Renewable Energy 24 (2001) 91–111www.elsevier.nl/locate/renene

Water–zeolite adsorption heat pump combinedwith single effect evaporation desalination

process

Ahmad Al-Ansari a, Hisham Ettouney b,*,Hisham El-Dessouky b

a College of Technological Studies, P.O. Box: 42325, Shuwaikh, Kuwait 70654b Chemical Engineering Department, College of Engineering and Petroleum, Kuwait University, P.O.

Box 5969, Safat 13060, Kuwait

Received 29 March 2000; accepted 5 October 2000

Abstract

The single effect evaporation desalination process combined with adsorption heat pump(ADVC) is modeled analyzed as a function of the system design and operating parameters.The analysis gives variations in the thermal performance ratio, the specific heat transfer area,and the specific flow rate of cooling water. The performance evaluation is made as a functionof the brine boiling temperature, the difference in the temperature of the compressed vaporand the boiling brine, and the water content in the adsorption bed. Results show that thethermal performance ratio of this configuration is the highest among all single effect evapor-ation desalination systems. Moreover, the specific flow rate of the cooling water and the spe-cific heat transfer area are similar to those of other single effect configurations. It should bestressed these promising features makes the ADVC system highly attractive to small andremote communities and of special interest in situations where energy cost is high. 2001Elsevier Science Ltd. All rights reserved.

Keywords: Desalination; Heat pumps; Adsorption; Evaporation; Modeling

* Corresponding author. Tel.: +965-481-7662; +965-483-9498.E-mail address: hisham@kuc01.kuniv.edu.kw (H. Ettouney).

0960-1481/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved.PII: S 09 60 -1481( 00 )0 0192-0

92 A. Al-Ansari et al. / Renewable Energy 24 (2001) 91–111

Nomenclature

A Heat transfer area, m2

BPE Boiling point elevation, °CCp Heat capacity, kJ/kg °CH Enthalpy of liquid water, kJ/kgLMTD Logarithmic mean temperature difference, °CM Mass flow rate, kg/sMz Mass of adsorbing solids, kgP Pressure, kPaPR Performance ratio, PR=Md/Mm, dimensionlessQ Heat transfer rate, kJ/ssA Specific heat transfer area, sA=Ae/Md, m2/(kg/s)sMcw Specific cooling water flow rate, sMcw=Mcw/Md, dimensionless�T Temperature drop, °CT Temperature, °CU Overall heat transfer coefficient, kW/m2 °CV Vapor specific volume, m3/kgX Salt mass fraction

Greek letters

a Adsorption capacity, kg water/kg zeoliteh Efficiencyl Latent heat, kJ/kg

Subscripts

a State point at end of the adsorption processb Brinec State point at end of the desorption processcw Inlet cooling watercwo Outlet cooling waterd Distillate producte Evaporatore1 State point during desorptione2 State point during adsorptionf Feed seawaterm Motive steamo Outlet streams Compressed vaporv Formed vaporz Solid bed

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1. Introduction

Securing of fresh water resources is one of the pressing problems that face morethan half of the world population at the turn of the millennium. This problem iscaused in part by the poor distribution of fresh water resources, increase in the worldpopulation, and changes in consumption patterns and life styles. One solution methodis to adopt industrial desalination of seawater, which has been proved to be highlyreliable during the second half of the last century. Several countries have utilizedthermal and membrane desalination processes as the main, if not the only, sourceof fresh water to various human activities. The desalination market remains domi-nated by the multistage flash desalination process (MSF), which accounts forapproximately 55% of the desalination industry. The reverse osmosis process (RO)has a market share of about 35%. The remaining 10% is divided between single andmultiple effect evaporation processes. The MSF process is the workhorse of thedesalination industry with proven high reliability over the years especially for largeproduction volumes. On the other hand, the RO process and single effect evaporationare more flexible to situations where small production capacity is required. Orig-inally, the single effect units had very small production capacities with values lessthan 500 m3/d [1]. Progress in design of single effect units has resulted in increaseof the effect capacity to 5000 m3/d, which is sufficient for a population of 25,000inhabitants with an average consumption rate of 200 l/capita/day.

Single effect evaporation and vapor compression heat pumps include thermalvapor compression (TVC), mechanical vapor compression (MVC), absorption vaporcompression (ABVC), and adsorption vapor compression (ADVC) [2]. Preliminaryanalysis of the four systems and comparison of their performance was presented byAl-Juwayhel et al. [3]. Subsequent and more detailed analysis for the first threesystems was presented by El-Dessouky and Ettouney [4], for the TVC system, Ettou-ney et al. [5] for the MVC system, and Mandani et al. [6], for ABVC. This paperfocuses on detailed analysis of the ADVC system.

The main attraction of the thermal, absorption, or adsorption heat pumps over themechanical vapor compression heat pump is that they use low grade energy and donot contain moving parts. Faraday was the first to introduce the adsorption heat pumpin 1848. The system was used in the 1920s in adsorption refrigeration equipment.This configuration was then abandoned for more than 50 years upon developmentof the vapor compression refrigeration systems. Since the 1970s the system havebeen under development for applications in space cooling and heating [7]. NASAcontributed to additional development of the adsorption heat pump in the search fora long life and vibration free cooling system for the infrared sensors in outer spacemissions, which may last for more than 10 years [8]. In contrast to mechanical vaporcompression cooling and refrigeration systems, the adsorption heat pump operateswith benign fluids. The following solid/liquid pairs are used in adsorption heatpumps: calcium chloride/methylamine, silica-gel/water, zeolite/water, activecarbon/methanol, and active carbon/ammonia [9,10].

Research in adsorption heat pumps focuses on addressing design and operation

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problems that have the strongest effect on the system performance. These problemsinclude the following:

� Thermal conductivity of the solid bed, which affects the adsorption and desorptiontime. Therefore, during the heating or cooling cycles, a bed with low thermalconductivity would then heat transfer resistance inside the bed and would in turnreduce the heating or cooling rates of the bed. Hu et al. [11] compared the per-formance of raw zeolite versus zeolite coated with thermal polymer material.Results indicate enhancement in system performance and reduction in operatingtime. However, the type of adsorbent material does not affect the total amountof adsorbed water.

� Improvement of the thermal cycle of adsorption/desorption through use of differ-ent strategies for regenerative cycles. Douss and Meunier [12] proposed use ofseveral adsorbers, where heat recovery is operated between adsorbers at differenttemperatures. In this strategy the temperatures are maintained uniform inside theadsorbers. In a second strategy a thermal wave is generated to create large axialtemperature gradients within the adsorber. This strategy is technologically simpleand presents a very promising performance [13].

Use of several adsorbers or the regenerative cycles results in constant temperaturefor the energy recovery or release processes. This makes it possible to assume psuedosteady state conditions in system modeling [14].

This paper includes modeling and performance evaluation of the single effectevaporation desalination system combined with adsorption heat pump. The analysisfocuses on system performance as a function of design and operating parametersthat have a strong effect on the product unit cost. The next sections include processdescription, model, and analysis.

2. Process description

The ADVC system is shown diagrammatically in Fig. 1. The system includes theevaporator/condenser unit, two adsorption beds, feed preheaters, and a heatexchanger for the thermal fluid circulating between the adsorption and desorptionbeds. It is interesting to note that the evaporator and condenser form a single unitin this configuration, which replaces the individual condenser and evaporator in con-ventional adsorption heat pumps. Also, the feed preheaters are plate type and areused to exchange heat between the feed seawater and the condensed vapor and therejected brine. The adsorber plays the role of the bottom condenser in the TVCsystem. That is, this adsorber absorbs or rejects the excess heat added to the systemin the second adsorber.

The closed cycle of the heat pump is composed of the following steps:

1. Initially, bed I is assumed to be cold and saturated with water. The mass of thebed is the mass of the adsorbent Mz plus the associated water Md. The temperature

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Fig. 1. Single effect-evaporator driven by adsorption heat pump.

of the bed is Ta. The second bed is dry and hot at Tc. The temperature of the coldbed Ta must be less than the temperature of the water adsorbed in the bed. Thistemperature is fixed by the equilibrium relationship for the zeolite–water pair. Onthe other hand, the temperature of the hot bed Tc is equal to the temperature ofheating steam flowing to the first effect. The first step commences, when thecirculating fluid starts to transfer heat between the two beds. Thus, heating thefirst bed and cooling the second bed occurs simultaneously. During this phase,no heat is exchanged between the adsorbers and any external heat source or sink.The heat flowing into the first adsorber, Q2�1, is represented by the path abe1 onthe Clapeyron diagram (Fig. 2), while, the heat transferred from the second bed,Q2�1, is described by the route cde2 on the same diagram. The process is termin-ated when the first bed is heated to Te1

and second bed is cooled to Te2. For the

heat transfer to take place Te2should be higher than Te1

.2. The second step starts when the first bed is connected to the external source of

heating steam (boiler), where its temperature is increased from Te1to Tc. At the

96 A. Al-Ansari et al. / Renewable Energy 24 (2001) 91–111

Fig. 2. Clapeyron diagram for the adsorption/desorption vapor compression cycle.

same time, a stream of cooling-water is used to reduce the second bed temperaturefrom Te2

to Ta.3. During the heating process and once the pressure inside the first bed becomes

higher than the condenser pressure, the bed is opened to the tube side of theevaporator where the generated steam condenses.

4. At the same time, when the pressure in the second bed becomes less than theevaporator pressure, the bed is opened to the shell side of the evaporator wherethe vapor formed in the evaporator flows to the bed where it is adsorbed.

The previously described four steps represent the first half of the heat pump cycle.The second half of the cycle originates by circulating the heat transfer fluid in thereverse direction. During this second half of the cycle, bed I is cooled and adsorbsvapor from the evaporator. Simultaneously, bed II is heated and generates the heatingsteam, which condenses inside the evaporator tubes.

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3. Process model

The mathematical model for the single effect adsorption vapor compression desali-nation system includes balance equations for the evaporator, feed preheaters, adsorp-tion bed, and desorption bed. The model assumptions used in development includethe following:

� Steady state conditions. This implies use of a minimum of twoadsorption/desorption units. Therefore, as one of the two units go through theprocess of circulating the thermal fluid between the two beds the other unit isused for simultaneous absorption of vapor from the evaporator and generation ofheating steam.

� The adsorber pressure is uniform. Therefore, the vapor pressure and the adsorbenttemperature are related by the adsorption equilibrium equation.

� The bed contents are in thermal equilibrium. Therefore, the adsorbent and theadsorbate have the same temperature.

� No heat losses to the surroundings.� Model parameters, such as the fluid density, heat transfer coefficients, and velocity

are assumed constant.� The mass of vapor adsorbed in the second bed is equal to the amount of steam

generated in the first bed.� Constant and equal rates for adsorption and desorption, and� Constant rate of heat exchange between the two beds.

The model equations include the following:Overall material and salt balances

Mf�Md�Mb (1)

Mb�Mf(Xf/Xb) (2)

Preheaters energy balance

MfCp(Tf�Tcw)�Md(H(Td)�H(To))�MbCp(Tb�To) (3)

Evaporator energy balance

MfCp(Tb�Tf)�Mdlv�Mdld�MdCpv(Ts�Td) (4)

Boiling point elevation

Tb�Tv�BPE(Tb,Xb) (5)

Evaporator heat transfer area

Ae�Mdld+MdCpv

(Ts−Td)

Ue(Td−Tb)(6)

Feed/distillate preheater heat transfer area

98 A. Al-Ansari et al. / Renewable Energy 24 (2001) 91–111

Ad�Md(H(Td)−H(To))

Ud(LMTD)d(7)

(LMTD)d�(Td−Tf)−(To−Tcw)

lnTd−Tf

To−Tcw

(8)

Feed/brine preheaters heat transfer area

Ab�MbCp(Tb−To)Ub(LMTD)b

(9)

(LMTD)b�(Tb−Tf)−(To−Tcw)

lnTb−Tf

To−Tcw

(10)

Correlations for the overall heat transfer coefficient in the evaporator

Ue�1.9394�1.40562�10−3Tb�2.0752�10−4(Tb)2�2.3186�10−6(Tb)3 (11)

where Ue is the overall heat transfer coefficient in the evaporator in kW/m2 °C andTb is the brine boiling temperature in °C [15].Energy balance during cooling of the second bed from Te2

to Ta

McwCp(Tcwo�Tcw)�MzCpz

(Te2�Ta) (12)

Heat transferred from the second to the first bed

Q21�Mdlv�MzCpz(Tc�Te2

)�Md(H(Tv)�H(Ta)) (13)

Energy required to heat the first bed

Q21�Mmlm�Mdls�MzCpz(Tc�Ta)�Md(H(Tc)�H(Ta)) (14)

Combined energy balance [Eqs. (13) and (14)]

Mmlm�Md(ld�lv)�MzCpz(Te2

�Ta)�Md(H(Tc)�H(Tv)) (15)

Combined energy balance [Eqs. (13) and (15)]

Mmlm�Md(ld�lv)�McwCp(Tcwo�Tcw)�MdCp(Tc�Tv) (16)

Efficiency of the circulating fluid heat exchanger

h�MzCpz(Te2

�Ta)/(McwCp(Te2�Tcw)) (17)

Energy balance of the circulating fluid heat exchanger

MzCpz(Te2

�Ta)�McwCp(Tcwo�Tcw) (18)

Combined energy balance and heat exchanger efficiency for circulating fluid [Eqs.(17) and (18)]

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Te2�(Tcwo

�Tcw(1�h))/h (19)

Constraint on the temperature of inlet/outlet cooling water

Tcw�Tcw (20)

Tcwo�Te2

��T (21)

Equilibrium relations for adsorber and desorber

ln(P)�a�b/T (22)

where:

� P and T are the equilibrium pressure and temperature of the adsorber and desorber.In the above relation T is in K and P is in mbar. For the absorber P is equal tovapor pressure in the evaporator and for the desorber P is equal to the heatingsteam vapor pressure. Also, T is equals to Ta for the absorber and equal to Tc forthe desorber.

� a and b are functions of the water content and are defined by

a�20.49�60.4a�787a2�2.14�103a3

b��8013�33.83�103a�3�105a2�7.9�105a3

where a is in kg of water per kg of zeolite [16].Water balance in adsorber betweenpoints a and c

Mz�Mm/(ag�aa) (23)

Other system constraints include the following:

� �T varies between 3 and 5°C,� h varies between 0.85 and 0.9,� aa varies between 0.06 and 0.15 kg H2O/kg zeolite,� Tc is higher than Ts by 3–10°C, and� Tm is higher than Tc by 3–10°C.� Tf is lower than Tb by 2–5°C.� Td is higher than Tb by 2 to 5°C.

4. Performance parameters

The system performance is evaluated in terms of the following parameters:

� The performance ratio, which is defined as the flow rate ratio of product freshwater to motive steam, where PR=Md/Ms.

� The specific heat transfer area, which is defined as the ratio of the heat transfer

100 A. Al-Ansari et al. / Renewable Energy 24 (2001) 91–111

area of the evaporator to the flow rate of the product fresh water, whereAs=Ae/Md.

� Specific flow rate of cooling water, which is defined as the flow rate ratio ofcooling water to product fresh water, sMcw=Mcw/Md.

5. Solution method

The solution procedure is shown in Fig. 3 and it includes the following steps:

� The system capacity, brine temperature, intake seawater temperature, the watercontent in the adsorber at point (a), the heat exchanger efficiency, and the tempera-ture difference in the heat exchanger, the equilibrium water content at point (a),and salinity of intake seawater and rejected brine are specified.

� The system constraints are defined, which includes the saturation temperature ofthe condensate and the feed seawater temperature.

� Eqs. (1) and (2) are solved to determine the feed and brine flow rates.� The boiling point elevation and the vapor temperature in the evaporator are calcu-

lated from the correlation given in Appendix A and Eq. (3).� An initial guess is assumed for Ts and To. This is followed by iterative solution

of Eqs. (4) and (5). Newton’s method is used with an iteration error of 1×10−4.� The evaporator and preheaters heat transfer areas are determined from Eqs.

(6)–(11).� The constraints on the desorber temperature at point g and the motive steam tem-

perature are used to determine both temperatures.� The absorber temperature, Ta, is evaluated from Eq. (22).� The temperatures of inlet and outlet cooling seawater, Tcw and Tcwo

, and thedesorber temperature at point (e2), Te2

, are obtained from Eqs. (19)–(21).� The desorber water content, ag, is obtained from Eq. (22).� The solid mass in the adsorber is determined from Eq. (23).� The motive steam and the cooling seawater flow rates are obtained from Eqs. (15)

and (16).

6. System performance

The ADVC performance is evaluated as a function of the thermal performanceratio, the specific heat transfer area, and the specific flow rate of cooling water. TheADVC system is evaluated at the following conditions:

� Brine reject concentration, Xb=70,000 ppm� Intake seawater salinity, Xf=42,000 ppm� Intake seawater temperature, Tcw=25°C

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Fig. 3. Solution algorithm of the adsorption heat pump and the single effect evaporation desalination sys-tem.

102 A. Al-Ansari et al. / Renewable Energy 24 (2001) 91–111

� System capacity, Md=1 kg/s� Boiling temperature, Tb=40�110°C� The temperature difference between the condensing vapor and boiling brine,

Td�Td=2�8°C.� Feed seawater temperature, Tf=(Tb�2)°C� Desorber temperature, Tc=(Ts+5) °C� Motive steam temperature, Tm=(Tc+5) °C� Temperature difference of heat exchanger in adsorber, �T=5°C� Water content in adsorber, aa=0.05�0.15 kg H2O/kg solids� Efficiency of heat exchanger in adsorber, h=0.9.

The physical properties of the seawater, liquid water, and water vapor are calculatedas a function of temperature and concentration and temperature from the correlationsgiven in Appendix A. As for the specific heat of the vapor at constant pressure,Cpv

, it is assumed constant with a value of 1.884 kJ/kg °C. Similarly, the specificheat of zeolite, Cpz

, is assumed constant and equal to 0.9 kJ/kg °C.The results are shown in Figs. 4–9 and it includes variations in the thermal per-

formance ratio, the specific heat transfer area, and the specific flow rate of coolingwater. Variations in the thermal performance ratio are shown in Fig. 4 as a function

Fig. 4. Effect of boiling temperature and the temperature difference of condensed vapor and boilingbrine on the thermal performance ratio of the ADVC system.

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Fig. 5. Effect of boiling temperature and the temperature difference of condensed vapor and boilingbrine on the evaporator specific heat transfer area for the ADVC system.

of the brine boiling temperature, Tb, and the temperature difference between thecondensing vapor and the boiling brine, Td�Tb. As is shown the thermal performanceratio increases at higher boiling temperatures and larger difference in the temperatureof the condensing vapor and boiling brine. As is shown a thermal performance ratioclose to 10 can be reached as the brine boiling temperature increases to 110°C.However, it should be noted that achieving such higher thermal performance is sub-ject to reducing the water content in the adsorber at point (c) to values between zeroand 0.01 kg H2O/kg zeolite. On the other hand, the thermal performance ratio variesaround a value of 4–5 for brine boiling temperatures between 40 and 60°C. Thesuperior performance of the ADVC is certainly pronounced in comparison with othersingle effect systems.

Irrespective of the high thermal performance ratio, the ADVC system has similardesign features to other single effect vapor compression systems. As is shown inFig. 5 the evaporator heat transfer area decreases drastically upon the increase ofthe temperature difference of the condensing vapor and the boiling brine. This isbecause of the increase in the temperature driving force between the condensing

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Fig. 6. Effect of boiling temperature and the temperature difference of condensed vapor and boilingbrine on the specific flow rate of cooling water for the ADVC system.

vapor and the boiling brine. A similar effect takes place in the cooling seawaterheat exchanger, where increase in the system temperature increases the driving forcebetween the bed and the cooling seawater stream. This in turn reduces the flow rateof the cooling seawater stream.

System performance as a function of the water content in the adsorber at point(a) and the brine boiling temperature are shown in Figs. 7–9. As is shown in Fig.7 the thermal performance ratio varies between 2 and 7. As discussed before, thehigh performance ratio of 13 can only be achieved if the water content of the adsorberat point (c) is reduced to values below 0.01 kg H2O/kg zeolite. As is shown in Fig.8, the evaporator heat transfer area has no dependence on the water content in theadsorber bed at point (a) and it only depends on the brine boiling temperature. Asfor the specific flow rat of cooling water it depends on both parameters, where itdecreases with the increase of the brine boiling temperature. Effect of the watercontent in the adsorber varies, where at low boiling temperatures its increase reducesthe specific flow rate of cooling water. The opposite effect is obtained at higherboiling temperatures.

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Fig. 7. Effect of boiling temperature and the water content in adsorber at point (a) on the thermalperformance ratio of the ADVC system.

7. Comparison of single effect evaporation systems

Comparison is made between the adsorption vapor compression system and theother single effect vapor compression processes, which include the thermal vaporcompression (TVC), mechanical vapor compression (MVC), and absorption vaporcompression (ABVC). Performance data for the other three configurations areextracted from the studies by El-Dessouky and Ettouney [4] for TVC, Ettouney etal. [5] for MVC, and Mandani et al. [6] for ABVC. Table 1 shows performance ofthe three systems, which includes the performance ratio, specific heat transfer area,and specific flow rate of cooling water. As is shown, the highest thermal performanceratio is obtained for the ADVC system, while the lowest is for the TVC system. Asfor the MVC system it is rated in terms of the specific power consumption, whichis given in kWh/m3. The value shown here is typical of the MVC industry and highlycompetitive against that of the reverse osmosis process [5]. As for the specific heattransfer area it depends on the temperature difference between the condensing vaporand the boiling brine, or the driving force for heat transfer during evaporation. Asis shown the specific heat transfer areas for the ADVC and MVC systems are ident-ical, while the lowest heat transfer area is obtained for the TVC. This is because ofthe large temperature difference between the compressed vapor and the boiling brine

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Fig. 8. Effect of boiling temperature and the water content in adsorber at point (a) on the evaporatorspecific heat transfer area for the ADVC system.

in the TVC system. The specific heat transfer area for the ABVC system is lowerthan that in the ADVC and MVC system, because part of the evaporation processtakes place in the absorber [6]. As for the specific flow rate of cooling water, thehighest value is found for the TVC system, which is dependent on the amount ofvapor entrained by the ejector. As for the specific flow rate of the cooling water forADVC and ABVC systems, both have similar values and are much lower than theTVC system. This indicates rejection of a small amount of heat to the surroundingsin the ADVC and ABVC systems and their higher efficiency. It should be noted thatthe MVC system does not use any cooling water because the entire vapor formedduring evaporation is routed to the mechanical compressor. Although it may seemthat the TVC system is the least attractive among the four systems, it should, how-ever, be stressed that the TVC system is the basic unit forming the multiple effectevaporation desalination systems. Also, the TVC system has a simple vapor com-pression scheme, i.e. the steam jet ejector, which is relatively inexpensive in compari-son with other vapor compression heat pumps and it does not require moving partsor pumping units.

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Fig. 9. Effect of boiling temperature and the water content in adsorber at point (a) on the specific flowrate of cooling water for the ADVC system.

8. Conclusions

The ADVC system is one of the most efficient single effect vapor compressiondesalination systems. The system includes conventional unit processes found in othersingle effect configuration, i.e. evaporator and feed preheaters. In addition, its heatpump is rather simple and it includes two zeolite beds for adsorption and desorption.Operation of these beds is controlled by the design pressure and temperature forvapor adsorption and generation of the compressed vapor. A steady state mathemat-ical model is presented to design and evaluate the system performance. The systemperformance is presented as a function main design and operating parameters. Resultsare presented in terms of variations in the thermal performance ratio, specific heattransfer area for the evaporator, and the specific flow rate of the cooling water. Thesystem performance ratio is highest among all other single effect vapor compressionconfigurations. Also, the specific heat transfer area for the evaporator and the specificflow rate of the cooling water are similar to systems.

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Table 1Performance of the single effect evaporation vapor compression desalination systems

Parameter ABVC ADVC MVC TVC

Boiling brine 80 80 80 80temperature Tb (°C)Condensing vapor 82 82 82 109temperature Td (°C)Compressed vapor 82 98.3 96.9 109temperature Ts (°C)Seawater salinity, 42,000 42,000 42,000 42,000Xf (ppm)Reject brine 70,000 70,000 70,000 70,000salinity, Xb (ppm)Intake seawater 25 25 25 25temperature, Tcw

(°C)Feed seawater 72.97 78 77.4 75temperature, Tf

(°C)Thermal 2.74 7.25 9.68* 1.29performance ratio,PRSpecific flow rate 1.54 1.11 – 4.99of cooling water,sMcw

Specific heat 324 463 463 75transfer area, sA[m2/(kg/s)]

Appendix A. Model correlations

The correlation for pressure drop in the demister, �Pp, is developed by El-Dessouky et al. [17] for industrial type wire pads. The ranges of the experimentalvariables were V (0.98–7.5 m/s), rp (80.317–208.16 kg/m3), L (100–200 mm), dw

(0.2–0.32 mm), and dp (1–5 mm). This correlation is given by

�Pp�3.88178(rp)0.375798(V)0.81317(dw)−1.56114147 (27)

where �Pp is the demister pressure drop in Pa/m, dw is the wire diameter, V is thevapor velocity in the demister, and r is the demister density. In Eq. (27) the subscriptp denotes the demister.

The boiling point elevation is obtained as a function of the brine salinity andtemperature. The value of BPE is obtained from the following empirical correlation,which is valid for 20,000�X�160,000 ppm and 20�T�180°C,

BPE�X(B�CX)10−3 (28)

with

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B�(6.71�6.34�10−2T�9.74�10−5T 2)10−3

C�(22.238�9.59�10−3T�9.42�10−5T 2)10−8

where BPE is in °C.The seawater specific heat, Cp, is given by the following correlation

Cp�(A�BT�CT 2�DT 3)�10−3 (29)

The variables A, B, C and D are evaluated as a function of the water salinityas follows:

A=4206.8−6.6197 S+1.2288×10−2 S 2

B=−1.1262+5.4178×10−2S−2.2719×10−4 S 2

C=1.2026×10−2−5.3566×10−4S+1.8906×10−6 S 2

D=6.8777×10−7+1.517×10−6 S−4.4268×10−9 S 2

where Cp is in kJ/kg °C, T in °C, and S is the water salinity in gm/kg. The abovecorrelation is valid over salinity and temperature ranges of 20,000�X�160,000 ppmand 20�T�180°C, respectively.

The correlation for the saturation pressure of water vapor is given by

ln(P/Pc)�� Tc

T+273.15�1��8

i�1

fi(0.01(T�273.15�338.15))(i−1) (30)

where Tc=647.286 K and Pc=22,089 kPa and the values of fi are given below:

f1 f2 f3 f4�7.419242 0.29721 �0.1155286 0.008685635f5 f6 f7 f80.001094098 �0.00439993 0.002520658 �0.000521868

where P and T are in kPa and °C, respectively, with the following ranges 0.872�P�1553.8 and 5�T�200. The percentage errors for the calculated versus the steamtable values are less than 0.2%.

The saturation temperature correlation is given by

T��42.6776�3892.7

(ln(P/1000)−9.48654)��273.15 (31)

where P is in kPa and T is in °C. The above correlation is valid for the calculatedsaturation temperature over a pressure range of 10–1750 kPa. The percentage errorsfor the calculated versus the steam table values are less than 0.1%.

The correlation for the specific volume of saturated water vapor is given by

V�Vc� Tc

T+273.15�1�exp��6

i�1

fi(T�273.15)(i−1)� (32)

110 A. Al-Ansari et al. / Renewable Energy 24 (2001) 91–111

where Tc=647.286 K and Vc=0.003172222 m3/kg and the values of fi are given below:

f1 f2 f3 f4 f5 f683.63213098 �0.668265339 0.002495964 �5.04185E-06 5.34205E-09 �2.3279E-12

where V is in m3/kg and T is in °C. The temperature range for the above correlationis 5–200°C. The percentage errors for the calculated versus the steam table valuesare less than 0.025%.

The correlation for latent heat of water evaporation is given by

l�2501.897149�2.407064037 T�1.192217�10−3 T 2�1.5863 (33)

�10−5T 3

In the above equation, T is the saturation temperature in °C and l is the latent heatin kJ/kg. This correlation is valid over a temperature range of 5–200°C with a per-centage error less than 0.026% against the corresponding values from the steam tabl-es.

The correlation for the water vapor enthalpy is given by

H��2501.689845�1.806916015 T�5.087717�10−4 T 2 (34)

�1.1221x10−5T 3

In the above equation, T is the saturation temperature in °C and H� is the enthalpyin kJ/kg. This correlation is valid over a temperature range of 0.01–200°C withpercentage errors less than 0.017% against the corresponding values from thesteam tables.

The correlation for enthalpy of saturated liquid water is given by

H��0.033635409�4.207557011 T�6.200339�10−4 T 2�4.459374 (35)

�10−6T 3

In the above equation, T is the saturation temperature in °C and H is the enthalpyin kJ/kg. This correlation is valid over a temperature range of 5–200 with percentageerrors less than 0.04% against the corresponding values from the steam tables.

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