Irreversible transfers, limits

If the liqmd-phase reaction is extremely fast and irreversible, the rate of absorption may in some cases be completely governed by the gas-phase resistance. For practical design purposes one may assume (for example) that this gas-phase mass-transfer limited condition will exist when the ratio yj/y is less than 0.05 everywhere in the apparatus. 

Figure 14-10 illustrates the gas-film and liquid-film concentration profiles one might find in an extremely fast (gas-phase mass-transfer limited) second-order irreversible reaction system. The solid curve for reagent B represents the case in which there is a large excess of bulk-liquid reagent B. The dashed curve in Fig. 14-10 represents the case in which the bulk concentration B is not sufficiently large to prevent the depletion of B near the liquid interface and for which the equation ( ) = I -t- B /vCj is applicable. 

For an isothermal absorber involving a dilute system in which a liquid-phase mass-transfer limited first-order irreversible chemic reaction is occurring, the packed-tower design equation is derived as... 

M sulfuric acid to air [34]. As discussed above, for the aqueous-DCE interface, the rate of this irreversible transfer process (with the air phase acting as a sink) was limited only by diffusion of Bt2 in the aqueous phase. A lower limit for the interfacial transfer rate constant of 0.5 cm s was found [34]. 

There are a number of examples of tube waU reactors, the most important being the automotive catalytic converter (ACC), which was described in the previous section. These reactors are made by coating an extruded ceramic monolith with noble metals supported on a thin wash coat of y-alumina. This reactor is used to oxidize hydrocarbons and CO to CO2 and H2O and also reduce NO to N2. The rates of these reactions are very fast after warmup, and the effectiveness factor within the porous wash coat is therefore very smaU. The reactions are also eternal mass transfer limited within the monohth after warmup. We wUl consider three limiting cases of this reactor, surface reaction limiting, external mass transfer limiting, and wash coat diffusion limiting. In each case we wiU assume a first-order irreversible reaction. 

A similar correction to IET is inherent in MET as well. For irreversible transfer (Ay, P 0), the quenching kinetics represented by P A (t) was obtained in Ref. 203 with the original program designed to solve the differential form of IET and MET equations. As seen from Figure 3.84, the difference between the curves representing these solutions is insignificant within the validity limits for IET established in Ref. 39... 

However, at still larger concentrations only DET/UT is capable of reaching the kinetic limit of the Stem-Volmer constant and the static limit of the reaction product distribution. On the other hand, this theory is intended for only irreversible reactions and does not have the matrix form adapted for consideration of multistage reactions. The latter is also valid for competing theories based on the superposition approximation or nonequilibrium statistical mechanics. Moreover, most of them address only the contact reactions (either reversible or irreversible). These limitations strongly restrict their application to real transfer reactions, carried out by distant rates, depending on the reactant and solvent parameters. On the other hand, these theories can be applied to reactions in one- and two-dimensional spaces where binary approximation is impossible and encounter theories inapplicable. 

If, under experimental conditions internal mass transfer limitations are present then for an nth-order irreversible reaction the observed reaction rate can be written as ... 

FIG. 14-10 Gas-ph ase and liquid-phase solute-concentration profiles for an extremely fast (gas-phase mass-transfer limited) irreversible reaction system A -I-vB products. 

In order to assign and compare catalyst reactivity rates, measured conversions were "normalized" to 3000 GHSV by multiplying observed conversions by the factor actual GHSV/3000. The normalized conversions were used to specify rates to individual products and rates for overall CO conversion. The reaction has b n shown not to be mass or heat transfer limited (12). CO and irreversible H2 chemisorption were measured at room temperature, the former using a pulse injection system and a thermal conductivity detector, and the latter using a static system. Prior to measurements, catalysts were reduced under the same schedule as for reactor runs. 

Criteria are usually derived so that deviations from the ideal situation are not larger than 5%. In order for external mass transfer limitations to be negligible, for an isothermal, n order irreversible reaction in a spherical particle, a criterion for the Carberry number can be derived, which assures that the observed rate does not deviate more than 5% from the ideal rate ... 

A measure of the absence of internal (pore diffusion) mass transfer limitations is provided by the internal effectiveness factor, t, which is defined as the ratio of the actual overall rate of reaction to the rate that would be observed if the entire interior surface were exposed to the reactant concentration and temperature existing at the exterior of the catalyst pellet. A value of 1 for rj implies that all of the sites are being utilized to their potential, while a value below, say, 0.5, signals that mass transfer is limiting performance. The value of rj can be related to that of the Thiele modulus, 4>, which is an important dimensionless parameter that roughly expresses a ratio of surface reaction rate to diffusion rate. For the specific case of an nth order irreversible reaction occurring in a porous sphere,... 

In the previous section we found that, in certain special cases, the directions of energy and mass transfer are limited by gradients in certain intensive properties. In this section we show that, during irreversible transfers of heat and work, not only are there constraints on the directions, but constraints also apply to the magnitudes. To develop the argument, we reconsider irreversible, isothermal, constant-mass work as discussed in 7.2.2. For such a process, we have already seen that the combined laws reduce to... 

Most of the previously used expressions to account for incomplete catalyst wetting in trickle-beds are summarized in Table I. All of these, with the exception of the last one, are based on the assumptions of a) plug flow of liquid, b) no external mass transfer limitations, c) isothermal conditions, d) first order irreversible reaction with respect to the liquid reactant, e) nonvolatile liquid reactant, f) no noncatalytic homogeneous liquid phase reaction. 

This result was also seen from Example 5.3. For large q, the forward reaction dominates and thus the reaction process is completely irreversible. Though the Tafel equation predicts the forward reaction for large q, it does not account the mass transfer limited current at high q. If electrode kinetics are fairly fast, then mass transfer limited currents are easily reached at high q. For such cases, the Tafel equation does not apply well. On the other hand, when the electrode kinetics is slow, then the significant overpotential is required and the Tafel relationship holds good. 

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