(745c) Real-Time Optimization of a Reduced-Order Residue Fluidized Catalytic Cracker Model with Trust Region Method

Authors: 
Masuku, C. M., Carnegie Mellon University
Chen, X., Carnegie Mellon University
Wu, K., Carnegie Mellon University
Bai, A., Carnegie Mellon University
Niederberger, J., Petrobas
Liporace, F. S., Petrobras S.A
Biegler, L., Carnegie Mellon University
Real-time optimization (RTO) is an efficient way to optimize process decision variables and improve economic performance. Petrobras’ RECAP unit in Mauá, Brazil currently runs a refinery (Distillation + RFCC + Solvents) RTO on Aspen Plus Equation-Oriented System. The system can track the last time period’s data of the process and put them in the RTO to maximize profit by calculating decision variables for the next time period subject to some operating constraints. A reduced-order model (ROM) is built to simplify calculations by replacing the complex truth model of the residue fluid catalytic cracking (RFCC) unit. In order to guarantee convergence to the optimum of the truth model, we apply a trust-region filter (TRF) strategy that takes advantage of the ROM-based optimization with occasional information from the truth model.

The ROM of the RFCC unit is based on a general plug flow reactor (PFR) model and is visualized as an Aspen Custom model (ACM) connecting to the whole RECAP flowsheet as well as to the detailed model. Since ROMs are sufficiently accurate only in a restricted zone around the point in decision variable space where they are constructed [1], the TRF strategy is applied to optimize this RTO problem. Here, a trust-region sub-problem (TRSP) incorporates the ROM-RFCC model including (i) adding the penalty term to the objective function; (ii) adding the correction terms to the ROM to form the full reduced-order model; and (iii) adding the TR radius constraints on the degrees of freedom. In particular, the penalty term on the objective function avoids the expensive compatibility check in the trust-region algorithm [2]. The correction terms on the PFR model are used to pass the criticality check since they can reduce the gap between the truth model and the ROM at different inputs.

Python programming platform is used to develop the trust-region algorithm driver, which reads data from and writes data back to Aspen files for TRSP, truth model (RFCC), and the ROM-RECAP. For each iteration, the driver first transfers the input values into the isolated truth model and the isolated ROM to calculate the Jacobian matrices. Then, this driver collects the matrices and sends them to the TRSP part as the correction terms and solves the TRSP. Next, the driver reads the solution of the TRSP and helps it go through the filter check, optimality check, and step-type check to calculate the radius for the next iteration. Finally, the new location is fed back to the isolated ROM and the isolated truth model to calculate new Jacobian matrices. Their results, with the new radius, are then moved to the TRSP for the next iteration until the optimality check holds.

This approach will be illustrated on a number of real-world examples in order to demonstrate the effectiveness and efficiency of this ROM-based optimization approach.

[1] A. Agarwal, L.T. Biegler, A trust-region framework for constrained optimization using reduced-order modeling, Optim. Eng. 14 (2013) 3–35.

[2] J.P. Eason, L.T. Biegler, A trust region filter method for glass box/black-box optimization, AIChE J. 62 (2016) 3124–3136.

Keywords: Real-Time Optimization, Reduced Order Models, Crude Distillation, Equation-Oriented Optimization, Trust Region Method.