Interpretation of Laboratory Kinetic Data

Assume a form for f C) (first order, second order, etc.). 

From the appropriate curve in Fig. 11-7 obtain O and then evaluate k from the defining expression for [for example, Eq. (11-50) for a first-order rate on spherical catalyst pellets]. 

Repeat steps 2 to 4 for all sets of data to see whether the assumed form of /(Q is valid (for a first-order rate equation the evaluation would be to see if k- is constant for data at various concentrations but constant temperature). 

Finally, the values of k for different temperatures would be plotted as In k vs 1/T to obtain. A and E in the Arrhenius equation, k = 

The resultant values of A and E and the nature of/(C) establish the desired equation for the intrinsic rate. However, for step 3 we must know or estimate the effective diffusivity. Alternately, the global rate may be measured for small catalyst particles for which - 1.0. Now internal (and usually external) transport resistances are negligible the bulk temperature and concentrations may be taken as equal to those at a catalyst site, and the observed rate and bulk temperature and concentration data can thus be used directly to obtain /(Q and A and E. 

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Many of the same factors which complicate the interpretation of laboratory kinetic studies are among the most important limitations on the application of laboratory dissolution rate data to natural systems. These include uncertainty about 1) the effective surface area in natural systems (56,57) 2) the extent to which surface area and surface roughness change with reaction progress ( 18) and 3) the magnitude of solution composition effects on rates in natural systems. 

The chief significance of reaction rate functions is that they provide a satisfactory framework for the interpretation and evaluation of experimental kinetic data. This section indicates how a chemical engineer can interpret laboratory scale kinetic data in terms of such functions. Emphasis is placed on the problems involved in the evaluation and interpretation of kinetic data. 

Equations (10-6) and (10-7) show that for the intermediate case the observed rate is a function of both the rate-of-reaction constant, ic and.. the mass-transfer coefficient k. In a design problem k and k would be known, so that Eqs. (10-6) and (10-7) give the global rate in terms of Cj. Alternately, in interpreting laboratory kinetic data k would be measured. If k is known, k can be calculated from Eq. (10-7). In the event that the reaction is not first order Eqs. (10-1) and (10-2) cannot be combined easily to eliminate C. The preferred approach is to utilize the mass-transfer coefficient to evaluate Q and then apply Eq. (10-2) to determine the order of the reaction n and the numerical value of k. One example of this approach is described by Olson et al. ... 

A central problem in kinetics is the interpretation of laboratory data on rates of reaction. We have treated rates and selectivities to this point as if all the parameters such as reaction orders, rate constants, and activation energies were known. Suppose that this is not so [ None of them know the color of the sky, S. Crane]. How does one go about the testing of rate or conversion information on a certain reaction in terms of the expressions we have been dealing with Further, and importantly, what is the influence of experimental error on the parameters we determine from a given set of data To what extent are the apparent kinetics of a reaction useful in providing information on the elementary steps of that reaction ... 

In the preceding sections we cited several practical examples of solid-solid reactions, proceeding through gaseous intermediates. While these reaction systems are of industrial interest and some laboratory scale kinetic measurements have been made, unlike the case of simple gas-solid reactions there are no general modeling equations available for the interpretation of the experimental data. 

Everyday laboratory reactions are emphasized, and the working practice of kinetics takes precedence over the theoretical. The audience remains the first-year graduate student (or advanced undergraduate) as well as research workers from other areas who seek guidance in the concepts and practice of kinetics and in the evaluation and interpretation of kinetic data. 

The main objectives of this chapter are to (1) review the different modeling techniques used for sorption/desorption processes of organic pollutants with various solid phases, (2) discuss the kinetics of such processes with some insight into the interpretation of kinetic data, (3) describe the different sorption/ desorption experimental techniques, with estimates of the transport parameters from the data of laboratory tests, (4) discuss a recently reported issue regarding slow sorption/desorption behavior of organic pollutants, and finally (5) present a case study about the environmental impact of solid waste materials/complex... 

The experimental batch reactor is usually operated isothermally and at constant volume because it is easy to interpret the results of such runs. This reactor is a relatively simple device adaptable to small-scale laboratory set-ups, and it needs but little auxiliary equipment or instrumentation. Thus, it is used whenever possible for obtaining homogeneous kinetic data. This chapter deals with the batch reactor. 

Thermogravimetry is an attractive experimental technique for investigations of the thermal reactions of a wide range of initially solid or liquid substances, under controlled conditions of temperature and atmosphere. TG measurements probably provide more accurate kinetic (m, t, T) values than most other alternative laboratory methods available for the wide range of rate processes that involve a mass loss. The popularity of the method is due to the versatility and reliability of the apparatus, which provides results rapidly and is capable of automation. However, there have been relatively few critical studies of the accuracy, reproducibility, reliability, etc. of TG data based on quantitative comparisons with measurements made for the same reaction by alternative techniques, such as DTA, DSC, and EGA. One such comparison is by Brown et al. (69,70). This study of kinetic results obtained by different experimental methods contrasts with the often-reported use of multiple mathematical methods to calculate, from the same data, the kinetic model, rate equation g(a) = kt (29), the Arrhenius parameters, etc. In practice, the use of complementary kinetic observations, based on different measurable parameters of the chemical change occurring, provides a more secure foundation for kinetic data interpretation and formulation of a mechanism than multiple kinetic analyses based on a single set of experimental data. 

There are two main types of laboratory tests used to get kinetic data batch or integral reactor studies, and tests in a differential reactor. Batch tests are discussed first, since they are more common and often more difficult to interpret. Differential reactors are used primarily for reactions over solid catalysts, which are discussed in Chapter 2. 

Kinetics of the absorption of CO2 into MDEA-DEA-H2O system was investigated over a temperature range varying from 293K to 313K and total amine concentration from 0.5M to 2M using a laboratory stirred cell reactor. It was observed that the addition of small amounts of DEA to MDEA resulted in a significant enhancement of CO2 absorption rates. A first-order reaction model for MDEA and a zwitterions mechanism for DEA were used to interpret the kinetic data and derive the kinetic parameters associated to the reaction. Beside DEA, H2O and OH, also MDEA acts as a base for the removal of a proton from the zwitterion intermediate. 

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