(612d) Model-Based Control for Optimal Transitions in Polyethylene Solution Polymerization

Authors: 
Shi, J., Carnegie Mellon University
Biegler, L. T., Carnegie Mellon University
Hamdan, I., The Dow Chemical Company



Among the large family of polyethylene products, linear low-density polyethylene (LLDPE) has penetrated almost all traditional polyethylene markets. There are various grades of LLDPE tailored to different applications, with each grade defined by specifications of product properties such as melt index and density. Typically, LLDPE is made by solution copolymerization of ethylene with longer-chain olefins in continuous plant such as loop reactor and continuous stirred-tank reactor (CSTR). A single-site catalyst is preferred, as it tends to provide a narrow distribution of molecular weight. Several different grades of LLDPE are produced in the same production line. In certain instances, complex transitions rely heavily on operator/expert experience. Thus, an opportunity exists to improve and automate complex transition schemes, which have largely been avoided or have required long start up times.

Given the large market of LLDPE and the current experience-based transitions, there is a need, and also  room for improvement, to perform transitions and to change operation conditions in a smarter way so that the transition time, which is usually a long period wasted to produce off-grade product, as well as the raw material usage could be minimized. The goal of this study is obtaining optimal transition policies using a simultaneous dynamic optimization strategy, which has shown potential in solving related problems in previous studies. 

In this study, a mathematical model is developed to capture the dynamics of the solution polymerization process carried out in a CSTR. Besides the traditional mass balance and energy balance equations, the model has two important components: one is the molecular weight moment model applied to estimate product properties, melt index (MI) and density; the other includes a simple, yet accurate, vapor-liquid equilibrium (VLE) model derived from rigorous calculation. Here, VLE is a crucial constraint to the problem in order to ensure proper reactor operation. After the model development, the resulting model is validated via input step responses and then used to compute different steady state operation conditions for different grades of LLDPE.

Next, orthogonal collocation on finite elements is applied to fully discretize the problem; in this way, we translate the original DAE problem into a large-scale nonlinear programming problem which could be solved by nonlinear optimization solvers such as GAMS/IPOPT. The results of this optimization formulation lead to significant reductions in grade transition times and resource requirements. In addition the resulting profiles are compared to current operations, and the trade-offs between faster transitions and simpler control schemes are discussed.