TREATMENT OF EXPERIMENTAL DATA

Data of the behavior of chemical reactions are obtained from laboratory units designed for or adapted to the purpose, or from pilot plant or commercial units. The larger units have the advantages of more instrumentation and controls but have less flexibility. Fundamentally what is determined is the time dependence of composition or pressure, or some measurement that can be related to these properties, and of the temperature. 

Various kinds of laboratory reactors differ in some important respects, some definitely better than others. The criteria include  

In terms of cost and versatility the batch reactor is the unit of choice. One disadvantage is the need for frequent sampling or monitoring of the performance, although instrumentation can be provided at moderate cost nowadays. The residence time can be varied over a wide range and many different reactions can be handled at different times. The quality of mixing and heat transfer may not be easy to relate to those in an eventual commercial unit. 

Tubular flow units, like the CSTR, usually are operated at steady state. It is not always easy to measure the temperature profile accurately. In some high temperature operations, the coil is immersed in a fluidized sand bed or ft lead bath so there is fairly good temperature control. Sometimes it is felt desirable to do the laboratory work in a tubular unit if the commercial unit is to be of that type, but rate data from any kind of equipment are adaptable [ to the design of PFR. 

Reactions between phases — gas-liquid, liquid-liquid or fluid-solid — is carried out in CSTR-like devices. With granular solids such as catalysts or Immobilized enzymes, the preferred laboratory equipment nowadays is a rotating basket or fixed basket through which the fluid is recirculated continuously, with net input and output to the chamber. 

Our concern with the treatment of experimental data does not end when we have obtained a numerical result for the quantity of interest. We must also answer the question How good is the numerical result Without an answer to this question, the numerical result may be next to nseless. The expression of how good the result may be is usually couched in terms of its accuracy, i.e., a statement of the degree of the uncertainty of the resnlt. A related question, often to be asked before the experiment is begun, is How good does the resnlt need to be The answer to this question may influence important decisions as to the experimental design, equipment, and degree of effort required to achieve the desired accuracy. 

Indeed, it may be useful to discuss the matter also in econontic terms. The econontic valne of the numerical result of an experiment often depends on its degree of accuracy. To claim too high an accuracy through ignorance, carelessness, or self-deception is to cheat the consumer who makes decisions on the basis of this result. To claim too low an accuracy through overconservatism or intellectual laziness lessens the value of the result to the consumer and wastes resomces that have been employed to achieve the accuracy that could rightfully have been claimed. These issues of errors and the accuracy of a result are dealt with in Part B of this chapter. 

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The subject of entropy is introduced here to illustrate treatment of experimental data sets as distinct from continuous theoretical functions like Eq. (1-33). Thermodynamics and physical chemistry texts develop the equation... 

Young, H. D., 1962. Statistical Treatment of Experimental Data. McGraw-Hill, New York. 

Flow Models. Many flow models have been proposed (10,12), which are useful for the treatment of experimental data or for describing flow behavior (Table 1). However, it is likely that no given model fits the rheological behavior of a material over an extended shear rate range. Nevertheless, these models are useful for summarizing rheological data and are frequently encountered in the Hterature. 

Equation 46 is a general expression that may be applied to the treatment of experimental data to evaluate exponent a. This, however, is a cumbersome approach that can be avoided by rewriting the equation in dimensionless form. Equation 42 shows that there are n = 5 dimensional values, and the number of values with independent measures is m = 3 (m, kg, sec.). Hence, the number of dimensionless groups according to the ir-theorem is tc = 5 - 3 = 2. As the particle moves through the fluid, one of the dimensionless complexes is obviously the Reynolds number Re = w Upl/i. Thus, we may write ... 

This is the same case with which in Eqs. (2)-(4) we demonstrated the elimination of the time variable, and it may occur in practice when all the reactions of the system are taking place on the same number of identical active centers. Wei and Prater and their co-workers applied this method with success to the treatment of experimental data on the reversible isomerization reactions of n-butenes and xylenes on alumina or on silica-alumina, proceeding according to a triangular network (28, 31). The problems of more complicated catalytic kinetics were treated by Smith and Prater (32) who demonstrated the difficulties arising in an attempt at a complete solution of the kinetics of the cyclohexane-cyclohexene-benzene interconversion on Pt/Al203 catalyst, including adsorption-desorption steps. 

The treatment of experimental data constitutes an essential step in any chemical kinetics study. Although a large part of the present section is based on the investigations in transient flow degradation, the procedure should be general enough to be applicable to other experimental flow arrangements. 

Quantitative XRF analysis has developed from specific to universal methods. At the time of poor computational facilities, methods were limited to the determination of few elements in well-defined concentration ranges by statistical treatment of experimental data from reference material (linear or second order curves), or by compensation methods (dilution, internal standards, etc.). Later, semi-empirical influence coefficient methods were introduced. Universality came about by the development of fundamental parameter approaches for the correction of total matrix effects... 

Many computer libraries contain programs that perform the necessary statistical calculations and relieve the engineer of this burden. For discussions of the use of weighted least squares methods for the analysis of kinetic data, see Margerison s review (8) on the treatment of experimental data and the treatments of Kittrell et al. (9), and Peterson (10). 

Margerison, D., The Treatment of Experimental Data in The Practice of Kinetics, Volume I of Comprehensive Chemical Kinetics, edited by C. H. Bamford and C. F. H. Tipper, Elsevier, New York, 1969. 

Application of this equation to the treatment of experimental data leads to curve C in Figure 5.8c. At smaller H202 concentrations, its consumption... 

Worthing, A.G. and Geffiier, J., 1946. Treatment of experimental data. John Wiley and Sons, New York. 

This section explores the mathematical basis for the statistical treatment of experimental data. Most measurements required for the completion of the experiments can be made in duplicate, triplicate, or even quadruplicate, but it would be impractical and probably a waste of time and materials to make numerous determinations of the same measurement. Rather, when you perform an experimental measurement in the laboratory, you will collect a small sample of data from the population of infinite values for that measurement. To illustrate, imagine that an infinite number of experimental measurements of the pH of a buffer solution are made, and the results are written on slips of paper and placed in a container. It is not feasible to... 

The treatment of experimental data is an essential activity to calculate precise kinetic variables in the equations above. The quality of the kinetic analysis, the identification of relevant phenomena and, subsequently, model parameter fitting, are directly dependent on the initial data. 

This section discusses treatment of experimental data, especially for conditions where state variables change over time. These are the most difficult data to treat and correspond to cultures from batch, fed-batch, or any continuous transient phase. In continuous steady state, the state variables and rates values do not alter with time, and the rate calculation results from the algebraic equation solution. 

J.R. Green and D. Margerison, Statistical treatment of experimental data, Elsevier, Amsterdam, 1977. 

E. Treatment of Experimental Data, Based on the Nonequilibrium Statistical Thermodynamics Approach... 

On the basis of such a classification an empirical approach based on the so-called solvent empirical parameters was formulated to evaluate solvent effects on nuclear shieldings. In brief, this approach, originally proposed by Kamlet, Taft and co-workers [20] for electronic excitations, does not involve QM or other types of calculations but introduces a numerical treatment of experimental data obtained for a given reference system to obtain an estimate of solvent effects on various properties. 

Treatment of experimental data and their comparison to theoretical predictions are impeded due to the dependence of film lifetime on critical thickness of rupture (see Section 3.2.2.1.). The latter on its turn depends on film radius. In that sense the empirical relation... 

A disadvantage of the differential reactor is the inaccuracy in the determination of conversion and selectivity due to the small concentration changes. The second difficulty in the treatment of experimental data is caused by possible flow nonuniformities. Since the average residence time is short and the fluid elements moving with different axial velocities do not mix, the simplified Equation 5.30 may not be valid. This is because the reactor operates as a segregated flow reactor rather than a plug flow or ideal mixed reactor, on which Equation 5.30 is based. 

A general discussion of the graphical treatment of experimental data is given in Chapter II. As part of that discussion, the proper technique for plotting experimental data is fully described for both computer-generated plots and any that may be prepared manually. 

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