Alternative representations and formulations for the economic optimization of multicomponent distillation columns (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.
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.
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).
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
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.
Journal of Process Control, 1996
A method is presented for the simultaneous optimization of a batch distillation column design and its operation, for single and multiple separation duties, each involving different multicomponent mixtures and complex operations with intermediate cuts. For operation structures selected a priori, the formulation presented permits the use of general distillation design and cost models. The objective function and constraints include capital and operating cost. In particular, the number of internal plates is optimized along with the most significant operating variables (recoveries in various cuts and reflux ratio profiles and times). The multiple duty formulation presented accounts for the different importance of each duty and setup time between batches. Application of the method to single duty multicomponent separation from the literature shows that significant profit improvements can be achieved within acceptable computing times. For multiple separation duties (two binary mixtures), the method clearly shows the importance of including allocation time to each duty and setup time for each batch in the objective function.
Economic Optimization of the Reflux Ratio of Two Components Stage Distillation Columns
2019
Distillation columns are complex processes for modeling and controlling. These columns are significant parts of most chemical industries for separation of components. Control of this process is essential for achieving certain purity for products with a minimum cost. However, nonlinearities, multivariable interaction, non-stationary behavior and severity of disturbances inside the column made this process too complex for controlling. In this study a graphical method is applied to model steady state continues tow components distillation column. First, a MATLAB code was developed to solve the mathematical model of the column. Then, the column was simulated using HYSYS software. Finally, the reflux ratio of this column was optimized to minimize the operating cost. A formula is presented to calculate the optimum value of this reflux ratio as an exponential function of a certain economic parameter of energy prices and depreciation costs. It is resulted that at low energy prices or high eq...
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 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.
A new exergoeconomic optimisation methodology applied to an industrial distillation system
International Journal of Exergy, 2017
In this work, we simulate and optimise an industrial distillation system to produce bioethanol manipulating design parameters to reduce the total exergy loss inside the columns and taking into account the economic parameters. The operational parameters are validated using Aspen Plus through the analysis of the exergy loss profile. However, the variation of the number of stages is not straightforward in processes simulators because requires to evaluate the optimal position to insert the stage in the column (i. e., stripping or rectification section). It is demonstrated that the number of stages tightly impacts the energy efficiency of the columns. The optimisation is realised in Matlab to relate the total exergy loss inside the columns with its cost identifying the sections with greater exergy loss, inserting new stages (defined by the user) and calculating the capital cost associated. The results show that is possible thermodynamically optimise the industrial distillation system.