A Kinetic Model for Non‐Oxidative Thermal Degradation of Nylon 66

Abstract

A model is developed to predict rates of undesirable reactions in the low‐moisture, high‐temperature finishing stage of nylon 66 production. The model contains 56 unknown parameters and initial conditions, which are ranked based on their influence on model predictions, correlation with other parameters and uncertainty in their initial guesses. A mean‐square‐error criterion is used to determine that 43 of 56 parameters should be estimated. The proposed model, which describes the effect of melt‐phase water concentration on degradation, matches the data well with typical errors of 6.1 and 2.9%, respectively, for amine ends (A) and carboxyl ends (C) and 4.3, 27.2, and 29.4%, respectively, for evolution rates of CO2, NH3, and cyclopentanone (CPK).

Mean‐squared‐error‐based method for parameter ranking and selection with noninvertible fisher information matrix

“…McLean et al used Wu's r CC criterion to simultaneously rank and select parameters for estimation in nonlinear dynamic models (Algorithm ) . In situations involving a noninvertible FIM, the r CC criterion can readily be used to rank or select parameters . The only assumption required is that the value of the weighted least‐squares objective function (i.e., Eq.…”

“…The two approaches for parameter ranking and selection (i.e., [using orthogonalization and fixing of parameters to achieve an invertible FIM] and [using a pseudoinverse]) were investigated. In Tables and the results are compared against the typical strategy that uses orthogonalization and r CC (without considering W ) so that the importance of using W when ranking and selecting parameters can be elucidated. Note that when the approach is used, only the first five columns corresponding to the first five parameters are included in W ext because the sixth and seventh parameters are automatically removed from the estimation problem during the preliminary orthogonalization/ranking step (i.e., they are held fixed at their initial guesses).…”

“…Several parameter subset‐selection techniques have been developed and used to decide which parameters in an EM should be estimated and which parameters should be fixed at their nominal values to create a corresponding SM . Orthogonalization‐based techniques (Algorithm ), which use the Fisher information matrix (FIM) to rank model parameters from most estimable to least estimable are popular for parameter ranking and selection, and have been widely used to estimate parameters in complex fundamental models . The FIM summarizes information about the effects of model parameters on predictions and accounts for uncertainties in measurements that are used for parameter estimation.…”

“…A singular FIM occurs in many high‐dimensional parameter estimation problems and also in system identification with over‐parameterized models . In many practical chemical engineering models, it is impossible to rank all of the model parameters using the orthogonalization‐based technique in Algorithm , due to a noninvertible FIM In this situation, the algorithm stops when numerical problems are encountered and some of the least influential parameters remain unranked. A singular FIM also leads to a significant complication in the analysis of parameter estimation problems and for the theory of the Cramér–Rao lower bound, which is a popular means to bound the variances of unbiased estimators …”

Parallel models for arborescent polyisobutylene synthesized in batch reactor

“…When developing fundamental models of polymerization reactors, it is important to determine whether all of the kinetic parameters in the model should be estimated, or whether only a subset of the parameters should be estimated from the available data . Estimating too many parameters using limited data leads to large uncertainty ranges for the parameters and can produce worse predictions than when fewer parameters are estimated.…”