No abstract

Principal differential analysis (PDA) is an alternative parameter estimation technique for differential equation models in which basis functions (e.g., B-splines) are fitted to dynamic data. Derivatives of the resulting empirical expressions are used to avoid solving differential equations when estimating parameters. Benefits and shortcomings of PDA were examined using a simple continuous stirred-tank reactor (CSTR) model. Although PDA required considerably less computational effort than traditional nonlinear regression, parameter estimates from PDA were less precise. Sparse and noisy data resulted in poor spline fits and misleading derivative information, leading to poor parameter estimates. These problems are addressed by a new iterative algorithm (iPDA) in which the spline fits are improved using model-based penalties. Parameter estimates from iPDA were unbiased and more precise than those from standard PDA. Issues that need to be resolved before iPDA can be used for more complex models are discussed.

A simplified steady‐state model to predict MWDs of ethylene/butene and ethylene/hexene copolymers produced industrially using heterogeneous Z‐N catalysts is developed. Estimability analysis is used to guide model simplification and to determine which parameters can be estimated using the available data. Scaling of response variables and parameters using information about their uncertainties ensures that appropriate results are obtained from the estimability analysis. Parameter estimates are obtained to provide good predictions of the measured MWDs. Although the parameter values obtained are specific to the Z‐N catalyst of our industrial sponsor, the method should be useful for parameter estimation and model simplification in other catalytic polymerization systems.magnified image

Fluidized-bed polyetliylene reactors are prone to unstable behavior and temperature oscillations (Choi and Ray, 1YNSb

A simplified steady‐state model has been developed to predict molecular weight distributions and average compositions of ethylene‐hexene copolymers produced using heterogeneous Ziegler‐Natta catalysts in gas‐phase reactors. The model uses a simplified reaction scheme to limit the number of parameters that must be estimated. The number of parameters is further reduced by assuming that different types of active sites share common rate constants for some reactions. Estimates of kinetic parameters are obtained using deconvolution analysis of industrial copolymer samples produced using a variety of isothermal steady‐state operating conditions. The parameter estimates should prove useful as initial guesses for future parameter estimation in a non‐isothermal model.magnified image