Data acquisition rate estimation

We next develop a method to estimate the data acquisition rate necessary to measure a first-order rate coefficient to a specified accuracy. The probability distribution of the signal pulses in time (with no background) is given by... 

The rate constants included in the kinetic expressions, rate equations, can seldom be estimated theoretically based on fundamental theories, such as collision and transition state theories, but an experimental determination of the reaction rates in laboratory-scale reactors is usually unavoidable. Based on experimentally recorded reactant and product concentrations, it is possible to estimate the numerical values of rate constants. Below we will give a brief introduction of the procedures involved in the data acquisition and estimation of kinetic parameters. 

However, a fast and simple mono-exponential on-line evaluation procedure included in the control software of an EEC relaxometer is not only possible but, in reality, is a must since it provides the operator with relaxation-rate data estimates essential for correct setting of acquisition parameters. The fact that the mono-exponential hypothesis may be inaccurate does not really change the fact that some kind of a preliminary estimate is essential for correct data acquisition. 

Dynamic crystallization under precise control of shear and temperature was studied in a prototype apparatus specially developed. The whole cell, similar to a Couette viscometer, was made out of glass. The inner cylinder rotated at a controlled speed, CO, while the outer wall was fixed. A double-mantel with a circulation of water allowed precise control of the temperature. Temperature of cocoa butter in the cell was measured with a chromel-alumel thermocouple. Measures were recorded with a data acquisition system. Shear rate imposed to cocoa butter in the system could be estimated from the rotation speed of the inner cylinder, assuming that the fluid is Newtonian and incompressible. There is no normal speed, only tangential speed. The shear rate, y> in the specimen is a single function of the radiu. In the rest of this work, shear in the cell was characterized by its average value, y, calculated by integration over the cell thickness (7). 

Graphical analysis must always precede the statistical analysis. It is imperative to keep short the time elapsed between data acquisition and data analysis, and in most cases, it is advisable to perform the graphical analysis even while the experiment is still in progress. Wien the data clearly define the nature ofthe rate or binding equation, statistical analysis is not needed to do this. Nevertheless, for a definitive work, statistical methods are necessary for parameter estimation as well as for model discrimination (Senear Bolen, 1992). Computer programs are now available for even the most sophisticated problems in enzyme kinetics (see Section 18.2.4). 

Procurement and Evaluation of the Data Base. Determination of reliability characteristics of components and structural parts requires extensive data acquisition and evaluation. Data acquisition can be done in the course of operation or through the systematic investigation of components and structural parts in the laboratory with simulation of operational stress. In the latter case, however, it is necessary to observe conditions necessary for the applicability of test results to actual in-plant behavior. In this connection, test frequencies should be mentioned by way of an example, since in the laboratory test they often have to be higher than actual frequencies during operation. It depends on the individual case whether such circumstances are significant or not. To estimate the failure rate of a component or structural part, it is necessary to examine a large number no of identical test pieces which are still operational at time / = 0. After time t, N t) test pieces should have failed and n t) test pieces should be intact. Accordingly,... 

In this chapter the aspects of model selection/discrimination and parameter estimation and the experimental acquisition of kinetic data are not dealt with, since they fall fell outside its scope. Moreover, in interpreting the observed temperature dependency of the rate coefficients in this chapter it was assumed that we are dealing with intrinsic kinetic data. As will be shown in a Chapter 7, other, parasitic, phenomena of mass and heat transfer may interfere, disguising the intrinsic kinetics. Criteria will be presented there, however, to avoid this experimental problem. 

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