Molecular design targets and optimization of low-temperature thermal desalination systems

Directional solvent extraction (DSE) is an emerging membrane-free liquid-liquid extraction process to desalinate water using low-grade heat. Several unique features make DSE a potentially disruptive desalination technology: 1) it is thermally driven and utilizes low-grade heat; 2) it does not require the use of membranes; 3) there are opportunities to intensify, modularize and customize the process; 4) there is a vast solvent molecular design space. This work establishes a technoeconomic modeling framework to simultaneous optimize and heat integrate the DSE process. We perform rapid bottom-up screening to predict the energy intensity levelized cost of water (LCOW) of organic acid and ionic liquid directional solvents (DS) in an optimized DSE process. Likewise, we perform top-down analysis to set continuous solvent property targets necessary to realize a LCOW of less than $0.5/m 3 . LCOW is most sensitive to the solubility of the DS in water and thermoresponsive ability (a.k.a. yield) of the solvent, i.e., the change in the solubility of water in the DS with temperature. Despite their lower cost, organic acids have a small thermoresponsive ability and LCOW of at least $1.3/m 3 . In contrast, we set modest quantitative thermophysical property targets for ionic liquid DS to achieve below $0.5/m 3 LCOW.

thermally driven and utilizes low-grade heat; 2) it does not require the use of membranes; 3) there are opportunities to intensify, modularize and customize the process; 4) there is a vast solvent molecular design space.This work establishes a technoeconomic modeling framework to simultaneous optimize and heat integrate the DSE process.We perform rapid bottom-up screening to predict the energy intensity levelized cost of water (LCOW) of organic acid and ionic liquid directional solvents (DS) in an optimized DSE process.Likewise, we perform top-down analysis to set continuous solvent property targets necessary to realize a LCOW of less than $0.5/m 3 .LCOW is most sensitive to the solubility of the DS in water and thermoresponsive ability (a.k.a.yield) of the solvent, i.e., the change in the solubility of water in the DS with temperature.Despite their lower cost, organic acids have a small thermoresponsive ability and LCOW of at least $1.3/m 3 .In contrast, we set modest quantitative thermophysical property targets for ionic liquid DS to achieve below $0.5/m 3 LCOW.
• Directional solvent extraction (DSE) is a potentially transformative lowgrade heat renewable desalination technology • Created a technoeconomic optimization framework for DSE with embedded heat integration and identified the most important solvent thermo-5 physical properties • Determined fatty acid directional solvents are unable to meet $0.50/m 3 levelized cost of water (LCOW) goal due to inadequate solvent thermophysical properties • Set quantitative solvent thermophysical property targets for ionic liquid 10 directional solvents to achieve less than $0.50/m 3 LCOW goal

Introduction
Water consumption is critical to modern society; the average American family uses approximation 1140 liters of municipal water per day [1], and 130 million Americans face severe water scarcity at least part of the year [2].Globally, 3.8 billion people currently experience water scarcity [3], and it is estimated that 66% of the world's population could be living under water-stressed conditions by 2025 [4].Although the costs of water obtained from desalination have fallen in the last decade, they are higher than obtaining freshwater from rivers, groundwater, or water recycling.In 2015, less than one percent of the water consumed globally was produced by desalination [5].
The expansion of oil and gas extraction in the US has created new water and environmental challenges [1].In 2012, 3.57 billion m 3 of produced water was extracted in the US.In the Delaware Basin, up to 4 barrels of water are produced per barrel of oil [6]; to put this number in perspective, around 0.50 liters of produced water may be generated to supply energy for one hour in an average American household.The salinity of produced water is typically 35,000 ppm to 300,000 ppm, which may be up to eight times higher than seawater salinity (35,000 ppm) [7].Unfortunately, current desalination technologies are unpractical to treat such high salinity brines [8].Large water volumes (about 20,000 m 3 on average per well) from oil and gas production also remain challenging, even after water supply chain optimization.[9,10].There is a pressing need and opportunity for new technologies to treat produced water.
There is no one-size-fits-all technology for water treatment.Instead, there is a growing emphasis on fit-for-purpose treatment in decentralized networks [12].
In this paradigm, water is treated to only the specifications needed for specific end uses.Table 1 highlights different water quality levels (salinity), appropriate end uses, and candidate desalination technologies.While evaporative and reverse osmosis desalination technologies are commonly deployed, they remain energy-intensive and unable to treat high salinity water sources.In the context of fit-for-purpose water, there is a great need for new technologies to treat a wide range of water quality levels in distributed networks while using renewable energy.
Directional solvent extraction (DSE) uses a thermoresponsive solvent to facilitate treatment over a wide salinity range [13].DSE does not require membranes, which often foul at high salinities, and can utilize low-grade heat, including waste or renewable (solar) sources.Prior work in DSE includes characterization of molecular phenomena, bench-scale demonstrations, and limited process analysis [14,15,13,16,17,18].This paper presents a techno-economic optimization framework with two new capabilities: first, we perform simultaneous process optimization and heat integration to rapidly screen directional solvent candidates in seconds.Second, we perform a sensitivity analysis to identify the necessary solvent properties to enable cost-effective DSE processes for a specific application.We emphasize these advances in process-scale models can rapidly accelerate DSE development by reducing the need for expensive experiments and guiding (computational) molecular design.To our knowledge, this is the first application of equation-oriented process optimization to facilitate bottom-up and top-down analysis of the DSE process.
The remainder of this paper is organized as follows.Section 2 reviews literature on desalination and DSE, with an emphasis on the scope for optimization.
Section 3 describes the optimization framework and mathematical models.Section 4 studies the impact of heat source temperature and solvent properties on the optimized process's minimum specific energy.Section 5 presents quantitative solvent property goals to achieve $0.50/m 3 LCOW target for two classes of molecules: carboxylic acids and ionic liquids.Finally, Section 6 summarizes conclusions, limitations, and future work.

Desalinaton technologies
Modern desalination technologies, including evaporative and reverse osmosis systems, are energy-intensive and not suitable to treat high salinity water.
Evaporative systems such as multi-stage flash (MSF) and multi-effect distillation (MED) utilize thermal energy (typically 90 • C and 55 • C, respectively) to evaporate and condensate water [7].These systems require highly corrosion-resistant and costly materials [19] and are heat-intensive (26.29-83.06kWh/m 3 ); they require three or four times the theoretical minimum energy of separation [8,7].
In contrast, membrane-based technologies such as reverse osmosis (RO) use mechanical work to overcome the osmotic pressure across a membrane.Membranebased technologies use significant electricity inputs, need frequent membrane replacement, and have limited effectiveness when treating concentrated brines [8].
New technologies, including electrodialysis and forward osmosis, show promise to reduce energy consumption and lower costs.For example, osmotically assisted reverse osmosis (OARO) and mechanical vapor compression (MVC) are suitable to treat high salinity brines (140,000 ppm and 150,000 ppm respectively) [20,21,22].Nevertheless, MVC energy consumption is high (singleeffect MVC 2342kWh/m 3 , double-effect MVC 20kWh/m 3 ) [22].OARO, RO, and other membrane-based technologies are often susceptible to membrane fouling at high salt concentrations [23].While hybrid desalination systems paired with renewable energy sources are well-studied [24,25,26], there is limited work of technologies suitable for high salinity brines.Amines [27] and alcohols [28] were explored over fifty years ago as the first directional solvents for desalination.These solvents can only treat low salinity water (5000 ppm) and have a high solubility in water, leading to high solvent losses [29].In the 1990s, The Puraq Company proposed a liquid polymers-based [30,31] directional solvent, which was commercially unsuccessful due to elevated solvent production costs [32], although recent work by Thanaplan et al. [33] reexamines the energetics of the Puraq Company's process.Recently, However, the chain end is hydrophilic, which helps ensure the solubility of the acids in water is negligible (30 -150 ppm) [15].In recent work, Guo et al. [34] proposed the use of ionic liquids, which have a greater thermoresponsivness ability compared to fatty acids.In this work, we will assess the technoeconomic 120 potential of fatty acid and ionic liquid directional solvents in the context of an optimized DSE process.amount of directional solvent dissolves in the freshwater and is lost (stream 6).Thus a small directional solvent make-up feed is added to the system (stream 12) to ensure steady-state operation.

Effectively utilize low-grade heat and no/limited membrane costs
Luo and co-workers [14,15,13,16,17,18] recently demonstrated octanoic and decanoic acid can efficiently desalinate water.Specifically, they experimen-125 tally observed the solubility of water in decanoic acid changes from 3.8 wt% at 34 • C to 5.9% at 80 • C, with negligible solubility of fatty acid in water [16].
This thermoresponsive characteristic of the directional solvent enables thermal regeneration and is essential to the DSE process.Luo and co-workers then demonstrated the DSE concept in a continuous bench-scale process, success-130 fully extracting 2.5 gallons of freshwater per day from a 700 ppm to 1100 ppm salinity feed (0.07-0.11 wt%) utilizing octanoic acid [16].Based on these experi-ments, they estimated a total energy consumption of 184 kWh/m 3 for decanoic acid and 101 kWh/m 3 for octanoic acid, assuming heat integration with 90% heat exchanger efficiency [16].

Demonstrated performance for higher salinities
Bajpayee et al. [14] demonstrated the effectiveness of octanoic acid to treat salty brines from 3,667 ppm to 58,333 ppm TDS (total dissolved solids).Likewise, they successfully treated saturated brines show water extraction with DSE of brine with 290,000 ppm (NaCl) [14].These results are promising for DSE to treat produced water with high TDS from oil and gas extraction (up to 460,000 ppm).

Scope for molecular-to-systems optimization
There are vast unexplored opportunities to optimize DSE across molecular and process scales.Existing fatty solvents require ≈90 m 3 of recycle per 1 m 3 of freshwater, which makes the processes remain energy-intensive.Alotaibi et al. [16] performed heat integration for a single-stage continuous process for DSE utilizing octanoic and decanoic acids using flowrates obtained from bench-scale experiments [16].Their analysis used the transshipment heat integration model, which assumes fixed flowrates and temperatures [35].While insightful, this analysis technique often overlooks opportunities to reduce energy intensity that are only realizable by simultaneously optimizing process conditions (flowrates, temperatures, compositions) and performing heat integration [36].In this work, we show the benefits of more extensive process optimization.At the molecular scale, Guo et al. [34] recently measured the thermophysical properties of a handful of ionic liquids as candidate directional solvents.However, there are well over a billion candidate solvents to consider.In this work, we use rigorous process modeling and optimization to set quantitative solvent thermophysical property targets as a means to narrow the vast molecular design space.

Methods: technoeconomic optimization framework
As a first step to realize molecular-to-system optimization of the DSE platform, we propose a computational framework for bottom-up rapid screening of candidate solvent and top-down identification of continuous solvent properties.
In this section, we fully define the mathematical models and computational implementation.

Problem statement
Given inlet water salinity (e.g., 35,000 ppm NaCl), water rejection ratio (e.g., 50% water rejection rate), physical properties of the directional solvent, and a maximum temperature of the heat input, manipulate the temperature and material flows in the DSE process (streams in Figure 1) to minimize the specific energy of the problem.We formulate this as a nonlinear optimization problem (M1): min Specific Thermal Energy s.t.Unit Operation Models Table 3 Embedded Heat Integration Eq. ( 4)-( 10 ables.Using the Julia [37] and JuMP [38] computational environment, we can efficiently solve (M1) using IPOPT solver [39] and HSL (MA27) [40] in approximately 0.2 seconds after thoughtful initialization.The remainder of this section describes all of the mathematical equations and input data used in (M1).

Unit Operation Models
The DSE process is a collection of tanks, heat exchangers, splitters, and mixers, as shown in Figure 1, connected by thirteen streams contained in set S. Variables flowrate F and temperature T are indexed by set S. The mole fraction variable is indexed by the set of streams (S) and the set of components (C) which includes the directional solvent, water, and salt.Mass and energy balances and liquid-liquid equilibria equations, which as shown in Table 3, are used to relate these variables for inlet and outlet streams.We assume the entire process operates at a steady-state and there are no chemical reactions.
Table 3: Each unit operation is modeled as a collection of equations that relate the inlet and outlet streams.The following variables are indexed over the set of streams S: the molar flow F (kmol/s), the temperature T (K), and the heat capacity Cp (J/mol-K).The molar fractions x are indexed over both S and the components C which include the solvent, water, and salt.

Liquid-liquid phase separation
The DSE process relies on temperature varying solubility of water in the directional solvent.Unfortunately, temperature-dependent ternary phase data for water, solvent, and salt are not available in the literature.For preliminary process analysis, we assume the solubility of water in the solvent is linearly 200 dependent on temperature shown in Eq. ( 1).We fit A and B via regression analysis using experimental data for the mixture decanoic acid, water, and salt from Bajpayee et al. [14] and Oliveira et al. [41] for the mixture decanoic acid and water.Figure 2 shows this simple model fits the data well.Fitted parameters are reported in Table 4.We assume the direction solvent has a fixed solubility 205 in the aqueous phase, denoted κ d .Values are given in Table 5.Likewise, we assume salt has a fixed solubility of κ s = 65 ppm (0.0199 mol/mol) in the solvent phase.

Single-phase heat exchanger
The heat duty in the heat exchanger is , where C p is the heat capacity, F in is the flowrate, and T out − T in is the temperature difference.We calculate C pi for the organic solvent i with the capacity group contribution method [43]: Eq. ( 2) captures the influence of N k times of functional group k appears in the organic component i.For water we use coefficients given in Table 7[43]: and for the ionic liquid, we use coefficients given in Table 7 and Eqs. ( 4) [44]. 210 We then calculate the C p of each stream (mixtures) using the the component heat capacities C pi and the mole fractions x i : The heat capacity of NaCl is considered constant with a value of 15.058 J/mol-K [43].Coefficients for Eqs. ( 2)-( 4) are given in Tables 6 and 7. We embed the Duran-Grossman heat integration equations [45] directly into the process optimization problem.This allows us to simultaneously optimize the  4) [44].process operating conditions (flowrates, compositions, temperatures) while minimizing the thermal energy input per unit of freshwater product.In contrast, Alotaibi et al. [16] only perform heat integration for a fixed process operat-220 ing conditions.We emphasize our approach is superior because it optimizes more degrees of freedom.The optimizer manipulates flowrates, compositions, and temperatures to balance complex interdependencies between temperaturedependent phase equilibria and the pinch point which limits heat integration.
For completeness, we now summarize the heat integration model.

225
Each single-phase heat exchanger half is designated as a hot stream (requires cooling) or a cold stream (requires heating), denoted with sets S H and S C , respectively.We then consider the inlet of each heat exchanger as a pinch candidate temperature T p and add the minimum driving force ∆T min to the cold stream temperatures: We use the set P = S C ∪ S H to denote all pinch candidate temperatures.
For each pinch candidate p ∈ P, we calculate the heat content above pinch temperature T p : Similarly, we calculate the heat content below pinch temperature T p : The minimum hot utility duty Q S must be larger than the difference between the heat contents below and above each pinch candidate.
Finally, we use an energy balance to calculate the minimum cold utility duty To ensure optimization problem is differentiable, we use a smoothed approximation for the max operator: This model is effective because the combinatorial search for the pinch candidate is cast as inequality constraint Eq. ( 9), which is efficiently handled in equation oriented process optimization.

Cost model
After solving (M1), we estimate equipment and operating costs and then 230 calculate the price per unit of freshwater production.
The heat integration model described above only computes the minimum hot and cold utilities when solving (M1).As a post-processing step, we perform sequential optimization to design the heat exchanger network.We first solve a mixed integer linear program to predict matches to minimize the number of heat exchangers.We then solve a nonlinear program to calculate the heat exchanger areas.[35,36].Finally, we use Guthrie's Method [36] to calculate the equipment costs.We use the present cost index of December 2018 (613.6) and a straight-line depreciation: Here, ADE is the Annual Depreciation Expense, CotA is the cost of the assets, SV is the salvage value after the useful life of the plant (20% of the cost of the assets), and U LA is the estimated useful life of the plant.We assume a cost of electricity of 0.05 $/kWh (average price of Texas, Oklahoma, Lousiana, New Mexico, Georgia, and Utah) [46].We assume a 2 psi pressure drop every 100 feet, and the heigh of the tanks is calculated for every process solution for pumping electricity.We assume a cost of heating utilities of 2.778 $/GJ from waste heat, a similar cost to solid waste, coal, or nuclear energy [47].We assume the system has a useful life of 20 years for cost calculations, and we selected stainless steel for the material of the equipment because the plant handles saline brines and freshwater.The cost of decanoic acid is set to 12 $/kg [48].

Results: Bottom-up Process Optimization
We now solve the optimization problem (M1) in several bottom-up case studies to predict the best possible performance of candidate directional solvents in a fully optimization process.We first compare our optimized reference design with Alotaibi et al. [16].Then, we perform a sensitivity analysis to quantify the impact of ∆T min (heat exchanger size) and the maximum temperature (heat source quality).Finally, we compare candidate organic acid solvents.

Reference Design for Decanoic Acid Directional Solvent
We set the temperature bounds between 34 • C and 80 • C, specify a 50% reject ratio, and set ∆T min = 6 • C1 to match Altoabi et al. [16].Results from solving (M1) are shown in Tables 8, 9, 10 and Figure 3. From the results, we draw these observations: Observation A1.A considerable portion of the decanoic acid (128 ppm) is solubilized in the outlet of freshwater and salty brine.We calculate that, at steady-state, the process requires 10 −4 kmol/s of make-up directional solvent.We emphasize this make-up was not considered by Alotaibi et al. [16], who based their process analysis on pseudo-steady-state experimental data.
Observation A2.Our approach finds the same pinch point, 50    Table 11: LCOW for three different directional solvents without consifering solvent recovery.
Costs of thermal energy, pumping electricity and equipment are lower using ionic liquid.
However the cost of the solvent make-up increases considerably.12 gives the stream information for a single design from the sensitivity analysis From these results, we observe: Observation B1.We find consistent trends with both sets of solubility data.Bajpayee et al. data [15] showed 2.6% more solubility of water in the solvent phase, which leads to 2 times lower energy-intensive process as the process needs fewer extractions per pass.The difference between the solubilities is because Oliveira et al.only considered binary water-acid mixtures.
Observation B2.As expected, higher maximum temperatures en- This suggests that manipulating the solvent chemistry to increase the per pass extraction at a lower temperature will decrease the energy intensity.
Observation B3.The specific energy difference between temperature ≤80 • C and ≤90 • C is negligible.This is because increasing the pass per extraction increases the fraction of water in the solvent-water emulsion, which decreases the C p of the mixture.As the amount of heat required to heat the mixture decreases at a higher maximum allowable temperature, so does the specific energy of the process.This result emphasizes little benefit for heat sources greater than 80 • C for off-the-shelf organic acid solvents.
Observation B4.Heat exchangers with a temperature difference of less than 3 • C are likely required to achieve less than 50kWh t /m 3 and 4 • C to achieve less than 100kWh t /m 3 utilizing decanoic acid as a solvent.The heat exchangers would need to have an effectiveness of approximately 96% or higher to achieve the 50kWh t /m 3 goal utilizing decanoic acid.
Observation B5.We observe the IL the solvent [emim][Tf 2 N] can achieve 50 kWh t /m 3 using maximum allowable temperature of 65 • C and ∆T min 310 of 6 • C. Our analysis shows that, from an energetics perspective, ILs are a more promising class of directional solvents.

Sensitivity Analysis: Length of the Chain of Carboxylic Acids
We now rapidly screen five carboxylic acids as directional solvents.We solve (M1) using acid-water mixture data for Oliveira et al. [41].We set the amount of acid dissolved in the aqueous phase as the solubility of the fatty acid at 20 • C, shown in Table 5.The minimum temperature for the process is set as the larger of the melting temperature of the acid or 25 • C at ambient temperature.The 120 instances of (M1) shown in Figure 6 were solved in approximately 25 seconds total.From the results, we observe: Observation C1.In Figure 2, we see there is not a clear relationship between the solubility of water in organic acid and the length of the carbon chain.However, we find the slope B, i.e., the thermoresponsiveness of solubility, is most influential on specific energy.5 for specific quantities of solvent loss.

Results: Top-Down Solvent Property Targets
Based on the bottom-up analysis in Section 5, we conclude that known carboxylic acids are not an economical solution for directional solvent extraction.
Although [emim][Tf 2 N] is, from an energetic perspective, a more promising directional solvent, limited data for IL-water-salt mixtures prevents bottom-up screening of more candidate IL solvents.
In this section, we generalize the optimization problem (M1) to consider hypothetical directional solvent molecule parameterized by three continuous properties: solubilities in the aqueous and solvent phases and cost of the solvent.
Thus we perturb four parameters in the technoeconomic analysis: A, B, solvent cost, and κ d .We then perform top-down sensitivity analysis to identify idealized directional solvent property targets to add in molecular discovery.
These continuous are a precursor to discrete molecular optimization [49].

Top-Down Analysis: Carboxylic Acids
We start by performing a sensitivity analysis for hypothetical carboxylic acid solvents over a grid for three properties: 1) the thermoresponsiveness of the solubility of the solvent (B), 2) the amount of water that solubilizes in the solvent at a reference temperature (A), and 3) the amount of solvent dissolved in the freshwater at the outlet of the DSE process (κ d ).Each candidate set of properties is first checked to ensure the solubility correlation Eq. ( 1) predicts a valid mole fraction between 0 and 1 at the process temperature bounds (T min and T max ): We found Eq. ( 13) is extremely effective at predicting if (M1) will be infeasible.
For each set of properties that satisfy Eq. ( 13), we solve (M1) to compute flowrates and temperatures that minimize specific energy.For each solution of (M1), we estimate LCOW for a few solvent costs.From the results shown in Figure 7, we conclude: Observation D1.For a directional solvent similar to a fatty acid, increasing thermoresponsive ability (B) and decreasing solubility of the solvent in water (κ d ) would cause the greatest reduction in LCOW.Likewise, increasing solubility of water in the solvent at a reference temperature (B) also reduces the recycle ratio by decreasing the amount of solvent needed for water to dissolve.
We calculate LCOW of $3.30/m 3 and $4.13/m 3 for decanoic and octanoic acids, respectively.Even though energy contribution to LCOW is lower from octanoic acid ($1.62/m 3 versus $2.20/m 3 ), the overall LCOW is larger because the higher solubility of the solvent κ d is larger (128 ppm for decanoic acid versus 300 ppm for octanoic acid), which causes larger solvent make-up costs ($1.03/m 3 of freshwater for decanoic acid versus $2.48/m 3 of freshwater for octanoic acid).
Observation D2.However, at the current price of the ionic liquid, the solvent loss (κ d ) is critical.Observation E2.Assuming a 90% cost reduction, the thermoresponsivness would need to be increased 1.5 times or the solubility of water 1.25 times.However, the solvent's solubility in water would need to be reduced by a ten-fold, as shown in Figure 8.
Observation E4.For a cost of [emim][Tf 2 N] of $10/kg, the solvent solubility in water would have to be 10 times lower, and the goal of $0.50/m 3 of freshwater would be achieved.However, it would still be possible to reach the target goal by increasing 1.2 the solubility of water in the solvent or increasing 1.5 the thermoresponsiveness.
2 IL recovery from the freshwater stream is achievable with off-the-shelf filtration systems.
Post-treatment for the brine reject is much more challenging due to concerns of membrane fouling.Full costing of the freshwater post-treatment system is beyond the scope of this work.Instead, we neglect capital costs and energy usage.As such, the property targets are optimistic but informative.inexpensive solar heating for sustainable and distributed desalination.

Figure 1 :
Figure 1: Illustration of the basic directional solvent extraction (DSE) process.Seawater (stream 1) is heated to the maximum allowable temperature (80 • C is shown) in the process and mixed with the directional solvent (stream 8).The mixed emulsion of water and directional solvent (stream 9) settles in the warm settling tank.Water dissolves in the directional solvent, and concentrated brine (stream 4) is extracted from the mixture by gravity.The directional solvent and dissolved water (stream 3) are then cooled down.Freshwater is expelled from the mixture and decanted (stream 6).Decanoic acid is reheated and recycled (stream 8).A small The sets I ⊂ S and O ⊂ S are the inlet and outlet streams of each unit operation.For simplicity, the index in or out is used if there is only one inlet or outlet, respectively.The settling tank outlets have indices o 1 and o 2 for the aqueous and solvent phases, respectively, such that {o 1 , o 2 } = O.We assume salt has a fixed solubility of κs (mole fraction) in the solvent phase and the directional solvent has a fixed solubility of κ d (mole fraction) in the aqueous phase.Equation Tanks Isothermal mixer Single phase heat exchanger Overall mass balance Fin =  j∈O Fj  i∈I Fi = Fout Fin = Fout Overall component balance Finxin,c =  j∈O Fjxj,c ∀c ∈ C  i∈I Fixi,c = Foutxout,c ∀c ∈ C xin,c = xout,c ∀c ∈ C Chemical equilibrium Water: xo 1 ,w = A + BTo 1 Salt: xo 1 ,s = κs Directional Solvent: xo 2 ,d = κd Summation equation  c∈C (xo 1 ,c − xo 2 ,c) = 0 Energy Balance Tin = To 1 = To 2 Ti = Tout ∀i ∈ I Q = CpFin(Tout − Tin)

Figure 2 :
Figure 2: We perform linear regression on solubility to calculate the temperature swing (thermoresponsiveness) of the solubility of water in the carboxylic acid (solvent phase) using two sets of experimental data.Bajpayee et al. [14] provides data for ternary mixtures C 8 and C 10 fatty acids, water, and salt.Oliveira et al. [41] provides data for binary mixtures of C 6 to C 10 fatty acids and water.

Figure 3 :
Figure 3: Composite curves for the reference design, including utilities.Most of the heat exchange is done in HX2 and HX3, which have the largest temperature difference and the highest flowrates.Recall HX1 heats inlet seawater to the temperature of the warm settling tank, HX2 cools the water-decanoic acid emulsion, and HX3 heats the recycled directional solvent.HX4 and HX5 cool the outlet concentrated brine and freshwater, respectively.Q S and Q W are defined as the minimum heating and cooling utility duties, respectively.

Figure 4
shows specific energy at six maximum temperature between 40 • C and 90 • C and ten different ∆T min between 1 • C and 10 • C. Figure 5 shows specific energy at five maximum temperature between 35 • C and 75 • C and ten different ∆T min between 1 • C and 10 • C. Solving (M1) 169 times to generate Figures 4 and 5 took less than 1 minute.Table able higher per pass extraction, which allows for a lower recycle flowrate (1.81 kmol/s for T max = 80 • C versus 4.91 kmol/s for T max =50 • C) and lower energy intensity (191.84kWht /m 3 for T max = 80 • C verus 551.90kWh t /m 3 for T max =50 • C).

Figure 4 :
Figure 4: Sensitivity of specific energy to maximum temperature (heat source quality) and∆T min (heat exchanger size).Bajpayee et al.[15] data showed 2.6% more solubility of water in the solvent phase from Oliveira et al.[41].The difference may be explained by the interaction of salt in the mixture.Higher maximum temperatures enable higher per pass extraction, which allows for a lower recycle flowrate and lower energy intensity.Solvents that enables higher per pass extraction at a lower temperature, the decrease in energy intensity would be higher.The specific energy difference between allowing (M1) to reach 80 • C and 90 • C is negligible.Heat exchangers with a temperature difference of less than 3 • C are to achieve less than 50 kWht/m 3 .

Figure 5 :
Figure 5: Effects of maximum temperature allowed for the process utilizing [emim][Tf 2 N] as solvent.The specific energy of the process is greatly reduced compared to carboxylic acids.

Observation C2 .
For solvent selection, the three most important factors are i) the change in water solubility for a fixed temperature change (thermoresponsiveness); ii) the melting temperature of the fatty acid, which limits the minimum operating temperature; and iii) the solubility of the directional solvent in freshwater.Observation C3.Similar to observation B4, high-performance heat exchangers are required to achieve less than 50 kWh t /m 3 using C 6 to C 10 fatty acids Observation C4.The cost of the process increases with the length of the carboxylic acid chain.The solvent solubility in water decreases as the carbon chain increases, diminishing the amount of solvent loss and the solvent make-up cost in the process.Observation C5.DSE process using fatty acids are not economically viable, with a best-case scenario of $1.29 per m 3 of freshwater for decanoic acid with heat exchangers with ∆T min of 1 • C.
(a) Effects on specific energy using different carboxylic acids as the DS.(b) Effects on the cost of the DSE process utilizing C6 to C10 fatty acids.

Figure 6 :
Figure 6: There is not a clear influence in the length of the chain of carbons (Nc) in the energy required for the separation and the cost of the process.DSE remains energy intensive utilizing any C 6 to C 10 carboxylic acid and suffers from solvent lost.The cost of the process increases with the increase of solubility of the solvent in water.The values of the cost at utilizing a ∆T min from 1 • C to • C 10 for different carboxylic acids are: for Nc = 6: $107.91-108.99 per m 3 , for Nc = 7: $21.91-23.55 per m 3 , for Nc = 8: $5.90-7.86 per m 3 , for Nc = 9: $3.00-6.18per m 3 , for Nc = 10: $1.29-3.79per m 3 .see Table5for specific quantities of solvent loss.

Figure 7 :
Figure 7: The colored contours show LCOW calculated using $12/kg cost of decanoic acid as a function of thermoresponsivness (A, vertical axis) and the solubility of water at 40 • C(B, horizontal axis).Both axes are scaled such that 1.0, which is marked with a , corresponds to decanoic acid.(Top) Using the current solubility of the solvent in water (κ d =128 ppm), a 2-fold improvement in both properties A and B result in a LCOW above $1/m 3 .(Bottom) Reducing the solubility of the solvent in water by 10-fold (κ d =12.8 ppm) reduces the LCOW to $2.88/m 3 .Even with this improvement, A and B both need to increase by 1.5-fold to reach the $0.5/m 3 LCOW goal.

Figure 7
gives quantitive targets to reduce LCOW for a fatty acid-like directional solvent.For example, doubling the thermoresponsive ability (B) and reducing the solubility of the solvent in water by 10-fold (κ d =128 ppm to 12.8ppm) relative to decanoic would give a LCOW less than $0.50 /m 3 .Observation D3.The recycle ratio is reduced as the thermoresponsive ability (B) of the solvent and the base solubility of water in the solvent (A) increase.This reduces the thermal and electric energy required to heat, pump, and cool the recycle of the DSE-water emulsion.Reducing the recycle ratio also drastically shrinks the size of the equipment.For example, increasing the thermoresponsiveness of the solvent by a factor of 2 decreases the recycle ratio by a factor of 20, which decreases the heat and electricity costs from $2.20 per m 3 of freshwater to $0.21 per m 3 of freshwater, and decreases equipment sizes by 400%.

Figure 8
Figure 8 predicts that a ten-fold decrease in κ d decrease LCOW to only 12% of the original cost.Improving the thermoresponsiveness (B) alone is insufficient for ILs to be LCOW-competitive with carboxylic acids.Assuming the current price of IL, the solvent would still require a 100 fold reduction of the solvent solubility (x o1,d ).

Figure 8 :
Figure 8: The colored contours show LCOW calculated using $1,000/kg cost of [emim][Tf 2 N] as a function of thermoresponsivness (A, vertical axis) and the solubility of water at 40 • C(B, horizontal axis).Both axes are scaled such that 1.0, which is marked with a , corresponds to [emim][Tf 2 N].Three scenarios for the solubility of IL in water κ d are considered: (top) baseline, (middle) 10-fold decrease, and (bottom) 100-fold decrease.

Figure 9 :
Figure 9: Colored contours show LCOW calculated using $100/kg of [emim][Tf 2 N].(Top) Assuming κ d =130 ppm, the solvent loss severely raises LCOW.(Bottom) Assuming a tenfold decrease in κ d , only a 1.25-fold increase in A or a 1.5-fold increase in B is needed to achieve a LCOW less than $0.50/m 3 .New unpublished data suggest these low solubility scenario is reasonable for a salty brine.(Bottom) A 100-fold decrease in κ d alone gives a LCOW of $0.49/m 3 under this low IL cost scenario.

Figure 10 :
Figure 10: Sensitivy of LCOW with a cost of $10/kg of [emim][Tf 2 N].(Top) With current solubility, the thermoresponsivness or the solubility of water would need to improve to achieve the required LCOW.(Bottom) With a 10 fold reduction of the solubility of the solvent in water we can achieve a LCOW of $0.50/m 3 of freshwater.

Fx
Inlet streams (for a specific unit operation) O ⊂ S Outlet streams (for a specific unit operation) Equipment inlet stream N c ∈ N Number of carbon atoms in fatty acid DS o 1 ∈ O Solvent phase (tank effluent) o 2 ∈ O Aqueous/salty phase (tank effluent) out ∈ O Equipment outlet stream Variables A Solubility of the solvent in water at a reference temperature B Thermoresponsiveness of the solubility of the solvent C p Heat capacity (J/mol-K) Molar flow (kmol/s) Q heat duty in the heat exchanger (kWh) Molar fraction (mol/mol) Parameters κ d Fixed solubility of directional solvent in the aqueous phase (tank effluent) (mol/mol) κ s Fixed solubility of salt in the solvent phase (tank effluent) (mol/mol) ∆T min Heat recovery approach temperature (K) T max Maximum allowable temperature of the process ( • C) T min Minimum allowable temperature of the process ( • C) N C Number of carbon atoms N k Number of functional groups

Table 1 :
Natural and man made sources of water range from freshwater (0-0.10%salinity) [11]lination industry[11], there remains a need for sustainable and energy efficient process to treat high salinity water.Directional Solvent Extraction (DSE) has been proven to be able to treat high salinity brines while utilizing low-grade heat.

Table 6 :
Heat capacity parameters for group contribution method[43].

Table 9 :
Heat exchanger sizes and temperatures for the reference design (decanoic acid as solvent, 80 • C as maximum allowable temperature).More than 90% of the heating and cooling occurs in heat exchangers HX3 and HX2, respectively.This is due to the large amount of decanoic acid that must be recycled to a achieve an overall 50% extraction ratio.For practical considerations, one may choose not to add HX6 due to the low heat duty of the heat exchanger and the small flow of solvent.

Table 10 :
Heat integration results for the reference design.QA h is the heat exchanged above the pinch temperature and QAc is the heat below the pinch temperature.Both streams S3and S4 are at the pinch temperature of 50 • C.
[34], we considered the sensitivity of process designs to both the maximum temperature and ∆T min , which controls the heat exchanger size and effective-acid-water-salt data from Bajpayee et al.[15], and [emim][Tf 2 N]-water-salt data from Guo et al.[34].

Table 12 :
Stream results for reference design with decanoic acid as solvent using 50 • C as maximum allowable temperature ∆T min =6 • C. See Figure1for stream numbers.
[51]ct economies of scale to dramatically reduce the cost of ILs as the market for these solvents grows.For example, Shiflett et al.[51]shows a price reduction of 92% for [C 2 MIM] + [Ace] − and 90% for [C 2 MIM] + [BF 4 ] − .Forthe sensitivity analysis, we consider three IL costs: $1,000/kg, $100/kg, and $10/kg.Due to these comparatively high costs, solvent loss is especially important for ILs compared to carboxylic acids.Thus, it is desirable to consider solvent recovery systems, such as a membrane for post-treatment.2Forsimplicity, we consider the complete recovery of the solvent from the freshwater feed product, which can be recovered with a nanofiltration polishing step.