Impulse response tests in completely mixed tanks and reactors. Key assumptions and steps in mathematical developments.

Stimulus-response technique is a method to obtain the Residence Time Distribution (RTD) for the elements of a fluid passing through a vessel. Generally speaking, in reactor science unsteady-state tests may often appear preferable to steady-state since they are made up of a chain of intermediate ones; but without any theoretical necessity holding. In RTD studies, however, non-steady state tests are the only conceivable ones if conservative tracers are employed, because once a transition is over there is no way to reconstruct it and assess the hydraulic behaviour of the tank. Only a series of tests with non-conservative tracers of known disappearance rate would achieve the task, but at the price of repeated runs at changing residence times. This paper deals only with Continuous Stirred Tank Reactors (CSTRs) subject to a pulse input of a conservative tracer. Mathematical expressions of response are derived starting from mass balance. To allow for the presence of anomalies two models for non-ideal CSTR are also illustrated, namely the dead volume and short-circuiting patterns. Theory and techniques are well established since long and in this paper they are simply recalled and retraced in order to explicitly list and highlight the effects on final equations of some hypotheses and mathematical steps which - though widely known - are sometimes undervalued to some extent.