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A computationally efficient technique for the solution of non‐isothermal nylon‐6 polymerization in batch reactors
Author(s) -
Nandrajog Sanjay,
Vimala P.,
Gupta Santosh K.,
Kumar Anil
Publication year - 1995
Publication title -
macromolecular theory and simulations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.37
H-Index - 56
eISSN - 1521-3919
pISSN - 1022-1344
DOI - 10.1002/mats.1995.040040415
Subject(s) - isothermal process , nonlinear system , polymerization , caprolactam , series (stratigraphy) , mathematics , ordinary differential equation , natta , materials science , domain (mathematical analysis) , thermodynamics , chemistry , differential equation , mathematical analysis , polymer chemistry , physics , composite material , paleontology , quantum mechanics , biology , polymer
The kinetic scheme of nylon‐6 polymerization consists of ring opening, polyaddition, step growth, reaction with monofunctional acids and cyclization. A set of ordinary differential equations (initial value problem) governing the concentrations and moments of the reacting species and the energy balance for batch reactors has been solved. We proposed a semianalytic technique somewhat similar to the finite element method in which the conversion domain has been divided into sequential subdomains. A series solution for the state variables has been assumed in terms of the incremental conversion of caprolactam in that domain. The coefficients are obtained using the balance equations. This technique of solution takes care of the nonlinearity of the problem in a natural way and involves the sequential evaluation of constant coefficients of the series. It gives comparable results with those from Gear's algorithm (which involves the evaluation of functions) in far fewer steps. Our scheme can be easily implemented on a PC‐XT and is considerably faster and more efficient.