A Simultaneous Parameter and State Estimator for Polymerization Process Based on Molecular Weight Distribution

Key polymer properties are substantially related to the polymer molecular weight distribution (MWD). Kinetic-based MWD models involves mass balances for all chain types and for all possible chain lengths. These models are predictive and exhibit a large-scale nature. The numerical solution is expensive, especially for on-line optimization in a state/parameter estimator. Thus, MWD monitoring using first-principles models has rarely been studied. In this work, we developed a simultaneous parameter and state estimator for MWD in the framework of moving horizon estimation (MHE). A reduced order model is proposed based on null-space projection method. The reformulated model predicts a MWD profile without calculating all possible chains. The large-scale MWD model is reduced to a manageable number of equations. Then, the MHE framework is designed based on the reformulated model, where the parameters and states are estimated simultaneously. Numerical results show that by introducing MWD as state variables, the prediction accuracy is significantly improved. It is advantageous to introduce the slow measurement of MWD for polymer quality monitoring/control although the different measurement rates need to be coordinated.