(534d) Dynamic Real-Time Optimization of a Gas-Phase Polymerization Reactor

Continuous
polyolefin manufacture is widely implemented, due to its high production rate
and strong economic advantages compared with batch polymerizations. A plant produces
polymers with different properties by traversing through a “wheel” of different
product grades. When the grades do not have overlapping property
specifications, the transitions between grades can take hours to complete and
generate a large amount of “off-specification” polymers sold at substantially
lower price than “on-specification” grades. The development of optimal grade
transition strategies to reduce this “off-spec” offers a way to improve the
line profitability / capacity without CAPEX.

The goal of this
work is to develop a dynamic real-time optimization (DRTO) for transitions in a
gas-phase propylene-ethylene copolymerization reactor. The optimization
requires a mathematical model to accurately predict process dynamic behavior
(e.g. monomer concentrations, reactor temperatures) and polymer product
properties (e.g. melt flow, polymer composition). Therefore, a detailed process
model is developed first. In some processes, a fluidized-bed reactor is used to
carry out polymerization reactions by gas-phase monomers/ comonomers
and solid catalysts. The reactor is represented by a two-phase model,
consisting of an emulsion phase and a bubble phase. In order to prevent runaway
reactions due to the highly exothermic reactions, the inlet gases are cooled
down to a low temperature or even partially condensed before entering the
reactor in industrial operations. However, this condensed mode operation is
hardly considered in most fluidized-bed polymerization studies. In this study,
we address the condensation of inlet gas flow by constructing a surrogate vapor-liquid
equilibrium model, derived
from Benedict-Webb-Rubin (BWR) equation of state, to reduce computational complexity.

With a concrete
process model, the DRTO is implemented for the online optimal grade transition.
Although the process is operated continuously, the grade transition can be
treated as a semi-batch process, requiring satisfaction of the end-point
quality constraints defined by the desired polymer grade. Consequently, a framework
to combine a shrinking horizon nonlinear model predictive control (sh-NMPC) and an expanding horizon least square estimation
(eh-LSE) [1] can be implemented. At each time step, eh-LSE estimates states and
parameters based on measurements obtained in the past. The updated model is
then implemented in the sh-NMPC to calculate optimal controls
in future steps to reduce the transition time. A multi-stage transition
formulation [2] is applied to directly optimize economic objective function
augmented with regularization terms. With
this online estimation-optimization framework, the optimal control scheme is
able to reduce the transition time and better preserve path and end-point
constraints under parameter uncertainties. 

References  

[1] Jung, T. Y., Nie, Y., Lee, J. H., & Biegler,
L. T. (2015). Model-based on-line optimization framework for semi-batch
polymerization reactors. IFAC-PapersOnLine, 48(8),
164-169..

[2] Shi, J. , Biegler, L. T. and Hamdan, I.
(2016). Optimization of grade transitions in polyethylene solution
polymerization processes. AIChE J., 62: 1126-1142.