A mixed-integer nonlinear programming (MINLP) formulation for the molecular design optimization of ionic liquids (ILs) to recuperate ethanol with a purity of 99 mol % or greater from a E85 system (a mixture containing 85 and 15 mol % of ethanol and water, respectively) is presented. The reason why the ethanol/water separation is difficult is because of the azeotropic behavior of this system. Therefore, the IL is designed to feature water affinity such that it can break the ethanol/water azeotrope, allowing the high-purity separation to take place. The MINLP formulation is based on the development of a superstructure that contains a set of cations and anions, whose combination forms different kinds of ILs that have the potential to separate azeotropic systems such as the ethanol/water system. Because most of the ILs to be optimally designed are novel solvents, their physical and thermodynamic properties are estimated by group contribution methods. The optimization formulation is composed of a set of constraints featuring vapor-liquid equilibrium conditions as well as constraints dealing with structural and allowed cation-anion combinations. We assume that the separation will take place at atmospheric pressure. For the sake of simplicity, the optimal IL is first synthesized in a single separation stage, although the separation was also addressed using a reboiled absorption column. The results indicate that the optimally designed IL is capable of performing the required separation meeting the high-purity ethanol constraint.

In this work, we address the optimal economical synthesis of an extractive distillation column for bioethanol purification, using ionic liquids as a type of solvent that can be designed to feature sustainable characteristics, such as low toxicity and low volatility, among other desirable properties. For the optimal synthesis of the separation scheme, we propose a mixed-integer nonlinear programming (MINLP) formulation, merged with disjunctive programming tools, to take care of modeling logical decisions [Yeomans and Grossmann, Ind. Eng. Chem. Res. 2000, 39, 1637−1648]. In a previous work [Chavez-Islas et al., submitted to Ind. Eng. Chem. Res.], we have addressed the design of a novel ionic liquid to separate the ethanol/water azeotropic system, up to high purities. The MINLP synthesis of the distillation column considers the feed tray location, the number of trays, and the operating and design parameters as decision variables. Because the ionic liquid used in this work is a novel solvent, its physical and thermodynamic properties are yet not available. Therefore, the physical properties of the ionic liquid are estimated using group contribution methods. The MINLP formulation is based on the application of the MESH equations for conditional trays, to reduce the size of the nonlinear subproblems and increase the robustness of the optimization formulation. The MINLP problem was solved using the SBB solver embedded in GAMS. Using the proposed MINLP formulation, we attained ethanol purities as good as 99.9 mol %, and 90% of the ethanol presented in the feed stream was recovered.

Optimization of an ammonia-water absorption refrigeration system, minimizing operating and annualized capital costs, is described. A mixed-integer nonlinear programming (MINLP) model, with the inclusion of discontinuous functions for capital costs for the main components of the system, is presented. The minimum total annualized cost is achieved with the simultaneous optimization of seven design variables. Practical limits of the design variables are established for the purpose of generating design parameters in accordance with the type of system studied. The model is applied to two examples. The analysis considers two types of heat rejection media: cooling water and air. The results obtained indicate that the selection of cooling medium is dependent on the refrigeration level that is required. The optimum configuration and operating conditions do not correspond to the best process integration and the coefficients of performance, and irreversibilities are high. The design variables with the highest impact on the objective function are dependent on the heat rejection medium characteristics and the process requirements. A sensitivity analysis of the effects of the evaluation criteria on the minimization of operating and capital costs is presented.

An equation-oriented model for the design of a simple ammonia/water absorption refrigeration cycle is presented, which due to the nature of the working mixture, includes high-quality thermodynamic and thermophysical property models. There are four versions of the model, depending on heat rejection media and distillation column feed conditions. Solution of the model requires the given variables and designer competence-based variables. The column equilibrium stages, diameter, and height use binary decision variables. The solution of the equation set was developed with a General Algebraic Modeling System (GAMS) general purpose nonlinear solver. An equation solution strategy is described. Once solved, exergy balances are made and irreversibilities and exergy efficiency are calculated globally and for each unit operation. Two examples are compared. The great number of factors that can be varied in the absorption refrigeration system makes manual optimization of an industrial design a formidable task. However, good design makes a decisive difference in regard to the use of waste heat absorption refrigeration. The model forms the basis for the simultaneous optimization of design variables with an appropriate objective function.

Optimization of the operating conditions and process scheme of an ammonia−water absorption refrigeration system, minimizing operating and annualized capital costs, is described. Various heat-exchanger technologies, the effect of the evaporator purge, and the thermodynamic restrictions of the system are taken into account. The objective is to make optimum use of various heat-exchange technologies to reduce the capital cost and meet the process refrigeration service requirements. A procedure to take account of the film coefficients and pressure drops of the different types of heat exchangers considered is proposed, which gives a solid basis for making decisions regarding the use of industrial ammonia−water absorption refrigeration.