A generalized disjunctive programming model for the optimal design of reverse electrodialysis process for salinity gradient-based power generation

Reverse electrodialysis (RED) is an emerging electro-membrane technology that generates electricity out of salinity differences between two solutions, a renewable source known as salinity gradient energy. Realizing full-scale RED would require more techno-economic and environmental assessments that consider full process design and operational decision space from the RED stack to the entire system. This work presents an optimization model formulated as a Generalized Disjunctive Programming (GDP) problem that incorporates a finite difference RED stack model from our research group to define the cost-optimal process design. The solution to the GDP problem provides the plant topology and the RED units´ working conditions that maximize the net present value of the RED process for given RED stack parameters and site-specific conditions. Our results show that, compared with simulation-based approaches, mathematical programming techniques are efficient and systematic to assist early-stage research and to extract optimal design and operation guidelines for large-scale RED implementation.This work was supported by the LIFE Programme of the European Union (LIFE19 ENV/ES/000143); the MCIN/AEI/10.13039/501100011033 and “European Union NextGenerationEU/PRTR” (PDC2021–120786-I00); and by the MCIN/AEI/10.13039/501100011033 and “ESF Investing in your future” (PRE2018–086454)

Alternate Approximation of Concave Cost Functions for Process Design and Supply Chain Optimization Problems

ABSTRACT. This short note presents an alternate approximation of concave cost functions used to reflect economies of scale in process design and supply chain optimization problems. To approximate the original concave function, we propose a logarithmic function that is exact and has bounded gradients at zero values in contrast to other approximation schemes. We illustrate the application and advantages of the proposed approximation. 1

Avanzando en la sostenibilidad del nexo agua-energía. Optimización de la recuperación de energía de gradientes salinos mediante electrodiálisis reversa

La energía del gradiente salino (EGS) es una fuente renovable abundante ampliamente desaprovechada para complementar y diversificar el mix energético actual, intensivo en emisiones y uso de agua, y apoyar la sostenibilidad y circularidad del, intensivo en energía, sector del agua. Esta tesis doctoral propone un marco metodológico para avanzar en el diseño óptimo en costes y medioambientalmente sostenible del proceso electrodiálisis reversa (EDR) en la recuperación de EGS de corrientes residuales del sector del agua. Este marco integra un modelo matemático del dispositivo EDR validado experimentalmente, una caracterización medioambiental mediante análisis de ciclo de vida, y un modelo de programación disyuntivo generalizado para la optimización de sistemas EDR a gran escala implementados en plantas desaladoras o estaciones depuradoras de aguas residuales. La herramienta de diseño propuesta puede ser de interés en del proceso de toma de decisiones que apoye la promoción y despliegue comercial de la EDR.Salinity gradient energy (SGE) is a vast yet largely untapped renewable source for complementing and diversifying the current carbon- and water-intensive energy mix and supporting the sustainability and circularity of the energy-intensive water sector. This doctoral thesis proposes a methodological framework for advancing the cost-optimal and environmentally sustainable design of reverse electrodialysis (RED) process for SGE recovery from waste streams in the water sector. This framework combines an experimentally validated mathematical model of the RED device, an environmental characterization through life cycle assessment, and a generalized disjunctive programming model to optimize large-scale RED systems deployed in desalination plants or wastewater treatment plants. The proposed design tool may be of interest in the decision-making process that supports the promotion and commercial deployment of RED technology.This research was financially supported through the R&D Projects CTM2017-87850-R and RTI2018-093310-B-I00 funded by the Spanish Ministry of Science and Innovation (MCIN/AEI/ 10.13039/501100011033) and by “ERDF A way of making Europe”, the R&D Project PDC2021-120786-I00 funded by the MCIN/AEI/10.13039/501100011033 and “European Union NextGenerationEU/PRTR, the R&D Project RM16-XX-046- SODERCAN/FEDER funded by SODERCAN, and the R&D Project LIFE19 ENV/ES/000143 funded by the LIFE Programme of the European Union. Carolina Tristán acknowledges the financial support from the research fellowship PRE2018-086454 funded by the Spanish Ministry of Science and Innovation (MCIN/AEI/ 10.13039/501100011033) and “ESF Investing in your future”