Federico Lozano Santamaria

Fouling in heat transfer applications affects process efficiency, safety, emissions, and economics. Models of different predictive accuracy, data requirement, and computational feasibility are available to quantify its effects on individual exchangers and whole networks, and the benefits of mitigation techniques. A key question is how much model detail is required for which use. This article compares two dynamic thermo-hydraulic models for heat exchanger networks under fouling: a high-fidelity model (A) suitable for simulation and a simpler model (B) suitable for optimization. It identifies conditions where the two models are broadly equivalent and presents a parameter estimation scheme to match them, and a validation methodology. A detailed comparison for 37 exchangers in 8 networks shows that the simpler model (with parameters fitted as indicated) can approximate well the high-fidelity model for relatively long periods. The simpler Model B is then successfully used to simultaneously optimize cleaning schedule and flow distribution of an industrial preheat train. This solution is validated against Model A, with a difference in predicted operational cost of 1.4% over 1 year. Results indicate that the simpler model and fitting procedure can be confidently used in a closed loop nonlinear model predictive control strategy.

Heat exchanger networks subject to fouling are an important example of dynamic systems where performance deteriorates over time. To mitigate fouling and recover performance, cleanings of the exchangers are scheduled and control actions applied. Because of inaccuracy in the models, as well as uncertainty and variability in the operations, both schedule and controls often have to be revised to improve operations or just to ensure feasibility. A closed-loop nonlinear model predictive control (NMPC) approach had been previously developed to simultaneously optimize the cleaning schedule and the flow distribution for refinery preheat trains under fouling, considering their variability. However, the closed-loop scheduling stability of the scheme has not been analyzed. For practical closed-loop (online) scheduling applications, a balance is usually desired between reactivity (ensuring a rapid response to changes in conditions) and stability (avoiding too many large or frequent schedule changes). In this paper, metrics to quantify closed-loop scheduling stability (e.g., changes in task allocation or starting time) are developed and then included in the online optimization procedure. Three alternative formulations to directly include stability considerations in the closed-loop optimization are proposed and applied to two case studies, an illustrative one and an industrial one based on a refinery preheat train. Results demonstrate the applicability of the stability metrics developed and the ability of the closed-loop optimization to exploit trade-offs between stability and performance. For the heat exchanger networks under fouling considered, it is shown that the approach proposed can improve closed-loop schedule stability without significantly compromising the operating cost. The approach presented offers the blueprint for a more general application to closed-loop, model-based optimization of scheduling and control in other processes.

The advantages of linear/nonlinear model predictive control (N)MPC for dealing with the multiple input multiple output problem, for performing optimization and for handling constraints are well-known and because of that it has been applied widely in the chemical industry. However, there is a recurrent problem for this kind of controllers and it is how to define the best tuning parameters to achieve a good closed-loop response. This is an open question for research even when the common practice is to define the (N)MPC tuning parameters by trial and error or by the expertise of the control engineer. There are some works that propose a systematic definition of the (N)MPC tuning parameters, but most of them are restricted to certain prediction models or do not define all the tuning parameters. This papers presents a general tuning algorithm for (N)MPC controllers that allows the systematic definition of all the tuning parameter and it is not restricted to a specific prediction model or to a problem formulation. It is based on multiobjective optimization for the definition of the objective function weights and on the optimization of a closed loop performance index for the definition of the horizon lengths. Three cases of chemical processes are considered in detail to illustrate the application and advantages of the proposed (N)MPC tuning algorithm.