External mass transfer control

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... 

FIG. 16-14 Constant separation factor batch adsorption curves for external mass-transfer control with an infinite fluid volume and n j = 0. 

Isocratic Elution In the simplest case, feed with concentration cf is apphed to the column for a time tp followed by the pure carrier fluid. Under trace conditions, for a hnear isotherm with external mass-transfer control, the linear driving force approximation or reaction kinetics (see Table 16-12), solution of Eq. (16-146) gives the following expression for the dimensionless solute concentration at the column outlet ... 

Before terminating the discussion of external mass transfer limitations on catalytic reaction rates, we should note that in the regime where external mass transfer processes limit the reaction rate, the apparent activation energy of the reaction will be quite different from the intrinsic activation energy of the catalytic reaction. In the limit of complete external mass transfer control, the apparent activation energy of the reaction becomes equal to that of the mass transfer coefficient, typically a kilocalorie or so per gram mole. This decrease in activation energy is obviously... 

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. 

The signal generated by the complex is governed by several physical phenomena associated with the matrix thickness. As soon as the probe is placed in contact with the analyte, external mass transfer controls the movement of the analyte toward the surface of the optical probe.(S4) The osmotic pressure and Gibbs free energy dictate the permeation of the analyte into the matrix. Once the analyte has penetrated the matrix, internal mass transfer resistance controls the movement of the analyte in the matrix. Eventually, the probe reaches a steady state of equilibrium with molecules continuously moving in and out of the matrix. 

Figure 7-9 Reactant concentration profiles around and within a porous catalyst pellet for the cases of reaction control, external mass transfer control, and pore difliision control. Each of these situations leads to different reaclion rate expressions.

Figure 7-10 Reactant concentration profiles around a catalyst pellet for reaction control (A > k") and for external mass transfer control ( tni k )-...

According to their analysis, if is zero (practically much lower than 1), then the liquid-film diffusion controls the process rate, while if tfis infinite (practically much higher than 1), then the solid diffusion controls the process rate. Essentially, the so-called mechanical parameter represents the ratio of the diffusion resistances (solid and liquid film). The authors did not refer to any assumption concerning the type of isotherm for the derivation of the above-mentioned criterion it is sufficient to be favorable (not only rectangular). They noted that for >1.6, the particle diffusion is more significant, whereas if < 0.14, the external mass transfer controls the adsorption rate. 

The mass transfer factor has also been correlated as a function of the Reynolds number only and thus taking account only of hydrodynamic conditions. If e is the voidage of the packed bed and the total volume occupied by all of the catalyst pellets is Vp, then the total reactor volume is Vp/(l - e). Hence the rate of mass transfer of component A per unit volume of reactor is NASx(l - e)/Vp. If we now consider a case in which only external mass transfer controls the overall reaction rate we have ... 

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. 

Experimental studies in our laboratory on the aldol condensation were carried out in a lin. CD column using Ambelite IRA-900 anion-exchange resin housed in fiberglass bags. The reboiler duty, which affected the flow rates, was found to play an important role in the selectivity to DAA. A rate-based three-phase CD model was developed, which accurately predicts the yield and selectivity obtained under steady-state and transient conditions. Model predictions and experimental data indicate that the production of DAA is external mass transfer controlled while the production of MO is kinetically controlled. The external mass transfer resistance was caused by the fiberglass bags. Recently,... 

---