Integral method of analysis

Sensitivity The sensitivity for a one-point fixed-time integral method of analysis is improved by making measurements under conditions in which the concentration of the monitored species is larger rather than smaller. When the analyte s concentration, or the concentration of any other reactant, is monitored, measurements are best made early in the reaction before its concentration has substantially decreased. On the other hand, when a product is used to monitor the reaction, measurements are more appropriately made at longer times. For a two-point fixed-time integral method, sensitivity is improved by increasing the difference between times t and f2. As discussed earlier, the sensitivity of a rate method improves when using the initial rate. 

Level 1 in the ehart indieates that when the reaetion rate law is known, the integral method of analysis may be used after performing an experiment to evaluate the speeifie reaetion rate. This proeedure... 

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

Determine the reaction order and rate constant for the reaction by both differential and integral methods of analysis. For orders other than one, C0 will be needed. If so, incorporate this term into the rate constant. 

There are two procedures for analyzing kinetic data, the integral and the differential methods. In the integral method of analysis we guess a particular form of rate equation and, after appropriate integration and mathematical manipulation, predict that the plot of a certain concentration function versus time... 

R.S. Dinit, L.L. Tavlaridis, Integral method of analysis of Fischer-Tropsch synthesis reactions in a catalyst pellet, Chem. Eng. Sci. 37 (1982) 539. 

Several approximate methods exist for solving the boundary layer equations. The momentum-integral method of analysis is an important method. The principal steps of the method are listed below. 

Even though the fluid motion is the result of density variations, these variations are quite small, and a satisfactory solution to the problem may be obtained by assuming incompressible flow, that is, p = constant. To effect a solution of the equation of motion, we use the integral method of analysis similar to that used in the forced-convection problem of Chap. 5. Detailed boundary-layer analyses have been presented in Refs. 13, 27, and 32. 

Example 5-2 Integral Method of Analysis of Pressure-Time Data... 

The parameters K and V , can readily be determined from batch reactor data by using the integral method of analysis, Dividing both sides of Equation (7-95) by tKJV and rearranging yields... 

In the integral method of analysis of rate data we are looking for the appropriate function of concentration correspondmg to a particular rate law that is linear with time. You should be thoroughly familiar with the methods of obtaining these linear plots for reactions of zero, first, and second order. 

The solutions of these equations have been obtained by using integral methods of analysis discussed in Section 3.10. Results for a vertical plate have been obtained, which is the most simple case and serves to introduce the dimensionless Grashof number discussed below. However, in other physical geometries the relations are too complex and empirical correlations have been obtained. These are discussed in the following sections. 

Chapter 2 covers the basic principles of chemical kinetics and catalysis and gives a brief introduction on classification and types of chemical reactors. Differential and integral methods of analysis of rate equations for different types of reactions—irreversible and reversible reactions, autocatalytic reactions, elementary and non-elementary reactions, and series and parallel reactions are discussed in detail. Development of rate equations for solid catalysed reactions and enzyme catalysed biochemical reactions are presented. Methods for estimation of kinetic parameters from batch reactor data are explained with a number of illustrative examples and solved problems. 

Determine the reaction order and the rate constant using the integration method of analysis. 

The integral method of analysis can be used when the available data are in the form of concentration (or fractional conversion) versus time or space time (or V/Fao or W/Fao)-As pointed out earlier in this chapter, this kind of data are obtained when an ideal batch reactor or an ideal plug-flow reactor is used. For these two reactors, use of the integral method avoids the need for numerical or graphical differentiation. 

Use either modal superposition of three components of earthquake motion or direct integration approach for time history analysis. The integration time step shall be justified if the time history direct integration method of analysis is used. 

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