(322b) Particle Filter-Based State Estimation in a Gas-Phase Fluidized Bed Polyethylene Reactor

Systems engineering of polymer processing has been a long studied problem. Important issues include reactor modeling, parameter and state estimation, optimal control and grade transition [1-3]. The problem considered here involves the gas-phase production process for linear low density polyethylene (LLDPE). The work introduces a novel solution to the simulation and control of the fluidized bed reactor (FBR) for polyethylene production.

The gas-phase polymer production process is a highly nonlinear process that is operated on a continuous basis. Though process parameters like temperature, pressure, and bed height are easily measured online, polymer properties (such as melt index, polymer density, molecular weight distributions) and particle properties (particle size) cannot be measured easily using online instruments. Usually, polymer properties are measured offline using laboratory methods; these are expensive and time consuming. However, the knowledge of polymer properties and particle properties are important to achieve good final polymer product specification.

In our case, a simulated first-principles dynamic continuous fluidized bed model is used to describe the reactor dynamics. The FBR model consists of a set of highly coupled and nonlinear differential (partial) equations that are computationally cumbersome to solve. Along with basic polymer properties such as melt index and polymer density, the model is able to predict the molecular weight and particle size distributions. Estimating the polymer and particle properties requires that we solve a nonlinear dynamic optimization problem, which in turn requires a good model and knowledge of measured disturbances. The model includes numerous states that are used to represent reactor internal conditions. It is important that the states be estimated accurately before the application of any advanced control algorithm. In the past, different state estimation approaches have been used to estimate the states, some of which are the extended Kalman filter (EKF), the linear Kalman filter, the recursive least squares approach, the use of deterministic observers and moving horizon estimation methods [4]. These estimation methods (except for moving horizon methods) have considered the process uncertainties and disturbances to be Gaussian, which may not be the case in highly non-linear systems. The Kalman filter provides an optimal solution in the case when the system is linear and the posterior density is Gaussian. The EKF, which is based on the assumption that the posterior probabilities are Gaussian, has been successfully used for nonlinear state estimation problems. However, in the case of highly nonlinear systems, the posterior densities are non-Gaussian and the EKF might give a high estimation error. In our case, the state estimation is considered as a filtering problem under the Bayesian framework and the plant-model mismatch is accommodated using the particle filtering approach. The particle filtering approach has been used successfully on various systems for estimation in the case of non-Gaussian noise [5-7]. Although the algorithm is computationally demanding, we look at the advantages it offers to achieve optimal control and optimal grade transition. Particle filters are used to improve the estimates of the states, and hence are a solution to handle process disturbances and uncertainty (uncertainty in rate constants, side reactions not included in the model) and measurement noise that propagate through the highly nonlinear system.

References

[1] McAuley, K. B., J. F. MacGregor and A. E. Hamielec, ?A Kinetic Model for Industrial Gas-Phase Ethylene Copolymerization ? , AIChE J., 36, 6, 837-850, 1990.

[2] Dompazis, G., V. Kanellopoulous, and C. Kiparissides, ?A multi-scale modeling approach for the prediction of molecular and morphological properties in multi-site catalyst, olefin polymerization reactors?, Macromol. Mtls. Eng., 290, 525-536, 2005.

[3] Chatzidoukas, C., J. D. Perkins, E. N. Pistikopoulos and C. Kiparissides, ?Optimal Grade Transition and Selection of Closed-loop Controllers in a Gas-phase Olefin Polymerization Fluidized Bed Reactor? , Chem. Eng. Sci., 58, 3643-3658, 2003.

[4] McAuley, K. B. and J. F. MacGregor, ?Nonlinear Product Property Control in Industrial Gas-Phase Polyethylene Reactors?, AIChE J., 39, 5, 855-866, 1993.

[5] Chen, T., J. Morris and E. Martin, ?Particle filters for State and Parameter Estimation in Batch Processes?, J. Proc. Control, 15(6), 665-673 (2005).

[6] Imtiaz, S. A., R. Kallol, B. Huang, S. L. Shah and P. Jampana, ?Estimation of states of nonlinear systems using a particle filter?, Proc. IEEE Int. Conf. Industrial Tech., 2432-2437, 2006.

[7] J. Prakash, S. C. Patwardhan, S. L. Shah, ?Constrained State Estimation Using Particle Filters?, Proc. of the 2008 IFAC World Congress, Seoul, Korea, July 2008, pp 6472-6477