Mass-Transfer Control

Controlled by diffusive mass transfer Controlled by chemical factors A major distinction is between reactions that are ... 

Linear Driving Force Approximation Simplified expressions can also be used for an approximate description of adsorption in terms of rate coefficients for both extrapai ticle and intraparticle mass transfer controlling. As an approximation, the rate of adsorption on a particle can be written as ... 

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 ... 

When two-phase mass transfer is required to supply reactants by mixing for a chemical reaction, the most important factor to consider is whether the mass transfer controls the operation or whether the chemical reaction controls it. This can be done by increasing the mixer speed to a point w here mass transfer effects become very high and the operation is limited by the chemical reaction. 

Fig. 10.5 Polarisation diagram representing corrosion and cathodic protection when the cathodic process is under mass transfer control. The values of fcorr and /cor, are lower than when there is no mass transfer restriction, i.e. when the cathodic kinetics follow the dotted line...

The simplest and most thoroughly studied solutions are those based on phosphoric acid at low temperatures (<35°C) which alone can fulfil all three requirements of acid solvent, film former (as metal phosphate) and diffusion agent by virtue of its viscosity. Thus copper and its main alloys of brasses and bronzes can be very effectively electropolished in 60-70% orthophos-phoric acid with the temperature maintained below 35°C under other conditions copper passivates or dissolves freely under mass transfer controlled conditions, but by varying the conditions appropriately polishing can be continued under mild agitation. An annotated polarisation curve is given in Fig. 11.7 readers are referred to recent studies for more detailed 2ispects " . 

In conclusion When no catalytic reaction is taking place on the gas-exposed electrode surface, only poor experimentation (blocking electrodes, inaccurate measurement of Uwr> and of course O) can cause deviations from Eq. (5.18) in presence of ion backspillover. In presence of a catalytic reaction Eq. (5.18) still holds unless the reaction is severely mass transfer controlled or an insulating layer is built on the catalyst surface. 

A more detailed study of this system using benzene and toluene has been reported by Soede et al. (1993) from The Netherlands. They have shown that the role of ZnS04 is to make the Ru hydrophlilic so that the catalyst particles are surrounded by a stagnant water layer. This aids in the rapid removal of the cyclohexene from the catalyst surface to the organic phase. The reaction is operated in mass transfer controlled conditions. 

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. 

Corresponding equations for the two special cases of gas-film mass-transfer control and surface-reaction-rate control may be obtained from these results (they may also be derived individually). The results for the latter case are of the same form as those for reaction-rate control in the SCM (see Table 9.1, for a sphere) with R0 replacing (constant) R (and (variable) R replacing rc in the development). The footnote in Example 9-2 does not apply here (explain why). 

The performance of a reactor for a gas-solid reaction (A(g) + bB(s) -> products) is to be analyzed based on the following model solids in BMF, uniform gas composition, and no overhead loss of solid as a result of entrainment. Calculate the fractional conversion of B (fB) based on the following information and assumptions T = 800 K, pA = 2 bar the particles are cylindrical with a radius of 0.5 mm from a batch-reactor study, the time for 100% conversion of 2-mm particles is 40 min at 600 K and pA = 1 bar. Compare results for /b assuming (a) gas-film (mass-transfer) control (b) surface-reaction control and (c) ash-layer diffusion control. The solid flow rate is 1000 kg min-1, and the solid holdup (WB) in the reactor is 20,000 kg. Assume also that the SCM is valid, and the surface reaction is first-order with respect to A. 

For gas-film mass transfer control, we use equation 22.2-16a for reaction control, we use equation 22.2-18 and for ash-layer diffusion control, we integrate equation 22.2-13 numerically in conjunction with 22.2-19, as described in Example 22-3(c). The results generated by the E-Z Solve software (file ex22-4.msp) are shown in Figure 22.4. 

Values of the ratio V(IVR given in Table 24.1 emphasize that most of the volume in a tower reactor (apart from a bubble column, data for which would be similar to a sparger-equipped tank) is occupied by the gas phase, and conversely for a tank reactor. This means that a, a in a tower and a, - a t in a tank. For mass transfer-controlled situations, a, is the more important quantity, and is much greater in a tower. For reaction-controlled situations, in which neither ai nor a is important, a sparger-equipped tank reactor, the cheapest arrangement, is sufficient. 

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