D Measurement Lag for Concentration in a Batch Reactor

The measurement lag for concentration in a reactor is depicted in Fig. 2.8. The actual reactant concentration in the reactor at any time t is given by C but owing to the slow response of the measuring instrument, the measured concentration, shown by the instrument, Cm, lags behind Cp as indicated in Fig. 2.9. 

The dynamic error existing between Cm and Cr depends on the relative magnitudes of the respective time constants. For the reactor, assuming a first-order constant volume reaction 

Assuming that the instrument response is first order, then as shown in Section 2.1.1.1, the instrument time constant rm is given by the value of time at the 63% point (response to a step-change disturbance), where 

The ratio of the time constants, Tr/Tm, which for this case equals (krm) will determine whether Cr is significantly different from Cm. When this ratio is less than 1.0 the measurement lag will be important. If Tr/rm 10, then Cm Cr and the measurement dynamics become unimportant. 

The effects of measurement dynamics are demonstrated in the simulation examples KLADYN, TEMPCONT and CONTUN. 

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