Deactivation, time constant

The activation and deactivation time constants represent the different dynamic characteristics of muscle under increasing and decreasing stimulation. 

Do not infer from the above discussion that all the catalyst in a fixed bed ages at the same rate. This is not usually true. Instead, the time-dependent effectiveness factor will vary from point to point in the reactor. The deactivation rate constant kj) will be a function of temperature. It is usually fit to an Arrhenius temperature dependence. For chemical deactivation by chemisorption or coking, deactivation will normally be much higher at the inlet to the bed. In extreme cases, a sharp deactivation front will travel down the bed. Behind the front, the catalyst is deactivated so that there is little or no conversion. At the front, the conversion rises sharply and becomes nearly complete over a short distance. The catalyst ahead of the front does nothing, but remains active, until the front advances to it. When the front reaches the end of the bed, the entire catalyst charge is regenerated or replaced. 

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

The elements of range in value from 0 to 1 and are the ratio of the reformer kinetic constants at time on stream t to the values at start of cycle. At any time on stream t, the deactivation rate constant matrix K(a) is determined by modifying the start-of-cycle K with a. From the catalytic chemistry, it is known that each reaction class—dehydrogenation, isomerization, ring closure, and cracking—takes place on a different combination of metal and acid sites (see Section II). As the catalyst ages, the catalytic sites deactivate at... 

Rate Decay. The decay time constant decreases as the olefin concentration increases. This is consistent with a deactivation mechanism... 

The rate decay time constant is independent of cation form of the zeolite in the ethene system (Figure 4) although the alkylation activity of the three forms is considerably different (Figure 2). This indicates that the active site within the zeolite (at least for deactivation) is the same for all three cation forms as expected from our current picture of active sites for acid-catalyzed reactions in these zeolites (8, 18, 19). The three catalysts should have different numbers of active sites because of their individual response to activation at 823°K, but these sites should be similar thus M2 should be independent of cation form, Mi should depend on it. 

Every (bio)catalyst can be characterized by the three basic dimensions of merit -activity, selectivity and stability - as characterized by turnover frequency (tof) (= l/kcat), enantiomeric ratio (E value) or purity (e.e.), and melting point (Tm) or deactivation rate constant (kd). The dimensions of merit important for determining, evaluating, or optimizing a process are (i) product yield, (ii) (bio)catalyst productivity, (iii) (bio)catalyst stability, and (iv) reactor productivity. The pertinent quantities are turnover number (TON) (= [S]/[E]) for (ii), total turnover number (TTN) (= mole product/mole catalyst) for (iii) and space-time yield [kg (L d) 11 for iv). Threshold values for good biocatalyst performance are kcat > 1 s 1, E > 100 or e.e. > 99%, TTN > 104-105, and s.t.y. > 0.1 kg (L d). ... 

The validity of a first-order decay law over time for the activity of enzymes according to Eq. (2.19), with [E]t and [E]0 as the active enzyme concentration at time t or 0, respectively, and kd as the deactivation rate constant, is based on the suitability of thinking of the deactivation process of enzymes in terms of Boltzmann statistics. These statistics cause a certain number of active protein molecules to deactivate momentarily with a rate constant proportional to the amount of active protein [ for evidence for such a catastrophic decomposition, see Craig (1996)]. 

Temperature along the Riser Height Temperature (T) affects the cracking (k.) and deactivation (VO constants (or functions). It also influences the gas density and, as a consequence, the flow rates, the superficial velocities, and the residence time of the gas in the riser. Its effect on ki makes the product distribution (gas, coke, etc.) dependent on T. 

Thus if one wants to improve the overall quantum yield of /3-diketonate complexes, removal of coordinated water molecules is absolutely necessary. By means of the estimated nonradiative deactivation rate constants, calculations showed that removal of these water molecules allows one to reach a maximum quantum yield of 2.6% in toluene for the Ybm-tta complex. However, water molecules are usually replaced with a coordinating secondary ligand, such as phenanthroline, which also contributes to the nonradiative deactivation ( Phen 3.6 x 104 s-1), but to a much lesser extent than water molecules. Further improvement can be reached by deuteration of the central C-H group in the /i-dikctonatc in Yb(ttax/i )3(phcn) for instance, deactivation due to C-H oscillators occurs eight times faster when compared to C-D oscillators. 

Activity-versus-time curves shown in Fig. 25 for alumina-supported Ni and Ni bimetallic catalysts show two significant facts (1) the exponential decay for each of the curves is characteristic of nonuniform pore-mouth poisoning, and (2) the rate at which activity declines varies considerably with metal loading, surface area, and composition. Because of large differences in metal surface area (i.e., sulfur capacity), catalysts cannot be compared directly unless these differences are taken into account. There are basically two ways to do this (1) for monometallic catalysts normalize time in terms of sulfur coverage or the number of H2S molecules passed over the catalysts per active metal site (161,194), and (2) for mono- or bimetallic catalysts compare values of the deactivation rate constant calculated from a poisoning model (113, 195). 

According to this relationship a plot of In [(1 — a)/a] versus t should result in a straight line with slope njc which enables calculation of deactivation rate constants from activity-versus-time curves like those in Figs. 25 and 26 if activity is proportional to the number of unpoisoned sites. 

Deactivation parameters obtained by plotting ln[(l — a) a)] versus time are listed in Table XIX for a number of nickel and nickel bimetallic catalysts. The fact that these plots were generally linear confirms that these data are fitted well by this deactivation model. These data, which include initial site densities for sulfur adsorption, deactivation rate constants, and breakthrough times for poisoning by 1-ppm H2S at a space velocity of 3000 hr-1 provide meaningful comparisons of sulfur resistance and catalyst life for both unsupported and supported catalysts. Table XIX shows that the... 

Up to this point, we have accepted without comment that we can get a value for R(0). To find R (0), all we have to do, in principle, is to measure the rate of reaction at time equal to zero. For many systems, in particular, those that deactivate with a time constant long compared to the time scale on which conversion measurements are made, determining the initial rate is relatively easy as depicted on Figure 4. In other systems, the deactivation rate is fast and the problem of determining the initial reaction rate is very difficult. A well-known example of this kind of system is the cracking of hydrocarbons. 

Conversions and production levels both increased with increases in the pellet deactivation time (pore-mouth) or time constant for poison deposition (uniform). 

Fig. 29. Relative activity as a function of time at various values of the deactivation rate constant (A) and at various values of the mean void radius (B). The time dependence of the critical radius is described by Eq. (49).

A modified form of eqn. 3, in which the time constants for catalyst deactivation were assumed to be independent of temperature, was used to analyze the deactivation of a different methanol-synthesis catalyst in a series of commercial, packed-bed reactors [ref. 8]. The values of a[T) shown in Fig. 5 are about an order of magnitude higher than those derived in ref. 8. 

From the values of TOF, the increasing order of activity for the fresh catalysts in the hydrogenation of ethylbenzene is Pd < Ni < Pt < Rh < Ru, Concerning the deactivation process, the intrinsic order of sulfur resistance appears to be Ru Rh Ni > Pd > Pt. On the other hand, the half deactivation time and the catalyst life decrease in the order Rh > Ru Pd Ni > Pt. This difference is due to the fact that the lifetime of a particular catalyst is an extensive property, which depends both on the deactivation rate constant (k l and the initial number of exposed metal atoms (N). Finally, we want to point out the small differences in the activity found for the fresh catalysts (CRu/CPd - 1.6), as compared with the greater values of their sulfur resistance (CRu/CPd = 6.5 or CRu/CPt = 12.5). 

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