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Optimization of nonvaporizing nylon 6 reactors with stopping conditions and end‐point constraints
Author(s) -
Ray Ajay K.,
Gupta Santosh K.
Publication year - 1986
Publication title -
polymer engineering and science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.503
H-Index - 111
eISSN - 1548-2634
pISSN - 0032-3888
DOI - 10.1002/pen.760261503
Subject(s) - monomer , residence time (fluid dynamics) , product (mathematics) , dimer , thermodynamics , materials science , polymerization , a priori and a posteriori , function (biology) , mathematics , polymer , physics , chemistry , organic chemistry , geometry , philosophy , geotechnical engineering , epistemology , engineering , composite material , evolutionary biology , biology
In this study, optimal temperature profiles (or histories), T(t) , are obtained for nonvaporizing plug‐flow (or batch) Nylon 6 reactors using the minimum principle. Two objective functions are studied, one in which the monomer conversion, conv tf , is maximized, and the other in which the undesirable side product (cyclic dimer) concentration in the output stream, [ C 2 ] tf , is minimized. The control variable, temperature, is constrained to lie between 220°C and 270°C in order to ensure single phase polymerization. The most significant difference between this study and earlier ones is that the residence (or reaction), time t f , is not specified a priori , but is determined optimally by the use of a ‘stopping’ condition such that the polymer product has a number‐average chain length, μ n , equal to some desired value μ n.d . Simultaneously, an end‐point constraint is used, which, depending on the objective function used, forces either the cyclic dimer concentration or the monomer conversion at the end of the reactor to lie at a specified value, [ C 2 ] d or conv d . Thus, this algorithm incorporates stopping conditions as well as end‐point constraints and so is more complex than earlier ones, but the results are more meaningful. Different nonisothermal optimal temperature profiles are obtained for the two objective functions studied, depending on the values of μ n.d , conv d , [C 2 ] d , and the feed water concentration, representing the complex interplay of several opposing factors.