(203c) Assessing the Reliability of Different Real-Time Optimization Methodologies Using Monte Carlo Analysis

There is not a general consensus about the benefits of implementing Real-Time Optimization (RTO) technologies to increase the profit of process plants (Darby et al, 2011). Lack of experimental and theoretical works focused on evaluating the scope and limitations of the different RTO approaches makes even harder the possibility of having a sensible opinion about this topic. Most works available in the open literature that study different RTO approaches use few (often one) operation conditions to draw general conclusions about the goodness of a particular methodology (Sequeira et al., 2002, Chachuat et al., 2009). But, How reliable is a RTO method to optimize various processes under different conditions and measurement noise? This question is of strong industrial relevance; suffice to say that this study is founded by PETROBRAS.

Since its creation in 1950's (Draper and Li, 1951) there have been proposed many RTO methodologies that can be classified as model free or model based algorithms. Popular model free strategies attempt to optimize the plant through direct search and experimental design, to aid the optimization, while other methods attempt to approximate the plant gradient (by stochastic approximation or simple dynamics model identification) using these information to predict the next operating point. Most of these methodologies are simple to implement, nonetheless, they require many perturbations of the plant to generate information of quality to identify the plant optimum what can drive the process to operating far from the optimal for so long specially for slow processes involving several optimization variables.

Model-based methods use process measurements and a mathematical model of the process to aid the plant optimization. Most of these methodologies can be classified (Chachuat et al., 2009) as Optimizing Control (OC) Model-Parameter Adaptation (MPA) and Modifier Adaptation (MA). Each methodology differs in the way they employ the plant information and the accuracy (complexity) of the mathematical model of the plant.

The basic idea of MPA methods is using the measurement of the plant to update some key parameters of the steady-state model to reduce the plant-model mismatch (Marlin and Hrymak, 1997). The updated model is used to predict the operational point that maximizes the profit of the plant. This method demands high-fidelity plant models to reduce the plant-model mismatch and enough information for updating the model parameters. Despite of these drawbacks MPA methods are, nowadays, the most used in real petro/chemical plants (Chen and Joseph, 1987), though there is no guarantee to converge to the real plant optimum.

Modifier Adaptation methods (Marchetti et al., 2009) differ from MPA in the way plant information is used, since measurements are employed to fulfill the necessary first-order optimality conditions (NOC) of the plant (through the so called modifiers) without updating the parameters of the model. In this way it is possible, for the ideal MA scheme, to calculate the plant optimum in presence of plant-model mismatch at the cost of obtaining accurate plant gradient that, until now, has been the main bottleneck for its industrial application.

In this work we compare the influence of the initial operational condition as well as the measurement noise on the reliability of model-based RTO approaches (MPA, MA and some custom variations) using a Monte Carlo methodology.

Preliminary results show that conventional MPA and MA are strongly influenced by the measurement noise and initial value of the model parameters. Some methods to overcome these difficulties are proposed and evaluated.

References

Darby, M., Nikolaou, J., Nicholson, D. ‘RTO An Overview and Assessment of Current Practice. J. Process Contr.21, 874–884, 2011.

Sequeira, S. E, Graells, M., Puigjaner, L. Real-Time Evolution for On-line Optimization of Continuous Processes. Ind. Eng. Chem. Res.41, 1815-1825, 2002.

Chachuat, B., Srinivasan, B., Bonvin, D. Adaptation strategies for Real-Time optimization. Comp. Chem. Eng.33:1557-1567, 2009.

Draper, C.S., Li, Y.T. Priciples of optimizing control systems and a application to internal combustion engine. American Society of Mechanical Engineers(Sept, 1951)

Skogestad, S. Self-optimizing control: the missing link between steady-state optimization and control. Comp. Chem. Eng.24, 569-575, 2000

Marlin, T.E., Hrymak, A.N. Real-Time Operations Optimization of Continuous processes In: AIChE Symposium Ser.1997

Chen, C. Y., Joseph, B. On-Line Optimization Using a Two-Phase Approach-An Application Study. Ind. Eng. Chem. Res.26, 1924–1930, 1987.

Marchetti, A., Chachuat, B., Bonvin, D. Modifier adaptation methodology for Real-Time Optimization. Ind. Eng. Chem. Res., 48: 6022-6033, 2009.