Water zeolite adsorption heat pump combined with single effect evaporation desalination process

Transcription

1 Renewable Energy 24 (2001) Water zeolite adsorption heat pump combined with 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 b 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 function of the brine boiling temperature, the difference in the temperature of the compressed vapor and the boiling brine, and the water content in the adsorption bed. Results show that the thermal performance ratio of this configuration is the highest among all single effect evaporation desalination systems. Moreover, the specific flow rate of the cooling water and the specific heat transfer area are similar to those of other single effect configurations. It should be stressed these promising features makes the ADVC system highly attractive to small and remote communities and of special interest in situations where energy cost is high Elsevier Science Ltd. All rights reserved. Keywords: Desalination; Heat pumps; Adsorption; Evaporation; Modeling * Corresponding author. Tel.: ; address: hisham@kuc01.kuniv.edu.kw (H. Ettouney) /01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S (00)

2 92 A. Al-Ansari et al. / Renewable Energy 24 (2001) Nomenclature A Heat transfer area, m 2 BPE Boiling point elevation, C C p Heat capacity, kj/kg C H Enthalpy of liquid water, kj/kg LMTD Logarithmic mean temperature difference, C M Mass flow rate, kg/s M z Mass of adsorbing solids, kg P Pressure, kpa PR Performance ratio, PR=M d /M m, dimensionless Q Heat transfer rate, kj/s sa Specific heat transfer area, sa=a e /M d,m 2 /(kg/s) sm cw Specific cooling water flow rate, sm cw =M cw /M d, dimensionless T Temperature drop, C T Temperature, C U Overall heat transfer coefficient, kw/m 2 C V Vapor specific volume, m 3 /kg X Salt mass fraction Greek letters a h l Adsorption capacity, kg water/kg zeolite Efficiency Latent heat, kj/kg Subscripts a b c cw cw o d e e 1 e 2 f m o s v z State point at end of the adsorption process Brine State point at end of the desorption process Inlet cooling water Outlet cooling water Distillate product Evaporator State point during desorption State point during adsorption Feed seawater Motive steam Outlet stream Compressed vapor Formed vapor Solid bed

3 A. Al-Ansari et al. / Renewable Energy 24 (2001) Introduction Securing of fresh water resources is one of the pressing problems that face more than half of the world population at the turn of the millennium. This problem is caused in part by the poor distribution of fresh water resources, increase in the world population, and changes in consumption patterns and life styles. One solution method is to adopt industrial desalination of seawater, which has been proved to be highly reliable during the second half of the last century. Several countries have utilized thermal and membrane desalination processes as the main, if not the only, source of fresh water to various human activities. The desalination market remains dominated by the multistage flash desalination process (MSF), which accounts for approximately 55% of the desalination industry. The reverse osmosis process (RO) has a market share of about 35%. The remaining 10% is divided between single and multiple effect evaporation processes. The MSF process is the workhorse of the desalination industry with proven high reliability over the years especially for large production volumes. On the other hand, the RO process and single effect evaporation are more flexible to situations where small production capacity is required. Originally, the single effect units had very small production capacities with values less than 500 m 3 /d [1]. Progress in design of single effect units has resulted in increase of the effect capacity to 5000 m 3 /d, which is sufficient for a population of 25,000 inhabitants with an average consumption rate of 200 l/capita/day. Single effect evaporation and vapor compression heat pumps include thermal vapor compression (TVC), mechanical vapor compression (MVC), absorption vapor compression (ABVC), and adsorption vapor compression (ADVC) [2]. Preliminary analysis of the four systems and comparison of their performance was presented by Al-Juwayhel et al. [3]. Subsequent and more detailed analysis for the first three systems was presented by El-Dessouky and Ettouney [4], for the TVC system, Ettouney et al. [5] for the MVC system, and Mandani et al. [6], for ABVC. This paper focuses on detailed analysis of the ADVC system. The main attraction of the thermal, absorption, or adsorption heat pumps over the mechanical vapor compression heat pump is that they use low grade energy and do not contain moving parts. Faraday was the first to introduce the adsorption heat pump in The system was used in the 1920s in adsorption refrigeration equipment. This configuration was then abandoned for more than 50 years upon development of the vapor compression refrigeration systems. Since the 1970s the system have been under development for applications in space cooling and heating [7]. NASA contributed to additional development of the adsorption heat pump in the search for a long life and vibration free cooling system for the infrared sensors in outer space missions, which may last for more than 10 years [8]. In contrast to mechanical vapor compression cooling and refrigeration systems, the adsorption heat pump operates with benign fluids. The following solid/liquid pairs are used in adsorption heat pumps: calcium chloride/methylamine, silica-gel/water, zeolite/water, active carbon/methanol, and active carbon/ammonia [9,10]. Research in adsorption heat pumps focuses on addressing design and operation

4 94 A. Al-Ansari et al. / Renewable Energy 24 (2001) problems that have the strongest effect on the system performance. These problems include the following: Thermal conductivity of the solid bed, which affects the adsorption and desorption time. Therefore, during the heating or cooling cycles, a bed with low thermal conductivity would then heat transfer resistance inside the bed and would in turn reduce the heating or cooling rates of the bed. Hu et al. [11] compared the performance of raw zeolite versus zeolite coated with thermal polymer material. Results indicate enhancement in system performance and reduction in operating time. However, the type of adsorbent material does not affect the total amount of adsorbed water. Improvement of the thermal cycle of adsorption/desorption through use of different strategies for regenerative cycles. Douss and Meunier [12] proposed use of several adsorbers, where heat recovery is operated between adsorbers at different temperatures. In this strategy the temperatures are maintained uniform inside the adsorbers. In a second strategy a thermal wave is generated to create large axial temperature gradients within the adsorber. This strategy is technologically simple and presents a very promising performance [13]. Use of several adsorbers or the regenerative cycles results in constant temperature for the energy recovery or release processes. This makes it possible to assume psuedo steady state conditions in system modeling [14]. This paper includes modeling and performance evaluation of the single effect evaporation desalination system combined with adsorption heat pump. The analysis focuses on system performance as a function of design and operating parameters that have a strong effect on the product unit cost. The next sections include process description, model, and analysis. 2. Process description The ADVC system is shown diagrammatically in Fig. 1. The system includes the evaporator/condenser unit, two adsorption beds, feed preheaters, and a heat exchanger for the thermal fluid circulating between the adsorption and desorption beds. It is interesting to note that the evaporator and condenser form a single unit in this configuration, which replaces the individual condenser and evaporator in conventional adsorption heat pumps. Also, the feed preheaters are plate type and are used to exchange heat between the feed seawater and the condensed vapor and the rejected brine. The adsorber plays the role of the bottom condenser in the TVC system. That is, this adsorber absorbs or rejects the excess heat added to the system in 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 the bed is the mass of the adsorbent M z plus the associated water M d. The temperature

5 A. Al-Ansari et al. / Renewable Energy 24 (2001) Fig. 1. Single effect-evaporator driven by adsorption heat pump. of the bed is T a. The second bed is dry and hot at T c. The temperature of the cold bed T a must be less than the temperature of the water adsorbed in the bed. This temperature is fixed by the equilibrium relationship for the zeolite water pair. On the other hand, the temperature of the hot bed T c is equal to the temperature of heating steam flowing to the first effect. The first step commences, when the circulating fluid starts to transfer heat between the two beds. Thus, heating the first 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, Q 2 1, is represented by the path abe 1 on the Clapeyron diagram (Fig. 2), while, the heat transferred from the second bed, Q 2 1, is described by the route cde 2 on the same diagram. The process is terminated when the first bed is heated to T e1 and second bed is cooled to T e2. For the heat transfer to take place T e2 should be higher than T e1. 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 T e1 to T c. At the

6 96 A. Al-Ansari et al. / Renewable Energy 24 (2001) 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 temperature from T e2 to T a. 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 the evaporator where the generated steam condenses. 4. At the same time, when the pressure in the second bed becomes less than the evaporator pressure, the bed is opened to the shell side of the evaporator where the 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 the reverse direction. During this second half of the cycle, bed I is cooled and adsorbs vapor from the evaporator. Simultaneously, bed II is heated and generates the heating steam, which condenses inside the evaporator tubes.

7 A. Al-Ansari et al. / Renewable Energy 24 (2001) Process model The mathematical model for the single effect adsorption vapor compression desalination system includes balance equations for the evaporator, feed preheaters, adsorption bed, and desorption bed. The model assumptions used in development include the following: Steady state conditions. This implies use of a minimum of two adsorption/desorption units. Therefore, as one of the two units go through the process of circulating the thermal fluid between the two beds the other unit is used for simultaneous absorption of vapor from the evaporator and generation of heating steam. The adsorber pressure is uniform. Therefore, the vapor pressure and the adsorbent temperature are related by the adsorption equilibrium equation. The bed contents are in thermal equilibrium. Therefore, the adsorbent and the adsorbate 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 M f M d M b (1) M b M f (X f /X b ) (2) Preheaters energy balance M f C p (T f T cw ) M d (H(T d ) H(T o )) M b C p (T b T o ) (3) Evaporator energy balance M f C p (T b T f ) M d l v M d l d M d C pv (T s T d ) (4) Boiling point elevation T b T v BPE(T b,x b ) (5) Evaporator heat transfer area A e M dl d +M d C pv (T s T d ) (6) U e (T d T b ) Feed/distillate preheater heat transfer area

8 98 A. Al-Ansari et al. / Renewable Energy 24 (2001) A d M d(h(t d ) H(T o )) U d (LMTD) d (7) (LMTD) d (T d T f ) (T o T cw ) Feed/brine preheaters heat transfer area ln T d T f T o T cw (8) A b M bc p (T b T o ) U b (LMTD) b (9) (LMTD) b (T b T f ) (T o T cw ) ln T b T f T o T cw (10) Correlations for the overall heat transfer coefficient in the evaporator U e T b (T b ) (T b ) 3 (11) where U e is the overall heat transfer coefficient in the evaporator in kw/m 2 C and T b is the brine boiling temperature in C [15]. Energy balance during cooling of the second bed from T e2 to T a M cw C p (T cwo T cw ) M z C pz (T e2 T a ) (12) Heat transferred from the second to the first bed Q 21 M d l v M z C pz (T c T e2 ) M d (H(T v ) H(T a )) (13) Energy required to heat the first bed Q 21 M m l m M d l s M z C pz (T c T a ) M d (H(T c ) H(T a )) (14) Combined energy balance [Eqs. (13) and (14)] M m l m M d (l d l v ) M z C pz (T e2 T a ) M d (H(T c ) H(T v )) (15) Combined energy balance [Eqs. (13) and (15)] M m l m M d (l d l v ) M cw C p (T cwo T cw ) M d C p (T c T v ) (16) Efficiency of the circulating fluid heat exchanger h M z C pz (T e2 T a )/(M cw C p (T e2 T cw )) (17) Energy balance of the circulating fluid heat exchanger M z C pz (T e2 T a ) M cw C p (T cwo T cw ) (18) Combined energy balance and heat exchanger efficiency for circulating fluid [Eqs. (17) and (18)]

9 A. Al-Ansari et al. / Renewable Energy 24 (2001) T e2 (T cwo T cw (1 h))/h (19) Constraint on the temperature of inlet/outlet cooling water T cw T cw (20) T cwo T e2 T (21) Equilibrium relations for adsorber and desorber ln(p) a b/t 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 to vapor pressure in the evaporator and for the desorber P is equal to the heating steam vapor pressure. Also, T is equals to T a for the absorber and equal to T c for the desorber. a and b are functions of the water content and are defined by (22) a a 787a a 3 b a a a 3 where a is in kg of water per kg of zeolite [16].Water balance in adsorber between points a and c M z M m /(a g a a ) (23) Other system constraints include the following: T varies between 3 and 5 C, h varies between 0.85 and 0.9, a a varies between 0.06 and 0.15 kg H 2 O/kg zeolite, T c is higher than T s by 3 10 C, and T m is higher than T c by 3 10 C. T f is lower than T b by 2 5 C. T d is higher than T b 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 fresh water to motive steam, where PR=M d /M s. The specific heat transfer area, which is defined as the ratio of the heat transfer

10 100 A. Al-Ansari et al. / Renewable Energy 24 (2001) area of the evaporator to the flow rate of the product fresh water, where A s =A e /M d. Specific flow rate of cooling water, which is defined as the flow rate ratio of cooling water to product fresh water, sm cw =M cw /M d. 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 water content in the adsorber at point (a), the heat exchanger efficiency, and the temperature 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 of the 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 calculated from the correlation given in Appendix A and Eq. (3). An initial guess is assumed for T s and T o. This is followed by iterative solution of Eqs. (4) and (5). Newton s method is used with an iteration error of 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 temperature are used to determine both temperatures. The absorber temperature, T a, is evaluated from Eq. (22). The temperatures of inlet and outlet cooling seawater, T cw and T cwo, and the desorber temperature at point (e 2 ), T e2, are obtained from Eqs. (19) (21). The desorber water content, a g, 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 performance ratio, the specific heat transfer area, and the specific flow rate of cooling water. The ADVC system is evaluated at the following conditions: Brine reject concentration, X b =70,000 ppm Intake seawater salinity, X f =42,000 ppm Intake seawater temperature, T cw =25 C

11 A. Al-Ansari et al. / Renewable Energy 24 (2001) Solution algorithm of the adsorption heat pump and the single effect evaporation desalination sys- Fig. 3. tem.

12 102 A. Al-Ansari et al. / Renewable Energy 24 (2001) System capacity, M d =1 kg/s Boiling temperature, T b = C The temperature difference between the condensing vapor and boiling brine, T d T d =2 8 C. Feed seawater temperature, T f =(T b 2) C Desorber temperature, T c =(T s +5) C Motive steam temperature, T m =(T c +5) C Temperature difference of heat exchanger in adsorber, T=5 C Water content in adsorber, a a = kg H 2 O/kg solids Efficiency of heat exchanger in adsorber, h=0.9. The physical properties of the seawater, liquid water, and water vapor are calculated as a function of temperature and concentration and temperature from the correlations given in Appendix A. As for the specific heat of the vapor at constant pressure, C pv, it is assumed constant with a value of kj/kg C. Similarly, the specific heat of zeolite, C pz, 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 performance ratio, the specific heat transfer area, and the specific flow rate of cooling water. 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 boiling brine on the thermal performance ratio of the ADVC system.

13 A. Al-Ansari et al. / Renewable Energy 24 (2001) Fig. 5. Effect of boiling temperature and the temperature difference of condensed vapor and boiling brine on the evaporator specific heat transfer area for the ADVC system. of the brine boiling temperature, T b, and the temperature difference between the condensing vapor and the boiling brine, T d T b. As is shown the thermal performance ratio increases at higher boiling temperatures and larger difference in the temperature of the condensing vapor and boiling brine. As is shown a thermal performance ratio close 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 subject to reducing the water content in the adsorber at point (c) to values between zero and 0.01 kg H 2 O/kg zeolite. On the other hand, the thermal performance ratio varies around a value of 4 5 for brine boiling temperatures between 40 and 60 C. The superior performance of the ADVC is certainly pronounced in comparison with other single effect systems. Irrespective of the high thermal performance ratio, the ADVC system has similar design features to other single effect vapor compression systems. As is shown in Fig. 5 the evaporator heat transfer area decreases drastically upon the increase of the temperature difference of the condensing vapor and the boiling brine. This is because of the increase in the temperature driving force between the condensing

14 104 A. Al-Ansari et al. / Renewable Energy 24 (2001) Fig. 6. Effect of boiling temperature and the temperature difference of condensed vapor and boiling brine 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 seawater heat exchanger, where increase in the system temperature increases the driving force between the bed and the cooling seawater stream. This in turn reduces the flow rate of 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 As is shown in Fig. 7 the thermal performance ratio varies between 2 and 7. As discussed before, the high performance ratio of 13 can only be achieved if the water content of the adsorber at point (c) is reduced to values below 0.01 kg H 2 O/kg zeolite. As is shown in Fig. 8, the evaporator heat transfer area has no dependence on the water content in the adsorber bed at point (a) and it only depends on the brine boiling temperature. As for the specific flow rat of cooling water it depends on both parameters, where it decreases with the increase of the brine boiling temperature. Effect of the water content in the adsorber varies, where at low boiling temperatures its increase reduces the specific flow rate of cooling water. The opposite effect is obtained at higher boiling temperatures.

15 A. Al-Ansari et al. / Renewable Energy 24 (2001) Fig. 7. Effect of boiling temperature and the water content in adsorber at point (a) on the thermal performance ratio of the ADVC system. 7. Comparison of single effect evaporation systems Comparison is made between the adsorption vapor compression system and the other single effect vapor compression processes, which include the thermal vapor compression (TVC), mechanical vapor compression (MVC), and absorption vapor compression (ABVC). Performance data for the other three configurations are extracted from the studies by El-Dessouky and Ettouney [4] for TVC, Ettouney et al. [5] for MVC, and Mandani et al. [6] for ABVC. Table 1 shows performance of the three systems, which includes the performance ratio, specific heat transfer area, and specific flow rate of cooling water. As is shown, the highest thermal performance ratio is obtained for the ADVC system, while the lowest is for the TVC system. As for the MVC system it is rated in terms of the specific power consumption, which is given in kwh/m 3. The value shown here is typical of the MVC industry and highly competitive against that of the reverse osmosis process [5]. As for the specific heat transfer area it depends on the temperature difference between the condensing vapor and the boiling brine, or the driving force for heat transfer during evaporation. As is shown the specific heat transfer areas for the ADVC and MVC systems are identical, while the lowest heat transfer area is obtained for the TVC. This is because of the large temperature difference between the compressed vapor and the boiling brine

16 106 A. Al-Ansari et al. / Renewable Energy 24 (2001) Fig. 8. Effect of boiling temperature and the water content in adsorber at point (a) on the evaporator specific heat transfer area for the ADVC system. in the TVC system. The specific heat transfer area for the ABVC system is lower than that in the ADVC and MVC system, because part of the evaporation process takes place in the absorber [6]. As for the specific flow rate of cooling water, the highest value is found for the TVC system, which is dependent on the amount of vapor entrained by the ejector. As for the specific flow rate of the cooling water for ADVC and ABVC systems, both have similar values and are much lower than the TVC system. This indicates rejection of a small amount of heat to the surroundings in the ADVC and ABVC systems and their higher efficiency. It should be noted that the MVC system does not use any cooling water because the entire vapor formed during evaporation is routed to the mechanical compressor. Although it may seem that the TVC system is the least attractive among the four systems, it should, however, be stressed that the TVC system is the basic unit forming the multiple effect evaporation desalination systems. Also, the TVC system has a simple vapor compression scheme, i.e. the steam jet ejector, which is relatively inexpensive in comparison with other vapor compression heat pumps and it does not require moving parts or pumping units.

17 A. Al-Ansari et al. / Renewable Energy 24 (2001) Fig. 9. Effect of boiling temperature and the water content in adsorber at point (a) on the specific flow rate of cooling water for the ADVC system. 8. Conclusions The ADVC system is one of the most efficient single effect vapor compression desalination systems. The system includes conventional unit processes found in other single effect configuration, i.e. evaporator and feed preheaters. In addition, its heat pump 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 for vapor adsorption and generation of the compressed vapor. A steady state mathematical model is presented to design and evaluate the system performance. The system performance is presented as a function main design and operating parameters. Results are presented in terms of variations in the thermal performance ratio, specific heat transfer area for the evaporator, and the specific flow rate of the cooling water. The system performance ratio is highest among all other single effect vapor compression configurations. Also, the specific heat transfer area for the evaporator and the specific flow rate of the cooling water are similar to systems.

18 108 A. Al-Ansari et al. / Renewable Energy 24 (2001) Table 1 Performance of the single effect evaporation vapor compression desalination systems Parameter ABVC ADVC MVC TVC Boiling brine temperature T b ( C) Condensing vapor temperature T d ( C) Compressed vapor temperature T s ( C) Seawater salinity, 42,000 42,000 42,000 42,000 X f (ppm) Reject brine 70,000 70,000 70,000 70,000 salinity, X b (ppm) Intake seawater temperature, T cw ( C) Feed seawater temperature, T f ( C) Thermal * 1.29 performance ratio, PR Specific flow rate of cooling water, sm cw Specific heat transfer area, sa [m 2 /(kg/s)] Appendix A. Model correlations The correlation for pressure drop in the demister, P p, is developed by El- Dessouky et al. [17] for industrial type wire pads. The ranges of the experimental variables were V ( m/s), r p ( kg/m 3 ), L ( mm), d w ( mm), and d p (1 5 mm). This correlation is given by P p (r p ) (V) (d w ) (27) where P p is the demister pressure drop in Pa/m, d w is the wire diameter, V is the vapor velocity in the demister, and r is the demister density. In Eq. (27) the subscript p denotes the demister. The boiling point elevation is obtained as a function of the brine salinity and temperature. 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

19 A. Al-Ansari et al. / Renewable Energy 24 (2001) B ( T T 2 )10 3 C ( T T 2 )10 8 where BPE is in C. The seawater specific heat, C p, is given by the following correlation C p (A BT CT 2 DT 3 ) 10 3 (29) The variables A, B, C and D are evaluated as a function of the water salinity as follows: A= S S 2 B= S S 2 C= S S 2 D= S S 2 where C p is in kj/kg C, T in C, and S is the water salinity in gm/kg. The above correlation is valid over salinity and temperature ranges of 20,000 X 160,000 ppm and 20 T 180 C, respectively. The correlation for the saturation pressure of water vapor is given by 8 T ln(p/p c ) c T f i (0.01(T )) (i 1) (30) i 1 where T c = K and P c =22,089 kpa and the values of f i are given below: f 1 f 2 f 3 f f 5 f 6 f 7 f where P and T are in kpa and C, respectively, with the following ranges P and 5 T 200. The percentage errors for the calculated versus the steam table values are less than 0.2%. The saturation temperature correlation is given by T (31) (ln(p/1000) ) where P is in kpa and T is in C. The above correlation is valid for the calculated saturation temperature over a pressure range of kpa. The percentage errors for 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 V c T c T exp (i 1) 6 1 f i (T ) (32) i 1

20 110 A. Al-Ansari et al. / Renewable Energy 24 (2001) where T c = K and V c = m 3 /kg and the values of f i are given below: f 1 f 2 f 3 f 4 f 5 f E E E-12 where V is in m 3 /kg and T is in C. The temperature range for the above correlation is C. The percentage errors for the calculated versus the steam table values are less than 0.025%. The correlation for latent heat of water evaporation is given by l T T (33) 10 5 T 3 In the above equation, T is the saturation temperature in C and l is the latent heat in kj/kg. This correlation is valid over a temperature range of C with a percentage error less than 0.026% against the corresponding values from the steam tables. The correlation for the water vapor enthalpy is given by H T T 2 (34) x10 5 T 3 In the above equation, T is the saturation temperature in C and H is the enthalpy in kj/kg. This correlation is valid over a temperature range of C with percentage errors less than 0.017% against the corresponding values from the steam tables. The correlation for enthalpy of saturated liquid water is given by H T T (35) 10 6 T 3 In the above equation, T is the saturation temperature in C and H is the enthalpy in kj/kg. This correlation is valid over a temperature range of with percentage errors less than 0.04% against the corresponding values from the steam tables. References [1] Zimerman Z. Development of large capacity high efficiency mechanical vapor compression (MVC) units. Desalination 1994;96:51 8. [2] Ettouney HM, El-Dessouky HT, Alatiqi I. Understand thermal desalination. Chem Eng Prog 1999;95: [3] Al-Juwayhel F, El-Dessouky HT, Ettouney HM. Analysis of single-effect evaporator desalination systems driven by vapor compression heat pumps. Desalination 1997;114: [4] El-Dessouky HT, Ettouney HM. Single effect thermal vapor compression desalination process: thermal analysis. Heat Transf Eng 1999;20: [5] Ettouney HM, El-Dessouky HT, Al-Roumi Y. Analysis of mechanical vapor compression desalination process. Int J Energy Res 1999;23:

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