Endre Rev

Rigorous simulation of energy integrated and thermally coupled distillation schemes for ternary mixture

Abstract Sharp (99% purity) separation of a ternary mixture, characterised by near uniformly distributed volatility, by direct separation sequence without, with forward, and with backward energy integration, by indirect separation sequence without, with forward, and with backward energy integration, by sloppy separation sequence with forward and with backward energy integration, and by thermally coupled sloppy separation sequence (Petlyuk system) is rigorously modelled and optimised. Three feed compositions, namely (Case 1) equimolar A/C ratio with 10% B, (Case 2) equimolar feed, and (Case 3) equimolar A/C ratio with 80% B are compared. Comparison is based on total annual costs (TACs) using European and American price systems. The savings in TAC of Petlyuk are uniformly about 28–33% in all the three cases, while the savings of the energy integrated systems increases together with increasing ratio of B in the feed. In Case 1, Petlyuk system is the winner, with 33% savings, but a conventional energy-integrated system is handicapped by just a very few percent. In Cases 2 and 3, Petlyuk system is not amongst the best structures. In Case 2, either the conventional energy-integrated systems or the energy-integrated sloppy structures win with 35–41%; while Case 3, the energy-integrated sloppy structures are the best with about 51% savings.

Energy savings of integrated and coupled distillation systems

Abstract Direct separation sequence without, with forward, and with backward energy integration, indirect separation sequence without, with forward, and with backward energy integration, sloppy separation sequence without (preflash system), with forward, with backward, and with double energy integration, and thermally coupled sloppy separation sequence (Petlyuk system) are compared with short-cut and rigorous modelling. Based on theoretical considerations and economically evaluated rigorous case studies for ternary mixtures it is demonstrated that in the most cases the Petlyuk system is not superior to the energy integrated configurations even in energy savings. According to the energy consumption of sharp separation determined by short-cut methodology, all the sloppy sequence structures are equivalent. According to the energy losses determined by short-cut methodology, derived here, the energy-integrated structures win almost everywhere in the studied conditions that include a range of relative volatility ratios and the whole feed composition triangle. According to rigorously simulated and optimised results, together with controllability studies, the advantageous application of the thermally coupled (Petlyuk) systems is constrained to a very small range of relative volatility ratio, feed composition, and price structure. This small range is situated somewhere around balanced relative volatility ratio A/B to B/C, small amount of the middle component B, balanced presence of the two swing components A and C in the feed, and high energy costs to investment costs ratio or slow depreciation rate.

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.

THE USE OF NONLINEAR PROGRAMMING TO OPTIMAL WATER ALLOCATION

Abstract Environmental protection, shortage of fresh-water and rising costs for wastewater treatment are all convincing motives for reducing fresh-water consumption and wastewater discharge of the chemical, petrochemical, petroleum refining and other process industries. Maximizing water reuse, regeneration re-use, and regeneration recycling within the chemical plant, as well as optimal distribution of waste streams for end-of-pipe treatment can reduce fresh-water usage and wastewater discharge, while they are also significant in shrinking capital investment in wastewater treatment systems. Optimal assignment and design of water consuming, regenerating, and treatment systems is a complicated task that can be mathematically formulated as mixed integer non-linear programming (MINLP). In the present article the superstructure based ‘Cover and Eliminate’ approach with NLP is applied with the tools of the GAMS/M1NOS/CONOPT package and compared to previous results. After introducing the problem in the context of chemical process synthesis, a mathematical model is described and the use of the methodology is explained. Experience with the use of GAMS is discussed. Several case studies are solved including basic examples from the literature and their variants. The main conclusion is that the application of the mathematical programming for the optimal water allocation problem is essential owing to the broad variety of the specification opportunities. The complex nature of re-use, regeneration re-use, and recycling with multiple pollutants and multiple treatment processes cannot be simultaneously taken into account by conceptual approaches. It is also shown that the assumption on the independency of contamination rates, generally applied in earlier works, are not necessarily valid; and the NLP approach can deal with the more reliable specifications.

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.

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.

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.

Optimal water use and treatment allocation

Abstract Water consumption and emission can be decreased by optimal allocation of water re-use, regeneration and re-use. regeneration and recycle in water consuming mass exchange networks and by applying optimally distributed effluent treatment processes in case of several emission sources of different contamination levels. Several example problems taken from the literature have been reproduced and solved by GAMS/MINOS/CONOPT package. In most cases our optimal solution is identical to those of others; in some other cases, however, we found better solutions. We also found our method more flexible than those based on targeting and conceptual design. Some example problems involve constraints and/or specifications of those kinds the referred methods cannot deal with. Namely, the constant mass load specification is substituted by either mass load proportional to the water flow rate (involving constant concentration shift) or some other, even more realistic, non-linear functions. The optimal systems have different structures according to the applied mass load relations.

Comparison of integrated and coupled distillation schemes using different utility prices

Abstract Separation of a ternary mixture by different distillation schemes was simulated rigorously at steady state. Conventional schemes, heat integrated schemes, and the fully thermally coupled structure (Petlyuk system) have been optimized over total annual cost including two different regional utility price systems (high and low utility prices): The results show that price ratios have considerable effect on the savings and consequently on the optimal schemes. Using low utility price the number of actual trays is reduced and the reflux ratios will be increased. At extreme high utility prices the Petlyuk system can be justified as one of the best schemes in savings, but not against the sloppy forward heat integrated scheme. The maximum savings in total annual cost in both cases are about 28%.