# (739e) Mathematical Optimization of Membrane-Free Desalination Systems That Utilize Low-Grade Heat

Authors:
University of Notre Dame
University of Notre Dame
University of Notre Dame
Mathematical Optimization of Membrane-free Desalination Systems that Utilize Low-grade Heat

Alejandro Garciadiego, Tengfei Luo, Alexander W. Dowling

Access to clean, fresh water is an ever-growing concern for modern society: water is critical to ensure human health, to protect threatened ecosystems, and to promote economic growth and prosperity. Modern seawater desalination technologies remain energy intensive; they required three to four times the theoretical minimum energy for separation[1]. This underscores the critical need for energy efficient and renewable driven desalination technologies to address these expanding needs for clean water.

Directional solvent extraction is a promising new desalination technology. It relies on liquid-liquid extraction with a thermoresponsive solvent that can be regenerated using low-grade heat. This approach has several unique features: (1) water can dissolve in the solvent, and the solubility is a function of temperature; (2) the solvent is virtually insoluble in water; (3) the solvent does not dissolve salts and 4) no membrane is required. Previous work includes initial concept demonstration as a batch process [2,3], molecular simulation to understand solvent performance [4], and heat integration for a single-stage continuous process [5].

In this work, we propose a mathematical optimization framework for the DSE process to explore trade-offs between product quality, energy requirements, and capital costs. This is done using an equation-oriented approach that simultaneously optimizes process operating conditions (such as temperatures, flow rates, compositions), design parameters (such as equipment sizes), and heat recovery opportunities [6,7]. The framework has the ultimate goal of systematically guiding molecular discovery of new thermoresponsive solvents. Results show that with the use of high-efficiency heat recovery DSE could be a competitive renewable membrane-free desalination technology.

Next, we consider sensitivity analysis and equipment costing to set physical property targets. We find two property targets are most important for DSE: i) the thermoresponsiveness of the solvent, i.e., the change in water solubility for a unit change in temperature, and ii) the solvent solubility in water.

Increasing the thermoresponsive from 0.0044 mol/mol / °C to 0.0022 mol/mol / °C decreases recycle ratio by from 80.2 kmole/s to 4 kmole/s. This decreases the heat and electricity costs from \$2.20 per m3 of fresh water to \$0.21 per m3 of fresh water, and equipment sizes by 400%. Lowering solubility of solvent in water decreases the solvent loss in the system and the costs associated with this. For decanoic acid, we calculate \$3.30 per m3 of fresh water. Results also show that by doubling thermoresponsive ability and reducing the solubility of solvent in water by a factor of ten, can make DSE economical competitive with modern seawater desalination technologies. As ongoing work, we are exploring the viability of alternative classes of solvents, such as ionic liquids.

References:

[1] M. Elimelech, W. A. Philip (2011). The Future of Seawater Desalination: Energy, Technology, and the Environment. Science 333 (6043), pp. 712-717.

[2] A. Bajpayee, T. Luo, A. Muto, G. Chen (2011). Very low temperature membrane-free desalination by directional solvent extraction. Energy Environ. Sci. 4, pp. 1672â€“1675.

[3] D. Rish, S. Luo, B. Kurtz, T. Luo (2014). Exceptional ion rejection ability of directional solvent for non-membrane desalination. Appl. Phys. Lett. 104 (2), p. 024102.

[4] T. Luo, A. Bajpayee, G. Chen (2011). Directional solvent for membrane-free water desalinationâ€”A molecular level study. J Appl. Physics., 110 (5), p. 054905.
[5] S. Alotaibi, O. M. Ibrahim, S. Luo, T. Luo (2017). Modeling of a continuous water desalination process using directional solvent extraction. Desalination 420, pp. 114-124.

[6] A.W. Dowling, L. T. Biegler (2015). A Framework for Efficient Large Scale Equation-Oriented Flowsheet Optimization. Comp. Chem. Eng. 72, pp. 3-20.

[7] A. W. Dowling, L. T. Biegler (2013). Optimization-based process synthesis for sustainable power generation. Chem. Eng. Trans. 35, pp. 1-12.

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