WO2024118724A1 - Multi-stage air conditioning systems and methods of use thereof - Google Patents

Multi-stage air conditioning systems and methods of use thereof Download PDF

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Publication number
WO2024118724A1
WO2024118724A1 PCT/US2023/081530 US2023081530W WO2024118724A1 WO 2024118724 A1 WO2024118724 A1 WO 2024118724A1 US 2023081530 W US2023081530 W US 2023081530W WO 2024118724 A1 WO2024118724 A1 WO 2024118724A1
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Prior art keywords
sorbent
air
stage
regeneration
humidity
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PCT/US2023/081530
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French (fr)
Inventor
Jordan CLARK
Saba ZAKERI SHAHVARI
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Ohio State Innovation Foundation
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Publication of WO2024118724A1 publication Critical patent/WO2024118724A1/en

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Classifications

    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
    • F24F3/00—Air-conditioning systems in which conditioned primary air is supplied from one or more central stations to distributing units in the rooms or spaces where it may receive secondary treatment; Apparatus specially designed for such systems
    • F24F3/12—Air-conditioning systems in which conditioned primary air is supplied from one or more central stations to distributing units in the rooms or spaces where it may receive secondary treatment; Apparatus specially designed for such systems characterised by the treatment of the air otherwise than by heating and cooling
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
    • F24F3/00—Air-conditioning systems in which conditioned primary air is supplied from one or more central stations to distributing units in the rooms or spaces where it may receive secondary treatment; Apparatus specially designed for such systems
    • F24F3/12—Air-conditioning systems in which conditioned primary air is supplied from one or more central stations to distributing units in the rooms or spaces where it may receive secondary treatment; Apparatus specially designed for such systems characterised by the treatment of the air otherwise than by heating and cooling
    • F24F3/14—Air-conditioning systems in which conditioned primary air is supplied from one or more central stations to distributing units in the rooms or spaces where it may receive secondary treatment; Apparatus specially designed for such systems characterised by the treatment of the air otherwise than by heating and cooling by humidification; by dehumidification
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
    • F24F2120/00—Control inputs relating to users or occupants
    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F24—HEATING; RANGES; VENTILATING
    • F24F—AIR-CONDITIONING; AIR-HUMIDIFICATION; VENTILATION; USE OF AIR CURRENTS FOR SCREENING
    • F24F3/00—Air-conditioning systems in which conditioned primary air is supplied from one or more central stations to distributing units in the rooms or spaces where it may receive secondary treatment; Apparatus specially designed for such systems
    • F24F3/12—Air-conditioning systems in which conditioned primary air is supplied from one or more central stations to distributing units in the rooms or spaces where it may receive secondary treatment; Apparatus specially designed for such systems characterised by the treatment of the air otherwise than by heating and cooling
    • F24F3/14—Air-conditioning systems in which conditioned primary air is supplied from one or more central stations to distributing units in the rooms or spaces where it may receive secondary treatment; Apparatus specially designed for such systems characterised by the treatment of the air otherwise than by heating and cooling by humidification; by dehumidification
    • F24F3/147—Air-conditioning systems in which conditioned primary air is supplied from one or more central stations to distributing units in the rooms or spaces where it may receive secondary treatment; Apparatus specially designed for such systems characterised by the treatment of the air otherwise than by heating and cooling by humidification; by dehumidification with both heat and humidity transfer between supplied and exhausted air

Definitions

  • multi-stage air conditioning systems comprising a first stage in fluid communication with an air supply, the first stage comprising a first sorbent, the first sorbent having a type IV or V water sorption isotherm, a first step_RH, and a first regeneration temperature; a second stage in fluid communication with the first stage, the second stage comprising a second sorbent, the second sorbent having a type IV or V water sorption isotherm, a second step_RH, and a second regeneration temperature; wherein the second step_RH is less than the first step_RH; and wherein the second regeneration temperature is greater than the first regeneration temperature; and a heat source in thermal communication with the second stage.
  • the second stage is configured to: receive air having a sixth humidity; receive an amount of heat from the heat source; contact the second sorbent with the air and the amount of heat to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air with the increased moisture content and decreased amount of heat to the first stage; the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the first sorbent; and subsequently effuse the air.
  • the third stage is configured to: receive air having the third humidity from the second stage, contact the air with the third sorbent to thereby transfer a fifth amount of moisture from the air to the third sorbent and decrease the moisture content of the air to an eighth humidity, the eighth humidity being less than the third humidity, and effuse the air having the eighth humidity.
  • the third stage is configured to: receive air having a ninth humidity; receive an amount of heat from the heat source; contact the third sorbent with the air and the amount of heat to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effuse the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to: receive the air effused by the third stage; contact the second sorbent with the air to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air having the increased humidity and decreased amount of heat to the first stage; and the first stage is configured to: receive the air having a ninth humidity; receive an amount of
  • the system further comprises: a fourth stage in fluid communication with the third stage, the fourth stage comprising a fourth sorbent, the fourth sorbent having a type IV or V water sorption isotherm, a fourth step_RH, and a fourth regeneration temperature; wherein the fourth step_RH is less than the third step_RH; and wherein the fourth regeneration temperature is greater than the third regeneration temperature.
  • the heat source is in thermal communication with the fourth stage.
  • the fourth stage is configured to: receive air having the tenth humidity from the third stage, contact the air with the fourth sorbent to thereby transfer a seventh amount of moisture from the air to the fourth sorbent and decrease the moisture content of the air to an eleventh humidity, the eleventh humidity being less than the tenth humidity, and effuse the air having the eleventh humidity.
  • the fourth stage is configured to: receive air having a twelfth humidity; receive an amount of heat from the source; contact the fourth sorbent with the air and the amount of heat to thereby increase the temperature of the fourth sorbent to the fourth regeneration temperature such that the fourth sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the fourth sorbent; and effuse the air having the increased humidity and decreased amount of heat to the third stage; the third stage is configured to: receive the air effused by the fourth stage; contact the third sorbent with the air to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effuse the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to: receive the air having a twelfth humidity;
  • the system further comprises one or more heat exchangers in thermal communication with the first stage, the second stage, the third stage (when present), the fourth stage (when present), or a combination thereof.
  • the first stage, the second stage, the third stage (when present), and the fourth stage (when present) each independently comprises a rotary desiccant wheel.
  • the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present) each independently comprises a metal-organic framework (MOF).
  • MOF metal-organic framework
  • the metal comprises Al, Ti, Zr, Co, or a combination thereof.
  • the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises an Al-based MOF.
  • the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present) each independently comprises MIL-100, MIL-101, HKUST-1, ISE-1, Basolite C300, Basolite A100, DUT-67(Zr), UiO-66, UiO-67, NU-1000, MOF-801, CPO-27(Ni), CAU-1, CAU-1(OH) 2 , CAU-3, CAU-3-NH 2 , CAU-8, CAU-10H, MIL-53, MIL-53-NH 2 , MIL-125, MIL- 125-NH2, MIL-140A, MIL-140C, UiO-66, ZIF-8, Ni-MOF-74, Co-MOF-74, MIL-53, Fe-
  • the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises CAU-10, CAU-23, Al-fumarate, KMF-1, MIL-125-NH 2 , MIL-125, MOF-841, Co 2 Cl 2 (BTDD), or a combination thereof.
  • the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present) each independently comprises MOF-841, Co 2 Cl 2 (BTDD), Al-fumarate, CAU-23, or a combination thereof.
  • the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), and the fourth regeneration temperature (when present) each independently is from 0°C to 140°C.
  • the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), and the fourth regeneration temperature (when present) each independently is from 40°C to 60°C, from 70°C to 90°C, from 50°C to 70°C, from 60°C to 80°C, from 80°C to 100°C, or from 120°C to 140°C.
  • the air supply comprises ambient air.
  • the system when the system is operated in the regeneration mode, the system has a regeneration efficiency of 20% or more, 40% or more, 60% or more, 80% or more, or 90% or more. In some examples, when the system is operated in regeneration mode, the system has a regeneration efficiency of 90% or more.
  • the methods comprise: operating the system in dehumidification mode to decrease the humidity of the air from the air supply; and/or operating the system in regeneration mode to regenerate the sorbents and optionally decrease the temperature of the air. Additional advantages of the disclosed devices, systems, and methods will be set forth in part in the description which follows, and in part will be obvious from the description.
  • FIG. 1 Dehumidification and regeneration of a solid sorbent.
  • Figure 2. Water adsorption isotherms of MIL-125, KMF-1, Silica gel and Zeolite at 25°C (Data from [75], [76], [77] and [15], respectively.).
  • Figure 3. Water uptake capacity as a function of surface relative humidity for MOF and Type I & Linear isotherms.
  • Figure 5. Schematic diagram of a rotary desiccant wheel and its air streams.
  • Regeneration Efficiency as a function of regeneration temperature of model compared with experimental results of Mandegari et al.2009 [79] for inlet temperature of 35.5°C and inlet air humidity ratio of 0.011 kg/kg dry air .
  • Figure 10. Regeneration Efficiency as a function of Inlet temperature of dynamic model in comparison with experimental work of Mandegari et al.2009 [79]. Regeneration temperature is fixed at 120°C for all.
  • Figure 11. Regeneration Efficiency as a function of regeneration temperature for different MOFs at different inlet conditions.
  • Figure 13
  • FIG. 14 Dehumidification and Regeneration times in a period of 500 seconds for sorbents with linear (Silica Gel) and Type V (CAU-23) isotherm.
  • Figure 14. Sample configuration of the multi-stage system.
  • Figure 15. Dehumidification and cooling processes in single-stage and multi-stage configurations.
  • Figure 16. Water Uptake isotherms of different MOFs at 25 o C (Data references: CAU-10 [A23], CAU-23 [A24], MIL-125 [A25], MIL-125-NH2 [A26])
  • Stage step_RH descending and regeneration temperature ascending from left to right in multi-stage configurations.
  • Figure 18. Single-stage desiccant wheel (CONFIG1).
  • Figure 27 Optimal step_RH used in each stage resulting in the maximum efficiency of each stage in a multi-stage configuration (notice inverted x-axis).
  • Figure 28 Regeneration efficiency, dehumidification effectiveness, and supply humidity ratio of all configurations as a function of number of stages for the inlet humidity ratios of 0.03 kg kg -1 , 0.02 kg kg -1 , and 0.01 kg kg -1 .
  • Figure 29 Comparison of regeneration efficiency of different configurations of the current work and from the literature (Sheng et al. [A1], Enteria et al. [A3], Ali Mandegari et al. [A21], Shahvari et al. [A22]).
  • Figure 30 Comparison of regeneration efficiency of different configurations of the current work and from the literature (Sheng et al. [A1], Enteria et al. [A3], Ali Mandegari et al. [A21], Shahvari et al. [A22]).
  • “Optional” or “optionally” means that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where the event or circumstance occurs and instances where it does not. Ranges can be expressed herein as from “about” one particular value, and/or to “about” another particular value. By “about” is meant within 5% of the value, e.g., within 4, 3, 2, or 1% of the value. When such a range is expressed, another aspect includes from the one particular value and/or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another aspect.
  • multi-stage air conditioning systems comprising a first stage in fluid communication with an air supply, the first stage comprising a first sorbent, the first sorbent having a type IV or V water sorption isotherm, a first step_RH, and a first regeneration temperature.
  • a “step_RH” is the relative humidity (RH) at which the sorbent shows a sudden increase in water uptake.
  • step_RH can be the relative humidity (RH) at which the sorbent shows an increase in water uptake of 50% or more (e.g., 75% or more, 100% or more, 125% or more, 150% or more, 175% or more, 200% or more, 250% or more, 300% or more, 350% or more, 400% or more, 450% or more, or 500% or more).
  • RH relative humidity
  • the systems further comprise a second stage in fluid communication with the first stage, the second stage comprising a second sorbent, the second sorbent having a type IV or V water sorption isotherm, a second step_RH, and a second regeneration temperature; wherein the second step_RH is less than the first step_RH; and wherein the second regeneration temperature is greater than the first regeneration temperature.
  • the systems further comprise a heat source in thermal communication with the second stage.
  • the systems can be configured to operate in a dehumidification mode and/or a regeneration mode. In some examples, the system can be configured to operate in the dehumidification mode and the regeneration more simultaneously.
  • the system can include a dehumidification portion (such as a dehumidification side), where the system is operated in a dehumidification mode, and a regeneration portion (such as a regeneration side), where the system is operated in a regeneration mode.
  • a dehumidification portion such as a dehumidification side
  • a regeneration portion such as a regeneration side
  • the first stage is configured to: receive air having a first humidity from the air supply; contact the air with the first sorbent to thereby transfer a first amount of moisture from the air to the first sorbent and decrease the moisture content of the air to a second humidity, the second humidity being less than the first humidity; and effuse the air having the second humidity.
  • the second stage is configured to receive the air having the second humidity from the first stage; contact the air with the second sorbent to thereby transfer a second amount of moisture from the air to the second sorbent and decrease the moisture content of the air to a third humidity, the third humidity being less than the second humidity; and effuse the air having the third humidity.
  • the second stage is configured to: receive air having a sixth humidity; receive an amount of heat from the heat source; contact the second sorbent with the air and the amount of heat to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air with the increased moisture content and decreased amount of heat to the first stage; and the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the first sorbent; and subsequently effuse the air.
  • the systems can further comprise a third stage in fluid communication with the second stage, the third stage comprising a third sorbent, the third sorbent having a type IV or V water sorption isotherm, a third step_RH, and a third regeneration temperature; wherein the third step_RH is less than the second step_RH; and wherein the third regeneration temperature is greater than the second regeneration temperature.
  • the third stage is present, then the heat source is in thermal communication with the third stage.
  • the third stage is configured to: receive air having the third humidity from the second stage, contact the air with the third sorbent to thereby transfer a fifth amount of moisture from the air to the third sorbent and decrease the moisture content of the air to an eighth humidity, the eighth humidity being less than the third humidity, and effuse the air having the eighth humidity.
  • the third stage is configured to: receive air having a ninth humidity; receive an amount of heat from the heat source; contact the third sorbent with the air and the amount of heat to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effusing the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to: receive the air effused by the third stage; contact the second sorbent with the air to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air having the increased humidity and decreased amount of heat to the first stage; and the first stage is configured to: receive the air having a ninth humidity; receive an amount of
  • the system can further comprise a fourth stage in fluid communication with the third stage, the fourth stage comprising a fourth sorbent, the fourth sorbent having a type IV or V water sorption isotherm, a fourth step_RH, and a fourth regeneration temperature; wherein the fourth step_RH is less than the third step_RH; and wherein the fourth regeneration temperature is greater than the third regeneration temperature.
  • the heat source is in thermal communication with the fourth stage.
  • the fourth stage is configured to: receive air having a twelfth humidity; receive an amount of heat from the source; contact the fourth sorbent with the air and the amount of heat to thereby increase the temperature of the fourth sorbent to the fourth regeneration temperature such that the fourth sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the fourth sorbent; and effuse the air having the increased humidity and decreased amount of heat to the third stage; the third stage is configured to: receive the air effused by the fourth stage; contact the third sorbent with the air to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effuse the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to:
  • the system can comprise one or more additional stages, where each subsequent stage is in fluid communication with the preceding stage, wherein each stage comprises a sorbent, the sorbent having a type IV or V water sorption isotherm, a step_RH that is less than the step_RH of the preceding stage, and a regeneration temperature that is higher than the regeneration temperature of the preceding stage.
  • the final stage of the system is in thermal communication with the heat source.
  • each of the one or more additional stages is configured to: receive air from the preceding stage, contact the air the sorbent to thereby decrease the humidity of the air, and effuse the air with the decreased humidity.
  • the final stage is configured to: receive air and receive an amount of heat from the heat source; contact the sorbent with the air and the amount of heat to thereby increase the temperature of the sorbent to the regeneration temperature such that the sorbent releases an amount of moisture into the air, thereby increasing humidity of the air, decreasing the amount of heat in the air, and regenerating the fourth sorbent; and effuse the air with the increased humidity and decreased temperature to the next stage; and said next stage is configured to: receive the air from the previous stage; contact the sorbent with the air and the amount of heat to thereby increase the temperature of the sorbent to the regeneration temperature such that the sorbent releases an amount of moisture into the air, thereby increasing humidity of the air, decreasing the amount of heat in the air, and regenerating the fourth sorbent; and effuse the air with the increased humidity and decreased temperature to the next stage (when present).
  • the step_RH of any of the stages herein can independently be 0 or more (e.g., 0.1 or more, 0.2 or more, 0.3 or more, 0.4 or more, 0.5 or more, 0.6 or more, 0.7 or more, 0.8 or more, or 0.9 or more).
  • the step_RH of any of the stages herein can independently be 1 or less (e.g., 0.9 or less, 0.8 or less, 0.7 or less, 0.6 or less, 0.5 or less, 0.4 or less, 0.3 or less, 0.2 or less, or 0.1 or less).
  • the value of step_RH for any of the stages can independently range from any of the minimum values described above to any of the maximum values described above.
  • the step_RH of any of the stages herein can independently be from 0 to 1 (e.g., from 0 to 0.5, from 0.5 to 1, from 0 to 0.2, from 0.2 to 0.4, from 0.4 to 0.6, from 0.6 to 0.8, from 0.8 to 1, from 0 to 0.9, from 0 to 0.8, from 0 to 0.7, from 0 to 0.6, from 0 to 0.5, from 0 to 0.4, from 0 to 0.3, from 0 to 0.2, from 0 to 0.1, from 0.1 to 1, from 0.2 to 1, from 0.3 to 1, from 0.4 to 1, from 0.5 to 1, from 0.6 to 1, from 0.7 to 1, from 0.8 to 1, from 0.9 to 1, from 0.1 to 0.9, from 0.2 to 0.8, from 0.3 to 0.7, or from 0.4 to 0.6).
  • 0 to 1 e.g., from 0 to 0.5, from 0.5 to 1, from 0 to 0.2, from 0.2 to 0.4, from 0.4 to 0.6, from
  • the system can further comprise one or more heat exchangers in thermal communication with the first stage, the second stage, the third stage (when present), the fourth stage (when present), the one or more additional stages (when present) or a combination thereof.
  • the first stage, the second stage, the third stage (when present), the fourth stage (when present), and the one or more additional stages (when present) can each independently comprise a rotary desiccant wheel.
  • the sorbent can be housed in a rotating wheel that moves the sorbent between the supply stream and regeneration stream.
  • the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can each independently comprise any suitable material.
  • the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can each independently comprises a metal-organic framework (MOF).
  • MOF metal-organic framework
  • Examples of metal-organic frameworks are described in the art, such as in Moosavi et al., “Understanding the diversity of the metal-organic framework ecosystem,” Nat Commun, vol.11, no.1, pp.1–10, 2020, which is hereby incorporated herein for its description of metal-organic frameworks.
  • the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can each independently comprises a metal-organic framework (MOF), wherein the metal comprises Al, Ti, Zr, Co, or a combination thereof.
  • MOF metal-organic framework
  • one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise an Al-based MOF.
  • one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MIL-100, MIL-101, HKUST-1, ISE-1, Basolite C300, Basolite A100, DUT-67(Zr), UiO-66, UiO-67, NU-1000, MOF-801, CPO-27(Ni), CAU-1, CAU-1(OH)2, CAU-3, CAU-3-NH2, CAU-8, CAU-10H, MIL-53, MIL-53-NH2, MIL-125, MIL- 125-NH 2 , MIL-140A, MIL-140C, UiO-66, ZIF-8, Ni-MOF-74, Co-MOF-74, MIL-53, Fe-BTC, Cu-BTC, Aluminum fumarate, DUT-67, MIL-96(Al) and MIL-100(A
  • one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MOF-841, MIL-101 (Cr), In-MIL-68, KMF-1, In-MIL-68-NH 2 , MOD- 801-P, CAU-10-H, CAU-23, MIL-160, Ti-MIL-125-NH2, CAU-10, CAU-23, Al-fumarate, KMF-1, MIL-125-NH 2 , MIL-125, MOF-841, Co 2 Cl 2 (BTDD), or a combination thereof.
  • one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MOF-841, MIL-101 (Cr), In-MIL-68, or a combination thereof.
  • one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise KMF-1, MOF-841, In-MIL-68-NH2, or a combination thereof.
  • one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MOF-801-P, CAU-10-H, CAU-23, or a combination thereof.
  • one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MIL-160, Ti-MIL-125-NH2, MOF-841, or a combination thereof.
  • one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise CAU-10, CAU-23, Al-fumarate, KMF-1, MIL-125-NH 2 , MIL-125, MOF-841, Co2Cl2(BTDD), or a combination thereof.
  • one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MOF-841, Co 2 Cl 2 (BTDD), Al-fumarate, CAU-23, or a combination thereof.
  • the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can each independently undergo multiple water sorption/desorption cycles without significant loss in performance.
  • the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can each independently be stable, lack hysteresis, be low cost, have a high water uptake capacity, or a combination thereof.
  • the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), the fourth regeneration temperature (when present), and the one or more additional regeneration temperatures (when present) can each independently be from 0°C-140°C.
  • the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), the fourth regeneration temperature (when present), and the one or more additional regeneration temperatures (when present) can each independently be 0°C or more (e.g., 20°C or more, 40°C or more, 60°C or more, 80°C or more, 100°C or more, or 120°C or more).
  • the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), the fourth regeneration temperature (when present), and the one or more additional regeneration temperatures (when present) can each independently be 140°C or less (e.g., 120°C or less, 100°C or less, 80°C or less, 60°C or less, 40°C or less, or 20°C or less).
  • the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), the fourth regeneration temperature (when present), and the one or more additional regeneration temperatures (when present) can each independently range from any of the minimum values described above to any of the maximum values described above.
  • the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), the fourth regeneration temperature (when present), and the one or more additional regeneration temperatures (when present) can each independently be from 0 to 140°C (e.g., from 0°C to 70°C, from 70°C to 140°C, from 0°C to 40°C, from 40°C to 80°C, from 80°C to 140°C, from 0°C to 120°C, from 0°C to 100°C, from 0°C to 80°C, from 0°C to 60°C, from 0°C to 40°C, from 20°C to 140°C, from 40°C to 140°C, from 60°C to 140°C, from 80°C to 140°C, from 100°C to
  • the air supply comprises ambient air, such as outdoor or exterior air.
  • the methods can comprise operating the system in dehumidification mode to decrease the humidity of the air from the air supply; and/or operating the system in regeneration mode to regenerate the sorbents and optionally decrease the temperature of the air.
  • the system and/or methods can have a regeneration efficiency of 20% or more (e.g., 30% or more, 40% or more, 50% or more, 60% or more, 70% or more, 80% or more, 90% or more, 95% or more, or 99% or more).
  • the system and/or methods when the system is operated in the regeneration mode, can have a regeneration efficiency of 90% or more. In some examples, the system and/or methods can have a regeneration efficiency approaching 100%.
  • a number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims.
  • the examples below are intended to further illustrate certain aspects of the systems and methods described herein, and are not intended to limit the scope of the claims. EXAMPLES The following examples are set forth below to illustrate the methods and results according to the disclosed subject matter. These examples are not intended to be inclusive of all aspects of the subject matter disclosed herein, but rather to illustrate representative methods and results.
  • Dehumidification systems including desiccant wheels and/or liquid sorbent systems are used in many different HVAC devices.
  • the sorbents employed in these devices have linear or shallow Type I or II water sorption isotherms which means an external energy input at high temperatures is required to regenerate the sorbent sufficiently to allow it to be used efficiently in a cycle, precluding the use of low-temperature heat sources.
  • Metal Organic Frameworks are a class of sorbents with Type IV or V water uptake isotherms featuring a steep adsorption step.
  • FIG. 1 shows a schematic of the dehumidification and regeneration processes for a solid sorbent.
  • the dehumidification process humid outdoor air passes over the surface of a solid sorbent, where the humidity difference between the humid air and the air in equilibrium with the sorbent surface creates a driving force for moisture transfer from the humid air to sorbent surface, decreasing the humidity of the air and increasing the water content of the sorbent.
  • the dehumidification process continues until the equilibrium humidity of sorbent is increased to the process air humidity and no driving force for moisture transport exists.
  • the sorbent needs to be regenerated by an increase in temperature, resulting in a driving force for moisture transfer from sorbent surface to the air.
  • the improvements sorbents offer for humidity control and efficiency of air conditioning systems are well documented [1]–[8].
  • the inorganic sorbents e.g., silica gel, zeolites, aqueous lithium chloride [9]–[13]
  • the inorganic sorbents typically employed in sorbent wheels or advanced liquid sorbent-enhanced systems have water sorption behavior such that high-temperature external energy is required to regenerate the sorbent sufficiently to allow it to be used efficiently in a cycle. This precludes the use of low-temperature heat sources for regeneration.
  • MOFs are a relatively new class of three-dimensional coordinated polymer sorbents comprised of a metal ion and organic linker in highly structured repeating form that results in a Type IV or V water uptake isotherm, discussed further below.
  • MOFs have also been shown to have tunable adsorption steps via replacement of either the metal ion or organic linker [25], and ability to simultaneously adsorb gaseous pollutants such as formaldehyde [26]– [34], benzene [35]–[37], and other volatiles [38], [39].
  • the isotherm shape is one of the primary differences between the class of MOF sorbents and commonly used inorganic sorbents such as zeolites and silica gel, as shown in Figure 2.
  • MOF sorbents have isotherms characterized by a steep jump, as shown for MIL-125 and KMF-1 in Figure 2, usually referred to as Type IV or V isotherms (this isotherm shape will be referred to as MOF isotherms from here forward).
  • commonly used inorganic sorbents such as zeolites have Type I isotherms characterized by monotonic increase in moisture content and then saturation (referred to as Type 1 isotherms from here forward).
  • Silica gel has a linear isotherm, characterized by near-linear relationship between air humidity and sorbent water content (referred to as linear isotherms from here forward).
  • linear isotherms For the purposes of demonstrating the effect of the isotherm shape on operation of sorbent-based dehumidification systems, Figure 3 shows idealized isotherms of each type-Type I, linear, and MOF (Type IV or V), assuming equal maximum water uptake capacities for all. Each of these three is idealized and exaggerated for the purposes of identifying their salient features.
  • the isotherm shape determines several secondary properties of sorbents, which are discussed presently. Maximum water uptake capacity, working capacity and required regeneration temperature. The isotherm shape directly determines the sorbent’s maximum water uptake capacity.
  • the maximum water uptake capacity is usually defined as the mass of water adsorbed per mass of sorbent when the relative pressure (partial pressure of water vapor divided by saturation vapor pressure) of air in equilibrium with the sorbent surface is 100%.
  • the working capacity of a sorbent is usually smaller than its maximum capacity depending on 1) the desired humidity under the application conditions and 2) the temperature at which the sorbent is regenerated.
  • the working capacity of a sorbent ( ⁇ ⁇ ) is defined herein as the difference in mass of adsorbed water (water content) between the dry and wet states of the sorbent during normal operation [78], as shown in Figure 3.
  • maximum capacity and working capacity can differ greatly, especially at low regeneration temperatures and especially for sorbents with shallow linear or near linear isotherms.
  • FIG 3 This is one key to the improved performance of the MOFs in such systems, as shown in Figure 3.
  • three different air states are plotted as vertical dashed lines: ambient air on a typical day (50% relative humidity); the same air heated to a low regeneration temperature (causing RH to decrease moderately); and the same air heated to a high regeneration temperature (causing RH to decrease substantially).
  • ambient air on a typical day 50% relative humidity
  • the same air heated to a low regeneration temperature causing RH to decrease moderately
  • the same air heated to a high regeneration temperature causing RH to decrease substantially.
  • the sorbent will dry to the point that its equilibrium relative humidity matches that of the air it is in equilibrium with (regeneration air). The degree to which this drying occurs determines the working capacity of the sorbent.
  • the working capacity of the Type V isotherm sorbent approaches its maximum capacity, because for an idealized, steep Type V isotherm, the degree to which the sorbent is dried is nearly a binary function of the temperature at which it is regenerated.
  • sorbents having a linear isotherm will have an effective working capacity that is a continuous function of the regeneration temperature rather than a binary function. While the working capacity is increased as the regeneration temperature is increased, the working capacity is smaller than the maximum capacity both at low and high regeneration temperatures.
  • the sorbent is typically housed in a rotating wheel that moves between supply and regeneration streams, as shown in Figure 5. 4. Regeneration occurs via heating the air entering the regeneration side of the wheel, rather than, for example, heating the sorbent itself.
  • Erkek et al. [73] simulated a small-scale sorbent coated heat exchanger to evaluate the performance of silica gel in comparison to a specific type of MOF (Aluminum Fumarate). Their results showed that under the same operating conditions, the heat exchanger coated with Aluminum Fumarate had greater dehumidification capacity by 8%, greater regeneration capacity by 11% and greater working capacity by 41% over the silica gel-coated heat exchanger. Xu et al.
  • [74] modeled a sorbent coated heat exchanger and compared the performance of silica gel and a specific MOF (Cu-BTC (HKUST-1)) as the sorbent.
  • the MOF-coated heat exchanger showed enhanced performance compared to the silica gel-coated heat exchanger although the MOF chosen in their system (HKUST-1) had a lower water uptake capacity compared to silica gel in high relative humidity.
  • Very little work has been done to systematically investigate how MOFs can benefit direct-air-contact sorbent dehumidification systems. To this end, the overarching motivation of this work is to systematically articulate the advantages conferred by MOFs to sorbent-based dehumidification wheels used in buildings.
  • a first-principles physical model of a sorbent wheel is developed, parameterized in such a way that it can take different sorbent isotherms as input and validate this model.
  • the validated model is used to quantify the benefits to the system of a number of selected MOFs that have been described in the literature, in terms of system performance and energy requirements.
  • the ideal MOF is identified for dehumidification in terms of regeneration energy requirement and performance, and regeneration temperature. Methodology.
  • a first-principles dynamic model of a sorbent dehumidification and regeneration system was first created and it was validated with experimental data from the literature.
  • the model heat and mass transfer coefficients, geometry, inlet conditions, and airflow rates are defined identical to the experimental work of [79].
  • the diameter of the wheel is 32 cm with a length of 20 cm, and hydraulic diameter of 2.1 mm.
  • the mass flow rates of process and regeneration air are 0.185 and 0.066 kg/s, respectively.
  • the rotational speed of the wheel and ratio of dehumidification/regeneration sections was optimized for each sorbent such that regeneration began immediately after the sorbent became “full” (at its working capacity) and stopped when the sorbent equilibrium humidity was that of the regeneration air.
  • the assumptions made to simulate the dehumidification and regeneration channels are as follows: - Dehumidification and regeneration channels are perfectly sealed and insulated, and no heat and mass transfer occur with the ambient.
  • a general form of the Type V isotherm can be idealized as three piecewise defined linear functions and described by five parameters: the relative humidity at the adsorption step (step RH), three slopes (m1, m2, m3) and maximum capacity as shown on Figure 6.
  • an isotherm relates equilibrium humidity to water uptake at a single temperature (hysteresis between adsorption and desorption isotherms is not modeled because for the MOFs chosen for this study no significant hysteresis has been reported [58], [72], [81]–[85].)
  • the Polanyi [86] and Dubinin [87] adsorption potential model was used, which relates water adsorption potential (AP) of any adsorbent to its surface temperature (T), equilibrium vapor pressure (p) and saturation vapor pressure (p 0 ) as shown in Equation 5.
  • Equation 6 Another influential parameter in the heat transport model is the heat of adsorption ( ⁇ ⁇ ⁇ ⁇ ), which varies based on sorbent and is a function of the water adsorption isotherm. Based on the Dubinin–Astakhov approach explained in the work of D. Lenzen et al. [82], the heat of adsorption or isosteric heat can be calculated using Equation 6 in which h ⁇ ⁇ ⁇ is the water heat of vaporization and ⁇ ⁇ is the adsorption potential.
  • Equation 6 is used to calculate the heat of adsorption in the numerical simulation by making heat of adsorption another output of the isotherm class.
  • the isotherm parameters, temperature of the surface, and water content are provided as input and surface humidity ratio and heat of adsorption are given as outputs.
  • the regeneration efficiency ( ⁇ ⁇ ⁇ ⁇ ) was defined as the ratio of moisture removal rate multiplied by heat of adsorption (minimum energy needed to remove moisture) divided by the regeneration power input, as shown in Equation 7.
  • Moisture removal power and can be calculated as shown in Equation 8, assuming the number of adsorption/desorption cycles per second ( ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ) is known.
  • the sorbent water uptake in each cycle is equal to the sorbent mass ( ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ) multiplied by the integral of sorbent working capacity ( ⁇ ⁇ ) over the time of one cycle ( ⁇ ⁇ ).
  • Equation 9 represents the least amount of power needed to get the sorbent to its regeneration temperature.
  • Isotherm shapes determine two influential terms in the regeneration efficiency formulation: the working capacity of the sorbent which is a function of isotherm shape as explained above; and the time needed for regeneration and dehumidification in each cycle. This latter variable is a function of the driving forces for moisture transfer, which in turn are a strong function of isotherm shape as explained below. The mechanisms of influence of these two terms in the performance of the system with different sorbents is explained in greater detail in the results and discussion section. Selection of MOF candidates for performance evaluation. A number of metal organic frameworks described in the literature were selected to evaluate their performance as sorbents in sorbent wheels under a variety of outdoor conditions.
  • MOFs containing aluminum nodes have shown desirable characteristics in the literature including high stability of water adsorption properties, low cost of production, and green and non-toxic nature [96].
  • MOFs containing aluminum nodes have shown desirable characteristics in the literature including high stability of water adsorption properties, low cost of production, and green and non-toxic nature [96].
  • Some of these MOFs include: ⁇ CAU-10: A layer of CAU-10 coated on a metallic layer placed on a heat exchanger plate has shown stability under over 10,000 adsorption/desorption cycles with temperatures ranging from 20 to 120°C. A minimum regeneration temperature of 70°C was reported to be sufficient to completely dry the material [81].
  • ⁇ CAU-23 (Al) another type of Al-based MOF has shown stability under a minimum of 5,000 adsorption/desorption cycles between 20 and 120°C, both in powder form and non- crystalline CAU-23-coated aluminum sheets, as well as a thermal stability under temperature as high as 400°C [82].
  • ⁇ Another Al-based MOF, Al-fumarate (Al) has shown to be stable under 4,500 adsorption/desorption cycles between 20°C and 125°C with a minimum regeneration temperature of 65°C reported [58].
  • ⁇ MIL-160 (Al) is another Al-based MOF which is expected to have long-term stability similar to other Al-based MOFs such as CAU-10, since the cyclability tests of MIL-160 have not shown any weight loss change between the second cycle and greater [72].
  • This MOF and CPO- 27 (described below) have nearly Type 1 isotherms. We include them to demonstrate the difference in performance of these different isotherm shapes.
  • ⁇ KMF-1 (Al) is also an Al-based MOF with green and high-yield synthesis and stable over at least the 50 adsorption/desorption cycles and a regeneration temperature of 70°C and lower [76].
  • MOFs were chosen for evaluation including: ⁇ MIL-125-NH 2 (Ti), with a reported stability measured under multiple adsorption/desorption cycles (between 313 to 383 K) showing that the water uptake capacity changed slightly after the first cycle but remained constant afterwards and a regeneration temperature of 348 K (75°C) [83]; ⁇ MIL-125 (Ti), exhibiting a similar shape to MIL-125-NH2; ⁇ MOF-841 (Zr), which has shown robust water adsorption stability after at least 5 cycles [97]; ⁇ CPO-27 (Ni) which has shown only 0.35% degradation of water adsorption after 10 cycles but requires a high regeneration temperature (which is expected due to the low step RH) [85] (nearly Type 1 isotherm, included for contrast as mentioned above); and ⁇ Co2Cl2(BTDD) (Co) which is stable over 30 cycles and has a water uptake capacity of 1 gr/gr which is more than twice the capacity of other MOFs [95].
  • the sorbent surface equilibrium humidity needs to be increased to a greater humidity for regeneration, compared to the case where the regeneration air stream is less humid. This requires a greater regeneration temperature in the more humid environment for the same sorbent, assuming that pure ambient air is used for regeneration.
  • different MOFs with different locations of Step Relative Humidity will result in different system performances.
  • the selected MOFs were examined under a variety of ambient (inlet) conditions and regeneration temperatures. The selected ambient conditions and regeneration temperatures are shown in Table 2. Table 2. Inlet conditions and regeneration temperature used in each case study.
  • Figure 10 shows the comparison between the model results for regeneration efficiency and experimental results of [79] for two inlet conditions of dry and humid and inlet temperature range of 27 to 47°C. Both figures show an acceptable error between the results of the model and experiments of [79].
  • Performance results for selected MOFs In this section, the results of the simulations are presented to evaluate the effect of sorbent isotherm parameters on the performance of the dehumidification/regeneration system for the selected MOFs mentioned in Table 1 and four different inlet conditions and regeneration temperatures shown in Table 2. Effect of regeneration temperature. As mentioned, one expected benefit of MOFs is their ability to be regenerated at low temperatures compared to traditional sorbents.
  • Figure 11 shows regeneration efficiency results as a function of regeneration temperature for different MOFs, in comparison with silica gel.
  • step RH Effect of inlet air humidity.
  • step RH Effect of relative humidity of the water adsorption step
  • MOFs are sorted with step RH increasing from left to right.
  • Minimum regeneration temperature is plotted as black dots for each MOF and each inlet condition. It can be seen that as step RH increases, minimum regeneration temperature decreases, and regeneration efficiency at the minimum temperature increases.
  • Figure 12 shows that at an inlet air humidity of 0.015 kg/kg dry air (a moderate ambient humidity), MOFs with step RH of 28% and greater (which include Al-Fumarate, Co2Cl2(BTDD) and CAU-23) can be regenerated at a temperature as low as 40°C. This makes these MOFs ideal candidates for regeneration with a low-temperature heat source such as inexpensive solar thermal or waste heat.
  • Table 3 the performance of the MOFs is categorized based on their step RH. Table 3.
  • Optimal Regeneration temperature for each MOF category.
  • MOF category * % The changes in regeneration efficiency with isotherm shape are a function of the three energy end-uses described above: sorbent heating, exhaust air losses, and moisture removal energy. The proportion of energy use attributable to each of these is a function of two intermediate variables: amount of time spent in each adsorption and desorption cycle, and the amount of moisture adsorbed and desorbed in each cycle. These two variables interact with the effects of regeneration temperature and ambient conditions to produce the behavior shown in Figure 11, which is explained mechanistically below. Regeneration temperature. Scavenging air losses and sorbent heating losses decrease when regeneration temperature decreases, resulting in greater regeneration efficiency.
  • minimum regeneration temperature is a strong function of step RH.
  • a MOF with a greater step RH will have a greater equilibrium humidity (and thus a great moisture driving force into regeneration air) than its counterpart with a lower step RH. This means it can be regenerated at a lower temperature.
  • Figure 11 shows CPO- 27 and MIL-160 (with step RH’s of 1% and 3%, respectively, approaching the behavior of zeolites or other sorbents with Type I isotherms), cannot be regenerated at temperatures where MOFs with greater step RH such as Co2Cl2(BTDD) and CAU-23 can be regenerated.
  • Working Capacity As shown in Figure 12, minimum regeneration temperature is a strong function of step RH.
  • Figure 13 shows that CAU-23 is capable of adsorbing a larger quantity of water in the dehumidification process even though its maximum capacity is nearly identical to that of Silica Gel. This is due to the differences in working capacity described above. Both of these lead to greater regeneration efficiency for CAU-23 than silica gel.
  • Figure 13 also compares the dehumidification and regeneration times of silica gel and CAU-23 for a period of 500 seconds. The regeneration time of CAU-23 is shorter compared to silica gel. Regeneration efficiency is strongly affected by the time needed to adsorb (or desorb) the working capacity of water.
  • step RH determines the moisture transport driving force in the regeneration and dehumidification processes. This is one of the main differences between a linear and a Type V isotherm as explained above. For a MOF with a greater step RH, the humidity difference between the surface equilibrium and regeneration air stream is greater, resulting in a faster regeneration process and thus a lower scavenging air exhaust loss (less scavenging air needs to be used for regeneration). This is one reason for the increase in regeneration efficiency with step RH shown in Figure 12.
  • MOF isotherms over those of sorbents traditionally used in desiccant systems are as follows: - With identical maximum water capacities, properly selected MOF sorbents can absorb more moisture than linear-shaped sorbents due the steep water uptake step, especially at lower regeneration temperatures. - MOF sorbents maintain a fairly constant surface humidity ratio during the moisture transfer process which results in a faster regeneration process and less energy loss compared to linear sorbents. Depending on relative humidity at which the water uptake step occurs, sorbents exhibiting MOF isotherms can be regenerated at a much lower temperature than those with linear or Type I isotherms.
  • MOF-based dehumidification/regeneration system can have a regeneration efficiency of two to ten times greater than silica gel-based systems, depending on inlet conditions.
  • MOF-841 Zr
  • Co 2 Cl 2 BTDD
  • Co Co
  • Al-fumarate Al-fumarate
  • CAU- 23 Al
  • Step RH 22%, 29%, 28% and 29%, respectively.
  • Table 4 summarizes the maximum regeneration efficiency corresponding to each of these MOFs at each of the four inlet conditions and the regeneration temperature at which the maximum regeneration efficiency occurs. Table 4.
  • Bin Dong “Cu(i)-MOF: Naked-eye colorimetric sensor for humidity and formaldehyde in single-crystal-to-single-crystal fashion,” Chem. Commun., vol.50, no.12, pp.1444–1446, Jan.2014. [27] E. X. Chen, H. Yang, and J. Zhang, “Zeolitic imidazolate framework as formaldehyde gas sensor,” Inorg. Chem., vol.53, no.11, pp.5411–5413, Jun.2014. [28] N.
  • Bin Ismail “A Universal Isotherm Model to Capture Adsorption Uptake and Energy Distribution of Porous Heterogeneous Surface,” Sci. Rep., vol.7, no.1, Dec.2017. [89] A. Cadiau et al., “Design of Hydrophilic Metal Organic Framework Water Adsorbents for Heat Reallocation,” Adv. Mater., vol.27, no.32, pp.4775–4780, Aug.2015. [90] M. F. De Lange, T. Zeng, T. J. H. Vlugt, J. Gascon, and F.
  • the humidity ratio of the supply can be decreased as much as desired, without the need for a very high regeneration temperature, as just a small portion of water is adsorbed on the MOF with small Step RH compared to a system where only one single MOF with small Step RH is used and all the moisture removed from air is adsorbed to that single MOF.
  • air exiting each stage can be cooled down to near ambient temperature using an air-to-air heat exchanger. This in turn will provide the opportunity to achieve a much lower humidity ratio as the heat of adsorption is removed in each process and so the humidity ratio of the MOF surface can be lower.
  • a multi-stage configuration can approach an isothermal dehumidification process which is more efficient than a constant enthalpy process that occurs in a single-stage configuration.
  • a multi-stage configuration can provide supply air with lower humidity ratio which in turn results in a colder supply leaving the indirect evaporative cooling (IEC) side, with a lower power required for regeneration.
  • Figure 14 shows a sample configuration of the multi-stage system, where four different dehumidification wheels are used, each containing one MOF with a different Step RH. From left to right, which is in the direction of the flow, the Step RH of the MOFs decrease.
  • the number of the dehumidification wheels and the values of the Step RH of the MOFs is dependent on the desired humidity ratio at the supply and can be tuned based on that.
  • the MOF with a smaller Step RH requires higher regeneration temperature, so from left to right, the temperature of the regeneration air should be increased.
  • Figure 15 compares the dehumidification and cooling processes of a single-stage dehumidification wheel of a small Step RH MOF with the dehumidification process in a multi- stage dehumidification wheel system. As shown in Figure 15 the multi-stage configuration can provide a lower humidity ratio in supply air which in turn will result in achieving a much lower temperature in the IEC side.
  • the multi-stage system both provides a drier and cooler supply and requires lower energy for the regeneration.
  • all the required mass flow rate of regeneration air should be provided at the highest regeneration temperature, while in the multi-stage configuration, only a small portion of the total regeneration air mass flow rate should be at the highest regeneration temperature which in turn results in a higher COP of the multi-stage system.
  • Table 5 Coefficient of performance for single-stage and multi-stage configurations.
  • a system that derives most, nearly all, of the energy needed to drive the cycle from the air being conditioned, thus removing the need for all but a small amount of external energy input.
  • This is made possible by staging adsorption of moisture in multiple types of MOFs with steps in their respective Type 5 isotherms located at relative humidity values that decrease with each stage. Alternating sensible heat exchangers are placed in between each stage, removing the heat of adsorption and using it for regeneration of the next stage MOF. This eliminates or nearly eliminates the need to add external energy to regenerate the MOF (the main energy input to the original system) for all but the very first stage.
  • Example 4 Approaching theoretical maximum energy performance for desiccant dehumidification using staged and optimized metal-organic frameworks Abstract.
  • Dehumidification systems including desiccant wheels are widely used in commercial and a few residential air conditioning systems to remove latent loads. These wheels require high-temperature heat to regenerate and are often quite inefficient, with a typical single- pass efficiency of around 20%.
  • a desiccant wheel system takes advantage of the unique behavior of metal-organic frameworks (MOF) sorbents. It is shown that for any given entering air condition, there exists an optimal MOF that if included in the dehumidification systems will results in maximum efficiency. Based on this idea, a multi-stage dehumidification system is developed in which each stage uses the optimal MOF. To do so, first a MOF-based desiccant wheel system was mathematically modeled and validated, which was then used to systematically identify an optimal MOF isotherm shape as a function of inlet air conditions. with the model is then extended to different multi-stage MOF-based desiccant wheel systems which are optimized to achieve energy performance far exceeding a single-desiccant wheel.
  • MOF metal-organic frameworks
  • a validated discretized dynamic model is used to compare the energy needed for operation of these systems with other possible configurations.
  • an optimized staged MOF system can approach the theoretical maximum energy performance for desiccant dehumidification, using nearly 100% of regeneration energy for desorption of water and wasting very little.
  • the results also show that a multi-stage MOF-based dehumidification system can have a regeneration efficiency 2 to 5 times greater than a single-stage system. Adding adsorption heat removal stages between the desiccant wheel stages can increase the regeneration efficiency by 5-20%, and the dehumidification effectiveness of the system 20-40%.
  • Desiccant-based dehumidification systems employing solid desiccant wheels, and increasingly liquid desiccant systems, are widely used in commercial and a few residential air conditioning systems to remove these latent loads [A1]-[A10].
  • the improvements in humidity control and of air conditioning efficiency offered by desiccants are well documented [A7], [A9], [A11]-[A16], [A17]-[A20].
  • the primary energy input in a desiccant system is the heat needed to regenerate the desiccant.
  • Regeneration efficiency compares the energy used to desorb moisture (useful energy) to the total amount of energy used (including losses). Regeneration efficiency is also called DCOP or Latent COP in the literature. In this work, the term “regeneration efficiency” is used and is formally defined in Equation A9, except when referring to the work of others in which case we use their terminology- the definitions are identical.
  • the regeneration efficiency would be equal to 1, meaning that the energy required for regeneration of the desiccant is exactly equal to the latent heat removed from the conditioned air.
  • the regeneration efficiency is less than 1.
  • Sheng et al. reported a DCOP value between 0.2 to 0.28 for a silica gel-based desiccant wheel for a regeneration temperature range of 58-65 o C, and for outdoor humidity ratios of 0.01-0.02 kg/kg [A1]. Enteria et al.
  • MOFs Metal Organic Frameworks
  • A22 Metal Organic Frameworks
  • a MOF-based desiccant wheel can have a regeneration efficiency in the range of 0.32-0.42 with a regeneration temperature of 40-60 o C, and for inlet humidity ratio of 0.015 to 0.035 kg/kg [A18].
  • the improved efficiency of the MOFs analyzed by Shahvari et al. is attributable to their water uptake behavior [A22], which is most often discussed with reference to their water uptake isotherms.
  • Figure 16 shows the water uptake isotherm of a number of MOFs.
  • the most prominent feature of these isotherms is that at a specific relative humidity, there is a sudden increase in the water uptake, characteristic of a Type V isotherm using Brunauer’s classification system [A27].
  • Shahvari et al. refer to the humidity at which this sudden increase occurs as “step_RH” [A22], and showed that performance of a MOF-based wheel is a strong function step_RH, and that this function changes for different inlet conditions.
  • Step_RH affects MOF wheel performance in two ways.
  • a lower MOF step_RH means that the air can be dried more deeply, since the MOF step_RH defines the minimum humidity ratio that can be achieved using that MOF.
  • step_RH reduces the moisture transport driving force in the regeneration side of the wheel, resulting in greater dehumidification time and thus more energy use.
  • MOFs have been studied for several applications in building indoor environmental control [A30], adsorption- driven heat transformation [A31], and air dehumidification via desiccant-coated heat exchangers [A32]-[A35], and desiccant wheel systems [A36]-[A39].
  • Table 6 summarizes previous work that has explored the application of MOFs for different air conditioning applications.
  • the application of MOFs as the desiccant material in a multi-stage dehumidification system the focus of the current work, has not yet been studied, and because of the unique properties of MOFs, such a system can be expected to be qualitatively different than any system previously studied. Table 6.
  • multi-stage MOF-based dehumidification systems can offer important advantages over either a single-stage configuration or a multi-stage configuration that uses common desiccants such as silica gel, such as those analyzed in all previous works.
  • Table 7. The salient features of previous works on multi-stage dehumidification.
  • Ref. Application Sorbent Type Number of Stages Approach [A63] Water Harvesting Silica Gel 1, 2, 4, 5 Mathematical Modeling on dehumidification performance, and how they related to MOF isotherm properties, were articulated [A22]. In this work, this understanding is used to: 1. First systematically identify optimal MOF properties for given operating conditions. 2.
  • the staged-MOF system proposed in this work is comprised of a series of desiccant wheels each having a MOF with a specific step_RH.
  • the first wheel that air enters is the wheel containing the MOF with the greatest step_RH, as shown in Figure 17. Air is dried in this wheel, then it passes to the next wheel containing a MOF with a smaller step_RH, where it is dried further.
  • the regeneration air is only heated up once before it enters the last stage (Stage N in Figure 17) moving in counterflow to the process air.
  • the exhaust of Stage N now slightly cooler than when it entered Stage N, is used to regenerate Stage N-1, and so on, as shown in Figure 17.
  • One is a separated multi-stage system (CONFIG3, Figure 20) in which each wheel can move with a different speed and this speed can be optimized for the specific MOF step_RH used in that stage. 4)
  • the other is the separated multi-stage system with adsorption heat removal stages between the dehumidification stages (CONFIG4, Figure 21).
  • Such system makes it possible to remove the heat of adsorption from the air exiting each stage.
  • CONFIG2, CONFIG3, and CONFIG4 the effect of varying the number of stages in from 2-7 stages was investigated.
  • Model development In order to model the configurations above, a first-principles dynamic model of a single desiccant wheel was developed.
  • the inputs to this model are the desiccant (MOF or any other type) isotherm parameters, inlet temperature and humidity, air flow rates, geometrical properties, and the wheel speed.
  • the model then outputs several variables for performance evaluation, including the temperatures and humidity of different air streams at different locations as a function of time.
  • the desired number of these desiccant wheel models were also connected in series which made the multi-stage configurations.
  • the Modelica language was used for performing the dynamic simulations of the model. For the calculation of heat and mass transfer coefficients, geometrical properties, and inlet airflow rates the work of Gao et al. [A72] was referred to.
  • the diameter of each wheel was selected to be 50 cm with a channel length of 20 cm, width of 2 mm, and wall thickness of 0.125 mm.
  • the velocity of the process air stream was 2.8 m s -1 .
  • the rotational speed of the wheel and ratio of dehumidification/regeneration sections ( ⁇ ) was optimized during the optimization process.
  • ⁇ For the composite multi-stage configuration (CONFIG2), wheels containing different MOFs, move with equal speeds, while in the separate multi-stage configuration (CONFIG3) the speed of each wheel is optimized during the optimization process.
  • CONFIG2 composite multi-stage configuration
  • CONFIG3 separate multi-stage configuration
  • Equations A1-A4 show the transient coupled heat and mass transfer equations based on the above assumptions. The coupled heat and mass transfer equations were discretized along the length of the channel ( Figure 22). In the course of the simulations, the system of equations was then solved for each discrete element.
  • ⁇ is the temperature
  • ⁇ is the humidity ratio
  • ⁇ ⁇ is the cross-sectional area of the channel
  • ⁇ ⁇ ⁇ is the channel perimeter
  • ⁇ h ⁇ thickness of the channel wall
  • ⁇ h ⁇ thickness of the air layer in the channel
  • ⁇ ⁇ is the isosteric heat of adsorption.
  • MOF type V isotherms used in this work are ideal, very steep isotherms shown in Figure 23. It should be mentioned that since the isotherm model used is a general, ideal Type V isotherm, it can represent any sorbent that possesses a Type V isotherm, and the results of the simulations are not limited to MOFs. However, since MOFs are one of the most prominent sorbents with Type V isotherms and there is a vast library of MOFs (about 90,000 MOF have been identified and 500,000 predicted to date [A28]), the ideal type-V sorbent modeled herein will be referred to as “MOF” throughout the rest of this description.
  • Step_RH of a MOF mostly depends on pore size and hydrophilicity. More hydrophilic MOFs generally exhibit a lower Step RH, but the position of water uptake step is a stronger function of the pore diameter [A73]. At any given temperature there exist a critical pore diameter above which the pore filling process becomes irreversible due to the capillary condensation occurring in the pores [A74]. This results in hysteresis between absorption and desorption isotherms in some MOFs with Type V isotherm.
  • Equation A5 ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ 5 ⁇
  • ⁇ represents the Sigmoid function defined in Equation A6.
  • This isotherm equation is inputs are isotherm parameters, and as a function of temperature and water uptake.
  • Equation A7 water adsorption potential (AP) of any desiccant to its surface equilibrium vapor pressure (p), temperature (T), and saturation vapor pressure (p 0 ) using Equation A7: ⁇ ⁇ ⁇ ⁇ , ⁇ ⁇ ⁇ ⁇ ⁇ ln ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ 7 ⁇ in which R is the universal gas one temperature to another.
  • R is the universal gas one temperature to another.
  • the isosteric heat of adsorption ( ⁇ ⁇ ) is also a function of the isotherm shape of the desiccant.
  • ⁇ ⁇ is defined as the moisture removal capacity over the regeneration heat input as shown in Equation A9: ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ 9 ⁇ where the moisture removal the rate at which the heat of desorption is consumed in occur and is calculated using Equation A10: ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ 10 ⁇ in which ⁇ ⁇ is the is the humidity ratio of the inlet air, and ⁇ ⁇ is the humidity ratio of the outlet air dry air leaving the wheel.
  • the total amount of heat input into the system to accomplish the regeneration ( ⁇ ⁇ ⁇ ) is calculated by Equation A11: ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ h ⁇ ⁇ h ⁇ ⁇ 11 ⁇ in which ⁇ ⁇ is the mass flow rate of the air h ⁇ is the of the hot regeneration air entering the the ambient air that is used for regeneration after heating up.
  • the regeneration heat input ( ⁇ ⁇ ⁇ ) is actually comprised of two constituent parts: the useful component and losses.
  • the useful component is the heat required to remove the moisture from the desiccant in each dehumidification/regeneration cycle, which is a function of the heat of adsorption as shown in Equation A12: ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ 12 ⁇ ⁇ where ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ is capacity, or, in other words, water dehumidification time and the water uptake of the sorbent leaving the regeneration side, and ⁇ ⁇ ⁇ ⁇ is the dehumidification time [A77]. Losses from the regeneration process can occur via two mechanisms. One is the energy lost in the hot exhaust air stream.
  • Equation A13 shows how this loss is calculated: ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ A13 ⁇ where ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ is ambient temperatures, respectively, ⁇ ⁇ is the air specific heat capacity, and ⁇ ⁇ is the regeneration time in each cycle.
  • a portion of the regeneration power input is used to increase the temperature of desiccant mass to the regeneration temperature at the start of each regeneration cycle as shown in Equation A14.
  • the dehumidification effectiveness was defined as the ratio of moisture removed in the dehumidification process to the maximum possible moisture removal as shown in Equation A15: ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ 15 ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ ⁇ in which ⁇ ⁇ is the humidity air leaving the wheel, and ⁇ ⁇ ⁇ Maximum moisture removal is a function of the ideal outlet humidity ratio, which is in turn a function of the sorbent isotherm.
  • the ideal humidity ratio ( ⁇ ⁇ ) at the outlet is the humidity ratio corresponding to the MOF step_RH at the inlet temperature, which is the minimum humidity ratio that can be achieved if the dehumidification process is isothermal, and no moisture transport resistances exist.
  • Optimization Process The optimization process is comprised of two sections; finding the optimal MOF step_RH values for each stage, and optimizing the operational parameters including wheel speeds, wheel thickness, and regeneration-to-dehumidification section ratio for the multi-stage configurations.
  • Optimal stage step_RH First, the optimal MOF step_RH for each stage of the multi- stage configuration needed to be identified. This optimal step_RH depends on the inlet conditions of that stage.
  • the wheel speed and the ratio of regeneration to dehumidification sections ( ⁇ ) of each wheel was also optimized.
  • the wheel speed can be optimized for each stage separately, meaning that each wheel can move with its unique speed.
  • the single-stage and the composite multi-stage configurations CONFIG1, and CONFIG2, respectively
  • Regeneration Efficiency f(thickness of the wheel in each stage, wheel speed in each stage, the ratio of regeneration to dehumidification sections ( ⁇ ) of the wheel in each stage)
  • Total thickness of the wheels 20 cm
  • the optimization tool of the Dymola was used (commercial interface of Modelica language) using the sequential quadratic programming and pattern search optimization methods to insure the independency of the optimization results from the optimization method [A78]. Investigation of the effect of adding stages to the system performance. In the final step of the investigation, the performance of a variety of multi-stage configurations were compared.
  • FIG 24 The results of the comparison between the model herein and the experimental reference [A8] are shown in Figure 24.
  • the supply humidity ratio is plotted as a function of wheel speed for two different inlet air velocities.
  • the difference between the model herein and the reference [A8] is less than 5%, which shows that average supply humidity ratio agrees well with the results of the reference experiments under identical conditions.
  • Optimal MOF step_RH depending on the inlet conditions.
  • Figure 26 shows the regeneration efficiency values of a single MOF-based desiccant wheel (Configuration 1) as a function of the MOF step_RH and for different inlet conditions.
  • the curve of the regeneration efficiency as a function of MOF step_RH is parabolic and thus has a maximum. This means that for each inlet condition, there exists a MOF step_RH that will maximize regeneration efficiency. This is attributable to two competing phenomena that affect the regeneration efficiency. On one hand, as the step_RH is increased, the minimum supply humidity ratio that can be achieved increases, meaning that with a greater step_RH, the air can be dried less. This decreases the useful portion of the regeneration efficiency as less useful work is being done, and thus results in decreased regeneration efficiency. This is shown in Figure 25. As shown on the left axis, the ratio of moisture removed to the initial moisture content of the air is decreased as the step_RH of the MOF increases.
  • Figure 26 shows that the optimal step_RH will vary as a function of inlet conditions and regeneration temperature. However, each set of conditions does indeed correspond to a single optimal value of step_RH. Energy and Dehumidification Performance Enhancement with Staged MOF Systems. The behavior shown in Figure 26 suggests the possibility of discretizing a single desiccant wheel into multiple stages containing different MOFs that are ideal for different inlet conditions. Each stage would then be optimized for the air entering that stage, as depicted in Figure 27, reducing losses and increasing efficiency.
  • the value of the optimal MOF step_RH in each stage depends on the inlet relative humidity of that stage, which in turn is determined by the step_RH of the previous stage, in a staged system, since as the air moves through each stage its humidity approaches the step_RH of that stage. This humidity is then the humidity of the air entering the next stage, based on which the MOF step_RH of the next stage is selected.
  • CONFIG1 single-stage
  • CONFIG2 combined multi-stage
  • CONFIG3 separate multi-stage
  • CONFIG4 separate multi-stage with adsorption heat removal stages
  • the MOF step_RH of each stage is the optimal MOF step_RH resulting in the maximum regeneration efficiency based on the results of Table 8.
  • Figure 28 shows the regeneration efficiency, dehumidification effectiveness, and supply humidity ratio of all configurations as a function of number stages and for inlet humidity ratios of 0.03 kg/kg, 0.02 kg/kg, and 0.01 kg/kg.
  • the regeneration efficiency of an ideal desiccant dehumidification system is equal to one, which can be achieved when no losses occur during the regeneration process, and all energy is used for removing adsorbed moisture.
  • typical silica gel- based systems typically only achieve 20-30% efficiency, and single stage MOF systems 30-40%.
  • Figure 28 shows a vast increase in efficiency over previously reported values, with the best performing configuration approaching the theoretical limit of 1 for some conditions.
  • Figure 29 further articulates the comparison between the performance of the systems analyzed in this work and those previously reported. MOF-based versus conventional systems. The first comparison that can be made from Figure 29 is between a silica gel-based system and a MOF-based system. It was previously demonstrated that MOF-based single stage systems offer substantial benefits over silica gel systems, shown again in Figure 29. Furthermore, Figure 29 shows that using a multi-stage silica gel wheel design, while holding the total mass of desiccant used equal to the baseline, not only does not add any benefit, but decreases the regeneration efficiency.
  • Figure 29 shows that adding stages to the system will increase the regeneration efficiency, since adding more stages with lower step_RH values can decrease the supply humidity ratio, increasing the moisture removed and at the same time, making it possible to use the heat from the exhaust of each stage for regenerating the next stage, which can increase the regeneration efficiency. Effect of number of stages on regeneration efficiency.
  • Figure 28 shows that regardless of the inlet humidity ratio, there exists a specific number of stages at which the regeneration efficiency is maximized.
  • step_RH Since different MOF step_RH values results in different moisture transport driving forces both in the dehumidification and regeneration side, there exists a specific speed for the wheel with each step_RH at which it will have the maximum efficiency. That would be the speed at which the time that takes for the MOF to become fully dried is equal to the time that the MOF spends in the regeneration process. If the wheel moves more slowly than that speed, some excess amount of hot air would be exhausted to the ambient without adding any benefit to the system. That is why the regeneration efficiency, and dehumidification effectiveness of the composite multi-stage system (CONFIG2) are less than that of the separate multi-stage system (CONFIG3) in most cases.
  • step_RH of the sorbent also affects the supply humidity ratio.
  • step_RH When the step_RH is approached by the process air, increasing the moisture removal rate by increasing water uptake capacity does not decrease the supply humidity further, reducing improvements to dehumidification effectiveness and regeneration efficiency.
  • Figure 33 the regeneration efficiency of the 4-stage model of CONFIG4 was plotted as a function of the amount of hysteresis as quantified by the difference in adsorption step_RH and desorption step_RH.
  • the effect of hysteresis on the regeneration efficiency is less than 2.5% or hysteresis up to 3%.
  • Hysteresis was limited to 3% to reflect the maximum of the candidate MOFs identified below.
  • the hysteresis of the MOF used in stage_4 has the most influential effect on the efficiency of the system since the supply humidity ratio of the system is limited by the step_RH of the final stage.
  • MOF Options for each stage In order to assess the feasibility of identifying ideal or near-ideal TYPE V isotherms needed for each stage in real-world applications, a number of real MOFs possessing the requisite characteristics for the best performing system (4-stage) are identified in Table 9. As shown in Table 9, in most cases a MOF with little or no hysteresis can be found in the literature with the desired step_RH, although further work is needed to understand the performance of these MOFs in real applications.
  • a multi-stage MOF-based dehumidification system can have a regeneration efficiency approximately 2 to 5 times greater than a single-stage system for two main reasons: o
  • the MOF with the optimal step_RH resulting in the maximum regeneration efficiency is used in each stage.
  • the descending MOF step_RH from first to last stage makes it possible to use the exhaust of the regeneration side of each stage for the previous stage, decreasing the total exhaust energy waste.
  • Increasing the number of stages up to four stages increases both the regeneration efficiency and dehumidification effectiveness, by decreasing the exhaust air temperature and the supply air humidity ratio. Benefits of adding more than four stages are minimal or negative in the systems investigated herein.
  • Pasdarshahri “Potential of a desiccant-evaporative cooling system performance in a multi-climate country,” International Journal of Refrigeration, vol.34, no.5, pp.1251–1261, Aug.2011, doi: 10.1016/J.IJREFRIG.2011.03.008.
  • Example 1 A multi-stage air conditioning system comprising: a first stage in fluid communication with an air supply, the first stage comprising a first sorbent, the first sorbent having a type IV or V water sorption isotherm, a first step_RH, and a first regeneration temperature; a second stage in fluid communication with the first stage, the second stage comprising a second sorbent, the second sorbent having a type IV or V water sorption isotherm, a second step_RH, and a second regeneration temperature; wherein the second step_RH is less than the first step_RH; and wherein the second regeneration temperature is greater than the first regeneration temperature; and a heat source in thermal communication with the second stage; wherein the system is configured to operate in a dehumidification mode and/or a regeneration mode, wherein: when the system is operated in the dehumidification mode, then: the first stage is configured to: receive air having a first humidity from the air supply; contact the air with the first sorbent to thereby transfer a first amount
  • Example 2 The system of any examples herein, particularly example 1, further comprising: a third stage in fluid communication with the second stage, the third stage comprising a third sorbent, the third sorbent having a type IV or V water sorption isotherm, a third step_RH, and a third regeneration temperature; wherein the third step_RH is less than the second step_RH; and wherein the third regeneration temperature is greater than the second regeneration temperature; wherein: when the third stage is present, the heat source is in thermal communication with the third stage; and when the system is operated in the dehumidification mode, then the third stage is configured to: receive air having the third humidity from the second stage, contact the air with the third sorbent to thereby transfer a fifth amount of moisture from the air to the third sorbent and decrease the moisture content of the air to an eighth humidity, the eighth humidity being less than the third humidity, and effuse the air having the eighth humidity; and when the system is operated in the regeneration mode, then: the third stage is configured to: receive air having a ninth humidity; receive
  • Example 3 The system of any examples herein, particularly example 2, further comprising: a fourth stage in fluid communication with the third stage, the fourth stage comprising a fourth sorbent, the fourth sorbent having a type IV or V water sorption isotherm, a fourth step_RH, and a fourth regeneration temperature; wherein the fourth step_RH is less than the third step_RH; and wherein the fourth regeneration temperature is greater than the third regeneration temperature; wherein: when the fourth stage is present, the heat source is in thermal communication with the fourth stage; and when the system is operated in the dehumidification mode, then the fourth stage is configured to: receive air having the tenth humidity from the third stage, contact the air with the fourth sorbent to thereby transfer a seventh amount of moisture from the air to the fourth sorbent and decrease the moisture content of the air to an eleventh humidity, the eleventh humidity being less than the tenth humidity, and effuse the air having the eleventh humidity; and when the system is operated in the regeneration mode, then: the fourth stage is configured to: receive air
  • Example 4 The system of any examples herein, particularly examples 1-3, further comprising one or more heat exchangers in thermal communication with the first stage, the second stage, the third stage (when present), the fourth stage (when present), or a combination thereof.
  • Example 5 The system of any examples herein, particularly examples 1-4, wherein the first stage, the second stage, the third stage (when present), and the fourth stage (when present) each independently comprises a rotary desiccant wheel.
  • Example 6 The system of any examples herein, particularly examples 1-5, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises a metal-organic framework (MOF).
  • MOF metal-organic framework
  • Example 7 The system of any examples herein, particularly example 6, wherein the metal comprises Al, Ti, Zr, Co, or a combination thereof.
  • Example 8 The system of any examples herein, particularly example 6 or example 7, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises an Al-based MOF.
  • Example 9 The system of any examples herein, particularly examples 6-8, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises MIL-100, MIL-101, HKUST-1, ISE-1, Basolite C300, Basolite A100, DUT-67(Zr), UiO-66, UiO-67, NU-1000, MOF-801, CPO-27(Ni), CAU-1, CAU-1(OH) 2 , CAU-3, CAU-3-NH 2 , CAU-8, CAU-10H, MIL-53, MIL-53-NH 2 , MIL-125, MIL- 125-NH2, MIL-140A, MIL-140C, UiO-66, ZIF-8, Ni-MOF-74, Co-MOF-74, MIL-53, Fe-BTC, Cu-BTC, Aluminum fumarate, DUT-67, MIL-96(Al) and MIL-100
  • Example 10 The system of any examples herein, particularly examples 6-9, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises CAU-10, CAU-23, Al-fumarate, KMF-1, MIL-125-NH 2 , MIL-125, MOF-841, Co2Cl2(BTDD), or a combination thereof.
  • Example 11 The system of any examples herein, particularly examples 6-10, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises MOF-841, Co 2 Cl 2 (BTDD), Al-fumarate, CAU-23, or a combination thereof.
  • Example 12 The system of any examples herein, particularly examples 1-11, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently can undergo multiple water sorption/desorption cycles without significant loss in performance.
  • Example 13 The system of any examples herein, particularly examples 1-12, wherein the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), and the fourth regeneration temperature (when present) each independently is from 0°C to 140°C.
  • Example 14 The system of any examples herein, particularly examples 1-13, wherein the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), and the fourth regeneration temperature (when present) each independently is from 40°C to 60°C, from 70°C to 90°C, from 50°C to 70°C, from 60°C to 80°C, from 80°C to 100°C, or from 120°C to 140°C.
  • Example 15 The system of any examples herein, particularly examples 1-14, wherein the air supply comprises ambient air.
  • Example 16 The system of any examples herein, particularly examples 1-15, wherein, when the system is operated in the regeneration mode, the system has a regeneration efficiency of 20% or more, 40% or more, 60% or more, 80% or more, or 90% or more.
  • Example 17 The system of any examples herein, particularly examples 1-16, wherein, when the system is operated in regeneration mode, the system has a regeneration efficiency of 90% or more.
  • Example 18 A method of use of the system of any examples herein, particularly examples 1-17, the method comprising: operating the system in dehumidification mode to decrease the humidity of the air from the air supply; and/or operating the system in regeneration mode to regenerate the sorbents and optionally decrease the temperature of the air.

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Abstract

Disclosed herein are multi-stage air conditioning systems and methods of use thereof. The multi-stage air conditioning system comprises a first stage in fluid communication with an air supply, the first stage comprising a first sorbent, the first sorbent having a type IV or V water sorption isotherm, a first step RH, and a first regeneration temperature; a second stage in fluid communication with the first stage, the second stage comprising a second sorbent, the second sorbent having a type IV or V water sorption isotherm, a second step RH, and a second regeneration temperature; and a heat source in thermal communication with the second stage. The system can be configured to operate in a dehumidification mode and/or a regeneration mode.

Description

MULTI-STAGE AIR CONDITIONING SYSTEMS AND METHODS OF USE THEREOF CROSS-REFERENCE TO RELATED APPLICATIONS This application claims the benefit of priority to U.S. Provisional Application No. 63/428,576 filed November 29, 2022, which is hereby incorporated herein by reference in its entirety. BACKGROUND Dehumidification systems including desiccant wheels and/or liquid sorbent systems are used in many different HVAC devices. However, these devices suffer from a critical shortcoming: The sorbents employed in these devices have linear or shallow Type I or II water sorption isotherms which means an external energy input at high temperatures is required to regenerate the sorbent sufficiently to allow it to be used efficiently in a cycle, precluding the use of low-temperature heat sources. Improved devices, methods, and systems are needed. The devices, methods, and systems discussed herein address these and other needs. SUMMARY In accordance with the purposes of the disclosed devices, methods, and systems as embodied and broadly described herein, the disclosed subject matter relates to multi-stage air conditioning systems and methods of use thereof. Disclosed herein are multi-stage air conditioning systems comprising a first stage in fluid communication with an air supply, the first stage comprising a first sorbent, the first sorbent having a type IV or V water sorption isotherm, a first step_RH, and a first regeneration temperature; a second stage in fluid communication with the first stage, the second stage comprising a second sorbent, the second sorbent having a type IV or V water sorption isotherm, a second step_RH, and a second regeneration temperature; wherein the second step_RH is less than the first step_RH; and wherein the second regeneration temperature is greater than the first regeneration temperature; and a heat source in thermal communication with the second stage. The system is configured to operate in a dehumidification mode and/or a regeneration mode. When the system is operated in the dehumidification mode, then: the first stage is configured to: receive air having a first humidity from the air supply; contact the air with the first sorbent to thereby transfer a first amount of moisture from the air to the first sorbent and decrease the moisture content of the air to a second humidity, the second humidity being less than the first humidity; and effuse the air having the second humidity; and the second stage is configured to: receive the air having the second humidity from the first stage; contact the air with the second sorbent to thereby transfer a second amount of moisture from the air to the second sorbent and decrease the moisture content of the air to a third humidity, the third humidity being less than the second humidity; and effuse the air having the third humidity. When the system is operated in the regeneration mode, then: the second stage is configured to: receive air having a sixth humidity; receive an amount of heat from the heat source; contact the second sorbent with the air and the amount of heat to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air with the increased moisture content and decreased amount of heat to the first stage; the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the first sorbent; and subsequently effuse the air. In some examples, the system further comprises a third stage in fluid communication with the second stage, the third stage comprising a third sorbent, the third sorbent having a type IV or V water sorption isotherm, a third step_RH, and a third regeneration temperature; wherein the third step_RH is less than the second step_RH; and wherein the third regeneration temperature is greater than the second regeneration temperature. When the third stage is present, the heat source is in thermal communication with the third stage. When the system is operated in the dehumidification mode, then the third stage is configured to: receive air having the third humidity from the second stage, contact the air with the third sorbent to thereby transfer a fifth amount of moisture from the air to the third sorbent and decrease the moisture content of the air to an eighth humidity, the eighth humidity being less than the third humidity, and effuse the air having the eighth humidity. When the system is operated in the regeneration mode, then the third stage is configured to: receive air having a ninth humidity; receive an amount of heat from the heat source; contact the third sorbent with the air and the amount of heat to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effuse the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to: receive the air effused by the third stage; contact the second sorbent with the air to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air having the increased humidity and decreased amount of heat to the first stage; and the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decrease the amount of heat in the air, and regenerate the first sorbent; and subsequently effuse the air having the increased humidity and decreased temperature. In some examples, the system further comprises: a fourth stage in fluid communication with the third stage, the fourth stage comprising a fourth sorbent, the fourth sorbent having a type IV or V water sorption isotherm, a fourth step_RH, and a fourth regeneration temperature; wherein the fourth step_RH is less than the third step_RH; and wherein the fourth regeneration temperature is greater than the third regeneration temperature. When the fourth stage is present, the heat source is in thermal communication with the fourth stage. When the system is operated in the dehumidification mode, then the fourth stage is configured to: receive air having the tenth humidity from the third stage, contact the air with the fourth sorbent to thereby transfer a seventh amount of moisture from the air to the fourth sorbent and decrease the moisture content of the air to an eleventh humidity, the eleventh humidity being less than the tenth humidity, and effuse the air having the eleventh humidity. When the system is operated in the regeneration mode, then the fourth stage is configured to: receive air having a twelfth humidity; receive an amount of heat from the source; contact the fourth sorbent with the air and the amount of heat to thereby increase the temperature of the fourth sorbent to the fourth regeneration temperature such that the fourth sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the fourth sorbent; and effuse the air having the increased humidity and decreased amount of heat to the third stage; the third stage is configured to: receive the air effused by the fourth stage; contact the third sorbent with the air to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effuse the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to: receive the air effused by the third stage; contact the second sorbent with the air to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air having the increased humidity and decreased amount of heat to the first stage; and the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decrease the amount of heat in the air, and regenerate the first sorbent; and subsequently effuse the air having the increased humidity and decreased temperature. In some examples, the system further comprises one or more heat exchangers in thermal communication with the first stage, the second stage, the third stage (when present), the fourth stage (when present), or a combination thereof. In some examples, the first stage, the second stage, the third stage (when present), and the fourth stage (when present) each independently comprises a rotary desiccant wheel. In some examples, the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises a metal-organic framework (MOF). In some examples, the metal comprises Al, Ti, Zr, Co, or a combination thereof. In some examples, the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises an Al-based MOF. In some examples, the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises MIL-100, MIL-101, HKUST-1, ISE-1, Basolite C300, Basolite A100, DUT-67(Zr), UiO-66, UiO-67, NU-1000, MOF-801, CPO-27(Ni), CAU-1, CAU-1(OH)2, CAU-3, CAU-3-NH2, CAU-8, CAU-10H, MIL-53, MIL-53-NH2, MIL-125, MIL- 125-NH2, MIL-140A, MIL-140C, UiO-66, ZIF-8, Ni-MOF-74, Co-MOF-74, MIL-53, Fe-BTC, Cu-BTC, Aluminum fumarate, DUT-67, MIL-96(Al) and MIL-100(Al), FAM-Z01, Cu-BTC (HKUST-1), Al Fumarate, CAU-10, CAU-23, KMF-1, CPO-27, MOF-840, MIL-160, Co2Cl2(BTDD), MIL-101(Cr), MOF-841, In-MIL-68, or a combination thereof. In some examples, the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises CAU-10, CAU-23, Al-fumarate, KMF-1, MIL-125-NH2, MIL-125, MOF-841, Co2Cl2(BTDD), or a combination thereof. In some examples, the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises MOF-841, Co2Cl2(BTDD), Al-fumarate, CAU-23, or a combination thereof. In some examples, the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently can undergo multiple water sorption/desorption cycles without significant loss in performance. In some examples, the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), and the fourth regeneration temperature (when present) each independently is from 0°C to 140°C. In some examples, the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), and the fourth regeneration temperature (when present) each independently is from 40°C to 60°C, from 70°C to 90°C, from 50°C to 70°C, from 60°C to 80°C, from 80°C to 100°C, or from 120°C to 140°C. In some examples, the air supply comprises ambient air. In some examples, when the system is operated in the regeneration mode, the system has a regeneration efficiency of 20% or more, 40% or more, 60% or more, 80% or more, or 90% or more. In some examples, when the system is operated in regeneration mode, the system has a regeneration efficiency of 90% or more. Also disclosed herein are methods of use of any of the systems disclosed herein. In some examples, the methods comprise: operating the system in dehumidification mode to decrease the humidity of the air from the air supply; and/or operating the system in regeneration mode to regenerate the sorbents and optionally decrease the temperature of the air. Additional advantages of the disclosed devices, systems, and methods will be set forth in part in the description which follows, and in part will be obvious from the description. The advantages of the disclosed devices, systems, and methods will be realized and attained by means of the elements and combinations particularly pointed out in the appended claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the disclosed devices, systems, and methods, as claimed. The details of one or more embodiments of the invention are set forth in the accompanying drawings and the description below. Other features, objects, and advantages of the invention will be apparent from the description and drawings, and from the claims. BRIEF DESCRIPTION OF THE FIGURES The accompanying figures, which are incorporated in and constitute a part of this specification, illustrate several aspects of the disclosure, and together with the description, serve to explain the principles of the disclosure. Figure 1. Dehumidification and regeneration of a solid sorbent. Figure 2. Water adsorption isotherms of MIL-125, KMF-1, Silica gel and Zeolite at 25°C (Data from [75], [76], [77] and [15], respectively.). Figure 3. Water uptake capacity as a function of surface relative humidity for MOF and Type I & Linear isotherms. Figure 4. Water uptake capacity as a function of surface relative humidity for Type V and Linear isotherms (Mass Transfer driving force). Figure 5. Schematic diagram of a rotary desiccant wheel and its air streams. Figure 6. Definition of isotherm parameters. Figure 7. Piece-wise linear function fitted to Silica Gel isotherm and fitted isotherm parameters used as input to First-principles dynamic model (red triangles shows experimental data from [88]). Figure 8. Water Uptake isotherms of different MOFs at 25°C (Data references: CAU-10 from [89],[90],[81], CAU-23 from [82], MIL-125 from [75], Al-fumarate from [91],[85],[92], KMF-1 from [76], MIL-160 from [89], MIL-125-NH2 from [21],[93],[52],[94], MOF-841 from [84], CPO-27 from [85], Co2Cl2(BTDD) from [95]). Figure 9. Regeneration Efficiency as a function of regeneration temperature of model compared with experimental results of Mandegari et al.2009 [79] for inlet temperature of 35.5°C and inlet air humidity ratio of 0.011 kg/kgdry air. Figure 10. Regeneration Efficiency as a function of Inlet temperature of dynamic model in comparison with experimental work of Mandegari et al.2009 [79]. Regeneration temperature is fixed at 120°C for all. Figure 11. Regeneration Efficiency as a function of regeneration temperature for different MOFs at different inlet conditions. Figure 12. Minimum regeneration temperature and the Regeneration Efficiency at the minimum regeneration temperature for each MOF at each inlet condition. Figure 13. Dehumidification and Regeneration times in a period of 500 seconds for sorbents with linear (Silica Gel) and Type V (CAU-23) isotherm. Figure 14. Sample configuration of the multi-stage system. Figure 15. Dehumidification and cooling processes in single-stage and multi-stage configurations. Figure 16. Water Uptake isotherms of different MOFs at 25oC (Data references: CAU-10 [A23], CAU-23 [A24], MIL-125 [A25], MIL-125-NH2 [A26]) Figure 17. Stage step_RH descending and regeneration temperature ascending from left to right in multi-stage configurations. Figure 18. Single-stage desiccant wheel (CONFIG1). Figure 19. Single-stage desiccant wheel (CONFIG1) and composite multi-stage desiccant wheel (CONFIG2). Figure 20. Multi-stage desiccant wheel without adsorption heat removal stages (CONFIG3). Figure 21. Multi-stage desiccant wheel with adsorption heat removal stages (CONFIG4). Figure 22. moisture and energy transfer in each honey-comb channel of the desiccant wheel in each stage. Figure 23. Isotherms used in the model. Figure 24. Comparison of the supply humidity ratio results of the dynamic model results with experimental results of Yamaguchi et al. [A8]. Figure 25. Two competing phenomena resulting in an optimal point in the regeneration efficiency. Figure 26. Regeneration efficiency of the single-stage system as a function of MOF Step_RH for different inlet conditions. Figure 27. Optimal step_RH used in each stage resulting in the maximum efficiency of each stage in a multi-stage configuration (notice inverted x-axis). Figure 28. Regeneration efficiency, dehumidification effectiveness, and supply humidity ratio of all configurations as a function of number of stages for the inlet humidity ratios of 0.03 kg kg-1, 0.02 kg kg-1, and 0.01 kg kg-1. Figure 29. Comparison of regeneration efficiency of different configurations of the current work and from the literature (Sheng et al. [A1], Enteria et al. [A3], Ali Mandegari et al. [A21], Shahvari et al. [A22]). Figure 30. Effect of adding stages to the energy inefficiencies of a dehumidification system. Figure 31. Exhaust air temperature of the system for different number of stage configurations. Figure 32. Effect of maximum water uptake capacity of the MOF on the performance of the 4-stage model with CONFIG4. Figure 33. Effect of MOF step_RH hysteresis on the performance of the 4-stage model with CONFIG4. DETAILED DESCRIPTION The devices, methods, and systems described herein may be understood more readily by reference to the following detailed description of specific aspects of the disclosed subject matter and the Examples included therein. Before the present devices, methods, and systems are disclosed and described, it is to be understood that the aspects described below are not limited to specific synthetic methods or specific reagents, as such may, of course, vary. It is also to be understood that the terminology used herein is for the purpose of describing particular aspects only and is not intended to be limiting. Also, throughout this specification, various publications are referenced. The disclosures of these publications in their entireties are hereby incorporated by reference into this application in order to more fully describe the state of the art to which the disclosed matter pertains. The references disclosed are also individually and specifically incorporated by reference herein for the material contained in them that is discussed in the sentence in which the reference is relied upon. In this specification and in the claims that follow, reference will be made to a number of terms, which shall be defined to have the following meanings. Throughout the description and claims of this specification the word “comprise” and other forms of the word, such as “comprising” and “comprises,” means including but not limited to, and is not intended to exclude, for example, other additives, components, integers, or steps. As used in the description and the appended claims, the singular forms “a,” “an,” and “the” include plural referents unless the context clearly dictates otherwise. Thus, for example, reference to “a composition” includes mixtures of two or more such compositions, reference to “an agent” includes mixtures of two or more such agents, reference to “the component” includes mixtures of two or more such components, and the like. “Optional” or “optionally” means that the subsequently described event or circumstance can or cannot occur, and that the description includes instances where the event or circumstance occurs and instances where it does not. Ranges can be expressed herein as from “about” one particular value, and/or to “about” another particular value. By “about” is meant within 5% of the value, e.g., within 4, 3, 2, or 1% of the value. When such a range is expressed, another aspect includes from the one particular value and/or to the other particular value. Similarly, when values are expressed as approximations, by use of the antecedent “about,” it will be understood that the particular value forms another aspect. It will be further understood that the endpoints of each of the ranges are significant both in relation to the other endpoint, and independently of the other endpoint. “Exemplary” means “an example of” and is not intended to convey an indication of a preferred or ideal embodiment. “Such as” is not used in a restrictive sense, but for explanatory purposes. It is understood that throughout this specification the identifiers “first” and “second” are used solely to aid in distinguishing the various components and steps of the disclosed subject matter. The identifiers “first” and “second” are not intended to imply any particular order, amount, preference, or importance to the components or steps modified by these terms. Disclosed herein are multi-stage air conditioning systems and methods of use thereof. For example, disclosed herein are multi-stage air conditioning systems comprising a first stage in fluid communication with an air supply, the first stage comprising a first sorbent, the first sorbent having a type IV or V water sorption isotherm, a first step_RH, and a first regeneration temperature. As used herein, a “step_RH” is the relative humidity (RH) at which the sorbent shows a sudden increase in water uptake. For example, "step_RH” can be the relative humidity (RH) at which the sorbent shows an increase in water uptake of 50% or more (e.g., 75% or more, 100% or more, 125% or more, 150% or more, 175% or more, 200% or more, 250% or more, 300% or more, 350% or more, 400% or more, 450% or more, or 500% or more). The systems further comprise a second stage in fluid communication with the first stage, the second stage comprising a second sorbent, the second sorbent having a type IV or V water sorption isotherm, a second step_RH, and a second regeneration temperature; wherein the second step_RH is less than the first step_RH; and wherein the second regeneration temperature is greater than the first regeneration temperature. The systems further comprise a heat source in thermal communication with the second stage. The systems can be configured to operate in a dehumidification mode and/or a regeneration mode. In some examples, the system can be configured to operate in the dehumidification mode and the regeneration more simultaneously. For example, the system can include a dehumidification portion (such as a dehumidification side), where the system is operated in a dehumidification mode, and a regeneration portion (such as a regeneration side), where the system is operated in a regeneration mode. When the system is operated in the dehumidification mode, then the first stage is configured to: receive air having a first humidity from the air supply; contact the air with the first sorbent to thereby transfer a first amount of moisture from the air to the first sorbent and decrease the moisture content of the air to a second humidity, the second humidity being less than the first humidity; and effuse the air having the second humidity. When the system is operated in the dehumidification mode, then the second stage is configured to receive the air having the second humidity from the first stage; contact the air with the second sorbent to thereby transfer a second amount of moisture from the air to the second sorbent and decrease the moisture content of the air to a third humidity, the third humidity being less than the second humidity; and effuse the air having the third humidity. When the system is operated in the regeneration mode, then the second stage is configured to: receive air having a sixth humidity; receive an amount of heat from the heat source; contact the second sorbent with the air and the amount of heat to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air with the increased moisture content and decreased amount of heat to the first stage; and the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the first sorbent; and subsequently effuse the air. In some examples, the systems can further comprise a third stage in fluid communication with the second stage, the third stage comprising a third sorbent, the third sorbent having a type IV or V water sorption isotherm, a third step_RH, and a third regeneration temperature; wherein the third step_RH is less than the second step_RH; and wherein the third regeneration temperature is greater than the second regeneration temperature. When the third stage is present, then the heat source is in thermal communication with the third stage. When the system is operated in the dehumidification mode, then the third stage is configured to: receive air having the third humidity from the second stage, contact the air with the third sorbent to thereby transfer a fifth amount of moisture from the air to the third sorbent and decrease the moisture content of the air to an eighth humidity, the eighth humidity being less than the third humidity, and effuse the air having the eighth humidity. When the system is operated in the regeneration mode, then the third stage is configured to: receive air having a ninth humidity; receive an amount of heat from the heat source; contact the third sorbent with the air and the amount of heat to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effusing the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to: receive the air effused by the third stage; contact the second sorbent with the air to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air having the increased humidity and decreased amount of heat to the first stage; and the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decrease the amount of heat in the air, and regenerate the first sorbent; and subsequently effuse the air having the increased humidity and decreased temperature. In some examples, the system can further comprise a fourth stage in fluid communication with the third stage, the fourth stage comprising a fourth sorbent, the fourth sorbent having a type IV or V water sorption isotherm, a fourth step_RH, and a fourth regeneration temperature; wherein the fourth step_RH is less than the third step_RH; and wherein the fourth regeneration temperature is greater than the third regeneration temperature. When the fourth stage is present, the heat source is in thermal communication with the fourth stage. When the system is operated in the dehumidification mode, then the fourth stage is configured to: receive air having a twelfth humidity; receive an amount of heat from the source; contact the fourth sorbent with the air and the amount of heat to thereby increase the temperature of the fourth sorbent to the fourth regeneration temperature such that the fourth sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the fourth sorbent; and effuse the air having the increased humidity and decreased amount of heat to the third stage; the third stage is configured to: receive the air effused by the fourth stage; contact the third sorbent with the air to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effuse the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to: receive the air effused by the third stage; contact the second sorbent with the air to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air having the increased humidity and decreased amount of heat to the first stage; and the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decrease the amount of heat in the air, and regenerate the first sorbent; and subsequently effusing the air having the increased humidity and decreased temperature. In some examples, the system can comprise one or more additional stages, where each subsequent stage is in fluid communication with the preceding stage, wherein each stage comprises a sorbent, the sorbent having a type IV or V water sorption isotherm, a step_RH that is less than the step_RH of the preceding stage, and a regeneration temperature that is higher than the regeneration temperature of the preceding stage. The final stage of the system is in thermal communication with the heat source. When the system is operated in the dehumidification mode, then each of the one or more additional stages is configured to: receive air from the preceding stage, contact the air the sorbent to thereby decrease the humidity of the air, and effuse the air with the decreased humidity. When the system is operated in the regeneration mode, then the final stage is configured to: receive air and receive an amount of heat from the heat source; contact the sorbent with the air and the amount of heat to thereby increase the temperature of the sorbent to the regeneration temperature such that the sorbent releases an amount of moisture into the air, thereby increasing humidity of the air, decreasing the amount of heat in the air, and regenerating the fourth sorbent; and effuse the air with the increased humidity and decreased temperature to the next stage; and said next stage is configured to: receive the air from the previous stage; contact the sorbent with the air and the amount of heat to thereby increase the temperature of the sorbent to the regeneration temperature such that the sorbent releases an amount of moisture into the air, thereby increasing humidity of the air, decreasing the amount of heat in the air, and regenerating the fourth sorbent; and effuse the air with the increased humidity and decreased temperature to the next stage (when present). The step_RH of any of the stages herein (e.g., the first step_RH, second step_RH, third step_RH, fourth step_RH, etc.) can independently be 0 or more (e.g., 0.1 or more, 0.2 or more, 0.3 or more, 0.4 or more, 0.5 or more, 0.6 or more, 0.7 or more, 0.8 or more, or 0.9 or more). In some examples, the step_RH of any of the stages herein (e.g., the first step_RH, second step_RH, third step_RH, fourth step_RH, etc.) can independently be 1 or less (e.g., 0.9 or less, 0.8 or less, 0.7 or less, 0.6 or less, 0.5 or less, 0.4 or less, 0.3 or less, 0.2 or less, or 0.1 or less). The value of step_RH for any of the stages can independently range from any of the minimum values described above to any of the maximum values described above. For example, the step_RH of any of the stages herein (e.g., the first step_RH, second step_RH, third step_RH, fourth step_RH, etc.) can independently be from 0 to 1 (e.g., from 0 to 0.5, from 0.5 to 1, from 0 to 0.2, from 0.2 to 0.4, from 0.4 to 0.6, from 0.6 to 0.8, from 0.8 to 1, from 0 to 0.9, from 0 to 0.8, from 0 to 0.7, from 0 to 0.6, from 0 to 0.5, from 0 to 0.4, from 0 to 0.3, from 0 to 0.2, from 0 to 0.1, from 0.1 to 1, from 0.2 to 1, from 0.3 to 1, from 0.4 to 1, from 0.5 to 1, from 0.6 to 1, from 0.7 to 1, from 0.8 to 1, from 0.9 to 1, from 0.1 to 0.9, from 0.2 to 0.8, from 0.3 to 0.7, or from 0.4 to 0.6). In some examples, the system can further comprise one or more heat exchangers in thermal communication with the first stage, the second stage, the third stage (when present), the fourth stage (when present), the one or more additional stages (when present) or a combination thereof. The first stage, the second stage, the third stage (when present), the fourth stage (when present), and the one or more additional stages (when present) can each independently comprise a rotary desiccant wheel. For example, the sorbent can be housed in a rotating wheel that moves the sorbent between the supply stream and regeneration stream. The first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can each independently comprise any suitable material. In some examples, the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can each independently comprises a metal-organic framework (MOF). Examples of metal-organic frameworks are described in the art, such as in Moosavi et al., “Understanding the diversity of the metal-organic framework ecosystem,” Nat Commun, vol.11, no.1, pp.1–10, 2020, which is hereby incorporated herein for its description of metal-organic frameworks. In some examples, the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can each independently comprises a metal-organic framework (MOF), wherein the metal comprises Al, Ti, Zr, Co, or a combination thereof. In some examples, one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise an Al-based MOF. In some examples, one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MIL-100, MIL-101, HKUST-1, ISE-1, Basolite C300, Basolite A100, DUT-67(Zr), UiO-66, UiO-67, NU-1000, MOF-801, CPO-27(Ni), CAU-1, CAU-1(OH)2, CAU-3, CAU-3-NH2, CAU-8, CAU-10H, MIL-53, MIL-53-NH2, MIL-125, MIL- 125-NH2, MIL-140A, MIL-140C, UiO-66, ZIF-8, Ni-MOF-74, Co-MOF-74, MIL-53, Fe-BTC, Cu-BTC, Aluminum fumarate, DUT-67, MIL-96(Al) and MIL-100(Al), FAM-Z01, Cu-BTC (HKUST-1), Al Fumarate, CAU-10, CAU-23, KMF-1, CPO-27, MOF-840, MIL-160, Co2Cl2(BTDD), MIL-101(Cr), MOF-841, In-MIL-68, or a combination thereof. In some examples, one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MOF-841, MIL-101 (Cr), In-MIL-68, KMF-1, In-MIL-68-NH2, MOD- 801-P, CAU-10-H, CAU-23, MIL-160, Ti-MIL-125-NH2, CAU-10, CAU-23, Al-fumarate, KMF-1, MIL-125-NH2, MIL-125, MOF-841, Co2Cl2(BTDD), or a combination thereof. In some examples, one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MOF-841, MIL-101 (Cr), In-MIL-68, or a combination thereof. In some examples, one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise KMF-1, MOF-841, In-MIL-68-NH2, or a combination thereof. In some examples, one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MOF-801-P, CAU-10-H, CAU-23, or a combination thereof. In some examples, one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MIL-160, Ti-MIL-125-NH2, MOF-841, or a combination thereof. In some examples, one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise CAU-10, CAU-23, Al-fumarate, KMF-1, MIL-125-NH2, MIL-125, MOF-841, Co2Cl2(BTDD), or a combination thereof. In some examples, one or more of the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can independently comprise MOF-841, Co2Cl2(BTDD), Al-fumarate, CAU-23, or a combination thereof. In some examples, the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can each independently undergo multiple water sorption/desorption cycles without significant loss in performance. In some examples, the first sorbent, the second sorbent, the third sorbent (when present), the fourth sorbent (when present), and one or more additional sorbents (when present) can each independently be stable, lack hysteresis, be low cost, have a high water uptake capacity, or a combination thereof. The first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), the fourth regeneration temperature (when present), and the one or more additional regeneration temperatures (when present) can each independently be from 0°C-140°C. In some examples, the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), the fourth regeneration temperature (when present), and the one or more additional regeneration temperatures (when present) can each independently be 0°C or more (e.g., 20°C or more, 40°C or more, 60°C or more, 80°C or more, 100°C or more, or 120°C or more). In some examples, the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), the fourth regeneration temperature (when present), and the one or more additional regeneration temperatures (when present) can each independently be 140°C or less (e.g., 120°C or less, 100°C or less, 80°C or less, 60°C or less, 40°C or less, or 20°C or less). The first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), the fourth regeneration temperature (when present), and the one or more additional regeneration temperatures (when present) can each independently range from any of the minimum values described above to any of the maximum values described above. For example, the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), the fourth regeneration temperature (when present), and the one or more additional regeneration temperatures (when present) can each independently be from 0 to 140°C (e.g., from 0°C to 70°C, from 70°C to 140°C, from 0°C to 40°C, from 40°C to 80°C, from 80°C to 140°C, from 0°C to 120°C, from 0°C to 100°C, from 0°C to 80°C, from 0°C to 60°C, from 0°C to 40°C, from 20°C to 140°C, from 40°C to 140°C, from 60°C to 140°C, from 80°C to 140°C, from 100°C to 140°C, from 20°C to 120°C, from 40°C to 60°C, from 70°C to 90°C, from 50°C to 70°C, from 60°C to 80°C, from 80°C to 100°C, or from 120°C to 140°C). In some examples, the air supply comprises ambient air, such as outdoor or exterior air. Also disclosed herein are methods of use of any of the systems disclosed herein. For example, the methods can comprise operating the system in dehumidification mode to decrease the humidity of the air from the air supply; and/or operating the system in regeneration mode to regenerate the sorbents and optionally decrease the temperature of the air. In some examples, when the system is operated in the regeneration mode, the system and/or methods can have a regeneration efficiency of 20% or more (e.g., 30% or more, 40% or more, 50% or more, 60% or more, 70% or more, 80% or more, 90% or more, 95% or more, or 99% or more). In some examples, when the system is operated in the regeneration mode, the system and/or methods can have a regeneration efficiency of 90% or more. In some examples, the system and/or methods can have a regeneration efficiency approaching 100%. A number of embodiments of the invention have been described. Nevertheless, it will be understood that various modifications may be made without departing from the spirit and scope of the invention. Accordingly, other embodiments are within the scope of the following claims. The examples below are intended to further illustrate certain aspects of the systems and methods described herein, and are not intended to limit the scope of the claims. EXAMPLES The following examples are set forth below to illustrate the methods and results according to the disclosed subject matter. These examples are not intended to be inclusive of all aspects of the subject matter disclosed herein, but rather to illustrate representative methods and results. These examples are not intended to exclude equivalents and variations of the present invention which are apparent to one skilled in the art. Efforts have been made to ensure accuracy with respect to numbers (e.g., amounts, temperature, etc.) but some errors and deviations should be accounted for. Unless indicated otherwise, parts are parts by weight, temperature is in °C or is at ambient temperature, and pressure is at or near atmospheric. There are numerous variations and combinations of measurement conditions, e.g., component concentrations, temperatures, pressures and other measurement ranges and conditions that can be used to optimize the described process. Example 1 - Benefits of metal-organic frameworks sorbents for dehumidification wheels used in air conditioning systems. Abstract. Dehumidification systems including desiccant wheels and/or liquid sorbent systems are used in many different HVAC devices. However, these devices suffer from a critical shortcoming: The sorbents employed in these devices have linear or shallow Type I or II water sorption isotherms which means an external energy input at high temperatures is required to regenerate the sorbent sufficiently to allow it to be used efficiently in a cycle, precluding the use of low-temperature heat sources. Metal Organic Frameworks are a class of sorbents with Type IV or V water uptake isotherms featuring a steep adsorption step. In this work: 1) how different isotherm shapes can affect the dehumidification performance and energy requirements is analytically investigated, 2) a first-principles physical model is developed to quantify the benefits to the system of a number of selected MOFs, in terms of system performance and energy requirements and, 3) MOF candidates with high potential for dehumidification of humid air in different climates are identified. Results show MOF sorbents can be regenerated at a much lower temperature (40 to 60°C) than those with linear-shaped isotherms. Simulation results show a MOF-based dehumidification/regeneration system can be regenerated with half to 1/8 of the energy required for silica gel-based systems depending on inlet conditions. Several existing MOFs were identified with outstanding properties for dehumidification systems. Introduction. Sorbent-based dehumidification is widely used in commercial and a few residential air conditioning systems. Figure 1 shows a schematic of the dehumidification and regeneration processes for a solid sorbent. In the dehumidification process, humid outdoor air passes over the surface of a solid sorbent, where the humidity difference between the humid air and the air in equilibrium with the sorbent surface creates a driving force for moisture transfer from the humid air to sorbent surface, decreasing the humidity of the air and increasing the water content of the sorbent. The dehumidification process continues until the equilibrium humidity of sorbent is increased to the process air humidity and no driving force for moisture transport exists. At this point the sorbent needs to be regenerated by an increase in temperature, resulting in a driving force for moisture transfer from sorbent surface to the air. The improvements sorbents offer for humidity control and efficiency of air conditioning systems are well documented [1]–[8]. However, the inorganic sorbents (e.g., silica gel, zeolites, aqueous lithium chloride [9]–[13]) typically employed in sorbent wheels or advanced liquid sorbent-enhanced systems have water sorption behavior such that high-temperature external energy is required to regenerate the sorbent sufficiently to allow it to be used efficiently in a cycle. This precludes the use of low-temperature heat sources for regeneration. A new class of sorbents, called Metal-Organic Frameworks, has emerged recently with great benefits documented in a wide variety of water sorption applications. MOFs are a relatively new class of three-dimensional coordinated polymer sorbents comprised of a metal ion and organic linker in highly structured repeating form that results in a Type IV or V water uptake isotherm, discussed further below. Among the potentially beneficial properties of MOFs articulated in the literature are porosity and surface area that greatly exceed traditional porous materials such as zeolites [14], resulting in high water adsorption capacity [15]–[19], and a Type IV or V water adsorption isotherm with uptake steps occurring at intermediate relative humidity (10-30 %) [20]–[23] allowing them to be regenerated at low temperatures [24]. MOFs have also been shown to have tunable adsorption steps via replacement of either the metal ion or organic linker [25], and ability to simultaneously adsorb gaseous pollutants such as formaldehyde [26]– [34], benzene [35]–[37], and other volatiles [38], [39]. Recent studies have shown that MOFs can undergo hundreds or thousands of water adsorption/desorption cycles without significant losses in performance, allaying some of the early concerns about material stability [40],[41]. Over 90,000 individual MOFs have been described in the literature [42] and the availability of vast libraries of organic and inorganic building blocks offers a nearly infinite scope of possible combinations. As the subject of the current work is leveraging the differences in isotherm shapes for improving dehumidification performance, first a detailed accounting of the ways in which sorbent properties, particularly isotherm shape, affect dehumidification performance presently is given. The isotherm shape is one of the primary differences between the class of MOF sorbents and commonly used inorganic sorbents such as zeolites and silica gel, as shown in Figure 2. MOF sorbents have isotherms characterized by a steep jump, as shown for MIL-125 and KMF-1 in Figure 2, usually referred to as Type IV or V isotherms (this isotherm shape will be referred to as MOF isotherms from here forward). Meanwhile, commonly used inorganic sorbents such as zeolites have Type I isotherms characterized by monotonic increase in moisture content and then saturation (referred to as Type 1 isotherms from here forward). Silica gel has a linear isotherm, characterized by near-linear relationship between air humidity and sorbent water content (referred to as linear isotherms from here forward). For the purposes of demonstrating the effect of the isotherm shape on operation of sorbent-based dehumidification systems, Figure 3 shows idealized isotherms of each type-Type I, linear, and MOF (Type IV or V), assuming equal maximum water uptake capacities for all. Each of these three is idealized and exaggerated for the purposes of identifying their salient features. The isotherm shape determines several secondary properties of sorbents, which are discussed presently. Maximum water uptake capacity, working capacity and required regeneration temperature. The isotherm shape directly determines the sorbent’s maximum water uptake capacity. The maximum water uptake capacity is usually defined as the mass of water adsorbed per mass of sorbent when the relative pressure (partial pressure of water vapor divided by saturation vapor pressure) of air in equilibrium with the sorbent surface is 100%. However, the working capacity of a sorbent is usually smaller than its maximum capacity depending on 1) the desired humidity under the application conditions and 2) the temperature at which the sorbent is regenerated. The working capacity of a sorbent (Δ ^^) is defined herein as the difference in mass of adsorbed water (water content) between the dry and wet states of the sorbent during normal operation [78], as shown in Figure 3. In practice, maximum capacity and working capacity can differ greatly, especially at low regeneration temperatures and especially for sorbents with shallow linear or near linear isotherms. This is one key to the improved performance of the MOFs in such systems, as shown in Figure 3. In Figure 3, three different air states are plotted as vertical dashed lines: ambient air on a typical day (50% relative humidity); the same air heated to a low regeneration temperature (causing RH to decrease moderately); and the same air heated to a high regeneration temperature (causing RH to decrease substantially). During the regeneration process, the sorbent will dry to the point that its equilibrium relative humidity matches that of the air it is in equilibrium with (regeneration air). The degree to which this drying occurs determines the working capacity of the sorbent. As shown in Figure 3, at both low and high regeneration temperatures, the working capacity of the Type V isotherm sorbent approaches its maximum capacity, because for an idealized, steep Type V isotherm, the degree to which the sorbent is dried is nearly a binary function of the temperature at which it is regenerated. In stark contrast, sorbents having a linear isotherm will have an effective working capacity that is a continuous function of the regeneration temperature rather than a binary function. While the working capacity is increased as the regeneration temperature is increased, the working capacity is smaller than the maximum capacity both at low and high regeneration temperatures. In further contrast to linear and MOF isotherms, the working capacity of a Type I isotherm (common in zeolites, idealized and exaggerated as green line in Figure 3) is small both at low and high regeneration temperatures, because the isotherm shape is such that the sorbent must be heated to very high temperatures before it releases its moisture. Driving forces for dehumidification and regeneration. The isotherm shape also strongly affects the driving forces for mass transfer into (and out of) the sorbent during dehumidification (and regeneration). In an idealized MOF isotherm shown in Figure 4, the surface equilibrium humidity changes very slightly as the water content is increased along the steep step keeping the difference between process air humidity and sorbent surface equilibrium humidity nearly constant during moisture transport process. However, in a Type I or linear isotherm, as the water uptake increases the surface equilibrium humidity increases as well, resulting in smaller moisture transfer driving force and slower mass transfer. Achievable supply humidity. The isotherm shape also strongly affects the supply air humidity that is achievable with the sorbent. A sorbent with lower surface equilibrium humidity can provide drier air. Since the surface humidity remains fairly constant during adsorption by a MOF sorbent, the humidity of the supplied dry air is not a strong function of where on the isotherm the sorbent is operating, so the MOF sorbent will supply relatively constant humidity air. However, for a sorbent with a Type I or linear isotherm, the surface humidity increases during water adsorption, and the humidity of the supply air continues to increase until the sorbent is regenerated. Other sorbent properties. Other sorbent material properties, including specific heat capacity and density, are not as influential as the isotherm shape is. This is mainly due to the fact that when integrated into dehumidification systems, the sorbent is coated on a structural substrate (often metal) and the mass of sorbent is small compared to the total mass of structure plus sorbent. Thus, the effect of the specific heat capacity and density of the sorbent material is small in the total mass weighted average density and specific heat capacity of the sorbent coated wall. Considering the performance advantages offered by MOFs, there has been growing interest in MOFs for adsorption-based heat pumps, chillers, and cooling systems [15], [16], [41], [43]–[72]. However, there is limited work on direct-contact air conditioning applications [73],[74]. Unlike adsorption heat pumps, for which a great deal of work has been done to investigate the benefits of MOFs, direct contact dehumidification systems used in building air conditioning differ in a few distinct ways: 1. A single working fluid, which is the air eventually being supplied to the building, is used and contacted directly with the sorbent. 2. Incoming fluid conditions are those of ambient air outside that is being conditioned, those of return air from the building, or a mixture of the two. 3. The sorbent is typically housed in a rotating wheel that moves between supply and regeneration streams, as shown in Figure 5. 4. Regeneration occurs via heating the air entering the regeneration side of the wheel, rather than, for example, heating the sorbent itself. Erkek et al. [73] simulated a small-scale sorbent coated heat exchanger to evaluate the performance of silica gel in comparison to a specific type of MOF (Aluminum Fumarate). Their results showed that under the same operating conditions, the heat exchanger coated with Aluminum Fumarate had greater dehumidification capacity by 8%, greater regeneration capacity by 11% and greater working capacity by 41% over the silica gel-coated heat exchanger. Xu et al. [74] modeled a sorbent coated heat exchanger and compared the performance of silica gel and a specific MOF (Cu-BTC (HKUST-1)) as the sorbent. The MOF-coated heat exchanger showed enhanced performance compared to the silica gel-coated heat exchanger although the MOF chosen in their system (HKUST-1) had a lower water uptake capacity compared to silica gel in high relative humidity. Very little work has been done to systematically investigate how MOFs can benefit direct-air-contact sorbent dehumidification systems. To this end, the overarching motivation of this work is to systematically articulate the advantages conferred by MOFs to sorbent-based dehumidification wheels used in buildings. In order to do this: 1) A first-principles physical model of a sorbent wheel is developed, parameterized in such a way that it can take different sorbent isotherms as input and validate this model. 2) The validated model is used to quantify the benefits to the system of a number of selected MOFs that have been described in the literature, in terms of system performance and energy requirements. 3) The ideal MOF is identified for dehumidification in terms of regeneration energy requirement and performance, and regeneration temperature. Methodology. In order to quantify the ways in which these differences in material properties result in differences in the operation of sorbent dehumidification systems employing them, a first-principles dynamic model of a sorbent dehumidification and regeneration system was first created and it was validated with experimental data from the literature. Then, keeping all geometrical properties and heat and mass transport coefficients constant, different sorbent isotherm types were employed to examine the effect of sorbent isotherm on the results. For this purpose, several existing MOFs for outdoor air dehumidification purposes were selected and their performance was evaluated using the model at four different outdoor conditions. Finally, the results are discussed using an analytical framework that relates sorbent water adsorption isotherm shape to performance of a sorbent dehumidifier made of that material. First-principles dynamic model. Dynamic simulations of a honeycomb sorbent wheel system were conducted using a first-principles discretized heat and mass exchanger model built in the Dymola platform. The model heat and mass transfer coefficients, geometry, inlet conditions, and airflow rates are defined identical to the experimental work of [79]. The diameter of the wheel is 32 cm with a length of 20 cm, and hydraulic diameter of 2.1 mm. The mass flow rates of process and regeneration air are 0.185 and 0.066 kg/s, respectively. The rotational speed of the wheel and ratio of dehumidification/regeneration sections was optimized for each sorbent such that regeneration began immediately after the sorbent became “full” (at its working capacity) and stopped when the sorbent equilibrium humidity was that of the regeneration air. The assumptions made to simulate the dehumidification and regeneration channels are as follows: - Dehumidification and regeneration channels are perfectly sealed and insulated, and no heat and mass transfer occur with the ambient. - Flows are laminar and fully developed in all channels. - All fluid properties including density, thermal conductivity and specific heat are constant and independent of pressure and temperature. - Heat and mass transfer in the flow direction is negligible. Based on these assumptions, the transient coupled heat and mass transfer equations are as follows. Energy balance on air: ^^ ^^^ ^^ ^^ ^^^^^ ^^ ^^ℎ^^^ ^^ ^^ ^ೌ^^ ^^ ^^ ^ ^^^ ^^^ ^^ ^^^ ^ೌ^^ ^^ ^^ ൌ ℎ ^^^ ^^ ^௪ െ ^^ ^^^ ^ (1) Mass
Figure imgf000024_0001
^^ ^^^ ^^ ^^ ^^^^^ ^^ ^^ℎ^^^ ^^ ^^ ^ೌ^^ ^^ ^^ ^ ^^^ ^^^ ^^ ^^^ ^ೌ^^ ^^ ^^ ൌ ℎ ^ ^^൫ ^^ ^^,^௪ െ ^^ ^^^ ൯ (2)
Figure imgf000024_0002
^^ ^^ ^^ ^^^ ^௪ ^^ ^^ℎ^^^ ^^^^^ ^^ ^^ ൌ ℎ ^^^ ^^ ^^^ െ ^^ ^௪ ^ ^ ^^ ^ௗ^ ℎ ^ ^^൫ ^^ ^^^ െ ^^ ^^,^௪ ൯ (3) (4)
Figure imgf000024_0003
^^ ^^ ^^ and ^^^^^ are mass weighted average of the wall and sorbent material density and specific heat capacity, respectively. All the details of the calculations of the transport coefficients as well as the geometry of the channels are based on references [79] and [80]. Representation of sorbent in numerical model. The system of governing energy and mass balance equations are completed with the sorbent water uptake isotherm equation which provides the surface equilibrium humidity of the sorbent as a function of the water content at any temperature. In order to do this, the isotherm is first idealized and parameterized as explained below, and then this parametrized sorbent isotherm is modeled as a pre-defined class in the Dymola software, which can be used in a dehumidifier heat exchanger or any other applications. A general form of the Type V isotherm can be idealized as three piecewise defined linear functions and described by five parameters: the relative humidity at the adsorption step (step RH), three slopes (m1, m2, m3) and maximum capacity as shown on Figure 6. By definition, an isotherm relates equilibrium humidity to water uptake at a single temperature (hysteresis between adsorption and desorption isotherms is not modeled because for the MOFs chosen for this study no significant hysteresis has been reported [58], [72], [81]–[85].) In order to generalize this relationship for any temperature, the Polanyi [86] and Dubinin [87] adsorption potential model was used, which relates water adsorption potential (AP) of any adsorbent to its surface temperature (T), equilibrium vapor pressure (p) and saturation vapor pressure (p0) as shown in Equation 5. ^^ ^^^ ^^, ^^^ ൌ െ ^^ ^^ ln ^^ ൬ ^^^^ ^^^ ^ (5) in which R is the universal all
Figure imgf000025_0001
temperatures collapse into one curve with an adsorption step appearing at a specific AP value (Figure 6). This model was used to relate water uptake and equilibrium humidity at all operating conditions. It is also worth-mentioning that Type I and linear isotherms can also be approximated with this piece-wise linear function as well. Figure 7 shows the piece-wise linear isotherm parameters of silica gel representing a linear isotherm as an example. Another influential parameter in the heat transport model is the heat of adsorption ( ^^ ^^ ^^ ^^), which varies based on sorbent and is a function of the water adsorption isotherm. Based on the Dubinin–Astakhov approach explained in the work of D. Lenzen et al. [82], the heat of adsorption or isosteric heat can be calculated using Equation 6 in which ℎ ^^ ^^ ^^ is the water heat of vaporization and ^^ ^^ is the adsorption potential. ^^^ௗ^ ^ ^^ ^ ൌ ℎ௩^^ ^ ^^ ^ ^ ^^ ^^ ^ ^^, ^^ ^ (6) Equation 6 is used to calculate the heat of adsorption in the numerical simulation by making heat of adsorption another output of the isotherm class. The isotherm parameters, temperature of the surface, and water content are provided as input and surface humidity ratio and heat of adsorption are given as outputs. Definition of system performance. In order to quantify the performance of the dehumidification/regeneration system, the regeneration efficiency ( ^^ ^^ ^^ ^^) was defined as the ratio of moisture removal rate multiplied by heat of adsorption (minimum energy needed to remove moisture) divided by the regeneration power input, as shown in Equation 7. This is similar to the regeneration effectiveness introduced in [79]. ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ൬ ^^ ^^ ^^ ௪ ^ ൈ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ൬ ^^ ^^ ^^ (7)
Figure imgf000025_0002
to elucidate the individual sources of efficiency loss in sorbent dehumidifiers. The useful component of the Regeneration Power Input is the energy required to transform the moisture adsorbed on the sorbent into a gaseous state, which is defined as moisture removal power and is equal to the numerator of the regeneration efficiency, making ^^ ^^ ^^ ^^=1 for a perfect system. Moisture removal power and can be calculated as shown in Equation 8, assuming the number of adsorption/desorption cycles per second ( ^^ ^^ ^^ ^^ ^^ ^^) is known. The sorbent water uptake in each cycle is equal to the sorbent mass ( ^^ ^^ ^^ ^^ ^^) multiplied by the integral of sorbent working capacity (Δ ^^) over the time of one cycle (Δ ^^). ∆௧ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ൌ ^^^௬^^^ ^^^^^^ ^ ∆ ^^ ^^^ௗ^ ^^ ^^ (8) ^
Figure imgf000026_0001
mechanisms. These include the power needed to increase the temperature of sorbent mass to the regeneration temperature at the start of the regeneration process, and the power lost in exhausted regeneration air. These two losses can be described mathematically with Equation 9 and Equation 10. ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ℎ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ൌ ^^^௬^^^ ^^^^^^ ^^^ೞ^^್൫ ^^^^^ െ ^^^^^൯ (9) ∆௧ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ℎ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ൌ ^^^௬^^^ ^ ^^^ ^^^ ^^^ೌ^^ ^ ^^^௫^ െ ^^^^^ ^ ^^ ^^ (10) It
Figure imgf000026_0002
that accounts for the heating of the structure housing the sorbent that similarly must take place every cycle, and that Equation 9 represents the least amount of power needed to get the sorbent to its regeneration temperature. Isotherm shapes determine two influential terms in the regeneration efficiency formulation: the working capacity of the sorbent which is a function of isotherm shape as explained above; and the time needed for regeneration and dehumidification in each cycle. This latter variable is a function of the driving forces for moisture transfer, which in turn are a strong function of isotherm shape as explained below. The mechanisms of influence of these two terms in the performance of the system with different sorbents is explained in greater detail in the results and discussion section. Selection of MOF candidates for performance evaluation. A number of metal organic frameworks described in the literature were selected to evaluate their performance as sorbents in sorbent wheels under a variety of outdoor conditions. The criteria for selection of these MOFs included: 1) reported maximum water uptake capacity, 2) location of water uptake relative humidity step, and 3) documented stability under water adsorption/desorption cycles. Figure 8 shows the water uptake isotherms of the selected MOFs. MOFs containing aluminum nodes have shown desirable characteristics in the literature including high stability of water adsorption properties, low cost of production, and green and non-toxic nature [96]. Some of these MOFs include: ^ CAU-10: A layer of CAU-10 coated on a metallic layer placed on a heat exchanger plate has shown stability under over 10,000 adsorption/desorption cycles with temperatures ranging from 20 to 120°C. A minimum regeneration temperature of 70°C was reported to be sufficient to completely dry the material [81]. ^ CAU-23 (Al), another type of Al-based MOF has shown stability under a minimum of 5,000 adsorption/desorption cycles between 20 and 120°C, both in powder form and non- crystalline CAU-23-coated aluminum sheets, as well as a thermal stability under temperature as high as 400°C [82]. ^ Another Al-based MOF, Al-fumarate (Al) has shown to be stable under 4,500 adsorption/desorption cycles between 20°C and 125°C with a minimum regeneration temperature of 65°C reported [58]. ^ MIL-160 (Al) is another Al-based MOF which is expected to have long-term stability similar to other Al-based MOFs such as CAU-10, since the cyclability tests of MIL-160 have not shown any weight loss change between the second cycle and greater [72]. This MOF and CPO- 27 (described below) have nearly Type 1 isotherms. We include them to demonstrate the difference in performance of these different isotherm shapes. ^ KMF-1 (Al) is also an Al-based MOF with green and high-yield synthesis and stable over at least the 50 adsorption/desorption cycles and a regeneration temperature of 70°C and lower [76]. Other MOFs were chosen for evaluation including: ^ MIL-125-NH2 (Ti), with a reported stability measured under multiple adsorption/desorption cycles (between 313 to 383 K) showing that the water uptake capacity changed slightly after the first cycle but remained constant afterwards and a regeneration temperature of 348 K (75°C) [83]; ^ MIL-125 (Ti), exhibiting a similar shape to MIL-125-NH2; ^ MOF-841 (Zr), which has shown robust water adsorption stability after at least 5 cycles [97]; ^ CPO-27 (Ni) which has shown only 0.35% degradation of water adsorption after 10 cycles but requires a high regeneration temperature (which is expected due to the low step RH) [85] (nearly Type 1 isotherm, included for contrast as mentioned above); and ^ Co2Cl2(BTDD) (Co) which is stable over 30 cycles and has a water uptake capacity of 1 gr/gr which is more than twice the capacity of other MOFs [95]. Derivation of the isotherm parameters for selected MOFs. In order to input the isotherm shape of the selected MOFs into the dynamic model, the isotherm parameters defined above for each of the selected MOFs need to be derived. To do so, piece-wise linear functions were fitted to the isotherm of the MOFs at 25°C and the corresponding isotherm parameters were found, shown in Table 1. Table 1. Regeneration efficiency of the system for different sorbent types. Reference Sorbent Type Step RH m1 m2 m3 Maximum capacity [g/g] 89 90 81 CAU 10 Al 02 013 867 013 038
Figure imgf000028_0001
Selected inlet condition and regeneration temperatures. The dehumidification and regeneration air inlet conditions strongly affect the performance of a dehumidification/regeneration system. In a more humid environment, the sorbent surface equilibrium humidity needs to be increased to a greater humidity for regeneration, compared to the case where the regeneration air stream is less humid. This requires a greater regeneration temperature in the more humid environment for the same sorbent, assuming that pure ambient air is used for regeneration. Also, depending on the ambient humidity and temperature, different MOFs with different locations of Step Relative Humidity will result in different system performances. Thus, the selected MOFs were examined under a variety of ambient (inlet) conditions and regeneration temperatures. The selected ambient conditions and regeneration temperatures are shown in Table 2. Table 2. Inlet conditions and regeneration temperature used in each case study. Inlet Inlet Regeneration Case Study Temperature Humidity Ratio Temperature Sorbent Type el el el el
Figure imgf000029_0001
Validation of Numerical Model. First, the model was validated with the experimental results of Mandegari et al. [79] having identical geometrical properties, heat and mass transfer coefficients and dehumidification and regeneration air flow rates, under inlet conditions and regeneration temperature shown in Table 2. The sorbent used for this simulation is silica gel with the isotherm parameters shown in Figure 7. Figure 9 shows the comparison between the model results and experimental results of [79] as a function of regeneration temperature for inlet temperature of 35.5°C and inlet air humidity ratio of 0.011 kg/kgdry air and for a regeneration temperature range of 50 to 150°C. Figure 10 shows the comparison between the model results for regeneration efficiency and experimental results of [79] for two inlet conditions of dry and humid and inlet temperature range of 27 to 47°C. Both figures show an acceptable error between the results of the model and experiments of [79]. Performance results for selected MOFs. In this section, the results of the simulations are presented to evaluate the effect of sorbent isotherm parameters on the performance of the dehumidification/regeneration system for the selected MOFs mentioned in Table 1 and four different inlet conditions and regeneration temperatures shown in Table 2. Effect of regeneration temperature. As mentioned, one expected benefit of MOFs is their ability to be regenerated at low temperatures compared to traditional sorbents. Figure 11 shows regeneration efficiency results as a function of regeneration temperature for different MOFs, in comparison with silica gel. At low regeneration temperatures, the regeneration efficiency is small since the MOF is not fully regenerated yet. As the regeneration temperature increases, the MOF becomes fully dry and the regeneration efficiency reaches its maximum. From that point, increasing the temperature does not add any benefit and the regeneration efficiency decreases since more energy is used to increase the temperature. Thus, for each MOF there exists a regeneration temperature at which the MOF can be regenerated (minimum regeneration temperature) and a temperature at which the regeneration efficiency is maximum (optimal regeneration temperature). Both the minimum and optimal regeneration temperatures are a function of inlet air humidity and the relative humidity of the water adsorption step (referred to as step RH), which are discussed below. Effect of inlet air humidity. In more humid inlet conditions, a greater temperature is required to increase the surface equilibrium humidity of the sorbent and create the necessary humidity difference between air and sorbent to induce moisture transport. So, as Figure 11 shows for the same MOF, as the inlet humidity is decreased, the MOF starts regenerating at a lower regeneration temperature. For example, at inlet of 36°C and 0.035 kg/kgdry air, MOF-841 is not regenerated until regeneration temperature of 70°C, while as the inlet humidity is decreased to 0.015 kg/kgdry air, MOF-841 is regenerated at 50°C. Effect of relative humidity of the water adsorption step (“step RH”). Figure 12 shows the relationship between step RH and minimum regeneration temperature, and the combined effect these variables have on regeneration efficiency. In Figure 12, MOFs are sorted with step RH increasing from left to right. Minimum regeneration temperature is plotted as black dots for each MOF and each inlet condition. It can be seen that as step RH increases, minimum regeneration temperature decreases, and regeneration efficiency at the minimum temperature increases. Figure 12 shows that at an inlet air humidity of 0.015 kg/kgdry air (a moderate ambient humidity), MOFs with step RH of 28% and greater (which include Al-Fumarate, Co2Cl2(BTDD) and CAU-23) can be regenerated at a temperature as low as 40°C. This makes these MOFs ideal candidates for regeneration with a low-temperature heat source such as inexpensive solar thermal or waste heat. In Table 3, the performance of the MOFs is categorized based on their step RH. Table 3. Optimal Regeneration temperature (optimal Treg) for each MOF category. MOF category * %
Figure imgf000030_0001
The changes in regeneration efficiency with isotherm shape are a function of the three energy end-uses described above: sorbent heating, exhaust air losses, and moisture removal energy. The proportion of energy use attributable to each of these is a function of two intermediate variables: amount of time spent in each adsorption and desorption cycle, and the amount of moisture adsorbed and desorbed in each cycle. These two variables interact with the effects of regeneration temperature and ambient conditions to produce the behavior shown in Figure 11, which is explained mechanistically below. Regeneration temperature. Scavenging air losses and sorbent heating losses decrease when regeneration temperature decreases, resulting in greater regeneration efficiency. As shown in Figure 12, minimum regeneration temperature is a strong function of step RH. At a given temperature, a MOF with a greater step RH will have a greater equilibrium humidity (and thus a great moisture driving force into regeneration air) than its counterpart with a lower step RH. This means it can be regenerated at a lower temperature. As a counterexample, Figure 11 shows CPO- 27 and MIL-160 (with step RH’s of 1% and 3%, respectively, approaching the behavior of zeolites or other sorbents with Type I isotherms), cannot be regenerated at temperatures where MOFs with greater step RH such as Co2Cl2(BTDD) and CAU-23 can be regenerated. Working Capacity. Other factors including the sorbent moisture working capacity also affect the regeneration efficiency. Figure 13 shows that CAU-23 is capable of adsorbing a larger quantity of water in the dehumidification process even though its maximum capacity is nearly identical to that of Silica Gel. This is due to the differences in working capacity described above. Both of these lead to greater regeneration efficiency for CAU-23 than silica gel. Time spent in each adsorption and desorption cycle. Figure 13 also compares the dehumidification and regeneration times of silica gel and CAU-23 for a period of 500 seconds. The regeneration time of CAU-23 is shorter compared to silica gel. Regeneration efficiency is strongly affected by the time needed to adsorb (or desorb) the working capacity of water. This is a function of the driving forces for mass transfer into (or out of) the sorbent, which is in turn a function of the isotherm shape. The slope m2 and step RH determine the moisture transport driving force in the regeneration and dehumidification processes. This is one of the main differences between a linear and a Type V isotherm as explained above. For a MOF with a greater step RH, the humidity difference between the surface equilibrium and regeneration air stream is greater, resulting in a faster regeneration process and thus a lower scavenging air exhaust loss (less scavenging air needs to be used for regeneration). This is one reason for the increase in regeneration efficiency with step RH shown in Figure 12. Similarly, sorbents with linear isotherms rather than vertical (MOF) isotherms will see driving forces diminished during a cycle as equilibrium humidity gradually reaches ambient as explained above, with similar consequences for time spent in each cycle. Conclusions. In this work, the effect of sorbent isotherm shape on the performance and energy requirements of a dehumidification system was investigated. A first-principles dynamic model of the proposed system was developed in Dymola software including the definition of a specific sorbent class based on the parametrized isotherm shape for any sorbent. The performance of the system was evaluated under four different inlet conditions and for 11 different solid sorbents, including 10 known Metal Organic Frameworks possessing steep Type V isotherms, and for silica gel. The minimum required regeneration temperature was investigated for each MOF under each inlet condition and the performance of the system was compared at the minimum regeneration temperature. The advantages of MOF isotherms over those of sorbents traditionally used in desiccant systems are as follows: - With identical maximum water capacities, properly selected MOF sorbents can absorb more moisture than linear-shaped sorbents due the steep water uptake step, especially at lower regeneration temperatures. - MOF sorbents maintain a fairly constant surface humidity ratio during the moisture transfer process which results in a faster regeneration process and less energy loss compared to linear sorbents. Depending on relative humidity at which the water uptake step occurs, sorbents exhibiting MOF isotherms can be regenerated at a much lower temperature than those with linear or Type I isotherms. The First-principles dynamic model simulation results showed that a MOF-based dehumidification/regeneration system can have a regeneration efficiency of two to ten times greater than silica gel-based systems, depending on inlet conditions. Of the subset investigated, the MOFs exhibiting the greatest regeneration efficiencies at different inlet conditions were MOF-841 (Zr), Co2Cl2(BTDD) (Co), Al-fumarate (Al) and CAU- 23 (Al), having Step RH of 22%, 29%, 28% and 29%, respectively. Table 4 summarizes the maximum regeneration efficiency corresponding to each of these MOFs at each of the four inlet conditions and the regeneration temperature at which the maximum regeneration efficiency occurs. Table 4. Maximum regeneration efficiency of the MOFs at four inlet conditions and the regeneration temperature at which maximum regeneration efficiency occurs. 36°C, 36°C, 29°C, 29°C, 0.035 kg/kgdry air 0.022 kg/kgdry air 0.023 kg/kgdry air 0.015 kg/kgdry air )
Figure imgf000033_0001
l- fumarate (Al) and CAU-23 (Al) with Step RH of 29%, 28% and 29%, respectively. The minimum regeneration temperatures required for these MOFs were between 40°C to 60°C, depending on the inlet conditions. The scope of this study was limited to validated numerical analysis. Subsequent experiments can investigate MOF dehumidification systems under normal operating conditions. Future work in this area can also include investigation into integration of MOF sorbents with other air conditioning components and synergies that can be leveraged. Nomenclature Greek Symbols AP Adsorption Potential (J/mol) ΔW Sorbent Working capacity (kgwater/kgsorbent) Cp Specific heat capacity (J/kgK) ηreg regeneration efficiency (-) h heat transfer coefficient (W/m2K) ρ Density (kg/m3) Hads heat of adsorption (J/kg) ω humidity ratio (kgwater/kgdry air) hm mass transfer coefficient (kg/m2s) hvap water heat of vaporization (J/kg) Subscripts m slope of isotherm (-) 1 first linear segment of isotherm second linear segment of M Mass (kg) 2 isotherm MAX Sorbent maximum water uptake 3 third linear segment of isotherm Capacity capacity (kgwater/kgsorbent) ^^^ mass flow rate (kg/s) air air Number of adsorption/desorption cycles Ncycle amb ambient air per second (1/s) P equilibrium vapor pressure (Pa) cycle adsorption/desorption cycle P0 Saturation vapor pressure (Pa) cw channel wall R universal gas constant (J/mol.K) eq equilibrium RH Relative Humidity (-) exh exhaust air Relative Humidity of adsorption in step RH m mass isotherm @25°C (-) th dehumidification channel thickness (m) sorb sorbent T Temperature (°C) t Time (s) W sorbent water uptake (kgwater/kgsorbent) w dehumidification channel width (m) location on the dehumidification x channel length (m) References [1] P. 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Janiak, “Programming MOFs for water sorption: Amino-functionalized MIL-125 and UiO-66 for heat transformation and heat storage applications,” Dalt. Trans., vol.42, no.45, pp.15967–15973, Dec.2013. [95] A. J. Rieth, S. Yang, E. N. Wang, and M. Dincǎ, “Record Atmospheric Fresh Water Capture and Heat Transfer with a Material Operating at the Water Uptake Reversibility Limit,” ACS Cent. Sci., vol.3, no.6, pp.668–672, Jun.2017. [96] M. P. Silva et al., “MIL-160(Al) MOF’s potential in adsorptive water harvesting,” vol.27, pp.213–226, 2021. [97] H. Furukawa et al., “Water adsorption in porous metal-organic frameworks and related materials,” J. Am. Chem. Soc., vol.136, no.11, pp.4369–4381, Mar.2014. Example 2 – multi-stage MOF system Different MOFs have different locations for their Step RH, which mainly defines the supply humidity ratio of the air being dehumidified using the MOF. If the Step RH of the MOF is smaller, the MOF can provide a lower humidity ratio in the supply air. At the same time, when the MOF has a small Step RH, a high temperature is required to remove the water adsorbed in the MOF (regenerate the MOF). This initiates the idea of a staged MOF dehumidification system, in which instead of using one single MOF with a specific Step RH, a number of MOFs with different values of Step RH are used in parallel dehumidification wheels. The first wheel that air enters is the wheel containing the MOF with the biggest Step RH and then as air dries, is passed to the next wheel containing the MOF with smaller Step RH that can dry the air further. Using such a design, the humidity ratio of the supply can be decreased as much as desired, without the need for a very high regeneration temperature, as just a small portion of water is adsorbed on the MOF with small Step RH compared to a system where only one single MOF with small Step RH is used and all the moisture removed from air is adsorbed to that single MOF. In addition to the above-mentioned benefit, in a multi-stage configuration, air exiting each stage can be cooled down to near ambient temperature using an air-to-air heat exchanger. This in turn will provide the opportunity to achieve a much lower humidity ratio as the heat of adsorption is removed in each process and so the humidity ratio of the MOF surface can be lower. In other words, a multi-stage configuration can approach an isothermal dehumidification process which is more efficient than a constant enthalpy process that occurs in a single-stage configuration. A multi-stage configuration can provide supply air with lower humidity ratio which in turn results in a colder supply leaving the indirect evaporative cooling (IEC) side, with a lower power required for regeneration. Figure 14 shows a sample configuration of the multi-stage system, where four different dehumidification wheels are used, each containing one MOF with a different Step RH. From left to right, which is in the direction of the flow, the Step RH of the MOFs decrease. The number of the dehumidification wheels and the values of the Step RH of the MOFs is dependent on the desired humidity ratio at the supply and can be tuned based on that. As explained above, the MOF with a smaller Step RH requires higher regeneration temperature, so from left to right, the temperature of the regeneration air should be increased. Figure 15 compares the dehumidification and cooling processes of a single-stage dehumidification wheel of a small Step RH MOF with the dehumidification process in a multi- stage dehumidification wheel system. As shown in Figure 15 the multi-stage configuration can provide a lower humidity ratio in supply air which in turn will result in achieving a much lower temperature in the IEC side. While in the single-stage configuration, since the heat of adsorption is not removed, the temperature of the MOF surface increase during the constant enthalpy process, in turn increasing its surface humidity ratio resulting in a higher humidity ratio in the supply air compared with the multi-stage system. In the regeneration side, in the multi-stage configuration, only a small portion of the total moisture removed is adsorbed on the small Step RH MOF, meaning that only a small mass flow rate of high temperature regeneration air is required to regenerate the small Step RH MOF in the multi-stage configuration. In contrast, in the single stage configuration all the mass flow rate of regeneration air should be provided at the high regeneration temperature. Table 5 compares the coefficient of performance (COP) of single-stage and multi-stage configurations. As shown in Table 5, the multi-stage system both provides a drier and cooler supply and requires lower energy for the regeneration. In the single-stage configuration, all the required mass flow rate of regeneration air should be provided at the highest regeneration temperature, while in the multi-stage configuration, only a small portion of the total regeneration air mass flow rate should be at the highest regeneration temperature which in turn results in a higher COP of the multi-stage system. Table 5. Coefficient of performance for single-stage and multi-stage configurations. Single-Stage COP Multi-Stage COP ^^^ ^௨^^^௬∆ℎ^௨^^^௬ೞ^^^^^ ೞ^ೌ^^ ^^^ ^௨^^^௬∆ℎ^௨^^^௬^ೠ^^^ ೞ^ೌ^^ ^ర
Figure imgf000044_0001
A Metal-Organic Framework- based open-cycle adsorption air conditioning has been described that employs a low-temperature external heat source to drive the cycle. Herein, a system is developed that derives most, nearly all, of the energy needed to drive the cycle from the air being conditioned, thus removing the need for all but a small amount of external energy input. This is made possible by staging adsorption of moisture in multiple types of MOFs with steps in their respective Type 5 isotherms located at relative humidity values that decrease with each stage. Alternating sensible heat exchangers are placed in between each stage, removing the heat of adsorption and using it for regeneration of the next stage MOF. This eliminates or nearly eliminates the need to add external energy to regenerate the MOF (the main energy input to the original system) for all but the very first stage. This provides two simultaneous benefits: 1) removing sensible heating (making air colder as air conditioners are supposed to do) and 2) using this energy to displace external energy for regeneration of MOF. This concept can also be enhanced with evaporative air conditioning to provide sensible cooling rather than just dehumidification. Example 4 - Approaching theoretical maximum energy performance for desiccant dehumidification using staged and optimized metal-organic frameworks Abstract. Dehumidification systems including desiccant wheels are widely used in commercial and a few residential air conditioning systems to remove latent loads. These wheels require high-temperature heat to regenerate and are often quite inefficient, with a typical single- pass efficiency of around 20%. In this work, a desiccant wheel system is disclosed that takes advantage of the unique behavior of metal-organic frameworks (MOF) sorbents. It is shown that for any given entering air condition, there exists an optimal MOF that if included in the dehumidification systems will results in maximum efficiency. Based on this idea, a multi-stage dehumidification system is developed in which each stage uses the optimal MOF. To do so, first a MOF-based desiccant wheel system was mathematically modeled and validated, which was then used to systematically identify an optimal MOF isotherm shape as a function of inlet air conditions. with the model is then extended to different multi-stage MOF-based desiccant wheel systems which are optimized to achieve energy performance far exceeding a single-desiccant wheel. A validated discretized dynamic model is used to compare the energy needed for operation of these systems with other possible configurations. Finally, it is shown that an optimized staged MOF system can approach the theoretical maximum energy performance for desiccant dehumidification, using nearly 100% of regeneration energy for desorption of water and wasting very little. The results also show that a multi-stage MOF-based dehumidification system can have a regeneration efficiency 2 to 5 times greater than a single-stage system. Adding adsorption heat removal stages between the desiccant wheel stages can increase the regeneration efficiency by 5-20%, and the dehumidification effectiveness of the system 20-40%. Introduction. Air conditioning accounts for approximately 5% of energy demand in the United States and rapidly increasing demand in the developing world. A large fraction of this demand is from latent loads, especially in humid climates. Desiccant-based dehumidification systems employing solid desiccant wheels, and increasingly liquid desiccant systems, are widely used in commercial and a few residential air conditioning systems to remove these latent loads [A1]-[A10]. The improvements in humidity control and of air conditioning efficiency offered by desiccants are well documented [A7], [A9], [A11]-[A16], [A17]-[A20]. The primary energy input in a desiccant system is the heat needed to regenerate the desiccant. Heat is added either to scavenging air or to the desiccant itself, and some of this heat is used to enact the phase change in the adsorbed water, while some is lost in the exhaust air. A desiccant system’s “regeneration efficiency” compares the energy used to desorb moisture (useful energy) to the total amount of energy used (including losses). Regeneration efficiency is also called DCOP or Latent COP in the literature. In this work, the term “regeneration efficiency” is used and is formally defined in Equation A9, except when referring to the work of others in which case we use their terminology- the definitions are identical. In an ideal dehumidification system, where no heat is wasted, the regeneration efficiency would be equal to 1, meaning that the energy required for regeneration of the desiccant is exactly equal to the latent heat removed from the conditioned air. However, in real dehumidification systems, the regeneration efficiency is less than 1. Sheng et al. reported a DCOP value between 0.2 to 0.28 for a silica gel-based desiccant wheel for a regeneration temperature range of 58-65 oC, and for outdoor humidity ratios of 0.01-0.02 kg/kg [A1]. Enteria et al. reported a Latent COP in the range of 0.1-0.3 for a silica gel-based desiccant wheel in a regeneration temperature range of 60-80 oC, and outdoor humidity ratio of 0.016 kg/kg [A3]. Mandegari et al. reports a regeneration effectiveness value of 0.15 to 0.28 for a silica gel-based desiccant wheel in a regeneration temperature range of 60-150 oC, and an inlet humidity ratio of 0.011 kg/kg [A21]. Shahvari et al. showed that Metal Organic Frameworks (MOFs), a new class of sorbents, can be regenerated at temperatures as low as low as 40 oC to 60 oC, reducing the energy requirements of the dehumidification systems by 1/2 to 1/8 of the conventional desiccant wheels [A22]. They reported that a MOF-based desiccant wheel can have a regeneration efficiency in the range of 0.32-0.42 with a regeneration temperature of 40-60 oC, and for inlet humidity ratio of 0.015 to 0.035 kg/kg [A18]. The improved efficiency of the MOFs analyzed by Shahvari et al. is attributable to their water uptake behavior [A22], which is most often discussed with reference to their water uptake isotherms. Figure 16 shows the water uptake isotherm of a number of MOFs. The most prominent feature of these isotherms is that at a specific relative humidity, there is a sudden increase in the water uptake, characteristic of a Type V isotherm using Brunauer’s classification system [A27]. Shahvari et al. refer to the humidity at which this sudden increase occurs as “step_RH” [A22], and showed that performance of a MOF-based wheel is a strong function step_RH, and that this function changes for different inlet conditions. Step_RH affects MOF wheel performance in two ways. A lower MOF step_RH means that the air can be dried more deeply, since the MOF step_RH defines the minimum humidity ratio that can be achieved using that MOF. At the same time, reducing step_RH reduces the moisture transport driving force in the regeneration side of the wheel, resulting in greater dehumidification time and thus more energy use. This suggests that for a given entering air condition, and a given desired supply air condition, there exists an optimal step_RH. However, as air moves through a desiccant wheel, its state changes and thus the ideal sorbent for treating the air changes with it. Another way of thinking about this is if the wheel is discretized in the direction of flow, each discrete element has a different “inlet” condition, and thus a different optimal MOF. This suggests a multi-stage MOF-based dehumidification system, in which instead of using one single MOF with a specific Step_RH, a number of MOFs with different values of Step_RH can be used in series. As over 90,000 individual MOFs have been identified and over 500,000 MOFs have been predicted in the literature [A28], and multiple means of “shifting” the step_RH have been shown [A29], it is expected to eventually be able to specify a MOF with any step_RH desired, which enables the current investigation. MOFs have been studied for several applications in building indoor environmental control [A30], adsorption- driven heat transformation [A31], and air dehumidification via desiccant-coated heat exchangers [A32]-[A35], and desiccant wheel systems [A36]-[A39]. Table 6 summarizes previous work that has explored the application of MOFs for different air conditioning applications. However, the application of MOFs as the desiccant material in a multi-stage dehumidification system, the focus of the current work, has not yet been studied, and because of the unique properties of MOFs, such a system can be expected to be qualitatively different than any system previously studied. Table 6. Applications of MOFs for dehumidification and air conditioning purposes. Application Metal Organic Frameworks Reference Adsorption Driven MIL-100, MIL-101, HKUST-1, ISE-1, [A40], [A41], [A42],
Figure imgf000047_0001
Multi-stage dehumidification systems have been used for different applications including water harvesting [A63], [A64], heat pumps [A65], [A66], evaporative cooling [A67], and desiccant cooling [A69], [A69]. Table 7 summarizes the salient features of these previous works. As can be seen, the potential benefits of a staged MOF-based desiccant system have not yet been investigated. Based on previous work [A22], [A71], multi-stage MOF-based dehumidification systems can offer important advantages over either a single-stage configuration or a multi-stage configuration that uses common desiccants such as silica gel, such as those analyzed in all previous works. Table 7. The salient features of previous works on multi-stage dehumidification. Ref. Application Sorbent Type Number of Stages Approach [A63] Water Harvesting Silica Gel 1, 2, 4, 5 Mathematical Modeling on
Figure imgf000048_0001
dehumidification performance, and how they related to MOF isotherm properties, were articulated [A22]. In this work, this understanding is used to: 1. First systematically identify optimal MOF properties for given operating conditions. 2. Then investigate whether it is possible to operate a dehumidification system at or near these optimal conditions throughout the system by staging optimized MOFs, while at the same time delivering air at a state required for a certain application. 3. Finally four different configurations for doing so were investigated. The overarching goal is to propose and analyze a system with regeneration efficiency well beyond that of systems described previously. Methodology. In this section, first the four different configurations of staged MOF-based dehumidification systems analyzed in this work are explained. Next, the process of optimization of the multi-stage systems is explained. Then, details of the first-principles dynamic model developed for analyzing these systems, and the validation process employed are explained. Finally, the metrics used to quantify performance of these systems are explained. System configuration description. The staged-MOF system proposed in this work is comprised of a series of desiccant wheels each having a MOF with a specific step_RH. The first wheel that air enters is the wheel containing the MOF with the greatest step_RH, as shown in Figure 17. Air is dried in this wheel, then it passes to the next wheel containing a MOF with a smaller step_RH, where it is dried further. On the regeneration side of the system, the regeneration air is only heated up once before it enters the last stage (Stage N in Figure 17) moving in counterflow to the process air. The exhaust of Stage N, now slightly cooler than when it entered Stage N, is used to regenerate Stage N-1, and so on, as shown in Figure 17. This is only possible when the MOF step_RH of Stage N- 1 is greater than that of Stage N because a MOF with a greater step_RH requires a lower regeneration temperature [A22]. Such a design would be considerably more difficult to achieve for a silica-gel or any other linear desiccant-based multi-stage system, as the variation in regeneration temperatures is not nearly as distinct, and fewer sorbents in that class exist. In this work, the performance of four different configurations, depicted in Figure 18- Figure 19 and Figure 20-Figure 21 along with a diagram of their respective psychrometric processes, were compared: 1) The first is a single-stage desiccant wheel which was used as a baseline (CONFIG1, Figure 18) 2) The second is a composite multi-stage configuration, meaning that all stages, although coated with different MOFs with different step_RHs, are physically joined in one wheel and therefore all move at a single speed as shown in Figure 19 (CONFIG2). 3) Figure 20-Figure 21 shows the other two configurations. One is a separated multi- stage system (CONFIG3, Figure 20) in which each wheel can move with a different speed and this speed can be optimized for the specific MOF step_RH used in that stage. 4) The other is the separated multi-stage system with adsorption heat removal stages between the dehumidification stages (CONFIG4, Figure 21). Such system makes it possible to remove the heat of adsorption from the air exiting each stage. For CONFIG2, CONFIG3, and CONFIG4, the effect of varying the number of stages in from 2-7 stages was investigated. Model development. In order to model the configurations above, a first-principles dynamic model of a single desiccant wheel was developed. The inputs to this model are the desiccant (MOF or any other type) isotherm parameters, inlet temperature and humidity, air flow rates, geometrical properties, and the wheel speed. The model then outputs several variables for performance evaluation, including the temperatures and humidity of different air streams at different locations as a function of time. The desired number of these desiccant wheel models were also connected in series which made the multi-stage configurations. Model assumptions. The Modelica language was used for performing the dynamic simulations of the model. For the calculation of heat and mass transfer coefficients, geometrical properties, and inlet airflow rates the work of Gao et al. [A72] was referred to. The diameter of each wheel was selected to be 50 cm with a channel length of 20 cm, width of 2 mm, and wall thickness of 0.125 mm. The velocity of the process air stream was 2.8 m s-1. The rotational speed of the wheel and ratio of dehumidification/regeneration sections (φ) was optimized during the optimization process. For the composite multi-stage configuration (CONFIG2), wheels containing different MOFs, move with equal speeds, while in the separate multi-stage configuration (CONFIG3) the speed of each wheel is optimized during the optimization process. The following assumptions were made before modeling the heat and mass transfer processes in the desiccant wheel: ^ Desiccant wheel channels are perfectly sealed. ^ Flows in the desiccant wheel channels are laminar and fully developed. ^ In the direction of the flow in the desiccant wheel channels, heat and mass transfer is negligible. Equations A1-A4 show the transient coupled heat and mass transfer equations based on the above assumptions. The coupled heat and mass transfer equations were discretized along the length of the channel (Figure 22). In the course of the simulations, the system of equations was then solved for each discrete element. In Equations A1 to A4, ^^ is the temperature, ^^ is the humidity ratio, ^^^^^^^ is the cross-sectional area of the channel, ^^ ^^ ^^ is the channel perimeter, ^^ℎ^௪ is thickness of the channel wall, ^^ℎ^^^ is thickness of the air layer in the channel, and ^^^ௗ^ is the isosteric heat of adsorption. Also, the average heat and mass transfer coefficients are shown as ℎ and ℎ^, respectively, with ^^^௪ and ^^^^௪ showing the mass weighted average of the wall and desiccant density and specific heat capacity, respectively. Energy conservation equation on air in the wheel channels (Equation A1): ^^ ^^^^ ^^ ^^ ^^^^^^^ ൈ ^^^^^ ^^ ^ ^^^^ ^^ ^^ ൌ ^^ ^^ ^^ ൈ ℎ^ ^^ ^௪ െ ^^ ^^^ ^ െ ^^^ ^^^ ^^ ^^^ ^^^^ ^^ ^^ ^ ^^1^ Mass
Figure imgf000050_0001
^^^^^^^ ൈ ^^ ^^ ^^^^^ ^^^ ^^ ^^ ൌ ^^ ^^ ^^ ൈ ℎ^൫ ^^^^,^௪ െ ^^^^^൯ െ ^^^ ^^ ^^^^^ ^^^ ^^ ^^ ^ ^^2^
Figure imgf000050_0002
A3): ^^ ^^ ^^ ^^ ^^ ൈ ^^ℎ^௪ ൈ ^^^௪ ^^ ^௪ ^ ൌ ^^ ^^ ^^ ൈ ℎ ^ ൫ ^^ ^^^ െ ^^ ^^,^௪ ൯ ൈ ^^ ^ௗ^ ^ ^^ ൈ ℎ^ ^^ ^^^ െ ^^ ^ ^ ^^3^
Figure imgf000050_0003
A4): ^^ ^^ ^^ ^^ ^^ ൈ ^^ℎ ^^^ ൈ ^^ ^௪ ൌ ^^ ^^ ^^ ൈ ℎ ^൫ ^^ ^^^ െ ^^ ൯ ^ ^^4^ Defining the
Figure imgf000050_0004
with the additional isotherm equation, which at each temperature relates the equilibrium surface humidity of the desiccant ( ^^^^) to its mass of water uptake W which is per mass of desiccant. The MOF type V isotherms used in this work are ideal, very steep isotherms shown in Figure 23. It should be mentioned that since the isotherm model used is a general, ideal Type V isotherm, it can represent any sorbent that possesses a Type V isotherm, and the results of the simulations are not limited to MOFs. However, since MOFs are one of the most prominent sorbents with Type V isotherms and there is a vast library of MOFs (about 90,000 MOF have been identified and 500,000 predicted to date [A28]), the ideal type-V sorbent modeled herein will be referred to as “MOF” throughout the rest of this description. In order to further ensure the availability of a MOF with an isotherm close to the type-V isotherm used in this model, a number of MOFs possessing each of the selected type-V isotherm are identified in the results. Step_RH of a MOF mostly depends on pore size and hydrophilicity. More hydrophilic MOFs generally exhibit a lower Step RH, but the position of water uptake step is a stronger function of the pore diameter [A73]. At any given temperature there exist a critical pore diameter above which the pore filling process becomes irreversible due to the capillary condensation occurring in the pores [A74]. This results in hysteresis between absorption and desorption isotherms in some MOFs with Type V isotherm. In the ideal Type V isotherm, hysteresis was not considered. Some real MOFs do show this ideal behavior and also have isotherm shapes desired for the current application. However, it is not yet clear if these MOFs will be suitable candidates for this particular application, owing to cost and stability concerns, for example. In order to quantify the effect of any hysteresis on the performance of the system studied herein, a sensitivity analysis was conducted. Additionally, a number of selected MOFs were identified from the literature possessing the Type V isotherm with the ideal step_RH and with less than 3% reported hysteresis and they are reported toward the end of this example. The maximum water uptake capacity selected is 0.4 kg kg-1 to be comparable with silica gel. However, in order to further investigate the effect of water uptake capacity of the sorbent on the performance of the dehumidification system, Type V isotherms with greater water uptake capacities were tested as well. The silica gel real isotherm was also used for a validation section, since the desiccant wheel models that exist in the literature used silica gel as the desiccant material. In order to quantify the isotherm shape into an equation that can be used in the dynamic model, Equation A5 introduced in the work of Shahvari et al. [A71] was used as a representation of the MOF Type V. This model uses four parameters of ^^, ^^, ^^, and ^^ to define the Type V isotherm. These parameters were fitted for ideal MOF isotherms and then Equation A5 was used to complete the system of equations. ^^^ ^^ ^^^ ൌ ^^ ^^^ ^^ ^^ ^^ െ ^^ ^^^ ^ ^^ ^^ ^^ െ ^^^െ ^^ ^^^ ^^^ ^^ െ ^^ ^^^ ^ ^^ െ ^^^െ ^^ ^^^ ^ ^^5^ In Equation A5, ^^ represents the Sigmoid function defined in Equation A6. ^ 1 ^^ ^^^ ൌ 1 ^ exp^െ ^^^ ^ ^^6^ This isotherm equation is inputs are isotherm parameters, and
Figure imgf000052_0001
as a function of temperature and water uptake. Then, the Polanyi [A75] and Dubinin [A76] adsorption potential model was used. This model relates water adsorption potential (AP) of any desiccant to its surface equilibrium vapor pressure (p), temperature (T), and saturation vapor pressure (p0) using Equation A7: ^^ ^^^ ^^, ^^^ ൌ െ ^^ ^^ln ^^ ൬ ^^^ ^ ^^^ ^ ^ ^^7^ in which R is the universal gas
Figure imgf000052_0002
one temperature to another. In addition to the surface equilibrium humidity ratio, the isosteric heat of adsorption ( ^^^ௗ^) is also a function of the isotherm shape of the desiccant. The Dubinin–Astakhov approach, explained in the work of D. Lenzen et al. [A24], gives the formulation needed to calculate the isosteric heat of adsorption having the adsorption potential ^^ ^^ model and the water heat of vaporization ℎ௩^^ (Equation A8). ^^ ^ௗ^ ^ ^^^ ൌ ℎ ௩^^ ^ ^^^ ^ ^^ ^^^ ^^, ^^^ ^ ^^8^ System performance evaluation. Several metrics were used to quantify different aspects of performance of the systems analyzed. Regeneration Efficiency. The regeneration efficiency ( ^^^^^) of the system describes the portion of energy used for regeneration that is actually used for desorption of water from the MOFs. ^^^^^ is defined as the moisture removal capacity over the regeneration heat input as shown in Equation A9: ^ ^^ ^ ^^^ ^^ ^^ ^^ ^௧௨^^ ^^^^௩^ௗ ^^^ ൌ ௧ ^ ^^9^ where the moisture removal the rate at which the heat of
Figure imgf000052_0003
desorption is consumed in occur and is calculated using Equation A10: ^^ ^ ^^^^௧௨^^ ^^^^௩^ௗ^ ^^ ^^^ ൌ ^^^ ^^^ ^^^ௗ^^ ^^^^ െ ^^^௨௧^ ^ ^^10^ in which ^^^ ^^^ is the
Figure imgf000052_0004
is the humidity ratio of the inlet air, and ^^^௨௧ is the humidity ratio of the outlet air dry air leaving the wheel. The total amount of heat input into the system to accomplish the regeneration ( ^^ ^ ^^^) is calculated by Equation A11: ^^^ ^^^ ^ ^^ ^^^ ൌ ^^^ ^^^൫ ℎ ^^^ െ ℎ ^^^^^^௧൯ ^ ^^11^ in which ^^^ ^^^ is the mass flow rate of the air ℎ^^^ is the of the hot regeneration air entering the
Figure imgf000053_0001
the ambient air that is used for regeneration after heating up. The regeneration heat input ( ^^^ ^^^) is actually comprised of two constituent parts: the useful component and losses. The useful component is the heat required to remove the moisture from the desiccant in each dehumidification/regeneration cycle, which is a function of the heat of adsorption as shown in Equation A12: ∆௧ ^^ ^ ௨^^^௨^^ ^^^ ൌ ^^^^^^ ^ ∆ ^^ ^^^ௗ^ ^^ ^^ ^ ^^12 ^ ^ where ^^^^^^^ ^^ ^^^^^^^^௧^ is
Figure imgf000053_0002
capacity, or, in other words, water dehumidification time and the water uptake of the sorbent leaving the regeneration side, and ∆ ^^ ^ ^^^ is the dehumidification time [A77]. Losses from the regeneration process can occur via two mechanisms. One is the energy lost in the hot exhaust air stream. This is the primary loss mechanism [A22] and can potentially be reduced in a multi-stage configuration where the exhaust of each stage is used as the regeneration stream of the previous stage and as a result its temperature approaches the ambient as it passes through the stages. Equation A13 shows how this loss is calculated: ∆௧ ^^ ^ ^௫^^௨^௧ ൌ ^ ^^^ ^^^ ^^^ಲ^^ ^ ^^ா௫^ െ ^^^^^ ^ ^^ ^^ ^ A13 ^ where ^^^ ^^^ ^ ^^ ^^ ^^ି^^ is
Figure imgf000053_0003
ambient temperatures, respectively, ^^^ಲ^^is the air specific heat capacity, and ∆ ^^ is the regeneration time in each cycle. In addition to the regeneration exhaust loss, a portion of the regeneration power input is used to increase the temperature of desiccant mass to the regeneration temperature at the start of each regeneration cycle as shown in Equation A14. ^^^ ^^^^ ^^^௧^^^ ൌ ^^ ^^^^ ^^ ^^^ೞ൫ ^^ ^^^ െ ^^ ^^^൯ ^ ^^14^ where ^^^^^^^ ^^ ^^^^^^^^௧^
Figure imgf000053_0004
temperatures, respectively, and ^^^^^ೞ is its thermal heat capacitance of the desiccant. Dehumidification Effectiveness. Next, the dehumidification effectiveness was defined as the ratio of moisture removed in the dehumidification process to the maximum possible moisture removal as shown in Equation A15: ^௧ ^ ^^^^ െ ^^^௨௧ ^ ^^ ^^ ^^ௗ^^ ൌ ^ ^^15^ ^௧ ^ ^^ ^^ െ ^^ ^ௗ^^^ ^ ^^ ^^ in which ^^^^ is the humidity air leaving the wheel, and ^^
Figure imgf000054_0001
^ௗ^^^ Maximum moisture removal is a function of the ideal outlet humidity ratio, which is in turn a function of the sorbent isotherm. Here, it was assumed that the ideal humidity ratio ( ^^^ௗ^^^) at the outlet is the humidity ratio corresponding to the MOF step_RH at the inlet temperature, which is the minimum humidity ratio that can be achieved if the dehumidification process is isothermal, and no moisture transport resistances exist. Optimization Process. The optimization process is comprised of two sections; finding the optimal MOF step_RH values for each stage, and optimizing the operational parameters including wheel speeds, wheel thickness, and regeneration-to-dehumidification section ratio for the multi-stage configurations. Optimal stage step_RH. First, the optimal MOF step_RH for each stage of the multi- stage configuration needed to be identified. This optimal step_RH depends on the inlet conditions of that stage. The optimization objective and inputs are given below: Given: Inlet Air Temperature and Relative Humidity, Regeneration Temperature Optimize: Regeneration Efficiency = f(MOF step_RH) Table 8 summarizes the conditions used for this investigation. Table 8. Conditions used for finding the optimal Step_RH of each stage. Case Inlet Relative Inlet Temperature MOF Regeneration o o )
Figure imgf000054_0002
Optimization of the wheel-related parameters. After finding the optimal value of MOF step_RH for each inlet conditions, optimization of the multi-stage configurations started with the optimal step_RH selected for each stage. In this process, the thickness of the wheel in each stage was also optimized, to make sure the optimal mass of desiccant is used in each stage. The wheel speed and the ratio of regeneration to dehumidification sections ( ^^) of each wheel was also optimized. For the separated multi-stage configurations (CONFIG3, and CONFIG4), the wheel speed can be optimized for each stage separately, meaning that each wheel can move with its unique speed. For the single-stage and the composite multi-stage configurations (CONFIG1, and CONFIG2, respectively) there is only one single wheel speed that is optimized for the whole system. The optimization objective and inputs are shown below. Given: Inlet Air Temperature & relative Humidity, Regeneration Temperature, optimal MOF step_RH Optimize: Regeneration Efficiency = f(thickness of the wheel in each stage, wheel speed in each stage, the ratio of regeneration to dehumidification sections (φ) of the wheel in each stage) With constraints: Total thickness of the wheels = 20 cm For the optimization process, the optimization tool of the Dymola was used (commercial interface of Modelica language) using the sequential quadratic programming and pattern search optimization methods to insure the independency of the optimization results from the optimization method [A78]. Investigation of the effect of adding stages to the system performance. In the final step of the investigation, the performance of a variety of multi-stage configurations were compared. Different numbers of stages were tested to see the effect of adding more stages on different performance metrics of the system. For each configuration, the investigation started with a single-stage configuration and then stages were systematically added. During this process, the optimal step_RH values were used for each stage, and the wheel speed, wheel thickness, and regeneration to dehumidification section ratios ( ^^) were optimized. The number of stages were increased up to 7 stages, at which point performance began to decrease. For this set of tests, three different inlet humidity ratios – 0.03, 0.02, and 0.01 kg kg-1 – were used to investigate the performance of different configurations under a variety of inlet humidity values. Results and discussions. In this section, the results of the validation of the first- principles dynamic model with the experimental work of Yamaguchi et al. [A8] are shown first, and then the results of the validated model for finding the optimal Step_RH for different inlet conditions are presented. Then, the effect of using the optimal values of Step_RH at each stage of the sorbent wheel system on the regeneration efficiency and dehumidification effectiveness is shown. Validation. The first-principles dynamic model was validated with the experimental work of Yamaguchi et al. [A8]. For this validation, a silica gel isotherm was used in the desiccant wheel and an inlet air temperature of 32 oC, humidity ratio of 0.0195 kg kg-1, regeneration temperature of 70 oC, and wheel thickness of 50 mm were used, identical to the reference [A8]. The results of the comparison between the model herein and the experimental reference [A8] are shown in Figure 24. In Figure 24, the supply humidity ratio is plotted as a function of wheel speed for two different inlet air velocities. The difference between the model herein and the reference [A8] is less than 5%, which shows that average supply humidity ratio agrees well with the results of the reference experiments under identical conditions. Optimal MOF step_RH depending on the inlet conditions. In this section, the results of the investigation of the optimal MOF step_RH for different inlet conditions shown in Table 8 are discussed. Figure 26 shows the regeneration efficiency values of a single MOF-based desiccant wheel (Configuration 1) as a function of the MOF step_RH and for different inlet conditions. As shown in Figure 26, the curve of the regeneration efficiency as a function of MOF step_RH is parabolic and thus has a maximum. This means that for each inlet condition, there exists a MOF step_RH that will maximize regeneration efficiency. This is attributable to two competing phenomena that affect the regeneration efficiency. On one hand, as the step_RH is increased, the minimum supply humidity ratio that can be achieved increases, meaning that with a greater step_RH, the air can be dried less. This decreases the useful portion of the regeneration efficiency as less useful work is being done, and thus results in decreased regeneration efficiency. This is shown in Figure 25. As shown on the left axis, the ratio of moisture removed to the initial moisture content of the air is decreased as the step_RH of the MOF increases. On the other hand, at equal regeneration temperatures, when the MOF step_RH is increased the difference between the surface equilibrium humidity ratio of the MOF and the regeneration air will be increased, which results in a greater driving force for moisture transport from the MOF to the regeneration air stream Figure 25 (panel A). This means that the regeneration process will happen more quickly. This is also shown in Figure 25 (panel B). The regeneration time, which is the inverse of wheel speed ( ఝ ^^^) increases as the MOF step_RH is increased. Shorter regeneration time means less heat lost via the exhaust air stream, increasing the regeneration efficiency. These two competing phenomena will result in an optimal point for step_RH at which the regeneration efficiency is maximum, as shown in Figure 26. Figure 26 shows that the optimal step_RH will vary as a function of inlet conditions and regeneration temperature. However, each set of conditions does indeed correspond to a single optimal value of step_RH. Energy and Dehumidification Performance Enhancement with Staged MOF Systems. The behavior shown in Figure 26 suggests the possibility of discretizing a single desiccant wheel into multiple stages containing different MOFs that are ideal for different inlet conditions. Each stage would then be optimized for the air entering that stage, as depicted in Figure 27, reducing losses and increasing efficiency. The value of the optimal MOF step_RH in each stage depends on the inlet relative humidity of that stage, which in turn is determined by the step_RH of the previous stage, in a staged system, since as the air moves through each stage its humidity approaches the step_RH of that stage. This humidity is then the humidity of the air entering the next stage, based on which the MOF step_RH of the next stage is selected. To demonstrate the improvement in efficiency that can be gained by leveraging the staged system shown above, in Figure 28 the results of the analysis of the four different configurations are presented: single-stage (CONFIG1), combined multi-stage (CONFIG2), separate multi-stage (CONFIG3), and separate multi-stage with adsorption heat removal stages (CONFIG4). In all configurations the MOF step_RH of each stage is the optimal MOF step_RH resulting in the maximum regeneration efficiency based on the results of Table 8. Figure 28 shows the regeneration efficiency, dehumidification effectiveness, and supply humidity ratio of all configurations as a function of number stages and for inlet humidity ratios of 0.03 kg/kg, 0.02 kg/kg, and 0.01 kg/kg. As mentioned earlier, the regeneration efficiency of an ideal desiccant dehumidification system is equal to one, which can be achieved when no losses occur during the regeneration process, and all energy is used for removing adsorbed moisture. However, typical silica gel- based systems typically only achieve 20-30% efficiency, and single stage MOF systems 30-40%. Figure 28 shows a vast increase in efficiency over previously reported values, with the best performing configuration approaching the theoretical limit of 1 for some conditions. Figure 29 further articulates the comparison between the performance of the systems analyzed in this work and those previously reported. MOF-based versus conventional systems. The first comparison that can be made from Figure 29 is between a silica gel-based system and a MOF-based system. It was previously demonstrated that MOF-based single stage systems offer substantial benefits over silica gel systems, shown again in Figure 29. Furthermore, Figure 29 shows that using a multi-stage silica gel wheel design, while holding the total mass of desiccant used equal to the baseline, not only does not add any benefit, but decreases the regeneration efficiency. This is because the total amount of moisture removed would be equal in single-stage and multi-stage configurations, while at the same time a slower wheel speed would be required to ensure complete regeneration of all stages, since the regeneration air temperature drops at each stage, which in turn decreases the regeneration efficiency. In contrast, for the MOF-based configurations, Figure 29 shows that adding stages to the system will increase the regeneration efficiency, since adding more stages with lower step_RH values can decrease the supply humidity ratio, increasing the moisture removed and at the same time, making it possible to use the heat from the exhaust of each stage for regenerating the next stage, which can increase the regeneration efficiency. Effect of number of stages on regeneration efficiency. Figure 28 shows that regardless of the inlet humidity ratio, there exists a specific number of stages at which the regeneration efficiency is maximized. The following is a discussion of why this maximum exists. The use of MOFs in the pattern described above makes it possible to use the exhaust regeneration air of one stage for the other, since as the step_RH increases, required regeneration temperature decreases. The temperature of this exhaust air then drops as it passes through each stage and approaches the ambient temperature. This is shown in Figure 31, in which the temperature of the exhaust air is plotted for different configurations. As shown in Figure 31, increasing the number of stages decreases the exhaust air temperature of the whole system. The energy in the exhaust air is one of the main loss mechanisms of the dehumidification system, as described in Equation A13 above. This phenomenon is also depicted in Figure 30, which shows that when the number of stages is increased above one, total system losses decrease as energy from exhaust of one stage is utilized for regeneration in the next stage rather than lost. However, at the same time, when the number of stages is increased, the first stages need to move very slowly in order for the regeneration to be completed. This results in a longer regeneration time, which despite the reduced exhaust temperature may result in greater overall losses. This trade-off results in an optimal number of stages to exist at which the regeneration efficiency is maximized, which was 4-5 stages for all systems analyzed as shown in Figure 28. Effect of number of stages on dehumidification effectiveness and supply humidity ratio: As shown in Figure 28, adding to the number of stages usually results in greater dehumidification effectiveness. One exception to this trend is in the composite multi-stage configuration (CONFIG2), which is due to the non-optimized rotational speed of each stage. Adding a stage means adding a lower-step_RH MOF to the whole system which will decrease the supply air humidity ratio and increase dehumidification effectiveness. This phenomenon also affects the regeneration efficiency since a lower supply humidity ratio means more moisture removed which increases the regeneration efficiency. Effect of adding the adsorption heat removal stages: In all plots in Figure 28, the multi- stage with adsorption heat removal (CONFIG4) has better performance regardless of the number of stages. Adsorption heat removal stages remove the heat of adsorption released in the previous stage. As a result, the air enters the next stage at a lower temperature close to ambient. This has two effects: 1) When the temperature of the air passing through the wheel is lower, it results in a lower equilibrium surface humidity ratio of the MOF, in turn resulting in drier air leaving the wheel; and 2) Exhaust air temperature is reduced, reducing losses. This will in turn increase both dehumidification effectiveness and the regeneration efficiency. Comparison between composite and separate multi-stage configurations: In Figure 28, the performance of the composite and separate multi-stage configurations are shown (CONFIG2 and CONFIG3, respectively). The main difference between these two configurations is that in the composite configuration, all stages move with equal rotational speeds, rather than their individual optimal speeds. In the separate configuration, each wheel moves at its optimal speed which may result in a better performance of the whole multi-stage configuration. Since different MOF step_RH values results in different moisture transport driving forces both in the dehumidification and regeneration side, there exists a specific speed for the wheel with each step_RH at which it will have the maximum efficiency. That would be the speed at which the time that takes for the MOF to become fully dried is equal to the time that the MOF spends in the regeneration process. If the wheel moves more slowly than that speed, some excess amount of hot air would be exhausted to the ambient without adding any benefit to the system. That is why the regeneration efficiency, and dehumidification effectiveness of the composite multi-stage system (CONFIG2) are less than that of the separate multi-stage system (CONFIG3) in most cases. However, there are some cases where these parameters have the same value for both CONFIG2 and CONFIG3, which are the cases where the speed of the composite wheel has been identical to the optimal speed that each stage requires, resulting in similar performance as shown in Figure 28. Analysis of the effect of maximum water uptake capacity on the performance: In order to further investigate the effect maximum water uptake capacity of the sorbent on performance, in Figure 32 the regeneration efficiency and dehumidification effectiveness of the best performing system (4-stage CONFIG 4) is shown as a function of the maximum water uptake capacity of the MOF. As shown in Figure 32, increasing the maximum water uptake capacity increases the dehumidification effectiveness and regeneration efficiency of the system. This is related to the fact that the sorbent with greater water uptake capacity can absorb more moisture in each cycle, resulting in a lower supply humidity ratio (more useful work done per cycle). In addition, fewer cycles leads to less energy wasted for heating the mass of sorbent and housing to the temperature required to regenerate, although this effect is small. These effects result in the best-performing system (4 independent stages treating humid air) having a regeneration efficiency of 94% for a sorbent with 1 g/g capacity as opposed to 90% for 0.4 g/g. It is expected that if sorbents with even greater capacities are developed, the regeneration efficiency could approach 100%, the theoretical limit. However, it can also be seen that the effect of water uptake capacity on both dehumidification effectiveness and regeneration efficiency is more substantial at lower water uptake capacities. This is because, in addition to the water uptake capacity, the step_RH of the sorbent also affects the supply humidity ratio. When the step_RH is approached by the process air, increasing the moisture removal rate by increasing water uptake capacity does not decrease the supply humidity further, reducing improvements to dehumidification effectiveness and regeneration efficiency. Analysis of hysteresis effects. In order to see the effects of hysteresis on the performance of the system, in Figure 33 the regeneration efficiency of the 4-stage model of CONFIG4 was plotted as a function of the amount of hysteresis as quantified by the difference in adsorption step_RH and desorption step_RH. As shown in Figure 33, the effect of hysteresis on the regeneration efficiency is less than 2.5% or hysteresis up to 3%. Hysteresis was limited to 3% to reflect the maximum of the candidate MOFs identified below. It is also shown the hysteresis of the MOF used in stage_4 has the most influential effect on the efficiency of the system since the supply humidity ratio of the system is limited by the step_RH of the final stage. MOF Options for each stage. In order to assess the feasibility of identifying ideal or near-ideal TYPE V isotherms needed for each stage in real-world applications, a number of real MOFs possessing the requisite characteristics for the best performing system (4-stage) are identified in Table 9. As shown in Table 9, in most cases a MOF with little or no hysteresis can be found in the literature with the desired step_RH, although further work is needed to understand the performance of these MOFs in real applications.
Table 9. Real MOF options for application in different stages of the 4-stage configuration. Stage 1 ^^ ^^ ^^ k k -1 step_RH MOF Options Hysteresis Capacity Stability Ref. ] ] ] . ] ] ] . ] ] ] . ] ] ]
Figure imgf000061_0001
Discussion on the pressure drop of the multi-stage system. From a pressure drop point of view, the total thickness of the wheels is constant and thus the total pressure drop (for composite configurations) is as well. The thickness of the Gao et al. [A72] paper was replicated in this work, which was 20 cm. No pressure drop was reported in that work but Yamaguchi et al. [A8] did include pressure drop analysis for a very similar geometry, and the model was re- validated with their work. Using the results of Yamaguchi et al. [A8] and a modification for the slightly different hydraulic diameter used in the current work via the equation below: ^^ ^^ ଶ ^^ ^^ ൌ െ ^^ ^^ ^^ 2 ^^^ ^ ^^16^ in which ^^ is pressure, ^^ is location on the wheel thickness, ^^ is the friction factor, ^^ is the density of air, ^^ is the velocity of air, and ^^^ is the hydraulic diameter of the wheel, the pressure drop in the system can be approximated to be about 255 Pa regardless of the number of stages. This is the case for Configuration 1, 2, and 3. For CONFIG 4, the inlet effects (entrance region) also needs to be considered since the wheels are separated as well as the heat exchangers used in the cooling stages. Yamaguchi et al. [A8] have shown that their predicted pressure drop with the entrance region effect is 14% higher than that without the entrance region effect at a superficial velocity of 2.8 m/s (which is the superficial velocity for our system). For the heat exchangers, [A66] has a reported a maximum of 500 Pa pressure drop for a four-stage similar system. The total maximum fan power associated with such pressure drop is less than 1 kW which is less than 10% of the total energy consumption of this 4-stage dehumidification system. Conclusion. In this work, a path to hyper-efficient desiccant dehumidification, enabled by the unique properties of metal-organic frameworks sorbents, was articulated. The efficiency of the best performing systems identified in this work is multiple times that of those discussed in the literature. As more and more robust MOFs are developed, this offers a path to large reductions in the energy required to condition air. Below the main findings are summarized: • For each inlet condition of a MOF-based desiccant wheel, there exists a specific MOF step_RH that results in the maximum regeneration efficiency of the wheel. • Using a multi-stage configuration, one can take advantage of this optimal MOF step_RH values resulting in maximum efficiency of the multi-stage system. • A multi-stage MOF-based dehumidification system can have a regeneration efficiency approximately 2 to 5 times greater than a single-stage system for two main reasons: o The MOF with the optimal step_RH resulting in the maximum regeneration efficiency is used in each stage. o The descending MOF step_RH from first to last stage, makes it possible to use the exhaust of the regeneration side of each stage for the previous stage, decreasing the total exhaust energy waste. • Increasing the number of stages up to four stages, increases both the regeneration efficiency and dehumidification effectiveness, by decreasing the exhaust air temperature and the supply air humidity ratio. Benefits of adding more than four stages are minimal or negative in the systems investigated herein. • Adding adsorption heat removal stages between the desiccant wheel stages can increase the regeneration efficiency by only 1.05 to 1.2 times, and the dehumidification effectiveness of the system by 1.2 to 1.4 times. This means that the composite configuration, which is simpler to construct, performs close to the more complex separated system from a regeneration efficiency point of view. The current investigation was limited to validated mathematical modeling of ideal systems. The cost-benefit analysis and experimental evaluation of these ideas that will need to be conducted prior to market entry were not performed. An experimental investigation and an economic analysis focused on application of MOFs as substitutes for conventional sorbents should be the focus of the future work in this area. Nomenclature ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^ ^^ ^^ ି^ ^ Greek Symbols ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ℎ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^ ^^ ି^ ^^ ି^ ^ ∆ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^௪^௧^^ ^^ ^^^ ି ^^ ^^^ ℎ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^ ିଶ ^^ ି^ ^^ The ratio of regeneration to dehumidification sections ^^^ௗ^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^ ^^ି^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^ ^^ିଷ^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^ ^^ ିଶ ^^ ି^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^ ^ ^^ ^^ ^^ ^^ ^^ℎ ^^ ^^ ^^ ^^ ^^
Figure imgf000063_0001
^^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^ ^^ ି^ ^ ^^ ^^ ^^ air ^^ ^௬^^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ି^ ^ ^^ ^^ ^^ ambient air ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^^ ^^ ^^ ^^ ^^ ^^adsorption/desorption cycle ^^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^^ ^^ ^^ Desiccant wheel channel wall Per Perimeter of the channel (m) ^^ ^^ Desiccant wheel ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^ ^^ ^^ି^ ^^ି^^ ^^ ^^ equilibrium ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^െ^ ^^ ^^ℎ exhaust air ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ Mass transfer ^^ℎ ^^ ^^ℎ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ℎ ^^ ^^ ^^ ^^ ^^ ^^ℎ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^ ^^ ^^ desiccant ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^^ ^^ water ^^ ^^ ^^ ^^ ^^ ^ ^^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^ ^^ ^^௪^௧^^ ^^ ^^^ ି ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ℎ ^^ ^^ ^^ℎ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ ^^ℎ ^^ ^^ References: [A1] Y. 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Cadiau et al., “Design of Hydrophilic Metal Organic Framework Water Adsorbents for Heat Reallocation,” Advanced Materials, vol.27, no.32, pp.4775–4780, Aug. 2015, doi: 10.1002/ADMA.201502418. EXEMPLARY ASPECTS In view of the described systems and methods, herein below are described certain more particularly described aspects of the inventions. The particularly recited aspects should not, however, be interpreted to have any limiting effect on any different claims containing different or more general teaching described herein or that the “particular” aspects are somehow limited in some way other than the inherent meanings of the language and formulas literally used therein. Example 1: A multi-stage air conditioning system comprising: a first stage in fluid communication with an air supply, the first stage comprising a first sorbent, the first sorbent having a type IV or V water sorption isotherm, a first step_RH, and a first regeneration temperature; a second stage in fluid communication with the first stage, the second stage comprising a second sorbent, the second sorbent having a type IV or V water sorption isotherm, a second step_RH, and a second regeneration temperature; wherein the second step_RH is less than the first step_RH; and wherein the second regeneration temperature is greater than the first regeneration temperature; and a heat source in thermal communication with the second stage; wherein the system is configured to operate in a dehumidification mode and/or a regeneration mode, wherein: when the system is operated in the dehumidification mode, then: the first stage is configured to: receive air having a first humidity from the air supply; contact the air with the first sorbent to thereby transfer a first amount of moisture from the air to the first sorbent and decrease the moisture content of the air to a second humidity, the second humidity being less than the first humidity; and effuse the air having the second humidity; and the second stage is configured to: receive the air having the second humidity from the first stage; contact the air with the second sorbent to thereby transfer a second amount of moisture from the air to the second sorbent and decrease the moisture content of the air to a third humidity, the third humidity being less than the second humidity; and effuse the air having the third humidity; and when the system is operated in the regeneration mode, then: the second stage is configured to: receive air having a sixth humidity; receive an amount of heat from the heat source; contact the second sorbent with the air and the amount of heat to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air with the increased moisture content and decreased amount of heat to the first stage; the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the first sorbent; and subsequently effuse the air. Example 2: The system of any examples herein, particularly example 1, further comprising: a third stage in fluid communication with the second stage, the third stage comprising a third sorbent, the third sorbent having a type IV or V water sorption isotherm, a third step_RH, and a third regeneration temperature; wherein the third step_RH is less than the second step_RH; and wherein the third regeneration temperature is greater than the second regeneration temperature; wherein: when the third stage is present, the heat source is in thermal communication with the third stage; and when the system is operated in the dehumidification mode, then the third stage is configured to: receive air having the third humidity from the second stage, contact the air with the third sorbent to thereby transfer a fifth amount of moisture from the air to the third sorbent and decrease the moisture content of the air to an eighth humidity, the eighth humidity being less than the third humidity, and effuse the air having the eighth humidity; and when the system is operated in the regeneration mode, then: the third stage is configured to: receive air having a ninth humidity; receive an amount of heat from the heat source; contact the third sorbent with the air and the amount of heat to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effuse the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to: receive the air effused by the third stage; contact the second sorbent with the air to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air having the increased humidity and decreased amount of heat to the first stage; and the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decrease the amount of heat in the air, and regenerate the first sorbent; and subsequently effuse the air having the increased humidity and decreased temperature. Example 3: The system of any examples herein, particularly example 2, further comprising: a fourth stage in fluid communication with the third stage, the fourth stage comprising a fourth sorbent, the fourth sorbent having a type IV or V water sorption isotherm, a fourth step_RH, and a fourth regeneration temperature; wherein the fourth step_RH is less than the third step_RH; and wherein the fourth regeneration temperature is greater than the third regeneration temperature; wherein: when the fourth stage is present, the heat source is in thermal communication with the fourth stage; and when the system is operated in the dehumidification mode, then the fourth stage is configured to: receive air having the tenth humidity from the third stage, contact the air with the fourth sorbent to thereby transfer a seventh amount of moisture from the air to the fourth sorbent and decrease the moisture content of the air to an eleventh humidity, the eleventh humidity being less than the tenth humidity, and effuse the air having the eleventh humidity; and when the system is operated in the regeneration mode, then: the fourth stage is configured to: receive air having a twelfth humidity; receive an amount of heat from the source; contact the fourth sorbent with the air and the amount of heat to thereby increase the temperature of the fourth sorbent to the fourth regeneration temperature such that the fourth sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the fourth sorbent; and effuse the air having the increased humidity and decreased amount of heat to the third stage; the third stage is configured to: receive the air effused by the fourth stage; contact the third sorbent with the air to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effuse the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to: receive the air effused by the third stage; contact the second sorbent with the air to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air having the increased humidity and decreased amount of heat to the first stage; and the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decrease the amount of heat in the air, and regenerate the first sorbent; and subsequently effuse the air having the increased humidity and decreased temperature. Example 4: The system of any examples herein, particularly examples 1-3, further comprising one or more heat exchangers in thermal communication with the first stage, the second stage, the third stage (when present), the fourth stage (when present), or a combination thereof. Example 5: The system of any examples herein, particularly examples 1-4, wherein the first stage, the second stage, the third stage (when present), and the fourth stage (when present) each independently comprises a rotary desiccant wheel. Example 6: The system of any examples herein, particularly examples 1-5, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises a metal-organic framework (MOF). Example 7: The system of any examples herein, particularly example 6, wherein the metal comprises Al, Ti, Zr, Co, or a combination thereof. Example 8: The system of any examples herein, particularly example 6 or example 7, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises an Al-based MOF. Example 9: The system of any examples herein, particularly examples 6-8, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises MIL-100, MIL-101, HKUST-1, ISE-1, Basolite C300, Basolite A100, DUT-67(Zr), UiO-66, UiO-67, NU-1000, MOF-801, CPO-27(Ni), CAU-1, CAU-1(OH)2, CAU-3, CAU-3-NH2, CAU-8, CAU-10H, MIL-53, MIL-53-NH2, MIL-125, MIL- 125-NH2, MIL-140A, MIL-140C, UiO-66, ZIF-8, Ni-MOF-74, Co-MOF-74, MIL-53, Fe-BTC, Cu-BTC, Aluminum fumarate, DUT-67, MIL-96(Al) and MIL-100(Al), FAM-Z01, Cu-BTC (HKUST-1), Al Fumarate, CAU-10, CAU-23, KMF-1, CPO-27, MOF-840, MIL-160, Co2Cl2(BTDD), MIL-101(Cr), MOF-841, In-MIL-68, or a combination thereof. Example 10: The system of any examples herein, particularly examples 6-9, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises CAU-10, CAU-23, Al-fumarate, KMF-1, MIL-125-NH2, MIL-125, MOF-841, Co2Cl2(BTDD), or a combination thereof. Example 11: The system of any examples herein, particularly examples 6-10, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises MOF-841, Co2Cl2(BTDD), Al-fumarate, CAU-23, or a combination thereof. Example 12: The system of any examples herein, particularly examples 1-11, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently can undergo multiple water sorption/desorption cycles without significant loss in performance. Example 13: The system of any examples herein, particularly examples 1-12, wherein the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), and the fourth regeneration temperature (when present) each independently is from 0°C to 140°C. Example 14: The system of any examples herein, particularly examples 1-13, wherein the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), and the fourth regeneration temperature (when present) each independently is from 40°C to 60°C, from 70°C to 90°C, from 50°C to 70°C, from 60°C to 80°C, from 80°C to 100°C, or from 120°C to 140°C. Example 15: The system of any examples herein, particularly examples 1-14, wherein the air supply comprises ambient air. Example 16: The system of any examples herein, particularly examples 1-15, wherein, when the system is operated in the regeneration mode, the system has a regeneration efficiency of 20% or more, 40% or more, 60% or more, 80% or more, or 90% or more. Example 17: The system of any examples herein, particularly examples 1-16, wherein, when the system is operated in regeneration mode, the system has a regeneration efficiency of 90% or more. Example 18: A method of use of the system of any examples herein, particularly examples 1-17, the method comprising: operating the system in dehumidification mode to decrease the humidity of the air from the air supply; and/or operating the system in regeneration mode to regenerate the sorbents and optionally decrease the temperature of the air. Other advantages which are obvious and which are inherent to the invention will be evident to one skilled in the art. It will be understood that certain features and sub-combinations are of utility and may be employed without reference to other features and sub-combinations. This is contemplated by and is within the scope of the claims. Since many possible embodiments may be made of the invention without departing from the scope thereof, it is to be understood that all matter herein set forth or shown in the accompanying drawings is to be interpreted as illustrative and not in a limiting sense. The methods of the appended claims are not limited in scope by the specific methods described herein, which are intended as illustrations of a few aspects of the claims and any methods that are functionally equivalent are intended to fall within the scope of the claims. Various modifications of the methods in addition to those shown and described herein are intended to fall within the scope of the appended claims. Further, while only certain representative method steps disclosed herein are specifically described, other combinations of the method steps also are intended to fall within the scope of the appended claims, even if not specifically recited. Thus, a combination of steps, elements, components, or constituents may be explicitly mentioned herein or less, however, other combinations of steps, elements, components, and constituents are included, even though not explicitly stated.

Claims

CLAIMS What is claimed is: 1. A multi-stage air conditioning system comprising: a first stage in fluid communication with an air supply, the first stage comprising a first sorbent, the first sorbent having a type IV or V water sorption isotherm, a first step_RH, and a first regeneration temperature; a second stage in fluid communication with the first stage, the second stage comprising a second sorbent, the second sorbent having a type IV or V water sorption isotherm, a second step_RH, and a second regeneration temperature; wherein the second step_RH is less than the first step_RH; and wherein the second regeneration temperature is greater than the first regeneration temperature; and a heat source in thermal communication with the second stage; wherein the system is configured to operate in a dehumidification mode and/or a regeneration mode, wherein: when the system is operated in the dehumidification mode, then: the first stage is configured to: receive air having a first humidity from the air supply; contact the air with the first sorbent to thereby transfer a first amount of moisture from the air to the first sorbent and decrease the moisture content of the air to a second humidity, the second humidity being less than the first humidity; and effuse the air having the second humidity; and the second stage is configured to: receive the air having the second humidity from the first stage; contact the air with the second sorbent to thereby transfer a second amount of moisture from the air to the second sorbent and decrease the moisture content of the air to a third humidity, the third humidity being less than the second humidity; and effuse the air having the third humidity; and when the system is operated in the regeneration mode, then: the second stage is configured to: receive air having a sixth humidity; receive an amount of heat from the heat source; contact the second sorbent with the air and the amount of heat to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air with the increased moisture content and decreased amount of heat to the first stage; the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the first sorbent; and subsequently effuse the air.
2. The system of claim 1, further comprising: a third stage in fluid communication with the second stage, the third stage comprising a third sorbent, the third sorbent having a type IV or V water sorption isotherm, a third step_RH, and a third regeneration temperature; wherein the third step_RH is less than the second step_RH; and wherein the third regeneration temperature is greater than the second regeneration temperature; wherein: when the third stage is present, the heat source is in thermal communication with the third stage; and when the system is operated in the dehumidification mode, then the third stage is configured to: receive air having the third humidity from the second stage, contact the air with the third sorbent to thereby transfer a fifth amount of moisture from the air to the third sorbent and decrease the moisture content of the air to an eighth humidity, the eighth humidity being less than the third humidity, and effuse the air having the eighth humidity; and when the system is operated in the regeneration mode, then the third stage is configured to: receive air having a ninth humidity; receive an amount of heat from the heat source; contact the third sorbent with the air and the amount of heat to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effuse the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to: receive the air effused by the third stage; contact the second sorbent with the air to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air having the increased humidity and decreased amount of heat to the first stage; and the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decrease the amount of heat in the air, and regenerate the first sorbent; and subsequently effuse the air having the increased humidity and decreased temperature.
3. The system of claim 2, further comprising: a fourth stage in fluid communication with the third stage, the fourth stage comprising a fourth sorbent, the fourth sorbent having a type IV or V water sorption isotherm, a fourth step_RH, and a fourth regeneration temperature; wherein the fourth step_RH is less than the third step_RH; and wherein the fourth regeneration temperature is greater than the third regeneration temperature; wherein: when the fourth stage is present, the heat source is in thermal communication with the fourth stage; and when the system is operated in the dehumidification mode, then the fourth stage is configured to: receive air having the tenth humidity from the third stage, contact the air with the fourth sorbent to thereby transfer a seventh amount of moisture from the air to the fourth sorbent and decrease the moisture content of the air to an eleventh humidity, the eleventh humidity being less than the tenth humidity, and effuse the air having the eleventh humidity; and when the system is operated in the regeneration mode, then the fourth stage is configured to: receive air having a twelfth humidity; receive an amount of heat from the source; contact the fourth sorbent with the air and the amount of heat to thereby increase the temperature of the fourth sorbent to the fourth regeneration temperature such that the fourth sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the fourth sorbent; and effuse the air having the increased humidity and decreased amount of heat to the third stage; the third stage is configured to: receive the air effused by the fourth stage; contact the third sorbent with the air to thereby increase the temperature of the third sorbent to the third regeneration temperature such that the third sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the art, and regenerating the third sorbent; and subsequently effuse the air having the increased moisture content and the decreased amount of heat to the second stage; the second stage is configured to: receive the air effused by the third stage; contact the second sorbent with the air to thereby increase the temperature of the second sorbent to the second regeneration temperature such that the second sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decreasing the amount of heat in the air, and regenerating the second sorbent; and subsequently effuse the air having the increased humidity and decreased amount of heat to the first stage; and the first stage is configured to: receive the air effused by the second stage; contact the first sorbent with the air to thereby increase the temperature of the first sorbent to the first regeneration temperature such that the first sorbent releases an amount of moisture into the air, thereby increasing the moisture content of the air, decrease the amount of heat in the air, and regenerate the first sorbent; and subsequently effuse the air having the increased humidity and decreased temperature.
4. The system of any one of claims 1-3, further comprising one or more heat exchangers in thermal communication with the first stage, the second stage, the third stage (when present), the fourth stage (when present), or a combination thereof.
5. The system of any one of claims 1-4, wherein the first stage, the second stage, the third stage (when present), and the fourth stage (when present) each independently comprises a rotary desiccant wheel.
6. The system of any one of claims 1-5, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises a metal-organic framework (MOF).
7. The system of claim 6, wherein the metal comprises Al, Ti, Zr, Co, or a combination thereof.
8. The system of claim 6 or claim 7, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises an Al-based MOF.
9. The system of any one of claims 6-8, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises MIL-100, MIL-101, HKUST-1, ISE-1, Basolite C300, Basolite A100, DUT-67(Zr), UiO-66, UiO-67, NU-1000, MOF-801, CPO-27(Ni), CAU-1, CAU-1(OH)2, CAU-3, CAU-3- NH2, CAU-8, CAU-10H, MIL-53, MIL-53-NH2, MIL-125, MIL-125-NH2, MIL-140A, MIL- 140C, UiO-66, ZIF-8, Ni-MOF-74, Co-MOF-74, MIL-53, Fe-BTC, Cu-BTC, Aluminum fumarate, DUT-67, MIL-96(Al) and MIL-100(Al), FAM-Z01, Cu-BTC (HKUST-1), Al Fumarate, CAU-10, CAU-23, KMF-1, CPO-27, MOF-840, MIL-160, Co2Cl2(BTDD), MIL- 101(Cr), MOF-841, In-MIL-68, or a combination thereof.
10. The system of any one of claims 6-9, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises CAU-10, CAU-23, Al-fumarate, KMF-1, MIL-125-NH2, MIL-125, MOF-841, Co2Cl2(BTDD), or a combination thereof.
11. The system of any one of claims 6-10, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently comprises MOF-841, Co2Cl2(BTDD), Al-fumarate, CAU-23, or a combination thereof.
12. The system of any one of claims 1-11, wherein the first sorbent, the second sorbent, the third sorbent (when present), and the fourth sorbent (when present), each independently can undergo multiple water sorption/desorption cycles without significant loss in performance.
13. The system of any one of claims 1-12, wherein the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), and the fourth regeneration temperature (when present) each independently is from 0°C to 140°C.
14. The system of any one of claims 1-13, wherein the first regeneration temperature, the second regeneration temperature, the third regeneration temperature (when present), and the fourth regeneration temperature (when present) each independently is from 40°C to 60°C, from 70°C to 90°C, from 50°C to 70°C, from 60°C to 80°C, from 80°C to 100°C, or from 120°C to 140°C.
15. The system of any one of claims 1-14, wherein the air supply comprises ambient air.
16. The system of any one of claims 1-15, wherein, when the system is operated in the regeneration mode, the system has a regeneration efficiency of 20% or more, 40% or more, 60% or more, 80% or more, or 90% or more.
17. The system of any one of claims 1-16, wherein, when the system is operated in regeneration mode, the system has a regeneration efficiency of 90% or more.
18. A method of use of the system of any one of claims 1-17, the method comprising: operating the system in dehumidification mode to decrease the humidity of the air from the air supply; and/or operating the system in regeneration mode to regenerate the sorbents and optionally decrease the temperature of the air.
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