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CORRELATIONS Mass-Transfer Correlations for Dehumidification of Air by Triethylene Glycol in a Structured Packed Column Esam Elsarrag* Technical Studies Institute, Zayed Military City, Suwihan, Abu Dhabi, UAE
Elsheikh E. M. Magzoub† Mechanical Engineering Department, Faculty of Engineering & Architecture, University of Khartoum, Sudan
Sanjeev Jain‡ Faculty of Mechanical Engineering, Indian Institute of Technology, Delhi, Hauz Khas, New Delhi 110016, India
Structured packing represents the newest development in high-efficiency, high-capacity packing for heat and mass transfer in contrast to the traditional, randomly placed packing material. An experimental study for evaluating the heat- and mass-transfer coefficients in an air-desiccant contact system employing triethylene glycol and cross-corrugated cellulose structured packing (Celdek type) is carried out. The important design variables found to have the largest effect on the mass-transfer coefficient are as follows: the air and liquid flow rates, the air vapor pressure, and the solution vapor pressure. It is found that high liquid flow rates do not have a significant effect on the mass-transfer coefficient when the liquid to air flow rate ratio exceeds the value of 2. Two mass-transfer coefficient correlations are developed for normal and high liquid flow rates. These correlations predict the mass-transfer coefficient within 15%. Introduction The use of desiccant cooling and dehumidification systems for building comfort conditioning has increased steadily during the past several years. Liquid and solid desiccant systems are occasionally incorporated into commercial heating, ventilating and air conditioning (HVAC) systems; they are much more common in industry. The main types of absorbers used in previous studies are packed absorbers, falling-film absorbers, and spray towers. Different types of absorbers are detailed by Ramm.1 Packed-tower configurations have received more attention. Although randomly packed towers facilitate more mass transfer by providing a large area in a relatively small volume, the air pressure drop through the packing is generally high. This paper deals with a type of packing material called structured packing used for liquid desiccant systems. Structured packings have shown excellent performance characteristics with a relatively low ratio of pressure drop to heat- and mass-transfer coefficient per unit volume.2 The design of liquid desiccant dehumidification systems with structured packing requires * To whom correspondence should be addressed. Tel.: 00971-50-7160317. Fax: 00971-84-680127. E-mail: elsarrag@ emirates.net.ae or
[email protected]. † Tel.: 00249-83-774407. Fax: 00249-83-779973. E-mail:
[email protected]. ‡ Tel.: 91-11-26591060. Fax: 91-11-26582053. E-mail:
[email protected].
correlations for heat- and mass-transfer coefficients, but a limited number of correlations are found in the literature. Potnis and Lenz3 conducted experiments with random and structured packings in the dehumidifier/regenerator of a solar-assisted liquid desiccant system using LiBr. Chung et al.4 developed correlations for heat- and mass-transfer coefficients of a structured packing column using Celdek as the packing and triethlene glycol (TEG) as the desiccant. The average value of the errors between predicted values and experimental data was about 10%. Chung et al.5 developed correlations for heat- and mass-transfer coefficients of a packed column for random and structured packings using LiCl. The average value of the errors between predicted values and experimental data was about 4%. Al-Farayedhi et al.6 indicated a method to calculate heat- and mass-transfer coefficients in a gauze-type structured packing tower suitable for dehumidification/ regeneration of air of liquid desiccants using CaCl2, LiCl, and their mixture CELD. The correlations developed by the above researchers are summarized in Table 1. From the literature survey, it is clear that only a few publications have appeared to date for using structured packing in the liquid desiccant applications. Furthermore, only one correlation using TEG as the desiccant has been reported.4
10.1021/ie049802j CCC: $27.50 © 2004 American Chemical Society Published on Web 10/06/2004
Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7677 Table 1. Summary of Dimensionless Correlations for Mass-Transfer Coefficients in Structured Packed Absorbers from the Literature
author
experimental setup
Pontis and Lenz3
Chung et al.4 Chung et
al.5
Al-Farayedhi et al.6
column/ packed height (cm)
correlation
structured packing (Munters Celdek)
structured packing (Munters Celdek) structured packing [polyvinyl chloride and Munters Celdek] gauze-type structured packing
KG ) 0.02ml′0.9
30
ShG ) 0.04ReG0.9ScG0.5 KG ) 0.015ml′ ShG ) 0.03ReGScG0.5 KGa(Mwdeq2/DvFv) ) 9.03 × 10-6(1 X)0.05(ml/ma)0.25Scv0.333Rev1.34 ShG ) 2.25 × 10-4(1 X)0.25(ml/ma)0.1Scv0.333Rev1.0
55
KGa ) 0.55ULe0.1UGe0.79 exp(-0.0293TG)
Table 2. Physical Characteristics of Celdek Packing property
value
surface area (m2/m3) flute height (cm) equivalent diameter (cm) void space (%)
440 0.7 0.72 70
The objective of the present study is to define the variables that affect the heat- and mass-transfer coefficients and develop an overall mass-transfer coefficient correlation in the gas phase for a structured packing absorber. Experimental Procedure Figure 1 shows the experimental setup used in this study for air dehumidification. The tower has a total height of 50 cm with a structured-type packing consisting of three to five layers of corrugated cellulose pads (Munters Celdek). The properties of Celdek structured packing are shown in Table 2. During each experiment, 250 kg of TEG was stored in a tank and its temperature was adjusted by circulating the cooling tower water through the heat exchanger. TEG was allowed to recirculate to remove any temperature concentration gradients. The desiccant temperature and concentration were measured before starting the experiment; also a sample from the tank was taken for certainty. Desiccant at the required temperature, concentration, and flow rate was pumped to the top of the tower. It was sprayed in a manner counter to the air flow. The measurements were taken after allowing enough time
desiccant LiBr
42
TEG
42
LiCl
theoretical LiCl, CaCl2, and study CELD
for steady-state readings. The measurements during the experiment are shown in Figure 1. The following instruments were used to measure the variables: (a) Digital RTD type thermometers, ranging from 0 to 100 °C, with a resolution of 0.1 °C. These were used to measure and indicate both dry and wet bulb temperatures for all locations. (b) A portable digital vane anemometer to measure the air velocity. (c) Rotameters with a range from 1 to 8 gal/min to measure the desiccant and water flow rates. The desiccant rotameter was calibrated under different desiccant temperatures. (d) A hand refractometer, ranging from 1.445 to 1.52 refractive indices, with a resolution of 0.001 to measure the desiccant concentration. The refractometer was calibrated using different types of materials with known refractive indices. Several sets of experiments were performed for a tower height range of 40-50 cm. In some sets, the desiccant and air flow rates were varied while the solution and air inlet conditions were kept constant. In other sets, the inlet solution and air conditions were varied while the desiccant and air flow rates were kept constant. The weak desiccant was regenerated in a packed regenerator. The regeneration temperature ranged from 65 to 80 °C. Calculation of Heat- and Mass-Transfer Coefficients The overall gas-phase mass-transfer coefficient can be calculated assuming that the water is transferred from air to the liquid desiccant solution through a stagnant film of liquid. The expression for calculating the coefficient after correcting for bulk flow is derived by Hines and Maddox:7
KGa )
Figure 1. Schematic diagram of the packed absorber and accessories: DBT, dry bulb temperature sensor; WBT, wet bulb temperature sensor; T, temperature sensor; F, flowmeter.
ma′ MZ
∫yy
(1 - yA)*M dyA 1 - yA yA - yA*
A,b
A,a
(1)
The gas-side heat-transfer coefficient was calculated by assuming that the column was operated adiabatically. The expression for calculating the heat-transfer coefficient after the correction is made for mass transfer as derived by Treybal8 follows:
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hG′a )
dω dZ
-ma′Cpv
1 - emaCpv (dω/dz)/hGa
(2)
where
hG′a )
ma′Cpm ta,i - ti ln Z ta,o - ti
(3)
The integration of the above equations was carried out numerically using a computer program by dividing the packed bed into small segments starting from the bottom to the top of the tower. Results and Discussion The design variables assumed to have the greatest effect on the mass-transfer coefficient are the desiccant and air flow rates, the desiccant vapor pressure, and the water vapor pressure in air. The results are depicted graphically to show the influence of the design variables on the heat- and masstransfer coefficients. The heat- and mass-transfer coefficient values are compared with correlations reported by Chung et al.,4 as reproduced below:
[ ]
Mwdeq2 ) KGa DvFv 9.03 × 10-6(1 - X)-0.05
hGa
[ ]
deq2 ) kv 1.76 × 10-6(1 - X)0.07
() ml ma
0.26
() ml ma
Scv0.333Rev1.34 (4)
Figure 2. Influence of the air flow rate on (a) the mass-transfer coerfficient and (b) the heat-transfer coefficient.
0.49
Prv0.333Rev1.62 (5)
As shown in Figure 2, the mass-transfer coefficient increased from 0.14 to 0.23 kmol/m3‚s and the heattransfer coefficient from 2.26 to 5.63 kW/m3‚s when the specific air flow rate was changed from 0.94 to 2 kg/m2‚s. It can be observed that the values obtained by Chung et al.’s4 correlations are close to those of the present study when low air flow rates were employed, but a big discrepancy is observed at higher air flow rate ratios. This discrepancy can be attributed to low liquid to air flow rates used in this study, and the liquid flow is limiting the mass transfer at high air flow rates. This also emerges from the next result. An increase in the heat- and mass-transfer coefficients with the liquid flow rate was observed; see Figure 3. The values of the mass-transfer coefficients varied from 0.16 to 0.27 kmol/m3‚s and that of the heat-transfer coefficient from 5.4 to 7.56 kW/m3‚s when the specific liquid flow rate was changed from 1.75 to 2.2 kg/m2‚s based on low liquid to air flow rate ratios (1-1.3). It can be observed that the discrepancy between the experimental values of this study and that obtained by Chung et al.’s4 correlations decreased by increasing the liquid flow rate. This is mainly because correlations reported by Chung et al.4 were performed for high liquid to air flow rate ratios (6-11). The influence of a high liquid flow rate was also represented graphically. As shown in Figure 4, there is no significant change in the mass-transfer coefficient
Figure 3. Influence of the liquid flow rate on (a) the mass-transfer coefficient and (b) the heat-transfer coefficient.
with an increase of the desiccant flow rate, based on liquid to air flow rate ratios of 1.9-2.3. This showed a
Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7679 Table 3. Summary of the Resultsa independent variable author
desiccant
present study
TEG
coefficient KGa hGa
m1′
(kg/m2‚s)
1.75-2.2 + +
ma′
(kg/m2‚s)
0.94-2.2 + +
m1′/ma′
Ps (mmHg)
Pw (mmHg)
1.9-2.3 ++-
10.2-13.8 -
20.5-29.2 + +
independent variable author Chung et
al.4
desiccant
coefficient
m1′ (kg/m2‚s)
ma (kg/m2‚s)
X (kg/kg)
KGa hG a
6-11 ++-
0.1-1.2 + +
0.9-0.95 + +
TEG
a +: coefficient increases with increasing variable. -: coefficient parameter decreases with increasing variable. +-: variable has no significant effect on the coefficient.
Figure 4. Influence of the high liquid flow rate on the masstransfer coefficient.
Figure 5. Influence of the solution vapor pressure on the masstransfer coefficient.
good agreement when compared with the experimental values obtained by Chung et al.,4 but the Chung correlation (eq 4) overpredicted the mass-transfer coefficient by about 100% (see Figure 4). This is mainly because the correlation included the liquid flow rate (ml′), which did not show any dependency on the mass-transfer coefficient in his experimental data (ml′/ma′ ) 6-11). From above, it can be concluded that the effect of the liquid flow rate on the mass-transfer coefficient is limited. In this study the mass-transfer coefficient increased with the liquid flow rate, but when the liquid flow rate was increased to a limit where ml′/ma′ g 2, no significant effect on the mass-transfer coefficient was observed. Another more important design variable is the solution vapor pressure, which measures the tendency of desiccant to absorb moisture [Ps ) f(X,ts)]. An increase in the solution concentration or a decrease in its temperature reduces the liquid vapor pressure and vice versa. As shown in Figure 5, the mass-transfer coefficient decreased with an increase of the liquid vapor pressure. This reduction is due to the low driving force
Figure 6. Influence of the air water vapor pressure on the masstransfer coefficient.
when the liquid vapor pressure increases. The Chung correlation (eq 4) included the desiccant concentration as the effective variable and did not consider the effect of desiccant temperature. Therefore, eq 4 will not be valid for different ranges of desiccant temperatures. The correlation may include either the desiccant temperature and concentration or the solution vapor pressure. On the contrary, the mass-transfer coefficient increased with the inlet water vapor pressure of air (see Figure 6). Chung et al.4 ignored the effect of inlet air conditions on the mass-transfer coefficient. The results are summarized in Table 3. It can be concluded that the Chung correlation did not give good predictions for all experiments in this study. This is mainly because the dependency of the variables was not accurately shown. However, only one correlation for desiccant dehumidification using structured packing and TEG to predict the mass-transfer coefficient was found in the literature. Therefore, a new correlation containing nondimensional groups is needed that can accurately predict the mass-transfer coefficient, as a function of the design variables. This study presents two mass-transfer coefficient correlations obtained for the dehumidifier. Development of Correlations The variables found to influence the gas-phase masstransfer coefficient are the air flow rate, the liquid flow rate, the physical properties of both air and liquid, the packing volume and equivalent diameter, the molecular weight of the vapor phase, the diffusion coefficient of water in air, the air inlet vapor pressure, and the liquid vapor pressure. Two functions are suggested to correlate the mass coefficient depending on the effect of the liquid flow rate on the coefficient. From the experimental results as presented in the previous section, this de-
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Figure 7. Relationship between the experimental and predicted mass-transfer coefficients.
pendency can be divided into two intervals: (a) low liquid to air flow ratio of 1 e ml′/ma′ < 2; (b) high liquid to air flow ratio of ml′/ma′ g 2.
Figure 8. Relationship between the experimental and predicted mass-transfer coefficients for high liquid flow rates.
present study were analyzed. A functional form of the correlation was suggested as
(
ShG ) c1 1 -
Low Liquid to Gas Flow Rates The mass-transfer coefficient for a low liquid to air flow ratio, 1 e ml′/ma′ < 2, can be expressed as a function of the following parameters:
KG ) f(a,Mw,deq,Dv,Fa,dc,ma′,ml′,µa,pw,ps)
ShG )
KGaMwdeq2 Dv F a
(7)
The Sherwood number (ShG) will be a function of the following groups:
ShG ) f
(
Ps ml′ , ,Sc ,Re Pw ma′ G G
)
(8)
where
a
ml′ b ScGcReGd ma′
(9)
The term (Pw - Ps)/Pw represents the driving force between the desiccant and air. Using a computer program with curve-fitting capabilities, eq 9 will be
(6)
A dimensional analysis using the Bukingham Π method was employed to obtain the pertinent dimensionless groups. The mass-transfer coefficient is represented by the nondimensional group:
)( )
Ps Pw
(
) ( )
Ps Pw
ShG ) 6.18 × 10-6 1 -
-0.77
ml′ ma′
0.55
ScG0.333ReG1.3 (10)
As shown in Figure 7, the correlation derived in the present investigation predicts the mass-transfer coefficient values within (15%. High Liquid to Gas Flow Rates For high liquid flow rates, ml′/ma′ g 2, the masstransfer coefficient becomes independent of the ratio of liquid to gas flow rates and can be expressed as a function of the following parameters:
KG ) f(a,Mw,deq,Dv,Fa,dc,ma′,µa,pw,ps) ShG will be a function of the following groups:
(
ScG ) µa/FaDv
ShG ) f
ReG ) ma′dc/µa To obtain a curve fit, experimental data from the
)
Ps ,Sc ,Re Pw G G
(11)
A functional form of the correlation was suggested as
Table 4. Validity of Mass-Transfer Coefficient Correlations correlation
m1′/ma′
Ps/Pw
ReG
ShG ) 6.18 × 10-4(1 - P3/Pw)-0.37(ml′/ma′)0.55ScG0.333ReG13 ShG ) 0.52(1 - Ps/Pw)-0.48ScG0.333ReG0.2
0.88-1.9 2-11
0.35-0.63 0.22-0.63
19900-43000 7500-66200
remarks the experimental data provided by Chung were fitted along with the present study to expand the range of validity
Ind. Eng. Chem. Res., Vol. 43, No. 23, 2004 7681
(
ShG ) R 1 -
)
Ps b ScGcReGd Pw
(12)
Using a computer program with curve-fitting capabilities and experimental data from this study and that obtained by Chung et al.,4 eq 12 will be
(
ShG ) 0.52 1 -
)
Ps Pw
-0.48
ScG0.333ReG0.2
(13)
As shown in Figure 8, the correlation derived in the present investigation predicts the mass-transfer coefficient values within (15%. The range of validity of the above correlations is summarized in Table 4. The heat-transfer coefficient can be predicted using the correlations obtained and the Reynolds analogy9
hG ) KGMwCpa,mLe2/3
(14)
Le ) Sc/Pr
(15)
where
m′ ) superficial flow rate (molar velocity), kmol/m2‚s M ) molecular weight, kg/kmol P ) pressure, Pa Pr ) Prandtl number Re ) Reynolds number Sc ) Schmidt number Sh ) Sherwood number t ) temperature, °C X ) desiccant concentration, kg of desiccant/kg of solution yA ) water mole fraction, kmol of water/kmol of air y* ) equilibrium mole fraction, kmol of water/kmol of air Z ) tower height, m Greek Letters µ ) viscosity, N‚s/m2 F ) density, kg/m3 ω ) humidity ratio, kg of water/kg of dry air Subscripts a ) air w ) water G ) gas phase i ) inlet or interface l ) liquid s ) solution v ) vapor
Conclusions
Literature Cited
The variables found to have the largest impact on the mass-transfer coefficient of the packed dehumidifier are the air and liquid flow rates, the air vapor pressure, and the solution vapor pressure. An experimental study of evaluating the heat- and mass-transfer coefficients in an air-desiccant contact system employing TEG and cross-corrugated cellulose structured packing was carried out. It was found that high liquid flow rates have no significant effect on the mass-transfer coefficient if the desiccant to air flow rate ratio exceeded the value of 2. Two correlations for the mass-transfer coefficient have been developed for low and high liquid flow rates. The correlations predicted the mass-transfer coefficient within (15% of experimental data.
(1) Ramm, V. H. Absorption of Gases; Israel Program for Scientific Translation: Jerusalem, Israel, 1968. (2) Bravo, J. L.; Rocha, J. A.; Fair, J. R. Mass Transfer in Gauze Packings. Hydrocarbon Process. 1985, 64 (1), 91. (3) Potnis, S. V.; Lenz, T. G. Dimensionless Mass-Transfer Correlations for Packed-Bed Liquid Desiccant Contactors. Ind. Eng. Chem. Res. 1996, 35 (11), 4185. (4) Chung, T.-W.; Ghosh, T. K.; Hines, A. L.; Novosel, D. Dehumidification of Moist Air with Simultaneous Removal of Selected Indoor Pollutants by Triethylene Glycol Solutions in a Packed-Bed Absorber. Sep. Sci. Technol. 1995, 30, 1807. (5) Chung, T.-W.; Ghosh, T. K.; Hines, A. L. Comparison between Random and Structured Packings for Dehumidification of Air by Lithium Chloride Solutions in a Packed Column and Their Heat and Mass Transfer Correlations. Ind. Eng. Chem. Res. 1996, 35 (1), 192. (6) Al-Farayedhi, A. A.; Gandhidsan, P.; Al-Mutairi, M. A. Evaluation of Heat and Mass Transfer Coefficients in a GauzeType Structured Packing Air Dehumidifier Operating with Liquid Desiccant. Int. J. Refrig. 2002, 25, 330. (7) Hines, A. L.; Maddox, R. N. Mass Transfer Fundamentals and Applications; Prentice Hall: Englewood Cliffs, NJ, 1985. (8) Treybal, R. E. Mass Transfer Operations; McGraw-Hill: New York, 1981. (9) Kern, D. Q. Process Heat Ttransfer; McGraw-Hill: New York, 1995.
Nomenclature a ) surface area density, m2/m3 Cp ) specific heat, kJ/kg‚K Dv ) diffusion coefficient, m2/s deq ) equivalent diameter for structured packing, m dc ) column diameter, m h ) heat-transfer coefficient, kW/m2‚K K ) mass-transfer coefficient, kmol/m2‚s k ) thermal conductivity, W/m‚K Le ) Lewis number m ) flow rate, kg/s
Received for review March 13, 2004 Revised manuscript received June 3, 2004 Accepted August 18, 2004 IE049802J
