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)

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)

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)

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

Multi-objective optimization of combined synthesis gas reforming technologies

Synthesis gas (syngas) is a mixture of H2, CO and occasionally CO2, whose main application is as a building block of chemical compounds. The desired product dictates the syngas characteristics, which are also affected by the employed syngas synthesis technology. In this work, we study the process of producing syngas under desired specifications while consuming CO2 in the synthesis. We propose a superstructure that includes seven reforming technologies for the syngas production, as well as a variety of auxiliary units to control the final composition of the syngas. Each potential solution is assessed, in terms of the economic and environmental performance, by the Total Annualized Cost (TAC) and the Global Warming Potential (GWP) indicator. As the problem statement involves discrete decision, we use disjunctions to model the system. The resulting MINLP multi-objective problem is solved by the epsilon constraint method. Results show that at low syngas H2/CO ratios and pressures, dry methane reforming (DMR) is capable of net consuming CO2. Partial Oxidation (POX) is the technology that exhibits the minimum TAC, although shows the maximum value for the GWP. Synergistic combination of two processes allows reducing the cost and CO2-equivalent emissions through the pairing of DMR and bi-reforming (BR) and BR with steam methane reforming (SMR). Furthermore, increasing the CO2 content in the syngas at a fixed (H2 − CO2)/(CO + CO2) ratio proves that TAC and GWP decrease as the CO2/CO ratio increases.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)

Water Management in Shale Gas: A Perspective from the Cooperative Games Theory

This project has received funding from the European Union's Horizon 2020 Research and Innovation Program under grant agreement No. 640979

Guidelines for the design of efficient sono-microreactors

Possible drawbacks of microreactors are inefficient reactant mixing and the clogging of microchannels when solid-forming reactions are carried out or solid (catalysts) suspensions are used. Ultrasonic irradiation has been successfully implemented for solving these problems in microreactor configurations ranging from capillaries immersed in ultrasonic baths to devices with miniaturized piezoelectric transducers. Moving forward in process intensification and sustainable development, the acoustic energy implementation requires a strategy to optimize the microreactor from an ultrasound viewpoint during its design. In this work, we present a simple analytical model that can be used as a guide to achieving a proper acoustic design of stacked microreactors. An example of this methodology was demonstrated through finite element analysis and it was compared with an experimental study found in the literature.This research is funded by the EU project MAPSYN: Microwave, Acoustic and Plasma SYNtheses, under grant agreement No. CP-IP 309376 of the European Union Seventh Framework Program