Kinetic regime, control

Figure 7 - Various kinetic regimes controlling a gas-phase reaction around and inside a porous solid catalyst, D step corresponds to AE a AE% activation energies cited in the text, C to AE eUnd AE p B to AE d and A to AE c (adapted from Ref. 52)...

The reference snbstance method is based on the addition to the solntion, containing the species for which the transfer rate is going to be investigated, of another inert component for which the rate of extraction is known to be controlled only by diffnsion. By following the simultaneous transfer of the species of interest and of the reference component as function of the hydro-dynamic conditions in the extraction apparatns, a diffusional regime will be indicated by a similar functional dependence, whereas a kinetic regime is indicated by a sharply different one. 

In the case of constant interfacial-area-stirred cells, although zone A is certainly an indication that the process is controlled by diffusional processes, the opposite is not true for zone B. In fact, in spite of the increased stirring rate, it may happen that the thickness of the diffusion films never decreases below a sufficiently low value to make diffusion so fast that it can be completely neglected relative to the rate of the chemical reactions. This effect, sometimes called slip effect, depends on the specific hydrodynamic conditions of the apparatus in which the extraction takes place and simulates a kinetic regime. 

In a kinetic regime system, the kinetics of solvent extraction can be described in terms of chemical reactions occurring in the bulk phases or at the interface. The number of possible mechanisms is, in principle, very large, and only the specific chemical composition of the system determines the controlling mechanism. Nevertheless, some generalizations are possible on considerations based... 

The rate equation is indistinguishable from that of an extraction process occurring in a kinetic regime, which is controlled by a slow, interfacial partition reaction ... 

The diffusion-controlled process [see Eqs. (5.66), (5.68), and (5.69)] can be experimentally differentiated from the process occurring in the kinetic regime [see Eq. (5.75)] only by measnring the variations of k and with 5 , and 8o. Otherwise, the identical rate laws will not permit one to distinguish between the two mechanisms. 

The approaches described previously assume that reactions will be suppressed, without giving any specific mechanism, and then rationalise the behaviour of the process using calculated metastable equilibria. A more innovative approach was taken by Saunders (1984) and Saunders and Miodownik (1985, 1987) for the prediction of phases formed by vapour co-deposition of alloys. It was postulated that the formation of phases on the substrate is controlled by the diffiisional breakdown of iiiUy intermixed depositing atoms so that three kinetic regimes are observed ... 

The approach of this work is to measure product compositions and mass balances in much detail in a time resolved manner and to relate this to the controlling kinetic principles and elemental reactions of product formation and catalyst deactivation. Additionally the organic matter, which is entrapped in the zeolite or deposited on it, is determined. The investigation covers a wide temperature range (250 - 500 °C). Four kinetic regimes are discriminated autocatalysis, retardation, reanimation and deactivation. A comprehensive picture of methanol conversion on HZSM5 as a time on stream and temperature function is developed. This also explains consistently individual findings reported in literature [1 4]. 

Since we know the mass of ozone transferred has to have reacted or left the system, it is relatively easy to determine the reaction rate for slow reactions, which are controlled by chemical kinetics with this method. For kinetic regimes with mass transfer enhancement, the two rates, mass transfer and reaction rate are interdependent. Whether kLa or kD can be determined in such a system and how depends on the regime. Possible methods are similar to those described below in Section B 3.3.3 (see Levenspiel and Godfrey, 1974). 

Terms such as diffusion limited or diffusion controlled are undesirable because a rate may be larger in regimes of heat or mass transfer than in the kinetic regime of operation, i.e., when gradients are negligible. 

Initially, when the ApBq layer is very thin, the reactivity of the A surface is realised to the full extent because the supply of the B atoms is almost instantaneous due to the negligibly short diffusion path. In such a case, the condition kom kW]/x is satisfied. Therefore, if the surface area of contact of reacting phases A and ApBq remains constant, chemical reaction (1.1) takes place at an almost constant rate. In practice, this regime of layer growth is usually referred to as reaction controlled. The terms interface controlled regime and kinetic regime are also used, though less suited. 

Because rates of reduction by Fe° vary considerably over the range of treatable contaminants, it is possible that there is a continuum of kinetic regimes from purely reaction controlled, to intermediate, to purely mass transport controlled. Fig. 9 illustrates the overlap of estimated mass transport coefficients (kmt) and measured rate coefficients (kSA). The values of kSA are, in most cases, similar to or slower than the kmi values estimated for batch and column reactors. The slower kSA values suggest that krxu < kml, and therefore removal of most contaminants by Fe° should be reaction limited or only slightly influenced by mass transport effects (i.e., an intermediate kinetic regime). 

In catalysis, molecular structure determines the catalytic activity in the kinetic regime, and supramolecular structure controls the degree of usage of this catalytic activity in applied catalysis, as well as heat and mass transfer, mechanical and other properties. In other words, the absence of proper molecular structure causes the absence of catalysis, but one is restricted in preparation of a catalyst by the necessity to improve the supramolecular structure.4... 

Figure 3. Transition from the kinetic regime to the diffusion-controlled regime of a heterogeneous catalytic fluid-solid reaction carried out on a porous catalyst.

However, when the view is restricted to simple, irreversible reactions obeying an nth order power rate law and, if additionally, isothermal conditions arc supposed, then—together with the results of Section 6.2.3—it can be easily understood how the effective activation energy and the effective reaction order will change during the transition from the kinetic regime to the diffusion controlled regime of the reaction. 

Figure 5 Activity versus temperature plot for a combustion catalyst. A kinetic regime. B light-off, C mass transfer control. D homogeneous reactions. (From Ref. 15.)...

In the overall picture, different expressions are proposed for the rate of gas absorption with chemical reaction, depending on the forms of the enhancement factor E corresponding to different kinetic regimes, going from reaction-controlling to mass transfer-controlling. Typical cases are ... 

The experimental approaches [11-13] on the growth rate of silicon on silicon substrate confirm the presence of two growth regimes depending on the temperature a regime controlled by chemical kinetics for temperatures below 1,000°C and a regime controlled by mass transfer regime for temperatures above 1,000°C (Fig. 10.3). 

An increasing number of investigations report that chemical reaction kinetics, especially at the LM-receiving phase interface, play a sometimes critical role for overall transport kinetics [57-60]. When one or more of the chemical reactions are sufficiently slow in comparison with the rate of diffusion to and away from the interfaces, diffusion can be considered instantaneous, and the solute transport kinetics occur in a kinetic regime. Kinetic studies of chemical reactions between solute and reagent (carrier) seek to elucidate the mechanisms of such reactions. Infomiation on the mechanisms that control solvent exchange and complex formation is reported briefly below. 

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