Ind. Eng. Chem. Res. 1996, 35, 4185-4193
4185
Dimensionless Mass-Transfer Correlations for Packed-Bed Liquid-Desiccant Contactors Shailesh V. Potnis† and Terry G. Lenz* Chemical and Bioresource Engineering, Colorado State University, Fort Collins, Colorado 80523
Random and structured packings were studied with varying bed depths in the regenerator and the dehumidifier of a solar-assisted liquid-desiccant system. The slopes of the log-log plots of mass-transfer rate vs solution flow rate were found to be close to 0.8, which indicated that the conditions for the liquid phase were turbulent for the operating conditions in both contactors. The small intercepts obtained for the Wilson plots indicated that the gas-phase mass-transfer resistance was negligible compared to the liquid-phase mass-transfer resistance. Liquid-phase mass-transfer coefficients for the packed bed alone were obtained by separating the contributions of the other mass-transfer regions in the contactors. The random packing mass transfer coefficients varied from 0.48 to 2 mol/(s m2), while the double-layer, structured packing masstransfer coefficients varied from 0.018 to 0.035 mol/(s m2). These mass-transfer coefficients were converted into a dimensionless form, utilizing experimentally obtained diffusivity values. Introduction Desiccant systems utilize the moisture affinity of a desiccant material to control the humidity of the air used for a process or for comfort purposes. Commonly used desiccants include aqueous lithium chloride or lithium bromide solution and zeolites. The moisture content of these materials approaches saturation as they remove moisture from the incoming air. They can then be regenerated to restore their capacity to remove moisture by heating them in the presence of relatively dry air. Desiccant systems are particularly useful for air conditioning applications where the latent heat load is large compared to the sensible heat load. Energy savings, relative-to-conventional vapor compression systems, of up to 40% can be achieved by using a desiccantassisted air conditioning system (Griffiths, 1987). Also, the regeneration temperatures required by desiccants, such as lithium bromide solution, usually vary between 60 and 75 °C, which can easily be obtained using flat plate solar collectors. Thus, fossil fuel energy savings can be increased further if solar energy is utilized for the regeneration of the desiccant. The major process components of interest regarding mass transfer for such a system are the regenerator and the dehumidifier. The mass-transfer rates achieved in these units determine the capacity of these systems. However, the process of mass transfer in these contactors is not well understood, and as a result, the measured performance of many absorption chillers and heat pumps, using similar components, is smaller than expected (Wahlig, 1993). These contactors are usually designed assuming air-solution contact to be the same as air-water contact (Khan and Ball, 1992). Lo¨f et al. (1984) studied reconcentration of lithium chloride solution in an open-cycle absorption chiller by passing solarheated air through a packed column. They found that mass-transfer coefficients show considerable variability and generally lower values than would be predicted by use of the heat/mass-transfer ratio for air and pure * Corresponding author. Phone: (970) 491-2540. Fax: (970) 491-7369. † Present address: Energy Concepts Co., 627 Ridgely Ave., Annapolis, MD 21401.
S0888-5885(96)00212-6 CCC: $12.00
water. This indicates that mass transfer in air-solution contacting is not the same as in air-water contacting. Gandhidasan et al. calculated (1986) the coefficients and analyzed (1987) the processes of heat and mass transfer in a calcium chloride-based liquid-desiccant system. They assumed the heat-transfer resistance of the liquid phase to be negligible and found that the desiccant-air system has a mass-transfer resistance in the liquid phase unlike that for the air-water system. Thus, it is necessary to calculate the liquid-phase masstransfer resistance to obtain the overall mass-transfer resistance, which ultimately determines the air and solution flow rates, auxiliary power input, contactor size, solar collector area, and performance of the system. A better understanding of the process of mass transfer in these contactors can thus significantly improve the contactor efficiency and suggest ways to reduce the initial and operating costs. The present research probes the variation of masstransfer rate with solution flow rate to obtain the relative magnitudes of mass-transfer resistances offered by each phase. Packed-bed liquid-phase mass-transfer coefficients were obtained from the contactor liquidphase mass-transfer coefficients by separating contributions of other mass-transfer regions. These masstransfer coefficients were then converted into a dimensionless form using the experimentally measured diffusivity values. Experimental Apparatus Figure 1 shows a schematic diagram of the experimental system employed in these studies. The dehumidifier is an 81-cm-diameter, 200-cm high fiberglass tower. The solution entering the dehumidifier is distributed on top of a packed bed using a manifold of three spray nozzles. An electric steam humidifier permits variable moisture addition to the air before it enters the dehumidifier. A mist eliminator is used to minimize the liquid entrainment before the air exits the dehumidifier. In a decoupled mode, the solution exiting the dehumidifier is cooled in a cooling unit before it is sent back to the top of the dehumidifier. In coupled mode, this solution is sent to the regenerator through the economizer where it is heated by heat exchange with the hot solution from the regenerator. The regenerator is © 1996 American Chemical Society
4186 Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996
Figure 1. Schematic diagram of the solar-assisted liquid-desiccant system.
Figure 2. Comparison of mass-transfer rates obtained using different packings in the dehumidifier.
similar in dimension and construction to the dehumidifier unit. Hot air to the regenerator is provided by a flat-plate solar collector array having a total area of 55.7 m2. Auxiliary heat is also supplied by three electric strip heaters to increase the air temperature and maintain a high regeneration rate under varying ambient conditions. The hot solution exiting the regenerator is cooled in the economizer by exchanging heat with the solution from the dehumidifier. After passing through the economizer, the warm solution is further cooled by water in a four-pass shell-and-tube heat exchanger. A cooling tower with a capacity of 28 kW supplies water to the heat exchanger. Mass-Transfer-Rate Studies Initially, energy balance studies were carried out to identify the reliably measured parameters and to minimize the errors. The experimental system employed provided energy balance data having a maximum error of 10% in the decoupled mode (Lenz and Potnis, 1991). Precautions suggested by these studies were observed during subsequent experiments conducted to obtain the relative magnitudes of mass-transfer resistances. The mass-transfer rate in the packed-bed contactors (the dehumidifier and the regenerator) depends on various parameters such as air flow rate, solution concentration, height of the packed bed, air and solution inlet temperatures, and solution flow rate. All these parameters except the solution flow rate were maintained constant (with a solution concentration of 51% by weight) in a decoupled mode, for each contactor, to study the dependency of the mass-transfer rate on solution flow rate. Packed beds of random packing (Polypropylene Tripack), with height 30 cm, and structured packing (Munters CELDEK), with heights 30 and 55 cm, were used to study the variation of mass-transfer rates with types and heights of packings. The masstransfer rate between the two phases was obtained from the rate of enthalpy change associated with the phase change of water. A log-log plot of Sherwood number vs Reynolds number is generally employed to correlate various flow parameters. However, since all parameters except the solution flow rate were kept constant, a plot of masstransfer rate vs solution flow rate was constructed to represent the conventional plot. Figures 2 and 3 show that these plots are straight lines with slopes near 0.8. This indicates that the dehumidifier and the regenerator were operated under well-mixed, near-turbulent conditions for liquid flow for all the variations of the packed
Figure 3. Comparison of mass-transfer rates obtained using different packings in the regenerator.
bed. However, for the random packed bed, the evaporation rates in the regenerator were found to be approximately 300% and 130% greater and the condensation rates in the dehumidifier were found to be approximately 60% and 45% greater than the packed beds of structured packing with heights 30 and 55 cm, respectively. Considering the experimental error, there was no significant difference between the condensation rates offered by the structured packed beds of heights 55 and 30 cm. Therefore, there was no advantage associated with the additional height of structured packing observed for the dehumidifier. Figures 4 and 5 show Wilson plots constructed using the mass-transfer-rate data. The small magnitudes of the intercepts obtained for these plots indicate that the gas-phase mass-transfer resistance is negligible compared to the liquid-phase mass-transfer resistance for these contact operations. Therefore, a dimensionless mass-transfer correlation to estimate the liquid-phase mass-transfer coefficient would be a very useful tool for the design of these systems. However, to convert the data obtained from the mass transfer experiments into dimensionless form, it is necessary to know the diffusivity of water in lithium bromide solution. Diffusivity Studies A diffusivity apparatus was developed by suitably combining the twin-bulb method and the diaphragm cell method (Potnis et al., 1995). The diffusivity of water in aqueous lithium bromide solutions was measured,
Ind. Eng. Chem. Res., Vol. 35, No. 11, 1996 4187
contactor is small (0.2%),
Nw ) Kxa(x - x*av)SZ
Figure 4. Wilson plots for the dehumidifier.
Figure 5. Wilson plots for the regenerator.
using tritiated water as the tracer, for concentrations ranging from 0.5 to 11 M. The value of diffusivity was found to increase from 13.2 × 10-10 to 16.7 × 10-10 m2/s for the concentration variation of 0.5 to 4 M and then to decrease to a steady value of approximately 6.5 × 10-10 m2/s from 8 to 11 M. Packed-Bed Mass-Transfer Coefficients Overall mass-transfer coefficients for the contactors were calculated using the data obtained from the masstransfer experiments. These mass-transfer coefficients are composite coefficients for the packing, the spray droplets, and the film flowing on the wall of the contactor. The coefficients for the packing alone were obtained from the composite coefficients for the contactors by separating the other contributions. Contactor Overall Mass-Transfer Coefficients. The Wilson plots obtained from the mass-transfer studies (Figures 4 and 5) have indicated that the gasphase mass-transfer resistance is negligible for these contact operations. Therefore,
kx ) Kx
xi ) x*
(1)
The height of a contactor can be expressed as
Z)
L dx ∫K (x - x*)aS(1 - x)
(2)
x
Since the change of solution mole fraction across the
(3)
The values of inlet humidities were obtained from a knowledge of dew points. The values of the outlet humidities were obtained using the mass transfer rates. The values of x*inlet and x*outlet were obtained from these humidities using an equilibrium chart for aqueous lithium bromide solutions. The volumetric masstransfer coefficients (Kxa) were then evaluated using the mass-transfer rates (Nw) obtained earlier. Processes Influencing the Overall Mass Transfer. The process of mass transfer in the contactors occurs in three separate regions: a first region of small droplets created by the spray nozzles, a second region of thin films of solution flowing on the packing surface, and a third region of the film flowing down the wall of the contactor. To obtain the mass-transfer rate due to the packing alone, it was necessary to separate the mass-transfer contributions due to the other two regions. In order to estimate the magnitude of the masstransfer contribution for the wall film, a thin plastic ring was mounted at the bottom of the regenerator, just above the pan. A tight fit was provided so that the ring collected all the liquid flowing down the wall. The solution flow rate on the wall was determined by measuring the liquid collected by the ring in a known time duration, using an external valve connected to the ring. To allow for a maximum amount of liquid to flow toward the wall, the measurements were done in the absence of any packing. It was found that the solution flow rates on the wall were only about 10% of the total solution flow rates. This value was close to the other experimental errors involved. Also, in the presence of packing, the amount of solution flowing on the wall would be further reduced due to the repeated redistribution of liquid over the packing surface at the contact points of the wall and the packing. Therefore, the masstransfer contributions due to the films flowing down the walls of the contactors were neglected. To separate the contribution of the region of small droplets created by the spray nozzles, mass-transfer studies were conducted using only spray nozzles in both of the contactors (no packing). The experimental and analytical procedure followed for these studies was similar to the procedure followed for the mass transfer studies with packings, described earlier. Packing Kxa. Since the mass-transfer contribution of the solution film on the wall is negligible, the total mass-transfer rate in a contactor can be expressed as
Nw ) (Kxa)contactor(x - x*av)contactorSZt ) (Kxa)spray(x - x*av)spraySZs + (Kxa)packing(x - x*av)packingSZp
(4)
Since the concentration change of solution across the tower was very small (0.2 wt %), x was taken to be constant. The change of x* due to spray alone was found to be very small (
