Optimal synthesis of complex distillation columns using rigorous models (original) (raw)
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Industrial & Engineering Chemistry Research, 2000
This paper presents a modeling procedure for the derivation of generalized disjunctive programming (GDP) models for the optimal design of complex or thermally coupled distillation columns. Optimization models for the separation of ideal and azeotropic mixtures are derived on the basis of superstructures reported previously in the literature. The GDP models use rigorous design equations, where the trays in the column can be considered permanent or conditional, depending on the functions they perform (i.e., heat supply/removal, draw streams and feeds). The conditional trays are modeled with disjunctions to decide whether or not vapor-liquid equilibrium mass transfer should be applied in each potential tray. The GDP models derived are solved with a logic-based outer approximation algorithm. The performance of the proposed procedure is evaluated with three examples: (a) the separation of an ideal mixture, (b) the separation of an azeotropic mixture, and (c) an industrial problem involving ideal mixtures. These examples show that the proposed method produces fairly robust and computationally efficient models.
Computer Aided Chemical Engineering, 2005
The optimal economic design of a distillation column involves the selection of the number of trays, feed and side-streams locations and operating conditions. In this paper we present a superstructure based optimization algorithm that combines the capabilities of commercial process simulators -taking advantage of the specially tailored algorithms designed for distillation and property estimation implemented in these simulators-and generalized disjunctive programming (GDP). The algorithm iterates between two types of sub-problems: an NLP sub-problem, in which the trays are divided in existing and non-existing (non-existing trays behave like simple bypasses without mass or heat exchange) and an especially suited master (MILP) problem. NLP sub-problems are solved connecting the process simulator with an NLP external solver. An example is also included showing promising results.
Computers & Chemical Engineering, 2003
This paper examines alternative models for the economic optimization of multicomponent distillation columns. Different column representations are modeled involving rigorous MINLP (Mixed Integer Nonlinear Programming) and GDP (General Disjunctive Programming) formulations. The different representations involve various ways of representing the choices for the number of trays and feed tray location. Also, alternatives are considered for modeling the heat exchange when the number of trays of the column must be determinated. A preprocessing procedure developed in a previous paper (Barttfeld and Aguirre, 2002a) is extended in this work to provide good initial values and bounds for the variables involved in the economic models. This initialization scheme increases the robustness and usefulness of the optimization models. Numerical results are reported on problems involving the separation of zeotropic and azeotropic mixtures. Trends about the behavior of the different proposed alternative models are discussed.
A robust strategy for optimizing complex distillation columns
Computers & Chemical Engineering, 2005
This work introduces a strategy for the optimal design of distillation systems based on continuous optimization. The approach is similar to the one proposed earlier by . A distributed stream method for tray optimization. AIChE Journal, 48, 582], avoiding the need of solving extremely large and non-linear discrete optimization problems. When used with complex distillation units, it can identify interesting design configurations not considered by other continuous formulations, and also relieve some of the numerical difficulties associated with the use of distribution functions for the optimal location of feed and side-streams. The method considers a relaxation of the original problem, where the streams are initially split to several trays in the column, not necessarily adjacent. The optimal location of each stream is converged by constraining the optimization problem, using adjustable parameters that control the minimum amount of aggregation allowed. The methodology is illustrated with the application to several industrial case studies, including sets of distillation columns. Models up to 17,000 variables/equations were solved, revealing large economic benefits in the design of new units and optimization of sets of existing ones. (F.J.M. Neves), dulce@eq.uc.pt (D.C.M. Silva), nuno@eq.uc.pt (N.M.C. Oliveira).
Optimization of Distillation Processes
Distillation, 2014
In this work we present an overview of the main advances in column sequence optimization in zeotropic systems, ranging from systems using only conventional columns, each with a condenser and a reboiler, to fully thermally coupled systems with a single reboiler and a single condenser in the entire sequence. We also review the rigorous design of distillation columns, or column sequences. In all the cases we focus on mathematical programming approaches.
A disjunctive programming approach for the optimal design of reactive distillation columns
Computers & Chemical Engineering, 2001
A generalized disjunctive programming formulation is presented for the optimal design of reactive distillation columns using tray-by-tray, phase equilibrium and kinetic based models. The proposed formulation uses disjunctions for conditional trays to apply the MESH and reaction kinetics equations for only the selected trays in order to reduce the size of the nonlinear programming subproblems. Solution of the model yields the optimal feed tray locations, number of trays, reaction zones, and operating and design parameters. The disjunctive program is solved using a logic-based outer-approximation algorithm where the MILP master problem is based on the big-M formulation of disjunctions, and where a special initialization scheme is used to reduce the number of initial NLP subproblems that need to be solved. Two examples are presented that include reactive distillation for the metathesis reaction of 2-pentene and for the production of ethylene glycol. The results show that the proposed method can effectively handle these difficult nonlinear optimization problems.
Chemical Engineering Research and Design, 2012
The optimal design of complex distillation systems is a highly non-linear and multivariable problem, with several local optimums and subject to different constraints. In addition, some attributes for the design of these separation schemes are often conflicting objectives, and the design problem should be represented from a multiple objective perspective. As a result, solving with traditional optimization methods is not reliable because they generally converge to local optimums, and often fail to capture the full Pareto optimal front. In this paper, a method for the multiobjective optimization of distillation systems, conventional and thermally coupled, with less than N ā 1 columns is presented.
We analyze the effect of using adjusted parameters, corresponding to local and global optimums, in the NRTL thermodynamic model on the complete process synthesis (design, optimization and control) of homogeneous azeotropic distillation columns. The adjusted parameters that corresponding to a global optimum were obtained with simulated annealing technique, while the adjusted parameters that corresponding to a local optimum were taken from Dechema Collection. Both sets of parameters were used to design a conventional sequence, a side-stream column and a Petlyuk sequence. These designs were used as initial solution to a multiobjective genetic algorithm with constraints handling, coupled to a processes simulator, where the number of stages and heat duty of each column were considered as objectives; as result, a set of optimal designs, called Pareto front, was obtained. Then, we choose some designs in order to analyze their theoretical control properties and the dynamic performance. Resu...
Optimal design of complex distillation system for multicomponent zeotropic separations
The optimal design of complex distillation system for separation of multicomponent zeotropic mixtures is studied. Super column with the ability to separate any specified products from the given feed is introduced for defining integration upper limit of design alternatives. The improved state-space (SS) superstructure incorporating all basic mass and heat transfer elements are adopted to capture all configurations in the framework of super column. Specifically, by adding stages-cascade process operator in the original representation, a series of optimal flowsheets with multiple thermal links, which have never been included within previous superstructure are easily generated. The mathematical modeling of the proposed superstructure is performed with mixed integer non-linear programming (MINLP). It advocates the use of rigorous physical model for each mass/heat transfer stage to ensure the practical reliability and optimality of the attained designs. Then the derived optimization model is solved by a modified solution procedure, in which the key item is an iterative initialization scheme. Three multicomponent zeotropic separation examples are employed to illustrate the effectiveness of the proposed approach. These optimum designs yield significant savings in total annual cost (TAC) relative to Petlyuk columns and some guidelines for distillation flowsheet retrofit based on thermodynamic analysis are proposed.