On the limiting form of the residence-time distribution for a constant-volume recycle system

✍ Scribed by B.A. Buffham; E.B. Nauman

• Publisher: Elsevier Science
• Year: 1975
• Tongue: English
• Weight: 512 KB
• Volume: 30
• Category: Article
• ISSN: 0009-2509
• DOI: 10.1016/0009-2509(75)85030-5

✦ Synopsis

The residence-time density function for a recycle system usually tends to exponential form, with mean equal to the ratio of the volume to the volumetric flow-rate, when the recycle rate is increased at constant throughput. Two conditions each suffidient to guarantee this behaviour are: (i) that the normalized once-through residence-time density functions become independent of the recycle rate for recycle rates in excess of some finite value; or (ii) that the moments of all orders of the normalized density functions are bounded. In the former case the existence of only the zeroth and first moments for the once-through density functions is required which conditions are themselves consequences of the principle of conservation of mass. In the latter case the form of the once-through normalized density functions may change with the recycle rate. When the first n moments of the normalized once-through densities are bounded, the limits of the first n moments of system residence-time density exist and are the same as those of the exponential density function.