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Characterization and analysis of continuous recycle systems: Part II. Cascade
Author(s) -
Mann Uzi,
Rubinovitch Michael
Publication year - 1981
Publication title -
aiche journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.958
H-Index - 167
eISSN - 1547-5905
pISSN - 0001-1541
DOI - 10.1002/aic.690270518
Subject(s) - cascade , residence time distribution , joint probability distribution , residence time (fluid dynamics) , random variable , mathematics , distribution (mathematics) , flow (mathematics) , extension (predicate logic) , statistics , computer science , mathematical analysis , engineering , geometry , geotechnical engineering , chemical engineering , programming language
A general analysis of a cascade of identical recycle units is presented by means of studying the fluid history inside the system. This is an extension of Part I (Mann et al., 1979) in which a single recycle unit was analyzed. The history of a fluid element is expressed in terms of the number of cycles it completes, the time it resides in the system and the total time it resides in a specific section of the system—all are random variables. Concepts from probability theory and stochastic processes are used to derive the number of cycles distribution (NCD), residence time distribution (RTD) and various total regional residence time distributions (TRRTDs) as well as their means and variances. Expressions for the joint distributions of pairs of these random variables are also derived as well as explicit expressions for their covariances and correlation coefficients. Two applications of the results are illustrated: one in analyzing a continuous spouted‐bed coating unit and the second in using the cascade as a flexible, physically based multi‐parameter flow model.