Anton Friedl, Jiří J. Klemeš, Stefan Radl, Petar S. Varbanov, Thomas Wallek (Eds.) Proceedings of the 28th European Symposium on Computer Aided Process Engineering June 10th to 13th, 2018, Graz, Austria. © 2018 Elsevier B.V. All rights reserved. https://doi.org/10.1016/B978-0-444-64235-6.50135-2
Superstructure optimization (MINLP) within ProSimPlus Simulator Qiao Zhaoa,b, Thibaut Neveuxb, Mounir Mecherib, Romain Privata, Philippe Guittardc, Jean Noël Jaubert a* a
LRGP-CNRS, 1 Rue Grandville, 54000 Nancy, France
b
EDF R&D, 6 quai Watier 78401 Chatou, France
c
PROSIM SA, 51, RUE AMPERE 31670 Labège France
[email protected]
Abstract Although the methodologies of optimization-based process synthesis have evolved significantly during the last thirty years, the ability to robustly and accurately solve industrially-relevant global flowsheet problems remains limited. Engineering expertise and simulation-based sensitivity analysis still remain an essential guide for system alternatives generation and key devices selection. The purpose of this study is to provide a superstructure mixed-integer nonlinear programming (MINLP) optimization within the commercial simulator ProSimPlus. The entire optimization loop is directly managed by the simulator and both continuous variables and discrete integer variables are optimized simultaneously by an external metaheuristic optimizer called MIDACO (Mixed Integer Distributed Ant Colony Optimization). Keywords: Superstructure, Optimization, Process Simulator, MINLP, Ant Colony Optimization
1. Introduction Thanks to the advances made in artificial intelligence and mathematical programming, the computer-aided approaches in process synthesis (e.g., superstructure optimization) have evolved significantly during last thirty years (Voll et al., 2013). Nevertheless, low disseminations of such optimization into the industrial community are noticed because that real-world industrial studies are complex non-linear and non-convex problems (Barnicki and Siirola, 2004; Quaglia et al., 2015). One of the widely applied approach is the equation-based optimization, yet there is a known compromise on solution quality obtained (i.e., rigorousness) since linear approximation or surrogate models are frequently applied (Chen and Grossmann, 2017). On the other hand, simulator-based optimization approach has been received more attention recently since it can benefit directly from the reliably and rigor of process simulator. Regarding this topic, studies have been carried out in different applications such as distillation systems (Bravo-Bravo et al., 2010; Leboreiro and Acevedo, 2004; Caballero et al., 2005; Corbetta et al., 2016), chemical processes retrofit, (Diwekar et al., 1992; Gross and Roosen, 1998; Brunet et al., 2012; Chen et al., 2015) as well as
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energy conversion system application (Wang et al., 2014). The MINLP optimizations carried out within process simulator (Flowtran, Aspen Plus, Aspen Hysys, PRO/II or Ebsilon Professional) require an additional interface (i.e., GAMS, C++), requiring tedious supporting tool construction. In this work, a superstructure MINLP optimization of SC-CO2 Brayton cycle is brought out with ProSimPlus, a commercial simulator. Unlike researches cited above, our strategy is to use ProSimPlus as main (and the only) interface to both manage the graphical representation of the superstructure as well as the MINLP optimizer. An external solver MIDACO (Schluter et al., 2009), an Ant Colony Optimization (ACO) metaheursitic algorithm is applied for the MINLP problem discussed in this paper. The rigorous models for unit operations implemented in ProSimPlusare directly used during the MINLP optimization without approximation.
2. Methodology 2.1. Metaheursitic optimization with MIDACO The motivation of using metaheuristic optimizer MIDACO in this study is its black-box and stochastic probabilistic nature. The first property allows to optimize non-convex MINLP problem without explicit expression of the objective and constraint functions. Secondly, the stochastic nature of ACO makes it possible to selectively search a much smaller fraction of the solution space thus reduces the computational time efforts. 2.2. Optimization unit in ProsimPlus The link with an external optimizer is made possible in ProSimPlus thanks to predefined communication interfaces that are implemented in the ProSimPlus standard optimization unit.
Figure 1 Illustration superstructure graphic representation (left) and optimization unit (right) in ProSimPlus, case of a Two Reactors Problem (blue dashed lines are information streams: 1 objective function, 1 constraint, 1 integer decision and 1 continuous variables)
If a user does not want to use the native stochastic optimization (genetic algorithm) or the default nonlinear programming optimization algorithm (based on a SQP method), it
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is possible to select an external dynamic library which implements these communication interfaces and is statically or dynamically liked with the external algorithm. When the external solver is provided as a dynamic link library, a wrapper dll is needed to perform the communication between ProSimPlus and the external algorithm. The value of the objective function as well as the values of the equality and inequality constraints are automatically passed to the external dynamic library to make them available to the external algorithm, which calculates the new values of the optimization variables. A customizable table of parameters, available in the graphical user interface of the optimization unit, allows to access to the parameters of the external algorithm, see the example in Figure 1 for a simple two reactors problems (such as in Diwekar et al., 1992). 2.3. Formulation strategy in process simulator 2.3.1. Superstructure connectivity Defining the component connection in superstructure is to characterize the existence of component and to remove the redundant component when it is not used. For our superstructure formulation in this study, redundant component is only virtually removed by simply setting their flow rate to zero. A multipath (2 or more) logical switch is coded in ProSimPlus. The switch level yi is thus defined as the integer decision variable in the superstructure optimization and enables to select a specific path between all possible alternatives.
Figure 2 Logic switch defined in this study
2.3.2. Other rules in formulation stage The result of a MINLP optimization is known to be strongly influenced by the formulation of the problem and the selection of variables. It is thus important to formulate the problem in the way that allows fast and easy convergences of the process simulator flowsheet with all the values in the range between lower and upper bounds (Corbetta et al., 2016). Several rules are set in this paper: a) Tear Stream. When the superstructure involves a closed loop or recycle loop, it is necessary to choose tear stream(s) in the simulator (both feasible path and infeasible path approaches can be used). b) Fictive unit. Components situated in the middle of a simulation sequence need to be combined with a fictive unit if the component is to be optimized with constraints along with dependency of other optimized variable. The fictive unit will only be activated if the evaluated scenario is infeasible. When it is active, the work (or heat) consumed by the entire fictive unit need to be considered in the objective function. Consider turbine outlet pressure optimization as an example: its fictive unit is composed of a fictive compressor and a fictive cooler in order to avoid infeasible engineering scenario (when the ratio is smaller than 1). It is preferred to have fictive units than additional inequality constraints (force the pressure ratio greater than 1) since the latter case introduces more non-convexity to the optimization problem. c) Counter-current exchangers’ separation. The counter-current exchangers used in the superstructure optimization should be divided into two simple parts: a heater and a
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cooler. This modification avoids additional simulation iterations inside the countercurrent exchanger and reduces the possible divergent cases. The optimization itself benefits faster iteration from the relaxation of counter exchangers.
3. Application examples 3.1. Case study: SC-CO2 Brayton cycle superstructure optimization The fundamental aspects of supercritical CO2 (SC-CO2) Brayton cycle are under worldwide development, hence importance of optimization. Current optimizations of SC-CO2 Brayton cycle have only been done to maximize the cycle efficiency with parametric optimization with fixed process topology (cycle configuration). However, an optimal-synthesis searching for the most energy efficient cycle layout can further reveal its real potential in its future deployment.
Figure 3 Superstructure of SC-CO2 Brayton cycle with fictive unit (23=8 structural alternatives)
The superstructure in Figure 3 integrates some configurations based on previous experiences as well as some innovative design solutions created by the combination. Note that the rules discribed in section 2.3.2 are respected and a fictive unit is implemented after turbine T1. The indicator of the energy performance, cycle efficiency, is seen as the objective function. 10 variables (3 integer variable y1, y2, y3) are to be optimized in this MINLP problem. 3.2. Results and discussion
Figure 4 Optimization progress of four runs with different random seeds
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Four different optimization runs are carried out with four different pseudo random number (seed) in MIDACO, Figure 4. Note that different random seed has indeed diverse progress of optimization, different corresponding populations are generated. Moreover, at the end of 6 hours evaluation (up to 16,000 generations), the structural result of the best individual is identical (i.e., identical set of {x,y}), which also confirms that this layout is the best known solution to the defined optimization problem.
a) optimal configuration y={1,1,1}
b) Temperature-Entropy diagram
Figure 5 Process synthesis result: optimal flowsheet for the SC-CO2 Brayton cycle
This optimal process layout with cycle net efficiency as high as 51.4 % is composed of two compressors, two recuperators, and one reheat (thus two turbines). Compared with the initial proposal of SC-CO2 Brayton cycle by Feher, 1967 and Angelino, 1969, the optimal process configuration has an enforced heat integration. Figure 5 indicates all the exchangers have a minimal accepted thermal pinch (10 K). Furthermore, entropy loss is avoided at mixer since stream 3' and 3'' have the identical temperature and pressure (isoentropy) before mixing.
4. Conclusion In this work, we presented a simulator-based approach for superstructure optimization in process simulator ProSimPlus. Compared with other simulator-based optimization methods, the proposed superstructure optimization approach is more general on terms of component and optimizer. Any component available in the simulator can be used in the superstructure generation and external optimizers can be linked with ProSimPlus through its optimization unit. Furthermore, this paper illustrated how the simulator enables to manage the entire optimization loop while both continuous variables and discrete integer variables are optimized simultaneously by MIDACO. The case study carried out in this paper illustrate the above advantages of the presented optimization strategy. The obtained results are the best known optimal design for both application studies. In addition, the formulation rules provided in this paper guarantees the convergence of simulation which helps to reduce the infeasible region search while optimizing both continuous and integer variables.
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