MIL-160 as an Adsorbent for Atmospheric Water Harvesting

Nowadays, the rapidly growing population, climate change, and environment pollution put heavy pressure on fresh water resources. The atmosphere is the immense worldwide and available water source. The Adsorptive Water Harvesting from the Atmosphere (AWHA) method is considered a promising alternative to desalination technologies for remote arid regions. The development of novel adsorbents with advanced water-adsorption properties is a prerequisite for practical realization of this method. Metal–organic frameworks (MOFs) are a novel class of porous crystalline solids that bring a great potential for AWHA due to their extremely high specific surface area, porosity, and tailored adsorption properties. This work addresses MIL-160 as a water adsorbent for AWHA. The water-adsorption equilibrium of MIL-160 was studied by volumetric method, the isosteric heat of adsorption was calculated, and finally, the potential of MIL-160 for AWHA was evaluated for climatic conditions of the deserts of Saudi Arabia, Mongolia, the Sahara, Atacama, and Mojave as reference arid regions. MIL-160 was shown to ensure a maximum specific water productivity of 0.31–0.33 gH2O/gads per cycle. High fractions of water extracted (0.90–0.98) and collected (0.48–0.97) could be achieved at a regeneration temperature of 80 °C with natural cooling of the condenser by ambient air. The specific energy consumption for water production varied from 3.5 to 6.8 kJ/g, which is acceptable if solar heat is used to drive the desorption. The AWHA method employing MIL-160 is a promising way to achieve a fresh water supply in remote arid areas.


Introduction
Climate change leading to the desertification of a vast area, environmental pollution, and a rapidly growing world population make the fresh water supply one of the major issues of our time [1]. Although the worldwide resources of fresh water are quite abundant (1·10 5 km 3 ), most parts of them are in the form of hard-to-reach glaciers and deep underground water. The rest (rivers, lakes, and shallow underground water) is distributed very unevenly, which puts enormous pressure on water resources in arid regions. Nowadays, 1.5 billion people are facing portable water scarcity, and by 2025 this number is expected to grow to 3 billion. The most water-scarce regions include North Africa, the Near and Middle East, Northern China, India, Eastern Australia, Mexico, northeastern Brazil, and the west coast of South America [2,3].
At the same time, the total amount of moisture in the Earth's atmosphere-about 13,000 km 3 -significantly exceeds the world's requirements [4,5]. Due to its worldwide availability, interest in atmospheric water harvesting has been observed since ancient times. Artificial springs and ponds were described in [6] that accumulated moisture from the air during dewfall. Currently, water harvesting from the air is considered a promising method for water supply in arid and inland regions [7]. There are two basic types of atmospheric water extraction: passive, which does not require additional energy input (rainwater, fog, and dew collection), and active, which can operate only with an external modifying both organic linkers and inorganic clusters makes it possible to tailor the MOFs with required sorption properties and hydrolytic stability [31,32], which inspired high hopes for enhancement of AWHA performance [33].
Seo et al. [34] first proposed mesoporous MIL-100 and MIL-101 as desiccants for AWHA. Since then, the study of AWHA employing MOFs has been attracting steadily increasing interest [4,13,35,36]. For a humid climate at the relative humidity of ambient air RH > 40-50%, MIL-100(Cr) and MIL-101(Cr) are promising adsorbents that display a high working capacity of up to 1.2 mL/g [37]. A Co2Cl2BTDD designed for AWHA was able to deliver 0.82 mL/g of water under moderately humid conditions at RH = 30% [38]. The performance of MOFs as adsorbents for arid climates is essentially lower. Kim et al. [39] showed that at the ambient RH = 20%, potentially ~0.2 mL/g per cycle can be harvested with MOF-801 by utilizing solar thermal energy to drive desorption. A microporous MOF-303 has recently been developed and tested at AWHA [40], and the water harvester operating for several cycles per day generated 0.7 and 1.3 L/kg per day at 10 and 32% relative humidity, respectively. MIL-160(Al) was suggested as a promising adsorbent for AWHA regions with arid climates [13]. Chang et al. [41] evaluated the potential of application of MIL-160(Al) as a material for water harvesting in a bench-scale fixed-bed unit, and demonstrated its capable of maximum water productivity of 305 L/(day·ton) at regeneration and condensation temperatures of 80 °C and 10 °C, respectively.
This research focuses on the study of MIL-160 as an adsorbent for the AWHA process and evaluation of its potential under climatic conditions of extremely arid regions (the Mojave and Sahara Deserts, Chile, Algeria, the central part of Saudi Arabia, and Mongolia). The performance characteristics of AWHA employing MIL-160 were estimated in terms of the specific consumption of thermal energy for the water production, the specific mass of the water harvested, and the fractions of water extracted from the air and water collected. These fractions are important performance indexes, as they determine the specific electric energy consumption for air blowing through the fixed-bed adsorber, which can be significant due to a small moisture content in the atmosphere in arid regions.
The structure of MIL-160 is formed by inorganic AlO6 octahedra, which form ciscorner-sharing chains linked via carboxylate groups of the ligand (2,5-furandicarboxylic acid) (Figure 1) [42]. It possesses both strong and weak adsorption sites, which allows AWHS to promote high efficiencies of water extraction and collection.

Sample Synthesis
MIL-160 was synthesized by a hydrothermal method according to a slightly modified procedure described in [42]. 2,5-furandircaboxilic acid (4.680 g, 30 mmol, >99%), AlCl 3 ·6H 2 O (7.240 g, 30 mmol), and NaOH (1.212 g, 30 mmol) were dissolved in distilled H 2 O (60 mL) with stirring using a magnetic stirrer (~500 rpm) for 15 min. The obtained mixture of reagents was placed in a Teflon container inside a 100 mL cylindrical stainlesssteel autoclave and heated at temperature T = 120 • C for 24 h in a convection oven. After cooling down to the ambient temperature, the mixture was separated from the solution with a small-pore paper filter using a water-jet pump and washed with hot water to remove the unreacted organic ligand. Finally, the obtained white solid precipitate was activated at 150 • C for 15 h under continuous evacuation.

Characterization
The structure of the obtained MIL-160 sample was confirmed by PXRD analysis using a Bruker D8 ADVANCE diffractometer with an XRK-900reaction chamber. The measurements were carried out using CuK α -radiation (λ = 1.54 Å) in scanning mode (2θ = 5-60 • ), with a step width of 2θ = 0.02 • and an accumulation time of 10 s at each point.
IR-spectra were recorded on an Agilent Cary 660 FT-IR spectrometer using an attenuated total reflection (ATR) attachment, the 025-2018 MIRacle ZnSe Perf Crystal Plate, at 25 • C in the 500-4000 cm −1 range.
The BET surface area, the micropore volume, and total pore volume of the synthesized MIL-160 were determined by low-temperature nitrogen adsorption at 77 K using a Quantachrome Nova 1200e gas sorption analyzer. The samples were degassed in a vacuum at 150 • C for 3 h before measurement of N 2 sorption isotherms. The specific surface area was calculated by the BET analysis of the adsorption branch of the isotherm in a relative pressure range of 0.01-0.025. The total pore volume was obtained from the amount of N 2 adsorbed at a relative pressure close to unit P/P 0 = 0.99. The micropore volume was calculated using the statistical thickness analysis of the isotherm adsorption branch and de Boer's t-method. The pore-size distribution was calculated using the Dubinin-Astakhov method.

Water-Adsorption Equilibrium
The water-adsorption isotherms of MIL-160 were measured by a volumetric method at T = 50, 35, and 20 • C and in the water-vapor pressure range P = 0.8-40.0 mbar. Before the measurements, a preliminary degassing was carried out at 80 • C for 3 h under continuous evacuation (the residual pressure was 0.1 mbar) for drying the MIL-160 sample. The dry sample weight m 0 was 0.50216 ± 0.00002 g. Afterward, the sample was cooled down to a fixed temperature, which was controlled by a thermostat connected to the adsorber with an accuracy of ±0.1 K. The temperature was measured with a K-type thermocouple placed at the bottom of the adsorber. Then, the measuring cell with the adsorbent was connected to the buffering vessel filled with water vapor, which resulted in a jump in water-vapor pressure over the sample. The vapor pressure was measured using an MKS Baratron ® Type 626a pressure sensor with an accuracy of ± 0.01 mbar. The vapor-pressure jump initiated the adsorption, which led to a gradual decrease in the pressure. The sample was maintained at a fixed temperature for 1-4 h to reach equilibrium. The amount of water vapor sorbed (∆w (g/g)) was calculated from the temporal pressure dependence P(t) using the ideal gas equation: where M H2O -the water molar mass, V-the system volume, -the universal gas constant, and T-the steam temperature. Subsequently, based on the data obtained, a set of watersorption isotherms w(P) of the MIL-160 sample was calculated.

Structure Characterization of as-Prepared MIL-160
The texture characteristics of MOF-801 determined from the N 2 sorption isotherm at 77 K ( Figure 2a) belonged to the I-type according to the IUPAC classification, and the hysteresis loop was absent, which is typical for microporous solids. The synthesized MIL-160 possessed the specific surface area S BET = 830 m 2 /g and the total pore volume V p = 0.40 cm 3 /g, which agreed with the literature data [42]. The micropore volume V µ coincided with the V p . Hence, the synthesized MIL-160 was microporous without mesoor macropores. The pore-size distribution obtained by the Dubinin-Astakhov method ( Figure 2b) demonstrated a narrow peak in the micropore-size region. As shown in the curve obtained, the average pore diameter is 0.42 nm, which is consistent with the data presented in [42].
where MH2O-the water molar mass, V-the system volume, -the universal gas const and T-the steam temperature. Subsequently, based on the data obtained, a set of wa sorption isotherms w(P) of the MIL-160 sample was calculated.

Structure Characterization of as-Prepared MIL-160
The texture characteristics of MOF-801 determined from the N2 sorption isotherm 77 K (Figure 2a) belonged to the I-type according to the IUPAC classification, and hysteresis loop was absent, which is typical for microporous solids. The synthesized M 160 possessed the specific surface area SBET = 830 m 2 /g and the total pore volume Vp = 0 cm 3 /g, which agreed with the literature data [42]. The micropore volume Vμ coincided w the Vp. Hence, the synthesized MIL-160 was microporous without meso-or macropo The pore-size distribution obtained by the Dubinin-Astakhov method (Figure 2b) dem strated a narrow peak in the micropore-size region. As shown in the curve obtained, average pore diameter is 0.42 nm, which is consistent with the data presented in [42]. The XRD pattern (Figure 3a) of the synthesized sample was consistent with that ported in the literature [42,43]. The FT-IR spectrum of the prepared MIL-160 sample (F ure 3b) agreed well with the literature data [41,[43][44][45]. The characteristic bands with h intensity were attributed to asymmetric (1649 cm −1 ) and symmetric stretching (1405 cm vibrations of carboxylate groups, along with the C=C bonds' stretching vibrations of furan ring at 1583 cm −1 [41,44,45]. The strong band at 630 cm −1 corresponded to the vib tions of the Al-O bond in the MIL-160 structure [41]. The peaks in the range of 1000-1 cm −1 could be attributed to the asymmetric and symmetric stretching vibrations of the O-C in the furan rings [41]. A band at 782 cm −1 ascribed to the out-of-plane deformat vibrations of C-H bonds in the furan ring also was observed [44]. The broad band arou 3500 cm −1 was assigned to the vibrations of the water molecules adsorbed from the am ent air, while the weak peak around 3200 cm −1 represented the vibration of bridging droxyl groups μ-OH in the metal-oxide clusters AlO6 [41,44]. It is worth noting that lack of a band at 1700 cm −1 indicated the absence of residual free 2,5-furandicarbox acid in the pore-synthesized MIL-160 [44,45]. Thus, the characterization of the synthesi MIL-160 by XRD, nitrogen adsorption, and FTIR analysis verified its genuine struct and high purity. The XRD pattern (Figure 3a) of the synthesized sample was consistent with that reported in the literature [42,43]. The FT-IR spectrum of the prepared MIL-160 sample (Figure 3b) agreed well with the literature data [41,[43][44][45]. The characteristic bands with high intensity were attributed to asymmetric (1649 cm −1 ) and symmetric stretching (1405 cm −1 ) vibrations of carboxylate groups, along with the C=C bonds' stretching vibrations of the furan ring at 1583 cm −1 [41,44,45]. The strong band at 630 cm −1 corresponded to the vibrations of the Al-O bond in the MIL-160 structure [41]. The peaks in the range of 1000-1300 cm −1 could be attributed to the asymmetric and symmetric stretching vibrations of the C-O-C in the furan rings [41]. A band at 782 cm −1 ascribed to the out-of-plane deformation vibrations of C-H bonds in the furan ring also was observed [44]. The broad band around 3500 cm −1 was assigned to the vibrations of the water molecules adsorbed from the ambient air, while the weak peak around 3200 cm −1 represented the vibration of bridging hydroxyl groups µ-OH in the metal-oxide clusters AlO 6 [41,44]. It is worth noting that the lack of a band at 1700 cm −1 indicated the absence of residual free 2,5-furandicarboxylic acid in the pore-synthesized MIL-160 [44,45]. Thus, the characterization of the synthesized MIL-160 by XRD, nitrogen adsorption, and FTIR analysis verified its genuine structure and high purity.

Water-Vapor Adsorption on MIL-160
The isotherms of water adsorption on the MIL-160 were S-shaped curves ( Figure 4) showing a small water uptake (0.02 gH2O/gads) at low pressures, followed by a steep increase in uptake up to 0.25-0.30 gH2O/gads in a narrow pressure range, which depended on the temperature. Upon further increase in vapor pressure, the uptake gradually rose to 0.34 gH2O/gads, which was somewhat smaller than the specific volume of micropores Vμ = 0.40 cm 3 /g. This indicated that a fraction of the pore space in the vicinity of hydrophobic sites (organic linker) remained unoccupied by water molecules. Based on the obtained data on water adsorption equilibrium on MIL-160, isosteres of water adsorption were plotted in ln(P) − 1/T coordinates ( Figure 5a). The isosteric heat ΔHads of the water adsorption was calculated according to the Clausius-Clapeyron equation:

Water-Vapor Adsorption on MIL-160
The isotherms of water adsorption on the MIL-160 were S-shaped curves ( Figure 4) showing a small water uptake (0.02 g H2O /g ads ) at low pressures, followed by a steep increase in uptake up to 0.25-0.30 g H2O /g ads in a narrow pressure range, which depended on the temperature. Upon further increase in vapor pressure, the uptake gradually rose to 0.34 g H2O /g ads , which was somewhat smaller than the specific volume of micropores V µ = 0.40 cm 3 /g. This indicated that a fraction of the pore space in the vicinity of hydrophobic sites (organic linker) remained unoccupied by water molecules.

Water-Vapor Adsorption on MIL-160
The isotherms of water adsorption on the MIL-160 were S-shaped curves ( Figure 4 showing a small water uptake (0.02 gH2O/gads) at low pressures, followed by a steep in crease in uptake up to 0.25-0.30 gH2O/gads in a narrow pressure range, which depended on the temperature. Upon further increase in vapor pressure, the uptake gradually rose to 0.34 gH2O/gads, which was somewhat smaller than the specific volume of micropores Vμ = 0.40 cm 3 /g. This indicated that a fraction of the pore space in the vicinity of hydrophobic sites (organic linker) remained unoccupied by water molecules. Based on the obtained data on water adsorption equilibrium on MIL-160, isosteres o water adsorption were plotted in ln(P) − 1/T coordinates (Figure 5a). The isosteric hea ΔHads of the water adsorption was calculated according to the Clausius-Clapeyron equa tion: Based on the obtained data on water adsorption equilibrium on MIL-160, isosteres of water adsorption were plotted in ln(P) − 1/T coordinates (Figure 5a). The isosteric heat ∆H ads of the water adsorption was calculated according to the Clausius-Clapeyron equation: The adsorption heat Qaдc varied in the range of 49 to 52 ± 1 kJ/mol at w = 0.05-0.25 g/g (Figure 5b). The obtained values of adsorption heat somewhat exceeded the latent condensation heat of water ΔL = 43.9 kJ mol -1 at 303 K, which pointed to a moderately strong interaction of water molecules with the MIL-160′s surface. Experimentally measured water adsorption isobars on the MIL-160 presented as a function of the Polanyi adsorption potential ΔF = −RTln[P/P0(T)], where P is the partial vapor pressure, P0 is the saturation vapor pressure at temperature T, merged into one characteristic curve w(ΔF) ( Figure 6). This meant that the water adsorption equilibrium of the MIL-160 obeyed the Polanyi principle of temperature invariance [46]. The characteristic curve w(ΔF) was approximated by an empiric equation:  The adsorption heat Q a∂c varied in the range of 49 to 52 ± 1 kJ/mol at w = 0.05-0.25 g/g (Figure 5b). The obtained values of adsorption heat somewhat exceeded the latent condensation heat of water ∆L = 43.9 kJ mol −1 at 303 K, which pointed to a moderately strong interaction of water molecules with the MIL-160 s surface.
Experimentally measured water adsorption isobars on the MIL-160 presented as a function of the Polanyi adsorption potential ∆F = −RTln[P/P 0 (T)], where P is the partial vapor pressure, P 0 is the saturation vapor pressure at temperature T, merged into one characteristic curve w(∆F) (Figure 6). This meant that the water adsorption equilibrium of the MIL-160 obeyed the Polanyi principle of temperature invariance [46]. The characteristic curve w(∆F) was approximated by an empiric equation: The adsorption heat Qaдc varied in the range of 49 to 52 ± 1 kJ/mol at w = 0.05-0.25 g/g (Figure 5b). The obtained values of adsorption heat somewhat exceeded the latent condensation heat of water ΔL = 43.9 kJ mol -1 at 303 K, which pointed to a moderately strong interaction of water molecules with the MIL-160′s surface. Experimentally measured water adsorption isobars on the MIL-160 presented as a function of the Polanyi adsorption potential ΔF = −RTln[P/P0(T)], where P is the partial vapor pressure, P0 is the saturation vapor pressure at temperature T, merged into one characteristic curve w(ΔF) (Figure 6). This meant that the water adsorption equilibrium of the MIL-160 obeyed the Polanyi principle of temperature invariance [46]. The characteristic curve w(ΔF) was approximated by an empiric equation:   The characteristic curve w(∆F) was used to evaluate the performance of AWHA employing MIL-160 for climatic conditions of several arid regions located on different continents (Figure 7). The Mojave Desert in North America; the Atacama in Chile, South America; Tamanrasset in Algeria; the Sahara Desert; Riyadh-Old in the central part of Saudi Arabia; and Noyon in Mongolia were selected as reference regions, characterized by their extremely arid climates. The climatic data (the average temperatures T n and T d , and the average relative humidity RH n and RH d during night and day, respectively) were collected from the Meteonorm Global Climate Database. They were used to calculate the values of adsorption potential ∆F ads and ∆F re (Table 1), corresponding to the boundary conditions of adsorption and desorption stages, respectively: ∆F re = −RT re [lnP am /P 0 (T re )], where T re is the regeneration temperature. (ΔFweak) and strongest (ΔFstr) adsorption sites. The blue area shows the ΔF range for the boundary conditions of the AWHA cycle in Riyadh-Old during the dry season (July).

Specific Water Productivity
The characteristic curve w(ΔF) was used to evaluate the performance of AWHA employing MIL-160 for climatic conditions of several arid regions located on different continents (Figure 7). The Mojave Desert in North America; the Atacama in Chile, South America; Tamanrasset in Algeria; the Sahara Desert; Riyadh-Old in the central part of Saudi Arabia; and Noyon in Mongolia were selected as reference regions, characterized by their extremely arid climates. The climatic data (the average temperatures Tn and Td, and the average relative humidity RHn and RHd during night and day, respectively) were collected from the Meteonorm Global Climate Database. They were used to calculate the values of adsorption potential ΔFads and ΔFre (Table 1), corresponding to the boundary conditions of adsorption and desorption stages, respectively: where Tre is the regeneration temperature. The characteristic curve of water adsorption on the MIL-160 demonstrated that the strongest adsorption sites adsorbed water vapor at ∆Fstr ≈ 9.0-10.0 kJ/mol (Figure 6), which was lower than ∆Fre = 11.3-17.4 kJ/mol at Tre = 80 °C in all the reference regions (Table 1). Thus, the retained water could be desorbed completely at a quite low temperature of 80 °C, allowing usage of a simple solar collector for the adsorbent regeneration.   The characteristic curve of water adsorption on the MIL-160 demonstrated that the strongest adsorption sites adsorbed water vapor at ∆F str ≈ 9.0-10.0 kJ/mol (Figure 6), which was lower than ∆F re = 11.3-17.4 kJ/mol at T re = 80 • C in all the reference regions (Table 1). Thus, the retained water could be desorbed completely at a quite low temperature of 80 • C, allowing usage of a simple solar collector for the adsorbent regeneration.
The maximum specific water productivity SPmax per cycle can be achieved in the AWHA process if water retained in the adsorbent during the adsorption stage is completely removed and collected during the desorption/condensation stage. The productivity SPmax was calculated from the characteristic curve ( Figure 6) as the uptake variation ∆w = w max − w min = w(∆F ad ) − w(∆F re ). In all the selected regions, MIL-160 exchanged ∆w = 0.31-0.33 g H2O /g ads at T re = 80 • C, which surpassed respective values for various adsorbents, both traditional and novel (Figure 8). The maximum specific water productivity SPmax per cycle can be achieved in the AWHA process if water retained in the adsorbent during the adsorption stage is completely removed and collected during the desorption/condensation stage. The productivity SPmax was calculated from the characteristic curve ( Figure 6) as the uptake variation Δw = wmax − wmin = w(ΔFad) − w(ΔFre). In all the selected regions, MIL-160 exchanged Δw = 0.31-0.33 gH2O/gads at Tre = 80 °C, which surpassed respective values for various adsorbents, both traditional and novel (Figure 8).

The Fractions of Water Extraction and Collection
Along with the specific water productivity, the fractions δex of water extracted from the air during adsorption and δcol of water collected during condensation are also the crucial performance indexes of AWHA. They determine the volume of air to be passed through the adsorber, for harvesting a unit mass of water, and consequently, the energy demand of the system for the air blowing.
The fractions of water extracted δex and collected δcol in a simple fixed-bed flowing adsorber (Figure 9a) with MIL-160 as the adsorbent can be evaluated as [13]: where Pam-the partial pressure of water vapor in the ambient air; Pout.ad-the water vapor pressure in the outlet air during adsorption stage; Pout.re-the water vapor pressure in the

The Fractions of Water Extraction and Collection
Along with the specific water productivity, the fractions δ ex of water extracted from the air during adsorption and δ col of water collected during condensation are also the crucial performance indexes of AWHA. They determine the volume of air to be passed through the adsorber, for harvesting a unit mass of water, and consequently, the energy demand of the system for the air blowing.
The fractions of water extracted δ ex and collected δ col in a simple fixed-bed flowing adsorber (Figure 9a) with MIL-160 as the adsorbent can be evaluated as [13]: δ ex = (P am − P out.ad )/P am = 1 − P out.ad /P am (6) δ col = [P out.re − P 0 (T d )]/P out.re = 1 − P 0 (T d )/P out.re (7) where P am -the partial pressure of water vapor in the ambient air; P out.ad -the water vapor pressure in the outlet air during adsorption stage; P out.re -the water vapor pressure in the outlet air during regeneration stage; and P 0 (T d )-the pressure of saturated water vapor at a day temperature of ambient air T d .
adsorption equaled the equilibrium pressure over the dry adsorbent (Figure 9d). The strongest adsorption centers of the MIL-160 adsorbed water vapor at ΔFstr ≈ 10.0 kJ/mol ( Figure 6). Consequently, the outlet vapor pressure Pout.ad during the adsorption stage could be calculated as: Pout.ad = P0(Tn) exp(-ΔFstr/RTn) (8) Figure 9. Scheme of a fixed-bed flowing adsorber (a) and distribution of water uptake (b,c) and vapor partial pressure (d) along the adsorber.
The δex values evaluated according to Equations (6) and (8) varied from 0.90 for Riyadh-Old to 0.96 for the Atacama regions during the dry season ( Figure 10). During the humid season, δex was even higher due to the increase in RH of the ambient air ( Figure  10), and reached 0.96-0.98 for the selected regions. Consequently, the affinity of the strongest adsorption sites MIL-160 to water vapor provided effective extraction of water vapor from the ambient air. That promoted a reduced air volume blown through the adsorber to extract a unit volume of water, and consequently, lowering energy consumption for the air purging.
During the regeneration stage, the outlet air was in equilibrium with the adsorbent, saturated with water up to wmax right after the adsorption stage (Figure 9c,d). The weakest adsorption sites adsorbed water vapor at ΔFweak ≈ 3.0 kJ/mol ( Figure 6). Consequently, at ΔF > ΔFweak, these sites released adsorbed water, and the outlet vapor pressure Pout.re during the desorption stage could be calculated as: Here, we assumed that the adsorption front thickness ∆L in a fixed-bed adsorber was negligible in comparison with the adsorber length L >> ∆L (Figure 9a-c). In this case, the dynamic adsorption capacity w d of the adsorbent equaled the equilibrium capacity w(P,T). Until the concentration front was inside the bed, the outlet vapor pressure P out.ad during adsorption equaled the equilibrium pressure over the dry adsorbent (Figure 9d). The strongest adsorption centers of the MIL-160 adsorbed water vapor at ∆F str ≈ 10.0 kJ/mol ( Figure 6). Consequently, the outlet vapor pressure P out.ad during the adsorption stage could be calculated as: P out.ad = P 0 (T n ) exp(−∆F str /RT n ) The δ ex values evaluated according to Equations (6) and (8) varied from 0.90 for Riyadh-Old to 0.96 for the Atacama regions during the dry season ( Figure 10). During the humid season, δ ex was even higher due to the increase in RH of the ambient air (Figure 10), and reached 0.96-0.98 for the selected regions. Consequently, the affinity of the strongest adsorption sites MIL-160 to water vapor provided effective extraction of water vapor from the ambient air. That promoted a reduced air volume blown through the adsorber to extract a unit volume of water, and consequently, lowering energy consumption for the air purging.
During the regeneration stage, the outlet air was in equilibrium with the adsorbent, saturated with water up to w max right after the adsorption stage (Figure 9c,d). The weakest adsorption sites adsorbed water vapor at ∆F weak ≈ 3.0 kJ/mol ( Figure 6). Consequently, at ∆F > ∆F weak , these sites released adsorbed water, and the outlet vapor pressure P out.re during the desorption stage could be calculated as: P out.re = P 0 (T re )exp(−∆F weak /RT re ) It should be noted that for the dry season, the ∆F ad > ∆F weak for all regions except Atacama (Table 1). This meant that the weakest adsorption sites remained unsaturated with water during the adsorption stage, and maximum uptake in the cycle equaled w = w(∆F ad ). Accordingly, for the dry season, the pressure P out.re was calculated using the following expression: P out.re = P 0 (T re )exp(−∆F ad /RT re ) Energies 2021, 14, x FOR PEER REVIEW 11 of 1 Figure 10. Water-extraction fraction δex for the AWHA system based on MIL-160.
It should be noted that for the dry season, the ΔFad > ΔFweak for all regions excep Atacama (Table 1). This meant that the weakest adsorption sites remained unsaturate with water during the adsorption stage, and maximum uptake in the cycle equaled w w(ΔFad). Accordingly, for the dry season, the pressure Pout.re was calculated using the fol lowing expression: Then, the fraction δcol was evaluated as a function of temperature Tre using Equatio (7). If the condenser was cooled by the ambient air at Td, δcol values for the selected region varied in the range 0.48-0.95 and 0.88-0.97 during the dry (July) and humid (January seasons, respectively, at Tre = 80 °C ( Figure 11). The increase in the regeneration tempera ture enhanced the water collection fraction: at Tre = 100 °C, the collection fraction rose t 0.77-0.97 and 0.95-0.98 for the dry and humid seasons, respectively. On the contrary, low ering the regeneration temperature to 70 °C resulted in a dramatic reduction of this frac tion, particularly for the dry season, down to 0.15-0.9. This showed the necessity of a external heat source for the water desorption, which could be solar or waste heat.
(a) (b) Figure 11. Effect of the regeneration temperature on the water-collection fraction δcol of the AWHA system based on MIL-160 during the dry (a) and humid (b) seasons, with the condenser cooled by the ambient air. Then, the fraction δ col was evaluated as a function of temperature T re using Equation (7). If the condenser was cooled by the ambient air at T d , δ col values for the selected regions varied in the range 0.48-0.95 and 0.88-0.97 during the dry (July) and humid (January) seasons, respectively, at T re = 80 • C ( Figure 11). The increase in the regeneration temperature enhanced the water collection fraction: at T re = 100 • C, the collection fraction rose to 0.77-0.97 and 0.95-0.98 for the dry and humid seasons, respectively. On the contrary, lowering the regeneration temperature to 70 • C resulted in a dramatic reduction of this fraction, particularly for the dry season, down to 0.15-0.9. This showed the necessity of an external heat source for the water desorption, which could be solar or waste heat. It should be noted that for the dry season, the ΔFad > ΔFweak for all regions except Atacama (Table 1). This meant that the weakest adsorption sites remained unsaturated with water during the adsorption stage, and maximum uptake in the cycle equaled w = w(ΔFad). Accordingly, for the dry season, the pressure Pout.re was calculated using the following expression: Then, the fraction δcol was evaluated as a function of temperature Tre using Equation (7). If the condenser was cooled by the ambient air at Td, δcol values for the selected regions varied in the range 0.48-0.95 and 0.88-0.97 during the dry (July) and humid (January) seasons, respectively, at Tre = 80 °C ( Figure 11). The increase in the regeneration temperature enhanced the water collection fraction: at Tre = 100 °C, the collection fraction rose to 0.77-0.97 and 0.95-0.98 for the dry and humid seasons, respectively. On the contrary, lowering the regeneration temperature to 70 °C resulted in a dramatic reduction of this fraction, particularly for the dry season, down to 0.15-0.9. This showed the necessity of an external heat source for the water desorption, which could be solar or waste heat.
(a) (b) Figure 11. Effect of the regeneration temperature on the water-collection fraction δcol of the AWHA system based on MIL-160 during the dry (a) and humid (b) seasons, with the condenser cooled by the ambient air. Figure 11. Effect of the regeneration temperature on the water-collection fraction δ col of the AWHA system based on MIL-160 during the dry (a) and humid (b) seasons, with the condenser cooled by the ambient air.
Another efficient method of increasing the fraction δ col is a decrease in the condensation temperature T con . A tank with a heat exchanger located underground or a condenser connected to a heat pump or adsorptive chiller can be used as a condenser [48,49] instead of that cooled by the ambient air. Figure 12 shows that reducing T con from T d = 36.1 • C to 10 • C allowed the growth of δ col from 0.48-0.77 to 0.90-0.95 at T re = 80-100 • C under the climatic conditions of Riyadh-Old during the dry season.
Another efficient method of increasing the fraction δcol is a decrease in the condensation temperature Tcon. A tank with a heat exchanger located underground or a condenser connected to a heat pump or adsorptive chiller can be used as a condenser [48,49] instead of that cooled by the ambient air. Figure 12 shows that reducing Tcon from Td = 36.1 °C to 10 °C allowed the growth of δcol from 0.48-0.77 to 0.90-0.95 at Tre = 80-100 °C under the climatic conditions of Riyadh-Old during the dry season.

The Specific Energy Consumption
An important performance index of the AWHA system is the specific consumption of thermal energy SEC for the water production, which can be calculated as: where Cpad = 1.63 J/(g·K) is the specific heat of MIL-160 at 80 °C [50]), CpH2O = 4.19 J/(g·K) is the specific heat of water at 80 °C, and Qads = 2.84 kJ/g is the average isosteric heat of adsorption in the range w = 0.05-0.30 gH2O/gads. For the selected regions during the dry season, the SEC ranged from 3.7 to 6.8 kJ/gH2O at a regeneration temperature of 80 °C ( Figure 13). The SEC was affected by the watercollection fraction δcol (Equation (11)). Accordingly, during the humid season (January), SEC decreased to 3.5-3.8 kJ/gH2O due to a higher water-collection fraction δcol. The decrease in condensation temperature was another way to reduce SEC. Thus, when the condenser was cooled to 10 °C, SEC for the Riyadh-Old region was reduced to 3.6 kJ/gH2O as compared to 6.8 kJ/gH2O for the condenser cooled by the ambient air at temperature Td (Table  2), owing to an appropriate increase in the water-collection fraction δcol. Thus, the calculated δ ex and δ col values showed a high performance of the AWHA system employing MIL-160 as an adsorbent. This MOF possessed both strong and weak adsorption sites, exchanged up to 0.33 g H2O /g ads under climatic conditions of the selected arid regions, and provided high fractions δ ex = 0.90-0.98 and δ col = 0.48-0.97 at T re = 80-100 • C.

The Specific Energy Consumption
An important performance index of the AWHA system is the specific consumption of thermal energy SEC for the water production, which can be calculated as: SEC = Q sp.re /(∆w·δ col ) = [∆w·Q ads + (C pad + w ads ·C pH2O )·(T re − T ad )]/(∆w·δ col ), (11) where C pad = 1.63 J/(g·K) is the specific heat of MIL-160 at 80 • C [50]), C pH2O = 4.19 J/(g·K) is the specific heat of water at 80 • C, and Q ads = 2.84 kJ/g is the average isosteric heat of adsorption in the range w = 0.05-0.30 g H2O /g ads . For the selected regions during the dry season, the SEC ranged from 3.7 to 6.8 kJ/g H2O at a regeneration temperature of 80 • C ( Figure 13). The SEC was affected by the watercollection fraction δ col (Equation (11)). Accordingly, during the humid season (January), SEC decreased to 3.5-3.8 kJ/g H2O due to a higher water-collection fraction δ col . The decrease in condensation temperature was another way to reduce SEC. Thus, when the condenser was cooled to 10 • C, SEC for the Riyadh-Old region was reduced to 3.6 kJ/g H2O as compared to 6.8 kJ/g H2O for the condenser cooled by the ambient air at temperature T d ( Table 2), owing to an appropriate increase in the water-collection fraction δ col . Table 2. SEC for water production in the AWHA process employing MIL-160 in the Riyadh-Old region at T re = 80 • C (dry season). These SEC values were higher than the heat of water vaporization (2.26 kJ/g H2O at 100 • C). Therefore, the energy consumption for AWEA was higher than the energy consumption for conventional water desalination. However, taking into account that in arid regions, solar heat is usually available in abundance and can be used for adsorbent regeneration, the obtained SEC-values for water production were quite acceptable. Accordingly, the AWEA method employing MIL-160 as an adsorbent is promising for arid regions remote from other sources of water.  These SEC values were higher than the heat of water vaporization (2.26 kJ/gH2O at 100 °C). Therefore, the energy consumption for AWEA was higher than the energy consumption for conventional water desalination. However, taking into account that in arid regions, solar heat is usually available in abundance and can be used for adsorbent regeneration, the obtained SEC-values for water production were quite acceptable. Accordingly, the AWEA method employing MIL-160 as an adsorbent is promising for arid regions remote from other sources of water.

Conclusions
In this paper, the water-vapor adsorption on MIL-160 was studied, and the assessment of the feasibility of MIL-160 for the AWHA process in arid climatic regions was carried out. The water-vapor adsorption isotherms were S-shaped curves with a maximum uptake of 0.34 g/g. The isosteric heat of water adsorption equaled 49-52 ± 1 kJ/mol at a water-uptake range of 0.05 to 0.25 g/g. Under conditions of several arid regions, namely Riyadh-Old (Saudi Arabia), the Sahara Desert, the Mojave Desert, Atacama (Chile), and Noyon (Mongolia), a high maximum specific water productivity of 0.31-0.33 gH2O/gads per cycle could be achieved with MIL-160. Employing MIL-160 allows a fraction of water extracted δex = 0.90-0.98 during the adsorption stage. The fraction of water collected varied in the range of 0.48-0.76 and 0.85-0.97 during the dry and humid seasons, respectively, at Tre = 80 °C with natural cooling of the condenser by ambient air. Further increase in the fraction of water collected could be achieved by lowering the condensation temperature to 10 °C and increasing the regeneration temperature to 100 °C. The specific energy consumption for water production varied from 3.5 to 6.8 kJ/g. This is quite acceptable if solar heat, available in abundance in arid regions, can be used to drive the desorption. The AWHA method employing MIL-160 is a promising way to achieve a fresh water supply in arid areas remote from coast-line.  . SEC for water production in the AWHA process employing MIL-160 as an adsorbent at T re = 80 • C and T con = T d .

Conclusions
In this paper, the water-vapor adsorption on MIL-160 was studied, and the assessment of the feasibility of MIL-160 for the AWHA process in arid climatic regions was carried out. The water-vapor adsorption isotherms were S-shaped curves with a maximum uptake of 0.34 g/g. The isosteric heat of water adsorption equaled 49-52 ± 1 kJ/mol at a water-uptake range of 0.05 to 0.25 g/g. Under conditions of several arid regions, namely Riyadh-Old (Saudi Arabia), the Sahara Desert, the Mojave Desert, Atacama (Chile), and Noyon (Mongolia), a high maximum specific water productivity of 0.31-0.33 g H2O /g ads per cycle could be achieved with MIL-160. Employing MIL-160 allows a fraction of water extracted δ ex = 0.90-0.98 during the adsorption stage. The fraction of water collected varied in the range of 0.48-0.76 and 0.85-0.97 during the dry and humid seasons, respectively, at T re = 80 • C with natural cooling of the condenser by ambient air. Further increase in the fraction of water collected could be achieved by lowering the condensation temperature to 10 • C and increasing the regeneration temperature to 100 • C. The specific energy consumption for water production varied from 3.5 to 6.8 kJ/g. This is quite acceptable if solar heat, available in abundance in arid regions, can be used to drive the desorption. The AWHA method employing MIL-160 is a promising way to achieve a fresh water supply in arid areas remote from coast-line.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.