Methods are developed for describing flow and transport phenomena in chemical process equipment in terms of random time delays that are undergone by material or energy elements in passing through the process. It is shown how these methods may be applied to typical chemical engineering processes including exchange processes in packed beds, distillation and multiple reactions in complex flow regimes. A new mixing concept, dynamic dispersion, is defined which may be used to account, in a formal way, for the disparity that sometimes exists between the behaviour of a process in the steady state and predictions based on the axial dispersion concept.