Danckwerts’ law for mean residence time revisited

This paper shows that Danckwerts’ law for mean residence time in a vessel with continuous and steady throughflow holds for a stochastic model based on a Markov chain for the particle spatial position, under a set of three very general conditions on the transfer probabilities. These are natural conditions and represent mass balance conditions on the transfer between spatial regions in the process. It is shown that a stochastic model for particle residence time distribution with these three conditions may describe almost any physical flow configuration, and also covers published mathematical RTD models, independent of their mathematical form or the nature of the associated boundary conditions, models for which Danckwert's law has hitherto been shown to be satisfied on a case-by-case basis. Two examples, namely those birth–death Markov chains and fluidized bed models are discussed.