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Absorption of water vapour into falling films of aqueous lithium bromide
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UTTERWORTH E I N E M A
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0140-7007(95)00007-0
Int. J. Rel?ig. VoL 18, No. 7, pp486 494, 1995 Copyright ~i' 1995 Elsevier Science Ltd and IIR Printed in Great Britain. All rights reserved 0140-7007'95/$ I 0.00 -~ .00
Absorption of water vapour into falling films of aqueous lithium bromide K. J. Kim* and N. S. Berman Department of Chemical, Bio and Materials Engineering, Arizona State University, Tempe, AZ 85287, USA
D. S. C. Chau and B. D. Wood Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287, USA Received 3 November 1994; revised 20 M a r c h 1995
In this study, experiments have been performed for water vapour absorption into 50 and 60 mass% aqueous lithium bromide solution films flowing down a vertical surface to investigate the effects of liquid diffusivity values, molecular properties of the concentrated solutions and non-absorbable gases. The experimental results for wavy films over a film Reynolds number range of 15-90 indicate larger dimensionless mass transfer rates than for strictly laminar flow when the diffusivity of water in a concentrated lithium bromide solution is less than that in a dilute solution. The complete set of results shows that the physical property data for lithium bromide solutions including the diffusivities measured by Kashiwagi 1 are sufficient to explain mass transfer behaviour. (Keywords: wavy films; absorption; lithium bromide; vertical failing film)
Absorption de vapeur d'eau dand des films tombants de solution de bromure de lithium Dans cette ktude, on a effectuk des expkriences sur l'absorption de vapeur d'eau dans une solution aqueuse de bromure de lithium (50% 5 60% en masse) en forme de film en kcoulement sur une surface verticale, qfin dWudier les effets des gaz non absorbbs, des valeurs de diffusivit~ de liquide, ainsi que les propri~tOs moleculaires des solutions concentr~es. Les rksultats exp&imentaux pour les films ondulks sur une 9amme de nombres de Reynolds allant de 15 5 90 laissent supposer que les taux sans dimension de transfert massique sont plus importants que clans le cas d'un kcoulement strictment laminaire, lorsque le diffusivitb de l'eau dans une solution concentrke de bromure de lithium est moins importante que celle d'une solution diluke. L'ensemble des rksultats montre que les donnkes sur les propriktks physiques des solutions de bromure de lithium, y compris les diffusivit~s mesur~es par Kashiwag, sont suffisantes pour expliquer le comportement du transfert de masse.) (Mots
¢l/~s:absorption; bromure de lithium; film tombant vertical; r6gime turbulent; r6gime laminaire) In this paper we report results of experimental studies of water vapour absorption into 50 and 60 mass% lithium bromide in a falling-film apparatus. We examine the effect of changes in non-absorbables, length of absorber and overall driving potential. The interpretation of results is highly dependent on the value of the diffusivity of water in these concentrated solutions and we will discuss this problem in the paper. The fluid dynamics of the liquid film is governed by the film Reynolds number
Gas absorption into a falling liquid film is a classical problem with applications in absorption heat pumps. A liquid absorbent (or desiccant) has an affinity for an absorbate (normally a vapour). Mass transfer is due to the difference between the absorbate pressure and the vapour pressure of the absorbent at the given temperature and concentration. In the case of an aqueous lithium bromide solution that has 60 m a s s % concentration and 40 °C temperature introduced into an absorber with the pressure of water vapour set by an evaporator at 7 °C, there is 2.18 m m H g of driving potential based on the overall gas phase or a 3% differential concentration based on the liquid phase. Once absorption starts, the vapour pressure of absorbent at the interface is increased owing to the increased temperature and the decreased concentration of lithium bromide. Experimentally, it is impossible to remove non-absorbable gases completely so the driving potential at the liquid gas interface can be further reduced.
4F
Ref = - -
~t
(1)
where F is the mass flowrate per unit perimeter and F is the dynamic viscosity. Sherwood and Pigford z categorized the flow regimes as: laminar without rippling (Ref < 4-25); laminar with rippling (the wavy regime, 4-25 < Ref < 10002000); and turbulent flow (Ref> 1000-2000). Empirical or semi-empirical approaches are essential in order to develop absorber relationships that can be used for design in the wavy regime. For a lithium bromide-water system the Lewis
* Author to whom correspondence should be addressed. Present address is Center for Environmental Energy Engineering (CEEE), University of Maryland, College Park, M D 20742, USA
486
Absorption of water vapour into falling films of aqueous lithium bromide:
487
Nomenclature A C Cair D Eff g hm L Le LMPD M P Pv
Ref Sh T~i. t
x Yo
Contact area (m 2) Solution concentration (mass%) Air concentration (vol%) Mass diffusivity (m 2 s-1) Absorption effectiveness Gravitational acceleration (m s-2) Mass transfer coefficient (m s - l ) Absorber length (m) Lewis number Logarithmic mean concentration difference of pressure difference (mmHg) Mass flowrate (kg s-1) Pressure (mmHg) Absorber pressure (mmHg or mbar) Reynolds number Sherwood number Cooling water temperature (°C) Exposure time (s)
number Le, the ratio of thermal diffusivity to mass diffusivity, is on the order of 10 2. Thus a slowly developed diffusion boundary layer appears relative to a thermal boundary layer. In the laminar regime, molecular diffusion in the liquid phase governs the absorption process. One way to overcome the weak mass transfer rate is to use wavy motions caused by hydrodynamic instabilities so as to break the slowly developed diffusion boundary layer; then enhanced mixing in the liquid phase can increase the mass transfer rate significantly. Mass transfer enhancement (usually a 50-200% increase in mass transfer coefficient compared with that of a smooth laminar flow) by wavy motion has been demonstrated experimentally3 6. Vertical falling-film absorption with the lithium bromide-water system has been studied by a limited number of investigators. Nakoryakov et al. v tested the following parameters: a film Reynolds number of 80-800, 58-60 mass% lithium bromide inlet solution concentration, 7 15 mmHg absorber pressure. A comparison between the vertical tube absorber and horizontal tube absorber was experimentally investigated by Burdukov et al. 8. The lithium chloride--water absorption system was studied by Ameel 9, Yang 1° and Yang and Wood 11. None of the previous experimental studies compared the results with short- and long-time laminar flow mass transfer in a falling film, or developed a universal correlation that would fit all of the data. Sherwood et al. ~2 give mass transfer correlations for gas absorption into a falling liquid film process where the liquid is a steady laminar flow with constant concentration at the gas liquid interface. For short contact time the penetration theory produces a dimensionless mass transfer coefficient
hmpx -1.695x//3 F f~
(2)
where h m is the mass transfer coefficient, p is the liquid density, x is the distance in the flow direction, and F is
Distance in flow direction (m) Mean film thickness (m)
Greek letters /3 Dimensionless quantity defined in Equation (3) Mass flowrate per unit perimeter (kg s-1 F m ~) Dynamic viscosity (kg s-1 m - l ) ~t Kinematic viscosity (m 2 s-1) V Liquid density (kg m-3) P Subscripts Absorption abs Equilibrium eq f Film sin Solution inlet sout Solution outlet 1,2 Inlet, outlet of the absorber
the liquid feed. The dimensionless quantity fl is given by
Dt /4\~ f y \~ = 2/-/Dx/~/ fl= .~o \3J \v R e f J
(3)
where D is the mass diffusivity, t is the exposure time, yo is the mean film thickness, g is gravitational acceleration, and v is the kinematic viscosity. The left side of Equation (2) can also be expressed in terms of the Sherwood number Sh, defined as
hm Sh-
D
(4)
Considering the velocity gradient as a parabola (large value of /3), the long contact time solution can be approximated as
hmpx
--
F
=0.24+ 5.1fl
(5)
For gas absorption in a vertical column, where the liquid is a smooth film, Equations (2) and (4) can be used to draw a baseline for the cases of both short and long contact time. For a higher Ref, the film becomes wavy; then mass transfer will be increased owing to improved mixing. When non-absorbables are present in the gas phase, the use of the overall driving force to determine the experimental mass transfer coefficient could give hmpx/F greater or less than that determined from Equation (2) and (5), depending on the diffusivity in the liquid phase. Yang and Chen 13 show that for a liquid diffusivity about the same as in pure water, the mass transfer is drastically reduced when only 0.01% air is present in the gas phase. Concentrated lithium salt solutions contain very little free water because the lithium ion coordinates with four water molecules 14 16. The movement of water molecules
K.J. Kim et al.
488
is restricted, leading to a lower mass diffusivity compared with water in low salt concentrations. Three recent studies report diffusivities as shown in Figure 1. Enderby iv measured a local diffusivity using nuclear magnetic resonance (NMR) spectroscopy, and Kashiwagi 1 obtained concentration profiles in a stagnant absorption experiment using holographic inteferometry. Kashiwagi's results are a factor of 3 lower for 60 mass% lithium bromide than typical diffusivities used previously in absorption calculations 18.
Experimental The main components of the system are an absorber unit, an evaporator, a cooling water system, a circulation system, a vacuum-generating system, and measuring devices. The system operates in a batch mode. A schematic diagram of the system is shown in Figure 2. Details can be found in ref. 19. The absorber has two concentric tubes: an inner stainless steel tube of outside diameter 38.1 mm and length 1.83 m, and an outer Pyrex tube of inside diameter 148 mm and length 1.22 m. The absorbent solution flows down the outside of the inner tube. The outer Pyrex tube serves to maintain the vacuum pressure and to facilitate flow observation. The absorption of water vapour takes place at the outer wetted surface of the inner stainless tube, and the heat of absorption is removed by the upward flow of cooling water inside the stainless tube. The inner tube has an inside diameter of 34.9 mm. The outer Pyrex tube with 169 mm outside diameter is made from a KIMAX drainline pipe. Two brass end-plates are mounted on the ends of the outer tube using four threaded steel rods. Rubber ring seals are attached to the place between the ends and glass tube. The solution distributor, made of Plexiglass, is mounted on the upper plate. The distributor can hold approximately 1.051 of absorbent solution. The absorbent solution is introduced through the solution inlet, stays more than 20 s in the solution distributor so as to eliminate possible disturbances, and flows into the annular space between the head and the stainless steel tube. The weak solution is collected at the bottom part of the absorber by a funnel, and flows into a Plexiglass collector. The effective absorber length can be varied by moving the collector and funnel up towards the 5
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Figure 1 Diffusivities of water for lithium salts solutions Figure 1
Diffi~sivitds de l'eau les solutions de sels de lithium
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distributor. The maximum absorber length available is 85 cm. In order to supply water vapour into the absorber unit, a 2 gal (7.5 l) electric water heater with a 1.44 kW heating element is used as the evaporator. The evaporator temperature can be controlled with a temperaturecontrolling unit to maintain the required absorber pressure. The deionized water that is used as the absorbate can be de-aerated by evacuating the evaporator. The cooling water system is composed of a constant head tank with a 250 gal (950 1) capacity, a centrifugal pump that circulates the cooling water, and a watertemperature controller unit. This controller unit, with four Chromalox heaters that are rated at 1.5, 2.5, 5.0 and 7.5 kW capacity, is able to control the cooling water temperature to +0.1 °C. As the constant-head tank is located outside the building, a heat exchanger is used to control the cooling water temperature. The building's chilled water system supplies chilled water to the heat exchanger. Both rotameter and a Rockwell flowmeter indicate the flowrate of the cooling water. The lithium bromide solution circulation system consists of the strong solution tank, a collecting tank, a mass flowmeter, and a circulation pump. The strong solution tank has a 40 gal (150 1) capacity, and is sealed so that it can be de-aerated by the vacuum pump. The tank can be heated to regenerate the weak solution and reduce the amount of air dissolved. The temperature of the inlet solution is controlled by the use of a screw plug heater, a heat exchanger, and heating tape, which is wrapped around the tubing. A rotary gear pump is used to introduce the strong solution into the absorber and to circulate the strong solution during de-aeration. Two mechanical vacuum pumps are used to evacuate the absorber and the collecting tank. Commercial dry-ice cold traps that condense the water vapour and molecular sieves that prevent oil contamination from the mechanical pumps are connected to the inlet side of each pump. Each pump is connected to the different locations in the experimental system by Viton TM vacuum hoses and copper tubing. The flowrate of the strong solution is determined by a mass flowmeter. This meter includes a flow control valve in order to adjust the required flowrate of the strong solution. The inlet and outlet solutions are sampled by collection into pre-evacuated samplers. In the process of preparing the inlet solution, a quick check of the concentration is determined from a hydrometer reading. More precise measurements for the inlet solution concentration are performed with a pycnometer. A curve fit to the aqueous lithium bromide density presented in Washburn 2° as a function of concentration at 30 °C is used to determine the inlet and outlet lithium bromide concentrations. Type K thermocouples are located at the absorber inlet and outlet, the cooling water inlet and outlet, the evaporator, and the two gas sample vessels. A dry vacuum containing little water vapour is measured by a thermocouple gauge. This thermocouple gauge can be used only during the de-aeration process, as the main component of the gas contained in the absorber during the experiment is water vapour. The absorber pressure is monitored by a piezoelectric gauge. This pressure transducer is installed at the top of the absorber. The
Absorption of water vapour into falling films of aqueous lithium bromide.
489
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RM: Rotameter SAI,2: Sampling Bottle ST: StrongSolution Tank SV1,2: SieveTrap V P I , 2 : Vacuum Pump WI: Walexinlet WP: WaterPump
Figure 2 Schematic diagram of the experimental system Figure 2 Schdma du sust&ne expdrimental
piezoelectric absolute pressure gauge was calibrated by comparing with a McLeod gauge for the pressure range of 1-10 mmHg. The non-absorbable concentration is determined by the 'freezing out' method 9. Gas samples from the absorber are collected in a stainless steel container and cooled to approximately 203 K to remove the water from the vapour phase. The non-absorbable mass is determined from the pressure, temperature and volume of the remaining vapour.
Test conditions
Test solutions were prepared from aqueous lithium bromide with impurities less than 0.5%, purchased from F M C Lithium Corporation. Approximately 0.01 mol% lithium hydroxide as a corrosion inhibitor was added to raise the pH of the lithium bromide-water solution to approximately 10. The concentration of non-absorbable gas was maintained at less than 2% unless the effect of the non-absorbable was to be studied. Control variables that included inlet solution concentration, inlet solution
490
K.J. Kim et al.
Table 1 The base and variations in operating conditions Tableau 1 Conditions de fonctionnement, param~tres de base et leurs variations Base
Inlet solution concentration, Csi. Inlet solution temperature, T~. Absorber pressure, Pv Cooling water temperature, Tci. Absorber length, L Absorbent flow rate, Ref Air concentration, C~
Range
57.7-60.5 mass% 60 mass% LiBr/H20
of absorption were obtained from AndberglS: heat capacity and viscosity from L6weraX; vapour pressure from Siebe22; and enthalpy from ASHRAE 23. The liquid diffusivity results of Kashiwagi l were used. For each run, properties were evaluated at the average conditions of the absorption.
35-45 °C 40 °C 7.6 mmHg" 30°C 85 cm ~60 < 2%
7.6-12 mmHg 25-35 °C 40-85 cm 15-150 < 2%
aThis absorber pressure corresponds to the evaporator temperature of 7°C temperature, absorber pressure, cooling water temperature, absorber length and absorbent flowrate were investigated. The base operating condition and the range of changes investigated in this work are summarized in Table 1.
Results and discussion
The mass transfer in the liquid falling film depends upon the flowrate and the transport properties of the liquid. Other parameters that influence the mass transfer as boundary conditions may be the non-absorbable gas concentration, the inlet solution temperature, the cooling water temperature, the absorber pressure, the inlet solution concentration, the absorber length, and the heat of absorption. The heat of absorption can be removed from the group of independent parameters, as the heat of absorption remained essentially constant over most of the test conditions. Flow observation
Data reduction
F r o m a species balance, the absorption rate Mab~ is determined by Mabs = Msout- Msi n
=
M(
)
sin~Csout -- 1
(6)
where Msout and M s i n a r e the outlet and inlet solution flowrates, and Csout and Csi, are the outlet and inlet solution concentrations respectively. The mass transfer coefficient h m is obtained from Mab s = hmAz~C where
(7)
AC is the
mass transfer driving potential and A is the contact area. The logarithmic mean concentration difference of pressure difference ~2, L M P D , is used for the driving potential: (AC=AP.dC/dP)
LMPD =
AP 1 - AP 2
(8)
ln(API~
\S j
where AP~ and AP 2 are the difference between the partial pressure of water in the gas phase and the vapour pressure of the bulk liquid at the inlet and outlet of the absorber respectively. Similarly, the logarithmic mean concentration diference is found from the concentration of water giving a vapour pressure equal to the partial pressure in the bulk gas phase minus the bulk liquid concentration at the inlet and outlet. If the inlet and outlet solution and gas temperatures and concentrations are known, the corresponding vapour pressures or concentration can be obtained. Then the logarithmic mean can be determined. Finally, a mass transfer coefficient can be obtained from Equation (7).
Without absorption, uniform wetting could be achieved at very low flowrates, Ref=O(1). With absorption, a smooth film flow could be maintained only when Ref > 16. When solution flowrates were varied in the range of film Reynolds number from 30 to 90, the flow was characterized as a 'wavy laminar' flow. Wave inception 24 starts between 10 and 20 cm from the top of the absorber for these flowrates. The measured values of wave inception distance are compared with ones from Brauner and M a r o n 25 in Figure 3. The wave inception starts earlier than expected, as the absorber surface is not perfectly smooth and a vertical falling film is always unstable 26. The wave amplitude increases with increasing solution flowrate, as Fulford z7 indicates. However, it seems that the increase is not directly proportional to the absorbent flowrate. As the flowrate increases, small and regular waves at the lower flowrates become irregular waves: so-called 'roll waves' distinguished by their steep front, a long and gently sloping tail, and a set of preceding small waves termed 'push waves '9. Occasionally, wetting became a problem when the film Reynolds number was less than 30. The slight difference in flow patterns between the falling film and the falling film under absorption seems 0.4
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A complete discussion of the property database can be found in ref. 19. Density, thermal conductivity and heat
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theory (Braunerand Maron, 1982) experiment(this work)
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Figure 3 Wave reception vs film Reynolds number
Figure 3 D~butde laformation du r~gimeturbulent, dans lefilm tornbant, en fonction du nombre de Reynolds
Absorption of water vapour into falling films of aqueous lithium bromide.
to be decreased wave frequency and decreased wave amplitude during the absorption. No attempt was made to measure the local wave amplitude or film thickness in the present study.
Absorbent flowrate effect Absorption data for 60 mass% lithium bromide were measured at the approximate absorbent film Reynolds numbers of 15, 30, 60 and 90. The mass transfer coefficient in the form of the Sherwood number as a function of film Reynolds number is shown in Figure 4. For the short-time penetration theory result, Sh is proportional to the Reynolds number to the one-third power, and within experimental error the experimental result shows a similar trend.
491
interracial gas phase concentration, inlet solution temperature, cooling water temperature, absorber pressure, and inlet solution concentration were independently varied. Figures 5-8 show the change in Sherwood number as a function of these variables when the partial pressure at the interface is given by the absorber pressure minus the measured bulk non-absorbable partial pressure. If the non-absorbable gas effect is negligible, the
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= 59.7
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= 400
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Pv
= 7 6 rnmHg
L
= 85 cm
Re r
- 59 I
6 4
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Driving potential effects The actual driving potential at the liquid-gas interface is the partial pressure of water in the gas phase (the gas phase is composed of water vapour and an unknown amount of non-absorbable gases) minus the local vapour pressure of the aqueous lithium bromide at the given temperature and composition. The problem is complicated because the local conditions are unknown. In order to investigate the effect of the operating variables on the '
C.,.
= 59.5 mass%
T.,.
= 40.2
°C
T~,~
= 300
°C
p.
= 7.6 mmHg
L
= 85 crn
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Cooling water temperature effect on mass transfer rate
Figure 6 Effet de la temperature de l'eau de re[~'oidissement sur le taux de transfert de masse 10
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C.,.
= 595
mass%
T~
= 297
°C
T.,.
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°C
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= 85 cm
Ref
= 60.0
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Figure 4
Absorbent flowrate effect on dimensionless mass transfer rate (Sherwood number)
Figure 7 Absorber pressure effect on mass transfer rate {mmHg/ m b a r =0.75)
Figure 4 l~ffet du dkbit de I'absorbant sur le taux sans dimension de tran,~yert massique (hombre de Sherwood)
Figure 7 Effet de la pression de rabsorbeur sur le taux de transfert massique (mmHg/mbar = 0,75)
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Figure 5 l~ffet de la tempdrature de la solution ~ rentrOe sur le taux de transfert massique
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Figure 8 Effet de la concentration de la solution fi l'entrde sur le taux de transfert massique
K. ,,I. Kim et al.
492
Sherwood number should be constant. In every case, as shown in these figures, there is a trend that indicates that the true partial pressure of water at the interface is less than the assumed value: that is, the non-absorbable concentration at the interface is higher than in the bulk gas phase. It is difficult to assign a numerical value to the non-absorbable concentration at the interface. There can be both increases and decreases in the driving force along the length of the absorber. When the driving force was nearly the same at the inlet and outlet, there was little change in the Sherwood number when other variables were changed. This is consistent with the assumptions above.
Absorber length effect The effective contact length of the absorber was set at 40, 60, and 85 cm and the flowrates of Ref= 30.3, 57.6 and 91.5 were investigated. The results are presented in Figure 9 in terms of the concentration profiles based upon the negative concentration difference between inlet and outlet solution. As Yang 1° showed, the concentration profiles are linear in this range.
N on-absorbables effects The experiments shown in Figure 5 involving a change in the inlet solution temperature with all other variables
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Concentration
Profil de concentration le long de l'absorbeur
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L
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p,
= 7,6 mmHg
given in Table 1 held constant can be used to estimate the non-absorbable concentration at the interface. When the inlet temperature was 35.8°C, the uncorrected Sherwood number was 3.7, and when the inlet temperature was 43.3 °C, the Sherwood number was 1.7. The liquid phase overall logarithmic mean driving force was 4.10% differential concentration for the lower inlet temperature and 1.85% differential concentration for the higher temperature. With 10% air at the interface, these driving forces drop to 3.0 and 0.4% differential concentration respectively. This means that the Sherwood numbers should be multiplied by 1.36 and 4.66 respectively, so that the actual air concentration must be somewhat less than 10% to get the results to match. As the driving force at the inlet for the higher-temperature inlet experimental is small, this particular experiment is very sensitive to the selection of the air concentration at the interface. We leave our estimate at 10%, although 9% is closer and 8% does not give enough correction, because the assumption that the non-absorbable concentration at the inlet and outlet is the same may be in question. In ref. 13 the vapour flow is co-current at the same velocity as the liquid interface, and the cooling water is just sufficient to hold the inner wall of the falling film at constant temperature; then the concentration of nonabsorbables at the interface is a function of distance from the inlet. In this work the vapour flow is an annular pipe flow counter-current to the liquid flow, and the cooling water flowrate is high enough to cool the falling film at the exit compared with the inlet. The 10% air at the interface would mean that the base case in this work should have a mass transfer coefficient 1.5 times that measured if no air were present. Fiyure 10 shows non-absorbable concentration effects on Sherwood number. The Sherwood number is decreased as much as 20% as air content is increased from 0.5 to 15% at this particular operating condition. Nonabsorbable effects appear constant as long as the concentration is maintained at less than 2%. This result shows the same trends as ref. 9. However, Yang and Chen 13 find that there can be a large drop in mass transfer from zero non-absorbable concentration to 0.01% (mass transfer rate drops by a factor of 5 at a length of 1 m) and only small changes from 0.01% to 30% similar to those observed here. Our results on the variation of the driving force suggest a much smaller decrease of possibly 50%, as shown for the experiments with different inlet temperatures for the zero to any non-absorbables. An examination of the mass transfer correlation and the liquid diffusivity used in the calculation is necessary to explain the difference between this work and that of Yang and Chen.
= 59,0
Mass transfer correlations 4
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10 Cair
Figure
,
1 on
i
,i,,
100
(%) mass transfer
rate
Effet des gaz non absorbables sur le taux de transfert massique
In gas absorption processes, the liquid-side resistance controls the mass transfer phenomena in the absence of non-absorbables. Figure 11 shows the comparisons between the present experimental work and the laminar approximation solutions by Sherwood et al. 12 for short and long contact time. The contact length in the range of 40-85 cm and the flowrate in the range of Ref = 15-90 for 60 mass% lithium bromide were employed in this analysis.
493
Absorption of water vapour into falling films of aqueous fithium bromide.
Further improvement in absorption efficiency
100 •
60 m a s % LiBr 50 mass% LiBr
When the vapour pressure of the absorbent reaches the absorber pressure, absorption stops. Therefore the absorption effectiveness Eel, the ratio of the actual absorption mass transfer to the overall mass transfer driving potential, is
10
hmpx --I F
"j
actual concentration change O. 1
Eff --
Long a n d S h o r t Conlacl Time Solution by S h c r w o o d el al. ( 1 0 7 5 )
0.01
. . . . . . . .
t
to
. . . . . . . .
.y,,2
-] h
Ioo
. . . . . . . .
C~. - Ceq(T~., P 3 (10)
I
looo
Dt Figure II
maximum driving potential
C~i. - C~o.!
M a s s t r a n s f e r c o r r e l a t i o n for 50 a n d 60 m a s s % s o l u t i o n s
Correlation de transfert de masse pour des solutions 5 50 et Zt 60%o en masse Figure ll
If we had used the diffusivity of water in a dilute solution of lithium bromide instead of Kashiwagi's results, the points in Figure 11 would move to the left. Then the experimental results would fall under the laminar theoretical lines, indicating that the nonabsorbable concentration less than 2% did have a large effect on the mass transfer. In fact, for the points that would fall under the long-time approximation, the reduction in mass transfer coefficient would be about that predicted by Yang and Chen. The implication is that non-absorbables have less effect in the high concentration solution absorption because the liquid diffusivity is lower than that used by Yang and Chen (the resistance of the liquid phase is controlling for the high-concentration lithium bromide solutions with non-absorbables in the gas phase under the conditions of these experiments). The experimental data can be correlated by a dimensionless form of mass transfer coefficient and a dimensionless reciprocal contact time as in Equation (2):
where Ceq(T~i,, Pv) is the equilibrium solution concentration at given temperature and absorber pressure. Note that the inlet cooling water temperature is used to define the equilibrium condition, as the inlet cooling water temperature is the minimum temperature that can be achieved. Absorption effectiveness for contact lengths in the range of 40-85 cm and flowrates in the range Re r = 30-100 are plotted in Figure 12. A higher absorption effectiveness could be achieved by lower absorbent flowrates. There is still considerable potential to improve the absorption efficiency, as the maximum effectiveness achieved was approximately 40%. Wavy motions are able to enhance the mass transfer rate. However, maximum mass transfer has not been achieved for the given geometry and the given conditions. In order to achieve the maximum mass transfer, it is necessary to break up the diffusion boundary layer more rigorously or to obtain a longer contact time. Increasing the contact length or decreasing the flowrate provides a longer contact time. However, increased length increases absorber size and requires higher construction costs. Adding small amounts of surface-active agents has been found to enhance the heat and mass transfer by introducing interfacial turbulence and providing better wetting 28. Experiments to determine the mass transfer correlation with 2-ethyl-l-hexanol as an additive are discussed in ref. 29.
Summary and conclusion hmpx
/V 2\h
-a~t)
(9)
where a = 3 . 9 4 and b = - 0 . 6 0 for 60 mass% lithium bromide. The characteristics of aqueous lithium bromide solution are dependent upon the number of water molecules associated with the lithium ion. When the lithium bromide concentration exceeds 55.6 mass%, all of the water molecules are tied up in the first coordination ring. Based upon the free water available in the solution, 50 and 60 mass% lithium bromide may have to be treated as two different absorbents. Experimental studies for a 50 mass% aqueous lithium bromide were also performed in the film flow Reynolds number range of approximately 60-200 (see Figure 11) to test the free water effect. The fitted values of a = 3.906 and b = - 0 . 5 9 for the 50 mass% lithium bromide are not significantly different from the values for 60 mass%, The experiments were set up so that driving force neglecting non-absorbables would be the same for 50 and 60 mass% solutions; thus any effect of the coordination of water with lithium is accounted for by the vapour pressure behaviour.
Experiments on absorption of water vapour into a falling film of 60 mass% lithium bromide solution were performed in the wavy film range of Reynolds numbers. When the dimensionless mass transfer coefficients were
80
!
!
= 2(~9 °('
60
40
P.
= 76mmH
- " "@" ~
L = 85 c m
- - "~"-
L = 60 cm
20
0
l
20
l
~
l
40
l l l l
60
Re[ Figure 12
A b s o r p t i o n effectiveness
F i g u r e 12
Efficacit~ de l'absorption
80
100
K.J. Kim et al.
494
calculated using physical properties from previous absorption studies except for the diffusivity of water in the solution, the dimensionless mass transfer coefficients were higher than predicted for a laminar film. This is consistent with an expected increase for a wavy film. The results of varying the parameters in the experiments showed that the base case with 1% non-absorbables in the bulk vapour had about 10% non-absorbables at the liquid-gas interface. This leads to about 50% less mass transfer than if no air were present in the vapour Yang and Chen 13 predict from numerical calculations that the decrease due to non-absorbables would be much larger; however, the diffusivity used by Yang and Chert was higher than that used in this work. In terms of the dimensionless mass transfer coefficient correlated in the manner of Sherwood et al.12, there was no difference between 50 mass% and 60 mass% lithium bromide solutions, although vapour pressures, diffusivities and viscosities have larger difference. This result confirms that the mass transfer for these high concentration salts depends on the Reynolds and Schmidt numbers and the dimensionless distance from the inlet, not on any other parameters. The results of the correlation of the data and the analysis of the effects of non-absorbables support the use of the diffusivity measurements of KashiwagiL
8
9 10 II 12 13 14 15 16 17 18
Acknowledgements
19
The authors acknowledge the support of the Gas Research Institute under contract number 5089-260-1874. Dr Timothy A. Ameel provided suggestions for successful experiments.
20 21 22
References 1 2 3 4 5 6
7
Kashiwagi, T. The activity of surfactant in high-performance absorber and absorption enhancement Reito (1985) 60(687) 72-79 (in Japanese) Sherwood, T.K., Pigford, R.L. Absorption and Extraction McGraw-Hill (1952) Banerjee, S., Rhodes, E., Scott, D.S. Mass transfer to falling wavy liquid films at low Reynolds numbers Chem Eng Sci (1967) 22 43-48 Penev, V., Krylov, V.S., Boyadjiev, C.H., Vorotilin, V.P. Wavy flow of thin liquid films Int J Heat Mass Tran~fer (1972) 15 1395 1406 Oliver, D.R., Atherinos, T.E. Mass transfer to liquid films on an inclined plane Chem Enq Sci (1968) 23 525-536 Emmert, R.E., Pigford, R.L. A study of gas absorption in falling liquid films Chem Eng Progr (1954) 50(2) 87-93 Narkoryakov, V.Ye., Bufetov, N.S., Grigor'yeva, N.I. Heat and mass transfer in film absorption Fluid Mechanics-Soviet Res (1982) 11(3) 97-115
23 24 25 26 27 28
29
Burdukov,A.P., Bufetov, N.S., Deriy, N.P., Dorokhov, A.R.. Kazakov, V.I. Experimental study of the absorption of water vapour by thin films of aqueous lithium bromide Heat TransJer-Soviet Res (1980) 12(3) 118-123 Ameel, T.A. Non-absorbable gas effects on heat and mass transfer in falling film absorption PhD Dissertation Arizona State University, Arizona (1991) Yang, R. Heat and mass transfer in laminar wavy film absorption with the presence of non-absorbable gases PhD Dissertation Arizona State University (1987) Yang, R., Wood, B.D. Experimental study for heat and mass transfer in wavy film absorption with the presence of nonabsorbables Chem Eng Comm (1993) 125 77-90 Sherwood, T.K., Pigford, R.L., Wilke, C.R. Mass Tran,s]br McGraw-Hill (1975) Yang, R., Chen, J.H. A numerical study of the non-absorbable effects on the falling liquid film absorption Warme- und Stoffubertragung ( 1991) 26 219-224 Valeev, A.Kh., Sishkin, I.V., Trostin, V.N. Structural study of aqueous solution of lithium bromide by X-ray diffraction Russ J Phys Chem (1993) 67(7) 1239-1242 Chau,D.S., Wood, B.D., Berman, N.S., Kim, K.J. Solubility of oxygen in aqueous lithium bromide lnt Comm Heat Mass Transfer (1993) 20(5) 643-652 Kim, K.J., Janule, V.P. Dynamic surface tension of aqueous lithium bromide with 2-ethyl-l-hexanol lnt Comm Heat Mass Transj& (1994) 21(6) 839 848 Eoderby, J.E. Neutron scattering from ionic solutions Ann Rev Phys Chem (1983) 34 155 185 Andberg, J.W. Absorption of vapors into liquid films flowing over horizontal tubes PhD Dissertation University of Texas at Austin (1986) Kim, K.J. Heat and mass transfer enhancement in absorption cooling PhD Dissertation Arizona State University (1992) Washburn, E.W, International Critical Tables of Numerical Data, Physics, Chemistry, and Technologarithmicy McGraw-Hill (1926) Lfwer, H. Thermodynamische und physikalische Eigenschaften der Wassrigen Lithium Bromide-losung PhD Dissertation Karlsruhe, Germany (1960) Siebe, D.A. Evaluation of air-conditioning system utilizing liquid absorbents regenerated by solar energy PhD Dissertation Arizona State University (1986) ASHRAE Handbook of Fundamentals American Society of Heating, Refrigerating and Air Conditioning Engineers (1989) Pierson, F.W., Whitaker, S. Some theoretical and experimental observations of the wave structure of falling liquid films lnd Eng Chem Fund (1977) 16(4) 401M.08 Brauner, N., Maron, D.M. Characteristics of inclined thin film, waviness and the associated mass transfer lnt J Heat Mass Transfer (1982) 25(1) 99-110 Miller, C.A., Neogi, P. Interjacial Phenomena Marcel Dekker, Inc. (1985) Fulford, G.D. The flow of liquids in thin films Advan Chem Eng (1964) 5 151 236 Kim, K.J., Berman, N.S., Wood, B.D. Experimental investigation of enhanced heat and mass transfer mechanisms using additives for vertical falling film absorber International Absorption Heat Pump Con]erence New Orleans (1994) 41-47 Kim, K.J., Bermao, N.S., Wood, B.D. Effects of 2-ethyl-1hexanol on the absorption of water vapor into lithium bromide solutions AICHE J (1995) accepted for publication
UTTERWORTH E I N E M A
N
N
0140-7007(95)00007-0
Int. J. Rel?ig. VoL 18, No. 7, pp486 494, 1995 Copyright ~i' 1995 Elsevier Science Ltd and IIR Printed in Great Britain. All rights reserved 0140-7007'95/$ I 0.00 -~ .00
Absorption of water vapour into falling films of aqueous lithium bromide K. J. Kim* and N. S. Berman Department of Chemical, Bio and Materials Engineering, Arizona State University, Tempe, AZ 85287, USA
D. S. C. Chau and B. D. Wood Department of Mechanical and Aerospace Engineering, Arizona State University, Tempe, AZ 85287, USA Received 3 November 1994; revised 20 M a r c h 1995
In this study, experiments have been performed for water vapour absorption into 50 and 60 mass% aqueous lithium bromide solution films flowing down a vertical surface to investigate the effects of liquid diffusivity values, molecular properties of the concentrated solutions and non-absorbable gases. The experimental results for wavy films over a film Reynolds number range of 15-90 indicate larger dimensionless mass transfer rates than for strictly laminar flow when the diffusivity of water in a concentrated lithium bromide solution is less than that in a dilute solution. The complete set of results shows that the physical property data for lithium bromide solutions including the diffusivities measured by Kashiwagi 1 are sufficient to explain mass transfer behaviour. (Keywords: wavy films; absorption; lithium bromide; vertical failing film)
Absorption de vapeur d'eau dand des films tombants de solution de bromure de lithium Dans cette ktude, on a effectuk des expkriences sur l'absorption de vapeur d'eau dans une solution aqueuse de bromure de lithium (50% 5 60% en masse) en forme de film en kcoulement sur une surface verticale, qfin dWudier les effets des gaz non absorbbs, des valeurs de diffusivit~ de liquide, ainsi que les propri~tOs moleculaires des solutions concentr~es. Les rksultats exp&imentaux pour les films ondulks sur une 9amme de nombres de Reynolds allant de 15 5 90 laissent supposer que les taux sans dimension de transfert massique sont plus importants que clans le cas d'un kcoulement strictment laminaire, lorsque le diffusivitb de l'eau dans une solution concentrke de bromure de lithium est moins importante que celle d'une solution diluke. L'ensemble des rksultats montre que les donnkes sur les propriktks physiques des solutions de bromure de lithium, y compris les diffusivit~s mesur~es par Kashiwag, sont suffisantes pour expliquer le comportement du transfert de masse.) (Mots
¢l/~s:absorption; bromure de lithium; film tombant vertical; r6gime turbulent; r6gime laminaire) In this paper we report results of experimental studies of water vapour absorption into 50 and 60 mass% lithium bromide in a falling-film apparatus. We examine the effect of changes in non-absorbables, length of absorber and overall driving potential. The interpretation of results is highly dependent on the value of the diffusivity of water in these concentrated solutions and we will discuss this problem in the paper. The fluid dynamics of the liquid film is governed by the film Reynolds number
Gas absorption into a falling liquid film is a classical problem with applications in absorption heat pumps. A liquid absorbent (or desiccant) has an affinity for an absorbate (normally a vapour). Mass transfer is due to the difference between the absorbate pressure and the vapour pressure of the absorbent at the given temperature and concentration. In the case of an aqueous lithium bromide solution that has 60 m a s s % concentration and 40 °C temperature introduced into an absorber with the pressure of water vapour set by an evaporator at 7 °C, there is 2.18 m m H g of driving potential based on the overall gas phase or a 3% differential concentration based on the liquid phase. Once absorption starts, the vapour pressure of absorbent at the interface is increased owing to the increased temperature and the decreased concentration of lithium bromide. Experimentally, it is impossible to remove non-absorbable gases completely so the driving potential at the liquid gas interface can be further reduced.
4F
Ref = - -
~t
(1)
where F is the mass flowrate per unit perimeter and F is the dynamic viscosity. Sherwood and Pigford z categorized the flow regimes as: laminar without rippling (Ref < 4-25); laminar with rippling (the wavy regime, 4-25 < Ref < 10002000); and turbulent flow (Ref> 1000-2000). Empirical or semi-empirical approaches are essential in order to develop absorber relationships that can be used for design in the wavy regime. For a lithium bromide-water system the Lewis
* Author to whom correspondence should be addressed. Present address is Center for Environmental Energy Engineering (CEEE), University of Maryland, College Park, M D 20742, USA
486
Absorption of water vapour into falling films of aqueous lithium bromide:
487
Nomenclature A C Cair D Eff g hm L Le LMPD M P Pv
Ref Sh T~i. t
x Yo
Contact area (m 2) Solution concentration (mass%) Air concentration (vol%) Mass diffusivity (m 2 s-1) Absorption effectiveness Gravitational acceleration (m s-2) Mass transfer coefficient (m s - l ) Absorber length (m) Lewis number Logarithmic mean concentration difference of pressure difference (mmHg) Mass flowrate (kg s-1) Pressure (mmHg) Absorber pressure (mmHg or mbar) Reynolds number Sherwood number Cooling water temperature (°C) Exposure time (s)
number Le, the ratio of thermal diffusivity to mass diffusivity, is on the order of 10 2. Thus a slowly developed diffusion boundary layer appears relative to a thermal boundary layer. In the laminar regime, molecular diffusion in the liquid phase governs the absorption process. One way to overcome the weak mass transfer rate is to use wavy motions caused by hydrodynamic instabilities so as to break the slowly developed diffusion boundary layer; then enhanced mixing in the liquid phase can increase the mass transfer rate significantly. Mass transfer enhancement (usually a 50-200% increase in mass transfer coefficient compared with that of a smooth laminar flow) by wavy motion has been demonstrated experimentally3 6. Vertical falling-film absorption with the lithium bromide-water system has been studied by a limited number of investigators. Nakoryakov et al. v tested the following parameters: a film Reynolds number of 80-800, 58-60 mass% lithium bromide inlet solution concentration, 7 15 mmHg absorber pressure. A comparison between the vertical tube absorber and horizontal tube absorber was experimentally investigated by Burdukov et al. 8. The lithium chloride--water absorption system was studied by Ameel 9, Yang 1° and Yang and Wood 11. None of the previous experimental studies compared the results with short- and long-time laminar flow mass transfer in a falling film, or developed a universal correlation that would fit all of the data. Sherwood et al. ~2 give mass transfer correlations for gas absorption into a falling liquid film process where the liquid is a steady laminar flow with constant concentration at the gas liquid interface. For short contact time the penetration theory produces a dimensionless mass transfer coefficient
hmpx -1.695x//3 F f~
(2)
where h m is the mass transfer coefficient, p is the liquid density, x is the distance in the flow direction, and F is
Distance in flow direction (m) Mean film thickness (m)
Greek letters /3 Dimensionless quantity defined in Equation (3) Mass flowrate per unit perimeter (kg s-1 F m ~) Dynamic viscosity (kg s-1 m - l ) ~t Kinematic viscosity (m 2 s-1) V Liquid density (kg m-3) P Subscripts Absorption abs Equilibrium eq f Film sin Solution inlet sout Solution outlet 1,2 Inlet, outlet of the absorber
the liquid feed. The dimensionless quantity fl is given by
Dt /4\~ f y \~ = 2/-/Dx/~/ fl= .~o \3J \v R e f J
(3)
where D is the mass diffusivity, t is the exposure time, yo is the mean film thickness, g is gravitational acceleration, and v is the kinematic viscosity. The left side of Equation (2) can also be expressed in terms of the Sherwood number Sh, defined as
hm Sh-
D
(4)
Considering the velocity gradient as a parabola (large value of /3), the long contact time solution can be approximated as
hmpx
--
F
=0.24+ 5.1fl
(5)
For gas absorption in a vertical column, where the liquid is a smooth film, Equations (2) and (4) can be used to draw a baseline for the cases of both short and long contact time. For a higher Ref, the film becomes wavy; then mass transfer will be increased owing to improved mixing. When non-absorbables are present in the gas phase, the use of the overall driving force to determine the experimental mass transfer coefficient could give hmpx/F greater or less than that determined from Equation (2) and (5), depending on the diffusivity in the liquid phase. Yang and Chen 13 show that for a liquid diffusivity about the same as in pure water, the mass transfer is drastically reduced when only 0.01% air is present in the gas phase. Concentrated lithium salt solutions contain very little free water because the lithium ion coordinates with four water molecules 14 16. The movement of water molecules
K.J. Kim et al.
488
is restricted, leading to a lower mass diffusivity compared with water in low salt concentrations. Three recent studies report diffusivities as shown in Figure 1. Enderby iv measured a local diffusivity using nuclear magnetic resonance (NMR) spectroscopy, and Kashiwagi 1 obtained concentration profiles in a stagnant absorption experiment using holographic inteferometry. Kashiwagi's results are a factor of 3 lower for 60 mass% lithium bromide than typical diffusivities used previously in absorption calculations 18.
Experimental The main components of the system are an absorber unit, an evaporator, a cooling water system, a circulation system, a vacuum-generating system, and measuring devices. The system operates in a batch mode. A schematic diagram of the system is shown in Figure 2. Details can be found in ref. 19. The absorber has two concentric tubes: an inner stainless steel tube of outside diameter 38.1 mm and length 1.83 m, and an outer Pyrex tube of inside diameter 148 mm and length 1.22 m. The absorbent solution flows down the outside of the inner tube. The outer Pyrex tube serves to maintain the vacuum pressure and to facilitate flow observation. The absorption of water vapour takes place at the outer wetted surface of the inner stainless tube, and the heat of absorption is removed by the upward flow of cooling water inside the stainless tube. The inner tube has an inside diameter of 34.9 mm. The outer Pyrex tube with 169 mm outside diameter is made from a KIMAX drainline pipe. Two brass end-plates are mounted on the ends of the outer tube using four threaded steel rods. Rubber ring seals are attached to the place between the ends and glass tube. The solution distributor, made of Plexiglass, is mounted on the upper plate. The distributor can hold approximately 1.051 of absorbent solution. The absorbent solution is introduced through the solution inlet, stays more than 20 s in the solution distributor so as to eliminate possible disturbances, and flows into the annular space between the head and the stainless steel tube. The weak solution is collected at the bottom part of the absorber by a funnel, and flows into a Plexiglass collector. The effective absorber length can be varied by moving the collector and funnel up towards the 5
] --o-
4
g ~.
Er~,y o9s3, LiCl) ]
.......[ - - -0- -
F
Kashiw~
(1984,
LiBr)
[ ............... " ......................
[ -- "El -- Andberg (1986, LiSr)
]
i
...................... : ......................... i......................... i......................... i ......................
3
2
.................
.....................
.............
............~..... :
0
,
0
,
i
................:... :..:. ~ .....~=:~.............
i
i
i
,
l
l
i
J
4 8 12 16 Salt C o n c e n t r a t i o n (Molar)
Figure 1 Diffusivities of water for lithium salts solutions Figure 1
Diffi~sivitds de l'eau les solutions de sels de lithium
i
r
20
distributor. The maximum absorber length available is 85 cm. In order to supply water vapour into the absorber unit, a 2 gal (7.5 l) electric water heater with a 1.44 kW heating element is used as the evaporator. The evaporator temperature can be controlled with a temperaturecontrolling unit to maintain the required absorber pressure. The deionized water that is used as the absorbate can be de-aerated by evacuating the evaporator. The cooling water system is composed of a constant head tank with a 250 gal (950 1) capacity, a centrifugal pump that circulates the cooling water, and a watertemperature controller unit. This controller unit, with four Chromalox heaters that are rated at 1.5, 2.5, 5.0 and 7.5 kW capacity, is able to control the cooling water temperature to +0.1 °C. As the constant-head tank is located outside the building, a heat exchanger is used to control the cooling water temperature. The building's chilled water system supplies chilled water to the heat exchanger. Both rotameter and a Rockwell flowmeter indicate the flowrate of the cooling water. The lithium bromide solution circulation system consists of the strong solution tank, a collecting tank, a mass flowmeter, and a circulation pump. The strong solution tank has a 40 gal (150 1) capacity, and is sealed so that it can be de-aerated by the vacuum pump. The tank can be heated to regenerate the weak solution and reduce the amount of air dissolved. The temperature of the inlet solution is controlled by the use of a screw plug heater, a heat exchanger, and heating tape, which is wrapped around the tubing. A rotary gear pump is used to introduce the strong solution into the absorber and to circulate the strong solution during de-aeration. Two mechanical vacuum pumps are used to evacuate the absorber and the collecting tank. Commercial dry-ice cold traps that condense the water vapour and molecular sieves that prevent oil contamination from the mechanical pumps are connected to the inlet side of each pump. Each pump is connected to the different locations in the experimental system by Viton TM vacuum hoses and copper tubing. The flowrate of the strong solution is determined by a mass flowmeter. This meter includes a flow control valve in order to adjust the required flowrate of the strong solution. The inlet and outlet solutions are sampled by collection into pre-evacuated samplers. In the process of preparing the inlet solution, a quick check of the concentration is determined from a hydrometer reading. More precise measurements for the inlet solution concentration are performed with a pycnometer. A curve fit to the aqueous lithium bromide density presented in Washburn 2° as a function of concentration at 30 °C is used to determine the inlet and outlet lithium bromide concentrations. Type K thermocouples are located at the absorber inlet and outlet, the cooling water inlet and outlet, the evaporator, and the two gas sample vessels. A dry vacuum containing little water vapour is measured by a thermocouple gauge. This thermocouple gauge can be used only during the de-aeration process, as the main component of the gas contained in the absorber during the experiment is water vapour. The absorber pressure is monitored by a piezoelectric gauge. This pressure transducer is installed at the top of the absorber. The
Absorption of water vapour into falling films of aqueous lithium bromide.
489
ST CL HE
a x l II It::: OUt m
Chilled
T
Walcr
PG2
VP1
CR2 SV2
-"O AS1
MS
AS2
HE4
VP2
CRI SVI
~'~1
HEI
CT
SAI CPI
AB: CL: CO: C'PI,2: CR1,2: CT: AS1,2: DM:
Absorber Cooling Tank Collector Circulation Pump Cold Trap CollecLingTank Air Smnples MassFlow Meter
DS: EV: FC: HE1-4: HXI,2: MS: PG 1,2: RF:
Solution Dismbutor Evaporator Flow Controller Heater Hem Exchanger MassSpectrometer PressureGauge WaterFlow Meter
RM: Rotameter SAI,2: Sampling Bottle ST: StrongSolution Tank SV1,2: SieveTrap V P I , 2 : Vacuum Pump WI: Walexinlet WP: WaterPump
Figure 2 Schematic diagram of the experimental system Figure 2 Schdma du sust&ne expdrimental
piezoelectric absolute pressure gauge was calibrated by comparing with a McLeod gauge for the pressure range of 1-10 mmHg. The non-absorbable concentration is determined by the 'freezing out' method 9. Gas samples from the absorber are collected in a stainless steel container and cooled to approximately 203 K to remove the water from the vapour phase. The non-absorbable mass is determined from the pressure, temperature and volume of the remaining vapour.
Test conditions
Test solutions were prepared from aqueous lithium bromide with impurities less than 0.5%, purchased from F M C Lithium Corporation. Approximately 0.01 mol% lithium hydroxide as a corrosion inhibitor was added to raise the pH of the lithium bromide-water solution to approximately 10. The concentration of non-absorbable gas was maintained at less than 2% unless the effect of the non-absorbable was to be studied. Control variables that included inlet solution concentration, inlet solution
490
K.J. Kim et al.
Table 1 The base and variations in operating conditions Tableau 1 Conditions de fonctionnement, param~tres de base et leurs variations Base
Inlet solution concentration, Csi. Inlet solution temperature, T~. Absorber pressure, Pv Cooling water temperature, Tci. Absorber length, L Absorbent flow rate, Ref Air concentration, C~
Range
57.7-60.5 mass% 60 mass% LiBr/H20
of absorption were obtained from AndberglS: heat capacity and viscosity from L6weraX; vapour pressure from Siebe22; and enthalpy from ASHRAE 23. The liquid diffusivity results of Kashiwagi l were used. For each run, properties were evaluated at the average conditions of the absorption.
35-45 °C 40 °C 7.6 mmHg" 30°C 85 cm ~60 < 2%
7.6-12 mmHg 25-35 °C 40-85 cm 15-150 < 2%
aThis absorber pressure corresponds to the evaporator temperature of 7°C temperature, absorber pressure, cooling water temperature, absorber length and absorbent flowrate were investigated. The base operating condition and the range of changes investigated in this work are summarized in Table 1.
Results and discussion
The mass transfer in the liquid falling film depends upon the flowrate and the transport properties of the liquid. Other parameters that influence the mass transfer as boundary conditions may be the non-absorbable gas concentration, the inlet solution temperature, the cooling water temperature, the absorber pressure, the inlet solution concentration, the absorber length, and the heat of absorption. The heat of absorption can be removed from the group of independent parameters, as the heat of absorption remained essentially constant over most of the test conditions. Flow observation
Data reduction
F r o m a species balance, the absorption rate Mab~ is determined by Mabs = Msout- Msi n
=
M(
)
sin~Csout -- 1
(6)
where Msout and M s i n a r e the outlet and inlet solution flowrates, and Csout and Csi, are the outlet and inlet solution concentrations respectively. The mass transfer coefficient h m is obtained from Mab s = hmAz~C where
(7)
AC is the
mass transfer driving potential and A is the contact area. The logarithmic mean concentration difference of pressure difference ~2, L M P D , is used for the driving potential: (AC=AP.dC/dP)
LMPD =
AP 1 - AP 2
(8)
ln(API~
\S j
where AP~ and AP 2 are the difference between the partial pressure of water in the gas phase and the vapour pressure of the bulk liquid at the inlet and outlet of the absorber respectively. Similarly, the logarithmic mean concentration diference is found from the concentration of water giving a vapour pressure equal to the partial pressure in the bulk gas phase minus the bulk liquid concentration at the inlet and outlet. If the inlet and outlet solution and gas temperatures and concentrations are known, the corresponding vapour pressures or concentration can be obtained. Then the logarithmic mean can be determined. Finally, a mass transfer coefficient can be obtained from Equation (7).
Without absorption, uniform wetting could be achieved at very low flowrates, Ref=O(1). With absorption, a smooth film flow could be maintained only when Ref > 16. When solution flowrates were varied in the range of film Reynolds number from 30 to 90, the flow was characterized as a 'wavy laminar' flow. Wave inception 24 starts between 10 and 20 cm from the top of the absorber for these flowrates. The measured values of wave inception distance are compared with ones from Brauner and M a r o n 25 in Figure 3. The wave inception starts earlier than expected, as the absorber surface is not perfectly smooth and a vertical falling film is always unstable 26. The wave amplitude increases with increasing solution flowrate, as Fulford z7 indicates. However, it seems that the increase is not directly proportional to the absorbent flowrate. As the flowrate increases, small and regular waves at the lower flowrates become irregular waves: so-called 'roll waves' distinguished by their steep front, a long and gently sloping tail, and a set of preceding small waves termed 'push waves '9. Occasionally, wetting became a problem when the film Reynolds number was less than 30. The slight difference in flow patterns between the falling film and the falling film under absorption seems 0.4
'
o
o ,=
A complete discussion of the property database can be found in ref. 19. Density, thermal conductivity and heat
'
'
'
I
'
'
'
I
'
'
'
I
'
theory (Braunerand Maron, 1982) experiment(this work)
0.2
J
o
~:
0.1 0
,
0 Physical properties
I
•
0.3 g "=,q.
'
,
I
20
,
,
,
I
40
i
l
eeI
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,
,
,
1oo
Figure 3 Wave reception vs film Reynolds number
Figure 3 D~butde laformation du r~gimeturbulent, dans lefilm tornbant, en fonction du nombre de Reynolds
Absorption of water vapour into falling films of aqueous lithium bromide.
to be decreased wave frequency and decreased wave amplitude during the absorption. No attempt was made to measure the local wave amplitude or film thickness in the present study.
Absorbent flowrate effect Absorption data for 60 mass% lithium bromide were measured at the approximate absorbent film Reynolds numbers of 15, 30, 60 and 90. The mass transfer coefficient in the form of the Sherwood number as a function of film Reynolds number is shown in Figure 4. For the short-time penetration theory result, Sh is proportional to the Reynolds number to the one-third power, and within experimental error the experimental result shows a similar trend.
491
interracial gas phase concentration, inlet solution temperature, cooling water temperature, absorber pressure, and inlet solution concentration were independently varied. Figures 5-8 show the change in Sherwood number as a function of these variables when the partial pressure at the interface is given by the absorber pressure minus the measured bulk non-absorbable partial pressure. If the non-absorbable gas effect is negligible, the
I0
'
'
'
I
'
'='
'
I
'
'
'
I
8
0
'
'
I
'
'
C.~
= 59.7
mass%
T,,.
= 400
°C
Pv
= 7 6 rnmHg
L
= 85 cm
Re r
- 59 I
6 4
'
'
0
S
Driving potential effects The actual driving potential at the liquid-gas interface is the partial pressure of water in the gas phase (the gas phase is composed of water vapour and an unknown amount of non-absorbable gases) minus the local vapour pressure of the aqueous lithium bromide at the given temperature and composition. The problem is complicated because the local conditions are unknown. In order to investigate the effect of the operating variables on the '
C.,.
= 59.5 mass%
T.,.
= 40.2
°C
T~,~
= 300
°C
p.
= 7.6 mmHg
L
= 85 crn
'
'
I
'
'
f
I
2 I
0
I
t
I
Figure 6
,
,
,
24
20
1
1
1
,
I
,
t
|
I
28 32 Tcin (°C)
i
i
i
36
40
Cooling water temperature effect on mass transfer rate
Figure 6 Effet de la temperature de l'eau de re[~'oidissement sur le taux de transfert de masse 10
'
'
8 6
I
'
'
'
I
C.,.
= 595
mass%
T~
= 297
°C
T.,.
= 40.0
°C
L
= 85 cm
Ref
= 60.0
'
'
I
'
~
'
I
'
'
J
,
'
a-
.gg
o c ~ oO
OC
%
4
O O
8
O (23 2 0
,
l
,
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I
1
J
l
20
I
t
i
,
40
1
L
,
,
0
60
80
100
~
,
,
Re t
,
I
8
,
,
I
,
,
,
I
,
J
,
12 14 Pv (millibar)
10
I
16
L
18
Figure 4
Absorbent flowrate effect on dimensionless mass transfer rate (Sherwood number)
Figure 7 Absorber pressure effect on mass transfer rate {mmHg/ m b a r =0.75)
Figure 4 l~ffet du dkbit de I'absorbant sur le taux sans dimension de tran,~yert massique (hombre de Sherwood)
Figure 7 Effet de la pression de rabsorbeur sur le taux de transfert massique (mmHg/mbar = 0,75)
10
'
'
'
I
'
'
'
'1""
'
'
'
I
'
8
'
'
I
'
"
'
i
'
Cm
= 59.7
mllssa/*
T¢.
= 29.9
*C
P,
=
er
10
....
8
7.6 mmHg
= 58.3 = 85 cm
6
6
I ....
I ' ' ' ' 1 ' ' ' '
T,~
= 29.9
T.,.
= 400
P.
= 76
L
= 85 cm
Ret
= 60.1
'"''1
....
t ' ' ' '
°C °C mmHg
r~
4
o
o
4
o
o
~
2
oO
2
0
oo
oO
°o
Oo
0 34
Figure 5
O0
36
38
40 Tsin (°C)
42
44
46
Inlet solution temperature effect on mass transfer rate
Figure 5 l~ffet de la tempdrature de la solution ~ rentrOe sur le taux de transfert massique
57
57.5
58
58.5
59
59.5
60
60.5
LiBr Cont.(mass%) Figure 8
Inlet solution concentration effect on mass transfer rate
Figure 8 Effet de la concentration de la solution fi l'entrde sur le taux de transfert massique
K. ,,I. Kim et al.
492
Sherwood number should be constant. In every case, as shown in these figures, there is a trend that indicates that the true partial pressure of water at the interface is less than the assumed value: that is, the non-absorbable concentration at the interface is higher than in the bulk gas phase. It is difficult to assign a numerical value to the non-absorbable concentration at the interface. There can be both increases and decreases in the driving force along the length of the absorber. When the driving force was nearly the same at the inlet and outlet, there was little change in the Sherwood number when other variables were changed. This is consistent with the assumptions above.
Absorber length effect The effective contact length of the absorber was set at 40, 60, and 85 cm and the flowrates of Ref= 30.3, 57.6 and 91.5 were investigated. The results are presented in Figure 9 in terms of the concentration profiles based upon the negative concentration difference between inlet and outlet solution. As Yang 1° showed, the concentration profiles are linear in this range.
N on-absorbables effects The experiments shown in Figure 5 involving a change in the inlet solution temperature with all other variables
1
~ ¢ [ g
0.5
C.,. P.
- 59 5 mass% = 7 6 mmHg
T.,.
40 2 °C - 29 9 °C
T,,~
0 -0.5
~)
-1
J.5 Reo = 57.6 Re', = 30.3 Ref =91.5
" ' - ~,) O
i
il
-2
- - -~ -
/
--
-2.5
i
-e-
i
i
0
i
I
i
i
20
,
,
,
,
I
40
,
,
,
I
60
,
,
i
100
80
L (cm) Figure
9
Figure 9
profile along the absorber length
Concentration
Profil de concentration le long de l'absorbeur
10
,
'
, .....
i
........
........
i
8 6
C.=
= 59.6 mass%
To,~ T.,.
= 30.0 °C = 400 °C
L
= 85 cm/Ret
p,
= 7,6 mmHg
given in Table 1 held constant can be used to estimate the non-absorbable concentration at the interface. When the inlet temperature was 35.8°C, the uncorrected Sherwood number was 3.7, and when the inlet temperature was 43.3 °C, the Sherwood number was 1.7. The liquid phase overall logarithmic mean driving force was 4.10% differential concentration for the lower inlet temperature and 1.85% differential concentration for the higher temperature. With 10% air at the interface, these driving forces drop to 3.0 and 0.4% differential concentration respectively. This means that the Sherwood numbers should be multiplied by 1.36 and 4.66 respectively, so that the actual air concentration must be somewhat less than 10% to get the results to match. As the driving force at the inlet for the higher-temperature inlet experimental is small, this particular experiment is very sensitive to the selection of the air concentration at the interface. We leave our estimate at 10%, although 9% is closer and 8% does not give enough correction, because the assumption that the non-absorbable concentration at the inlet and outlet is the same may be in question. In ref. 13 the vapour flow is co-current at the same velocity as the liquid interface, and the cooling water is just sufficient to hold the inner wall of the falling film at constant temperature; then the concentration of nonabsorbables at the interface is a function of distance from the inlet. In this work the vapour flow is an annular pipe flow counter-current to the liquid flow, and the cooling water flowrate is high enough to cool the falling film at the exit compared with the inlet. The 10% air at the interface would mean that the base case in this work should have a mass transfer coefficient 1.5 times that measured if no air were present. Fiyure 10 shows non-absorbable concentration effects on Sherwood number. The Sherwood number is decreased as much as 20% as air content is increased from 0.5 to 15% at this particular operating condition. Nonabsorbable effects appear constant as long as the concentration is maintained at less than 2%. This result shows the same trends as ref. 9. However, Yang and Chen 13 find that there can be a large drop in mass transfer from zero non-absorbable concentration to 0.01% (mass transfer rate drops by a factor of 5 at a length of 1 m) and only small changes from 0.01% to 30% similar to those observed here. Our results on the variation of the driving force suggest a much smaller decrease of possibly 50%, as shown for the experiments with different inlet temperatures for the zero to any non-absorbables. An examination of the mass transfer correlation and the liquid diffusivity used in the calculation is necessary to explain the difference between this work and that of Yang and Chen.
= 59,0
Mass transfer correlations 4
03 2
0
i
i
0.1
i I ,ill
,
10
Figure 10
Non-absorbables
i
,,,,,I
effect
,
,
10 Cair
Figure
,
1 on
i
,i,,
100
(%) mass transfer
rate
Effet des gaz non absorbables sur le taux de transfert massique
In gas absorption processes, the liquid-side resistance controls the mass transfer phenomena in the absence of non-absorbables. Figure 11 shows the comparisons between the present experimental work and the laminar approximation solutions by Sherwood et al. 12 for short and long contact time. The contact length in the range of 40-85 cm and the flowrate in the range of Ref = 15-90 for 60 mass% lithium bromide were employed in this analysis.
493
Absorption of water vapour into falling films of aqueous fithium bromide.
Further improvement in absorption efficiency
100 •
60 m a s % LiBr 50 mass% LiBr
When the vapour pressure of the absorbent reaches the absorber pressure, absorption stops. Therefore the absorption effectiveness Eel, the ratio of the actual absorption mass transfer to the overall mass transfer driving potential, is
10
hmpx --I F
"j
actual concentration change O. 1
Eff --
Long a n d S h o r t Conlacl Time Solution by S h c r w o o d el al. ( 1 0 7 5 )
0.01
. . . . . . . .
t
to
. . . . . . . .
.y,,2
-] h
Ioo
. . . . . . . .
C~. - Ceq(T~., P 3 (10)
I
looo
Dt Figure II
maximum driving potential
C~i. - C~o.!
M a s s t r a n s f e r c o r r e l a t i o n for 50 a n d 60 m a s s % s o l u t i o n s
Correlation de transfert de masse pour des solutions 5 50 et Zt 60%o en masse Figure ll
If we had used the diffusivity of water in a dilute solution of lithium bromide instead of Kashiwagi's results, the points in Figure 11 would move to the left. Then the experimental results would fall under the laminar theoretical lines, indicating that the nonabsorbable concentration less than 2% did have a large effect on the mass transfer. In fact, for the points that would fall under the long-time approximation, the reduction in mass transfer coefficient would be about that predicted by Yang and Chen. The implication is that non-absorbables have less effect in the high concentration solution absorption because the liquid diffusivity is lower than that used by Yang and Chen (the resistance of the liquid phase is controlling for the high-concentration lithium bromide solutions with non-absorbables in the gas phase under the conditions of these experiments). The experimental data can be correlated by a dimensionless form of mass transfer coefficient and a dimensionless reciprocal contact time as in Equation (2):
where Ceq(T~i,, Pv) is the equilibrium solution concentration at given temperature and absorber pressure. Note that the inlet cooling water temperature is used to define the equilibrium condition, as the inlet cooling water temperature is the minimum temperature that can be achieved. Absorption effectiveness for contact lengths in the range of 40-85 cm and flowrates in the range Re r = 30-100 are plotted in Figure 12. A higher absorption effectiveness could be achieved by lower absorbent flowrates. There is still considerable potential to improve the absorption efficiency, as the maximum effectiveness achieved was approximately 40%. Wavy motions are able to enhance the mass transfer rate. However, maximum mass transfer has not been achieved for the given geometry and the given conditions. In order to achieve the maximum mass transfer, it is necessary to break up the diffusion boundary layer more rigorously or to obtain a longer contact time. Increasing the contact length or decreasing the flowrate provides a longer contact time. However, increased length increases absorber size and requires higher construction costs. Adding small amounts of surface-active agents has been found to enhance the heat and mass transfer by introducing interfacial turbulence and providing better wetting 28. Experiments to determine the mass transfer correlation with 2-ethyl-l-hexanol as an additive are discussed in ref. 29.
Summary and conclusion hmpx
/V 2\h
-a~t)
(9)
where a = 3 . 9 4 and b = - 0 . 6 0 for 60 mass% lithium bromide. The characteristics of aqueous lithium bromide solution are dependent upon the number of water molecules associated with the lithium ion. When the lithium bromide concentration exceeds 55.6 mass%, all of the water molecules are tied up in the first coordination ring. Based upon the free water available in the solution, 50 and 60 mass% lithium bromide may have to be treated as two different absorbents. Experimental studies for a 50 mass% aqueous lithium bromide were also performed in the film flow Reynolds number range of approximately 60-200 (see Figure 11) to test the free water effect. The fitted values of a = 3.906 and b = - 0 . 5 9 for the 50 mass% lithium bromide are not significantly different from the values for 60 mass%, The experiments were set up so that driving force neglecting non-absorbables would be the same for 50 and 60 mass% solutions; thus any effect of the coordination of water with lithium is accounted for by the vapour pressure behaviour.
Experiments on absorption of water vapour into a falling film of 60 mass% lithium bromide solution were performed in the wavy film range of Reynolds numbers. When the dimensionless mass transfer coefficients were
80
!
!
= 2(~9 °('
60
40
P.
= 76mmH
- " "@" ~
L = 85 c m
- - "~"-
L = 60 cm
20
0
l
20
l
~
l
40
l l l l
60
Re[ Figure 12
A b s o r p t i o n effectiveness
F i g u r e 12
Efficacit~ de l'absorption
80
100
K.J. Kim et al.
494
calculated using physical properties from previous absorption studies except for the diffusivity of water in the solution, the dimensionless mass transfer coefficients were higher than predicted for a laminar film. This is consistent with an expected increase for a wavy film. The results of varying the parameters in the experiments showed that the base case with 1% non-absorbables in the bulk vapour had about 10% non-absorbables at the liquid-gas interface. This leads to about 50% less mass transfer than if no air were present in the vapour Yang and Chen 13 predict from numerical calculations that the decrease due to non-absorbables would be much larger; however, the diffusivity used by Yang and Chert was higher than that used in this work. In terms of the dimensionless mass transfer coefficient correlated in the manner of Sherwood et al.12, there was no difference between 50 mass% and 60 mass% lithium bromide solutions, although vapour pressures, diffusivities and viscosities have larger difference. This result confirms that the mass transfer for these high concentration salts depends on the Reynolds and Schmidt numbers and the dimensionless distance from the inlet, not on any other parameters. The results of the correlation of the data and the analysis of the effects of non-absorbables support the use of the diffusivity measurements of KashiwagiL
8
9 10 II 12 13 14 15 16 17 18
Acknowledgements
19
The authors acknowledge the support of the Gas Research Institute under contract number 5089-260-1874. Dr Timothy A. Ameel provided suggestions for successful experiments.
20 21 22
References 1 2 3 4 5 6
7
Kashiwagi, T. The activity of surfactant in high-performance absorber and absorption enhancement Reito (1985) 60(687) 72-79 (in Japanese) Sherwood, T.K., Pigford, R.L. Absorption and Extraction McGraw-Hill (1952) Banerjee, S., Rhodes, E., Scott, D.S. Mass transfer to falling wavy liquid films at low Reynolds numbers Chem Eng Sci (1967) 22 43-48 Penev, V., Krylov, V.S., Boyadjiev, C.H., Vorotilin, V.P. Wavy flow of thin liquid films Int J Heat Mass Tran~fer (1972) 15 1395 1406 Oliver, D.R., Atherinos, T.E. Mass transfer to liquid films on an inclined plane Chem Enq Sci (1968) 23 525-536 Emmert, R.E., Pigford, R.L. A study of gas absorption in falling liquid films Chem Eng Progr (1954) 50(2) 87-93 Narkoryakov, V.Ye., Bufetov, N.S., Grigor'yeva, N.I. Heat and mass transfer in film absorption Fluid Mechanics-Soviet Res (1982) 11(3) 97-115
23 24 25 26 27 28
29
Burdukov,A.P., Bufetov, N.S., Deriy, N.P., Dorokhov, A.R.. Kazakov, V.I. Experimental study of the absorption of water vapour by thin films of aqueous lithium bromide Heat TransJer-Soviet Res (1980) 12(3) 118-123 Ameel, T.A. Non-absorbable gas effects on heat and mass transfer in falling film absorption PhD Dissertation Arizona State University, Arizona (1991) Yang, R. Heat and mass transfer in laminar wavy film absorption with the presence of non-absorbable gases PhD Dissertation Arizona State University (1987) Yang, R., Wood, B.D. Experimental study for heat and mass transfer in wavy film absorption with the presence of nonabsorbables Chem Eng Comm (1993) 125 77-90 Sherwood, T.K., Pigford, R.L., Wilke, C.R. Mass Tran,s]br McGraw-Hill (1975) Yang, R., Chen, J.H. A numerical study of the non-absorbable effects on the falling liquid film absorption Warme- und Stoffubertragung ( 1991) 26 219-224 Valeev, A.Kh., Sishkin, I.V., Trostin, V.N. Structural study of aqueous solution of lithium bromide by X-ray diffraction Russ J Phys Chem (1993) 67(7) 1239-1242 Chau,D.S., Wood, B.D., Berman, N.S., Kim, K.J. Solubility of oxygen in aqueous lithium bromide lnt Comm Heat Mass Transfer (1993) 20(5) 643-652 Kim, K.J., Janule, V.P. Dynamic surface tension of aqueous lithium bromide with 2-ethyl-l-hexanol lnt Comm Heat Mass Transj& (1994) 21(6) 839 848 Eoderby, J.E. Neutron scattering from ionic solutions Ann Rev Phys Chem (1983) 34 155 185 Andberg, J.W. Absorption of vapors into liquid films flowing over horizontal tubes PhD Dissertation University of Texas at Austin (1986) Kim, K.J. Heat and mass transfer enhancement in absorption cooling PhD Dissertation Arizona State University (1992) Washburn, E.W, International Critical Tables of Numerical Data, Physics, Chemistry, and Technologarithmicy McGraw-Hill (1926) Lfwer, H. Thermodynamische und physikalische Eigenschaften der Wassrigen Lithium Bromide-losung PhD Dissertation Karlsruhe, Germany (1960) Siebe, D.A. Evaluation of air-conditioning system utilizing liquid absorbents regenerated by solar energy PhD Dissertation Arizona State University (1986) ASHRAE Handbook of Fundamentals American Society of Heating, Refrigerating and Air Conditioning Engineers (1989) Pierson, F.W., Whitaker, S. Some theoretical and experimental observations of the wave structure of falling liquid films lnd Eng Chem Fund (1977) 16(4) 401M.08 Brauner, N., Maron, D.M. Characteristics of inclined thin film, waviness and the associated mass transfer lnt J Heat Mass Transfer (1982) 25(1) 99-110 Miller, C.A., Neogi, P. Interjacial Phenomena Marcel Dekker, Inc. (1985) Fulford, G.D. The flow of liquids in thin films Advan Chem Eng (1964) 5 151 236 Kim, K.J., Berman, N.S., Wood, B.D. Experimental investigation of enhanced heat and mass transfer mechanisms using additives for vertical falling film absorber International Absorption Heat Pump Con]erence New Orleans (1994) 41-47 Kim, K.J., Bermao, N.S., Wood, B.D. Effects of 2-ethyl-1hexanol on the absorption of water vapor into lithium bromide solutions AICHE J (1995) accepted for publication