Pio A. Aguirre

Optimal Synthesis of Complex Distillation Columns Using Rigorous Models

The synthesis of complex distillation columns has remained a major challenge since the pioneering work by [Sargent, R.W.H., & Gaminibandara, K. (1976). Optimal design of plate distillation columns. In L.C.W. Dixon (Ed.), Optimization in action. New York: Academic Press]. 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, mixed-integer nonlinear programming (MINLP) and generalized disjunctive programming (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. 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.

An improved piecewise outer-approximation algorithm for the global optimization of MINLP models involving concave and bilinear terms

In this paper a new version of the Outer Approximation for Global Optimization Algorithm by Bergamini et al. [Bergamini, M.L., Aguirre, P., & Grossmann, I.E. (2005a). Logic based outer approximation for global optimization of synthesis of process networks. Computers and Chemical Engineering 29, 1914] is proposed, in order to speed up the convergence in nonconvex MINLP models that involve bilinear and concave terms. Bounding problems are constructed replacing these nonconvex terms by piecewise linear underestimators. These problems, which correspond to mixed-integer linear programs, are solved to generate approximate solutions with improved objective value. When no further feasible solution can be found, this guarantees that the upper bound cannot be improved in the nonconvex problem, thus providing a termination criterion. The new algorithm is applied to five different synthesis problems in the areas of water networks, heat exchanger networks and distillation sequences. The results show a significant reduction in the computational cost compared with the previous version of the algorithm.

Logic-based outer approximation for globally optimal synthesis of process networks

Process network problems can be formulated as generalized disjunctive programs where a logic-based representation is used to deal with the discrete and continuous decisions. A new deterministic algorithm for the global optimization of process networks is presented in this work. The proposed algorithm, which does not rely on spatial branch-and-bound, is based on the logic-based outer approximation that exploits the special structure of flowsheet synthesis models. The method is capable of considering non-convexities, while guaranteeing globality in the solution of an optimal synthesis of process network problem. This is accomplished by solving iteratively reduced NLP subproblems to global optimality and MILP master problems, which are valid outer approximations of the original problem. Piecewise linear under and overestimators for bilinear and concave terms have been constructed with the property of having zero gap in a finite set of points. The global optimization of the reduced NLP may be performed either with a suitable global solver or using the inner optimization strategy that is proposed in this work. Theoretical properties are discussed as well as several alternatives for implementing the proposed algorithm. Several examples were successfully solved with this algorithm. Results show that only few iterations are required to solve them to global optimality.

A decomposition method for synthesizing complex column configurations using tray-by-tray GDP models

This paper describes an optimization procedure for the synthesis of complex distillation configurations. A superstructure based on the Reversible Distillation Sequence Model (RDSM) is proposed embedding all possible alternative designs using tray-by-tray models. Generalize disjunctive programming (GDP) is used to model the superstructure. Each column section of the superstructure is modeled using rigorous MESH equations. Due to the large size and complexity of the formulation, as well as the great difficulty in coverging the corresponding equations, a decomposition solution strategy is proposed where discrete decisions are decomposed into two hierarchical levels within an iterative procedure. In the first level, the column sections are selected yielding a candidate configuration. In the second level, the feed location and the number of trays of the selected sections are optimized. A preprocessing phase including thermodynamic information is considered to provide a good starting point to the algorithm in order to improve the convergence and robustness of the method. Examples are presented for zeotropic and azeotropic multicomponent mixtures to illustrate the performance of the proposed method. Non-trivial configurations are obtained involving modest solution times.

Alternative representations and formulations for the economic optimization of multicomponent distillation columns

Abstract This paper examines alternative models for the economic optimization of multicomponent distillation columns. Different column representations are modeled involving rigorous Mixed Integer Nonlinear Programming (MINLP) and General Disjunctive Programming (GDP) 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 [Ind. Eng. Chem. Res. (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.

Optimal MSF plant design

The aim of this paper is to present a rigorous model for Multi-Stage Flash Evaporation System (MSF). The MSF system is represented as a No Linear Programming (NLP) model. The model incorporates a high number of non-linear restrictions; so the achievement of the global optimum is difficult. Here, the study of an algorithm for the system optimisation is presented.

Some aspects in the design of multicomponent reactive distillation columns including nonreactive species

Some aspects related to the design of reactive distillation columns are addressed in this paper. A new set of transformed composition variables is proposed for mixtures including one or more components that are inert under the process conditions. This set corresponds to an extension of that suggested by Barbosa and Doherty (1988a, Chem. Engng Sci.43, 1523–1537) and allows to compute by means of any traditional procedure, the concentration profiles along the column and therefore, the minimum reflux ratio. The compositions of product streams of a reactive distillation column are subject to constraints of thermodynamic nature that can be determined before any attempt to design the column. These thermodynamic constraints do not have a counterpart in conventional distillation and become an essential piece of information in order to select the design variables and specify their values. A parametric analysis of the simultaneous chemical reaction and liquid-vapor equilibrium is suggested as a very useful instrument to select thermodynamically feasible design specifications. In this work, we also present an initial discussion about possible columns sequences to obtain the reaction product free of inert species. The selection and calculation of the relevant variables that are common in the first steps of the design and synthesis of reactive distillation processes are discussed through examples. Finally, throughout the entire paper several interesting physical and operational conclusions regarding inert components in reactive distillation are given. The main conclusion is that the inerts play a key role in the design of a reactive column.

Life cycle assessment of corn-based ethanol production in Argentina

The promotion of biofuels as energy for transportation in the world is mainly driven by the perspective of oil depletion, the concerns about energy security and global warming. In Argentina, the legislation has imposed the use of biofuels in blend with fossil fuels (5 to 10%) in the transport sector. The aim of this paper is to assess the environmental impact of corn-based ethanol production in the province of Santa Fe in Argentina based on the life cycle assessment methodology. The studied system includes from raw materials production to anhydrous ethanol production using dry milling technology. The system is divided into two subsystems: agricultural system and refinery system. The treatment of stillage is considered as well as the use of co-products (distillers dried grains with solubles), but the use and/or application of the produced biofuel is not analyzed: a cradle-to-gate analysis is presented. As functional unit, 1MJ of anhydrous ethanol at biorefinery is chosen. Two life cycle impact assessment methods are selected to perform the study: Eco-indicator 99 and ReCiPe. SimaPro is the life cycle assessment software used. The influence of the perspectives on the model is analyzed by sensitivity analysis for both methods. The two selected methods identify the same relevant processes. The use of fertilizers and resources, seeds production, harvesting process, corn drying, and phosphorus fertilizers and acetamide-anillide-compounds production are the most relevant processes in agricultural system. For refinery system, corn production, supplied heat and burned natural gas result in the higher contributions. The use of distillers dried grains with solubles has an important positive environmental impact.

Global Optimal Design of Mechanical Vapor Compression (MVC) Desalination Process

Abstract This paper deals with the optimal design of Mechanical Vapor Compression (MVC) desalination process. Precisely, a detailed mathematical model of the process and a deterministic global optimization algorithm are applied to determine the optimal design and operating conditions for the system. The resulting model involves the real-physical constraints for the evaporation process. Nonlinear equations in terms of chemical-physical properties and design equations (efficiencies, Non-Allowance Equilibrium, Boiling Point Elevation, heat transfer coefficients, momentum balances, among others) are used to model the process. The model has been solved by using a deterministic global optimization algorithm previously developed by the authors [7] and implemented in a General Algebraic Modeling System GAMS [1]. The generalized reduced gradient algorithm CONOPT 2.041 [2] is used as NLP local solver. The model was successfully solved for different seawater conditions (salinity and temperature) and fresh water production levels. The influence of the production requirements on the process efficiency as well as the algorithms performance is presented.

Dual-purpose desalination plants. Part II. Optimal configuration

Abstract Large dual-purpose power desalination plants are used to reduce the production cost of both electricity and water. Various combinations of power-desalination systems are conceivable in order to satisfy both power and water demands. The preference of one scheme over another would depend mainly on many factors, such as the required power to water ratio, cost of fuel energy charged to the desalting process, electricity sales, capital costs, and local requirements. The allocation of the total annual cost of a dual-purpose plant to desalted water and electricity can be made by various methods. In this paper, credit method is adopted to calculate the total annual cost. Credit methods allocate a predetermined value to one of the products and determine the cost of the other product by subtraction from the total cost of the dual-purpose plant. In this way, according with the power credit method, the toal cost is calculated in the following way: Cwater=Ctotal − W; where W is the benefit of the net electrical generated. Non-linear equations are extensively used for the cost equipment and for the plant performance. The aim of this paper is to design a dual-purpose plant system at minimum cost determining the equipment configuration and its corresponding operating conditions given the water production. The optimal solution is selected from a superstructure containing different possible configurations. One case study illustrating the methodology, robustness and computational performance is presented.