STOCHASTIC MODELING OF TRANSIENT RESIDENCE-TIME DISTRIBUTIONS DURING START-UP

The theory of residence-time distribution, RTD theory in short, is a c ornerstone of chemical engineering science and practice, in general, a nd that of chemical reactor analysis and design, in particular. The cr eation of the modern, systematic RTD theory has been attributed to Dan ckwerts. As evident from his liberal adoption of terminologies of prob ability and statistics, he was apparently well aware of the stochastic nature of the process that gives rise to a residence-time distributio n. While Danckwerts steered the development of the RTD theory essentia lly along the path of deterministic physics, obviously, the descriptio n of RTD is better couched in the statistical or stochastic parlance. Stochastic modeling visualizes the fluid in a flow system as being com posed of discrete entities. This visualization reveals a greater insig ht into the underlying mechanism than deterministic modeling, thereby facilitating our understanding of the flow and mixing characteristic o f the system. In the present work, an attempt has been made to derive a unified mathematical model of the RTD during process start-up by rig orously resorting to the theories and methodologies of stochastic proc esses. Specifically, the expressions for RTDs of molecules, fluid part icles or any flowing entities passing through continuous flow systems have been derived from the stochastic population balance of these mole cules, particles or entities. The resultant expressions are applicable to both unsteady-state and steady-state flow conditions.