A disjunctive programming approach for the optimal design of reactive distillation columns (original) (raw)
Related papers
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.
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.
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.
Optimization-based design of reactive distillation columns using a memetic algorithm
Computers & Chemical Engineering, 2011
The design optimization of reactive distillation columns (RDC) is characterized by complex nonlinear constraints, nonlinear cost functions, and the presence of many local optima. The standard approach is to use MINLP solvers that work on a superstructure formulation where structural decisions are represented by discrete variables and lead to an exponential increase in the computational effort. The mathematical programming (MP)
Computer Aided Chemical Engineering, 2005
This contribution proposes a Mixed Integer Non Linear Programming (MINLP) formulation for optimal design of a catalytic distillation column based on a generic nonequilibrium model (NEQ). The solution strategy for the global optimization combines Simulated Annealing (SA) and Sequential Quadratic Programming (SQP) in order to minimize the objective function. The solution of this MINLP problem yields the optimal values for the temperature, composition and flow rate profiles, tray geometry, column diameter, reflux ratio, reboiler duty, feed tray location, number of trays and catalytic stage location. Hydraulic constraints (entrainment flooding, down-flow flooding, weeping-dumpling) are also considered. For the example, the production of ETBE (Ethyl tert-butyl ether) is presented here.
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).
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.
Industrial & Engineering Chemistry Research, 2012
New intensified schemes have been recently proposed as an attempt to reduce energy requirements and equipment costs in reaction−separation processes. A design methodology for thermally coupled reactive distillation systems is proposed in this work. To design the columns, a method based on the Fenske−Underwood−Gilliland (FUG) equations is proposed and tested. The FUG equations, the mass and energy balances, and the phase equilibrium equations are used to formulate the model of the intensified systems. Such a model is then solved as a nonlinear programming problem; the objective function is the minimization of the heat duty in the column. Biodiesel production through the esterification of oleic acid with supercritical methanol is used as a case study. Results show the feasibility of obtaining designs with low energy requirements by using the proposed methodology. Because of nonconvexities present in the formulation, the estimated interlinking flows for the reactive Petlyuk column might not correspond to a minimum for energy requirements. Nevertheless, the resulting designs not only show low heat duties, with a difference of less than 2% from that minimum, but also have the capacity of achieving the desired conversion and purities.