solutions are provided for external mass-transfer control, intraparticle diffusion control, and mixed resistances for the case of constant Vj and F, out = 0- The results are in terms of the fractional... 

Solutions are provided for external mass-transfer control, intraparticle diffusion control, and mixed resistances for the case of constant Vf and F0 in = FVi out = 0. The results are in terms of the fractional approach to equilibrium F = (ht — hf)/(nT — nf), where hf and are the initial and ultimate solute concentrations in the adsorbent. The solution concentration is related to the amount adsorbed by the material balance - (hi - nf )M,Ay. 

As indicated above, intraparticle diffusion lowers the apparent activation energy. The apparent activation energy is even further lowered under external mass-transfer control. Figure 7-9 illustrates how the rate-controlling step changes with temperature, and as a result the dependence of the apparent first-order rate constant on temperature also changes, from a very strong dependence under kinetic control to virtual independence under external mass-transfer control. 

For the given rate expression, equations (7-124) to (7-127) can be numerically integrated, e.g., in Fig. 7-13 for reaction control and Fig. 7-14 for intraparticle diffusion control, both with negligible external mass-transfer resistance x is the fractional conversion. 

Zn(II) as presented in Table 24.2 [6], or Cr(VI), more than 99% of which was removed from industrial electroplating wastewater [20], The modeling of the experimental breakthrough of lead (II) onto activated carbon fibers in a fixed bed, using axial dispersion and diffusion equations solved by the orthogonal collocation method, demonstrated that the intraparticle and external mass transfer is not the rate-controlling step, due to the short diffusion path for the adsorbate in activated carbon fibers [21]. 

Inter- and Intraphase Mass Transfer Limitations in the DeNOx Reaction. It is well established that in both laboratory and power plant conditions, extruded monolithic SCR catalysts work under combined intraparticle and external diffusion control because of the high reaction rate and of the laminar flow regime prevailing in the channels of the monolith catalysts. As an example. Figure 12 points out that, for the same reaction conditions, different extents of NO reduction are observed over SCR honeycomb catalysts with identical composition but different channel openings. 

Mass transfer through the external fluid film, and macropore, micropore and surface diffusion may all need to be accounted for within the particles in order to represent the mechanisms by which components arrive at and leave adsorption sites. In many cases identification of the rate controlling mechanism(s) allows for simplification of the model. To complicate matters, however, the external film coefficient and the intraparticle diffusivities may each depend on composition, temperature and pressure. In addition the external film coefficient is dependent on the local fluid velocity which may change with position and time in the adsorption bed. 

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