Residence Time Analysis in Systems Having Many Connections with Their Environment

Abstract

The mathematical relationships describing the residence-time distribution functions in "closed" systems having many connections with their environment are presented and experimental methods for their determination are suggested. Application of these relationships to systems having one inlet and one exit is shown to produce the familiar expressions for such systems, while the application to systems having two inlets and one exit produce equations consistent with those of Treleaven and Tobgy (1971). The relationship describing the overall residence-time frequency function differs however from that of Buffham and Kropholler (1970). The results should be of interest in areas in which tracer experiments are used such as chemical reactor design, physiology, hydrology, and the study of dispersion processes in rivers and estuaries.

Tracer Methods in Chemical Reactors. Techniques and Applications

“…Extensions of residence time distributions to systems with multiple inlets and outlets have been described (27)(28)(29). If the system contains M inlets and N outlets one can define a conditional density function Eii(t) as the normalized tracer impulse response in outlet j to input in inlet i as shown schematically in Figure 2.…”

“…1 - (27) While that based on a CSTR model is: (28) Nauman and Buffham (4) report that the difference between eq. (27) and eq.…”

“…We consider here the RTD based on the generalized tanks in series model, i.e. (27), (28) and (32). When ~ < 1 this model represents a generalization of the tanks in series model but at a~ > 1 it becomes an attractive description of stagnancy or bypassing.…”