Batch reactors nonlinear regression

We can also use nonlinear regression to determine the rate law parameters from concentr on-time data obtained in batch experiments. We recall that the combined rate law-stoichiometty-mole balance for a constant-volume batch reactor is... 

Batch reactors are used primarily to determine rate law parameters for hotr geneous reactions. This determination is usually achieved by measuring cc centraiion as a function of time and then using either the differential, integr or nonlinear regression method of data analysis to determine the reacti order, a, and specific reaction rate constant, k. If some reaction parame other than concentration is monitored, such as pressure, the mole balance mi be rewritten in terms of the measured variable (e.g.. pressure as shown in t example in Solved Problems on the CD). 

Inadequate stoichiometry and poor calibration of the analytical device are interconnected problems. The kinetic model itself follows the stoichiometric rules, but an inadequate calibration of the analytical instrument causes systematic deviations. This can be illustrated with a simple example. Assume diat a bimolecular reaction, A + B P, is carried out in a liquid-phase batch reactor. The density of the reaction mixture is assumed to be constant. The reaction is started with A and B, and no P is present in the initial mixture. The concentrations are related by cp=CoA-Cj=Cob -Cb, i e. produced product, P, equals with consumed reactant. If the concentration of the component B has a calibration error, we get instead of the correct concentration cb an erroneous one, c n ncs, which does not fulfil the stoichiometric relation. If the error is large for a single component, it is easy to recognize, but the situation can be much worse calibration errors are present in several components and all of their effects are spread during nonlinear regression, in the estimation of the model parameters. This is reflected by the fact that the total mass balance is not fulfilled by the experimental data. A way to check the analytical data is to use some fonns of total balances, e.g. atom balances or total molar amounts or concentrations. For example, for the model reaction, A + B P, we have the relation ca+cb+cp -c()a+c0 -constant (again c0p=0). 

The differential and integral methods are used primarily in analyzing batch reactor data. Because a number of software packages (e.g.. Polymath, MATLAB) are now available to analyze data, a rather extensive discussion of nonlinear regression is included. 

---