Initial transient rates

Initial transient rates and selectivities of Fischer-Tropsch synthesis with CO2 as carbon source... 

P.H. Choi, K.W. Jun, S.J. Lee, M.J. Choi, K.W. Lee, Catalysis Letters 40 (1996) 115 H. Schulz, K. Beck, E. Erich, Stud. Surf. Sci. Catal. 36 (1988) 457 H. Schulz, S. Nehren, Erdol und Kohle - Erdgas - Petrochemie 39 (1986) 93 H. Schulz, G. Schaub, M. Claeys, T. Riedel, S. Walter, "Initial transient rates and selectivities of Fischer-Tropsch synthesis with CO2 as carbon source",... 

Figure 4.14 shows a similar galvanostatic transient obtained during C2H4 oxidation on Rh deposited on YSZ.50 Upon application of a positive current 1=400 pA with a concomitant rate of O2 supply to the catalyst I/2F=2.M0 9 mol O/s the catalytic rate increases from its open-circuit value r0=1.8 10 8 mol O/s to a new value r= 1.62-1 O 6 mol O/s which is 88 times larger than the initial unpromoted rate value. The rate increase Ar is 770 times larger than the rate of supply of O2 ions to the Rh catalyst surface. 

In all four cases, tlie initial reaction rates at the start of illumination in the continuous-feed photoreactor were higher than the pseudo-steady-state reaction rates the reaction rates declined over time until pseudo-steady-state operation was achieved. Tliis apparent deactivation phenomenon, often observed with aromatic contaminants, is discussed in Sec. III.E. In a transient reaction system, the time required to reach pseudo-steady-state operation also appears to increase in the same order as the reaction rates. For example, for the continuous photocatalytic oxidation of aromatic contaminants at 50 mg/m in a powder-layer photoreactor, the time required for pseudo-steady-state operation to be achieved was reported to be approximately 90 min for benzene, 120 min for toluene, and as long as 6 hr for wz-xylene [50,51]. Under such conditions, the difference in reaction rates between the aromatic contaminants is magnified by the fact that the more reactive aromatics retain their higher transient reaction rates for longer periods (Fig. 7). 

The fact that there are now two equations, viz. (8.12) and (8.9), implies that no longer is y(t) determined by /(0) alone, but by the initial vaue of a2 as well. One might hope that, after a short initial transient time, o2 adjusts itself by rapidly approaching an asymptotic value depending on the instantaneous y(t) alone, so that a renormalized equation for / holds after the initial transient. However, this is not the case the time scale on which a2 approaches (8.10) is determined by the coefficient a in (8.9) and is therefore comparable to the rate at which / itself varies, see (8.7). There is no separation of time scales and therefore no single equation for / by itself. 

As described in Section 9.2.2, grain-boundary diffusion rates in the Type-C diffusion regime can be measured by the surface-accumulation method illustrated in Fig. 9.12. Assume that the surface diffusion is much faster than the grain-boundary diffusion and that the rate at which atoms diffuse from the source surface to the accumulation surface is controlled by the diffusion rate along the transverse boundaries. If the diffusant, designated component 2, is initially present on the source surface and absent on the accumulation surface and the specimen is isothermally diffused, a quasi-steady rate of accumulation of the diffusant is observed on the accumulation surface after a short initial transient. Derive a relationship between the rate of accumulation... 

Solution. Because of the fast surface diffusion, the concentrations of the diffusant on both surfaces are essentially uniform over their areas. After the initial transient, the quasi-steady rate (per unit area of surface) at which the diffusant diffuses along the transverse boundaries between the two surfaces is... 

Although the purpose of this investigation was to study the initial transient behavior of heatless adsorption, the best removal of hydrogen sulfide occurred in the run with 3.01% H S and a y = 2.88, cycle time of 12 minutes and feed rate of 190 sCCM. Removal was down to 99.55% in three hours. For the 6.32% feed the best removal for the same time period was 98.49%. 

Some materials exhibit nearly steady mass loss rates when exposed to a fixed radiant heat flux. The surface temperature for these materials reaches a steady value after a short initial transient period, and all terms in Equation 14.7 are approximately constant at a specified heat flux level. L can then be obtained by measuring steady mass loss rates at different radiant heat flux levels, and... 

X 10 and 1.6 X 10 cm /sec for steps 1 and 2, respectively). It is seen that the initial diffusion rate increases with concentration in the polymer (based on the initial slope of the curves), until, at higher concentrations, a two-stage absorption transient occurs. This behavior, which is typical of glassy polymers, is due to the fact that diffusion begins to become faster than die polymer relaxations [95]. 

The d -law assumes a constant Tg. However, in many practical situations the temperature of the droplet when introduced into the evaporator is far below this final, equilibrium value. Hence an initial transient heating period exists during which y, and Tf all increase whereas H decreases. Furthermore it can be estimated also that the sensible heat required to heat the droplet is of the same order as the latent heat of vaporization. Hence droplet transient heating effects on the bulk vaporization characteristics are expected to be significant. Two such models, representing extreme rates of internal heating, will be discussed. 

A batch reactor by its nature is a transient closed system. While a laboratory batch reactor can be a simple well-stirred flask in a constant temperature bath or a commercial laboratory-scale batch reactor, the direct measurement of reaction rates is not possible from these reactors. The observables are the concentrations of species from which the rate can be inferred. For example, in a typical batch experiment, the concentrations of reactants and products are measured as a function of time. From these data, initial reaction rates (rates at the zero conversion limit) can be obtained by calculating the initial slope (Figure 3.5.1b). Also, the complete data set can be numerically fit to a curve and the tangent to the curve calculated for any time (Figure 3.5. la). The set of tangents can then be plotted versus the concentration at which the tangent was obtained (Figure 3.5.1c). 

In a first series of experiments, transient kinetics were studied. After a certain time on stream at a constant flow rate of, e.g., 120 ml - min l a steady state was reached (Figure 1). This was characterised by a constant conversion and an exact stoichiometry according to equ. (1), in agreement with earlier results. When the flow rate was suddenly lowered, i.e., the contact time increased, the expected increase in conversion was observed. However, first an excess of benzene was produced but the new steady-state yield, Y, of benzene was relatively quickly reached. By contrast, the yield of diethylbenzenes only slowly increased from low values to the new steady-state. This indicates a preferential adsorption of the product diethylbenzene. The effect was reversible. When the initial flow rate was re-adjusted, the original conversion was approached, whereby the initial steady-... 

Here (g feed/g cat/h) are the rate constants determined at time zero which is the time required for the initial transients to disappear (/ 40 hours). With the already-determined a, and r , Eq.(12) gives A, at any on-stream time after t. Figure 11 shows excellent agreement between the predicted and measured time evolutions of the rate constants at 517 kPa, 750 K, and H nCv = 3 [15], thus permitting the prediction of the time evolution of the product compositions. Moreover, the assumption that the reforming reactions and coking have the same ( ) is reasonable. 

Another aspect49 is the initial presence of persistent species in nonzero concentrations [Y]o, and it will be discussed more closely in section IV. In the absence of any additional initiation, the excess [Y]o at first levels the transient radical concentration to an equilibrium value [R]s = A[I]o/[Y]o. This is smaller than that found without the initial excess and lowers both the initial conversion rate and the initially large PDI. Further, it provides a linear time dependence of ln-([M]o/[M]), which is directly proportional to the equilibrium constant. Later in the reaction course, [Y] may exceed [Y]0 because of the self-termination, then [R] is given by eq 18. If there is additional radical generation, the first stages will eventually be replaced by a second stationary state that was described above. Further effects are expected from a decay or an artificial removal of the persistent species that increases the concentration of the transient radicals and the polymerization rate (see section IV). Radical transfer reactions to polymer, monomer, or initiator have not yet been incorporated in the analytical treatments. 

In this catalytic system, as schematically shown in Fig. 10.9 [48], a most probable pathway is that over the Au surfaces O2 and H2 react with each other to form H2O2, which then move to isolated sites of Ti cations to form Ti-OOH species [49]. This oxidic species react with propylene adsorbed on the support surfaces to form PO. It has recently been verified that Ti-OOH species is a true reaction intermediate and that a bidentate propoxy species is probably a spectator on the surface [50]. The coverage, 6, of the Ti-hydroperoxo species was determined from the area of the pre-edge peak in the Ti K-edge XANES spectra at reaction conditions. Measurement of the changes in Ti-hydroperoxo coverage, dO/dt, under transient experiments at reaction conditions with H2/02/Ar and C3H6/H2/O2 gas mixtures, allowed the estimation of initial net rate of propylene epoxidation (3.4 x 10 s ), which closely matched the TOP (2.5 x 10 s ) obtained for the same catalyst at steady-state conditions. 

---