Residence-time distribution stimulus-response technique

The time that a molecule spends in a reactive system will affect its probability of reacting and the measurement, interpretation, and modeling of residence time distributions are important aspects of chemical reaction engineering. Part of the inspiration for residence time theory came from the black box analysis techniques used by electrical engineers to study circuits. These are stimulus-response or input-output methods where a system is disturbed and its response to the disturbance is measured. The measured response, when properly interpreted, is used to predict the response of the system to other inputs. For residence time measurements, an inert tracer is injected at the inlet to the reactor, and the tracer concentration is measured at the outlet. The injection is carried out in a standardized way to allow easy interpretation of the results, which can then be used to make predictions. Predictions include the dynamic response of the system to arbitrary tracer inputs. More important, however, are the predictions of the steady-state yield of reactions in continuous-flow systems. All this can be done without opening the black box. 

Except for the case of an ideal plug flow reactor, different fluid elements will take different lengths of time to flow through a chemical reactor. In order to be able to predict the behavior of a given piece of equipment as a chemical reactor, one must be able to determine how long different fluid elements remain in the reactor. One does this by measuring the response of the effluent stream to changes in the concentration of inert species in the feed stream—the so-called stimulus-response technique. In this section we will discuss the analytical form in which the distribution of residence times is cast, derive relationships of this type for various reactor models, and illustrate how experimental data are treated in order to determine the distribution function. 

The experimental technique used for finding this desired distribution of residence times of fluid in the vessel is a stimulus-response technique using tracer material in the flowing fluid. The stimulus or input signal is simply tracer introduced in a known manner into the fluid stream enter-... 

Thus we see that the stimulus-response technique using a step or pulse input function provides a convenient experimental technique for finding the age distribution of the contents and the residence-time distribution of material passing through a closed vessel. 

To understand the behavior of the fluidized bed, one can determine the average residence time or the residence time distribution (RTD) from the tracer technique. For instance, RTD in fluidized bed dryer is usually carried out by means of the stimulus-response technique, in which an impulse of solids marked with some appropriate tracer is fed to the dryer and its time of elution and concentration measured at the exit of the dryer. The material of the tracer has to be such that it can be detected and does not react with the substrate material, and its form of application and response are well known (Levenspiel, 1972). 

In these models, the interactions between the chemical reaction and the transport processes are described in some more details than in first category. The numerous elementary transport processes are lumped together into some effective terms, using different simplification rules. These models are generally based on the Residence Time Distribution (R.T.D.) of the fluid phases. This formulation is convenient because the R.T.D. can be determined experimentally by well established stimulus-response techniques. The resultant R.T.D. reflects bulk pheno-... 

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