Introduction In recent years attempts have been made to use packed beds in open-cycle liquid desiccant cooling systems for the dehumidification process and/or for regenerating weak aqueous solutions. The possibility of reconcentrating the aqueous solution in a packed bed by means of solar-heated air was investigated by Leboeuf and Lof [1]  and Factor and Grossman [2]. The schematic of the reconcentration process is shown in  A step-wise heat and mass balance across the bed is used to determine the performance of the reconcentration process. However, due to the abundance of variables involved with the packed bed, the analysis becomes increasingly complex. To reduce the high computational cost, an air moisture removal effectiveness for the dehumidification process was defined (see reference  In this paper dimensionless vapor pressure and temperature difference ratios suitable for application in the reconcentration of aqueous solutions are defined. Further, a closed-form analytical solution is obtained to predict the mass of water evaporated from the weak absorbent solution, through a simplified vapor pressure correlation and the dimensionless vapor pressure and temperature difference ratios

P Gandhidasan

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P. Gandhidasan1 
Senior Lecturer, 
Mechanical Engineering Department, 
The University of the West Indies, 
St. Augustine, Trinidad, W.I. 
Mem. ASME 
Reconcentration of Aqueous 
Solutions in a Packed Bed: 
A Simple Approach 
Introduction 
In recent years attempts have been made to use packed beds 
in open-cycle liquid desiccant cooling systems for the dehu-
midification process and/or for regenerating weak aqueous 
solutions. The possibility of reconcentrating the aqueous so-
lution in a packed bed by means of solar-heated air was in-
vestigated by Leboeuf and Lof [1] and Factor and Grossman 
[2]. The schematic of the reconcentration process is shown in 
Fig. 1. The weak absorbent solution, which leaves the absorber, 
is pumped to the top of the packed bed after passing through 
a solution-to-solution heat exchanger where it is preheated by 
the strong solution. Solar-heated air enters the packed bed at 
the bottom. Since the weak solution vapor pressure exceeds 
the vapor pressure of water in air, the moisture transfer takes 
place from the solution to the air. Cooled and humidified air 
exits at the top and warm, concentrated solution leaves the 
bottom of the packed bed. For each kilogram of water evap-
orated from the solution in the packed bed, one kilogram may 
be absorbed in the absorber and thus evaporated in the evap-
orator to provide cooling. Hence, the performance of the cool-
ing system is directly related to the amount of water evaporated 
from the weak solution in the packed bed. 
A step-wise heat and mass balance across the bed is used to 
determine the performance of the reconcentration process. 
However, due to the abundance of variables involved with the 
packed bed, the analysis becomes increasingly complex. To 
reduce the high computational cost, an air moisture removal 
effectiveness for the dehumidification process was defined (see 
reference [3]) based on the rigorous calculation for the heat 
and mass transfer occurring in the packed bed. 
In this paper dimensionless vapor pressure and temperature 
difference ratios suitable for application in the reconcentration 
of aqueous solutions are defined. Further, a closed-form an-
alytical solution is obtained to predict the mass of water evap-
orated from the weak absorbent solution, through a simplified 
vapor pressure correlation and the dimensionless vapor pres-
sure and temperature difference ratios. 
Dimensionless Vapor Pressure and Temperature Dif-
ference Ratios for a Reconcentration Process 
In a packed bed, the reconcentration process involves si-
1 Presently at the Department of Mechanical Engineering, Texas Tech Uni-
versity, Lubbock, TX 79409-1021. 
Contributed by the Solar Energy Division of THE AMERICAN SOCIETY OF 
MECHANICAL ENGINEERS for publication in the JOURNAL OF SOLAR ENERGY EN-
GINEERING. Manuscript received by the ASME Solar Energy Division, Aug. 17, 
1989; final revision, June 13, 1990. 
multaneous heat and mass transfer. During the reconcentration 
process, the moisture from the absorbent solution transfers to 
the air stream. Hence, a dimensionless moisture difference 
ratio, suitable for the reconcentration process in the packed 
bed, can be defined as the ratio of the actual change in moisture 
content of air to the maximum possible change in moisture 
content under given conditions as: 
HR0 — IiRj 
HRo,max-HRj 
(1) 
The vapor pressure of hot and strong solution at the outlet of 
the bed is higher than that of warm and weak solution at the 
inlet. As long as the solution vapor pressure is higher than the 
air vapor pressure, reconcentration can take place. Therefore, 
the solution outlet conditions set a theoretical limit on the 
maximum vapor pressure, and therefore on the maximum hu-
midity ratio that air can achieve. 
In the limit, then 
a,o, max *s,o " ^ o , m a x - (2) 
Equation (1) can be written in terms of vapor pressure as 
P —P 
L s,o •* a, 
(3) 
For the reconcentration process the hot air is supplied from 
the solar collector, and therefore the air temperature is higher 
than the solution temperature. Hence, in addition to moisture 
transfer, heat will also transfer due to the difference in tem-
perature. Therefore it is necessary to define a dimensionless 
temperature difference ratio similar to the dimensionless vapor 
pressure difference ratio. For the range of operating conditions 
assumed in the analysis, the vapor pressure of air and solution 
vary approximately linearly with temperature. Further, the 
primary objective is the transfer of the water vapor from the 
solution, and hence the temperature difference ratio must be 
defined in accordance with the dimensionless vapor pressure 
difference ratio to obtain a simple relationship. It can be de-
fined as, 
13= ̂ rzl^_ (4) 
t —t 
la,l ls,o 
In this paper the aforementioned dimensionless vapor pressure 
and temperature difference ratios are used to derive a simple 
268 / Vol. 112, NOVEMBER 1990 Transactions of the ASME 
Copyright © 1990 by ASME
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SOLAR 
AIR 
HEATER. 
AIR IN 
HEAT 
EXCHANGER 
TO THEw A FROM THE 
ABSORBER ABSORBER 
expression to evaluate the performance of the reconcentration 
process. 
Fig. 1 Reconcentration of absorbent solution in a packed bed 
1 
o &,( \ GJ 
(8) 
The mass of water evaporated from the solution and ab-
Assuming constant specific heats for the fluids with respect sorbed by the air stream is given by 
to temperature, the overall heat balance of the packed bed can 
be written as 
Ga(cpJaJ+y PaJ) + GscpJs<l 
= Ga(cpJat0+y Pa-0) + GscpJSt0 
0.622 h', 
m=?£ (Pa,o-Pa,i)-
h' 
(9) 
fs 
(5) 
where y = -**• for small vapor pressures. 
Equation (5) can be rewritten in terms of a and j3 as 
Cp,aPUs,o-ta,i) +y a(Ps,0-Pa<i) = 
GscP 
By combining equations (3) and (9), the vapor pressure of 
the solution at the outlet of the packed bed can be obtained 
and is given by 
mh'f° ~ (10) 
(t,j-t.0). (6) 
p fs +p 
a Gj 
n . . c r. ... , . , , . . . The solution temperature at the outlet of the bed can be 
Ps 0 and L „ as a function of initial parameters can be obtained , . . , . _ . . . .. ,_. ,„. j / i m j - • 
J' f„ii„™'f -n,- ~iotJm.»,™ uotLan •!,. ,mnnr «r«.„™ „f obtained by combining equations (7), (8), and (10) and is given 
as follows: The relationship between the vapor pressure of 
the solution at the outlet and its temperature and concentration 
is given by reference [4], 
by 
PSt0 = a + b ts>0+ —, (7) 
m h' A 
a. G^ + Pa,r 
<-D ( i i ) 
where a, b, and c are empirical constants for the range of 
conditions of interest. By substituting the values for Pso and tSj0 from equations 
The effect of flow rate of solution on the rate of desorption (10) and (11), respectively, in equation (6), the mass of water 
is given in terms of inlet and outlet concentration of the solution evaporated from the absorbent solution can be determined. It 
as is given by 
Nomenclature 
C = heat capacity rate 
cp - specific heat 
G = mass flow rate 
h'fg = heat of vaporization of water 
from the absorbent solution 
HR = humidity ratio of air 
m = amount of water evaporated 
from the weak solution 
p 
t 
a 
P 
i, 
= water vapor pressure 
= temperature 
= dimensionless vapor pressure 
(moisture) difference ratio 
= dimensionless temperature 
difference ratio 
= concentration of the absorb-
ent solution 
Subscripts 
a = air 
b = barometric 
/ = inlet 
max = maximum 
o = outlet 
s = absorbent solution 
Journal of Solar Energy Engineering NOVEMBER 1990, Vol. 112 / 269 
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2.0 
•1.6 
0.4 
180 200 
MASS FLOW RATE OF AIR, Kg/hm 
Fig. 2 Effect of air inlet temperature on rate of desorption 
1.2 
0.6 
0.4 
0.2 
100 120 160 200 
MASS FLOW RATE OF AIR, Kg/hm 
Fig. 3 Effect of solution flow rate 
270 / Vol. 112, NOVEMBER 1990 Transactions of the ASME 
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1.2 
1.0 
0.8 
0.6 
0.4 
0.2 
50 kg/hm 
160 180 200 
MASS FLOW RATE OF AIR, Kg/hm2 
Fig. 4 Effect of initial water vapor pressure in air 
1.4 
50 Kg/hm 
M 1.0 
0 . 8 
0.2 
140 160 180 200 
MASS FLOW RATE OF AIR, Kg/hm2 
Fig. 5 Effect of preheating the solution 
Journal of Solar Energy Engineering NOVEMBER 1990, Vol. 112 / 271 
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CJajP + CjsJ- i (paJ-a-j-)(C£ + C,) 
m= j=— ^ (12) 
-(CB + C) lL&£&2 + £_£&£ +h> 
where C„ and Cs are the heat capacity rate of air and solution, 
respectively, and is given by C„ = Ga cPt0 and Cs = Gs cps. If 
the value h'jg is assumed constant with respect to temperature 
and concentration of the solution, then the rate of desorption 
becomes a function of initial parameters and the heat capacity 
rate of the fluids and dimensionless vapor pressure and tem-
perature difference ratios. 
Results and Discussion 
For the present study calcium chloride solution is used as 
the absorbent. For the range of operating conditions assumed 
in the present analysis, the constants a, b, and c in equation 
(7) for brine concentrations of 45-47 percent are found to be 
(i) for solution temperatures of 45-60°C, a = -290.8, b = 
3.2, and c = 6708.9 and (ii) for solution temperatures of 35-
45°C, a = -114.8, b = 1.51, and c = 3169.1. It is further 
assumed that for the weak solution, the heat of vaporization 
of water from the solution for these conditions is a constant 
of 2551.6 kJ/kg. It may be noted that a and B also depend 
upon the type of packing material used. A simple calculation 
based on the results of [5] indicates that for a packed bed with 
1-in. Raschig rings, a. and B varies from 0.5 to 0.8. However, 
in the present analysis, for numerical calculations it is assumed 
that a = B = 0.8. 
The effect of the regeneration temperature of air on rate of 
desorption of water is shown in Fig. 2. For a particular re-
generation temperature as the flow rate of air increases, the 
mass of water evaporated from the solution also increases. 
The higher regeneration temperature yields the greater rate of 
desorption. Figure 3 shows the water loss rate for different 
flow rates of air and solution. It is interesting to note that the 
change in solution flow rate has no significant effect on the 
system performance. 
The packed bed performance due to changes in initial water 
vapor pressure in air is shown in Fig. 4. If the initial water 
vapor pressure in air is less (that is, dry air), it tends to absorb 
more moisture from the solution, and hence the water loss rate 
is more. When the entering air is humid, the absorption rate 
is less due to low potential for mass transfer, and hence the 
desorption rate is less. 
The effect of preheating the solution (that is, inclusion of 
a heat exchanger in the cycle) on the rate of desorption is 
shown in Fig. 5. As the solution inlet temperature increases, 
the mass of water evaporated from the solution also increases 
owing to the increase in mass transfer potential. 
Conclusion 
A simple analytical investigation of reconcentration of 
aqueous solutions occurring in a packed bed using solar heated 
air is carried out through a simplified vapor pressure corre-
lation and dimensionless vapor pressure and temperature dif-
ference ratios. It is found that the air inlet temperature and 
its vapor pressure and the solution inlet temperature have sig-
nificant effect on the regeneration performance. For prelim-
inary design purposes, the simple expression derived in this 
paper can be used to predict the mass of water evaporated 
from the weak absorbent solution in the packed bed. 
Acknowledgments 
The author wishes to express his thanks to Prof. S. Satcu-
nanathan of the Mechanical Engineering Department for help-
ful discussions. 
References 
1 Leboeuf, C , and Lof, G. O. G., "Open Cycle Absorption Cooling Using 
Packed Bed Absorbent Reconcentration," Proceedings of the 1980 A nnual Meet-
ing of the American Section of the International Solar Energy Society, p. 205. 
2 Factor, H. M., and Grossman, G., "A Packed Bed Dehumidifier/Rege-
nerator for Solar Air Conditioning with Liquid Desiccants," Solar Energy, Vol. 
24, 1980, p. 541. 
3 Ullah, M. R., Kettleborough, C. F., and Gandhidasan, P., "Effectiveness 
of Moisture Removal for an Adiabatic Counterflow Packed Tower Absorber 
Operating with Cacl rAir Contact System," ASME JOURNAL OP SOLAR ENERGY 
ENGINEERING, Vol. 110, No. 2, 1988, p, 98. 
4 Kakabaev, A.,andKhandurdyev, A., "Absorption Solar Refrigeration Unit 
with Open Regeneration of Solution," Applied Solar Energy, Vol. 5, No. 4, 
1969, p. 69. 
5 Leboeuf, C. M., and Lof, G. O. G., "Analysis of a Licl Open-Cycle 
Absorption Air Conditioner which Utilizes a Packed Bed for Regeneration of 
the Absorbent Solution Driven by Solar Heated Air," Final Report, for U.S. 
Department of Energy, Colorado State University, Colo., Contract No. EG-77-
S-02-4546, Oct. 1978. 
272 / Vol. 112, NOVEMBER 1990 Transactions of the ASME 
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Reconcentration of Aqueous Solutions in a Packed Bed: A Simple Approach

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Reconcentration of Aqueous Solutions in a Packed Bed: A Simple Approach

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