Optimal synthesis of distillation columns: Integration of process simulators in a disjunctive programming environment (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.
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.
Industrial & Engineering Chemistry Research, 2000
A disjunctive programming model is presented for the design of ideal and nonideal distillation columns in which the feed tray location, number of trays, and operating and design parameters are determined. The proposed model is based on the identification and application of MESH equations for conditional trays in order to reduce the size of the nonlinear subproblems and to increase robustness. A logic-based outer approximation algorithm is proposed to solve the problem, where the mixed-integer linear programming (MILP) master problem based on the convex hull formulation of disjunctions is replaced with a big-M formulation. The algorithm is also modified with the introduction of two initialization schemes and the inclusion of convex envelopes to improve lower bounding in the MILP master problem. It is shown that the combination of a disjunctive model and the appropriate logic-based solution algorithm can greatly improve the robustness of the design procedure. The proposed disjunctive column model is extended to the synthesis of distillation column sequences, based on the state-equipment network representation. The robustness and computational efficiency of the model is tested with four examples involving single-column and distillation sequence configurations.
Optimal synthesis of complex distillation columns using rigorous models
2004
The synthesis of complex distillation columns has remained a major challenge since the pioneering work by Sargent and Gaminibanadara that was reported in 1976. In this paper we first provide a review of recent work for the optimal design of distillation of individual columns using tray-by-tray models. We examine the impact of different representations and models, NLP, MINLP and GDP, as well as the importance of appropriate initialization schemes. We next provide a review of the synthesis of complex column configurations for zeotropic mixtures and discuss different superstructure representations as well as decomposition schemes for tackling these problems. Finally, we briefly discuss extensions for handling azeotropic mixtures, reactive distillation columns and integration in process flowsheets. Numerical examples are presented to demonstrate that effective computational strategies are emerging that are based on disjunctive programming models that are coupled with thermodynamic initialization models and integrated through hierarchical decomposition techniques.
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).
A flexible algorithm for simulation and optimization of continuous distillation
Computers & Chemical Engineering, 1992
A flexible computer algorithm for simulation and optimization of a continuous distillation column has been developed. The specifications required from the user are component properties and the column setup in addition to specifications of distillate rate and reflux. Product specifications such as product yields or product purity can also be handled. A rigorous Naphtali-Sandholm procedure is used to solve the full set of column equations, for given values of distillate rate and reflux. An nested loop approach is used when product purities or yields are specified. It is based on exact column profile sensitivities with respect to changes in distillate rate or reflux. The sensitivities are easily calculated from the analytical derivatives used in the basic Naphtali-Sandholm procedure. The sensitivities may also be utilized to determine optimum feed stage locations.
Generalized modular framework for distillation column synthesis
2004
In this work the distillation column sequencing problem is addressed through the Generalized Modular Framework, based on formal superstructure optimization techniques. The proposed method overcomes structural complexities through the use of systematically composed structural models incorporating all the feasible sequencing alternatives. The generated sequences are evaluated with respect to their cost efficiency, based on aggregated physical models, enhanced with principles of the Orthogonal Collocation technique for distillation order reduction. This allows the generation of compact optimization problems, while avoiding the use of potentially limiting simplifying assumptions. The synthesis method coupled to a formal Mixed Integer Nonlinear Programming (MINLP) solution algorithm, was applied for a number of sequencing case studies generating substantial economic savings by finding systematically and accurately the most cost efficient column sequence.
Distillation is the most commonly used and the most versatile separation method for liquid components in boiling mixtures. Unfortunately, this unit operation is often one of the biggest energy consumers in industrial processes. The energy consumption of the distillation column is dependent on several operation variables; optimization of these variables means to minimize the energy demand while maintaining good product quality. In the classical optimization approach, only one variable is varied at a time, and its effect on the system is recorded. This so-called "univariate" approach often requires a considerable experimental or computational effort, and it neglects relationships between the variables. In the multivariate optimization approach, the variables are varied in a more efficient way, and their possible interaction is taken into account. In the present work, a multivariate approach is used to define the optimal operation variables for minimum energy consumption of a...