Reaction-Rate Data

We consider next the acquisition of data on the kinetics of a chemical reaction. We want rate expressions f(Cj, T) which we can insert into the relevant mass balance to predict reactor performance. The methods of acquiring these data, in order of increasing difficulty and expense, are 

Literature values. If the process is simple and well known, there may be rate expressions in the hterature that can be used. 

Estimations. If one can find a process similar to the one of interest, then rates can be estimated from these data. For example, if one finds a reactor for which a specified conversion is obtained with a specified reactant composition and temperature, then one may guess the orders of the reaction with respect to each species (guess first order) and proceed to formulate a reasonable rate expression. 

Theoretical rate calculations. Statistical mechanics permits one in principle to compute reaction-rate expressions from first principles if one knows the potential energy surface over which the reaction occurs, and quantum mechanics permits one to calculate this potential energy surface. In Chapter 4 we consider briefly the theory of reaction rates from which reaction rates would be calculated. In practice, these are seldom simple calculations to perform, and one needs to find a colleague who is an accomplished statistical mechanic or quantum mechanic to do these calculations, and even then considerable computer time and costs are usually involved. 

Kinetics measurements. When detailed literature data are not available and when one badly needs accurate kinetics, then the only recourse is to obtain kinetic data in the laboratory. 

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Many additional refinements have been made, primarily to take into account more aspects of the microscopic solvent structure, within the framework of diffiision models of bimolecular chemical reactions that encompass also many-body and dynamic effects, such as, for example, treatments based on kinetic theory [35]. One should keep in mind, however, that in many cases die practical value of these advanced theoretical models for a quantitative analysis or prediction of reaction rate data in solution may be limited. 

This involves knowledge of chemistry, by the factors distinguishing the micro-kinetics of chemical reactions and macro-kinetics used to describe the physical transport phenomena. The complexity of the chemical system and insufficient knowledge of the details requires that reactions are lumped, and kinetics expressed with the aid of empirical rate constants. Physical effects in chemical reactors are difficult to eliminate from the chemical rate processes. Non-uniformities in the velocity, and temperature profiles, with interphase, intraparticle heat, and mass transfer tend to distort the kinetic data. These make the analyses and scale-up of a reactor more difficult. Reaction rate data obtained from laboratory studies without a proper account of the physical effects can produce erroneous rate expressions. Here, chemical reactor flow models using matliematical expressions show how physical... 

Patterns in reaction rate data can often be identified by examining the initial rate of reaction, the instantaneous rate of change in concentration of a species at the instant the reaction begins (Fig. 13.6). The advantage of examining the initial rate is that the products present later in the reaction may affect the rate the interpretation of the rate is then quite complicated. There are no products present at the start of the reaction, and so any pattern due to the reactants is easier to find. 

Equation (1) consists of various resistance terms. l/Kj a is the gas absorption resistance, while 1/ K,a corresponds to the maleic anhydride diffusion resistance and l/i k represents the chemical reaction resistance. The reaction rate data obtained under the reaction conditions of 250°C and 70 atm were plotted according to equation (1). Although catalytic reaction data with respect to time on stream were not shown here, a linear correlation between reaction rate data and catalyst loading was observed as shown in Fig. 2. The gas absorption resistance (1/ a) was -1.26 h, while the combined reaction-diffusion resistance (lJK,a + 1 T]k) was determined to be 5.57 h. The small negative value of gas absorption resistance indicates that the gas-liquid diffusion resistance was very small and had several orders of magnitude less than the chanical reaction resistance, as similarly observed for the isobutene hydration over Amberlyst-15 in a slurry reactor [6]. This indicates that absorption of malei c anhydride in solvent was a rapid process compared to the reaction rate on the catalyst surface. 

The four constants in Equation 17.14 may be estimated by fitting the equation to the measured initial reaction rate data presented in Figure 17.3. Because equimolar concentrations of the two substrates, PCP and H202, were used in the experiments, Equation 17.14 may be simplified as follows ... 

Differential Methods for the Treatment of Reaction Rate Data... 

Test of reaction rate data by the integral method of analysis. 

Observation of curvature in tests of reaction rate data. 

Techniques for the Analysis of Reaction Rate Data that are Suitable for Use with Either Integral or Differential Methods... 

ILLUSTRATION 3.5 USE OF CONDUCTIVITY MEASUREMENTS IN CONJUNCTION WITH THE GRAPHICAL INTEGRAL METHOD FOR THE ANALYSIS OF REACTION RATE DATA... 

General Techniques for the Interpretation of Reaction Rate Data for Reversible Reactions. The determination of the mathematical form of a reaction rate expression is generally a two-step procedure. One first determines the dependence of the rate on the concentrations of the various reactant and product species at a fixed temperature and then evaluates the temperature dependence of the various rate... 

If an attempt is made to fit heterogeneous catalytic reaction rate data to a rate expression of the form... 

In kinetic studies of enzymatic reactions, rate data are usually tested to determine if the reaction follows the Michaelis-Menten model of enzyme-substrate interaction. Weetall and Havewala [Biotechnol. and Bioeng. Symposium 3 (241), 1972] have studied the production of dextrose from cornstarch using conventional... 

Reaction rate data were reported as a function of temperature and are shown in Figure 12P.4. Although the form of the intrinsic rate equation for ethylene hydrogenation for this specific catalyst is not known, one might anticipate an equation of the form... 

The reaction rate data developed for each chemical in the tables are used to select a reactivity class as described earlier, and hence a first-order rate constant for each medium. Often these rates are in considerable doubt thus the quantities selected should be used with extreme caution because they may not be widely applicable. The rate constants kj h 1 are used to calculate reaction D values for each medium DK as V/ k,. The rate of reactive loss is then DRif mol/h. 

Because of the lack of high-pressure experimental reaction rate data for HMX and other explosives with which to compare, we produce in Figure 15 a comparison of dominant species formation for decomposing HMX that have been obtained from entirely different theoretical approaches. The concentration of species at chemical equilibrium can be estimated through thermodynamic calculations with the Cheetah thermochemical code.32,109... 

Several other methods are available for analyzing reaction-rate data, such as utilizing linear least squares in the above methods, or such as the method of dimensionless curves. The procedures and their advantages and disadvantages... 

The hyperbolic model types have very commonly been used in the analysis of kinetic data, as discussed in Section I. Such applications are sometimes justified on the theoretical bases already alluded to, or simply because models of the form of Eq. (2) empirically describe the existing reaction-rate data. Considerably more complex models are quite possible under the Hougen-Watson formalism, however. For example, Rogers, Lih, and Hougen (Rl) have proposed the competitive-noncompetitive model... 

The usual data analysis procedures for the linearizable models typified by Eq. (2) consist of (1) isolating a class of plausible rival models by means of plots of initial reaction-rate data as a function of total pressure, feed composition, conversion, or temperature (2) fitting the models passing the screening requirements of the initial rates by linear least squares, and further rejecting models based upon physical grounds. 

For every set of reaction-rate data, a total amount of variability in the data may be expressed as... 

One important application of analysis of variance is in the fitting of empirical models to reaction-rate data (cf. Section VI). For the model below, the analysis of variance for data on the vapor-phase isomerization of normal to isopentane over a supported metal catalyst (Cl)... 

An augmented central composite design was used in obtaining reaction-rate data in a flow differential reactor the reaction occurring was the isomerization of normal pentane to isopentane in the presence of hydrogen (Cl). Using the subscripts 1, 2, and 3 for hydrogen, normal pentane, and isopentane respectively, an empirical rate equation can be written... 

While Table C8 includes reactions for the formation of thermal NO, it does not include those for prompt NO. Mechanisms and reaction rate data for prompt NO formation and various methods for the reduction of NO have been described by Miller and Bowman [Prog. Energy Combust. Sci. 15, 287(1989)]. 

Critical reviews of reaction rate data are constantly appearing in the literature and are an important source for mechanism construction. Some examples of recent reviews are given below. 

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