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Economic criteria in the design of cascades of CSTR's for the performance of enzyme‐catalyzed reactions
Author(s) -
Malcata F. Xavier
Publication year - 1997
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.5450750520
Subject(s) - cascade , maxima and minima , order (exchange) , substrate (aquarium) , investment (military) , continuous stirred tank reactor , mathematics , capital (architecture) , thermodynamics , chemistry , michaelis–menten kinetics , unit (ring theory) , economics , mathematical analysis , enzyme , physics , chromatography , finance , enzyme assay , organic chemistry , biology , law , history , archaeology , political science , politics , ecology , mathematics education
The mass balances on substrate in each unit of a series of CSTRs performing an enzyme‐catalyzed reaction described by Michaelis‐Menten kinetics (with parameter K m ) are written and the necessary and sufficient condition that must besatisfied by the intermediate concentrations in order to obtain a minimum overall capital investment is found on the assumption that the cost of each reactor unit scales up on its capacity according to a fractional factor exponential rule (with parameter n ). The asymptotic situations of pseudo‐zero order and pseudo‐first order behavior are explored. The ratio between consecutive concentrations leading to a minimum overall capital investment decreases as K m decreases at a rate that is slower for higher n , and tends to unity as the pseudo‐first order situation is approached. If fractional values of n are considered, local minima of the capital investment associated with the overall reactor cascade exist only in certain ranges of substrate conversion; below the lower limits of such ranges, the number of reactor units should actually be decreased. A graphical procedure aimed at obtaining the intermediate optimal concentrations is presented.