Fitting Batch and PFR Data

When kinetic measnrements are made in batch or piston flow reactors, the reaction rate is not directly determined. Instead, an integral of the rate is measured, and the rate itself mnst be inferred. All the parameters of the model must be specified, for example, 5 odei(, m, n,r, s,ko, Tact), but this will be done by the optimization rontine. The integration can be done analytically in simple cases or numerically in more complicated cases. For a batch reactor. 

An irreversible reaction A - B is occurring in an isothermal, constant-volume batch reactor. The concentration has been measured at various times. Find an objective function (i.e., SS ) that is suitable for fitting the model 01 = —ka -. 

SOLUTION This has aheady been done in the begirming of the chapter. Analytical integrals of Equation 7.12 (e.g., Equations 2.16 and 2.17) can be used for this th-order reaction, but recall that = 1 is a special case and that reactions with 1 can go to completion. Thus, 

Numerical integration of the rate equation with = —ka is simple and works for aU values of k and t, although large values of k will force small values of At to ensure convergence. 

The following data have been obtained in a constant-volume, isothermal reactor for a reaction with known stoichiometry A — B -f C. The initial concentration of component A was 2200 mol m . No B or C was charged to the reactor. Find a good kinetic model. 

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