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Research on ratio selection of a mixed liquid desiccant: Mixed LiCl– CaCl2 solution
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Solar Energy 82 (2008) 1161–1171 www.elsevier.com/locate/solener
Research on ratio selection of a mixed liquid desiccant: Mixed LiCl–CaCl2 solution Xiu-Wei Li *, Xiao-Song Zhang, Geng Wang, Rong-Quan Cao School of Energy and Environment, Southeast University, 210096 Nanjing, China Received 1 July 2007; received in revised form 26 May 2008; accepted 27 May 2008 Available online 1 July 2008 Communicated by: Associate Editor P. Gandhidasan
Abstract Liquid desiccant cooling system is a new type of air-conditioning system capable of saving energy. The dehumidification process dominates the performance of this system, while the thermal properties of the liquid desiccant play a key role in improving dehumidification effect. However, there is little work about how to choose a proper liquid desiccant that has a better performance. To settle this problem, a novel method is proposed to search an ideal liquid desiccant by applying the nonrandom two-liquid equation (NRTL equation). This idea is further applied to mixed LiCl and CaCl2 solution to work out the right mixture ratio with a better dehumidification effect under certain working conditions. Moreover, the related experiments were carried out. The results show that: compared to single LiCl solution, the dehumidification effect could be raised by more than 20% with mixed LiCl and CaCl2 solution. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Liquid-dehumidification; Mixed liquid desiccant; Activity coefficient; Dehumidification effect
1. Introduction Seeking a comfortable living condition in life is a popular trend today, which leads to the wide use of air-conditioner. However, that situation has its side effect, which upsets people by calling for a large amount of electric power to drive these ‘‘cooling machines”. Many new types of air-conditioner have been developed to shoulder off the heavy dependence on electric power while still guarantee a good comfort. Among these new faces, liquid desiccant cooling system, which mainly consists of a liquid-dehumidification unit and an evaporation-cooling unit, has attracted ever increasing attention from both researchers and consumers. The reason for this is mostly owing to the fact that this system could be driven by heat sources with relatively low temperature of around 70 °C. That *
Corresponding author. Tel.: +86 025 84442945; fax: +86 025 83792722. E-mail address: [email protected] (Xiu-Wei L.). 0038-092X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2008.05.015
means the work could be done by many renewable energies, such as solar power, geothermal power and waste heat (Zhang et al., 2003). The cycle of this system is shown in Fig. 1 (Khalid Ahmed et al., 1997). The cycle consists of a liquid desiccant system using liquid desiccant for both absorption and dehumidification processes and water as the refrigerant. The system operates on an open-cycle in which the weak absorbent solution is regenerated by losing the refrigerant to the Earth’s atmosphere. Cooling takes place by evaporating water from an external source in the evaporator. The weak absorbent solution (state 1) from the absorber is pumped (state 2) to the solar regenerator, which is partly open to the atmosphere, through the regenerative heat exchanger HE1. It is then heated and subsequently concentrated in the solar regenerator from state 3 to state 4. The strong solution passes through the regenerative heat exchanger HE1 on its way (state 5 and state 6) to the absorber. In the absorber, the strong desiccant absorbs water vapour as soon as the incoming refrigerant evaporates in
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Nomenclature aw A/ COP fw h Ix K Mw m P Q R r rd t T X x Z
activity of water (no units) Debye-Hu¨ckel constant for the osmotic coefficient (no units) coefficient of performance (no units) activity coefficient of water (no units) enthalpy (kJ/kg) ionic strength in mole fraction scale (no units) solubility product (no units) water molecular weight (kg/kmol) flow rate (kg/s) vapour pressure (Pa) energy (kJ) gas constant (no units) refrigerant moisture (kg/s) dehumidified moisture (kg/s) total moisture (kg/s) temperature (K) mass concentration (no units) mole fraction (no units) absolute value of ionic charge (no units)
s h q
NRTL binary interaction energy parameter (no units) reference temperature 298.15 K the closest approach parameter of the Pitzer– Debye-Hu¨ckel equation (no units)
Superscripts PDH long-range contribution, represented by the Pitzer– Debye-Hu¨ckel equation lc short-range contribution, represented by the local composition model Subscripts 0 00 a,a ,a anion 0 00 cation c,c ,c ca salt ca i,j,k any species 0 solvent s,s w water 1,2,3. . . related to the state number of Fig. 1 ± mean value
Greek symbols a NRTL nonrandomness factor (no units)
the evaporator (state 11) by absorbing the heat from the cold space, maintaining the reduced pressure required by the evaporator. The heat of absorption for the refrigerant-absorbent solution is removed by the cooling water loop. In the evaporator, water from an external source (state 10) is evaporated. The resultant weak desiccant is then pumped from the absorber back to atmospheric pressure through the regenerative heat exchanger and to the solar regenerator, completing the absorption-machine cycle. Part of the strong desiccant (state 5) from the solar regenerator is passed through the regenerative heat exchanger HE2 (state 7) to the dehumidifier, where the air to be conditioned is dehumidified in the counter-current direction. The actual dehumidification takes place due to the vapour pressure difference between the vapour in the air and the liquid desiccant. As the regenerated liquid desiccant is cooled and concentrated (state 8), its vapour pressure is less than the vapour pressure of the air, therefore the vapour present in the air tends to escape into the liquid desiccant, thereby diluting the liquid desiccant. The weak desiccant (state 9) from the dehumidifier is then pumped back for regeneration, along with the weak desiccant from the absorber (state 1). After regeneration the strong solution is supplied to the absorber and dehumidifier in the required proportions, as shown by states 6 and 7. The absorbent used in the cycle for absorption in the absorption-machine, as well as the desiccant in the dehumidifier is the same. The cooling water (states 12, 13 and 14) is cir-
culated to the dehumidifier and completes the cooling tower cycle. Fig. 2 shows the psychrometric chart for the process of dehumidification and sensible cooling. The mixture of return air from the room (state ‘e’) and fresh air from outdoors (state ‘a’) enters the dehumidifier (state ‘b’). The dry air at state ‘c’ is passed over the cooling coil where it is sensible cooled and enters the room at state ‘d’. The conditioned air picks up the load in the room and leaves at state ‘e’. Referring to Fig. 1 (the subscripts attached stand for the state number in Fig. 1), a total mass balance on the regenerator gives: (these symbols are listed in the nomenclature) m3 ¼ mt þ m4 ;
ð1Þ
where mt is the total moisture (refrigerant moisture mr and dehumidified moisture mrd ) and is given by: mt ¼ mr þ mrd ;
ð2Þ
where the liquid desiccant mass balance yields: (X 3 and X 4 stand for the concentration of liquid desiccant at states 3 and 4 in Fig. 1, respectively) m3 X 3 ¼ m4 X 4 :
ð3Þ
Solving Eqs. (1) and (3), we get, m4 X3 ¼ mt ðX 4 X 3 Þ
ð4Þ
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Fig. 1. Hybrid liquid desiccant based air-conditioning cycle (liquid desiccant cooling system).
This gives the ratio of total absorbent to total refrigerant flow rate. It is assumed that mst is the total mass of the solution reaching the solar regenerator and is given by mst ¼ ms þ m9 ;
ð5Þ
where ms is the flow rate of absorbent leaving the absorber and is given by the expression: ms mab ¼ þ 1; ð6Þ mr mr mab represents the flow rate of absorbent reaching the absorber. The heat balance for the heat exchangers HE1 and HE2 gives: m2 h2 þ m4 h4 ¼ m3 h3 þ m5 h5 ;
ð7Þ
and m7 h7 þ m13 h13 ¼ m8 h8 þ m14 h14 :
ð8Þ
Therefore, the evaporator capacity Qev is given by: Qev ¼ m11 ðh11 h10 Þ ¼ mr ðh11 h10 Þ:
ð9Þ
The mass balance in the dehumidifier results is: mrd þ m8 ¼ m9 : Fig. 2. Process on the psychrometric chart.
ð10Þ
The amount of solar energy collected for the regeneration of the weak desiccant is given by:
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Qgen ¼ mt ht þ m4 h4 mst h3 :
ð11Þ
The absorber load is given by: Qab ¼ m11 h11 þ m6 h6 m1 h1 :
ð12Þ
The dehumidifier load is given by: (here, the subscript ‘‘i” and ‘‘o” indicate the inlet parameter and the outlet parameter, respectively) Qrd ¼ mrd;i hrd;i þ m8 h8 m9 h9 mrd;o hrd;o :
ð13Þ
Therefore, integrating (1), (2), (4) and (5) together, the coefficient of performance for this system could be described as: COP ¼
Qev m11 ðh11 h10 Þ ¼ Qgen mt ht þ m4 h4 mst h3
¼
mr ðh11 h10 Þ ; mt ðht h3 Þ þ m4 ðh4 h3 Þ
ð14Þ
and COP ¼
Qev mr ðh11 h10 Þ ¼ 3 Qgen ðmr þ mrd Þ½ðht h3 Þ þ ðX XX ðh4 h3 Þ 4 3Þ ð15Þ
Exposed from (15) and provided the enthalpy related to every state in Fig. 1 stays unchanged, the cooling capacity will increase if the amount of absorption (or dehumidification) increases; while the COP decreases if the cooling capacity increases. However, it always fails to reach the right set states (like states ‘c’ and ‘d’ in Fig. 2) because its dehumidification ability is poor, which leads to the insufficient cooling and dehumidification capacity. Therefore, the properties of the liquid desiccant should be concerned in order to maximize the mass transfer in both the absorber and the dehumidifier so that this system could obtain ample cooling and dehumidification capacity. Solar energy is particularly suitable for this system. For one thing, solar energy is universal and could be easily gained in almost every corner of the Earth. For another thing, air-conditioner is needed badly at daytime in summer; when it always accompanies with the best sunshine of a day. That means plenty of solar energy could be gained at the right time to drive this system and obtain a good cooling effect. Beyond that, this system is fit to the solar energy storage, in that surplus liquid desiccant could be concentrated when solar energy is rich at daytime, and then be used for cooling at night when no solar energy is available. The conventional closed-cycle absorption chillers require heat source temperatures that are significantly higher than the temperatures of corresponding heat sinks. Thus, they have to be operated with high-grade heat extracted from natural gas, steam, concentrating solar collectors and the like. Nevertheless, the liquid desiccant cooling system could operate with a heat source of relatively lower temperature, which could in turn improves the effi-
ciency of utilizing solar energy to generate cooling effect (Zhang et al., 2003). Liquid-dehumidification process plays a key role in the performance of such a system. The thermal properties of liquid desiccants, especially their surface water vapour pressure, greatly influence the dehumidification effect. It is found that the lower the vapour pressure of the desiccant is, the better the dehumidification effect could be obtained. The reason for that is because the enlargement of the vapour pressure difference could promote the mass transfer in dehumidification (Gommed and Grossman, 2004). Generally, the liquid desiccants adopted in this system are always the electrolyte solutions including LiCl solution, CaCl2 solution, LiBr solution and mixed LiCl–CaCl2 solution (Grossman, 2002; Nelson and Goswami, 2002). Most researches about the thermal properties of liquid desiccants only take care of the single electrolyte solutions like LiCl solution or CaCl2 solution (Manuel, 2004). There is few works caring about the thermal properties of mixed liquid desiccants. Ertas et al. (1992) have carried out experimental works on the thermal properties of mixed LiCl–CaCl2 solution. The results revealed in their article have been later referred in many papers related to the topic of liquiddehumidification. In their work, they measured the vapour pressure of the mixed LiCl–CaCl2 solution with five different ratios. The total electrolyte mass concentration of the solution was maintained as 20%. There were five solution groups according to the changed LiCl/CaCl2 ratio: 100% LiCl, 70% LiCl and 30% CaCl2, 50% LiCl and 50% CaCl2, 30% LiCl and 70% CaCl2 and 100% CaCl2. Through experiments, they concluded that the 100% LiCl group got the lowest vapour pressure under different temperatures. However, considering the costeffectiveness, they suggested that the 50% LiCl and 50% CaCl2 group is a better choice. Nevertheless, their work was limited within a narrow scope of research on the thermal properties of mixed desiccant. They didn’t provide further solutions for acquiring the vapour pressure of the mixed LiCl–CaCl2 solutions with different concentrations and ratios beyond the scope provided in their paper. And it doesn’t seem to be feasible to get all the results just by numerous experiments. Ahmed and Gandhidasan (1998) attempted to engage a classical thermodynamics approach to predict the vapour pressure of the liquid desiccant including LiCl, CaCl2 and the mixture of these two electrolytes. However, as they described in their paper, the results obtained are not satisfied because those results did not agree well with the experimental results they referred. Those works mentioned above concentrated on selected liquid desiccants rather than proposed a method to determine which liquid desiccant will be an ideal one before using it. Putting aside the works on the thermal properties, there are no reports about dehumidification experiments of mixed LiCl–CaCl2 solutions with different concentrations and ratios.
Xiu-Wei L. et al. / Solar Energy 82 (2008) 1161–1171
In the sense of chemical field, there are many independent theories for research on electrolyte solutions (Pitzer, 1991; Chen et al., 1982; Chen and Evans, 1986). According to the Rault rule, the water vapour pressure of the solution can be obtained by calculating the activity of the water. Activity is always corresponding to the activity coefficient and the concentration (including mole fraction and mass fraction). A lot of theories have been developed to calculate the activity coefficient of the electrolyte solutions, single or mixed. The Debye-Hu¨ckel theory, the Pitzer theory, the Local Composition Model and the Perturbation theories are among these theories. Most of them are based on the statistical thermodynamics principles. Their calculation results proved agreeing well with the experimental results and have a very high precision. Since the NRTL equation of Local Composition Model has a good precision and its parameters are easy to obtain, it has been applied to calculate the activity coefficient of the mixed LiCl–CaCl2 solution in our paper (Chen and Evans, 1986). The related activity, which reflects the water vapour pressure of the solution has been further deduced. Beyond that, the dehumidification experiments were conducted with five mixed LiCl–CaCl2 solution groups of different concentration ratios. The results show that the group of lower activity has a better dehumidification effect as predicted. Those efforts provide us with a new idea of prejudging liquid desiccants by comparing their activity.
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tion, and so does the activity coefficient. Assuming the temperature is constant, the long-range interaction can be described as: ln fwPDH ¼
1 1000 2 2A/ I 3=2 x ; Mw I þ qI 1=2 x
ð18Þ
P 2 xi zi for short-range interaction, the equawhere I x ¼ 12 tion of activity coefficient calculation for water (one of the solvent) in a multi-component electrolyte could be expressed as: P P X j Gjw sjw P X s0 Gws0 X G 0s 0 j lc k k ks ks P P P þ s0 sws0 lnfw ¼ X G X G X G k
k
þ þ
kw
PP c
a0
PP a
c0
k
PX a0
X 00 a00 a
PX c0 c00
X c00
k
ks0
PX c Gwc;a0 c k
X k Gkc;a0 c
PX a Gwa;c0 a k
X k Gka;c0 a
k
k
ks0
P X G 0 s 0 k k kc;a c kc;a c swc;a0 c P ; k
X k Gkc;a0 c
P X G 0 s 0 k k ka;c a ka;c a swa;c0 a P X G k
k
ka;c0 a
ð19Þ in the form above: X j ¼ C j xj ; C j ¼ jzj j in the ion case and C j ¼ 1 in the molecule case. The relationship between those parameters could be defined as: Gji ¼ expðaji sji Þ; sji ¼ ðgji gii Þ=RT Gji;ki ¼ expðaji;ki sji;ki Þ; sji;ki ¼ ðgji gki Þ=RT Gas ¼ Gcs aas ¼ acs ¼ aca;s ; asc;ac ¼ asa;ca ¼ as;ca ; aca;s ¼ as;ca ;
2. Methods and experiments 2.1. The vapour pressure calculation The vapour–liquid equilibrium relation for water in an electrolyte solution can be simplified as (Hsiu-ling et al., 2003): Pw aw ¼ 0 ; Pw
ð16Þ
aw ¼ x w f w ;
ð17Þ
where P w and P 0w are the vapour pressure of solution and pure water, respectively. The vapour pressure of a solution can be calculated, if the activity aw of water has been determined in advance. At the same time, aw is the product of mole concentration and activity coefficient fw (this activity coefficient is corresponding to the mole fraction, and it will be different in the situation of using the mass concentration). NRTL equation, based on the Local Composition Model is adopted for the calculation of fw in this paper. The expression of NRTL for calculating the activity coefficient of the solvent could be divided into two parts, one part is known as the long-range interaction contribution and the other part is called the short-range interaction contribution (Manuel, 2004). The vapour pressure is affected mostly by two factors, the temperature and the concentra-
sas ¼ scs ¼ sca;s ; ssc;ac ¼ ssa;ca ¼ ss;ca ; P P a X a Gca;w c X c Gca;w ; Gaw ¼ P Gcw ¼ P 0 X a0 a c0 X c0 sca;c0 ¼ sc0;ca ; sca;ca0 ¼ sc0;ca : All the parameters have been listed in the nomenclature, and the meaning of them could be found from the reference (Chen and Evans, 1986). The whole interaction expression is: ln fw ¼ ln fwPDH þ ln fwlc :
ð20Þ
The activity coefficient could be obtained with (20) and later used to deduce the activity and the vapour pressure at a certain temperature with Eqs. (16) and (17). The effect of temperature will be reflected in the value of s, which stands for the energy parameter in the NRTL equation. Its varying with the temperature follows the form below (Chen and Evans, 1986): 1 1 hT T þc þ ln ; ð21Þ s¼aþb T h T h where the experienced parameters a, b and c could be checked from the references or obtained through regression of the experimental data.
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2.2. Activity coefficient calculation for mixed LiCl–CaCl2 solution In the case of mixed LiCl–CaCl2 solution, the form of long-range interaction is: ln fwPDH ¼ 5:829
2.3. Solubility of mixed liquid desiccant
ðxLiCl þ 3xCaCl2 Þ 1
ð22Þ
;
½1 þ 14:9ðxLiCl þ 3xCaCl2 Þ2
For a mixed liquid desiccant, the solubility should be concerned beyond the activity coefficient, as there is a boundary amount for an electrolyte solution to accept the electrolytes of other kinds. The solubility could be acquired by experiments and by calculating the solubility product (Pitzer, 1991). NRTL equation also provides the method to calculate the solubility product. The solubility product has the expression for a single solution with the form of CA:
assume that: expð0:2sLiCl;w Þ ¼ A; ¼ B;
expð0:2sCaCl2 ;w Þ expð0:2sLiCl;CaCl2 Þ
¼ C; expð0:2sw;LiCl Þ ¼ A0 ; 0
¼B;
expð0:2sw;CaCl2 Þ expð0:2sCaCl2 ;LiCl Þ ¼ C 0 ;
K CA ¼ aC aA ¼ x2CA f2 ¼ x2CA fC fA :
There exists the relationship: xLiCl þ xCaCl2 þ xw ¼ 1;
ð23Þ
2AsLiCl;w xLiCl þ4BsCaCl2 ;w xCaCl2 þðxLiCl A0 Þ ½1þð2A2ÞxLiCl þð4B3ÞxCaCl2
sw;LiCl xLiCl þ2½C 0 ðsw;LiCl sCaCl2 ;LiCl Þþ2sw;LiCl xCaCl2 ½ð12A0 ÞxLiCl þð2C 0 þ23A0 ÞxCaCl2 þA0
2
þð2B0 xCaCl2 Þ
½ðC þ12B0 ÞxLiCl þð23B0 ÞxCaCl2 þB0 2 sw;LiCl xLiCl þ2C 0 ðsw;LiCl sCaCl2 ;LiCl ÞxCaCl2 0
0
ðxLiCl þ2C xCaCl2 þA xw Þ
Cðsw;CaCl2 sLiCl;CaCl2 ÞxLiCl þ2sw;CaCl2 xCaCl2
þðxw Þ
2
ð2AxLiCl þ4BxCaCl2 þxw Þ2
P
PX a0 a0
c00
ka;c0 a
k
k
k
k
ka;c0 a
ð27Þ P P P P X s Gas X G 0 s 0 X G s X c0 1 lc k k ka;c a ac;c a k k ks ks P P P P lnf ¼ þ s as c0 s a Za X 00 X G 0 X G X G a00 c k k kc;a k k ks k k ks P PP X G 0s 0 X cG 0 X k k kc;a kc;a þ c a0 P a0X P X ac;a sac;a0 P G X G
þð2B xCaCl2 Þ ðCxLiCl þ2xCaCl2 þB0 xw Þ 2AsLiCl;w xLiCl þ4BsCaCl2 ;w xCaCl2
P P P X s Gcs X G 0 s 0 X G s k k kc;a c kc;a c k k ks ks P P P þ s cs s X 00 X G 0 X G X G a00 a k k kc;a c k k ks k k ks P PP X G 0 s 0 X aG 0a X k k ka;c a ka;c a þ a c0 P c0X P X ca;c sca;c0 a P G X G
ln fclc ¼
c00
2
ð26Þ
f represents the mean activity coefficient, while fC and fC0 represents the activity coefficient of cation, fA stands for the activity coefficient of anion. The calculation forms for fC , fC0 and fA share the same long-range interaction item as presented in Eq. (18). The forms of short-range interaction are as follows: 1 Zc
0
In the situation of a mixed one with the form as C 2 A C 0 A nH2 O, it could be written as:
½Cðsw;CaCl2 sLiCl;CaCl2 Þþsw;CaCl2 xLiCl þ2sw;CaCl2 xCaCl2
þðxLiCl A0 Þ
ð25Þ
K C2 AC0 AH2 O ¼ x2C xC0 x2A fC2 fC0 fA2 anw ;
so the short-range interaction can be described as: lnfwlc ¼
the subscript w represents water, and the whole interaction expression is just the same as Eq. (20). All the values of the parameters are presented in Table 1 (Chen and Evans, 1986).
a00
a00
k
k
kc;a0
k
k
kc;a0
ð28Þ
; ð24Þ
Table 1 Parameters for activity coefficient calculation (25 °C)
The solubility expression of single or mixed electrolyte with other forms could be found from the references (Pitzer, 1991). 2.4. The experimental system
Parameter
Value
A/ q Mw sLiCl,w sw,LiCl sCaCl2 ;w sw;CaCl2 sLiCl;CaCl2 sCaCl2 ;LiCl a
0.3910 14.9 18 –5.1737 10.1242 –5.2549 10.5126 0 0 0.2
To examine the dehumidification effects of different mixed LiCl–CaCl2 solution groups, a structured corrugated packing of inorganic material (Munters Celdek) was used as the dehumidifier and its appearance is shown in Fig. 3. The specific area of this packing is 396 (m2/m3). Fig. 3a and b display the shapes viewed from the upside and the sidepiece of the packing, respectively. The definition of the packing dimensions is shown in Fig. 3c. The desiccant solution dehumidifier is of the dimensions with height
Xiu-Wei L. et al. / Solar Energy 82 (2008) 1161–1171
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Air H
L W
(a) From the upside
(b) From the sidepiece
(c) Definition of the packing dimensions
Fig. 3. The shape and structure of the packing in the dehumidifier.
H = 0.5 m, width W = 0.2 m and length L = 0.5 m. During the experiments, the packing was well wetted. The schematic diagram of the liquid desiccant dehumidification is shown in Fig. 4. It is made up of a dehumidifier, a pump, a concentrated solution tank, a diluted solution tank, a rotameter and etc. An environmental chamber for providing the air with different temperatures and humidity ratios is shown in Fig. 5. The objective of the experimental apparatus is to obtain the inlet and outlet parameters of the air and the liquid desiccant. Those parameters include the drybulb temperature, the wet-bulb temperature and the flow rate of the inlet and outlet air; the temperature, the mass concentration and the flow rate of the liquid desiccant. All the experiments were carried out under steady state of the air and liquid desiccant. The temperatures were measured by some Pt100 RTDs (Resistance Temperature Detectors) with the accuracy of 0.01 °C and recorded by a data acquisition switch unit with the type of Agilent 34970A. The flow rate of the liquid desiccant was measured by an anticorrosive rotameter ranging from 40 l/h to 400 l/
h with the accuracy of 10 l/h. The air flow rate was measured by three standard nozzles with the accuracy of 1%. Their diameters were 70 mm, 80 mm and 110 mm, which are corresponding to the measure range of 208–485 m3/h, 424–990 m3/h and 513–1197 m3/h, respectively. The liquid desiccant used in our experiment was divided into five groups. Group1 is the pure LiCl solution whose mass fraction (the mass fraction of LiCl) is 39%; Group2 is the mixed LiCl–CaCl2 solution made by just adding pure solid CaCl2 into the LiCl solution being of the same mass concentration as Group1. The mass fraction of CaCl2 is set to be 5% in the new mixed solution, which leads to the mass fraction of LiCl falling to 37% in the new solution. In the same way, we obtained Group3 (35% LiCl and 10% CaCl2), Group4 (33% LiCl and 15% CaCl2) and Group5 (31.2% LiCl and 20% CaCl2). The mass of water and LiCl stays unchanged in these five groups though their mass concentrations vary. According to the results from solubility experiments, Group 5 has touched the edge of the maximum CaCl2 amount that could be accepted in the origin pure LiCl solution (Group 1).
Fan Humidifier Air
Air Evaporator
Dehumidifier
Compressor
Heater
Nozzle
Air Sampler
Environmental Chamber 1. Dehumidifier, 2. Rotameter, 3. Pump, 4. Concentrated solution tank, 5. Diluted solution tank
Fig. 4. Schematic diagram of desiccant dehumidification.
To condenser
From throttle
Fig. 5. Environmental chamber for the air.
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The temperature of the working liquid desiccant was regulated as 25 ± 0.5 °C, so the activity coefficient calculation could ignore the temperature influence on the value of the energy parameters. 3. Results and discussion 3.1. Results comparison Fig. 6 shows the different results about the water vapour pressure of single LiCl solution varying with the temperature, and they are compared with the vapour pressure of pure water at the same temperatures. The mass fraction of LiCl is fixed as 20%. Eqs. (22), (24), (25), (16), and (17) are applied to calculate the vapour pressure because the single electrolyte solution calculation could be considered as a special case of the mixed solution calculation. The energy parameters, which will be changed with the temperature is obtained by regressing the experimental data under different temperatures (Manuel, 2004). It could be found that the results obtained by using NRTL equation agree very well with the results revealed by Manuel (2004), whose work has been proved to have a good precision by comparing it with lots of experimental data he referred. The experimental results from A. Ertas seem to have a gap of around 700 Pa with the other two results. Fig. 7 shows the different results about the water vapour pressure of CaCl2 solution varying with the temperature. The mass fraction of CaCl2 is also fixed as 20%. It could be found that the results obtained by using NRTL equation also agree very well with the results revealed by Manuel, 2004, while the experimental results from Ertas et al. (1992) have a fairly large gap with the other two results. However, the results from Ertas et al. (1992) are not correct this time. Because in their results, the saturation vapour pressure of CaCl2 solution is even bigger than that of pure water at the same temperature, and that is impossible. Therefore, the results of mixed LiCl–CaCl2 solution from Ertas et al. (1992) seem not to be a reliable source
Fig. 6. Results comparison of the vapour pressure of LiCl solution.
Fig. 7. Results comparison of the vapour pressure of CaCl2 solution.
of experimental data to test the results of vapour pressure calculated by NRTL equation. So it may lack of direct experimental data about the vapour pressure of the mixed electrolyte solution. Nevertheless, the results of activity coefficient and activity calculated by NRTL equation could be trusted as the method is proved to be reliable and have a good accuracy through experiments (Chen and Evans, 1986). Based on that, the vapour pressure deduced by calculating the activity could also be reliable results. 3.2. Select an ideal liquid desiccant by activity map For a mixed solution whose components are already known, the best ratio could be acquired by pursuing the minimum of activity. Since the temperature of the liquid desiccant is always maintained in the dehumidification process, the minimum value of the activity can be obtained by solving the differential equations as follows: @ðfw xw Þ @ðfw xw Þ ¼ 0; ¼0 @xLiCl @xCaCl2
ð29Þ
Actually, it will be too difficult to work out xLiCl and xCaCl2 to get the minimum value because the expression of the derivation is too complex to analyse. Instead, considering the ratio of the components are limited in practical process, a certain range of xLiCl and xCaCl2 are selected to build a map at a constant temperature for analysing the activity of mixed liquid desiccant. The results for mixed LiCl– CaCl2 solution are shown in Fig. 8 (the temperature is 25 °C). X-axis represents the mass fraction of CaCl2 with the range of 0–20% and the Y-axis represents the mass fraction of LiCl with the range of 29–40%. The activity decreases with the increase of the concentration of both LiCl and CaCl2, and the mass fraction change of LiCl has a slightly greater influence on the activity than that of CaCl2. The minimum activity is obviously positioned at the foot of this map without considering the solubility.
Xiu-Wei L. et al. / Solar Energy 82 (2008) 1161–1171
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sLiCl;CaCl2 ¼ sCaCl2 ;LiCl ¼ 2 The results calculated with these three different groups of energy parameters are presented together in Fig. 9, where the X-axis and the Y-axis represent the same parameters as (Fig. 8). Seen from the side face of the figure, these three maps overlap each other and could not be separated apart. That indicates the values of the salt–salt energy parameters have few impacts on the activity calculation and their results within the selected ratio range is almost the same. 3.3. Field activity curve of the experiment
Fig. 8. Activity map of mixed LiCl–CaCl2 solution (25 °C).
According to the reference (Chen and Evans, 1986), the value of salt–salt energy parameters is set to be zero in an ideal situation, which means: sLiCl;CaCl2 ¼ sCaCl2 ;LiCl ¼ 0 That reflects the mixing rule of the model performing much like the Guggenheim equation for predicting osmotic coefficient and Harned’s rule for predicting mean ionic activity coefficients for aqueous multi-component electrolyte system. We could also calculate the activity map using different binary parameters as the reference (Chen and Evans, 1986) suggested: sLiCl;CaCl2 ¼ sCaCl2 ;LiCl ¼ 1
Fig. 9. Activity map of mixed LiCl–CaCl2 solution with different salt–salt energy parameters (25 °C).
Considering the solubility in our experiment, it is not convenient for us to describe the solubility in the activity map like (Fig. 8) as the mass fraction of LiCl varies with the mass fraction of CaCl2. To solve that problem, another activity map, which changed from Fig. 8, is introduced. The salt–salt energy parameters are set as 0. The drawing of this new activity map is shown in Fig. 10, where the X-axis represents the mass ratio of CaCl2/H2O (0–50%). H2O stands for the water mass of the original LiCl solution (39%) in the experiment. In the same way, the Y-axis represents the mass ratio of LiCl/H2O (40–68%). Since the mass of water has not been changed in the five groups, the mass ratio of CaCl2/H2O is changed from 0% to 41% within the range bordered by the solubility and the mass ratio of LiCl/H2O remains 64% (the mass of LiCl has not been changed in the five groups, either). Therefore, the activity curve at this solubility could be made in the activity map, which is exhibited in Fig. 11, where the X-axis and the Y -axis represent the same parameters as (Fig. 10). The curve AB expresses the activity variation while the mass ratio of LiCl/H2O is 64% and the mass ratio of CaCl2/ H2O varies from 0% (Group 1) to 41% (Group 5). Clearly,
Fig. 10. Activity map of mixed LiCl–CaCl2 solution with different X-axis and Y-axis (25 °C).
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Fig. 13. Dehumidification effect of mixed LiCl and CaCl2 solution with the original humidity of 11 g/(kg air).
Fig. 11. Activity curve of mixed LiCl–CaCl2 solution in experiment (25 °C).
it is very easy to find out that the activity of these five groups arranged from large to small is Group 1, Group 2, Group 3, Group 4 and Group 5. Group 5 is expected to have the best dehumidification performance in the experiments. 3.4. Experimental results Group1 to Group5 are adopted in the experiments, and the results are exhibited from Fig. 12 to Fig. 14, where Dd stands for the humidity reduction. The inlet air for dehumidification was controlled to maintain the dry-bulb temperature as 30 0:5 C, and the humidity was regulated as 10 g/(kg air), 11 g/(kg air) and 12 g/(kg air) in Fig. 12, Fig. 13 and Fig. 14, respectively. From the results, it could be seen that the arrangement of dehumidification effect from high to low exactly reflects the arrangement of activity from small to large. In other
Fig. 12. Dehumidification effect of mixed LiCl and CaCl2 solution with the original humidity of 10 g/(kg air).
words, the lower the activity is, the better dehumidification effect can be obtained, which is in accordance with the prediction. And the fifth group of the mixed solution has the best dehumidification effect. Compared to Group1, Group 5 has improved the average dehumidification amount by 26%, 25.3% and 24.3% under three conditions, respectively. On the other hand, it should be noticed that the dehumidification amount of Group 1 in Fig. 13 is near that of Group 5 in Fig. 12, which indicates that the original humidity variation of the inlet air may have a more powerful influence on the dehumidification effect than the vapour pressure variation of the liquid desiccant. The increase of original humidity from Fig. 12 to Fig. 13 is 1 g/(kg air), which embodies the vapour pressure variation of the inlet air as 120 Pa. However, the decrease of vapour pressure of the liquid desiccant is about 267 Pa from Group 1 to Group 5. According to the present mass transfer equation (Hsiu-ling et al., 2003): m ¼ bADP Dt;
ð30Þ
where m stands for the dehumidification amount, b is the mass transfer coefficient, A is the dehumidification area
Fig. 14. Dehumidification effect of mixed LiCl and CaCl2 solution with the original humidity of 12 g/(kg air).
Xiu-Wei L. et al. / Solar Energy 82 (2008) 1161–1171
and Dt stands for the dehumidification time. We have the differential equation as: dm ¼ bADP : dt
ð31Þ
It could be predicted from (31) that Group 5 in Fig. 12 may have a larger dehumidification amount than Group 1 in Fig. 13 as the former one has a larger vapour pressure difference and the other parameters are provided unchanged. However, that prediction does not conform to the experimental results. Nevertheless, in the situation of the comparison of Group 1 in Fig. 14 and Group 5 in Fig. 13, this phenomenon is not obvious. Completely addressing this issue calls for more work on the dehumidification process under different conditions. All in all, the variation of the original humidity of the inlet air may play a more active role in the dehumidification process. That may help further improve the present mass transfer equation that only counts on the difference of vapour pressure. A possible amendment may be needed for the mass transfer coefficient by taking the effect of the original humidity in concern. 4. Conclusions The NRTL equation is a reliable method for us to indirectly obtain the vapour pressure of the liquid desiccant by calculating the activity. This calculation method is not only fit the situation of a single solution but also fit the situation of mixed solution of different kinds. Furthermore, the equation could also be applied in the situation of mixed solvent. Based on the activity calculation, the activity maps of different liquid desiccants could be built up. Therefore an ideal one could be selected by judging its activity in the map before employing it in the dehumidification process. The mixed LiCl and CaCl2 solution could improve the dehumidification effect by more than 20% compared to the pure LiCl solution. Nevertheless, considering the cost of LiCl is more expensive than CaCl2, a proper group can be found to be more cost-effective. Actually, in the present Chinese market, LiCl is above 28.75 dollars/kg while CaCl2 is only around 2 dollars/kg. First, let is focus on the activity map shown in Fig. 10. The activity located in the region of the same colour indicates that there is no big difference between those activity values. Therefore, if we reduce the mass of LiCl in the solution and increase CaCl2 with the same mass (like group (LiCl/H2O = 0.68, CaCl2/H2O = 0) and the group (LiCl/H2O = 0.48, CaCl2/ H2O = 0.2), the total mass of the solution remains unchanged because of the mass of water staying unchanged), almost the same activity effect (as shown in the activity map) could be obtained while the initial cost could be greatly reduced. Secondly, we will consider the
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relation between the cost and the dehumidification effect from Fig. 12 to Fig. 14. Take the situation of Group 5 (31.2% LiCl and 20% CaCl2) for example, the dehumidification effect has been improved by more than 20% than Group 1 (pure LiCl solution), while the cost added (the CaCl2 cost) only takes up 4.5% of the original LiCl cost in Group 1. The original humidity of the air has a more active influence on the dehumidification process than the vapour pressure of the liquid desiccant, and that should be embodied in the mass transfer equation. So that will be meaningful to amend the present mass transfer equation. Acknowledgements This research was supported by the grants from the fund of National Natural Science Foundation of China under the Contract No. 50676018 and the fund of State Education Department for key projects of science and technology research under the Contract No. 307013. These supports are gratefully acknowledged. References Ahmed, S.Y., Gandhidasan, P., 1998. Thermodynamic analysis of liquid desiccant. Solar Energy 62 (1), 11–18. Chen, C.C., Evans, L.B., 1986. A local composition model for the excess Gibbs energy of aqueous electrolyte systems. AIChE Journal 32 (3), 444–454. Chen, C.C., Britt, H.I., Boston, J.F., Evans, L.B., 1982. Local composition model for excess Gibbs energy of electrolyte systems. Part 1: single solvent, single completely dissociated electrolyte systems. AIChE Journal 28 (4), 588–596. Ertas, A., Anderson, E.E., Kiris, I., 1992. Properties of a new liquid desiccant solution – lithium chloride and calcium chloride mixture. Solar Energy 49 (3), 205–212. Gommed, K., Grossman, G., 2004. A liquid desiccant system for solar cooling and dehumidification. Journal of Solar Energy Engineering 126, 879–885. Grossman, G., 2002. Solar-powered systems for cooling, dehumidification and air-conditioning. Solar Energy 49 (3), 205–212. Hsiu-ling, Hsu.Hsu, Yi-chou, Wu.Wu, Liang-sun, Lee, 2003. Vapor pressure of aqueous solution with mixed salts of NaCl + KBr and NaBr + KCl. Journal of Chemical and Engineering Data 48, 514–518. Khalid Ahmed, C.S., Gandhidasan, P., Al-Farayedhi, A.A., 1997. Simulation of a hybrid liquid desiccant based air-conditioning system. Applied Thermal Engineering 17 (2), 125–134. Manuel, R.C., 2004. Properties of aqueous solutions of lithium and calcium chlorides: formulations for use in air conditioning equipment design. International Journal of Thermal Science 43, 367–382. Nelson, F., Goswami, D.Y., 2002. Study of an aqueous lithium chloride desiccant system air dehumidification and desiccant regeneration. Solar Energy 72 (4), 351–361. Pitzer, K.S., 1991. Activity Coefficient in Electrolyte Solution, second ed. CRC Press, Boca Raton. Zhang, X.S., Fei, X.F., Shi, M.H., Cao, Y.R., 2003. Study on the dehumidifier of the energy storage liquid desiccant cooling systems. Journal of Southeast University 33 (1), 1–4.
Solar Energy 82 (2008) 1161–1171 www.elsevier.com/locate/solener
Research on ratio selection of a mixed liquid desiccant: Mixed LiCl–CaCl2 solution Xiu-Wei Li *, Xiao-Song Zhang, Geng Wang, Rong-Quan Cao School of Energy and Environment, Southeast University, 210096 Nanjing, China Received 1 July 2007; received in revised form 26 May 2008; accepted 27 May 2008 Available online 1 July 2008 Communicated by: Associate Editor P. Gandhidasan
Abstract Liquid desiccant cooling system is a new type of air-conditioning system capable of saving energy. The dehumidification process dominates the performance of this system, while the thermal properties of the liquid desiccant play a key role in improving dehumidification effect. However, there is little work about how to choose a proper liquid desiccant that has a better performance. To settle this problem, a novel method is proposed to search an ideal liquid desiccant by applying the nonrandom two-liquid equation (NRTL equation). This idea is further applied to mixed LiCl and CaCl2 solution to work out the right mixture ratio with a better dehumidification effect under certain working conditions. Moreover, the related experiments were carried out. The results show that: compared to single LiCl solution, the dehumidification effect could be raised by more than 20% with mixed LiCl and CaCl2 solution. Ó 2008 Elsevier Ltd. All rights reserved. Keywords: Liquid-dehumidification; Mixed liquid desiccant; Activity coefficient; Dehumidification effect
1. Introduction Seeking a comfortable living condition in life is a popular trend today, which leads to the wide use of air-conditioner. However, that situation has its side effect, which upsets people by calling for a large amount of electric power to drive these ‘‘cooling machines”. Many new types of air-conditioner have been developed to shoulder off the heavy dependence on electric power while still guarantee a good comfort. Among these new faces, liquid desiccant cooling system, which mainly consists of a liquid-dehumidification unit and an evaporation-cooling unit, has attracted ever increasing attention from both researchers and consumers. The reason for this is mostly owing to the fact that this system could be driven by heat sources with relatively low temperature of around 70 °C. That *
Corresponding author. Tel.: +86 025 84442945; fax: +86 025 83792722. E-mail address: [email protected] (Xiu-Wei L.). 0038-092X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.solener.2008.05.015
means the work could be done by many renewable energies, such as solar power, geothermal power and waste heat (Zhang et al., 2003). The cycle of this system is shown in Fig. 1 (Khalid Ahmed et al., 1997). The cycle consists of a liquid desiccant system using liquid desiccant for both absorption and dehumidification processes and water as the refrigerant. The system operates on an open-cycle in which the weak absorbent solution is regenerated by losing the refrigerant to the Earth’s atmosphere. Cooling takes place by evaporating water from an external source in the evaporator. The weak absorbent solution (state 1) from the absorber is pumped (state 2) to the solar regenerator, which is partly open to the atmosphere, through the regenerative heat exchanger HE1. It is then heated and subsequently concentrated in the solar regenerator from state 3 to state 4. The strong solution passes through the regenerative heat exchanger HE1 on its way (state 5 and state 6) to the absorber. In the absorber, the strong desiccant absorbs water vapour as soon as the incoming refrigerant evaporates in
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Nomenclature aw A/ COP fw h Ix K Mw m P Q R r rd t T X x Z
activity of water (no units) Debye-Hu¨ckel constant for the osmotic coefficient (no units) coefficient of performance (no units) activity coefficient of water (no units) enthalpy (kJ/kg) ionic strength in mole fraction scale (no units) solubility product (no units) water molecular weight (kg/kmol) flow rate (kg/s) vapour pressure (Pa) energy (kJ) gas constant (no units) refrigerant moisture (kg/s) dehumidified moisture (kg/s) total moisture (kg/s) temperature (K) mass concentration (no units) mole fraction (no units) absolute value of ionic charge (no units)
s h q
NRTL binary interaction energy parameter (no units) reference temperature 298.15 K the closest approach parameter of the Pitzer– Debye-Hu¨ckel equation (no units)
Superscripts PDH long-range contribution, represented by the Pitzer– Debye-Hu¨ckel equation lc short-range contribution, represented by the local composition model Subscripts 0 00 a,a ,a anion 0 00 cation c,c ,c ca salt ca i,j,k any species 0 solvent s,s w water 1,2,3. . . related to the state number of Fig. 1 ± mean value
Greek symbols a NRTL nonrandomness factor (no units)
the evaporator (state 11) by absorbing the heat from the cold space, maintaining the reduced pressure required by the evaporator. The heat of absorption for the refrigerant-absorbent solution is removed by the cooling water loop. In the evaporator, water from an external source (state 10) is evaporated. The resultant weak desiccant is then pumped from the absorber back to atmospheric pressure through the regenerative heat exchanger and to the solar regenerator, completing the absorption-machine cycle. Part of the strong desiccant (state 5) from the solar regenerator is passed through the regenerative heat exchanger HE2 (state 7) to the dehumidifier, where the air to be conditioned is dehumidified in the counter-current direction. The actual dehumidification takes place due to the vapour pressure difference between the vapour in the air and the liquid desiccant. As the regenerated liquid desiccant is cooled and concentrated (state 8), its vapour pressure is less than the vapour pressure of the air, therefore the vapour present in the air tends to escape into the liquid desiccant, thereby diluting the liquid desiccant. The weak desiccant (state 9) from the dehumidifier is then pumped back for regeneration, along with the weak desiccant from the absorber (state 1). After regeneration the strong solution is supplied to the absorber and dehumidifier in the required proportions, as shown by states 6 and 7. The absorbent used in the cycle for absorption in the absorption-machine, as well as the desiccant in the dehumidifier is the same. The cooling water (states 12, 13 and 14) is cir-
culated to the dehumidifier and completes the cooling tower cycle. Fig. 2 shows the psychrometric chart for the process of dehumidification and sensible cooling. The mixture of return air from the room (state ‘e’) and fresh air from outdoors (state ‘a’) enters the dehumidifier (state ‘b’). The dry air at state ‘c’ is passed over the cooling coil where it is sensible cooled and enters the room at state ‘d’. The conditioned air picks up the load in the room and leaves at state ‘e’. Referring to Fig. 1 (the subscripts attached stand for the state number in Fig. 1), a total mass balance on the regenerator gives: (these symbols are listed in the nomenclature) m3 ¼ mt þ m4 ;
ð1Þ
where mt is the total moisture (refrigerant moisture mr and dehumidified moisture mrd ) and is given by: mt ¼ mr þ mrd ;
ð2Þ
where the liquid desiccant mass balance yields: (X 3 and X 4 stand for the concentration of liquid desiccant at states 3 and 4 in Fig. 1, respectively) m3 X 3 ¼ m4 X 4 :
ð3Þ
Solving Eqs. (1) and (3), we get, m4 X3 ¼ mt ðX 4 X 3 Þ
ð4Þ
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Fig. 1. Hybrid liquid desiccant based air-conditioning cycle (liquid desiccant cooling system).
This gives the ratio of total absorbent to total refrigerant flow rate. It is assumed that mst is the total mass of the solution reaching the solar regenerator and is given by mst ¼ ms þ m9 ;
ð5Þ
where ms is the flow rate of absorbent leaving the absorber and is given by the expression: ms mab ¼ þ 1; ð6Þ mr mr mab represents the flow rate of absorbent reaching the absorber. The heat balance for the heat exchangers HE1 and HE2 gives: m2 h2 þ m4 h4 ¼ m3 h3 þ m5 h5 ;
ð7Þ
and m7 h7 þ m13 h13 ¼ m8 h8 þ m14 h14 :
ð8Þ
Therefore, the evaporator capacity Qev is given by: Qev ¼ m11 ðh11 h10 Þ ¼ mr ðh11 h10 Þ:
ð9Þ
The mass balance in the dehumidifier results is: mrd þ m8 ¼ m9 : Fig. 2. Process on the psychrometric chart.
ð10Þ
The amount of solar energy collected for the regeneration of the weak desiccant is given by:
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Qgen ¼ mt ht þ m4 h4 mst h3 :
ð11Þ
The absorber load is given by: Qab ¼ m11 h11 þ m6 h6 m1 h1 :
ð12Þ
The dehumidifier load is given by: (here, the subscript ‘‘i” and ‘‘o” indicate the inlet parameter and the outlet parameter, respectively) Qrd ¼ mrd;i hrd;i þ m8 h8 m9 h9 mrd;o hrd;o :
ð13Þ
Therefore, integrating (1), (2), (4) and (5) together, the coefficient of performance for this system could be described as: COP ¼
Qev m11 ðh11 h10 Þ ¼ Qgen mt ht þ m4 h4 mst h3
¼
mr ðh11 h10 Þ ; mt ðht h3 Þ þ m4 ðh4 h3 Þ
ð14Þ
and COP ¼
Qev mr ðh11 h10 Þ ¼ 3 Qgen ðmr þ mrd Þ½ðht h3 Þ þ ðX XX ðh4 h3 Þ 4 3Þ ð15Þ
Exposed from (15) and provided the enthalpy related to every state in Fig. 1 stays unchanged, the cooling capacity will increase if the amount of absorption (or dehumidification) increases; while the COP decreases if the cooling capacity increases. However, it always fails to reach the right set states (like states ‘c’ and ‘d’ in Fig. 2) because its dehumidification ability is poor, which leads to the insufficient cooling and dehumidification capacity. Therefore, the properties of the liquid desiccant should be concerned in order to maximize the mass transfer in both the absorber and the dehumidifier so that this system could obtain ample cooling and dehumidification capacity. Solar energy is particularly suitable for this system. For one thing, solar energy is universal and could be easily gained in almost every corner of the Earth. For another thing, air-conditioner is needed badly at daytime in summer; when it always accompanies with the best sunshine of a day. That means plenty of solar energy could be gained at the right time to drive this system and obtain a good cooling effect. Beyond that, this system is fit to the solar energy storage, in that surplus liquid desiccant could be concentrated when solar energy is rich at daytime, and then be used for cooling at night when no solar energy is available. The conventional closed-cycle absorption chillers require heat source temperatures that are significantly higher than the temperatures of corresponding heat sinks. Thus, they have to be operated with high-grade heat extracted from natural gas, steam, concentrating solar collectors and the like. Nevertheless, the liquid desiccant cooling system could operate with a heat source of relatively lower temperature, which could in turn improves the effi-
ciency of utilizing solar energy to generate cooling effect (Zhang et al., 2003). Liquid-dehumidification process plays a key role in the performance of such a system. The thermal properties of liquid desiccants, especially their surface water vapour pressure, greatly influence the dehumidification effect. It is found that the lower the vapour pressure of the desiccant is, the better the dehumidification effect could be obtained. The reason for that is because the enlargement of the vapour pressure difference could promote the mass transfer in dehumidification (Gommed and Grossman, 2004). Generally, the liquid desiccants adopted in this system are always the electrolyte solutions including LiCl solution, CaCl2 solution, LiBr solution and mixed LiCl–CaCl2 solution (Grossman, 2002; Nelson and Goswami, 2002). Most researches about the thermal properties of liquid desiccants only take care of the single electrolyte solutions like LiCl solution or CaCl2 solution (Manuel, 2004). There is few works caring about the thermal properties of mixed liquid desiccants. Ertas et al. (1992) have carried out experimental works on the thermal properties of mixed LiCl–CaCl2 solution. The results revealed in their article have been later referred in many papers related to the topic of liquiddehumidification. In their work, they measured the vapour pressure of the mixed LiCl–CaCl2 solution with five different ratios. The total electrolyte mass concentration of the solution was maintained as 20%. There were five solution groups according to the changed LiCl/CaCl2 ratio: 100% LiCl, 70% LiCl and 30% CaCl2, 50% LiCl and 50% CaCl2, 30% LiCl and 70% CaCl2 and 100% CaCl2. Through experiments, they concluded that the 100% LiCl group got the lowest vapour pressure under different temperatures. However, considering the costeffectiveness, they suggested that the 50% LiCl and 50% CaCl2 group is a better choice. Nevertheless, their work was limited within a narrow scope of research on the thermal properties of mixed desiccant. They didn’t provide further solutions for acquiring the vapour pressure of the mixed LiCl–CaCl2 solutions with different concentrations and ratios beyond the scope provided in their paper. And it doesn’t seem to be feasible to get all the results just by numerous experiments. Ahmed and Gandhidasan (1998) attempted to engage a classical thermodynamics approach to predict the vapour pressure of the liquid desiccant including LiCl, CaCl2 and the mixture of these two electrolytes. However, as they described in their paper, the results obtained are not satisfied because those results did not agree well with the experimental results they referred. Those works mentioned above concentrated on selected liquid desiccants rather than proposed a method to determine which liquid desiccant will be an ideal one before using it. Putting aside the works on the thermal properties, there are no reports about dehumidification experiments of mixed LiCl–CaCl2 solutions with different concentrations and ratios.
Xiu-Wei L. et al. / Solar Energy 82 (2008) 1161–1171
In the sense of chemical field, there are many independent theories for research on electrolyte solutions (Pitzer, 1991; Chen et al., 1982; Chen and Evans, 1986). According to the Rault rule, the water vapour pressure of the solution can be obtained by calculating the activity of the water. Activity is always corresponding to the activity coefficient and the concentration (including mole fraction and mass fraction). A lot of theories have been developed to calculate the activity coefficient of the electrolyte solutions, single or mixed. The Debye-Hu¨ckel theory, the Pitzer theory, the Local Composition Model and the Perturbation theories are among these theories. Most of them are based on the statistical thermodynamics principles. Their calculation results proved agreeing well with the experimental results and have a very high precision. Since the NRTL equation of Local Composition Model has a good precision and its parameters are easy to obtain, it has been applied to calculate the activity coefficient of the mixed LiCl–CaCl2 solution in our paper (Chen and Evans, 1986). The related activity, which reflects the water vapour pressure of the solution has been further deduced. Beyond that, the dehumidification experiments were conducted with five mixed LiCl–CaCl2 solution groups of different concentration ratios. The results show that the group of lower activity has a better dehumidification effect as predicted. Those efforts provide us with a new idea of prejudging liquid desiccants by comparing their activity.
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tion, and so does the activity coefficient. Assuming the temperature is constant, the long-range interaction can be described as: ln fwPDH ¼
1 1000 2 2A/ I 3=2 x ; Mw I þ qI 1=2 x
ð18Þ
P 2 xi zi for short-range interaction, the equawhere I x ¼ 12 tion of activity coefficient calculation for water (one of the solvent) in a multi-component electrolyte could be expressed as: P P X j Gjw sjw P X s0 Gws0 X G 0s 0 j lc k k ks ks P P P þ s0 sws0 lnfw ¼ X G X G X G k
k
þ þ
kw
PP c
a0
PP a
c0
k
PX a0
X 00 a00 a
PX c0 c00
X c00
k
ks0
PX c Gwc;a0 c k
X k Gkc;a0 c
PX a Gwa;c0 a k
X k Gka;c0 a
k
k
ks0
P X G 0 s 0 k k kc;a c kc;a c swc;a0 c P ; k
X k Gkc;a0 c
P X G 0 s 0 k k ka;c a ka;c a swa;c0 a P X G k
k
ka;c0 a
ð19Þ in the form above: X j ¼ C j xj ; C j ¼ jzj j in the ion case and C j ¼ 1 in the molecule case. The relationship between those parameters could be defined as: Gji ¼ expðaji sji Þ; sji ¼ ðgji gii Þ=RT Gji;ki ¼ expðaji;ki sji;ki Þ; sji;ki ¼ ðgji gki Þ=RT Gas ¼ Gcs aas ¼ acs ¼ aca;s ; asc;ac ¼ asa;ca ¼ as;ca ; aca;s ¼ as;ca ;
2. Methods and experiments 2.1. The vapour pressure calculation The vapour–liquid equilibrium relation for water in an electrolyte solution can be simplified as (Hsiu-ling et al., 2003): Pw aw ¼ 0 ; Pw
ð16Þ
aw ¼ x w f w ;
ð17Þ
where P w and P 0w are the vapour pressure of solution and pure water, respectively. The vapour pressure of a solution can be calculated, if the activity aw of water has been determined in advance. At the same time, aw is the product of mole concentration and activity coefficient fw (this activity coefficient is corresponding to the mole fraction, and it will be different in the situation of using the mass concentration). NRTL equation, based on the Local Composition Model is adopted for the calculation of fw in this paper. The expression of NRTL for calculating the activity coefficient of the solvent could be divided into two parts, one part is known as the long-range interaction contribution and the other part is called the short-range interaction contribution (Manuel, 2004). The vapour pressure is affected mostly by two factors, the temperature and the concentra-
sas ¼ scs ¼ sca;s ; ssc;ac ¼ ssa;ca ¼ ss;ca ; P P a X a Gca;w c X c Gca;w ; Gaw ¼ P Gcw ¼ P 0 X a0 a c0 X c0 sca;c0 ¼ sc0;ca ; sca;ca0 ¼ sc0;ca : All the parameters have been listed in the nomenclature, and the meaning of them could be found from the reference (Chen and Evans, 1986). The whole interaction expression is: ln fw ¼ ln fwPDH þ ln fwlc :
ð20Þ
The activity coefficient could be obtained with (20) and later used to deduce the activity and the vapour pressure at a certain temperature with Eqs. (16) and (17). The effect of temperature will be reflected in the value of s, which stands for the energy parameter in the NRTL equation. Its varying with the temperature follows the form below (Chen and Evans, 1986): 1 1 hT T þc þ ln ; ð21Þ s¼aþb T h T h where the experienced parameters a, b and c could be checked from the references or obtained through regression of the experimental data.
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2.2. Activity coefficient calculation for mixed LiCl–CaCl2 solution In the case of mixed LiCl–CaCl2 solution, the form of long-range interaction is: ln fwPDH ¼ 5:829
2.3. Solubility of mixed liquid desiccant
ðxLiCl þ 3xCaCl2 Þ 1
ð22Þ
;
½1 þ 14:9ðxLiCl þ 3xCaCl2 Þ2
For a mixed liquid desiccant, the solubility should be concerned beyond the activity coefficient, as there is a boundary amount for an electrolyte solution to accept the electrolytes of other kinds. The solubility could be acquired by experiments and by calculating the solubility product (Pitzer, 1991). NRTL equation also provides the method to calculate the solubility product. The solubility product has the expression for a single solution with the form of CA:
assume that: expð0:2sLiCl;w Þ ¼ A; ¼ B;
expð0:2sCaCl2 ;w Þ expð0:2sLiCl;CaCl2 Þ
¼ C; expð0:2sw;LiCl Þ ¼ A0 ; 0
¼B;
expð0:2sw;CaCl2 Þ expð0:2sCaCl2 ;LiCl Þ ¼ C 0 ;
K CA ¼ aC aA ¼ x2CA f2 ¼ x2CA fC fA :
There exists the relationship: xLiCl þ xCaCl2 þ xw ¼ 1;
ð23Þ
2AsLiCl;w xLiCl þ4BsCaCl2 ;w xCaCl2 þðxLiCl A0 Þ ½1þð2A2ÞxLiCl þð4B3ÞxCaCl2
sw;LiCl xLiCl þ2½C 0 ðsw;LiCl sCaCl2 ;LiCl Þþ2sw;LiCl xCaCl2 ½ð12A0 ÞxLiCl þð2C 0 þ23A0 ÞxCaCl2 þA0
2
þð2B0 xCaCl2 Þ
½ðC þ12B0 ÞxLiCl þð23B0 ÞxCaCl2 þB0 2 sw;LiCl xLiCl þ2C 0 ðsw;LiCl sCaCl2 ;LiCl ÞxCaCl2 0
0
ðxLiCl þ2C xCaCl2 þA xw Þ
Cðsw;CaCl2 sLiCl;CaCl2 ÞxLiCl þ2sw;CaCl2 xCaCl2
þðxw Þ
2
ð2AxLiCl þ4BxCaCl2 þxw Þ2
P
PX a0 a0
c00
ka;c0 a
k
k
k
k
ka;c0 a
ð27Þ P P P P X s Gas X G 0 s 0 X G s X c0 1 lc k k ka;c a ac;c a k k ks ks P P P P lnf ¼ þ s as c0 s a Za X 00 X G 0 X G X G a00 c k k kc;a k k ks k k ks P PP X G 0s 0 X cG 0 X k k kc;a kc;a þ c a0 P a0X P X ac;a sac;a0 P G X G
þð2B xCaCl2 Þ ðCxLiCl þ2xCaCl2 þB0 xw Þ 2AsLiCl;w xLiCl þ4BsCaCl2 ;w xCaCl2
P P P X s Gcs X G 0 s 0 X G s k k kc;a c kc;a c k k ks ks P P P þ s cs s X 00 X G 0 X G X G a00 a k k kc;a c k k ks k k ks P PP X G 0 s 0 X aG 0a X k k ka;c a ka;c a þ a c0 P c0X P X ca;c sca;c0 a P G X G
ln fclc ¼
c00
2
ð26Þ
f represents the mean activity coefficient, while fC and fC0 represents the activity coefficient of cation, fA stands for the activity coefficient of anion. The calculation forms for fC , fC0 and fA share the same long-range interaction item as presented in Eq. (18). The forms of short-range interaction are as follows: 1 Zc
0
In the situation of a mixed one with the form as C 2 A C 0 A nH2 O, it could be written as:
½Cðsw;CaCl2 sLiCl;CaCl2 Þþsw;CaCl2 xLiCl þ2sw;CaCl2 xCaCl2
þðxLiCl A0 Þ
ð25Þ
K C2 AC0 AH2 O ¼ x2C xC0 x2A fC2 fC0 fA2 anw ;
so the short-range interaction can be described as: lnfwlc ¼
the subscript w represents water, and the whole interaction expression is just the same as Eq. (20). All the values of the parameters are presented in Table 1 (Chen and Evans, 1986).
a00
a00
k
k
kc;a0
k
k
kc;a0
ð28Þ
; ð24Þ
Table 1 Parameters for activity coefficient calculation (25 °C)
The solubility expression of single or mixed electrolyte with other forms could be found from the references (Pitzer, 1991). 2.4. The experimental system
Parameter
Value
A/ q Mw sLiCl,w sw,LiCl sCaCl2 ;w sw;CaCl2 sLiCl;CaCl2 sCaCl2 ;LiCl a
0.3910 14.9 18 –5.1737 10.1242 –5.2549 10.5126 0 0 0.2
To examine the dehumidification effects of different mixed LiCl–CaCl2 solution groups, a structured corrugated packing of inorganic material (Munters Celdek) was used as the dehumidifier and its appearance is shown in Fig. 3. The specific area of this packing is 396 (m2/m3). Fig. 3a and b display the shapes viewed from the upside and the sidepiece of the packing, respectively. The definition of the packing dimensions is shown in Fig. 3c. The desiccant solution dehumidifier is of the dimensions with height
Xiu-Wei L. et al. / Solar Energy 82 (2008) 1161–1171
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Air H
L W
(a) From the upside
(b) From the sidepiece
(c) Definition of the packing dimensions
Fig. 3. The shape and structure of the packing in the dehumidifier.
H = 0.5 m, width W = 0.2 m and length L = 0.5 m. During the experiments, the packing was well wetted. The schematic diagram of the liquid desiccant dehumidification is shown in Fig. 4. It is made up of a dehumidifier, a pump, a concentrated solution tank, a diluted solution tank, a rotameter and etc. An environmental chamber for providing the air with different temperatures and humidity ratios is shown in Fig. 5. The objective of the experimental apparatus is to obtain the inlet and outlet parameters of the air and the liquid desiccant. Those parameters include the drybulb temperature, the wet-bulb temperature and the flow rate of the inlet and outlet air; the temperature, the mass concentration and the flow rate of the liquid desiccant. All the experiments were carried out under steady state of the air and liquid desiccant. The temperatures were measured by some Pt100 RTDs (Resistance Temperature Detectors) with the accuracy of 0.01 °C and recorded by a data acquisition switch unit with the type of Agilent 34970A. The flow rate of the liquid desiccant was measured by an anticorrosive rotameter ranging from 40 l/h to 400 l/
h with the accuracy of 10 l/h. The air flow rate was measured by three standard nozzles with the accuracy of 1%. Their diameters were 70 mm, 80 mm and 110 mm, which are corresponding to the measure range of 208–485 m3/h, 424–990 m3/h and 513–1197 m3/h, respectively. The liquid desiccant used in our experiment was divided into five groups. Group1 is the pure LiCl solution whose mass fraction (the mass fraction of LiCl) is 39%; Group2 is the mixed LiCl–CaCl2 solution made by just adding pure solid CaCl2 into the LiCl solution being of the same mass concentration as Group1. The mass fraction of CaCl2 is set to be 5% in the new mixed solution, which leads to the mass fraction of LiCl falling to 37% in the new solution. In the same way, we obtained Group3 (35% LiCl and 10% CaCl2), Group4 (33% LiCl and 15% CaCl2) and Group5 (31.2% LiCl and 20% CaCl2). The mass of water and LiCl stays unchanged in these five groups though their mass concentrations vary. According to the results from solubility experiments, Group 5 has touched the edge of the maximum CaCl2 amount that could be accepted in the origin pure LiCl solution (Group 1).
Fan Humidifier Air
Air Evaporator
Dehumidifier
Compressor
Heater
Nozzle
Air Sampler
Environmental Chamber 1. Dehumidifier, 2. Rotameter, 3. Pump, 4. Concentrated solution tank, 5. Diluted solution tank
Fig. 4. Schematic diagram of desiccant dehumidification.
To condenser
From throttle
Fig. 5. Environmental chamber for the air.
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The temperature of the working liquid desiccant was regulated as 25 ± 0.5 °C, so the activity coefficient calculation could ignore the temperature influence on the value of the energy parameters. 3. Results and discussion 3.1. Results comparison Fig. 6 shows the different results about the water vapour pressure of single LiCl solution varying with the temperature, and they are compared with the vapour pressure of pure water at the same temperatures. The mass fraction of LiCl is fixed as 20%. Eqs. (22), (24), (25), (16), and (17) are applied to calculate the vapour pressure because the single electrolyte solution calculation could be considered as a special case of the mixed solution calculation. The energy parameters, which will be changed with the temperature is obtained by regressing the experimental data under different temperatures (Manuel, 2004). It could be found that the results obtained by using NRTL equation agree very well with the results revealed by Manuel (2004), whose work has been proved to have a good precision by comparing it with lots of experimental data he referred. The experimental results from A. Ertas seem to have a gap of around 700 Pa with the other two results. Fig. 7 shows the different results about the water vapour pressure of CaCl2 solution varying with the temperature. The mass fraction of CaCl2 is also fixed as 20%. It could be found that the results obtained by using NRTL equation also agree very well with the results revealed by Manuel, 2004, while the experimental results from Ertas et al. (1992) have a fairly large gap with the other two results. However, the results from Ertas et al. (1992) are not correct this time. Because in their results, the saturation vapour pressure of CaCl2 solution is even bigger than that of pure water at the same temperature, and that is impossible. Therefore, the results of mixed LiCl–CaCl2 solution from Ertas et al. (1992) seem not to be a reliable source
Fig. 6. Results comparison of the vapour pressure of LiCl solution.
Fig. 7. Results comparison of the vapour pressure of CaCl2 solution.
of experimental data to test the results of vapour pressure calculated by NRTL equation. So it may lack of direct experimental data about the vapour pressure of the mixed electrolyte solution. Nevertheless, the results of activity coefficient and activity calculated by NRTL equation could be trusted as the method is proved to be reliable and have a good accuracy through experiments (Chen and Evans, 1986). Based on that, the vapour pressure deduced by calculating the activity could also be reliable results. 3.2. Select an ideal liquid desiccant by activity map For a mixed solution whose components are already known, the best ratio could be acquired by pursuing the minimum of activity. Since the temperature of the liquid desiccant is always maintained in the dehumidification process, the minimum value of the activity can be obtained by solving the differential equations as follows: @ðfw xw Þ @ðfw xw Þ ¼ 0; ¼0 @xLiCl @xCaCl2
ð29Þ
Actually, it will be too difficult to work out xLiCl and xCaCl2 to get the minimum value because the expression of the derivation is too complex to analyse. Instead, considering the ratio of the components are limited in practical process, a certain range of xLiCl and xCaCl2 are selected to build a map at a constant temperature for analysing the activity of mixed liquid desiccant. The results for mixed LiCl– CaCl2 solution are shown in Fig. 8 (the temperature is 25 °C). X-axis represents the mass fraction of CaCl2 with the range of 0–20% and the Y-axis represents the mass fraction of LiCl with the range of 29–40%. The activity decreases with the increase of the concentration of both LiCl and CaCl2, and the mass fraction change of LiCl has a slightly greater influence on the activity than that of CaCl2. The minimum activity is obviously positioned at the foot of this map without considering the solubility.
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sLiCl;CaCl2 ¼ sCaCl2 ;LiCl ¼ 2 The results calculated with these three different groups of energy parameters are presented together in Fig. 9, where the X-axis and the Y-axis represent the same parameters as (Fig. 8). Seen from the side face of the figure, these three maps overlap each other and could not be separated apart. That indicates the values of the salt–salt energy parameters have few impacts on the activity calculation and their results within the selected ratio range is almost the same. 3.3. Field activity curve of the experiment
Fig. 8. Activity map of mixed LiCl–CaCl2 solution (25 °C).
According to the reference (Chen and Evans, 1986), the value of salt–salt energy parameters is set to be zero in an ideal situation, which means: sLiCl;CaCl2 ¼ sCaCl2 ;LiCl ¼ 0 That reflects the mixing rule of the model performing much like the Guggenheim equation for predicting osmotic coefficient and Harned’s rule for predicting mean ionic activity coefficients for aqueous multi-component electrolyte system. We could also calculate the activity map using different binary parameters as the reference (Chen and Evans, 1986) suggested: sLiCl;CaCl2 ¼ sCaCl2 ;LiCl ¼ 1
Fig. 9. Activity map of mixed LiCl–CaCl2 solution with different salt–salt energy parameters (25 °C).
Considering the solubility in our experiment, it is not convenient for us to describe the solubility in the activity map like (Fig. 8) as the mass fraction of LiCl varies with the mass fraction of CaCl2. To solve that problem, another activity map, which changed from Fig. 8, is introduced. The salt–salt energy parameters are set as 0. The drawing of this new activity map is shown in Fig. 10, where the X-axis represents the mass ratio of CaCl2/H2O (0–50%). H2O stands for the water mass of the original LiCl solution (39%) in the experiment. In the same way, the Y-axis represents the mass ratio of LiCl/H2O (40–68%). Since the mass of water has not been changed in the five groups, the mass ratio of CaCl2/H2O is changed from 0% to 41% within the range bordered by the solubility and the mass ratio of LiCl/H2O remains 64% (the mass of LiCl has not been changed in the five groups, either). Therefore, the activity curve at this solubility could be made in the activity map, which is exhibited in Fig. 11, where the X-axis and the Y -axis represent the same parameters as (Fig. 10). The curve AB expresses the activity variation while the mass ratio of LiCl/H2O is 64% and the mass ratio of CaCl2/ H2O varies from 0% (Group 1) to 41% (Group 5). Clearly,
Fig. 10. Activity map of mixed LiCl–CaCl2 solution with different X-axis and Y-axis (25 °C).
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Fig. 13. Dehumidification effect of mixed LiCl and CaCl2 solution with the original humidity of 11 g/(kg air).
Fig. 11. Activity curve of mixed LiCl–CaCl2 solution in experiment (25 °C).
it is very easy to find out that the activity of these five groups arranged from large to small is Group 1, Group 2, Group 3, Group 4 and Group 5. Group 5 is expected to have the best dehumidification performance in the experiments. 3.4. Experimental results Group1 to Group5 are adopted in the experiments, and the results are exhibited from Fig. 12 to Fig. 14, where Dd stands for the humidity reduction. The inlet air for dehumidification was controlled to maintain the dry-bulb temperature as 30 0:5 C, and the humidity was regulated as 10 g/(kg air), 11 g/(kg air) and 12 g/(kg air) in Fig. 12, Fig. 13 and Fig. 14, respectively. From the results, it could be seen that the arrangement of dehumidification effect from high to low exactly reflects the arrangement of activity from small to large. In other
Fig. 12. Dehumidification effect of mixed LiCl and CaCl2 solution with the original humidity of 10 g/(kg air).
words, the lower the activity is, the better dehumidification effect can be obtained, which is in accordance with the prediction. And the fifth group of the mixed solution has the best dehumidification effect. Compared to Group1, Group 5 has improved the average dehumidification amount by 26%, 25.3% and 24.3% under three conditions, respectively. On the other hand, it should be noticed that the dehumidification amount of Group 1 in Fig. 13 is near that of Group 5 in Fig. 12, which indicates that the original humidity variation of the inlet air may have a more powerful influence on the dehumidification effect than the vapour pressure variation of the liquid desiccant. The increase of original humidity from Fig. 12 to Fig. 13 is 1 g/(kg air), which embodies the vapour pressure variation of the inlet air as 120 Pa. However, the decrease of vapour pressure of the liquid desiccant is about 267 Pa from Group 1 to Group 5. According to the present mass transfer equation (Hsiu-ling et al., 2003): m ¼ bADP Dt;
ð30Þ
where m stands for the dehumidification amount, b is the mass transfer coefficient, A is the dehumidification area
Fig. 14. Dehumidification effect of mixed LiCl and CaCl2 solution with the original humidity of 12 g/(kg air).
Xiu-Wei L. et al. / Solar Energy 82 (2008) 1161–1171
and Dt stands for the dehumidification time. We have the differential equation as: dm ¼ bADP : dt
ð31Þ
It could be predicted from (31) that Group 5 in Fig. 12 may have a larger dehumidification amount than Group 1 in Fig. 13 as the former one has a larger vapour pressure difference and the other parameters are provided unchanged. However, that prediction does not conform to the experimental results. Nevertheless, in the situation of the comparison of Group 1 in Fig. 14 and Group 5 in Fig. 13, this phenomenon is not obvious. Completely addressing this issue calls for more work on the dehumidification process under different conditions. All in all, the variation of the original humidity of the inlet air may play a more active role in the dehumidification process. That may help further improve the present mass transfer equation that only counts on the difference of vapour pressure. A possible amendment may be needed for the mass transfer coefficient by taking the effect of the original humidity in concern. 4. Conclusions The NRTL equation is a reliable method for us to indirectly obtain the vapour pressure of the liquid desiccant by calculating the activity. This calculation method is not only fit the situation of a single solution but also fit the situation of mixed solution of different kinds. Furthermore, the equation could also be applied in the situation of mixed solvent. Based on the activity calculation, the activity maps of different liquid desiccants could be built up. Therefore an ideal one could be selected by judging its activity in the map before employing it in the dehumidification process. The mixed LiCl and CaCl2 solution could improve the dehumidification effect by more than 20% compared to the pure LiCl solution. Nevertheless, considering the cost of LiCl is more expensive than CaCl2, a proper group can be found to be more cost-effective. Actually, in the present Chinese market, LiCl is above 28.75 dollars/kg while CaCl2 is only around 2 dollars/kg. First, let is focus on the activity map shown in Fig. 10. The activity located in the region of the same colour indicates that there is no big difference between those activity values. Therefore, if we reduce the mass of LiCl in the solution and increase CaCl2 with the same mass (like group (LiCl/H2O = 0.68, CaCl2/H2O = 0) and the group (LiCl/H2O = 0.48, CaCl2/ H2O = 0.2), the total mass of the solution remains unchanged because of the mass of water staying unchanged), almost the same activity effect (as shown in the activity map) could be obtained while the initial cost could be greatly reduced. Secondly, we will consider the
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relation between the cost and the dehumidification effect from Fig. 12 to Fig. 14. Take the situation of Group 5 (31.2% LiCl and 20% CaCl2) for example, the dehumidification effect has been improved by more than 20% than Group 1 (pure LiCl solution), while the cost added (the CaCl2 cost) only takes up 4.5% of the original LiCl cost in Group 1. The original humidity of the air has a more active influence on the dehumidification process than the vapour pressure of the liquid desiccant, and that should be embodied in the mass transfer equation. So that will be meaningful to amend the present mass transfer equation. Acknowledgements This research was supported by the grants from the fund of National Natural Science Foundation of China under the Contract No. 50676018 and the fund of State Education Department for key projects of science and technology research under the Contract No. 307013. These supports are gratefully acknowledged. References Ahmed, S.Y., Gandhidasan, P., 1998. Thermodynamic analysis of liquid desiccant. Solar Energy 62 (1), 11–18. Chen, C.C., Evans, L.B., 1986. A local composition model for the excess Gibbs energy of aqueous electrolyte systems. AIChE Journal 32 (3), 444–454. Chen, C.C., Britt, H.I., Boston, J.F., Evans, L.B., 1982. Local composition model for excess Gibbs energy of electrolyte systems. Part 1: single solvent, single completely dissociated electrolyte systems. AIChE Journal 28 (4), 588–596. Ertas, A., Anderson, E.E., Kiris, I., 1992. Properties of a new liquid desiccant solution – lithium chloride and calcium chloride mixture. Solar Energy 49 (3), 205–212. Gommed, K., Grossman, G., 2004. A liquid desiccant system for solar cooling and dehumidification. Journal of Solar Energy Engineering 126, 879–885. Grossman, G., 2002. Solar-powered systems for cooling, dehumidification and air-conditioning. Solar Energy 49 (3), 205–212. Hsiu-ling, Hsu.Hsu, Yi-chou, Wu.Wu, Liang-sun, Lee, 2003. Vapor pressure of aqueous solution with mixed salts of NaCl + KBr and NaBr + KCl. Journal of Chemical and Engineering Data 48, 514–518. Khalid Ahmed, C.S., Gandhidasan, P., Al-Farayedhi, A.A., 1997. Simulation of a hybrid liquid desiccant based air-conditioning system. Applied Thermal Engineering 17 (2), 125–134. Manuel, R.C., 2004. Properties of aqueous solutions of lithium and calcium chlorides: formulations for use in air conditioning equipment design. International Journal of Thermal Science 43, 367–382. Nelson, F., Goswami, D.Y., 2002. Study of an aqueous lithium chloride desiccant system air dehumidification and desiccant regeneration. Solar Energy 72 (4), 351–361. Pitzer, K.S., 1991. Activity Coefficient in Electrolyte Solution, second ed. CRC Press, Boca Raton. Zhang, X.S., Fei, X.F., Shi, M.H., Cao, Y.R., 2003. Study on the dehumidifier of the energy storage liquid desiccant cooling systems. Journal of Southeast University 33 (1), 1–4.