Teaching mathematical modeling software for multiobjective optimization in chemical engineering courses

This paper expects to give undergraduate students some guidelines about how to incorporate environmental considerations in a chemical supply chain and how the introduction of these concerns have an important effect on the results obtained in the multiobjective optimization problem where both economic and environmental aspects are considered simultaneously. To extend the economic and environmental assessment outside the chemical plant and to identify the tradeoffs associated with the reality of chemical and petrochemical industries, a simplified problem of a chemical supply chain is proposed as a case study. The inclusion of environmental concerns to this economic problem make this new case study a good example for undergraduate students interested in implementing simultaneous economic and environmental considerations in the chemical process design incorporating mathematical modeling software for solving this multiobjective problem. Thus, the final objective of this paper is to show to undergraduate students how environmental together with economic considerations could have an important impact in the logistics of a supply chain and how multiobjective optimization could be used to make better decisions in the design of chemical processes including its supply chain. To reach our purpose, the Pareto curve of the supply chain is obtained using the ɛ-constraint method. In addition, the tradeoffs of this multiobjective optimization have been identified and analyzed and ultimately a good decision based on the set of ‘equivalent’ optimal solutions for this chemical supply chain problem determined.Spanish Ministry of Education and Science (CTQ2009-14420)

Rigorous Design of Complex Distillation Columns Using Process Simulators and the Particle Swarm Optimization Algorithm

We present a derivative-free optimization algorithm coupled with a chemical process simulator for the optimal design of individual and complex distillation processes using a rigorous tray-by-tray model. The proposed approach serves as an alternative tool to the various models based on nonlinear programming (NLP) or mixed-integer nonlinear programming (MINLP) . This is accomplished by combining the advantages of using a commercial process simulator (Aspen Hysys), including especially suited numerical methods developed for the convergence of distillation columns, with the benefits of the particle swarm optimization (PSO) metaheuristic algorithm, which does not require gradient information and has the ability to escape from local optima. Our method inherits the superstructure developed in Yeomans, H.; Grossmann, I. E.Optimal design of complex distillation columns using rigorous tray-by-tray disjunctive programming models. Ind. Eng. Chem. Res.2000, 39 (11), 4326–4335, in which the nonexisting trays are considered as simple bypasses of liquid and vapor flows. The implemented tool provides the optimal configuration of distillation column systems, which includes continuous and discrete variables, through the minimization of the total annual cost (TAC). The robustness and flexibility of the method is proven through the successful design and synthesis of three distillation systems of increasing complexity.The authors would like to acknowledge financial support from the Spanish “Ministerio de Ciencia e Innovación” (CTQ2009-14420-C02-02 and CTQ2012-37039-C02-02)

Optimal carbon dioxide and hydrogen utilization in carbon monoxide production

Carbon monoxide is the building block of many relevant chemical products. However, the relatively high emissions (1.396–2.322 kg CO2-eq/kg CO) of its synthesis and separation process result in high emitting derivatives. Therefore, reducing CO synthesis emissions is the first step towards more sustainable end products. In order to tackle this problem, we propose a carbon monoxide synthesis and purification superstructure. We perform multi-objective optimizations minimizing the cost and emission of the final CO product across several case scenarios. Results show that the minimum cost solutions are achieved using partial oxidation of methane (POX) as the syngas synthesis process and cryogenic distillation as the CO separation technology. Emissions can be decreased using dry methane reforming (DMR) and pressure swing adsorption (PSA) but costs increase dramatically. Optimal H2 utilization results in a reverse water gas shift (RWGS) reactor where CO2 is consumed to produce additional CO. Off-gas valorization is key to further reducing the synthesis cost and emissions.The authors gratefully acknowledge financial support to the Spanish «Ministerio de Economía, Industria y Competitividad» under project CTQ2016-77968-C3-2-P (AEI/FEDER, UE). The authors would also like to thank «Generalitat Valenciana: Conselleria de Educación, Investigación, Cultura y Deporte» for the Ph.D grant (ACIF/2016/ 062)

Integration of modular process simulators under the Generalized Disjunctive Programming framework for the structural flowsheet optimization

The optimization of chemical processes where the flowsheet topology is not kept fixed is a challenging discrete-continuous optimization problem. Usually, this task has been performed through equation based models. This approach presents several problems, as tedious and complicated component properties estimation or the handling of huge problems (with thousands of equations and variables). We propose a GDP approach as an alternative to the MINLP models coupled with a flowsheet program. The novelty of this approach relies on using a commercial modular process simulator where the superstructure is drawn directly on the graphical use interface of the simulator. This methodology takes advantage of modular process simulators (specially tailored numerical methods, reliability, and robustness) and the flexibility of the GDP formulation for the modeling and solution. The optimization tool proposed is successfully applied to the synthesis of a methanol plant where different alternatives are available for the streams, equipment and process conditions.Spanish Ministry of Science and Innovation (CTQ2012-37039-C02-02)

A new technique for recovering energy in thermally coupled distillation using vapor recompression cycles

Even though it has been proved that a fully thermally coupled distillation (TCD) system minimizes the energy used by a sequence of columns, it is well-known that vapor/liquid transfers between different sections produce an unavoidable excess of vapor (liquid) in some of them, increasing both the investment and operating costs. It is proposed here to take advantage of this situation by extracting the extra vapor/liquid and subjecting it to a direct/reverse vapor compression cycle. This new arrangement restores the optimal operating conditions of some of the affected sections with energy savings of around 20–30% compared with conventional TCD columns. Various examples, including the direct and reverse vapor recompression cycles, are presented. Furthermore, in each example, all possible modes of distillation (direct, indirect and Petlyuk distillation) with and without vapor recompression cycles (VRC) are compared to ensure that this approach delivers the best results.The authors would like to acknowledge financial support from the Spanish Ministerio de Ciencias e Innovación (PPQ, CTQ2009–14420-C02-02 and CTQ2012–37039-C02-02)

MILP models for objective reduction in multi-objective optimization: Error measurement considerations and non-redundancy ratio

A common approach in multi-objective optimization (MOO) consists of removing redundant objectives or reducing the set of objectives minimizing some metrics related with the loss of the dominance structure. In this paper, we comment some weakness related to the usual minimization of the maximum error (infinity norm or δ-error) and the convenience of using a norm 1 instead. Besides, a new model accounting for the minimum number of Pareto solutions that are lost when reducing objectives is provided, which helps to further describe the effects of the objective reduction in the system. A comparison of the performance of these algorithms and its usefulness in objective reduction against principal component analysis + Deb & Saxena's algorithm (Deb & Saxena Kumar, 2005) is provided, and the ability of combining it with a principal component analysis in order to reduce the dimensionality of a system is also studied and commented.The authors acknowledge financial support from the Spanish “Ministerio de Economía, Industria y Competitividad” (CTQ2016-77968-C3-2-P, AEI/FEDER, UE)

Water Distribution Networks Optimization Considering Uncertainties in the Demand Nodes

The fluctuation in the consumption of treated water is a situation that distribution networks gradually face. In times of greater demand, this consumption tends to suffer unnecessary impacts due to the lack of water. The uncertainty that occurs in water consumption can be mathematically modeled by a finite set of scenarios generated by a normal distribution and attributed to the network design. This study presents an optimization model to minimize network installation and operation costs under uncertainties in water demands. A Mixed Integer Nonlinear Programming model is proposed, considering the water flow directions in the pipes as unknown. A deterministic approach is used to solve the problem in three steps: First, the problem is solved with a nominal value for each uncertain parameter. In the second stage, the problem is solved for all scenarios, with the independent variables of the scenario being fixed and obtained from the solution reached in the first stage, known as the deterministic solution. Finally, all scenarios are solved without fixing any variable values, in a stochastic approach. Two case studies were used to test the applicability of the model and global optimization techniques were used to solve the problem. The results show that the stochastic solution can lead to optimal solutions for robust and flexible water distribution networks, capable of working under different conditions, considering the uncertainties of node demand and variable pipe directions.The authors gratefully acknowledge the financial support from the National Council for Scientific and Technological Development (Brazil), process 309026/2022-9

Integration of different models in the design of chemical processes: Application to the design of a power plant

With advances in the synthesis and design of chemical processes there is an increasing need for more complex mathematical models with which to screen the alternatives that constitute accurate and reliable process models. Despite the wide availability of sophisticated tools for simulation, optimization and synthesis of chemical processes, the user is frequently interested in using the ‘best available model’. However, in practice, these models are usually little more than a black box with a rigid input–output structure. In this paper we propose to tackle all these models using generalized disjunctive programming to capture the numerical characteristics of each model (in equation form, modular, noisy, etc.) and to deal with each of them according to their individual characteristics. The result is a hybrid modular–equation based approach that allows synthesizing complex processes using different models in a robust and reliable way. The capabilities of the proposed approach are discussed with a case study: the design of a utility system power plant that has been decomposed into its constitutive elements, each treated differently numerically. And finally, numerical results and conclusions are presented.Spanish Ministry of Science and Innovation (CTQ2012-37039-C02-02)

An alternative disjunctive optimization model for heat integration with variable temperatures

This paper presents an alternative model to deal with the problem of optimal energy consumption minimization of non-isothermal systems with variable inlet and outlet temperatures. The model is based on an implicit temperature ordering and the “transshipment model” proposed by Papoulias and Grossmann (1983). It is supplemented with a set of logical relationships related to the relative position of the inlet temperatures of process streams and the dynamic temperature intervals. In the extreme situation of fixed inlet and outlet temperatures, the model reduces to the “transshipment model”. Several examples with fixed and variable temperatures are presented to illustrate the model's performance.The authors gratefully acknowledge financial support from the Spanish “Ministerio de Ciencia e Innovación” under project CTQ2012-37039-C02-02

Design of a Cooperative Sustainable Three-Echelon Supply Chain under Uncertainty in CO2 Allowance

Driven by the growing concern regarding greenhouse gas emissions, in this work, we provide a robust stochastic model for the design of a cooperative supply chain (SC) under uncertainty in CO2 allowance prices from the European Union Emissions Trading System (EU ETS). During the last years, CO2 allowance prices have undergone unexpected changes, having strong impact on the design and management of optimal SC. The consideration of uncertainty in the allowance prices has therefore become more important. We use an autoregressive integrated moving average (ARIMA) model to predict future allowance prices. A full discretization of the underlying probability space leads to a number of scenarios far too large to be handled, so we compare two approaches to reduce the number of scenarios to a feasible maximum, the ScenRed algorithm and K-means clustering. The obtained results are compared with a deterministic approach that is widely studied in the literature, showing an increase in the benefits and a reduction of emissions.The authors gratefully acknowledge financial support to the Conselleria de Innovacion, Universidades, Ciencia y Sociedad Digital of the Generalitat Valenciana, Spain, under project PROMETEO/2020/064