Applied Energy 90 (2012) 316–322

Contents lists available at ScienceDirect

Applied Energy

journal homepage: www.elsevier .com/ locate/apenergy

Thermodynamic cycles of adsorption desalination system

Jun W. Wu a, Eric J. Hu a,⇑, Mark J. Biggs b

a School of Mechanical Engineering, The University of Adelaide, South Australia 5005, Australiab School of Chemical Engineering, The University of Adelaide, South Australia 5005, Australia

a r t i c l e i n f o

Article history:Received 29 July 2010Received in revised form 10 April 2011Accepted 24 April 2011Available online 23 May 2011

Keywords:Adsorption desalinationCoolingSilica gel-waterThermodynamic cycles

0306-2619/$ - see front matter � 2011 Elsevier Ltd. Adoi:10.1016/j.apenergy.2011.04.049

⇑ Corresponding author. Tel.: +61 8313 0545; fax: +E-mail address: eric.hu@adelaide.edu.au (E.J. Hu).

a b s t r a c t

The potential to use waste heat to co-generate cooling and fresh water from saline water using adsorp-tion on silica is attracting increasing attention. A variety of different thermodynamic cycles of such anadsorption desalination (AD) system arise as the temperature of the saline water evaporator is varied rel-ative to temperature of the water used to cool the adsorbent as it adsorbs the evaporated water. In thispaper, all these possible thermodynamic cycles are enumerated and analysed to determine their relativeperformances in terms of specific energy consumption and fresh water productivity.

� 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Rising water scarcity due to climate change and over-exploita-tion of traditional water resources is of increasing concern aroundthe World, both because of its economic implications as well as thecontinued habitability of long-standing communities. One solutionto this issue is desalination of saline or brackish water, which haslong been used in regions that have traditionally faced water short-age such as the Middle East. There are several ways in which desa-lination is carried out, including multi-effect desalination, multi-stage flash desalination, and membrane-based reverse osmosis(RO) [1–10], which are all widely exploited commercially. The highenergy demands of these various current commercial technologieshave prompted some to investigate means by which the ‘carbonfootprint’ of desalination can be reduced. Examples include energyrecovery measures [11], heat integrated distillation [12], waste-heat driven barometric flash-type desalination [13], solar thermalassist synthetic energy desalination [14] and, of particular interesthere, adsorption-based desalination [15].

Adsorption-based desalination (AD) uses low-grade heat todesalinate saline or brackish water to produce potable water forboth industrial and residential applications [15]. There are six sig-nificant advantages of AD compared with more traditional desali-nation techniques and the potential alternatives [16,17]: (1) itrequires only low-grade heat from, for example, solar or waste heatto operate, (2) fewer moving parts, which reduces maintenancecosts, (3) reduced fouling and corrosion due to the low operatingtemperature and confinement of the saline/brackish solution to a

ll rights reserved.

61 8303 4367.

fraction of the total system, (4) ability to co-generate potable waterand cooling, (5) double distillation – the desalination process min-imizes the possibility of so-called ‘(bio) gen-contamination’; and(6) ability to treat/desalinate saline water containing organiccompounds.

Adsorption-based desalination has its origins in silica gel-wateradsorption-based chillers, which use fresh water as the refrigerantthat circulates between an evaporator, adsorption/desorption bedsand condenser. In AD, saline water replaces the fresh water of chil-ler-only systems, and at the end of each cycle the fresh water pro-duced by the condenser is drained off and the more concentratedbrine that remains in the evaporator is discharged. Fig. 1 shows aschematic of a two-bed adsorption-based desalinator, which isthe most basic module of such a system. This system consists ofthree major components: a condenser, two silica gel beds, and anevaporator. After the whole system is degassed, the pre-treated(e.g. de-aerated and filtered) saline source water is charged intothe evaporator. The evaporator is then vacuumed to a pressurecommensurate with the desired temperature of the chilled water,which is also circulated around the evaporator. Meanwhile, thepressure of the adsorption bed and condenser are maintained atthe saturation pressure corresponding to the temperature of thecooling water. Valve 1 is then opened to initiate evaporation ofthe source water, which then travels into bed 1 where it is ad-sorbed by the silica gel. The heat generated during the adsorptionprocess is removed by the cooling water circulating in the manifoldof bed 1. Once bed 1 is saturated with water vapour, valve 1 isclosed and the adsorbed water is driven off the silica gel and thepressure in the bed raised by circulating hot water in the manifoldof the bed. Valve 2 is opened once the pressure in bed 1 is equal tothat in the condenser. This valve is kept open and circulation of the

Nomenclature

C specific heat (kJ/kg K)C1 Case 1C2 Case 2C3 Case 3KI

0 adsorption equilibrium constant of the isotherm equa-tion (dimensionless)

m mass (kg)P pressure (Pa)X fraction of amount adsorbate adsorbed by the adsorbent

at equilibrium condition (kg/kg dry adsorbent)Q heat (kJ)Qads water vapour adsorption heat (kJ/kg)Qst isosteric heat of adsorption (kJ/kg)R gas constant (kJ/kg K)T temperature (K)SEC specific energy consumption (kJ/kg)

Superscripts/subscriptsads adsorptionbed adsorption or desorption bedchilled chilled water

C casecond condensercw cooling waterdes desorptionevap evaporatorheating(bed) bed heating capacitycooling(bed) bed cooling capacityhw hot waterin inletmax cycle maximummin cycle minimumout outletsg silica gelw water1 ? 2 state 1 to state 22 ? 3 state 2 to state 33 ? 4 state 3 to state 44 ? 1 state 4 to state 1

J.W. Wu et al. / Applied Energy 90 (2012) 316–322 317

hot water through the manifold in the bed is continued until muchof the adsorbed water is driven from the bed. Once valve 2 isclosed, the cycle for bed 1 is ready to start again. Beds 1 and 2are operated alternatively in this way to produce fresh water(and cooling capacity from the evaporator) in a continuousmanner.

It should be noted that the fresh water is distilled twice (i.e.double-distilled) in the system shown in Fig. 1. At the same time,a cooling effect is created in the evaporator, which can be usedfor air conditioning purposes as in a normal adsorption chiller orbe fed back to the bed or condenser. In other words, the adsorptiondesalination system has the ability to perform as a chiller and dou-

Fig. 1. Schematic of a two-bed ad

ble-distilling desalinator simultaneously. Silica gel is a popularadsorbent because it readily takes up water vapour without signif-icant structural or volume change and readily releases it undermild heating [18]. To improve energy efficiency, in practice mul-ti-beds system with two or four beds, are normally used [16]. How-ever, in this study, consideration will be restricted to a single-bedsystem for simplicity.

Previous research on AD has focused on the experimental study[16,17,19–22] and heat transfer modelling [23–26] of such sys-tems. Some research on the impact of the operating parameters(in particular, heat sources temperature and cooling water temper-ature) on the performance of AD has also been recently reported

sorption desalination system.

Fig. 2. Thermodynamic cycle of AD system when Tevap < Tcw.

318 J.W. Wu et al. / Applied Energy 90 (2012) 316–322

[15]. However, all above mentioned studies assumed the AD sys-tem was operated in the co-generation mode (i.e. the Case 1 cycledescribed below); none of the previous work has ever consideredcycles where desalination only is possible, which occurs whenthe evaporator temperature is equal to or greater than the coolingwater temperature (i.e. Cases 2 and 3 below). Therefore, this paperconsiders the thermodynamic cycles and the performance of an ADsystem for all possible evaporator temperature scenarios. The rel-ative ranking of the performance of these cycles, in terms of freshwater production and specific energy consumption (per cycle), isalso presented.

2. The thermodynamics of AD system

2.1. Adsorption isotherm

For a given adsorptive–adsorbent pair (water-silica gel in thepresent case), the adsorption equilibrium can be described by

X ¼ f ðP; TÞ ð1Þ

where X is the amount of adsorbate at equilibrium in kg of adsor-bate per kg of adsorbent, and P and T are the bed partial pressureand temperature respectively.

It has been shown that provided the loading is not too great,adsorption of water on silica gel can be adequately described byHenry’s law [28]:

h ¼ X=X0 ¼ KP ð2Þ

where X0 is the amount of adsorbate when the adsorbent is satu-rated. The heat released during adsorption, which is equal to theisosteric heat of adsorption, Qst, is related to the adsorption iso-therms at various temperatures by the van’t Hoff equation [27]:

d ln KdT

¼ �Qst

RT2 ð3Þ

where K is the equilibrium constant, and R is the Gas Constant. Byintegrating Eq. (3), we get:

K ¼ K0 exp½Qst=ðRTÞ� ð4Þ

where K0 is a constant. By utilizing Henry’s law in Eq. (2), the fol-lowing form of the P–T–X relationship can be obtained [28]:

X ¼ PKI0 exp½Qst=ðRTÞ� ð5Þ

where KI0ð¼ K0X0Þ is the adsorption constant. Once the Qst and KI

0

are determined for a particular adsorptive–adsorbent pair (e.g. fromexperiment [18]), then the P–T–X relationship of the pair is knownand the analysis of the associated AD cycle can be undertaken.

2.2. Possible AD cycles

Designating the silica gel bed as the system, the thermodynamiccycle may be conveniently presented by plotting the P–T–X rela-tionship of Eq. (5) on lnP vs. �1/T coordinates as illustrated in,for example, Fig. 2. At different evaporator temperature relativeto the cooling water temperature, the thermodynamic cycles havebeen found to form three unique shapes when they are presentedon this set of coordinates – each is described and discussed belowunder the conditions of no energy recovery measures and negligi-ble sensible heats of the bed and evaporator materials.

2.2.1. Case 1: Tevap < Tcw

2.2.1.1. Detailed cycle description. In the typical cogeneration oper-ation mode where the AD system generates both fresh water andcooling, the evaporator’s temperature, Tevap, is set lower than theambient and cooling water temperature for air conditioning/cool-

ing purpose (where the cooling water is for both bed and con-denser cooling), i.e. Tevap < Tcw. In this mode, the cycle can inprinciple be described by two isosters and two isobars as shownin Fig. 2.

Process 1 ? 2The process starts from state point 1, where the silica gel bed isat a temperature Tcw and pressure equal to the saturation pres-sure of the water at the evaporator temperature, and theamount of water adsorbed in the bed is at the cycle maximum,X1 (i.e. X1 = Xmax). The bed is isolated and hot water is circulatedthrough the manifold in the bed to increase its temperatureand, through consequent desorption of the water vapour, pres-sure. As the bed is isolated during the process, the process 1 ? 2is a constant concentration (i.e. isosteric) process (i.e. X1 = X2).This process continues until it reaches state point 2 whose pres-sure, P2, is equal to the saturation pressure of water at the con-denser temperature.Process 2 ? 3At state point 2, the bed is connected to the condenser by open-ing the valve between them whilst circulation of the hot waterand desorption continues. The desorbed moisture travels intothe condenser where it condenses as the product water. Theheat of condensation is taken away by the cooling water thatis circulated through the condenser. This cooling water alsohelps to fix the pressure in the condenser (i.e. the process is iso-baric) until the bed reaches its maximum temperature T3 that isequal to Thw. At state point 3, the bed is at its ‘driest’ state of thecycle, (i.e. X3 = Xmin). This process can be variously termed silicagel regeneration, condensing process, or fresh water productionprocess.Process 3 ? 4At state point 3, the silica gel bed is isolated and cooling water issupplied to the bed leading to a decrease in the bedtemperature and pressure at constant concentration until statepoint 4 is reached. In this process, the cooling lowers the pres-sure of the bed to match up the evaporator pressure, whichmeans at state point 4, the bed pressure is equal to the satu-rated pressure of salty water at the evaporator temperature(i.e. P4 = Pevap), so the following evaporation (in the evaporator)can occur at designed (low) temperature. Without coolingdown of the bed, there would be less useful cooling effect fromthe evaporator.Process 4 ? 1Once the process reaches state point 4, the valve between thebed and the evaporator is opened. The circulating cooling watercontinues to decrease the temperature of the bed, which is thedriving force for the evaporation of the salty water in the evap-

Fig. 3. Thermodynamic cycle of AD system when Tevap = Tcw.

J.W. Wu et al. / Applied Energy 90 (2012) 316–322 319

orator. The water vapour produced in the evaporator travels tothe bed and is adsorbed by the silica gel while the heat arisingfrom the adsorption process is taken away by the cooling water.During this adsorption process, the pressure in the bed andevaporator remains constant (i.e. P4 = P1), but the temperatureof the bed continues to decrease to T1. At state point 1, the con-centration of the water in the silica gel reaches the cycle max-imum (i.e. X1 = Xmax).

2.2.1.2. Thermodynamic modelling. Based on the cycle diagramshown in Fig. 2, the amount of fresh water that can be generatedin a single cycle from one bed (i.e. water productivity) is given by

mwater ¼ Dm2�3 ¼ m2 �m3 ¼ X2 �msg � X3 �msg ð6Þ

where msg is the mass of the silica gel in one bed, Dm2?3 is the masschange of the water adsorbed in the silica gel between state point 2and state point 3, and X2 and X3 are the water concentration in silicagel at equilibrium for state points 2 and 3. The water productivity isalso used to calculate the system specific energy consumption, SEC.

The total heating requirement of a single cycle is the sum of theheating required in processes 1 ? 2 and 2 ? 3, i.e.

Q heatingðbedÞ ¼ Q 1!2 þ Q 2!3 ð7Þ

where

Q 1!2 ¼ ðX1msgCwater þmsgCsgÞ � ðT2 � T1Þ ð8Þ

and

Q 2!3 ¼ msgCsg þX2 þ X3

2

� �msgCwater

� �� ðT3 � T2Þ þ ðX2 � X3Þ

�msgQ des ð9Þ

where Cwater is the specific heat of water, Csg is the average specificheat of silica gel, and Qdes is the amount of heat required to desorb 1kg of water.

Combining Eqs. (6), (8) and (9) leads to the energy required toproduce a kilogram of fresh water (the Specific Energy Consump-tion or SEC)

Fig. 4a. Thermodynamic cycle of AD system at the when Tevap = Tcw (option C2-A).

SEC ¼ðX1msgCwater þmsgCsgÞ � ðT2 � T1Þ þ msgCsg þ X2þX3

2

� �msgCwater

� � ðT3 � T2Þ þ ðX2 � X3Þ �msgQdes

X2 �msg � X3 �msgð10Þ

Meanwhile, the total cooling effect of a single cycle created is thesum of the heat to be removed in processes of 3 ? 4 and 4 ? 1, i.e.

Q coolingðbedÞ ¼ Q 3!4 þ Q 4!1 ð11Þ

where

Q 3!4 ¼ ðX3msgCwater þmsgCsgÞ � ðT3 � T4Þ ð12Þ

and

Q 4!1 ¼ msgCsg þX4 þ X1

2

� �msgCwater

� �� ðT4 � T1Þ þ ðX1

� X4Þ �msgQads ð13Þ

where Qads is the amount of heat required to adsorb 1 kg of water.Here, Qads is assumed to be equal to Qdes and Qst for all Xs.

The Case 1 cycle of the AD system described above has beenpreviously studied extensively, including modelling, validationand sensitivity analysis of the design and operational parameters[15–17,19–23,26]. The two cases that follow below have, on theother hand, never been reported before to our knowledge.

2.2.2. Case 2: Tevap = Tcw

2.2.2.1. Detailed cycle description. If desalination is the only purposeof the system, the evaporator can be operated at temperaturesequal to or greater than that of the cooling water. Such operationleads to a fundamental shift in the character of the thermodynamiccycle of the AD system. When Tevap = Tcw, the condenser and evap-orator are at the same pressure (i.e. Pcond = Pevap) and the cycle be-came 1 ? 2 ? (3) ? 1 as shown in Fig. 3.

Process 1 ? 2The process starts from state point 1 where the bed, condenserand evaporator are kept at the same temperature by the circu-lating cooling water (i.e. Tevap = Tcond = Tcw) and hence pressure(i.e. Pcond = Pevap = Pbed). The silica gel is also saturated. To startthe process, the valve between the silica gel bed and the evap-orator is closed and the valve between the bed and the con-denser is opened whilst the hot water is circulated throughthe bed. The water is driven from the silica gel by the hot waterbefore it passes into the condenser where it condenses. At statepoint 2, the silica gel reaches the cycle minimum water vapourcontent, Xmin.

Process 2 ? 3 ? 1After state point 2 is reached, the valve between the silica gelbed and the evaporator is re-opened whilst the valve betweenthe bed and the condenser is closed and the cooling water is cir-

Fig. 4b. Thermodynamic cycle of AD system when Tevap = Tcw (option C2-B). Fig. 5. Thermodynamic cycle of AD system when Tevap > Tcw.

Fig. 6a. Thermodynamic cycle of AD system when Tevap > Tcw (option C3-A).

320 J.W. Wu et al. / Applied Energy 90 (2012) 316–322

culated through the bed. Although this takes the process backtowards state point 1, as indicated by the dashed line inFig. 3, there are many paths along which the process may godepending on the system operational strategy (i.e. time man-agement of the valve operation). Two potential paths of interestare illustrated in Fig. 4 below.

The first potential path (option C2-A) is to drive the processfrom state point 2 to state point 1 under constant pressure (i.e.path 2 ? 3 ? 1 in Fig. 4a). This may be achieved by circulatingcooling water to the bed and opening the valve between the bedand the evaporator simultaneously whilst keeping the evaporatorat Tevap (=Tcw).

A second potential path (option C2-B) for taking the bed back tostate point 1 is shown in Fig. 4b, (i.e. path 2 ? 30 ? 1). This isachieved by circulating cooling water through the bed whilst keep-ing the valves between the bed and the evaporator and betweenthe bed and the condenser closed. When the bed temperaturedrops to Tcw or Tevap, (i.e. state point 3’ is reached), the valve be-tween the bed and the evaporator is opened whilst the bed tem-perature is maintained at Tcw by continuously circulating coolingwater through it.

2.2.2.2. Thermodynamic modelling. For the case 2 cycles in Fig. 3, theamount of fresh water that can be generated in a single cycle fromone bed (i.e. water productivity) is given by

mwater ¼ Dm1�2 ¼ m1 �m2 ¼ X1 �msg � X2 �msg ð14Þ

where msg is the mass of the silica gel in one bed and Dm1?2 is themass change of the water adsorbed in the silica gel between states 1and 2.

The total heating requirement of a single cycle is equal to theheat supplied in processes 1 ? 2, i.e.

Q heatingðbedÞ ¼ Q 1!2

¼ msgCsg þX1 þ X2

2

� �msgCwater

� �� ðT2 � T1Þ

þ ðX1 � X2Þ �msgQ des ð15Þ

where Cwater is the specific heat of water, Csg is the average silica gelspecific heat, and Qdes is the amount of heat required to desorb 1 kgof water.

Combining Eqs. (14) and (15), the specific energy consumptionis given by

SEC ¼msgCsg þ X1þX2

2

� �msgCwater

� � ðT2 � T1Þ þ ðX1 � X2Þ �msgQ des

X1 �msg � X2 �msg

ð16Þ

It should be noted that in the above discussion of this case, it hasbeen assumed the water-adsorbing capacity of the adsorbent is infi-nite. This is, of course, not possible in reality and, hence, X will al-ways be less than X1 (e.g. X = X3 as shown in Figs. 3 and 4).

2.2.3. Case 3: Tevap > Tcw

2.2.3.1. Detailed process description. If the temperature of the evap-orator is set at a temperature greater than the cooling water in thecondenser, the thermodynamic cycle of the AD system become1 ? 2 ? 3 ? 5 ? 1 as shown in Fig. 5. In this case, if the bed isby-passed, namely the water vapour from the evaporator travelsto the condenser and condenses directly, then the cycle is simplythat of a thermal flash system with single distillation.

Fig. 6b. Thermodynamic cycle of AD system when Tevap > Tcw (option C3-B).

J.W. Wu et al. / Applied Energy 90 (2012) 316–322 321

Process 1 ? 2The process starts at state point 1 where the bed is at the tem-perature, Tcw, and pressure Pevap, and the water content of thesilica gel is at the cycle maximum, X1. When the valve betweenthe bed and the evaporator is closed and the valve between thebed and condenser is opened, the pressure of the bed drops tothe condenser pressure and the water within the silica gel isdriven off by the pressure difference. This process is performedat constant temperature by circulating the cooling water inboth the condenser and the bed. This process stops once thepressure of the bed is equal to that of the condenser at statepoint 2 (i.e. P2 = Pcond). It should be noted that this process couldbe irreversible.Process 2 ? 3Once the bed pressure is equal to the condenser pressure (atstate point 2), the cooling water circulating in the silica gelbed is replaced by hot water. This hot water leads to waterdesorption from the bed and an increase in its temperature.As the cooling water is circulated through the condenser, thewater vapour output from the bed condenses in the condenserand the pressure in the bed and condenser remains at Pcond untilthe bed reaches its maximum temperature (i.e. T3 = Thw).Process 3 ? 5 ? 1At state point 3, the silica gel bed is at the maximum tempera-ture (i.e. Thw) and condenser pressure (i.e. P2 = Pcond). In order tocomplete the cycle, the bed needs to be restored from statepoint 3 back to state point 1. As with case 2, there are manypossible paths between these two state points depending onthe system operational strategy. The path from state point 3back to state point 1 is, therefore, shown in Fig. 5 by a dotedline. Two possible paths between state point 3 and state point1 that are of potential interest are illustrated in Fig. 6 below.

One possible path of interest (option C3-A) shown in Fig. 6a is todrive the bed from state point 3 to state point 4 by first opening thevalve between the bed and the evaporator whilst isolating the bedand the condenser and keeping the hot water circulating in thebed. This process continues until the bed pressure is equal to Pevap.Cooling water is then circulated through the bed to bring the bedtemperature down whilst the silica gel in the bed continues to ad-sorb water vapour from the evaporator. During the whole process3 ? 4 ? 1, the content of water in the silica gel increases from X3

to X4 then to X1.A second possible path of interest (option C3-B) for bringing the

bed back to state point 1, shown in Fig. 6b, is to reduce the pressureand temperature of the bed along the constant concentration (i.e.X3) line by circulating cooling water through the isolated bed first.Once the bed temperature drops to Tcw at state point 4’ (in Fig. 6b),

SECC1 � SECC2 ¼12

2CsgðT2;C2 � T1;C2Þ þ 2Q desðXmax;C2 � XminÞ þ CwaterðT2;C2 � T1;C2Þ � ðXmax;C2 þ XminÞðXmax;C2 � XminÞ

�

þ2CsgðT3;C1 � T1;C1Þ þ 2Q desðXmax;C1 � XminÞ þ CwaterXmax;C1½ðT2;C1 � T1;C1Þ þ ðT3;C1 � T1;C1Þ� þ XminðT3;C1 � T2;C1ÞðXmax;C1 � XminÞ

�ð22Þ

the valve between the bed and the evaporator is opened to allowwater adsorption on to the silica gel leading to an increase in thebed pressure until state point 1 is reached where the amount of ad-sorbed water reaches the cycle maximum and the pressure is equalto Pevap.

2.2.3.2. Thermodynamic modelling. For the case 3 cycles, the amountof fresh water that is generated in a single cycle from one bed (i.e.water productivity) is given by

mwater ¼ Dm1�3 ¼ m1 �m3 ¼ X1 �msg � X3 �msg ð17Þ

where msg is the mass of the silica gel in one bed, and D m1?3 is themass of water adsorbed on the silica gel between state points 1and 3.

The total heating requirement of a single cycle is the heat sup-plied in the process 2 ? 3, i.e.

QheatingðbedÞ ¼ Q2!3

¼ msgCsg þX2 þ X3

2

� �msgCwater

� �� ðT3 � T2Þ

þ ðX2 � X3Þ �msgQ des ð18Þ

where Cwater is the specific heat of water, Csg is the average silica gelspecific heat, and Qdes is the amount of heat required to desorb 1 kgof water.

Combining Eqs. (17) and (18), the specific energy consumption(SEC) is given by

SEC ¼msgCsg þ X2þX3

2

� �msgCwater

� � ðT3 � T2Þ þ ðX2 � X3Þ �msgQ des

X1 �msg � X3 �msg

ð19Þ

As in case 2, above analysis assumes the capacity of the silica gel isunbounded. In reality it will take on a finite maximum, indicatedhere by X5. In such a case, X1 in the above would be replaced withX5 whilst the remainder of the analysis above remains unchanged.

3. Ranking performance of the three cases

The relative performance of the above three cases is now con-sidered in terms of the specific energy consumption (SECCi) andcyclic specific fresh water production (mwater,Ci). The subscript Cihere and the followings, represent case i. The analysis is under-taken for identical heating and cooling water temperatures and sil-ica gel.

3.1. Specific energy consumption

For a given hot water temperature Thw, the minimum concen-trations for all three cases are equal, i.e.

Xmin;C1 ¼ Xmin;C2 ¼ Xmin;C3 ¼ Xmin ð20Þ

As shown in Figs. 2, 3 and 5, the maximum concentrations of the cy-cles for all three cases have the following relationship:

X0 P Xmax;C3 P Xmax;C2 P Xmax;C1 ð21Þ

where X0 is the theoretical maximum adsorption capacity of the sil-ica gel. Using Eqs. (10), (16) and (20), some algebra leads to

where T1,C1 represents the temperature of state point 1 in case 1. Asall the terms in Eq. (22) are positive, the following is true

SECC1 > SECC2 ð23Þ

From Figs. 3 and 5, the temperature changes during the heat inputprocesses for cases 2 and 3 are T2,C2 � T1,C2 and T3,C3 � T2,C3, respec-tively. For the same heating and cooling water temperatures, weobtain

T2;C2 � T1;C2 ¼ T3;C3 � T2;C3 ¼ Thw � Tcw ð24Þ

322 J.W. Wu et al. / Applied Energy 90 (2012) 316–322

Using Eqs. (16), (19), (20) and (24), some algebra leads to

SECC2 � SECC3 ¼ðThw � TcwÞ � ðXmax;C3 � Xmax;C2Þ � ðCsg þ CwaterXminÞ

ðXmax;C2 � XminÞ � ðXmax;C3 � XminÞð25Þ

This expression reveals that, when X0 P Xmax,C3 > Xmax,C2, the fol-lowing is true

SECC2 > SECC3 ð26Þ

However, because the cycle maximum concentrations of the adsor-bent can never exceed the adsorbent capacity for cases 2 and 3, ifX0 = Xmax,C3 = Xmax,C2 the following holds

SECC2 ¼ SECC3 ð27Þ

Therefore, from Eqs. (23), (26) and (27), the following can be gener-ally stated:

SECC1 > SECC2 P SECC3 ð28Þ

3.2. Water production rate

The amount of fresh water produced per cycle for each case isgiven by

mwater;Ci ¼ ðXmax;Ci � Xmin;CiÞ �msg ð29Þ

From Eq. (20), this becomes.

mwater;Ci ¼ ðXmax;Ci � XminÞ �msg ð30Þ

Using this with Eq. (21) gives

mwater;C1 6 mwater;C2 6 mwater;C3 ð31Þ

The actual water productivity of each cycle is dictated by the adsor-bent adsorption capacity, X0, although case 3 has the biggest poten-tial of producing highest amount of water comparing with othertwo cases, as show by Eq. (31), which means

For Eq. (31), if Xmax,C1 = Xmax,C2 = Xmax,C3 = X0, the following canbe stated

mwater;C1 ¼ mwater;C2 ¼ mwater;C3 ð32Þ

If Xmax,C1 < Xmax,C2 = Xmax,C3 = X0, Eq. (30) gives

mwater;C1 < mwater;C2 ¼ mwater;C3 ð33Þ

Similarly, if Xmax,C1 < Xmax,C2 < Xmax,C3 6 X0, the following holds

mwater;C1 < mwater;C2 < mwater;C3 ð34Þ

4. Conclusion

The temperature of the evaporator in an adsorption-based desa-lination (AD) cycle relative to the cooling water temperature signif-icantly impacts on the character of the cycle. In particular, whenthe temperature of the evaporator is set equal to or greater thanthe cooling water temperature – which restricts the AD systemto desalination only – the thermodynamic cycle changes funda-mentally from the co-generation mode. The three possible casesof the thermodynamic cycles of AD system that arise from consid-ering the possible evaporator temperatures relative to the coolingwater temperature have been presented and discussed. Analysis of

these cycles has shown that the best performance in terms of max-imum water production and minimum energy consumption isachieved when the temperature of the evaporator is greater thanthat of the water used to cool the silica-gel bed and condenser(i.e. Case 3 cycles).

References

[1] Zejli D, Benchrifa R, Bennouna A, Bouhelal OK. A solar adsorption desalinationdevice: first simulation results. Desalination 2004;168:127–35.

[2] Mosry H, Larger D, Genther K. Anew multiple-effect distiller system withcompact heat exchanger. Desalination 1994;96:59–70.

[3] Awerbuch L, May S, Soo-Hoo R, Van DV. Hybrid desalting systems. Desalination1989;76:189–97.

[4] Wazzan AI, Al-Modaf F. Seawater desalination in Kuwait using multistage flashevaporation technology: historical overview. Desalination 2001;134:257–67.

[5] Bruggen BVD, Vandecasteele C. Distillation vs. membrane filtration: overviewof process evolution in seawater desalination. Desalination 2002;143:207–18.

[6] Al-Shammiri M, Safar M. Multi-effect distillation plants: state of the art.Desalination 1999;126:45–59.

[7] Amjad Z. Reverse osmosis: membrane technology water chemistry andindustrial applications. New York: Chapman & Hall, International ThomsonPublishing; 1993. p. 105–15.

[8] Hummel RL. Solar distillation with economies of scale, innovation andoptimization. Desalination 2001;134:159–71.

[9] Sayyaadi H, Saffari A. Thermoeconomic optimization of multi effect distillationdesalination systems. Appl Energy 2010;87:1122–33.

[10] Al-Suleimani Z, Nair VR. Desalination by solar-powered reverse osmosis in aremote area of the Sultanate of Oman. Appl Energy 2000;65:367–80.

[11] Chua KJ, Chou SK, Yang WM. Advances in heat pump systems: a review. ApplEnergy 2010;87:3611–24.

[12] Jana AK. Heat integrated distillation operation. Appl Energy 2010;87:1477–94.[13] Maidment GG, Eames IW, Psaltas M, Lalzad A, Yiakoumetti K. Flash—type

barometric desalination plant powered by waste heat from electricity powerstations in Cyprus. Appl Energy 2007;84:66–77.

[14] Tchanche BF, Lambrinos G, Frangoudakis A, Papadakis G. Exergy analysis ofmicro-organic Rankine power cycles for a small scale solar driven reverseosmosis desalination system. Appl Energy 2010;87:1295–306.

[15] Wu JW, Biggs MJ, Hu EJ. Thermodynamic analysis of an adsorption-baseddesalination cycle. Chem Eng Res Des 2010;88:1541–7.

[16] Wang XL, Ng KC. Experimental investigation of an adsorption desalinationplant using low-temperature wasted heat. Appl Thermal Eng 2005;25:2780–9.

[17] Wang XL, Chakraborty A, Ng KC, Saha BB. How heat and mass recoverystrategies impact the performance of adsorption desalination plant: theoryand experiments. Heat Transfer Eng 2007;28:147–53.

[18] Ng KC, Chua HT, Chung CY, Loke CH, Kashiwagi T, Akisawa A, et al.Experimental investigation of the silica gel-water adsorption isothermcharacteristics. Appl Thermal Eng 2001;21:1631–42.

[19] EI-Sharkawy II, Thu K, Ng KC, Saha BB, Chakraborty A, Koyama S. Performanceimprovement of adsorption desalination plant: experimental investigation. IntRev Mech Eng 2007;1:25–31.

[20] Ng KC, Saha BB, Chakraborty A, Koyama S. Adsorption desalination quenchesglobal thirst. Heat Transfer Eng 2008;29:845–8. Editorial Paper.

[21] Thu K, Ng KC, Saha BB, Chakraborty A, Koyama S. Operational strategy ofadsorption desalination systems. Int J Heat Mass Transfer 2009;29:1811–6.

[22] Ng KC, Thu K, Chakraborty A, Saha BB, Chun WG. Solar-assisted dual-effectadsorption cycle for the production of cooling effect and potable water. Int JLow-Carbon Technol 2009;4:61–7.

[23] Chua HT, Ng KC, Chung CY, Malek A, Kashiwagi T, Akisawa A, et al. Modelingthe performance of two-bed, silica gel-water adsorption chillers. Int J Refrig1999;22:104–94.

[24] Chua HT, Ng KC, Wang W, Yap C, Wang XL. Transient modelling of a two-bedsilica gel-water adsorption chiller. Int J Heat Mass Transfer 2004;47:659–69.

[25] Wang XL, Chua HT. Two bed silica gel-water adsorption chillers: an effectuallumped parameter model. Int J Refrig 2007;30:1417–26.

[26] Wang DC, Xia ZZ, Wu JY, Wang RZ, Zhai H, Dou WD. Study of a novel silica gel-water adsorption chiller Part I. Design and performance prediction. Int J Refrig2005;28:1073–83.

[27] Atkins PW, Paula JD. Physical chemistry. 8th ed. UK: Oxford University Press;2006. p. 212.

[28] Chua HT, Ng KC, Malek A, Kashiwagi T, Akisawa A, Saha BB. Multi-bedregenerative adsorption chiller-improving the utilization of waste heat andreducing the chilled water outlet temperature fluctuation. Int J Refrig2001;24:124–36.