Intrinsic deactivation rate constant

In the following paragraphs, we will investigate the relationship between the observed deactivation rate constant kd obs and the intrinsic deactivation rate constant kd. 

A series of CoMo/Alumina-Aluminum Phosphate catalysts with various pore diameters was prepared. These catalysts have a narrow pore size distribution and, therefore, are suitable for studying the effect of pore structure on the deactivation of reaction. Hydrodesulfurization of res id oils over these catalysts was carried out in a trickle bed reactor- The results show that the deactivation of reaction can be masked by pore diffusion in catalyst particle leading to erro neous measurements of deactivation rate constants from experimental data. A theoretical model is developed to calculate the intrinsic rate constant of major reaction. A method developed by Nojcik (1986) was then used to determine the intrinsic deactivation rate constant and deactivation effectiveness factor- The results indicate that the deactivation effectiveness factor is decreased with decreasing pore diameter of the catalyst, indicating that the pore diffusion plays a dominant role in deactivation of catalyst. 

Fig.4. Intrinsic deactivation rate constant and apparent deactivation rate constant v.s. average pore diameter.

Generally, as the Thiele modulus of main reaction is smaller than unity, the order of deactivation is equal to unity and, therefore, the apparent deactivation rate constant can he extracted from the slope of -In Xs(t) versus t Krishnaswamy and Kittrell (ref. 10) have shown that the relationship between the intrinsic deactivation rate constant k and the apparent deactivation rate constant kda can be expressed as... 

When one metal ion is used as a donor for sensitizing the emission of a second accepting metal ion, the characteristic lifetimes r of their excited states, which are related to their deactivation rates by r = k l, are affected by the metal-to-metal communication process. This situation can be simply modeled for the special case of an isolated d-f pair, in which the d-block chromophore (M) sensitizes the neighboring lanthanide ion (Ln) thanks to an energy transfer process described by the rate constant k 1 ". In absence of energy transfer, excited states of the two isolated chromophores decay with their intrinsic deactivation rates kxl and kLn, respectively, which provides eqs. (32) and (33) yielding eqs. (34) and (35) after integration ... 

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). 

Bertole et al.u reported experiments on an unsupported Re-promoted cobalt catalyst. The experiments were done in a SSITKA setup, at 210 °C and pressures in the range 3-16.5 bar, using a 4 mm i.d. fixed bed reactor. The partial pressures of H2, CO and H20 in the feed were varied, and the deactivation, effect on activity, selectivity and intrinsic activity (SSITKA) were studied. The direct observation of the kinetic effect of the water on the activity was difficult due to deactivation. However, the authors discuss kinetic effects of water after correcting for deactivation. The results are summarized in Table 1, the table showing the ratio between the results obtained with added water in the feed divided by the same result in a dry experiment. The column headings refer to the actual experiments compared. It is evident that adding water leads to an increase in the overall rate constant kco. The authors also report the intrinsic pseudo first order rate-coefficient kc, where the overall rate of CO conversion rco = kc 6C and 0C is the coverage of active... 

Triplet decay in the [Mg, Fe " (H20)] and [Zn, Fe (H20)] hybrids monitored at 415 nm, the Fe " / P isosbestic point, or at 475 nm, where contributions from the charge-separated intermediate are minimal, remains exponential, but the decay rate is increased to kp = 55(5) s for M = Mg and kp = 138(7) s for M = Zn. Two quenching processes in addition to the intrinsic decay process (k ) can contribute to deactivation of MP when the iron containing-chain of the hybrid is oxidized to the Fe P state electron transfer quenching as in Eq. (1) (rate constant kj, and Forster energy transfer (rate constant kj. The triplet decay in oxidized hybrids thus is characterized by kp, the net rate of triplet disappearance (kp = k -I- ki -I- kj. The difference in triplet decay rate constants for the oxidized and reduced hybrids gives the quenching rate constant, k = kp — kj, = k, -I- k , which is thus an upper bound to k(. 

The intrinsic lifetime of triplet Ti state tp°, is the reciprocal of the rate constant kp, for phosphorescence emission and the actual lifetime if, is the reciprocal of the sum of all the steps which deactivate tne triplet. 

It is important to bear in mind the fact that the intrinsic reactivity of an excited state is given by the rate constant, not by the quantum yield. An excited state can be very reactive5 in terms of the rate constant, yet the reaction quantum yield can be very low if it is of very short lifetime as a result of other deactivation or quenching processes. 

Estimates of Model Parameters. The reactor models for FFB, MAT and riser include important features for translating the MAT and FFB data to steady state riser performance. A series of key parameters specific to a given zeolite and matrix component are needed for a given catalyst. Such key parameters are intrinsic cracking anc( coking activities (kj, A ), activation energies and heats of reaction (Ej, AHj), coke deactivation rate (exponents nj), and axial dispersion in the FFB unit (DA). Other feedstock dependent parameters include the inhibition constants (kHAj), the coking constants (XAj), and the axial molar expansion factor (a). 

The results ate consistent with the work of Stephens and Stohl (ref. 11). They used the catalyst of Run 242 for the hydrogenation of pyrene, a liquid—phase reaction. The catalysts were ground to obtain separate intrinsic rate constants. Their data indicate an efCectivenesB factor for the catalyst in sample 4 of 0.42 our numbers for thiophene EDS correspond to 0.36, in reasonable agreement. The results of Stephens and Stohl further indicate a drop in the rate constant for the ground catalyst with catalyst age (between 42 and 527 lb product/lb catalyst), while the calculated elective diffusivity is constant. These results, and ours, point to site suppression being the predominant mode of deactivation in this range. 

The rigorous definition of activity is the ratio of the rate of reaction (or rate constant) on a catalyst after some time, t, to the rate (or rate constant) on a fresh catalyst at the same conditions. Thus, the loss of catalytic ability with time in use is called deactivation. However, the term activity is also often used to merely refer to the rate constant, k, or to the intrinsic ability of a catalyst to carry out a reaction. 

In the simplest case, the catalytic activity is proportional to the number of active sites Nj, intrinsic rate constant and the effectiveness factor. Catalyst deactivation can be caused by a decrease in the number of active sites, changes in the intrinsic rate constant, e.g. changes in the ability of surface sites to promote catalysis and by degradation in accessibility of the pore space. When the reaction and deactivation rates are of different magnitudes, the reactions proceed in seconds while the deactivation can require hours, days or months, and moreover the deactivation does not affect the selectivity, the concept of separability is applied. The reaction rates and deactivation are treated by different equations. A quantity called activity, (a) is introduced to account for changes during the reaction. 

A separable form has been taken to relate the influence of deactivation on the main reaction, which is first order and irreversible with no volume change, intrinsic rate constant k. Thus, at any time the net rate constant for the main reaction is the product ks, with... 

In previous sections we have dealt with nonisothermal effects arising from the thermochemistry of the reactions involved. There is another type of thermal effect that appears in the operation of large-scale reactors such as those used in hydrotreating. These reactors are normally subject to slow catalyst deactivation, and constant conversion operation is required in order not to upset subsequent processing units. Here the reactor temperature is used to cope with the loss of intrinsic catalyst activity and the thermal parameters of the main and deactivation reactions, particularly the activation energies, have a great influence on the operation. Further, it has been common practice in many industrial laboratories for many years to evaluate catalyst activity and activity maintenance for such processes in laboratory experiments which are also conducted under constant-conversion conditions. In this procedure, catalyst deactivation effects are manifested in the rate of temperature increase needed to maintain constant conversion, that is, a temperature increase required (TIR). 

Ln-L distance, energy transfer occurs as long as the higher vibrational levels of the triplet state are populated, that is the transfer stops when the lowest vibrational level is reached and triplet state phosphorescence takes over. On the other hand, if the Ln-L expansion is small, transfer is feasible as long as the triplet state is populated. If the rate constant of the transfer is large with respect to both radiative and nonradiative deactivation of T, the transfer then becomes very efficient ( jsens 1, eqs. (11)). In order to compare the efficiency of chromophores to sensitize Ln - luminescence, both the overall and intrinsic quantum yields have to be determined experimentally. If general procedures are well known for both solutions (Chauvin et al., 2004) and solid state samples (de Mello et al., 1997), measurement of Q is not always easy in view of the very small absorption coefficients of the f-f transitions. This quantity can in principle be estimated differently, from eq. (7), if the radiative lifetime is known. The latter is related to Einstein s expression for the rate of spontaneous emission A from an initial state I J) characterized by a / quantum number to a final state J ) ... 

Subscript and superscript Ln have been added to avoid confusion with the other definition of quantum yield discussed below. The quantity defined in (16) is called the intrinsic quantum yield, that is, the quantum yield of the metal-centered luminescence upon direct excitation into the 4f levels. Its value reflects the extent of nomadiative deactivation processes occurring both in the inner- and outer-coordination spheres of the metal ion. The rate constant A obs is the sum of the rates of the various deactivation processes ... 

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