498
Ind. Eng Chem Fundam. 1986. 25. 498-503
Carlson, A . Presented at the AIChE National Meeting, Chicago, IL, Nov. 1985. Danckwerts, P. V. Chem. Eng. Sci. 1953, 2 . 1. Giddings. J. C. Dynamics of Chromatography; Marcel Dekker: New York, 1965: Vol. 1. Gill, W. N.: Sankarasubramanian. R. Proc R . SOC.London, A 1970, 3 7 6 , 341. Hougen, 0. A. Chemical Process Principles, 1st ed.; Wiley: New York. 1943: Part 111. Jandera, P.; Churacek, J. J . Chrornatogr. 1974, 97, 223. Kopaciewicz, W.; Rounds, M. A.; Fausnaugh, J.: Regnier. F E d . Chromatogr. 1983. 266, 3. Kucera, E. J . Cbromatogr. 1965, 19, 237. Langmuir, I . J . A m . Chem. SOC.1908, 3 0 , 1742. Lapidus. L.; Amundson, N. R. J . Phys. Chem. 1952, 56. 984. Lenhoff, A. M.. University of Delaware, personal communication, 1986. Liaw, C. H.: Wang, J. S . P.: Greenkorn, R. A,: Chao. K. C. A I C b E i 1979, 2 5 , 376. Parente, E. S.: Wetlaufer. D. B. J . Cbromatogr. 1986. 355, 29
Rasrnuson, A. AIChE J . 1981, 2 7 , 1032. Reis. J. F. G.: Lightfoot, E. N.; Noble, P. T.; Chiang, A. S . Sep. Sci. Tecbnol. 1979, 7 4 , 367. Rice, R . G. Chem. Eng. Sci. 1982, 3 7 , 83. Rosen, J. B. J . Chem. Phys. 1952, 2 0 , 387. Schnieder. P. Chem. Eng. Sci. 1984, 3 9 , 927. Snyder. L. R.; Stadalius, M. A.: Quarry, M. A. Anal. Chern. 1983, 55, 1412A. Stadalius. M. A.; Gold, H. S.; Snyder, L. R . J . Chromatogr. 1984. 296, 31 Suzuki. M.; Smith, J. M. Cbem. Eng. Sci. 1971, 2 6 , 221. Taylor, G. I. Proc. R SOC.London, A 1953, 219. 186 Thomas. H C. J . Cbem. Phys. 1951. 79, 1213. Tien. M.: Kirk. T. K. Proc. Nail. Acad. Sci. U . S . A . 1984, 87, 2280. Van Deemter J J.: Zuiderweg, F.J.: Klinkenberg. A. Cbem. Eng. Sci 1956, 5 , 271 Verrneulen. T: Hiester. N. K . Ind Eng. Chem. 1952, 4 4 , 636
Received for reuzen: July 3, 1986 A w e p t p d August 4, 1986
Transient Sorption of Water Vapor from Air Flowing through Beds of Zeolite 13X Daryl R. Haefner and George Thodos" Chemical Engineering Department, Northwestern University, Evanston, Illinois 6020 1
Experimental measurements have been carried out for the removal of water vapor from air flowing through fixed beds of zeolite 13X. Measurements were conducted under adiabatic conditions using different humidities, air flow rates, and bed depths up to 10.0 cm. This information has been used to develop an expression for the rate of adsorption as a function of average bulk humidity, air flow rate, and water content of the adsorbent. This rate expression, coupled with the differential mass and energy balances for the bed, describes the transient nature of the system. The simultaneous solution of these equations generates temperature and water content profiles for both the air stream and the solid desiccant. These solutions predict breakthrough curves which are in agreement with experimental measurements.
Desiccant heat pumps are receiving increased attention for space heating and cooling since they offer an advantage over conventional heat pumps, which require a refrigerant and also demand a relatively large electrical input to the compressor. The desiccant heat pump replaces the compressor with a fan which circulates the working fluid throughout the system. A number of choices are possible for the selection of a desiccant and a working fluid; however, for domestic use both components should be environmentally acceptable. This restriction would exclude methanol, ammonia, sulfur dioxide, and other volatile components. The combination of water and air presents attractive features since both are readily available, are nontoxic, and can be easily accommodated. A number of suitable desiccants, such as silica gel, alumina, activated carbon, and zeolites, can be used to sorb water vapor from air with the simultaneous release of energy. Exhaustive studies have been carried out with silica gel and alumina (Bullock and Threlkeld, 1966; Carter, 1966; Carter, 1968); however, the potential of zeolites has not yet been thoroughly explored. Zeolites are well suited for heat pump applications, since they maintain a high adsorptivity for water vapor at temperatures suitable for space heating. For this study, zeolite 13x was selected because of its relatively high capacity for holding water and its capability to withstand adsorption and desorption cycling.
Experimental Equipment and Procedure The experimental apparatus for the water sorptiondesorption cycle of zeolite 13X is shown schematically in 0196-4313/86/1025-0498$01.50/0
Figure 1. Compressed air from a building supply source was conditioned before introducing it into the zeolite column. For pretreatment, the compressed air was first passed through a filter and then pressure-regulated before being directed through a rotameter. The air was then introduced into two water saturators, connected in series and provided with Berl saddles. Then this humidified air was passed through a series of three glass traps to eliminate the possibility of water entrainment. The saturators and traps were all contained in a constant-temperature bath controlled within f O . l "C and equipped with a pump for water circulation. The humidity of the air leaving the saturators was controlled by the temperature of the bath as well as the pressure prevailing in the final saturator. The temperature of the air after leaving the final glass trap, was then raised to 22 "C by passing it through a long copper coil submerged in a second constant-temperature bath. This conditioned air was then introduced into a well-insulated adsorption column (i.d. = 7.62 cm) packed with zeolite. A copper-constantan thermocouple, located at the bed exit, indicated the temperature of the outlet air; the humidity was measured with a lithium chloride dew point sensor (General Eastern, Model 65s) which had a lower dew point limit of 0 O F . Both dry and dew point temperatures were continuously monitored and recorded. A typical experimental run is shown in Figure 2 for run 18. It is apparent from this figure that, during the early stages of adsorption, the air leaving the zeolite bed was essentially moisture-free. After a period of time, the outlet humidity began to rise and increased continuously until it apc' 1986 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986
499
Table I. Summarv of Exoerimental Conditions" run
G, kg/(m2 s)
Yo9 kg of water/kg of air
actual
min calcd
36.5 48.0 65.0 44.0 55.5 78.0 58.5 80.5 109.0
35.5 46.0 60.0 43.0 56.5 73.0 57.5 73.5 96.0
154.0 202.0 166.0 144.0
152.0 201.0 164.0 143.0
360.0 368.0 458.0 263.0 309.0 498.0
374.0 377.0 458.0 272.0 308.0 494.0
T~
zo = 1.5 cm Building Air Supply (350 kPa)
1 2 3 4 5 6 7 8 9
0.0608 0.0617 0.0619 0.0427 0.0429 0.0426 0.0285 0.0289 0.0287
10 11 12 13
0.0430 0.0433 0.0622 0.0620
14 15 16 17 18 19
0.0430 0.0430 0.0446 0.0423 0.0610 0.0282
Pressure
Regulator
0.010 52 0.007 60 0.005 47 0.012 01 0.008 64 0.006 34 0.013 33 0.009 55 0.006 88 zo = 4.0 cm
Constant Temperature Bath
Figure 1. Schematic diagram of experimental equipment.
c
t o=
1p r y o
0.009
0.008
D
y,=000809 t
B
O.OO'
t
Run 18 z.=IOcm t.=2ZoC G=0.0610kg/m2s y.=0.00809kg water/kg air
E
0003
zeolite bed was taken to be constant a t average bed conditions. The external void fraction of the sorbent was experimentally determined to be t = 0.375. The heat capacities for the air and the sorbent, expressed as J/(kg "C), depended on the amount of water present and were calculated from the expressions cg = 1005 + 1884y (1)
- predicted curves
t
5
o + experimental values
0002
x *
10.0 cm 0.009 26 0.009 18 0.006 99 0.013 74 0.008 09 0.010 30
"Inlet air and initial bed temperatures: t o = 22 "C.
r
0
0.008 73 0.006 19 0.005 43 0.006 41
000,~
and
I
00000
100
o
8
T,rnin
Figure 2. Typical humidity and temperature profiles for air leaving zeolite bed (run 18).
proached the humidity of the inlet air. The experiment was terminated at this stage. Note also that the temperature of the air leaving the zeolite bed exhibited an initial rapid increase before reaching a maximum plateau. This was then followed by a gradual decline. To regenerate the zeolite, air was heated to 125 OC and passed through the column. Residual water on the regenerated zeolite was determined by removing samples from the column, which were weighed and then dried further by placing them in an oven a t 400 OC for 24 h. In this manner, the residual water after regeneration was established to be approximately 0.0425 kg of water/kg of zeolite. Altogether, 19 runs were carried out with bed depths of 1.5,4.0, and 10.0 cm. The mass velocities ranged from 0.0282 to 0.0622 kg/(m2 s), and inlet humidities varied from 0.005 43 to 0.013 74 kg of waterfkg of air. Table I presents the conditions associated with each run.
Physical Properties of System The zeolite was designated by the manufacturer (Union Carbide) as 1/16-in. zeolite 13X pellets. These pellets were sieved, and only those ranging from 8 to 12 mesh were used. The bulk density of this fraction was determined to be 684 kg/m3. By use of pressure-drop measurements on the actual bed (Ergun, 1952), the equivalent particle diameter and the corresponding surface area per unit bed volume were found to be 1.97 x m and 1906 m2/m3, respectively. The density of the air flowing through the
c, = 920 + 4174w (2) The maximum water loading of zeolite 13X was determined by subjecting samples removed a t the completion of a run to drying a t 400 OC. The maximum loading was found to be wo 0.20 kg of water/kg of zeolite. Experimental heat of adsorption values (Barrer and Cram, 1971) were used to establish the average value for the heat of adsorption over the range of interest, AH = 3.63 X lo6 J/kg of water. Heat-transfer coefficients, h, for the air flowing through the packed bed were calculated from the j-factor correlation of Sen Gupta and Thodos (1962) 0.863 cj = 0.01 + (3) - 0.483 All this information was incorporated into the computer simulation for the adsorption column.
Mathematical Treatment for Zeolite-Water System A comprehensive mathematical analysis for the transfer of a component in a fluid flowing through a bed of sorbent must consider changes in concentration and temperature for both the fluid and solid phases as functions of time and position. For the general case, these requirements necessitate writing material and energy balances over a section of differential bed height. These balances must apply to the fixed bed as well as the fluid passing through its interstices. Consideration of a material balance over an elementary section of thickness dz measured in the direction of flow leads to the expression
500
Ind. Eng. Chem. Fundam., Vol. 25, No. 4 , 1986
0015'L
A
O
s OI
3
- ....
c
D
2
0.010 -
Bn
o predicted experimental curve values
OI
c
5
r
/---
0005-
f
U
Run 4 IO:
-
z,= 1.5 cm t.= 2 2 Y G = 0.0427 kg/m' s ye= 0.01201kg water/ kg air
z.=15cm t.=22'C G.00427 kg/m2s y.~o01201 kg water/kg air
c
n
s
S
'0 = 0.00809 kg of water/kg of air, G = 0.0610 kg/(m2 s), and t o = 22 O C .
1 pC5,tlOn
cm
Figure 6. Calculated humidity-position relationships for beds up to 10.0 cm deep and conditions corresponding to run 18.
6o
t
0
I
2
3
4 1.
5
6
7
8
9
IO
position, Cm
Figure 7. Calculated air temperature profiles for bed depths up to 10.0 cm and conditions corresponding to run 18.
0009t L
0
ooo8 ...~
~
..............
0
6 50 3 i
s D
p
40
5
$
30
Simulated Conditions
t.= 22 *C G;C.06IC kg/m2s y.:000809kguoter/kg
ZC
oir
Simulated Conditions 2 ,
G=00610kg/m2s y.=OOO809 kg water/kg air
T >minutes
Figure 5. Calculated breakthrough curves for bed depths up to 10.0 cm and conditions corresponding to run 18.
of the runs associated with beds 1.5, 4.0, and 10.0 cm deep. The close agreement between calculated and experimental values validates the computer simulation for predicting breakthrough curves and temperature profiles for the zeolite 13X-water vapor system. The numerical solution of eq 13-16 produces a t the nodal points, for which the system of equations was specified, temperatures t, and t , and water contents y and u: for the gas and solid phases, respectively. Figure 5 shows calculated breakthrough curves for bed lengths up to 10 cm with conditions corresponding to run 18. A cross plot
PoSltlon
:I"
Figure 8. Calculated solid temperature profiles for bed depths up to 10.0 cm and conditions corresponding to run 18.
of Figure 5 results in the humidity-position profiles shown in Figure 6. This figure provides information for establishing the breakthrough time, Tb, for any bed depth up to 10.0 cm. More specifically, for conditions corresponding to run 18 and bed depths of 1.5, 4.0, and 10.0 cm, the corresponding breakthrough times read from Figure 6 are 7 b = 43, 120, and 308 min. This figure also shows the development and movement of the mass-transfer zone at various times. For example, after 25 min most of the water vapor was removed by a 3-cm layer of sorbent at the bed entrance, while a t 150 min, the active zone was found between a depth of about 3-7 cm. The breakthrough for the 10-cm bed occurred when the transfer zone had traversed the full length of the bed. Figures 7 and 8 present the calculated temperature histories of the flowing air and the sorbent as a function
Ind. Eng. Chem. Fundam., Vol. 25, No. 4, 1986 503
heat recovery values, q, as a function of time, 7, for these reference temperatures are shown in Figure 9.
-
a W
%
:
Concluding Remarks The rate expression defined by eq 16 offers the advantage of simplifying the computations associated with the solution of eq 13-15. The results forthcoming from eq 16 were found to be in closer agreement than comparable models, as discussed earlier. Therefore, the model postulated by eq 13-16 adheres better to the actual performance of the adsorber considered in this study.
ye= 0.00809 kg water/kg air
l00,OOO-
8
h
Nomenclature
l 7
-
50,000
1': outlet heat exchanger temperature
1
OO'
100
I
I
I
I
I
200
I
L
I
I
I
300
1
I
I
1
I
400
T ,minutes Figure 9. Recoverable energy from air leaving bed with conditions corresponding to run 18 using different outlet heat-exchanger tem-
peratures.
of bed position. Each of these relationships possesses a maximum which shifts continuously to the right with increasing time. Note that the temperatures of the flowing air and solid sorbent are essentially the same with respect to time and position. During the early stage of adsorption, the temperature profiles exhibited maximum peaking which became less pronounced with increasing time. This peaking resulted from the fact that the air heated during adsorption transferred its heat content to the cooler adsorbent downstream. With time, this effect is dampened and changes to the shapes seen for T 1 25 min. A cross plot of Figure 7 a t zo = 10.0 cm produced the calculated temperature profile shown in Figure 2. Potential Recovery of Stored Energy In the course of water vapor adsorption, the air leaving a bed of zeolite is dried and is also heated, due to the exothermic nature of the process. The energy which is liberated within the solid desiccant is transferred to the flowing air stream and is manifest as an increase in air temperature. This warm air can then be utilized for space heating. However, due to its extreme dryness, it should not be mixed directly with air used in living quarters. To utilize this potential energy most efficiently, the warm air should be heat-exchanged with the space to be heated. This mode of operation requires a suitable temperature difference to prevail between the warm air and the environment to be heated; therefore. a reference temperature must be specified. If this temperature is taken to be the temperature of the air entering the bed, to, then the maximum recoverable energy becomes
where for all runs t o = 2 2 "C and m corresponds to the mass flow rate. The maximum energy recoverable for conditions corresponding to run 18 was q = 178000 J. For this run the zeolite's dry weight was 312 g. If more conservative and realistic reference temperatures are taken, then the amounts of energy transferred to the environment become q = 136, 107,81.2, and 56.8 kJ for reference temperatures of to = 25,30,35, and 40 "C, respectively. The
a, = surface area, m2/m3 cg = heat capacity of flowing gas, J/(kg "C) c, = heat capacity of solid, J/(kg O C ) D = diffusion coefficient, m2/s G = superficial mass velocity of air, kg/(m2 s) h = heat-transfer coefficient, J/(m2 s "C) j = heat-transfer factor AH = heat of adsorption, J/kg of water m = mass of sorbent in bed, kg of dry zeolite m = air mass flow rate, kg/s n = parameter defined by eq 10 q = recoverable energy, J or kJ Q = dimensionless water content ratio for zeolite, w / w o r = rate of adsorption, kg of water/(kg of zeolite s) ro = initial rate of adsorption, kg of water/(kg of zeolite s) R = rate of adsorption, kg of water/s S = cross-sectional area of bed, m2 t = temperature of flowing gas, "C .ik, = dimensionless gas temperature, t g / t o to = inlet air temperature and initial solid temperature, "C t, = temperature of sorbent, "C T , = dimensionless solid temperature, & / t o w = water content of sorbent, kg of water/kg of dry zeolite w o = water content of sorbent at maximum loading, kg of water/kg of dry zeolite y = humidity, kg of water/kg of air yo = inlet humidity, kg of water/kg of air Y = dimensionless humidity ratio, y/yo z = distance in direction of flow, m zo = bed depth, m 2 = dimensionless bed depth, z / z O
Greek Letters a = parameter defined by eq 10 /3 = dimensionless parameter, eq 16, @won E = void fraction of bed 8 = dimensionless time, T / T ~ Pb = bulk density of sorbent, kg/m3 pg = gas density, kg/m3 T = time, s Tb = time required for humidity of air leaving bed to reach T~
half of inlet humidity = characteristic time, p g z 0 t / G ,s Registry No. H20, 7732-18-5.
Literature Cited Ames, W. F. Numerical Methods for Partial DifferentialEquations ; Academic: New York, 1977. Barrer, R. M.; Cram, P. J. Adv. Chem. Ser. 1971, N o . 102, 105-125. Bullock, C. E.; Threlkeld, J. L. ASHRAE Trans. 1966, 72, 301-312. Carter, J. W. Trans. Inst. Chem. Eng. 1966, 4 4 , T253-T258. Carter, J. W. Trans. Inst. Chem. Eng. 1966, 4 6 , T213-T222. Ergun. Sabri Chem. Eng. Prog. 1952, 4 8 , 89-94. Haefner, D. R. Ph.D. Dissertation, Northwestern University, Evanston. IL, 1986. Hougen, 0.A,; Marshall, Jr., W. R. Chem. Eng. Prog. 1947, 4 3 , 197-208. Marcussen, Lis Chem. Eng. Sci. 1982, 37, 299-309. Sen Gupta, A,; Thodos, G. AIChE J . 1962, 8 , 608-610.
Received for reuieu; May 13, 1986 Accepted June 21, 1986
