Z. Lelkes

Optimization of hybrid ethanol dehydration systems

Abstract Hybrid ethanol dehydration systems are modeled and optimized using MINLP. The systems consist of a distillation column for approaching the ethanol/water azeotrope and of a pervaporation unit for producing pure ethanol. The optimal design and operating parameters including number of trays, feed location, reflux ratio, number of membrane sections in series and the number of membrane modules in each section are determined. Regression equations fitted to solutions of differential equations are employed for modeling the membrane modules. Quadratic and exponential regression, as well as metric and linear interpolation are studied for approximating the integral membrane model; the exponential approximation is selected. A new mathematical representation of the superstructure of the membrane subsystem is suggested and applied. A successive refinement method with non-increasing number of binary variables is developed and successfully applied. Computational experiences with gams/dicopt are presented. Using our new membrane superstructure representation, the hybrid system can be optimized effectively. The optimization method developed is also successfully applied for process intensification of an industrial scale dehydration plant. Compared to the existing plant, 12% savings in the total annual cost can be achieved by applying 32% additional membrane surface, in consequence of a radical decrease in the reflux ratio (3.3:1.4) in the column, and of producing less concentrated alcohol in the distillate. Sensitivity of the total annual cost to the specified ethanol yield, overall membrane surface and membrane replacement cost is studied. Total permeate recycling is found to be more economical, compared to partial recycling.

Batch extractive distillation: The process and the operational policies

The batch realisation of the extractive distillation and the role played by the different steps in the process are analysed and on the basis of this analysis several operational policies are presented. The different BED policies are studied by simulation and compared (with the example of the mixture acetone–methanol+water). A method is suggested for the comparison of the different BED operational policies. In a BED process the mole fraction of the more volatile component (A) in the distillate (xd,A) can be influenced not only by the variation of reflux ratio (R) but also by changing the flow rate of the solvent (F). The simulation results are experimentally investigated and verified for each operational policy. The original R=const.policy is modified by shortening the second preparatory step of the BED (R=∞,F>0). The possibilities of performing a constant distillate composition (xd,A=const.) policy are discussed. In order to increase the efficiency of the modified R=const.policy further, it is combined with the xd,A=const. policy, maintaining a high value of xd,A for a longer period during the production of A by gradually increasing R or F or R and F simultaneously. The feasibility of the cycling policy is also studied for the BED.

Homoazeotropic distillation of maximum azeotropes in a batch rectifier with continuous entrainer feeding I. Feasibility studies

Abstract Our former method for the assessment of the feasibility of extractive distillation in a batch rectifier was extended for the investigation of the separation of maximum azeotropes. The method is based on the calculation of the still path and possible composition profiles of the column sections. The sequence of the separation steps was determined, then limiting values and the influence of the most important parameters were investigated. The feasibility calculations performed to the mixture acetone—chloroform using benzene and toluene as solvent verified the benefits of the continuous feeding of the separating agent.

Feasibility studies for batch extractive distillation with a light entrainer

Abstract Our former method for the assessment of the feasibility of batch extractive distillation (usually performed in a rectifier with a heavy entrainer) was extended to the case where a light entrainer is fed continuously into a rectifier or a stripper. The method is based on the calculation of the vessel path and possible composition profiles of the column sections. The method is demonstrated for both configurations on the examples of separation of minimum boiling point azeotropic mixtures. For the rectifier the most important conclusions were also experimentally verified.

Process flowsheet superstructures: Structural multiplicity and redundancy Part I: Basic GDP and MINLP representations

Abstract Structural multiplicity has a significant effect on the solution of an MINLP model for process synthesis problems. The optimization model may also have built-in redundancy that cannot always be directly derived from the multiplicity of the superstructure. A basic GDP representation (BGR) involving logical relations is defined, and can be constructed by applying a standard natural representation of the process. Basic MINLP representation (BMR) is defined by transforming the logical relations to algebraic ones. MINLP representation (MR) is defined through a fixed form of BMR. Equivalency and representativeness of MR-s in general form can be analyzed by reducing them to their BMRs. BMR can be automatically generated, and can serve as a reference representation. Binary and continuous multiplicity of MR are defined. If the supergraph, i.e. the graph representing the superstructure, is structurally redundant (i.e. there are isomorphic graphs amongst their subgraphs) then BMR has binary multiplicity. Conversely, the structural redundancy of the graph does not follow from the binary multiplicity of its BMR. Different kinds of multiplicity and redundancy measures of the MINLP representation will be defined in Part II of this series in order to help inventing tools for decreasing their detrimental effect. Alternative MINLP representations will there be defined, constructed, and compared from the viewpoint of ideality, minimality, and solution properties.

Rigorous MINLP model for ethanol dehydration system

Abstract Ethanol dehydration systems are modeled and optimized using MINLP. The systems consist of a distillation column for approaching the ethanol/water azeotrope and a pervaporation system for producing pure ethanol. Rigorous modeling equations are employed for modeling both the column and the subsystem of membrane modules. Quadratic and exponential regression, as well as metric and linear interpolation are studied for approximating the integral membrane model. A method for radically decreasing the multiplicity of equivalent structures covered by the superstructure is suggested and applied. A successive refinement method with non-increasing number of binary variables is developed and successfully applied.

Feasibility and sequencing studies for homoazeotropic distillation in a batch rectifier with continuous entrainer feeding

Abstract A method has been developed for the assessment of the feasibility and for the sequencing of homoazeotropic distillation in a batch rectifier under continuous entrainer feeding. The method is based on the calculation of the still path and possible composition profiles of the column sections. The application of the method is presented by two examples. In both cases minimum boiling point azeotropic mixtures are separated. In the first case a heavy solvent, in the second a light entrainer is used. The most important conclusions were also experimentally verified.

Handling of removable discontinuities in MINLP models for process synthesis problems, formulations of the Kremser equation

This paper presents a new method for handling removable discontinuities in non-convex mixed integer non-linear programming (MINLP) models for chemical process synthesis and design. First, the occurrences of different kinds of discontinuities in design equations are discussed. Then methods so far developed for handling discontinuities in an MINLP design environment are summarized. In the main part of the paper, a new method is presented for handling removable discontinuities. Our new method is compared to five conventional literature methods applied to three mass exchange network synthesis problems of different size, where the Kremser equation is used for calculating the number of equilibrium stages. In addition, a heat exchange network synthesis problem is considered where the logarithmic mean temperature difference is calculated rigorously. Our method proved to be much faster than the other methods examined and shows less sensitivity to the change of initial values in terms of optimal objective function value and solution time.

Different operational policies for the batch extractive distillation

In our former papers the batch extractive distillation (BED) was investigated under constant reflux ratio (R=const.). In a BED process the mole fraction of the more volatile component (MVC) in the distillate xd,A can be influenced not only by the variation of R but also by changing the flow rate of the solvent (F). Several operational policies were developed, and these policies were studied by simulation (on the example of the mixture acetone-methanol + water) and compared. The xd,A=const. policies gave lower recoveries than the original R=const. policy. This latter policy was modified by shortening the second preparatory step of the BED (R=∞, F⪢0). The effectiveness of this modified policy was also experimentally verified. Finally this modified R=const. policy was combined with the xd,A=const. policy maintaining a high value of xd,A for a longer period during the production of the MVC by gradually increasing R or F or R and F simultaneously.

Process flowsheet superstructures: Structural multiplicity and redundancy Part II: Ideal and binarily minimal MINLP representations

Abstract The essential problems, namely representativeness and uniqueness, in defining mixed integer non-linear programming (MINLP) representation (MR) is solved in Part I by first defining a basic MR (BMR) that: (1) can be automatically constructed from an easier formable standard GDP representation and (2) serves as a reference representation. Binary and continuous multiplicity of MR are also defined in Part I, and relation is given there between structural redundancy and binary multiplicity. Based on this results, ideal and binarily minimal MR-s are defined, and the different MR-s are compared from numerical point of view in the present (and final) part. Ideal MR represents all the considered structures and not any other structure. Supposing the process graphs are distincted using binary variables, binarily minimal MR uses the minimal number of them. Solvability of the different MR-s, including some combined versions, are tested on a middle scale and an industrial scale process synthesis problems. Total solution time, solution time for subproblems, number of iterations, non-ideality and scale of the solvable problems are compared. Idealization of the representation and decreasing the number of binary variables, as suggested in the article, both enhance the solvability and decrease the solution time in a great extent.