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The residence time distribution functions for multistage systems with backmixing are derived. The effect of backmixing on the system behavior is analyzed. In addition, an analytical expression for the probabilities for backmixing is given.

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Equations are presented for the residence time distribution in multi‐stage systems in which part of the effluent stream is recycled to the inlet of the system. The cases considered include perfect mixing, piston flow and real systems defined by attenuation and time delay factors. Time delay in the recycle stream is also considered. Graphical solutions for several systems are presented. Recycle of part of the effluent stream results in broadening of the residence time distribution and, in addition, produces a discontinuity in the distribution when a time delay is present.