# Laboratory experiment: Residence Time Distribution (Cascade)

## Residence Time Distributions

The experimental determination of the residence time distribution is performed using indirect methods. Usually a disturbance by a tracer (pulse, step or other function) is administered at the reactor input. The response function is recorded at the reactor output.

The figure below shows the response functions to the input function of different ideal and non ideal reactors - (1) Plug Flow Reactor (2) Stirred Tank Reactor (3) Cascade of Ideally Stirred Tank Reactors a) Ideal b) Short Circuit Current c) Dead Zone. To simulate a pulse function (Dirac pulse) a tracer substance with the concentration $c A$ is injected at a very short time interval into the reactor.

Fig.1

The figure below shows the response function to a step input for (1) Plug Flow Reactor (2) Stirred Tank Reactor (3) Cascade of Ideally Stirred Tank Reactors a) Ideal b) Short Circuit c) Dead Zone. For a step function, the tracer is administered after a point in time t=0 continuously at a constant concentration $c A$ (positive step function).The analysis of the concentration at the output of the reactor dependent on time provides the summation curve.

Fig.2

The response function of the system is characteristic for the individual reactors. Non-ideal behaviour of the studied reactor are shown in the deviations from the response function of the ideal reactor. Several typical deviations from the ideal behaviour of the stirred tank reactor and plug flow reactor are shown diagrammatically in the figures above. Measurement of the concentration changes of the tracer (response function) is usually performed using methods from colorimetry, photometry, electrical conductivity or isotopic marking.

### Residence Time Models

The goal of residence time studies is, among other things, to find a model that describes the examined reactor. In order to do this, parameters need to be determined that adapt the model curves to the measured residence time curve optimally. Often used reactor models for description of the residence time behaviour are: the dispersion model, the tanks in series model and combination models (multiparameter models).

With multiparameter models, a breakdown of the total volume in parts occurs; the parts are then characterized using different reactor models. Using a combination of individual reactor models (plug flow, dispersed plug flow, mixed tanks etc.) interconnected in various ways (branched in parallel, in series recycle, crossflow, etc.), a model can be found that sufficiently describes the real situation. When using the tanks in series model for the description of non-ideal flow reactors, several ideal stirred tank reactors are connected in serie the total volume is then distributed across several reactors. The special case of the tanks in series model with n equally large connected stirred tank reactors has found a wide application. It describes systems with a complete mixture like the ideally stirred tank reactor (n=1) or the ideal cascade of continuously stirred tank reactors (n>1) and flow reactors where a partial back mixing occurs. The dispersion model describes the deviations of the flow profile of a flow reactor from the ideal plug flow by adding a diffusive axial transport.

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