(508d) How to Deal with Fast Process Dynamics of the Ethylene Solution Polymerization Process During Optimal Grade Transitions?

How to Deal with Fast Process Dynamics of the Ethylene
Solution Polymerization Process During Optimal Grade Transitions?

Karen V.
Pontes¹, Marcelo Embiruçu¹, Inga J. Wolf² and
Wolfgang Marquardt²

¹PEI ? Industrial
Engineering Postgraduate Program, Bahia Federal University

²AVT ? Process
Systems Engineering, RWTH Aachen

For highly non-linear processes with frequent product changes such
as polymerization processes, operators' and engineers' experience may not
suffice to operate the plant in an economically optimal way while maintaining
product quality. In this context, real-time optimization strategies coupled
with automatic process control offer opportunities for optimal process
operation during the production of target polymer grades.

Recent advances in the solution of dynamic optimization (DO)
problems have enabled their online solution, so that several approaches
considering real-time optimization strategies for polymerization processes have
been reported in the last years. The computational delay is usually lower than
the grade transition duration, which may take minutes or even hours to
complete. However, when approaching large-scale processes with fast dynamics,
computational delay may hinder online optimization. This is the case for the
ethylene polymerization in solution with catalyst in a series of stirred and
tubular reactors, introduced by Braskem S.A. (Camaçari Petrochemical Pole -
Brazil). A typical grade transition may take around 2-5 minutes due to high
loads and small residence time. These fast dynamics are confirmed by a
phenomenological mathematical model validated with industrial data. Bearing
this in mind, this work seeks to investigate how real-time optimization
strategies can be formulated to optimize the grade transition and production of
this ethylene polymerization process.

Firstly, a two-layer dynamic real-time optimization (D-RTO)
architecture, as formulated by Würth et al. (2011), is investigated which is
then compared to a modification of the established two-layer real-time
optimization (RTO) architecture (Marlin and Hrymak, 1997). The economic
optimization at the upper-layer is trigged periodically to compensate the
impact of slow disturbances (such as trends resulting from heat exchanger
fouling or catalyst decay) on economically optimal operation and to compute
trajectories for scheduled grade transitions. A linear time-varying MPC (Model-Predictive
Controller) on the lower-layer tracks the reference trajectories at a higher
sampling time to reject fast disturbances.

The D-RTO suggested here relies on a novel formulation of a
two-stage DO problem for polymer grade transitions, considering solely economic
goals in the objective function while the polymer properties are specified through
constraints. Results show that a typical optimal grade
transition problem, represented by a large-scale model made up of 140
differential and 2275 algebraic state variables can be efficiently solved in around
270 seconds. Furthermore, the
two-layer architecture avoids the solution of the rigorous DO problem at every
controller sampling time. Instead, it has to be solved less frequently. Other
approaches, such as the one suggested by Zavala et al. (2006) combine the optimizer and the controller into a single-layer so that
a DO problem has to be solved at every sampling time during the grade
transition of low-density polyethylene tubular reactors. The DAE model used in
the case study of Zavala et al. (2006), containing 294 differential and 64
algebraic state variables, is solved in around 351 seconds. Since grade transition in this case study is slow, a controller
sampling time of 6 minutes can be used.

However, since the polymerization process investigated here presents
very fast dynamics, a typical grade transition is completed already in around 2-5
minutes hindering the implementation of D-RTO in this industrial scenario. Attempting
to ensure profitable process operation during the whole production cycle while targeting
polymer properties, a modification of the established RTO approach is
investigated. The steady-state optimization followed by
the simulation of the optimal step response replaces the solution of the DO
problem in the upper-layer of the D-RTO architecture when computing the
reference trajectory.

Results show that the two-layer D-RTO allows higher profits and less
off-spec production than the modified RTO, as expected. Important to mention,
though, is that the RTO framework proposed here can already increase process
profitability up to 30% compared to standard process operation, thus presenting
itself as a promising alternative for implementation in industrial scenarios with
less computational load. The closed-loop responses of both approaches are
satisfactory since the underlying MPC can efficiently track the reference
trajectories for the controlled and manipulated variables in the presence of fast
disturbances.

Würth L, Hannemann R, Marquardt W. A
two-layer architecture for economically optimal process control and operation. J.
Proc. Cont. 21, 311-321 (2011);

Marlin TE, Hrymak AN. Real-time
operations optimization of continuous processes. In: AIChE
Symp. Ser. 93, 156-164 (1997);

Zavala VM, Laird CD, Biegler LT. Fast Implementations and Rigorous Models: Can both be accommodated
in NMPC? In: Int. J. Robust Nonlinear Control 1?20 (2006).