## Abstract

A thermodynamic model is developed for a forward osmosis (FO) absorption heat pump capable of purifying graywater and providing year-round space conditioning with low-temperature heat as the primary energy input. The model is applied to 16 potential absorbents, and six are selected for parametric studies on desorber temperature, absorber temperature, condenser temperature, and heat sink temperature to determine the effects on the energy ratio (defined as the ratio of total useful output to total power input) of the cycle and the required graywater flowrate. Experiments are conducted to test the water flux and reverse solute flux in FO for the most promising absorbents. Of the six selected absorbents, four to two salt-organic mixtures and two pure salts appear to have the most promising thermodynamic behavior, while an ionic liquid demonstrates the best FO behavior.

## 1 Introduction

Increased demand for energy and freshwater has emerged as one of the most significant challenges of the twenty-first century. Due to the global population growth and the improved quality of life, naturally occurring water sources will be unable to provide sufficient water to meet demand [1]. Thus, alternative sources of water, including saline water and wastewater, should be explored to provide an additional supply [24]. The same factors that drive higher demand for potable water contribute to higher demand for energy, as space conditioning and computing devices become more common in developing countries. To meet the demand for energy in a way that does not exacerbate current trends in climate change, the energy for these applications must be provided in a sustainable manner.

Forward osmosis (FO) has been proposed as an alternate water purification method. In FO, a concentrated draw solution is used to draw water through a semipermeable membrane from an impure feed solution [5]. The process requires almost no electrical energy, as the pressure drop for flow on either side of the membrane is very low when compared to the high pressure required for reverse osmosis (RO). However, the water that enters the draw solution must be separated to produce pure water and prepare the draw solution for reuse, which requires more energy than a direct RO process [6]. Thus, FO processes that provide additional benefits must be considered.

One technology that has received attention recently for its ability to provide both power and pure water is pressure retarded osmosis (PRO) [7]. PRO uses FO with a high-pressure draw solution to pressurize water from the feed that can be then expanded through a turbine to generate electricity [8]. The dilute draw solution can be reconcentrated using RO or a thermal separation technique, such as membrane distillation, to provide pure water [7,9,10].

As the efficiencies for PRO are relatively low and energy is required for space conditioning in many applications, an alternative is to combine FO with a process that provides heating or cooling directly. This can be done through integration with an absorption heat pump. In an absorption heat pump, heat is added to an absorbent-refrigerant solution to desorb the refrigerant. This refrigerant then condenses and evaporates as in a typical heat pump cycle. Following this, the evaporated vapor is combined with the solution returning from the desorber in the absorber to return the solution to its initial concentration. The solution is pumped back to the desorber for the cycle to begin anew.

One of the challenges in any FO or absorption process is the selection of the most suitable solute. Investigations on the effect of draw solute have been carried out for FO and PRO processes by a number of investigators [9,1114]. For absorption heat pumps, researchers have studied the effects of a working pair (i.e., absorbent and refrigerant) on performance [1518]. In this work, a model for a FO absorption cycle capable of providing year-round space conditioning and purification of graywater for direct potable reuse is developed and applied to potential absorbents to determine the effect on cycle performance. In addition, experiments are conducted on some of the most promising absorbents, from a thermodynamic point of view, to further investigate the effect of novel draw solutes for FO processes.

## 2 Model Development

Figure 1 shows the FO absorption cycle modeled in this analysis. Water is used as the refrigerant in all cases. As with a conventional absorption heat pump, it contains a desorber, a condenser, and an evaporator. The absorber of the conventional absorption cycle is replaced with an FO absorber, in which water is drawn from the graywater feed into the absorbent solution through an FO membrane, while water vapor that enters the absorber from the evaporator is absorbed. In addition, the cycle has a pump to increase the solution pressure from the low pressure encountered in the absorber to the high pressure encountered in the desorber and a solution heat exchanger (SHX) for recuperative heat exchange. In addition, the cycle is changed from a closed cycle to an open cycle. In the open cycle considered in this work, graywater is injected into the evaporator, and pure water is extracted at the condenser. Therefore, as long as the water load is less than the water evaporated to satisfy the cooling load, the water load can be satisfied without operating the FO portion of the cycle. A vacuum pump is used to remove noncondensable gases that are dissolved in the graywater as it enters the cycle and tends to collect in the absorber. The graywater feed is used as a heat transfer fluid for the heat rejected by the absorber and the condenser during cycle operation, and the feed is coupled to the ground, which allows it to maintain a temperature sufficiently low in the summer and sufficiently high in the winter to allow operation.

Fig. 1
Fig. 1
Close modal

For heating mode operation (Fig. 2), the graywater is routed to an additional heat exchanger with a heat transfer fluid coupled with the conditioned space. The additional heat exchanger is used to avoid the introduction of contaminants in the graywater to the conditioned space in the event of a leak in the system. The graywater leaving the conditioned-space heat exchanger is routed through the evaporator to provide the requisite heat for evaporation, allowing operation of the cycle at ambient temperatures below the freezing point of water.

Fig. 2
Fig. 2
Close modal

The thermodynamic model of the cycle closely follows the work of Boman and Garimella [19]. The model is initialized by specifying the outlet temperatures of the absorber, desorber, condenser, and evaporator, and the ground temperature, and incorporates the following assumptions:

1. The high-refrigerant concentration solution leaving the absorber, low-refrigerant concentration solution leaving the desorber, refrigerant leaving the condenser, and refrigerant leaving the evaporator is in saturated states at their respective component outlet temperatures.

2. There is no pressure drop between components.

3. Pure water vapor exits the desorber at the desorber pressure and outlet temperature.

4. The fluid flowing through the evaporator and condenser is pure refrigerant.

5. The throttling valves operate isenthalpically.

6. The fluid flowing through the pumps is incompressible.

The performance of the cycle is analyzed by calculating the energy ratio (ER), which combines the coefficient of performance (COP) from thermodynamic modeling, with the gained output ratio from desalination literature, which compares the mass of water produced to the mass of steam required to provide the thermal energy [4]. Because the heat released as steam condenses varies with temperature, a temperature of 100 °C is used as a basis to calculate the energy contained in the steam. Thus, the gained output ratio is referred to as the standardized gained output ratio.
$ER=COP+SGOR$
(1)
$COP=Q˙Q˙d+W˙p$
(2)
$SGOR=m˙w×2257kJ/kgQ˙d+W˙p$
(3)

In Eqs. (1)(3), the subscript w on the mass flowrate refers to pure water, the subscript d refers to the desorber, and the subscript p on the work refers to the pumps.

In Eq. (2), the heat in the numerator is the heat input to the cycle in the evaporator for the cooling mode operation and the heat delivered by the conditioned-space heat exchanger for heating mode operation. The heat delivered by the conditioned-space heat exchanger is not the same as the heat rejected by the condenser and the absorber because graywater enters the absorber near the temperature of the ground, but it exits the conditioned-space heat exchanger at a temperature constrained by the conditioned-space heat transfer fluid return temperature.

The analysis of the cycle is carried out by performing mass, species, and energy balances on each of the components. The mass balance on the desorber is expressed as follows:
$m˙hr=m˙lr+m˙r,looped+m˙w$
(4)
where the subscripts hr, lr, and r,looped refer to the high-refrigerant concentration solution, low-refrigerant concentration solution, and looped refrigerant, respectively. The looped refrigerant is refrigerant that flows from the condenser to the evaporator when the water load is lower than the amount of the vapor produced in the evaporator.
The species balance for absorbent on the desorber is expressed as follows:
$m˙hrwhr=m˙lrwlr$
(5)
where w is the mass fraction of absorbent.
The energy balances for the desorber, condenser, evaporator, and absorber are as follows. Heat and work are taken as positive when entering the cycle. Subscript numbers on specific enthalpies refer to state points from Figs. 1 and 2. The subscript r,e refers to refrigerant vapor generated in the evaporator, while the subscript FO,a refers to water entering the cycle through FO in the absorber.
$Q˙d=(m˙r,e+m˙FO,a)h1+m˙lrh8−m˙hrh7$
(6)
$Q˙c=(m˙r,e+m˙FO,a)(h2−h1)$
(7)
$Q˙e=m˙r,e(h4−h3)$
(8)
$Q˙a=m˙hrh5−m˙hrh10−m˙r,eh4−m˙FO,ah11$
(9)
The fluid in the pump is treated as incompressible; therefore, the work of both the solution pump and the pure water pump is calculated as follows:
$W˙p=m˙ηpΔpρ$
Effectiveness is assumed for the SHX; thus, the heat duty is calculated by
$Q˙SHX=εSHXmin{m˙hr(h(T8,whr)−h(T6,whr)),m˙lr(h(T8,wlr)−h(T6,wlr))}$
(10)

Energy balances on both sides of the SHX can be used to calculate the enthalpies at state points 7 and 9.

For the graywater, the energy balances for the absorber, condenser, conditioned-space heat exchanger, and evaporator are as follows. The subscript g,r refers to the graywater remaining after extraction of the pure water in the absorber has taken place.
$−Q˙a=m˙g,r(h12−h11)$
(11)
$−Q˙c=m˙g,r(h13−h12)$
(12)
$Q˙cs=m˙g,r(h14−h13)$
(13)
$−Q˙e=m˙g,r(h15−h14)$
(14)
The mass flowrate of graywater is determined by calculating the minimum required. For all components, a closest approach temperature (CAT) of 2 °C is assumed; thus, for cooling mode operation, the required graywater flowrate should be higher than the two flowrates. The first is that required to remove the heat rejected from the absorber without exceeding the absorber outlet temperature minus the CAT, and the second is the flowrate required to remove the heat rejected from both the absorber and the condenser without exceeding the condenser temperature minus the CAT.
$m˙g,c=max{−Q˙ah(Ta−CAT)−h11,−(Q˙a+Q˙c)h(Tc−CAT)−h11}$
(15)
For the heating mode, a third consideration is needed. The temperature of the graywater leaving the coupling heat exchanger must be higher than the temperature of the fluid returning from the conditioned space by the CAT. For this case, it is assumed that the graywater leaves the condenser at its maximum possible temperature.
$m˙g,h=max{−Q˙ah(Ta−CAT)−h11,−(Q˙a+Q˙c)h(Tc−CAT)−h11,Q˙csh(THTF,in+CAT)−h(Tc−CAT)}$
(16)

The heating load is selected to require a similar evaporator size to the baseline cooling load. The baseline water production is calculated using the average per capita indoor daily water use from the study by DeOreo et al. [20] with four people in the residence, reduced by 40% to account for the fact that some of the water rejected is black and cannot be processed with a graywater recycling system. The baseline operating parameters are presented in Table 1. Component temperatures are selected to allow operation at Air Conditioning, Heating, and Refrigeration Institute (AHRI) rating conditions [21].

Table 1

Cycle baseline operating parameters

ParameterValue
Absorber temperature (Ta)35 °C
Desorber temperature (Td)100 °C
Condenser temperature (Tc)50 °C
Evaporator temperature (Te)5 °C
Ground temperature (Tg)11 °C
HTF return temperature (THTF,in)28 °C
CAT2 °C
Pump efficiency (ηp)0.85
SHX effectiveness (ɛSHX)0.85
DWP570 kg/day
ParameterValue
Absorber temperature (Ta)35 °C
Desorber temperature (Td)100 °C
Condenser temperature (Tc)50 °C
Evaporator temperature (Te)5 °C
Ground temperature (Tg)11 °C
HTF return temperature (THTF,in)28 °C
CAT2 °C
Pump efficiency (ηp)0.85
SHX effectiveness (ɛSHX)0.85
DWP570 kg/day

Sixteen possible absorbents are selected from the water-based working pairs analyzed by Boman et al. [16] and the literature. These include salt-organic mixtures, salt mixtures, pure salts, and ionic liquids (ILs), which are salts with at least one organic ion that have melting temperatures below 100 °C. Properties for these working pairs are taken from the work of Boman et al. [16], with the exception of the solution enthalpies of 1,3-dimethylimidizolium dimethyl phosphate, which are taken from the work of Dong et al, [22]. The absorbents investigated and their types are listed in Table 2. Equations (1)(16) are solved, along with the thermodynamic properties of the graywater and the absorbent fluid, using the engineering equation solver [23] software platform.

Table 2

Investigated absorbents

AbsorbentType
LiBrSalt
LiBr + MEA (78:22)Salt-organic mixture
LiBr + 1,3-propanediol (78:22)Salt-organic mixture
LiBr + ZnBr2 + LiCl (33:59:8)Salt mixture
LiBr + ZnCl2 + CaBr2 (47:47:6)Salt mixture
NaOHSalt
NaOH + KOH + CsOH (10:9:6)Salt mixture
1,3-Dimethylimidazolium dimethyl phosphate ([mmim][DMP])IL
1-Ethyl-3-methylimidazolium dimethyl phosphate ([emim][DMP])IL
1-Ethyl-3-methylimidazolium diethyl phosphate ([emim][DEP])IL
1-Ethyl-3-methylimidzolium tetrafluoroborate ([emim][BF4])IL
1-Butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4])IL
1-ethyl-3-methylimidzaolium acetate ([emim][Ac])IL
1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([emim][Tf2N])IL
1-Ethyl-3-methylimidazolium thiocyanate ([emim][SCN])IL
1-Butyl-1-methylpyrroldinium dicyanamide ([bmpyr][DCA])IL
AbsorbentType
LiBrSalt
LiBr + MEA (78:22)Salt-organic mixture
LiBr + 1,3-propanediol (78:22)Salt-organic mixture
LiBr + ZnBr2 + LiCl (33:59:8)Salt mixture
LiBr + ZnCl2 + CaBr2 (47:47:6)Salt mixture
NaOHSalt
NaOH + KOH + CsOH (10:9:6)Salt mixture
1,3-Dimethylimidazolium dimethyl phosphate ([mmim][DMP])IL
1-Ethyl-3-methylimidazolium dimethyl phosphate ([emim][DMP])IL
1-Ethyl-3-methylimidazolium diethyl phosphate ([emim][DEP])IL
1-Ethyl-3-methylimidzolium tetrafluoroborate ([emim][BF4])IL
1-Butyl-3-methylimidazolium tetrafluoroborate ([bmim][BF4])IL
1-ethyl-3-methylimidzaolium acetate ([emim][Ac])IL
1-Ethyl-3-methylimidazolium bis(trifluoromethylsulfonyl)imide ([emim][Tf2N])IL
1-Ethyl-3-methylimidazolium thiocyanate ([emim][SCN])IL
1-Butyl-1-methylpyrroldinium dicyanamide ([bmpyr][DCA])IL

The absorbents are compared under baseline operating conditions to determine those that have the best performance. Parametric studies are then carried out on the most promising ones to determine the effect of desorber temperature, ground temperature, and condenser temperature on ER and required graywater flowrate.

## 3 Experimental Approach

The water flux across a semipermeable membrane can be expressed as follows:
$Jw=K(σΔΠ−Δp)$
(17)
where K is the permeability constant, σ is the reflection coefficient, ΔΠ is the osmotic pressure difference, and Δp is the static pressure difference. Estimating ΔΠ is not straightforward in most applications because concentration polarization (CP) effects lower ΔΠ from what is predicted using theoretical approaches [5]. This lowering of the effective ΔΠ can be mainly attributed to two factors. The first is known as external concentration polarization, which refers to the variation of solution concentration at either side of the membrane. The second is known as internal concentration polarization, where the concentration significantly varies in the support layer of the FO membrane, thus lowering the driving concentration difference in the active layer of the FO membrane. Overall, it has been observed that the effect of external concentration polarization (ECP) is very minor in similar FO processes, and by far the dominant mechanism for lowering the effective osmotic pressure difference is internal concentration polarization (ICP) [5,24]. Assuming the gas phases behave ideally, which is a valid assumption because the experiments were conducted near room temperature at atmospheric pressure [25,26], the theoretical ΔΠ when distilled water is used as the feed can be estimated as follows:
$ΔΠth=−ρRTln(pvpsat)$
(18)
where pv is the vapor pressure of the draw solution at a specified temperature and psat is the saturation pressure of pure water at the same temperature. When vapor pressure data or equations of state are not available, the solution can be assumed to be ideal, which simplifies Eq. (18) to
$ΔΠth=−ρRTln(xw)$
(19)
where xw is the mole fraction of water. A solution can be assumed to be ideal when it is dilute enough, and the solutions in the present study all have a water mole fraction of at least ∼97%, which the authors believe is dilute enough for the purposes of estimating the theoretical osmotic pressure difference.

To estimate the performance of the absorbents analyzed in the modeling portion of the study, experiments that measured the water flux and reverse solute flux (flow per unit area of draw solute into the feed solution) across a semi-permeable membrane operating in the FO mode were conducted. The facility is shown schematically in Fig. 3. Both the left loop, containing the feed solution, and the right loop, containing the draw solution, are maintained at 15 °C. Flow rates are varied to control the hydrostatic pressure difference. Between the two loops, a membrane test cell (Sterlitech CF016) that permits osmotic transport is installed. The membrane used in these experiments was a Dow Filmtec BW30LE Flat Sheet Membrane, with an active area of 20.6 cm2. This membrane is typically meant to be used in RO applications, but here it was used for RO and FO experiments. This means that the membrane has a thicker support layer than typical FO membranes (due to the large static pressure difference encountered in RO mode), but the underlying mechanics behind the mass transfer for both kinds of membranes are the same. The primary reason why an FO membrane was not used is because most commercially available FO membranes are not compatible with the low pHs of ILs.

Fig. 3
Fig. 3
Close modal

The two critical measurements obtained from this facility are the water flowrate and reverse solute flowrate across the membrane. Water flow across the membrane was calculated by measuring the change in the mass of the feed solution tank over time, using the mass balances shown in Fig. 3. This assumes that the mass gained in the feed solution tank due to reverse solute flux is negligible, which is typically the case for FO processes. The solute flowrate can be determined by measuring the electrical conductivity of the solution immediately after the experiment. The electrical conductivity sensor reading was correlated with a series of known solute concentrations, and this measurement, coupled with the feed solution mass, yields the mass of solute that entered the feed solution during the experiment. This mass divided by the time elapsed during the experiment provides the reverse solute flux. The electrical conductivity was measured using an Omega CDE-45P 4-electrode conductivity sensor. All experiments were done in triplicate, and uncertainties in measurements were calculated using the method of Taylor and Kuyatt [27].

The first set of experiments was used to estimate the membrane permeability constant K. The system was operated in the RO mode, where a static pressure difference was maintained across the membrane, with deionized (DI) water on both sides of the membrane. The permeability constant was obtained by measuring the water flux as a function of static pressure difference. In this case, the osmotic pressure difference term in Eq. (17) drops out, and the slope of the resulting line yields K. Next, water flux measurements were taken during FO operation, with NaCl as the draw solute. The concentration of the draw solution was varied to examine the effects of CP on the water flux. Finally, water flux and reverse solute flux measurements were taken in the FO mode using a subset of the absorbents analyzed in the screening portion of the study as draw solutes. LiBr, LiBr + MEA, LiBr + 1,3-Propanediol, and [mmim][DMP] were considered. Because accurate vapor pressure data are not available for LiBr + MEA and LiBr + 1,3-Propanediol, the theoretical ΔΠ cannot be calculated. However, the theoretical ΔΠ can be easily calculated if the solution is ideal, which is approximately true when the solute concentration is low. Therefore, lower concentrations than what is required in the absorption heat pump are used in the draw solutions. A summary of the experimental conditions for the FO tests is presented in Table 3.

Table 3

FO draw solution concentrations tested and references for vapor pressure data

SoluteMolar mass (g/mol)Concentration (wt%)Vapor pressure data
LiBr86.80.63, 1.3Klein [23]
LiBr + MEA61.01.6, 3.2Ideal solution
LiBr + 1,3-Propanediol76.11.7, 3.4Ideal solution
[mmim][DMP]2221.2, 2.3Dong et al. [22]
SoluteMolar mass (g/mol)Concentration (wt%)Vapor pressure data
LiBr86.80.63, 1.3Klein [23]
LiBr + MEA61.01.6, 3.2Ideal solution
LiBr + 1,3-Propanediol76.11.7, 3.4Ideal solution
[mmim][DMP]2221.2, 2.3Dong et al. [22]
The effects of CP were examined following the method of Rong et al. [28], which uses the water transmission coefficient (WTC).
$WTC≡Jw/KΔΠth$
(20)

The water flux was determined from the experimental measurements, K was determined from the RO studies, and the theoretical ΔΠ was calculated using Eq. (18) or Eq. (19).

## 4 Results and Discussion

The results of baseline operation for cooling and heating modes are shown in Fig. 4. Only 15 of the 16 absorbents investigated are included in the figure as [emim][Ac] is thermodynamically incapable of operating at the baseline conditions. Salt mixtures and pure salts have higher ER than ILs. Many of the worse-performing absorbents suffer from a small swing in absorbent concentration, which means more solution must be heated to desorber conditions to release the requisite amount of refrigerant, or from a high solution specific heat capacity, which increases the heat input required to raise the solution temperature from the absorber outlet temperature to the desorber inlet temperature. The energy ratios for the heating mode are nowhere near the ideal case (ERh = ERc + 1). This is due to the temperature constraint imposed by the heat transfer fluid returning from the conditioned space.

Fig. 4
Fig. 4
Close modal

### 4.1 Cycle Parametric Studies

#### 4.1.1 Effects of Desorber Temperature.

Based on the results at baseline conditions, the top six absorbents are chosen for parametric studies. The ER for cooling mode operation is plotted for each of the absorbents as a function of desorber temperature in Fig. 5. In the present study, the maximum desorber temperature is constrained to 100 °C to allow for operation with flat-plate solar collectors. LiBr + MEA and LiBr + 1,3-propanediol are the best performing, with both becoming viable with a desorber temperature of ∼90 °C and reaching an ER of nearly 1.4 at 100 °C. LiBr performs similarly, although its rate of increase is less. NaOH has performance similar to that of the other salts, although it becomes operational at a lower temperature and reaches a peak ER around 95 °C.

Fig. 5
Fig. 5
Close modal

Figure 6 shows the ER for heating mode operation for each of the absorbents as a function of desorber temperature. Due to the low ambient temperatures anticipated during heating mode operation, heat from solar collectors will likely need to be augmented with a natural gas burner or waste heat to reach sufficiently high desorber temperatures for efficient operation. Based on this, a maximum desorber temperature of 120 °C is selected. The performance trends in heating mode are very similar to those demonstrated in the cooling mode. The LiBr-based absorbents become viable at ∼85 °C, with both LiBr + MEA and LiBr + 1,3-propanediol reaching a high ER at temperatures > 100 °C. Both pure salts suffer from crystallization issues > 100 °C, limiting the maximum desorber temperature at which they can be used.

Fig. 6
Fig. 6
Close modal

Fig. 7
Fig. 7
Close modal

#### 4.1.2 Effects of Ground Temperature.

Although the temperature of the ground cannot be varied by the designer of a FO absorption system, it does vary depending on the geographical location. Ground temperature in the contiguous US can be estimated from water temperature in nonthermal wells greater than 10 m below the surface and varies from 3 °C in northern Minnesota to 25 °C in southern Florida [29]. The effect of ground temperature on the cycle depends on the operating mode. In the cooling mode, the heat rejected to the graywater coupled to the ground remains constant, but the available enthalpy difference between the graywater entering the system and the graywater leaving the condenser decreases as the ground temperature increases. The required mass flowrate of graywater for various ground temperatures in cooling mode is plotted for the six best absorbents in Fig. 8. The plots for LiBr + MEA and LiBr + 1,3-Propanediol and those for LiBr + ZnBr2 + LiCl, NaOH, and LiBr are plotted as a single plot because they lie within 2% of each other for the entire range of ground temperatures investigated. All absorbents demonstrate the increasing graywater flowrate with increased ground temperature for the reason presented earlier. A transition occurs between 20 and 25 °C between the two cases outlined in Eq. (15). For temperatures below the transition temperature, the graywater flowrate is governed by the total heat rejection of the cycle and the condenser temperature. For temperatures above the transition ground temperature, the graywater flowrate is controlled by the absorber heat rejection and temperature. The rate of increase of required graywater flowrate is higher for the absorber-controlled regime, primarily due to the small temperature difference between the graywater and the absorber. Comparing Fig. 8 with Fig. 4, it can be seen that the higher the ER of the absorbent, the later the transition from the total heat rejection regime to the absorber heat rejection regime, and consequently, the lower the required flowrate of graywater.

Fig. 8
Fig. 8
Close modal

#### 4.1.3 Effects of Absorber Temperature.

The change from the total heat rejection limited regime to the absorber limited regime, and the corresponding increase in the required graywater flowrate can be eliminated by changing the temperature of the absorber. The graywater flowrate as a function of absorber temperature is shown in Fig. 9 for the six most promising absorbents. The pure salts experience crystallization at low temperatures; thus, their plots do not extend to the lowest absorber temperatures. For all absorbents capable of operating over the entire temperature range, required graywater flowrate follows a similar trend. At low temperatures, the required flowrate is high because the temperature difference between the ground and the absorber is small. As the absorber temperature increases, the required flowrate decreases until the point is reached at which the combined heat rejection of the absorber and condenser and the condenser temperature govern the flowrate. At higher absorber temperatures, the required flowrate increases slightly. Higher absorber temperatures result in less absorbed refrigerant at the same pressure, which leads to a lower absorbent swing and thus increased absorber heat rejection. Even so, the rate of increase in the required graywater flowrate as the absorber temperature is increased from the transition point is significantly less than the rate of increase as the absorber temperature is decreased from the transition point. By operating the absorber at a temperature that falls within the total heat rejection controlled regime, the required graywater flowrate can be minimized.

Fig. 9
Fig. 9
Close modal

The need for processing the graywater in multiple passes is emphasized by the significant difference between graywater required for cooling and pure water flow through the membrane. For baseline conditions and LiBr + MEA, the required graywater flowrate is 0.19 kg/s, while the pure water flowrate is 0.0066 kg s−1 or 3.5% of the requirement. Without recirculating the graywater, this would result in an unacceptably low recovery. Recirculation allows the extraction of pure water over time, balancing the load on the system with the intermittent addition of graywater from the facility to which the system is coupled.

In the heating mode, the performance of the cycle is nearly insensitive to ground temperature at the conditions tested. The desorber temperature and the water load set the condenser load, and to reach the target condenser outlet temperature, the absorber heat duty is determined by the graywater inlet temperature. By varying the FO and evaporator water loads, a wide range of absorber heat duties can be achieved without affecting the desorber heat duty. Therefore, the ER remains the same.

#### 4.1.4 Effects of Condenser Temperature.

Heating mode performance can be modified by changing the temperature of the condenser. Figure 10 shows the ER for the six absorbents under investigation in the heating mode as the condenser temperature is varied. As the condenser temperature increases, there is a corresponding increase in the fraction of heat rejected to the graywater that can be delivered to the conditioned space. This is offset, however, by the higher condenser and desorber pressure that results in a lower absorbent swing. These competing phenomena lead to maxima in the ER plots for the absorbents studied. As with variations in the absorber temperature, both pure salts crystallize when the temperature is too low; this precludes them from reaching their maxima.

Fig. 10
Fig. 10
Close modal

The analysis to this point has focused on the thermodynamics of the FO absorption cycle; however, material compatibility is important for fabrication and operation. Many FO membranes are thin-film composites that are stable over a pH range of 2–11 [30]. Most of the absorbents studied in this article fit this criterion; however, NaOH and the ternary hydroxide salt mixture have pHs of 15 at the concentrations necessary for absorption cycle operation. This excludes these absorbents from the development of a practical cycle.

### 4.2 Forward Osmosis Experimental Results.

Results from the RO tests are shown in Fig. 11. As expected, as the static pressure difference increases, the water flux linearly increases. A linear regression analysis was performed on the data and showed excellent agreement (R2 = 0.9993), where the slope K was found to be 4274 mol/m2/h/MPa.

Fig. 11
Fig. 11
Close modal
The water flux versus NaCl molarity is shown in Fig. 12. Clearly, an increase in solute concentration does not yield a linear increase in the water flux. This is likely due to CP effects, reducing the driving force within the membrane. The study by Rong et al. [28] demonstrated that the WTC is directly related to the concentration difference between the draw solution and the feed solution:
$log(WTC)=a0log(ΔC)+a1$
(21)
where ΔC is the concentration difference between the draw solution and the feed solution in molarity (mol/L) and coefficients a0 and a1 are regression parameters. Because it is desired for WTC to be unity, the slope a0 should be as low as possible so that the WTC does not decrease too rapidly as the draw solution concentration increases. This trend is shown in Fig. 13, showing excellent agreement (R2 = 0.9994); thus, this CP model estimates the actual water flux across the membrane well. Therefore, it is likely that this same methodology can be applied to the other draw solutions considered.
Fig. 12
Fig. 12
Close modal
Fig. 13
Fig. 13
Close modal

Figure 14 shows the water flux and reverse solute flux during FO using the four absorbents analyzed at the highest concentrations tested. It was found that as water flux increases, reverse solute flux increases. This experimental trend has been observed and modeled by several studies in the literature [3133]. In the modeling effort by Phillip et al. [31], a differential control volume is taken inside the FO membrane support layer to determine the concentration profile in the support layer. After further analysis and experimental validation, they concluded that reverse solute flux is directly proportional to water flux when the ideal solution assumption is valid. The results also clearly show that the [mmim][DMP] draw solution consistently resulted in the largest water fluxes and salt fluxes, while all the LiBr solutions resulted in similar water fluxes and solutes fluxes.

Fig. 14
Fig. 14
Close modal

Figure 15 shows the WTC versus concentration difference for all the absorbents analyzed. [mmim][DMP] was found to have the lowest WTC among all absorbents analyzed, along with the lower slope. This suggests that the [mmim][DMP] is less affected by CP and WTC does not decrease much as concentration difference increases. Among the LiBr draw solutions, all showed similar WTC results, but the slope of the LiBr solution was lower than the slope of both the LiBr + MEA and LiBr + 1,3-Propanediol draw solutions. Therefore, it is likely that [mmim][DMP] solutions may yield greater effective osmotic pressure differences compared to conventional salt solutions. Overall, the experimental results show that [mmim][DMP] is the most promising draw solution, and all LiBr draw solutions perform at a similar level. [mmim][DMP] therefore requires lower membrane area but would most likely require more frequent replenishment due to the large reverse solute flux, especially because [mmim][DMP] has the largest molar mass out of all the solutes considered.

Fig. 15
Fig. 15
Close modal

## 5 Conclusions

A thermodynamic model is developed for a FO absorption cycle capable of providing water purification and space conditioning with low-grade heat as the primary energy input. Energy ratios in excess of 1.3 can be achieved for cooling mode and in excess of 1.5 for heading mode. Sixteen absorbents are modeled, and six are selected for further study, including salt-organic mixtures, salt mixtures, pure salts, and an IL. The effect of desorber temperature on the ER is investigated in both cooling and heating modes, while the effects of ground and absorber temperature on required graywater flowrate are studied for the cooling mode and the effects of condenser temperature on ER are investigated in the heating mode.

Of the absorbents investigated for the FO absorption cycle, the most promising two absorbents based on all parametric studies conducted are LiBr + MEA and LiBr + 1,3-propanediol. However, for water purification, the volatility of the absorbent should be considered; thus, NaOH or LiBr may be suitable candidates.

FO experiments were conducted to determine water and reverse solute flux for a subset of the absorbents analyzed (LiBr, LiBr + MEA, LiBr + 1,3-Propanediol, and [mmim][DMP]). In addition, the WTC was determined to estimate the effects of CP on the draw solutions. It was found that the reverse solute flux increases as the water flux increases and that the logarithm of the WTC is proportional to the logarithm of the concentration difference between the feed and the draw solution. All LiBr-based draw solutions had similar water fluxes, reverse solute fluxes, and WTC, while the [mmim][DMP] had significantly higher water flux, reverse solute flux, and WTC. This study can be further improved by experimentally investigating the water flux, reverse solute flux, and WTC at concentrations representative to typical absorption heat pump conditions, which requires more experimental vapor pressure data of LiBr + MEA and LiBr + 1,3-Propanediol at these concentrations.

## Acknowledgment

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request. The authors attest that all data for this study are included in the paper.

## Funding Data

• National Science Foundation Graduate Research Fellowship (Grant No. DGE-1650044; Funder ID: 10.13039/501100008982).

## Nomenclature

h =

specific enthalpy (kJ/kg)

p =

pressure (kPa)

v =

molar specific volume (m3/kmol)

w =

mass fraction of absorbent (–)

A =

area (m2)

C =

concentration (mol/L)

J =

molar flux (mol/m2/h)

K =

membrane constant (mol/m2/MPa/h)

M =

molar mass (kg/mmol)

R =

ideal gas constant (J/mol/K)

T =

temperature (°C or K)

$m˙$ =

mass flowrate (kg/s)

$Q˙$ =

heat transfer rate (kW)

$W˙$ =

pumping power (kW)

### Greek Symbols

ɛ =

effectiveness

η =

efficiency

Π =

osmotic pressure (MPa)

ρ =

density (kg/m3)

### Subscripts

a =

absorber

c =

condenser, cooling

cs =

conditioned-space heat exchanger

d =

desorber

e =

evaporator

eff =

effective

g =

graywater, ground

g,r =

remaining graywater after membrane

h =

heating

hr =

high-refrigerant concentration solution

HTF,in =

heat transfer fluid return

lr =

low-refrigerant concentration solution

mem =

membrane

p =

pump

r =

refrigerant

s =

solute

sat =

saturation

SHX =

solution heat exchanger

th =

theoretical

v =

vapor

w =

pure water

## References

1.
Rijsberman
,
F. R.
,
2006
, “
Water Scarcity: Fact or Fiction?
,”
Agric. Water Manage.
,
80
(
1–3
), pp.
5
22
.
2.
Achilli
,
A.
,
Cath
,
T. Y.
,
Marchand
,
E. A.
, and
Childress
,
A. E.
,
2009
, “
The Forward Osmosis Membrane Bioreactor: A Low Fouling Alternative to MBR Processes
,”
Desalination
,
239
(
1–3
), pp.
10
21
.
3.
Ghaffour
,
N.
,
Missimer
,
T. M.
, and
Amy
,
G. L.
,
2013
, “
Technical Review and Evaluation of the Economics of Water Desalination: Current and Future Challenges for Better Water Supply Sustainability
,”
Desalination
,
309
, pp.
197
207
.
4.
Ghalavand
,
Y.
,
Hatamipour
,
M. S.
, and
Rahimi
,
A.
,
2015
, “
A Review on Energy Consumption of Desalination Processes
,”
Desalin. Water Treat.
,
54
(
6
), pp.
1
16
.
5.
Cath
,
T. Y.
,
Childress
,
A. E.
, and
Elimelech
,
M.
,
2006
, “
Forward Osmosis: Principles, Applications, and Recent Developments
,”
J. Membr. Sci.
,
281
(
1–2
), pp.
70
87
.
6.
McGovern
,
R. K.
, and
Lienhard V
,
J. H.
,
2014
, “
On the Potential of Forward Osmosis to Energetically Outperform Reverse Osmosis Desalination
,”
J. Membr. Sci.
,
469
, pp.
245
250
.
7.
Han
,
G.
,
Zuo
,
J.
,
Wan
,
C.
, and
Chung
,
T.-S.
,
2015
, “
Hybrid Pressure Retarded Osmosis–Membrane Distillation (PRO–MD) Process for Osmotic Power and Clean Water Generation
,”
Environ. Sci.: Water Res. Technol.
,
1
(
4
), pp.
507
515
.
8.
Norman
,
R. S.
,
1974
, “
Water Salination: A Source of Energy
,”
Science
,
186
(
4161
), pp.
350
352
.
9.
Han
,
G.
,
Ge
,
Q.
, and
Chung
,
T.-S.
,
2014
, “
Conceptual Demonstration of Novel Closed-Loop Pressure Retarded Osmosis Process for Sustainable Osmotic Energy Generation
,”
Appl. Energy
,
132
, pp.
383
393
.
10.
Lee
,
J.-G.
,
Kim
,
Y.-D.
,
Shim
,
S.-M.
,
Im
,
B.-G.
, and
Kim
,
W.-S.
,
2015
, “
Numerical Study of a Hybrid Multi-Stage Vacuum Membrane Distillation and Pressure-Retarded Osmosis System
,”
Desalination
,
363
, pp.
82
91
.
11.
Achilli
,
A.
,
Cath
,
T. Y.
, and
Childress
,
A. E.
,
2010
, “
Selection of Inorganic-Based Draw Solutions for Forward Osmosis Applications
,”
J. Membr. Sci.
,
364
(
1–2
), pp.
233
241
.
12.
Hickenbottom
,
K. L.
,
Vanneste
,
J.
, and
Cath
,
T. Y.
,
2016
, “
Assessment of Alternative Draw Solutions for Optimized Performance of a Closed-Loop Osmotic Heat Engine
,”
J. Membr. Sci.
,
504
, pp.
162
175
.
13.
Luo
,
W.
,
Hai
,
F. I.
,
Price
,
W. E.
,
Elimelech
,
M.
, and
Nghiem
,
L. D.
,
2016
, “
Evaluating Ionic Organic Draw Solutes in Osmotic Membrane Bioreactors for Water Reuse
,”
J. Membr. Sci.
,
514
, pp.
636
645
.
14.
Bowden
,
K. S.
,
Achilli
,
A.
, and
Childress
,
A. E.
,
2012
, “
Organic Ionic Salt Draw Solutions for Osmotic Membrane Bioreactors
,”
Bioresour. Technol.
,
122
, pp.
207
216
.
15.
Kim
,
Y. J.
,
Kim
,
S.
,
Joshi
,
Y. K.
,
Fedorov
,
A. G.
, and
Kohl
,
P. A.
,
2012
, “
Thermodynamic Analysis of an Absorption Refrigeration System With Ionic-Liquid/Refrigerant Mixture as a Working Fluid
,”
Energy
,
44
(
1
), pp.
1005
1016
.
16.
Boman
,
D. B.
,
Hoysall
,
D. C.
,
Staedter
,
M. A.
,
Goyal
,
A.
,
Ponkala
,
M. J.
, and
Garimella
,
S.
,
2017
, “
A Method for Comparison of Absorption Heat Pump Working Pairs
,”
Int. J. Refrig.
,
77
, pp.
149
175
.
17.
Saravanan
,
R.
, and
Maiya
,
M. P.
,
1998
, “
Thermodynamic Comparison of Water-Based Working Fluid Combinations for a Vapour Absorption Refrigeration System
,”
Appl. Therm. Eng.
,
18
(
7
), pp.
553
568
.
18.
Yokozeki
,
A.
, and
Shiflett
,
M. B.
,
2010
, “
Water Solubility in Ionic Liquids and Application to Absorption Cycles
,”
Ind. Eng. Chem. Res.
,
49
(
19
), pp.
9496
9503
.
19.
Boman
,
D. B.
, and
Garimella
,
S.
,
2020
, “
Absorption Heat Pump Cycles for Simultaneous Space Conditioning and Graywater Purification
,”
Appl. Therm. Eng.
,
167
, p.
114587
.
20.
DeOreo
,
W. B.
,
Mayer
,
P.
,
Dziegielewski
,
B.
, and
Kiefer
,
J.
,
2016
, “
Residential End Uses of Water, Version 2: Executive Report
,”
Water Research Foundation
,
Denver, CO
, Report No. 4309A.
21.
AHRI
,
2017
,
2017 Standard for Performance Rating of Unitary Air-conditioning and Air-Source Heat Pump Equipment
,
Air-Conditioning, Heating, and Refrigeration Institute
,
Arlington, VA
.
22.
Dong
,
L.
,
Zheng
,
D.
,
Nie
,
N.
, and
Li
,
Y.
,
2012
, “
Performance Prediction of Absorption Refrigeration Cycle Based on the Measurements of Vapor Pressure and Heat Capacity of H2O + [DMIM]DMP System
,”
Appl. Energy
,
98
, pp.
326
332
.
23.
Klein
,
S. A.
,
2015
, “EES—Engineering Equation Solver,” F-Chart Software, Middleton, WI.
24.
Gray
,
G. T.
,
McCutcheon
,
J. R.
, and
Elimelech
,
M.
,
2006
, “
Internal Concentration Polarization in Forward Osmosis: Role of Membrane Orientation
,”
Desalination
,
197
(
1
), pp.
1
8
.
25.
Sereno
,
A. M.
,
Hubinger
,
M. D.
,
Comesaña
,
J. F.
, and
Correa
,
A.
,
2001
, “
Prediction of Water Activity of Osmotic Solutions
,”
J. Food Eng.
,
49
(
2
), pp.
103
114
.
26.
Choosri
,
T.
,
Koglbauer
,
G.
, and
Wendland
,
M.
,
2009
, “
A New Method for the Measurement of the Water Activity or Relative Humidity by Fourier Transform Infrared Spectroscopy
,”
J. Chem. Eng. Data
,
54
(
4
), pp.
1179
1182
.
27.
Taylor
,
B. N.
, and
Kuyatt
,
C. E.
,
1994
,
NIST Technical Note 1297: Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results
,
National Institute of Standards and Technology
,
Gaithersburg, MD
.
28.
Rong
,
K.
,
Zhang
,
T. C.
, and
Li
,
T.
,
2017
, “
Forward Osmosis: Definition and Evaluation of FO Water Transmission Coefficient
,”
J. Water Process. Eng.
,
20
, pp.
106
112
.
29.
Collins
,
W. D.
,
1925
, “
Temperature of Water Available for Industrial Use in the United States: Chapter F in Contributions to the Hydrology of the United States, 1923–1924
,” Report No. 520F,
Washington, D.C
.
30.
Zhao
,
S.
,
Zou
,
L.
,
Tang
,
C. Y.
, and
Mulcahy
,
D.
,
2012
, “
Recent Developments in Forward Osmosis: Opportunities and Challenges
,”
J. Membr. Sci.
,
396
, pp.
1
21
.
31.
Phillip
,
W. A.
,
Yong
,
J. S.
, and
Elimelech
,
M.
,
2010
, “
Reverse Draw Solute Permeation in Forward Osmosis: Modeling and Experiments
,”
Environ. Sci. Technol.
,
44
(
13
), pp.
5170
5176
.
32.
Yong
,
J. S.
,
Phillip
,
W. A.
, and
Elimelech
,
M.
,
2012
, “
Coupled Reverse Draw Solute Permeation and Water Flux in Forward Osmosis With Neutral Draw Solutes
,”
J. Membr. Sci.
,
392–393
, pp.
9
17
.
33.
Suh
,
C.
, and
Lee
,
S.
,
2013
, “
Modeling Reverse Draw Solute Flux in Forward Osmosis With External Concentration Polarization in Both Sides of the Draw and Feed Solution
,”
J. Membr. Sci.
,
427
, pp.
365
374
.