Design Methodology of Modifier-Adaptation RTO Systems

Optimization is used routinely in the process industry to reduce production costs, improve product quality, and meet safety requirements and environmental regulations. But when the optimal operating conditions are determined based on a process model, the resulting process operation can be highly sensitive to model uncertainty and process disturbances, which can lead to suboptimal or even infeasible operation. A natural approach to combat uncertainty and avoid conservatism is to incorporate measurements in the optimization framework.

Traditionally, the optimization is based on a first-principles model that is updated in real-time using the available measurements [1]. These two-step RTO systems are well-accepted by industrial practitioners, yet it is very difficult to ensure convergence to the actual plant optimum, due to the lack of integration between the model-update and optimization steps. In response to this, the modifier-adaptation methodology has been recently developed [2]. Similar to two-step RTO, the available process model is embedded within a nonlinear program (NLP) that is solved at each RTO execution. The key difference is that the process measurements are now used to update so-called modifiers that are added to the outputs in the optimization model. This methodology greatly alleviates the problem of offset from the actual plant optimum, but it comes at the cost of having to estimate the plant output gradients from process measurements.

An algorithm that combines modifier adaptation with an output gradient update scheme based on Broyden's method has previously been developed in [3]. In the presence of significant measurement noise, however, the error in output gradients can become arbitrarily large as the operation converges to the optimum, thereby leading to a peaking phenomenon. Stochastic programming offers a natural framework to handle the effect of measurement noise, yet it leads to on-line tractability issues from a real-time optimization perspective. Instead, a dual-modifier-adaptation methodology is considered in this work, which reconciles the conflicting objectives of optimality and gradient-prediction accuracy. This methodology starts with an off-line design phase, followed by the on-line execution phase:

• During the on-line phase, the required excitation needed to get accurate gradient estimates is enforced through the addition of constraints to the optimization model. These constraints take the form of an exclusion region around the current operating point.

• The prior off-line phase is concerned with the shaping of the exclusion region constraint. Our approach builds upon the so-called "design cost" procedure introduced by Forbes and Marlin [4] and its adaptation to modifier-adaptation RTO [3]. Specifically, the exclusion constraints are designed so as to maximize the expected RTO performance on account of the anticipated measurement noise and model mismatch. Two important developments include: (i) the ability to handle problems that feature changes in active constraints, by considering probabilistic constraints; and (ii) the computation of appropriate levels of constraint back-off to mitigate constraint violation problems.

The proposed dual-modifier-adaptation methodology is illustrated through numerical simulations for a selection of benchmark problems.

References

[1] Marlin T. E. and Hrymak A. N., "Real-time operations optimization of continuous process," AIChE Symp. Ser. 316:156-164, 1997.

[2] Marchetti, A., Chachuat, B., and Bonvin, D., "Modifier-adaptation methodology for real-time optimization," Ind. & Eng. Chem. Res. 48(13):6022-6033, 2009.

[3] Rodger, E., and Chachuat B., "Methodology for Technology Selection in RTO Systems," AIChE Annual Meeting 2009, Nashville (TN).

[4] Forbes, J. F., and Marlin, T. E., "Design cost: A systematic approach to technology selection for model-based real-time optimization systems," Comp. & Chem. Eng. 20(6/7):717-734, 1996.