A “MINLP” formulation for optimal design of a catalytic distillation column based on a generic non equilibrium model (original) (raw)
Related papers
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 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
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.
Optimization of reactive distillation processes with simulated annealing
Chemical Engineering Science, 2000
A simulated annealing-based algorithm (MSIMPSA) suitable for the optimization of mixed integer non-linear programming (MINLP) problems was applied to the synthesis of a non-equilibrium reactive distillation column. A simulation model based on an extension of conventional distillation is proposed for the simulation step of the optimization problem. In the case of ideal vapor}liquid equilibrium, the simulation results are similar to those obtained by Ciric and Gu (1994, AIChE Journal, 40(9), 1479) using the GAMS environment and to those obtained with the AspenPlus modular simulator. The optimization results are also similar to those previously reported and similar to those using an adaptive random search algorithm (MSGA). The optimizations were also performed with non-ideal vapor}liquid equilibrium, considering either distributed feed and reaction trays or single feed and reaction tray. The results show that the optimized objective function values are very similar, and mostly independent of the number of trays and of the reaction distribution. It is shown that the proposed simulation/optimization equation-oriented environments are capable of providing optimized solutions which are close to the global optimum, and reveal its adequacy for the optimization of reactive distillation problems encountered in chemical engineering practice.
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).
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.
A new approach for the optimization of nonsharp distillation superstructures
Asia-Pacific Journal of Chemical Engineering, 2017
In general, the optimization problem of the separation of a multicomponent feed stream into two or more multicomponent products with the use of nonsharp distillation columns is an MINLP with a nonlinear objective function. Due to the high number of variables and the high degree of nonlinearity, the presentation of a comprehensive and simple three‐phase approach was considered to solve the Mixed Integer Nonlinear Programming (MINLP) using the combination of mathematical and stochastic methods. In the method, the variables are classified into two groups: A set of variables are optimized by genetic algorithm as a stochastic algorithm; doing so converts MINLP to Linear Programming (LP), and the remaining variables are managed by solving an LP problem for known values of the former set by a regular and quick mathematical method such as simplex search. One advantage of this study is that it extracts some essential relationships between the first set of variables by the mathematical operat...
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.
Optimization of Distillation Column Operation by Simulated Annealing
Gas Processing Journal, 2013
In this paper, an exergy analysis approach is proposed for optimal design of distillation column by using simulated annealing algorithm. First, the simulation of a distillation column was performed by using the shortcut results and irreversibility in each tray was obtained. The area beneath the exergy loss profile was used as Irreversibility Index in the whole column. Then, First Optimization Algorithm (simulated annealing, SA) was implemented to Grassroots (Number of tray (N) vs. Reflux Ratio (RR)) and Retrofit (Nof vs. Feed splitting) cases, respectively. Next, SA was used to find the maximum recovery in a simple column by seven different variables (Feed Temperature, Feed Pressure, Reflux Rate, Number of theoretical stage, Feed Trays (Feed Splitting, three variables)) simultaneously. During the search for maximum recovery, it was tried to find a better Irreversibility Index. In the second part, SA optimization algorithm was used for a complex column with one pump-around and feed splitter to find a better condition, which means to find the best location for pump-around and feed trays in Distillation column. The main objective in SA was to maximize the recovery of the desired component and to find a better minimum Irreversibility Index. This method was implemented in de-ethanizer; in the first optimization without using pump-around with seven degrees of freedom, Recovery growth was 5.1% and reduction in irreversibility index was 3%. At the best Irreversibility Index, growth of recovery was about 3.7% and irreversibility index reduction was 25%. In the second optimization with pump-around or eight different variables, in the best condition, Recovery Growth was 6.2% but had a very high Irreversibility Index. At the best irreversibility index, recovery reduction was 17% but reduction in irreversibility index was about 21% comparing with initial point. As a result, it is shown that, regarding recovery and Irreversibility, pump-around shouldn t be used in a column. Without using pumparound, a better condition, considering both factors, can be achieved.
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.