FIXED-BED DRYING OF AIR USING MOLECULAR SIEVES J A M E S
I . N U T T E R l A N D G E O R G E B U R N E T , J R .
Department of Chemical Engineering, Iowa State University of Science and Technology, Ames, Iowa The rate of drying of air in a fixed b e d of molecular sieves was investigated. Exit air moisture content as a function of time was measured a t several values of inlet concentration, flow rate, fixed-bed height, and b e d temperature. Over-all, solid phase, and gas phase mass transfer coefficients and particle and pore diffusivities were calculated. The pore diffusion model of Vermeulen and Acrivos best reproduced experimental data and i s recommended as a bqsis for design calculations.
HE adsorption process for fixed-bed air drying can be Tcharacterized using modifications of standard design procedures. Application of the mass transfer zone ( M T Z ) method of Treybal ( 6 ) 'to the air-water-molecular sieves system was described by the authors, as was a combination of the h f T Z design method .with the mass transfer coefficient and particle diffusivity methods (3, 5). T h e latter two methods assume that the rate-controlling step of the adsorption mechanism occurs inside a spherical bead of molecular sieves. They failed individually to describe the air-water-molecular sieves system rigorously. T h e M T Z method of Treybal ( 6 ) simplifies interpretation of fixed bed data by eliminating the variable time. T h e adsorption zone is assumed to remain constant in length, W E - W E , and shape, f. Experirnental M T Z lengths, W E - W E ,and the value o f f for the air-water-molecular sieves system were included in the previious paper (5). T h e M T Z method require either experimental equations [Equations 2 and 3 (5)] values of the cumulative dry air weights, WE and W E ,a t the extremities of the adsorption zone or methods to calculate them. T h e present work deals with application of the pore diffusion model developed by Acrivos and Vermeulen ( 7 , 7) to the airwater-molecular sieves system and includes some experimental data not previously reported (4). T h e latter experiments were designed to demonstrate the effect of flow rate and particle size and shape on mass transfer coefficients and diffusivities.
Pore Diffusion Equatioins
T h e pore diffusion model is based on a n irreversible equilibrium (X*= Xo* for all C*) which can be used to approximate the isotherm for molecular sieves without appreciable material balance error (Figure 1 ) . Material balances are made for the saturation of each diffrrential layer of adsorbent and for the entire spherical particle. These material balances are combined with a simplified solid phase diffusion rate equation. Integration of the comb.ined equation yields Equation 1 relating D,,,,, to the cumulative dry air weight points a t the extremities of the adsorption zone--e.g., " E ' and W E ' , at the C/co = 1.0 and C/Co = 0.0 points, respectively.
1
Prrsent address, W'.
R.Grace and Co., Baltimore, Md.
I n evaluating W Y T Z ' a large error in the over-all diffusion rate and material balance would result if both ends of the breakthrough curve-e.g., C/Co < 0.05 and C / C , > 0.95-were neglected (as is the case in the M T Z method) in the scale-up from the one particle upon which the model is based to all the particles in the bed. Assuming that the explicit interpolation formula holds for approximating the air stream water content driving force, one obtains Acrivos and Vermeulen's ( 7 ) expression for the water content ratio:
where the term U E P , is usually negligible. Pore diffusion rate coefficients, kpareap, can be calculated using the following equation also reported by Acrivos and Vermeulen ( 7 ) : kporeap=
D p m e (1 -~ dp2Xo*Pb
60
e)Co~g
(3)
Design Data and Procedures for Molecular Sieves
Breakthrough curve data were obtained for various values of the independent variables. T h e experimental apparatus, procedures, runs, data, and calculations are detailed in the research of Nutter (3, 4). Table I summarizes the important run conditions and gives the mass transfer coefficients and diffusivities for past data and for the additional runs (39 through 83). T h e rate coefficients, koa,, k,ap, and K,a,, and the particle diffusivities, D,, were calculated using Equations 4, 5,6, and 10 of (5). These values have not been previously reported and are included here for comparison with similar values calculated using the pore diffusion equations. In Figure 2, curves calculated using these equations are compared to a representative experimental breakthrough curve. T h e pore diffusion breakthrough curve was determined using Equation 2. VOL. 5
NO. 1
JANUARY
1966
1
Table I.
a
Run Run Conditionsa No. 2 3 4 5 6 7 8 9 10 11 12 13 14 15 17 19 20 21 22 23 24 25 26 27 28 29 30 31 33 34 35 36 38 39 40 44 45 55 56 63 68 69 70 72 78 79 80 83 Bed heights, inches. a .
Principal Run Conditions and Calculated Values for Spherical Beads
Flow Rate G: Lb. Dry A i r / Hr. Sq. FL 1096 1118 1131 1131 1097 1107 469 469 47 1 1139 914 913 912 912 915 914 913 913 900 913 913 914 915 914 914 912 912 909 915 915 915 913 915 443 664 444 664 443 663 810 973 992 973 812 972 972 971 972 13.875.
G a s Phase Rate Coefficient, koa,: Lb. A i r / Hr. Lb.
Over-all Solid Phase Particle Rate CoRate CoDiffusiuity, eficient, eficient, D A 709, K,a,, Hour-l k,a,, Hour-' Solid Sq. Ft./Hr 3 080 3 155 2 667 317 3 475 3 490 315 2 930 428 3 090 3 090 2 613 3 100 3 121 502 2 640 378 3 213 3 250 2 748 2 942 2 968 2 512 430 2 995 2 950 2 533 447 2 740 2 855 2 415 111 2 667 2 710 2 292 190 4 770 4 848 4 105 41 5 4 227 4 280 504 3 620 4 600 4 855 4 110 240 5 300 5 518 4 665 435 3 892 3 928 3 325 982 5 345 5 350 4 520 530 5 315 5 410 548 4 575 2 693 2 703 205 2 288 2 842 2 873 586 2 432 2 600 293 2 200 2 560 5 825 536 4 930 5 760 3 772 4 315 4 455 290 3 940 277 3.334 3 860 3.163 3 695 3 738 428 4 282 4 345 384 3.676 3 760 365 3.180 3 692 4 890 278 4.137 4 795 2.915 3 445 386 3 402 3 590 274 3.037 3 490 4 111 2.963 529 4 040 569 1.702 2 360 2 302 4 065 314 2.930 3 985 590 3 645 2.158 3 600 3 992 655 2.362 3 942 4 550 393 3.850 4 483 4 962 309 4.200 4 850 3 310 405 2.800 3 300 3 550 443 3.000 3 508 3 352 352 2.420 3 290 48 3 2.890 4 000 3 958 391 3.893 4 412 4 605 47 1 4.800 5 680 5 550 3 755 380 3.175 3 700 2 248 419 1,903 2 228 378 3.837 4 538 4 512 2.267 2 680 509 2 690 1 573 1.331 518 1 566 746 1 158 0.835 1 160 935 3,920 4 635 5 070 25.875. Bed temperatures, a F. d. 66.5. e. 70. f . 80. g. 90.
Inlet Concn., C,, Lb. H20, Lb. Air 0.01101 0,01137 0 00988 0.01042 0.00988 0.01065 0.00998 0 01065 0.01119 0 01750 0.01244 0.01811 0.01841 0.01222 0.01870 0.01291 0.00784 0.00799 0.00772 0 01870 0 01542 0 01634 0 01542 0 01572 0 01083 0 01750 0 01083 0 01119 0 00988 0 00571 0 01222 0 00860 0 00860 0 01542 0 01542 0 00968 0 00988 0 00988 0 00988 0 01101 0 01542 0 01008 0 00571 0 01542 0 00681 0.00460 0,00336 0.00988
b.
79.875. c.
024-
0 Bed
I/
ole
0
I
1
2
1 4
90'F
temperoluie
I
6
6
Inlet a i r water content,
0
1 10
12
C., ( I b . H,O/lb.
I4
,
16
1 I
I8
dry a i r ) x 1 0 3
Figure 1. Experimental equilibrium isotherms for Type 4A molecular sieve beads at 90" F. 2
8 4 5 8 5 7 8 8 8 4 6 5 5 6 5 6 5 5 6 6 5 5 4 4 6 6 7 5 7 7 6 6 9 5 10 8 7 11
94 90
45 39 14 35 06 00 01
38 64 56 96 68 75 43 69 97
67 97
27 20 46 80 88 12 38 56 37 03 81 69 01 30 23 65 78 04
T h e Eagleton and Bliss (2) mass transfer coefficient approach gives a n asymptotic solution above C/C, = 0.80. This occurs because the equations do not have a finite boundary condition a t the limiting capacity point, ClC, = 1.0. I n adapting this method to design problems (5)a multiplying factor was applied to a smaller portion of the breakthrough curve than the total MTZ length. T h e multiplying factor was empirically determined from the experimental MTZ data. Equation 4 was found to be applicable for lY calculated by Equations 4, 5, and 6 of (5)
0 80
Water content
Pore Diffusiuty, D ~ 7 0 2 )~ Sq F t Hr 5 76 5 53 6 32 7 56 3 48 7 69 6 74 2 87 5 78
l&EC PROCESS DESIGN AND DEVELOPMENT
ri,
-
=
1.876
[w (g
=
-
n 7 B ]
(4)
Since there is very little difference in value between K , a p and k,ap, the adsorption is essentially controlled by the solid phase. T h e k o a p values can be determined only from the most inaccurate part of the breakthrough curve ; hence no generalizations can safely be made in this research for koa,. HoLvever,
~
~
(
I .o Pore diffusion model
Mass transfer coefficient
0.8
Ratio of
0.6
water content
of exit t o 0.4
inlet air, C/c,
00
00
-
0.2
0
E x p . run no. 2 6 (corrected to 100°/~moteriol bolonce) Pore diffusion controlling (using irreversible equilibrium conditions)
2 .o
1.6
2.4
2.8
Solid film controllinp Solid and gos films contributing
3.2
2.0
1.6
2.8
2.4
3.2
d r y air weight, W, Ib,
Cumulative Figure 2.
Exp. run no. 26 (corrected to I O O X moteriol bolonce)
Adsorption mechanism models for air-water-molecular sieves (Type 4A) system Inlet concentration. 0 . 0 1 5 4 2 Ib. HzO/lb. air Molecular sieves. 0 . 0 7 8 - t o 0 . 0 9 3 - i n c h b e a d s Flow r a t e . 0 0 3 2 8 Ib. d r y air/min. Bed t e m p e r a t u r e . 89.9' F. Bed height. 1 9 . 8 7 5 inches
the k,a, data are still of some use in correcting for gas film resistances in the minimum dew point portion of the breakthrough curve. This influence extends only u p to the 0.1 C/C, point of the curve Over-all solid phase ( K , a p ) and pore diffusion (kporeap) rate coefficients us. inlet air water contents are given in Figure 3. Values of kDoreapwere calculated using Equation 3. Particle (D,) and pore (Dpore) diffusivities (from Equation 2) us. inlet air water content are given in Figure 4 . Ksa,, D,, and D,,,, values are independent of air flow rate. A graphical example, Ksap us. G, is given in Figure 5 . D,,,,and kporeapvalues, as determined by Equations 1 and 3, respectively, reflect only the finite upper and lower material balance limits on a particle and on the MTZ itself. T h e
values of D, and Ksap,however, were calculated using the slope of the linear relationship, In(1 - C/CJ us. W, and thus reflect most of the experimental concentration behavior of the breakthrough curve, and not just the extremities of the M T Z . T h e pore diffusivities are approximately a decade higher than the Knudsen diffusivities-eg., D k = 3.09 X sq. foot per hour a t 90' F. for Type 4A molecular sieves. External surface areas, a p , for the spherical beads ranged from 10.9 to 11.8 sq. feet per pound of solid. Porosities, c , for spherical beads were calculated using an arithmetic mean particle diameter and the volume of a sphere equation. T h e values ranged from 0.382 to 0.453. Experimental run data and the subsequent calculated values for small granular particles are available ( 4 ) ,but are of limited design value. Data for some of these runs are given in Table
-
Rote coefficlenl,
K*
rote: 914 I b . /hr f t ? Adsorbent porficle size. 0 0 6 5 0 0 9 3 inch
Air flow
-
Porlicle diffurivity,
Qpr
hours-'
Q, 1
a V m25875" Bed ht
a
DO
I
i
0
4
L 6
L 8
IO
12
I 14
Inlot air wotinr content, Go, (Ib. H,O/lb.
I6
I8
3-
( f t2/ hr.) 1 io6 2 -
90DE Bed T
i -?
0 V
25 875" Bed ht.
o o rn
90°F Bed T,
0
20
dry o i r ) r IO'
21
I
4
Figure 3. Over-all solid phase and pore diffusion coefficients vs. inlet air woter content for Type 4A molecular sieve beads
6
1 6
I
IO
1 12
Inlet air woter content, C,,
I 14
(Ib. H,O/lb.
I 16
I I6
20
dry a i r ) x IO'
Figure 4. Particle and pore diffusivities vs. inlet air water content for Type 4A molecular sieve beads VOL. 5
NO
1
JANUARY
1966
3
Table II.
Principal Run Conditions" and Calculated Values for Granular Particles Gas Phase Rate Co-
a
Floie Rate G, L b l l r j Air Hr S q Ft
Rim .Yo. 41 42 43 46 65 66 67 71 75 76 77 81 82 Red height
Particle Sirr, I j l e r .Vrsh -14+20 452 -14+20 147 -14+20 294 -8+10 973 -24+32 443 -24+32 294 -24+32 148 -7+8 663 -7+8 443 -10+12 295 -10+12 442 -7+8 442 -10+12 442 79.875 inches. Bed temperature.
Our-all Solid Phasr efficiunt, Rate CoRat? Cok'a,, Lb efficient, efficirnt, Air Hr K,a,,. Hour-' k 7 a , , Hour-' Lb Solid 22 17 11 26 10 87 701 1 4 10 1 4 37 1247 12 63 12 90 1345 42 15 45 10 1537 1 3 70 13.88 2250 24 22 24 87 1570 12 80 1 3 06 940 9 07 444 8.63 13.96 14.67 599 18 45 19 16 758 8,88 9.19 695 12.20 12.86 591 90a F . Inlet concmtration. 0.01542 Ib. H2OlIb. air.
11. T h e granular particles \cere obtained by crushing pellets of molecular sieves. Over-all mass transfer rate coefficients cs. particle size are sho\vn in Figure 6 . X linear relationship of kr,r,renpand K,a, 1 s . d p for the G = 443 Ib. hr. s q , ft. floiv rate data points \\'as obtained on a log-log plot. More \vork is needed before generalizations on particle size effects can safely be made. It is believed that discontinuities or inhomogeneities in the structure of molecular sieves are somewhat responsible for the effects found ( 7 ) . I
4
-
Overail rate coefficient, 4 K,ap, hours",
I
1
1
P
Extensive experimental data for the air-Mater-molecular sieves system have made possible calculation of over-all, solid phase, and gas phase mass transfer coefficients. and particle and pore diffusivities. T h e coefficients and diffusivities were found to vary with inlet air water concentration and adsorbent particle size. but to be independent of air flow rate. A pore diffusivity approach gave a better duplication of the experimental breakthrough curve than the mass transfer coefficient method a n d is recommended as a basis for design calculations.
-
Nomenclature
-
MTZ
=
-
?*
= =
C,
=
sVL% 7 -
3 2 - Bed heiQhls V I 3 8 7 5 inches I -ox 1 9 8 7 5 inches ? 25 875 inches 0 I I
I
I
I
I
,
4 DP D,,,,
I 24
I
\
\
' /
-
Overall Rate Coefficient,20-
\'
Bed Temperature 90' F. Bed Height 19875 Inches Inlet Concentrotion: 001542 L b . H 2 0 / L b Air A i r Flow R a t e s (GI x 977 Lb /HI F t 2 663 L b / H r F t 2 T 443 L b / H I F t 2 0 294 L b / H i F t 2 V I 4 7 L b Hr F t 2
10-
=
= = =
G
=
G'
=
k,
=
k,,,,
=
k,
=
K,
= =
0
K s aP,l Hours'
11-
=
PI7,
=
0
=
12-
TI 7 M T z
=
ll.,hiTz'
=
X*
=
A',*
=
8-
0
002
Arithmetic
004
006
008
010
M e a n Particle Diameter d p , inch
Figure 6. Over-all rate coefficient vs. particle size for Type 4A molecular sieve beads 4
D,,,,(7021,
Sq Ft lHr 4 720 1 870 3 627 28 400 2 888 1 595 2 115 21 , 0 2 0 1 3 570 4 307 6 700 12 990 5 035
Summary
0
T = 6 6 5' F.
Pore DiffUsiLq.
I
1
Particle size -8+9 mesh spherical beads Inlet concentration x V ? 001101 lb. H,O/lb. dry air o 001542 Ib, H,O/lb d r y airT,900F: n
Particle I~iffU~lLitV. U p (7 0 6 ) Sq Ft Hr 3 970 1 948 2 575 15 410 2 910 0.895 1.605 15.600 1 0 . 820 6.120 7 990 10,970 5.360
l&EC PROCESS DESIGN A N D DEVELOPMENT
part of fixed bed in which water concentration change from C, to C E is occurring (C, and CE arbitrarily chosen as 0.05C, and 0.95 C,, respectively) surface area of particles, sq. ft.l'lb. solid air stream Ib-ater content in equilibrium with X*: Ib. HnO,'Ib.dry air inlet air \vater concentration, lb. H ? O / l b . dry air arithmetic mean particle diameter, feet particle phase diffusivitiy, sq. ft./hr. fluid phase pore diffusivity, sq. f t . ihr. fractional ability of adsorbent in MTZ still to adsorb !\-a ter mass flow rate of air per unit bed cross section, lb. dry air, h r . sq. ft. mass flo\c rate of air, Ib. dry airl'hr. gas film mass transfer coefficient. lb. H2O adsorbed1 hr. sq. ft., C-units pore diffusion mass transfer coefficient: lb. H20 adsorbed , h r . sq. f t . , X-units solid phase mass transfer coefficient. lb. H 2 0 adsorbed, 'hr. sq. ft.. X-units over-all mass transfer coefficient, Ib. so1id)hr. sq. ft. fixed bed volume, cu. f t . cumulative dry air passed u p to time t , lb. dry air cumulative dry air passed u p to breakthrough point, lb. dry air cumulative dry air passed u p to bed saturation point, Ib. dry air total air accumulated during breakthrough curve period from TI., to L I T E : lb. dry air-e.g.. ~lFhhiTz= Il-E - 11, total air accumulated during entire breakthrough curve period. Ib. dry air-e.g., from ll-,c cO-1.o) ivater content of adsorbent in equilibrium xvith C*, lb. H ? O lb. solid water content of adsorbent in equilibrium \vith C,: lb. HnO Ib. solid
IY
=
PI1 t
= =
PI,
=
intercept value of S* for linear isotherm approximation. Ib. H.0 lb. solid density of dry air. Ib. CLI. f t . bed void volume fraction. cu. i t . of voids CLI. f t . of bed bulk packed density of dry adsorbent. Ib. cu. f t .
l i t e r a t u r e Cited
(1) .\cri\.os. .\lidreas. Verriieulm, Throdore, Adr,nn. Chrm. En?. 2 , 147-208 (1958). (2) I.;it.lrton. I.. C . . I3liss. Harding, Chpm. En?. A o q r . 49, 543 (1953).
(.i) Xulter. J . 1 . . M.S. thesis. Ioiva State University, Arnes, Iowa,
1961, 14) Nuttrr, .I. I.. Ph.D. thesis, Iowa State University, Arnes. JO\\.d. 1963. (5) S u t t c r . .J. I.: Burnet, George, Jr., il.I.Ch.E. J . 9, 202 (1963). (6) Treybal. I
NUCLEI GROWTH REGION
0 DRUM
I
I
2000
3000
REVOLUTIONS, N
Figure 1 . Average pellet diameter as a function of number of drum revolutions for pulverized limestone VOL. 5
NO. 1
JANUARY
1966
5
