Comparison between Spray Towers with and without Fin Coils for Air

Apr 29, 2000 - Spray towers with and without fin coils were compared for their efficiency in air dehumidification using triethylene glycol (TEG) solut...
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Ind. Eng. Chem. Res. 2000, 39, 2076-2084

Comparison between Spray Towers with and without Fin Coils for Air Dehumidification Using Triethylene Glycol Solutions and Development of the Mass-Transfer Correlations Tsair-Wang Chung* and Honda Wu† Chemical Engineering Department, Chung-Yuan Christian University, Chungli, Taiwan 320, Taiwan

Spray towers with and without fin coils were compared for their efficiency in air dehumidification using triethylene glycol (TEG) solutions. Experiments were conducted using different air flow rates, liquid flow rates, temperature and air humidities, and aqueous TEG solution concentrations. Theoretically, an absorber with fin coils reduces the temperature of the desiccant solution, which leads to a greater amount of water vapor removal from the air. It was evident that the performance of the spray tower with fin coils was better than that of the spray tower without fin coils under similar operating conditions. Mass-transfer correlations were developed for both systems, which considered the changes in gas-liquid flow ratio, temperature, TEG concentration, and some physical properties. A dimensional analysis of the process variables was carried out using the Buckingham Pi method to obtain the dimensionless groups of the correlations. Most of the values predicted by the correlations were within (10% of the experimental data. Introduction

Table 1. Recent Studies Related to Spray Towers

Although packed towers and spray towers have been used for many years in air conditioning systems, experimental data on packed towers and spray towers were limited in the open literature, especially for spray towers. Recent studies related to spray towers are shown in Table 1. However, a comparison of spray towers with and without fin coils was rare. In 1988, Papadakis and King1,2 discussed the effects of temperature and humidity in a gas-liquid cocurrent spray tower. Both experimental results and theoretical analysis were reported in their study. Meyer et al.3 developed a theoretical model for the absorption of volatile organic components (VOCs) in a spray tower using energy and mass conservation concepts. The experimental data were consistent with their theoretical model. The spray towers were used to absorb SO2 using a lime suspension as well. Sahar and Kehat8 found that the presence of CO2 in the gas mixture reduced the absorption efficiency of SO2 from the mixture using a lime suspension. Furthermore, the spray towers were used successfully for HCl and CO2 removal. Actually, spray towers are useful in most gas separation processes. However, the dehumidification process was selected in this study. The studies using triethylene glycol (TEG) solutions in different spray tower or packed tower dehumidification systems are shown in Table 2. It was noted that both spray towers and packed towers have certain advantages and disadvantages. Because few reports related to spray towers were found in Table 2, the spray tower was selected in this study. The major disadvantage of spray towers is the solution carryover. To prevent the solution carryover, an improved “U-shape” air tunnel with eliminators was designed for the ab* To whom correspondence should be addressed. Phone: 886-3-4563171 ext. 4125. Fax: 886-3-4563171 ext. 4199. E-mail: [email protected]. † E-mail: [email protected].

investigation

author

mass-transfer model on a spray tower

Meyer et al.3 Brogren and Karlsson4 Gerbec et al.5 Papadakis and King1 Papadakis and King2 Millen and Murphy6 Taniguchi et al.7 Sahar and Kehat8

effect of temperature on a spray tower applications of a spray tower

sorber and stripper in this study. Experimental results reported by Park et al.18 showed that when the temperature of the TEG solution was higher than 37 °C, regeneration would occur. This means that lowering the temperature of the absorber or the desiccant solution would produce advantages in absorption (or dehumidification of air). Generally speaking, the lower the temperature of the absorber or the desiccant solution, the higher the mass-transfer rate. Therefore, the fin coils were set into the absorber to reduce the absorber temperature and to enhance the dehumidification rate. The water vapor pressure depression achieved by dissolving desiccant into the water is one of the important parameters for selecting the desiccant solution in dehumidification systems. Because the vapor pressure of the aqueous TEG solution is small and the flux of the water vapor is proportional to the vapor pressure difference between the moist air and the desiccant solution, an aqueous TEG solution is good for dehumidification usage. A similar concept was reported by Queiroz et al.16 TEG is not corrosive to the absorbers and does not crystallize during the dehumidification process. However, for inorganic desiccant solutions, such as lithium chloride and calcium chloride, crystallization of the desiccants occurs at concentrations higher than 40 wt % and corrosion was observed for metallic absorbers. Onda et al.19 developed a correlation for the gas-phase mass-transfer coefficient. For the system in which the solute is very soluble in the liquid, the overall gas-phase mass-transfer coefficient can be approximated by the

10.1021/ie990630d CCC: $19.00 © 2000 American Chemical Society Published on Web 04/29/2000

Ind. Eng. Chem. Res., Vol. 39, No. 6, 2000 2077 Table 2. Studies of the TEG Solution Used in Different Dehumidification Systems system

advantages

packed tower

spray tower

1. small pressure drop in liquid circuit 2. larger contact time for air

disadvantages 1. high pressure drop

investigator Lof et al.9

2. crystallization of desiccant in the line Grosso et al.10 anddeposition of dust and dirt on packings Andrew11 3. less problem with the mist and 3. periodic cleaning of packing materials Peng and Howell12 carryover of the liquid droplet into required the air stream Peng and Howell13 Chung et al.14 without fin coils 1. lower pressure drop 1. high pumping cost for the desiccant Johannsen15 solution 2. no deposition of scale or dirt in the 2. carryover of liquid droplets into the air tower stream 3. greater gas-liquid contact for high viscous liquid with fin coils 1. lower temperature of the tower 1. higher air velocity through fin coils Queiroz et al.16 required 2. higher absorption rate 2. periodic clearing of fin coils required Howell and Bantel17

Figure 1. Absorption-stripper system for this study.

local gas-phase coefficient. They suggested that their correlation was useful in most gas separation processes. Another correlation of the gas-phase mass-transfer coefficient was developed in a CaCl2-air contact system by Gandihasan et al.20 Recently, Chung et al.21 presented packed tower mass-transfer correlations for the lithium chloride-air contact system. Although the above correlations may be useful for predicting a spray tower, the error could be larger. Correlations of the masstransfer coefficient developed for the spray towers are rare in the open literature. However, these correlations are very important for spray tower design. Experimental Section A detailed schematic flow diagram of the absorberstripper system is shown in Figure 1. To enhance the dehumidification efficiency, the fin coils were set inside the absorber to reduce the temperature of the absorber or the aqueous desiccant solutions. The design of a U-shape air tunnel with eliminators in the absorber and stripper to allow the air and solution cocurrent contact reduces the carryover of the solution. In this spray tower, a liquid inlet was kept about 6 cm below the air

inlet and the liquid outlet was on the bottom of the absorber. The air inlet and outlet were on the top of both sides of the tower. The cross-sectional area of the absorber or stripper is 15 × 15 cm2. Only one nozzle was used in a spray tower. The fin coils, connected with a 3 RT refrigerator, were placed below the liquid inlet 15 cm to provide the absorber a lower temperature and better mass-transfer performance. The absorber was made of stainless steel. The stripper design was the same as the absorber. There were 16 fins in the coils, and the length ¥ width of the fin coils were 26 × 12.5 cm2. The total surface area of the fin coils was about 2.53 m2. A full-cone spray nozzle was used in the absorber or stripper. The rates of the nozzle varied from 1.5 to 3 L/min at different pressures. These corresponded to the spray angles of 55° and 70°, respectively. On the basis of the experimental flow rates and pressures, the diameters of the liquid particles from the nozzles were 290-410 µm. The absorption-stripper system can handle air flow rates from 1.94 to 3.77 kg/min and liquid flow rates from 2.17 to 3.31 kg/min. The aqueous desiccant solution (TEG) was sprayed to produce very fine particles using

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nozzles flowing through the absorber to contact with the moist air. The fin coils were employed in the absorber for the first set of experimental runs and were removed during the second set of experimental runs for comparison. During the process, the fine particles of the desiccant solutions absorbed the water vapor successfully. Regeneration of the solution was carried out in the stripper, and the regenerated solution was cooled and returned to the absorber. The heat source for the solution regeneration was an 80 L insulated water tank with a 2 kW electric heater. TEG solutions of 87-96.7 wt % were employed in this study. The solution concentration was measured using a refractometer. A Rotronic IDL 20K hygrometer with two humidity probes, which can measure the relative humidity (RH) from 0 to 100% at -20 to +60 °C, was used in this study. The accuracy of this hygrometer is about (0.2% RH. The air flow rates were controlled by transistor inverters on the 0.5 HP blowers. The liquid flow rates were measured by the rotameter, and the air flow rates were measured by the hot-wire flowmeter. The equilibrium vapor pressures of TEG solutions were obtained from A Guide to Glycols22 to calculate the mass-transfer coefficients. Results and Discussion The mass-transfer performance of this U-shape spray dehumidifier was evaluated by carrying out a series of experimental runs. The main parameters varied during the experiments included the air flow rate, the liquid flow rate, the temperature and humidity of inlet air, the average temperature of the fin coils, and the inlet desiccant solution concentration. The operating conditions are presented in Tables 3 and 4. The concentrations of the aqueous TEG solution were greater than 90 wt % for most of the dehumidification processes. In Table 3 (22) and Table 4 (25) the concentrations of the TEG solution were less than 90 wt %; therefore, the mass-transfer coefficients were significantly lower than those of the other operating conditions. No further discussion on the results with concentrations of the TEG solution lower than 90 wt % will be given in this paper. Absorption Efficiency. The efficiency of the absorber was calculated as the ratio of the actual change in moisture content of the air leaving the absorber to the maximum possible change in moisture content under a given set of operating conditions. Therefore, the absorption efficiency, e, can be expressed as

e)

Win - Wout Win - Wequ

(1)

where Win and Wout are the water contents of the inlet and outlet air streams, respectively. Wequ is the water content of the air, which is at equilibrium with the TEG solution at a particular concentration and temperature. Because the outlet temperature of the fin coils was higher than the inlet temperature, the heat was transferred from the TEG solution to the fin coils. This resulted in a reduction in the interfacial temperature between the gas and liquid phases. Therefore, the equilibrium humidity should be based on the average of the inlet and outlet temperatures of the fin coils for the system with fin coils. The liquid inlet temperature was used to estimate the equilibrium humidity for the system without fin coils. The absorption efficiencies calculated from the experimental data are presented in Tables 3 and 4. As

shown in Figure 2a, in the absorbers equipped with and without fin coils, the absorption efficiency increases as the liquid flow rate increases at a constant air flow rate. If the amount of treated air is fixed and the amount of absorbent (TEG) is increased, the column efficiency should increase. However, Figure 2c shows that the column efficiency decreases with the air flow rate increase when the liquid flow rate is kept constant. Similarly, when the amount of treated air is increased and the amount of absorbent (TEG) is fixed, the column efficiency should decrease. Generally speaking, the lower the inlet liquid temperature, the higher the masstransfer rate in the absorber. Therefore, the absorption efficiency in Figure 2b decreases as the inlet liquid temperature increases. As the air and liquid flow rates are maintained at a constant, the absorption efficiency in Figure 2d increases as the inlet air humidity increases. Furthermore, the column efficiency trends under different operating conditions in a spray tower with and without fin coils are similar. It is noted that the absorption efficiency in the spray tower with fin coils was always higher than that without fin coils, as shown in Figure 2. The column efficiencies of the absorber with fin coils were in the range from 60 to 82% and in the range from 37 to 62% for the absorber without fin coils. The differences in column efficiency between these two types of absorbers are about 20-30%. Overall Mass-Transfer Coefficient. The overall mass-transfer coefficient was derived from Geankoplis.23 For adiabatic mass transfer in a spray tower, the heatand mass-transfer control volume is shown in Figure 3. The rate of heat transfer due to latent heat and sensible heat transferred from the water vapor can be obtained as follows:

LCL dTL ) G dHy ) MBkyal0(Hi - HG) dz + hGa(Ti - TG) dz (2) Instead of using the temperature of the inlet liquid stream, the temperature TL2 in Figure 3 was assumed to be the average temperature of fin coils in the case of a spray tower with fin coils. Because the volume of each liquid droplet is very small, the temperature of the droplets is influenced by the fin coils easily. On the basis of this assumption, the formula of eq 2 was not changed in the system with fin coils. However, choosing the different TL2 could also reflect the energy removal in the liquid stream by fin coils because the temperature difference between TL1 and TL2 was changed and the amount of energy flux in the liquid stream was changed. This different choice results in the variations on the right-hand side of eq 2 in the interface temperature of Ti, the interface humidity of Hi, and the interface enthalpy of Hyi. The equilibrium humidity and the equilibrium enthalpy of the gas stream are also varied in the consideration of the overall mass-transfer coefficient in eq 8. This is the reason that in eq 1 the equilibrium humidity in the system without fin coils was determined by the temperature of the inlet liquid stream and the equilibrium humidity in the system with fin coils was determined by the average temperature of fin coils. Because of the continuous absorption-regeneration process, the concentration of the TEG solution could remain constant in each experimental run. The concentrations of the TEG solution to determine the equilibrium humidity in each experimental run were listed in Tables 3 and 4.

air flow rate (kg/min)

1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94 2.55 3.15 3.77 1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94

run no.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22

3.31 2.93 2.55 2.17 2.93 2.93 2.93 2.93 2.93 2.93 2.93 2.93 2.55 2.55 2.55 3.31 3.31 3.31 2.93 2.93 2.93 2.93

liquid flow rate (kg/min)

21.0 21.1 21.4 21.5 25.7 26.3 26.7 26.9 24.5 24.9 25.2 25.4 25.2 25.1 24.9 24.5 24.7 24.8 25.4 26.0 26.1 26.5

air inlet temp (°C) 23.6 24.2 24.2 24.1 27.5 28.4 29 30.4 27.0 28.1 28.4 28.4 27.3 26.4 26.4 26.5 26.1 25.7 27.3 27.8 27.3 27.3

air outlet temp (°C) 13.6 13.6 13.8 13.7 16.3 16.2 16.3 17.1 17.6 17.8 17.8 17.4 16.4 14.8 13.6 17.2 15.8 14.1 17.3 17.2 17.0 17.0

air inlet humidity (g of H2O/kg of dry air)

Table 3. Experimental Data of This Study (with Fin Coil)

5.8 6.3 6.9 7.6 8.1 8.5 9 10.4 7.7 8.8 9.4 9.9 7.4 7.2 7.1 6.5 6.4 6.3 8.2 9.4 10.5 11.6

air outlet humidity (g of H2O/kg of dry air) 22.7 22.6 22.3 22.4 25.1 25.8 27 30 24.3 24.7 25.0 25.2 23.7 23.5 22.8 23.3 23.1 23.6 24.2 24.7 25.1 25.0

liquid inlet temp (°C) 18.6 18.6 18.4 18.5 19.7 20.1 20.7 21.9 19.3 19.5 19.7 19.7 19.1 19 18.7 18.9 18.8 19.0 19.3 19.5 19.7 19.6

fin coils inlet temp (°C) 22.5 22.5 22.2 22.3 25.3 25.9 27.3 31.2 24.3 24.7 25.5 25.4 23.5 23.4 22.7 23.1 22.9 23.5 24.2 24.7 25.3 25.1

fin coils outlet temp (°C) 95.2 95.2 94.8 94.8 93.6 93.6 93.6 93.6 94.3 94.3 93.6 93.2 95.2 95.0 94.8 94.3 94.3 95.2 93.5 91.5 90.0 88.0

TEG conc (% wt) 3.6 3.6 3.5 3.5 5.3 5.4 5.8 6.6 4.7 4.8 4.9 5.0 3.9 3.8 3.6 4.1 4.1 3.9 5.0 6.5 7.9 8.4

equilibrium humidity (g of H2O/kg of dry air)

70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70

spray tower height (cm)

0.78 0.73 0.67 0.60 0.74 0.72 0.70 0.64 0.77 0.69 0.65 0.60 0.72 0.69 0.65 0.82 0.80 0.76 0.740 0.726 0.710 0.628

efficiency (%)

0.077 0.064 0.055 0.046 0.069 0.063 0.060 0.053 0.074 0.076 0.084 0.089 0.062 0.060 0.050 0.082 0.079 0.073 0.067 0.063 0.062 0.051

masstransfer coefficient (kmol/m3‚ s‚[mole fraction])

0.65 0.79 0.92 1.09 0.73 0.8 0.84 0.95 0.68 0.86 0.96 1.09 0.81 0.84 1.00 0.61 0.63 0.69 0.74 0.79 0.80 0.97

HTU (m)

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Figure 2. Effect of various operating conditions on the absorption efficiencies. Table 4. Experimental Data of This Study (without Fin Coil) massair liquid air air air inlet air outlet liquid equilibrium spray transfer flow humidity inlet TEG tower coefficient flow inlet outlet humidity humidity run rate rate temp temp (g of H2O/kg (g of H2O/kg temp conc (g of H2O/kg height efficiency (kmol/m3‚s‚ HTU no. (kg/min) (kg/min) (°C) (°C) of dry air) of dry air) (°C) (% wt) of dry air) (cm) (%) [mole fraction]) (m) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94 2.55 3.15 3.77 1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94 1.94

3.31 2.93 2.55 2.17 2.93 2.93 2.93 2.93 2.93 2.93 2.93 2.93 2.55 2.55 2.55 2.93 2.93 2.93 3.31 3.31 3.31 2.93 2.93 2.93 2.93

19.8 20.1 20.3 20.4 21.8 22.3 22.6 23.2 19.0 19.5 19.7 20.0 23.7 23.6 20.3 23.4 23.3 20.1 22.8 22.9 19.8 15.3 15.8 16.0 15.9

21.5 21.7 21.8 21.6 23.4 24.6 26.2 27.7 21.2 22.0 22.3 22.5 26.3 25.2 21.8 26.1 24.9 21.7 25.2 24.5 21.5 18.4 19.3 19.1 18.8

10.4 10.2 10.1 9.9 11.8 11.9 11.8 12.1 10.9 10.9 11.0 11.1 17.3 12.5 10.1 16.8 12.4 10.2 16.6 12.7 10.4 11.2 11.4 11.3 11.3

5.9 6.0 6.2 6.8 6.9 7.3 8.1 8.8 6.4 6.5 6.9 7.1 10.0 7.6 6.2 9.0 7.2 6.0 8.4 6.9 5.9 6.7 8.1 9.2 10.0

20.8 20.9 20.8 20.5 21.4 23.6 26.7 29.2 20.2 20.7 20.9 21.3 23.1 22.4 20.8 23.0 22.5 20.9 22.6 22.3 20.8 20.6 21.2 21.1 20.9

Because the ratio of the heat- and mass-transfer coefficients is approximately equal to the humid heat for a water vapor-air mixture, i.e.

hGa = Cs MBkya

(3)

Equation 2 becomes

G dHy ) MBkya dz [(CsTi + l0Hi) - (CsTG + l0HG)] (4) From the definition of the total enthalpy of an air-water vapor mixture,

97.5 97.5 97.5 97.5 96.7 96.7 96.7 96.7 97.0 97.0 97.0 97.0 96.3 97.0 97.5 96.3 97.0 97.5 96.3 97.0 97.5 97.0 94.3 90.3 86.0

1.6 1.6 1.6 1.5 2.5 2.9 3.6 4.1 1.5 1.6 1.6 1.7 3.4 1.9 1.6 3.4 1.9 1.6 3.3 1.8 1.6 1.5 4.4 6.9 8.4

70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70 70

0.51 0.49 0.46 0.37 0.53 0.51 0.45 0.41 0.48 0.47 0.44 0.43 0.53 0.46 0.46 0.58 0.50 0.49 0.62 0.53 0.51 0.46 0.47 0.48 0.45

0.056 0.052 0.047 0.035 0.052 0.050 0.037 0.027 0.053 0.065 0.070 0.081 0.049 0.047 0.047 0.057 0.054 0.052 0.065 0.061 0.056 0.053 0.043 0.037 0.014

Hy ) Cs(T - T0) + l0H

1.13 1.21 1.35 1.81 1.22 1.27 1.72 2.32 1.21 1.29 1.49 1.52 1.29 1.35 1.35 1.11 1.19 1.21 0.98 1.04 1.13 1.21 1.49 1.73 4.40

(5)

Equation 4 can be written as

G dHy ) MBkya dz (Hyi - Hy)

(6)

When rearranging eq 6 is rearranged, the average masstransfer coefficient becomes

(kya)avg )

G M Bz

∫HH

y2

y1

dHy Hyi - Hy

(7)

For the overall mass-transfer coefficient, eq 7 can be written as

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Hog )

Figure 3. Control volume of heat and mass transfer for this study.

(Kya)avg )

G MBz

∫HH

y2

y1

dHy Hy* - Hy

(8)

where Hy* is the equilibrium total enthalpy of an airwater vapor mixture and is determined by the equilibrium line in the temperature-enthalpy diagram of the spray tower. As expected, the effects of various operating conditions on the overall mass-transfer coefficients shown in Figure 4 are similar to the effects on the absorption efficiency in Figure 2 except for the effect of the air flow rate. An increase in the overall masstransfer coefficient with increasing air flow rate is observed in Figure 4c. This trend is different from that shown in Figure 2c. Because the molar flux of the system is proportional to the air flow rate, the masstransfer coefficient is proportional to the air flow rate. The overall mass-transfer coefficients in the spray tower with and without fin coils are in the ranges from 0.046 to 0.089 kgmol/m3‚s and from 0.014 to 0.081 kgmol/m3‚s, respectively. It is shown in Figure 4 that the overall mass-transfer coefficients in the absorber with fin coils are higher than that without fin coils. As shown in Tables 3 and 4, the overall mass-transfer coefficients reduce significantly as the concentration of the TEG solution less than 90 wt %. Height of a Transfer Unit. Most experimental data on packed towers are generally given in terms of the height of a transfer unit (HTU) rather than the masstransfer coefficients, because the HTU is less dependent on liquid or gas flow rates. This provides a means to evaluate the system performance under different operating conditions. Therefore, the HTU in the spray tower was calculated in comparison with the HTU in the packed tower. The definition of the HTU is

G MB(Kya)avg

(9)

From this definition, the effect of various operating conditions on the HTU shown in Figure 5 should be contrary to the effect on the overall mass-transfer coefficient except for the effect of air flow rate. An increase in the HTU with increasing air flow rate is observed in Figure 5c. For the concentrations of the TEG solution greater than 90 wt %, the HTU in the spray tower with and without fin coils are in the ranges from 0.61 to 1.09 and from 0.98 to 2.32 m, respectively. As shown in Tables 3 (8) and 4 (8), when the inlet temperature of the TEG solution is increased to about 30 °C, the mass-transfer performance reduced markedly. The result is similar to the report presented by Park et al.18 When the temperature of the TEG solution is higher than 37 °C, regeneration will occur at the absorber. This represents that the absorption capacity will decrease. Also, the HTU in the spray tower with fin coils is always smaller than that without fin coils in Figure 5. This means that the mass-transfer performance in the spray tower with fin coils is better. The HTU values in this study are higher than those reported in the literature for packed towers operating with similar solution concentrations. However, there was no flooding consideration in the spray towers as which exists in the operation of countercurrent packed towers. Packed towers are usually operated at 50-80% flooding. This results in a better mass-transfer performance. However, spray and packed towers have certain advantages and disadvantages as shown in Table 2. Predictions of the Mass-Transfer Coefficient in Spray Towers with and without Fin Coils. The mass-transfer coefficients calculated from eq 8 were correlated in terms of the process variables by employing a dimensional analysis. Variables that affect the gasphase mass-transfer coefficient include air and liquid flow rates, the physical properties of both the air and the liquid, the molecular weight of the vapor phase, the diffusion coefficient of water vapor in air, and the vapor pressure of the TEG solution (PTEG). In functional form the mass-transfer coefficient can be expressed as

Kya ) f(M, dc, µG, FG, PTEG/Ptotal, L, G, DG)

(10)

The above variables are arranged into pertinent dimensionless groups using the Buckingham Pi theory. The mass-transfer correlation obtained from the dimensional analysis is given as

( )()

PTEG KyaMdc2 ) aReGbScGc DGµG Ptotal

d

L G

e

(11)

where PTEG/Ptotal is defined as the fraction of the vapor pressure of the desiccant solution to the total pressure of the system. The flux of water vapor from the moist air to the desiccant solution is proportional to the difference between the vapor pressure of the solution and the vapor pressure of the water in the moist air. Therefore, the mass-transfer coefficient can be determined using this pressure difference. The mass-transfer coefficients are correlated in terms of vapor pressure and the process variables, as shown in eq 11. The constants a, b, c, d, and e were obtained by nonlinear regression of the experimental data. Correlations for the absorber with and without fin coils are given as follows:

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Figure 4. Effect of various operating conditions on the overall mass-transfer coefficients.

Figure 5. Comparison between predicted and experimental mass-transfer coefficients for spray towers with and without fin coils.

mass-transfer correlation for the absorber with fin coils

( ) ()

PTEG KyaMdc2 ) 4.0 × 10-5ReG1.73ScG0.33 DGFG Ptotal

-0.5

L G

1.15

(12)

mass-transfer correlation for the absorber without fin coils

( ) ()

KyaMdc2 PTEG ) 2.0 × 10-5ReG1.74ScG0.33 DGFG Ptotal

-0.51

L G

correlations. As shown in Figure 6, the correlations for the mass-transfer coefficient predict data within (10% and the average error is about 8%. Because the vapor pressure of the TEG solution was used to predict the mass-transfer coefficient in eqs 12 and 13, it could be extended to the systems of different desiccant solutions by using the vapor pressures of these desiccant solutions. Further experiments will be conducted into the spray towers using different desiccant solutions.

1.05

(13)

The above equations have been tested successfully for air flow rates from 1.94 to 3.77 kg/min, liquid flow rates from 2.17 to 3.31 kg/min, air temperatures from 20 to 30 °C, and liquid temperatures from 20 to 30 °C. The mass-transfer coefficients calculated from the experimental data using eq 8 were employed to obtain the values of constant and exponents for the above

Conclusions A U-shape spray tower with or without fin coils in the absorber-stripper system was designed and tested successfully for the dehumidification of air. For a given height of a spray tower, the absorption efficiency increases as either the air flow rate decreases or the liquid flow rate increases. The overall mass-transfer coefficients increase with increasing air and liquid flow rates. As expected, lowering the liquid temperature improves the column efficiency significantly. Because

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Figure 6. Comparison between predicted and experimental masstransfer coefficients for spray tower with and without fin coils.

fin coils reduce the temperature of the working solution, the mass-transfer performance for the absorber with fin coils should be better than that without fin coils, and on the basis of this study, the differences of the column efficiency in between then are about 20%. There exist many discussions on mass-transfer correlations for packed towers; however, correlations for spray towers are limited in the open literature. Therefore, correlations of the gas-phase overall volumetric mass-transfer coefficient were developed in this study. Correlations for the absorber with and without fin coils not only provide a prediction of the mass-transfer coefficients but also represent the importance of the vapor pressure parameter in the dehumidification processes. The vapor pressure of the work solution represents the composition, temperature, and concentration of the solutions. Compared to the other correlations, this parameter is more direct and simple. This is the first time that the vapor pressure of a desiccant solution was considered as a parameter in the mass-transfer correlation, and this correlation fitted the experimental data very well. Acknowledgment This work is supported by the National Science Council of the Republic of China under Grant NSC882214-E-033-004. Nomenclature a ) surface area-to-volume ratio of the packing material, m2/m3 CL ) heat capacity of liquid, kJ/kg of liquid‚K CS ) humid heat of air-water vapor mixture, kJ/kg of dry air‚K dc ) column diameter, m DG ) diffusion coefficient for the key component, m2/s G ) superficial air mass velocity, kg/m2‚s H ) humidity of air, kg of water/kg of dry air HG ) humidity of gas in the bulk gas phase, kg water/kg dry air

hGa ) volumetric heat-transfer coefficient in the gas, W/m3‚ K Hi ) humidity of the gas at the interface, kg of water/kg of dry air HOG ) height of an overall gas enthalpy transfer unit, m Hy ) enthalpy of an air-water vapor mixture, J/kg of dry air Hy1 ) enthalpy of an air-water vapor mixture at the inlet of the absorber, J/kg of dry air Hy2 ) enthalpy of an air-water vapor mixture at the outlet of the absorber, J/kg of dry air Hyi ) enthalpy of an air-water vapor mixture at the interface, J/kg of dry air Kya ) overall volumetric mass-transfer coefficient, kmol/ m3‚s‚[mole fraction] kya ) volumetric mass-transfer coefficient, kmol/m3‚s‚[mole fraction] L ) superficial liquid mass velocity, kg/m2‚s M ) molecular weight of the transferred component, kg/ kgmol MB ) molecular weight of air, kg/kmol P ) vapor pressure, Pa Ptotal ) total pressure at 25 °C, Pa ReG ) Reynolds number, µGVdc/µG ScG ) Schmidt number, µG/DGFG TG ) gas temperature, K Ti ) interface temperature, K V ) gas flow rate through the column, m/s Wequ ) minimum possible water content at the outlet of absorber, kg of water/kg of dry air Win ) water content of air at the inlet of absorber, kg of water/kg of dry air Wout ) water content of air at the outlet of absorber, kg of water/kg of dry air Z ) height of the spray tower, m e ) absorption efficiency of the spray tower, % l0 ) latent heat of water, J/kg of water µG ) viscosity of the gas, kg/m‚s FG ) density of the gas, kg/m3 Subscripts G ) gas phase i ) interface 0 ) at 0 °C or 273 K TEG ) triethylene glycol

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Received for review August 19, 1999 Revised manuscript received March 13, 2000 Accepted March 16, 2000 IE990630D