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Performance of tanks in series for non‐ideal mixing
Author(s) -
Chiang David,
Cholette A.
Publication year - 1970
Publication title -
the canadian journal of chemical engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.404
H-Index - 67
eISSN - 1939-019X
pISSN - 0008-4034
DOI - 10.1002/cjce.5450480311
Subject(s) - mixing (physics) , series (stratigraphy) , mathematics , negative binomial distribution , binomial theorem , product (mathematics) , function (biology) , square (algebra) , imperfect , statistics , combinatorics , geometry , physics , paleontology , quantum mechanics , poisson distribution , biology , linguistics , philosophy , evolutionary biology
The performance of tanks in series, for imperfect mixing, is evaluated by resorting to a model characterized by two parameters, m and n , describing the level of mixing and the intensity of channeling or short‐circuit present in any one tank. An expression is obtained for the variation with time of the outlet concentration from the last tank, after subjecting the feed to a step change; it involves the summation of a number of terms, equal to the number of tanks in series, each term being the product of two expressions, the Binomial Probability Function and the Probability Integral of Chi‐Square Distribution, for which values are readily available in statistical and mathematical tables. When no short‐circuit is present, a single reading in the tables is required, whatever the number of tanks in series or the level of mixing; this includes perfect mixing, as a special case. For any given value of n , one family of curves is sufficient to correlate the variables, whatever may be the value of m or level of mixing. Five graphs depict clearly the overall influence of parameters m and n on the performance of reservoirs in series and can be used as working tools in many cases.