CF1 = da
D F
Q
Vsa Zo 2,
= = =
= = =
=
ratio of volume concentration of floc t o solid iron blue average (equivalent) aggregate diameter, p diamet’er of settling tube, cm volume ppm of flocculating ageiit/g of iron blue initial or masinium settling rate, cm/sec Stokes settling velocity of a single aggregate, cmjsec initial height of slurry column, cni final height of sett’led bed, cm
GREEKLETTERS 1.1
+i
= =
literature Cited Bodman, S. W., Shah, Y. T., Skriba, hf. C., Ind. Eng. (:hem. Process Des. Develop., 11,46 (1972). Fitch, B., Ind. Eng. Chem., 58 (lo), 18 (1966);, Kakar, K., “Settling of Iron Blue in Water, AIS thesis, University of Pithburgh, Pittsburgh, PA (1972). RIichaels, A. S., Bolger, J. C., Ind. Eng. Chem. Fundam., 1, 24 (1962a). Michaels, A. S., Bolger, J. C., ibid., I53 (1962b). Smith, J., personal communication, American Cyanamid co., Willow Island, WV (1971).
viscosity of solution, cP solid iron blue volume concentration
RSCEIVCD for review September 14, 1971 ACCEPTED December 27, 1971
Downloaded by STOCKHOLM UNIV on August 29, 2015 | http://pubs.acs.org Publication Date: April 1, 1972 | doi: 10.1021/i260042a028
COMMUNICATIONS
Mass Transfer in Through-Circulation Drying of Packed Beds
Experimental results on mass transfer obtained during the constant rate period of the through-circulation drying of packed beds, were analyzed. The results, expressed as j factors, were correlated using a theoretical model for fluid-particle mass transfer in fixed beds. A good agreement was found, which allows us to deduce that a laminar boundary layer exists over the range of Reynolds numbers investigated.
I n a through-circulation dryer a material generally dries at a constant rate until a critical moisture content is reached; then it dries at a progressively slower rate until drying is complete. This work is limited t o study the constant-rate period in which the flow of air through the bed provides only gas-film resistance to heat and mass transfer. The present investigation measures overall integral coefficients for a packed bed in the low range of air velocities commonly used in through-circulation drying. The results are correlated using Carberry’s model (1960) for fluid-particle mass transfer in fixed beds. Experimental Apparatus
The laboratory through-circulation dryer consists of a centrifugal fan which blows the air over 12 1-kW bar elements into a chamber at the base, and thence upward through a vertical duct. A removable basket containing the wet bed rests at the upper end of the duct. The vertical duct had a flow-smoothing section of 5 cm of small glass spheres. The air velocity was measured by a n orifice plate connected to a n inclined manometer. The inlet dry-bulb temperature was regulated by a thermostat and relay which controls one of the heaters. The humidities at inlet and outlet of the bed were determined with dry- and wet-bulb thermometers. The bed was made of ceramic cylinders 1.50 0.03 cm nominal size; these cylinders were capable of absorbing 31 2 Ind.
Eng. Chem. Process Des. Develop., Vol. 1 1, No. 2, 1972
sufficient quantities of water to exhibit constant drying rates. The bed was 500 cm2 in area and 7 cm in thickness; it had a void fraction of 37y0 calculated from the dimensions of the empty basket and the number and average size of the cylinders. To measure the temperatures of the surface of the cylinders in the bed, fine wire thermocouples (0.02-cm diam) were installed in several cylinders by drilling and inserting the wire through the hole until the couple junction reached a point just below the opposite surface. Experimental Procedure
The experimental technique applied to these studies represents a quantitative analysis of water evaporation rates from the available transfer surface in the bed of porous cylinders. All experimental measurements were restricted to the predetermined constant rate period to ensure transfer under steady-state conditions. T o provide a margin of safety, the runb were restricted t o a maximum of 75% of this predetermined constant rate period. The cylinders were soaked for 3 hr in distilled water. Then the water was poured off and surface droplets were removed with a cloth prior to placing them in the bed. An initial period of operation was allowed for the system to reach the steady state (about 10 min); the bed was then quickly removed, weighed, and returned to the dryer. After a time interval, the bed was again removed and weighed;
E '.,
the differential weight loss of the bed accounted for the water transferred to the gas phase. The mass transfer coefficients determined in this work are defined by
N A = b A ( p s - palm
010 L 008
006
t
(1)
The mean driving force was taken as the log-mean driving forces a t the bed inlet and outlet. The log-mean driving force is satisfactory for determining heat and mass transfer coefficients when the ratio of inlet to outlet driving forces is not large-Le., ( p s - pa)i/(ps- p&, less than 6 (Bradshaw and Myers, 1963).
- experimental _ _ _ _ theoretical
Jbi0,04
1I
I-
002
1
100
I
200
400
1000
2000
4000
Experimental Results and Discussion
Downloaded by STOCKHOLM UNIV on August 29, 2015 | http://pubs.acs.org Publication Date: April 1, 1972 | doi: 10.1021/i260042a028
According to Carberry (1960), the process of fluid-particle mass transfer in fixed beds a t Reynolds numbers (Re,) less than 1000, is viewed in terms of transient molecular diffusion within a boundary layer developed and destroyed repeatedly as the fluid travels through the bed. The following equation was developed by Carberry in terms of a boundary layer j factor, bed void fraction, and the average superficial yelocity based upon bed cross-sectional area: jbl
=
IC -
Sc2'% = 1.15 Re,-0,50
(2)
210
I n view of t'he model invoked, Equation 2 should be applicable until the flow rate approaches the value corresponding to turbulent boundary layer development. The precise value of the Reynolds number a t which the transition occurs in a packed bed is difficult to specify. By comparison of the theoretical Equation 2 with some empirical correlations, Carberry suggested that the model is valid to about Re, of 1000. The results of the present work can now be used to test the above suggestion. The experimental information was analyzed to determine the mass traiisfer factors, j , (Chilton and Colburn, 1934); these were corrected with the void fraction of the bed, and the resulting j values were plotted against the Reynolds number based upon average velocity in the bed. Figure 1 shows the comparison of experimental and theoretical data. The experimental relationship can be expressed as follows: jbu
=
1.22 Rep-0,5a
(3)
Figure 1. Comparison of theoretical and experimental data
usually found in through-circulat'ion drying, thus providing a theoretical support for predicting constant drying rates. Nomenclature
A j,,
transfer area, m2 boundary layer mass transfer factor defined by Equation 2 j , = mass transfer factor = kg N m p,, ( S C ) ~ ' ~ / G kg = mass transfer coefficient, kg mol/hr m2 atm SA= rate of mass transfer, kg mo1;hr p , = vapor pressure of water on surface of particle, atm pa = partial pressure of water in airstream, a t m Re, = Reynolds number, Dppu,/@ = ReJc Re, = Reynolds number, DppvJp u, = superficial velocity, cm/sec up = average velocity in the bed, cni,/sec GREEKLETTERS E = void fraction, dimensionless Y = kinematic viscosity, cmz/sec p = fluid densit,y, g/cm3 p = dynamic viscosity, P Literature Cited
Bradshan-, R.D., lIyers, J. E., dZChEJ., 9, 395 (19631. Carberry, J. J., ihid., 6 , 460 (1960). Chilton, T. H., Colburn, A. P., Znd.Eng. Chem., 26, 1183 (1934).
valid in the Reynolds range, 900
< Re, < 4000
whereRe, = Dppv,/l = Reo/€ Equation 3 compares fairly well with Equation 2 ; this means that the approximate upper limit of Reynolds number suggested by Carberry, Re, = 1000, could be extended t o about Re, = 4000. It is of great importance that Equation 3 is valid in the range of Reynolds numbers, 900-4000, since this range is
= =
JORGE C H I R I F E ' ROBERT G. GARD;"JER2 Departamento de Industrias Falcultad de Ciencias Exactas y Naturales rniuersidad de Buenos Aires, Argentina To whom correspondence jhould be addresaed. Present address, Department of Pure and Applied Chemistry, Univeriity of Strathclyde, Glasgow. 1
2
RECIXVED for review March 26, 1971 A4CCEPTED Allgust
Ind. Eng. Cham. Process Des. Develop., Vol. 1 1,
24, 1971
NO. 2, 1972 313
