Reaction Time-scales

In stark contrast to the transport considerations, typical time-scales for elementary and non-elementary steps in organometallic chemistry and homogeneous catalysis range from vibrational motions of ca. 10 s or less [44], to ca. hours or even days for the formation of products and side products. Moreover, the three pri- 

1) The experimentalist should treat this optimistic time with caution. Our group s first attempts at CSTR recycle with in-Une cells resulted in characteristic times of the order of 

300-500 s in the presence of g-1 mass transfer. The presence of dead volumes should not be casually dismissed. 

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). 

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In order to derive specific numbers for the temperature rise, a first-order reaction was considered and Eqs. (10) and (11) were solved numerically for a constant-density fluid. In Figure 1.17 the results are presented in dimensionless form as a function of k/tjjg. The y-axis represents the temperature rise normalized by the adiabatic temperature rise, which is the increase in temperature that would have been observed without any heat transfer to the channel walls. The curves are differentiated by the activation temperature, defined as = EJR. As expected, the temperature rise approaches the adiabatic one for very small reaction time-scales. In the opposite case, the temperature rise approaches zero. For a non-zero activation temperature, the actual reaction time-scale is shorter than the one defined in Eq. (13), due to the temperature dependence of the exponential factor in Eq. (12). For this reason, a larger temperature rise is foimd when the activation temperature increases. 

Figure 1.18 Lines of constant temperature rise AT = 10 K) for micro channels of different radius in a plane spanned by the adiabatic temperature rise of the reaction and the reaction time-scale, obtained from [114]. The properties of nitrogen at 300 °C and 1 atm and a Nusselt number of 3.66 were used for this calculation.

In order to exemplify the potential of micro-channel reactors for thermal control, consider the oxidation of citraconic anhydride, which, for a specific catalyst material, has a pseudo-homogeneous reaction rate of 1.62 s at a temperature of 300 °C, corresponding to a reaction time-scale of 0.61 s. In a micro channel of 300 pm diameter filled with a mixture composed of N2/02/anhydride (79.9 20 0.1), the characteristic time-scale for heat exchange is 1.4 lO" s. In spite of an adiabatic temperature rise of 60 K related to such a reaction, the temperature increases by less than 0.5 K in the micro channel. Examples such as this show that micro reactors allow one to define temperature conditions very precisely due to fast removal and, in the case of endothermic reactions, addition of heat. On the one hand, this results in an increase in process safety, as discussed above. On the other hand, it allows a better definition of reaction conditions than with macroscopic equipment, thus allowing for a higher selectivity in chemical processes. 

In Table 1.4, the characteristic time-scales for selected operations are listed. The rate constants for surface and volume reactions are denoted by and respectively. Furthermore, the Sherwood number Sh, a dimensionless mass-transfer coefficient and the analogue of the Nusselt number, appears in one of the expressions for the reaction time-scale. The last column highlights the dependence of z p on the channel diameter d. Apparently, the scale dependence of different operations varies from dy f to (d ). Owing to these different dependences, some op-... 

The spatio-temporal variations of the concentration field in turbulent mixing processes are associated wdth very different conditions for chemical reactions in different parts of a reactor. This scenario usually has a detrimental effect on the selectivity of reactions when the reaction time-scale is small compared with the mixing time-scale. Under the same conditions (slow mixing), the process times are increased considerably. Due to mass transfer inhibitions, the true kinetics of a reaction does not show up instead, the mixing determines the time-scale of a process. This effect is known as mixing masking of reactions [126]. 

The standard example is A + B - P, where the reaction time scale is much shorter than the Kolmogorov time scale. 

A purely thermodynamic treatment of detonation ignores the important question of reaction time scales. The finite time scale of reaction leads to strong deviations in detonation velocities from values based on the Chapman-Jouguet theory.16 The kinetics of even simple molecules under high-pressure conditions is not well understood. 

As an analyst, if we were to perform a series of simple experiments to study the kinetics of bromine consumption, we would start the experiment (at a time we call t = 0) and then monitor the amount of bromine remaining as a function of time after t = 0. Probably the simplest way of monitoring this process would be to remove aliquots of reaction solution after various lengths of time, and titrate each of these, e.g. with thiosulfate, to determine the amount of bromine remaining in each sample. In effect, we say here that chemical kinetics is the study of the proportion of the matter that is initially present as a function of the reaction time-scale r. 

The subsurface liquid phase generally is an open system and its composition is a result of dynamic transformation of dissolved constituents in various chemical species over a range of reaction time scales. At any particular time the liquid phase is an electrolyte solution, potentially containing a broad spectrum of inorganic and organic ions and nonionized molecules. The presently accepted description of the energy characteristics of the liquid phase is based on the concept of matrix and osmotic potentials. The matrix potential is due to the attraction of water to the solid matrix, while the osmotic potential is due to the presence of solute in the subsurface water. 

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. 

Treact — superficial chemical reaction time scale = H/fciR Then after a short calculation we get the non-dimensional form of Equation (24) ... 

Question (b) is a matter of chemical kinetics and reduces to the need to know the rate equation and the rate constants (customarily designated k) for the various steps involved in the reaction mechanism. Note that the rate equation for a particular reaction is not necessarily obtainable by inspection of the stoichiometry of the reaction, unless the mechanism is a one-step process—and this is something that usually has to be determined by experiment. Chemical reaction time scales range from fractions of a nanosecond to millions of years or more. Thus, even if the answer to question (a) is that the reaction is expected to go to essential completion, the reaction may be so slow as to be totally impractical in engineering terms. A brief review of some basic principles of chemical kinetics is given in Section 2.5. 

A ratio of Cas to the rate of catalytic reaction under steady-state conditions (r) gives a rough estimation for the reaction time scale. For typical heterogeneous catalytic processes applied for the production of bulk chemicals and petrochemicals, this value is estimated to be 10-2—101 s (Fig. 5). The changes of the reaction rate caused by the side processes of catalyst modification can take considerably longer. This is attributed to the higher capacity of substances in the catalyst bulk phase that can be involved in side interactions and to a slow rate of side processes in comparison with the stages of the catalytic cycle. 

In order to find the evolution of species concentration or temperature with time, the above equations must be integrated. For complex reaction mechanisms this usually means integration by numerical methods. There are a large number of schemes for the numerical integration of coupled sets of differential equations, but not all will be suitable for the types of mechanisms we are discussing. Chemical systems form a difficult problem because of the differences in reaction time-scale between each of the... 

Comparison of equations 3 and 10 shows the essential difference between the stationary states of closed and continuous, open systems. For the closed system, equilibrium is the time-invariant condition. The total of each independently variable constituent and the equilibrium constant (a function of temperature, pressure, and composition) for each independent reaction (ATab in the example) are required to define the equilibrium composition Ca- For the continuous, open system, the steady state is the time-invariant condition. The mass transfer rate constant, the inflow mole number of each independently variable constituent, and the rate constants (functions of temperature, pressure, and composition) for each independent reaction are requir to define the steady-state composition Ca- It is clear that open-system models of natural waters require more information than closed-system models to define time-invariant compositions. An equilibrium model can be expected to describe a natural water system well when fluxes are small, that is, when flow time scales are long and chemical reaction time scales are short. 

Ratio of convective time scale to reaction time scale ratio of convective transport to rate of generation due to chemical reaction... 

When local micromixing is slow compared to the reaction time scale and the macromixing time scale is smaller than the process time scale, the performance of a reactive flow process is controlled only by the micromixing. In such cases, though there is no macroscopic segregation, reactants are not mixed on a molecular scale (see the right bottom case of Fig. 5.5). Several micromixing models have been developed to simulate such reactive flow processes. Some of the widely used models are ... 

A simple, homogeneous (slow) first-order reaction was considered. Simulations were carried out for cases with and without impeller in the same cubical reactor. Initial and boundary conditions are shown in Fig. 7.20. It can be seen that the mean residence time of the reactor is 10 s. Three cases with different first-order reaction rate constants (0.01s", 0.1s", 1.0s" ) were simulated (samples of the results are listed with Fig. 7.20). Results of simulations with an impeller velocity of 5 m s" are discussed first. As expected, for the lowest reaction rate constant, where the characteristic reaction time scale is much higher than mean residence time, the simulated results agree quite well with the analytical solution obtained based on the assumption of a completely mixed reactor. Even for the case of characteristic reaction time scale of 10 s (which is the same as the residence time), deviation from the analytical solution (of predicted outlet concentration of reactant) is just about 1% (for the case with rate constant 0.1 s" ). As the reaction time scale becomes smaller than residence time (rate constant 1.0 s" ), deviation increases and is equal to 33% If the reaction... 

Develop initial guesses on mechanism, reaction time scale, and potential kinetic models from the literature, scoping experiments, similar chemistries, and computational chemistry calculations, when possible. 

Selection of the laboratory reactor type and size, and associated feed and product handling, control, and analytical schemes depends on the type of reaction, reaction time scales, and type of analytical methods required. The criteria for selection include equipment cost, ease of operation, ease of data analysis, accuracy, versatility, temperature uniformity, and controllability, suitability for mixed phases, and scale-up... 

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