Deactivation kinetics

Evaluation of F(x) for Second Order Deactivation. As mentioned earlier for the case of second order decay F(x) cannot be derived analytically, however numerical calculation of F(x) or Its evaluation from simulated rate data Indicates that the function defined In Equation 11 provides an excellent approximation. This was also confirmed by the good fit of model form 12 to simulated polymerization data with second order deactivation. Thus for second order deactivation kinetics the rate expression Is Identical to Equation 12 but with 0 replacing 02. 

The sitosterol hydrogenation and deactivation kinetics was determined in a shaking constant-pressure batch reactor by using the new type of synthetic support material (mesoporous carbon Sibunit) for palladium (4wt% Pd) [55]. 

At initial reaction times, i.e. for the first ca. 100 s, all three phenomena should be controlled by transport considerations. If the induction kinetics are intrinsically fast compared to transport, then the evolution of the system is transport controlled, and most of the precursor cannot be converted to intermediates before 100 s is reached. Furthermore, if both induction kinetics and turnover frequency are intrinsically fast compared to transport, the system may experience only ca. one turnover vithin the first 100 s. Finally, if deactivation kinetics are intrinsically fast compared to transport, a significant fraction of precursor has been degraded to inactive species vithin the first 100 s. The net effect, for better or worse, is that transport effects bias the in situ observations and hence the accessible set of observable species in Eq. (4). 

One can and should enquire about the time-scale of the spectroscopic measurements and the reaction time-scales. In general, there will be a few observable species i. e. organometallics, associated with the induction kinetics, and the deactivation kinetics. Therefore, the kinetic time-scales are similar to the half-lives of these species. If is short compared to the half-lives of these species, both the induction and deactivation kinetics can be modeled accurately. 

Actually there is no particular advantage in using varying flow over constant flow when testing for the kinetics of Eq. 14 or any other independent deactivation. However, for other deactivation kinetics this reactor system is by far the most useful because it allows us to decouple the three factors C, T, and a and study them a pair at a time. 

Deactivation is caused by strong absorption of unavoidable and irremovable trace impurities in the feed, giving third-order deactivation kinetics, or... 

The model includes fundamental hydrocarbon conversion kinetics developed on fresh catalysts (referred to as start-of-cycle kinetics) and also the fundamental relationships that modify the fresh-catalyst kinetics to account for the complex effects of catalyst aging (deactivation kinetics). The successful development of this model was accomplished by reducing the problem complexity. The key was to properly define lumped chemical species and a minimum number of chemical reaction pathways between these lumps. A thorough understanding of the chemistry, thermodynamics, and catalyst... 

In this chapter the following topics will be reviewed KINPTR s start-of-cycle and deactivation kinetics, the overall program structure of KINPTR, the rationale for the kinetic lumping schemes, the model s accuracy, and examples of KINPTR use within Mobil. As an example, the detailed kinetics for the C6 hydrocarbons are provided. 

The hydrocarbon lumps and reaction network for both the start-of-cycle and the deactivation kinetics were defined. 

The start-of-cycle kinetic problem was uncoupled from the deactivation kinetics by taking advantage of their widely different time constants. 

An experimental design was developed which uncoupled the overall problem into a number of smaller parameter estimation problems. This approach reduced confounding between parameters, for both start-of-cycle and deactivation kinetics. 

For the deactivation kinetics, the following assumptions were made. 

The same criteria were used for start-of-cycle and deactivation lumping. Start-of-cycle lumping was based on thermodynamics and molecular-reaction similarity. The deactivation kinetic lumps contain the start-of-cycle lumps as a subset. The additional deactivation lumps were required to properly describe the effect of carbon number on aging rate. 

While the 13 hydrocarbon lumps accurately represent the hydrocarbon conversion kinetics, they must be delumped for the deactivation kinetics. In addition, delumping is necessary to estimate many of the product properties and process conditions important to an effective reformer process model. These include H2 consumption, recycle gas H2 purity, and key reformate properties such as octane number and vapor pressure. The following three lump types had to be delumped the C5- kinetic lump into Cl to C5 light gas components, the paraffin kinetic lumps into isoparaffin and n-paraffin components, and the Cg+ kinetic lumps into Cg, C9, C10, and Cn components by molecular type. 

Data used to develop the deactivation kinetics consisted of over 50 balances in the isothermal fixed bed reactor. Experimental conditions were 756 and 794 K isothermal reactor temperature, 551-1378 kPa H2 partial pressure, 137-344 kPa hydrocarbon partial pressure, and 1-26 liquid hourly space... 

The deactivation kinetics were determined through a series of seven separate parameter estimation problems. As with the start-of-cycle case, separate estimating problems resulted from uncoupling the reactions of each carbon number by properly selecting the charge stock. This allowed the independent determination of submatrices in the rate constant matrix Dp [Eq. (37)]. 

A Diagonal matrix of catalyst state veclor Mj Hydrocarbon partial pressure exponent in deactivation kinetics... 

CN Weight average C6. product carbon number P Hydrocarbon partial pressure vector in deactivation kinetics... 

Various reports can be found in the literature in connection with catalyst deactivation kinetics (Wojchiechowsky, 1968), some of them also taking into account the effects of diffusion resistance (Beeckman and Froment, 1980). 

Bunemann, M., Bucheler, M. M., Philipp, M., Lohse, M. J., and Hein, L. (2001). Activation and deactivation kinetics of alpha(2A)- and alpha(2C)-adrenergic receptor-activated G protein-activated inwardly rectifying K+ channel currents. / Biol. Chem. 276, 47512-47517. 

Enzymes with Incomplete Stability Deactivation Kinetics 119... 

For the optimal strategy of maintaining operational stability, Lee et al. have calculated the optimal profile of addition of fresh, non-deactivated enzyme into a CSTR under different deactivation kinetics. If a CSTR is charged initially with an amount of enzyme of initial activity N0, at time t under deactivation, the amount remaining is given by Eq. (5.83), where k(t) denotes an arbitrary deactivation function (J. Y. Lee, 1990). 

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