Characteristic reaction time Definition

This chapter covers the second fundamental concept used in chemical reaction engineering—chemical kinetics. The kinetic relationships used in the analysis and design of chemical reactors are derived and discussed. In Section 3.1, we discuss the various definitions of the species formation rates. In Section 3.2, we define the rates of chemical reactions and discuss how they relate to the formation (or depletion) rates of individual species. In Section 3.3, we discuss the rate expression that provides the relationship between the reaction rate, the temperature, and species concentrations. Without going into the theory of chemical kinetics, we review the common forms of the rate expressions for homogeneous and heterogeneous reactions. In the last section, we introduce and define a measure of die reaction rate—the characteristic reaction time. In Chapter 4 we use the characteristic reaction time to reduce the reactor design equations to dimensionless forms. 

Definition and determination of the characteristic reaction time as a measure... 

To gain insight into the structure of the dimensionless reaction-hased design equations, recall tiie definition of the characteristic reaction time, Eq. 3.5.1, ter = Co/ro. It follows that the scaling factor is ta/Cq) = I/tq, where tq is the reference rate of a selected chemical reaction. Substituting fliis relation into Eqs. 4.4.4,... 

The Damkoehler number Da represents the ratio of a characteristic reaction time to the kinetic time constant of the reaction and is therefore a measure for the reaction time. The attribute characteristic refers to the individual definition necessary for each... 

The equality in reactor behaviour of the stationary PFTR and unsteady BR, which was explained in Section 4.1.5, allows the direct formulation of the heat balance for the cooled BR. If the length of the PFTR is substituted by the characteristic reaction time for the batch process, and if the Stanton munber formulation is based on its general definition regarding the overall heat removal mechanism, the unsteady heat balance of the cooled BR is obtained. 

According to this definition, Damkohler number gives the ratio of the characteristic process time to the characteristic reaction time (Doherty and Malone, 2001) and captures effectively the major dependence of conversion, production rate and product purities on the feed flowrate, catalyst level and holdup (Chen et al., 2002). For an open... 

If we compare this equation with the definition of the Damkoehler number [Eq. (4.3.19)], we see that Da can be regarded as the ratio of the reaction time and the characteristic reaction time ... 

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. 

The mean reaction time or reaction timescale (also called relaxation timescale relaxation denotes the return of a system to equilibrium) is another characteristic time for a reaction. Roughly, the mean reaction time is the time it takes for the concentration to change from the initial value to 1/e toward the final (equilibrium) value. The mean reaction time is often denoted as x (or Xr where subscript "r" stands for reaction). The rigorous definition of x is through the following equation (Scherer, 1986 Zhang, 1994) ... 

Nauk (UkrainRSR) 1966(7), 871-74 CA 65, 19919 (1966) "Criterion of Uni-dimensional Instability of Gas Detonations (The criterion was derived by using Zel dovich-Von Neumann model, which represents a detonation wave in an ideal gas as a stationary complex consisting of a shock wave and the front of an instantaneously occurring reaction with a characteristic induction time that follows the shock wave at a definite distance. The results showed that the criterion assumes the form dependent... 

At high-mass-transfer Peclet numbers, sketch the relation between average residence time divided by the chemical reaction time constant (i.e., r/co) for a packed catalytic tubular reactor versus the intrapeUet Damkohler number Aa, intrapeiiet for zeroth-, first-, and second-order irreversible chemical kinetics within spherical catalytic pellets. The characteristic length L in the definition of Aa, intrapeiiet is the sphere radius R. The overall objective is to achieve the same conversion in the exit stream for all three kinetic rate laws. Put all three curves on the same set of axes and identify quantitative values for the intrapeiiet Damkohler number on the horizontal axis. 

Turnover Frequency. Two definitions for turnover frequency (TOF) appear in the literature. The first and most commonly used, is a rate of formation of D divided by the nominal moles of transition-metal used (precursor) IVtm- For convenience, this will be denoted as TOF. The second is the instantaneous rate of formation of D divided by the instantaneous moles of intermediates N. This will be denoted TOF. It is immediately apparent that TOF < TOF and that the two terms can vary greatly due to actual moles of intermediates present. The actual moles of intermediates present at a particular reaction time will depend, in large part, on the kinetics and selectivity of the precataljrtic transformations. Statistical and numerical aspects concerning the evaluation of TOF from in situ spectroscopic data are well vmderstood (15). The characteristic time scale for the catalysis will be denoted ttof, which has units of seconds, and it will be defined as Ttof = TOF-i. 

Only one partly mechanistic study has been reported [264], based on the chemometric optimisation of the reaction of o-nitrostilbene to afford 2-phenylindole, catalysed by Ru3(CO)i2. Evidence was gained for two different mechanisms, one of which involves a mononuclear complex, likely Ru(CO)s, whereas the other requires the presence of a cluster complex as catalyst. However, the equilibration between Ru3(CO)i2 and Ru(CO)s should be relatively slow under the reaction conditions, compared to the total reaction time. So the conclusions drawn should not be considered as completely definitive. Other characteristics of this system have already been discussed in detail in Chapter 5.3. and will not be further discussed here. 

The heat-transfer coefficient between the measuring kettle and the thermostat has a defined, finite value in accordance with which the heat transfer between their fillings occurs in a definite way The process is marked by a characteristic thermal time constant Trti,. Just so, a definite transfer coefficient exists for the heat flow from the reaction mixture into the temperature sensor, i.e. the heat flow is also marked by a characteristic time constant Tp. 

The development of a quantitative theory of a free-radical copolymerization implies the derivation of equations for the rate of the monomers depletion and the statistical characteristics of the chemical structure of macromolecules present in the reaction system at the given conversion p of monomers. Elaborating such a theory one should take into account a highly important peculiarity inherent to any free-radical copolymerization. This peculiarity is that the characteristic time of a macroradical life is appreciably less than the time of the process duration. Consequently, its products represent definitely... 

I consider there to be a sharp distinction between the most polar form of a molecule and its ionically dissociated form. The reason for this is empirical An ion is defined as a species carrying a charge equal to an integral multiple of the electronic charge, and this definition implies that it will have a characteristic predictable electronic spectrum and, under suitable conditions, mobility in an electric field. There is so far no evidence which would compel one to abandon this definition, and I think it is important to distinguish clearly in this context between reaction intermediates (chain carriers, active species) of finite life-time, and transition states. 

See Note 7 at the end of Chapter 2 for a definition of the characteristic time scales of reactions. 

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