Ind. Eng. Chem. Fundam. 1986, 25, 405-409
z = 0;
T = 8 = TI + HI sin
(wt)
405
the largest deviation in the axial direction would occur near the bed entrance due to cooling effects from the incoming gas. This was found to be the case. (A7)
where b and a are the radius of the outer stainless steel shell and the catalyst bed, respectively, and L is the bed depth. Recall, our analysis is based on the concept of a mean effective thermal conductivity. Boundary conditions A5 and A6 reflect this approach. These two-dimensional time-dependent differential equations with associated boundary and initial conditions allow us to calculate the temperature profile within the bed under the transient conditions. The orthogonal collocation technique described by Finlayson (1980) with third-order Legendre polynomial used by Kreyszig (1979) and the biased-difference methods proposed by Heydweiller and Patel (1982) are used to eliminate the radial and axial direction dependences of eq A1 and A2. The software package developed by Byrne and Hindmarsh (1975,1976) is used to solve the resulting ordinary differential equations numerically. The temperature distribution in the axial direction was calculated layer by layer. Thus, the number of layers used for calculation in the axial direction may affect the final numerical results. To ensure that the temperature gradients are not affected by the choice of the number of layers used in the calculation, a reasonable number of layers has to be employed. We assume a hypothetical configuration of the catalyst particles in the bed to be in the form of individual particle layers. A bed with 5-mm depth will consist of 23 layers of 0.225-mm-diameter catalyst particles in the axial direction. To explore how the number of layers in the calculation affects the calculated derivative of temperature with respect to axial distance, the calculation was made for 10 layers and 26 layers. The results showed that differences between the 10-layer calculation and 26-layer calculation were negligible. In other words, the results are independent of the number of layers used in the axial direction when the number of layers is larger than 10. I t is interesting to note that because the gas residence time above the bed is short (-2 s), it was expected that
Nomenclature a = radius of catalyst bed, m b = radius of outer stainless steel shell, m (C,),, (C,), = specific heat of gas and catalyst particles, respectively, kJ/(kg K) HI = amplitude of temperature modulation, K k,ff = mean effective thermal conductivity of catalyst bed, W/(m K) kshell = thermal conductivity of reactor shell, W/(m K) r = radius position in catalyst bed, m T = temperature of catalyst bed, K t = time, s TI = common temperature, K u, = superficial velocity per unit area, m/s z = axial position in catalyst bed, m Greek Letters tb
= porosity of catalyst bed
8 = temperature of outer shell, K pg, ps = densities of gas and catalyst particles, kg/m3 w = modulation frequency, s-l 7 = cycle time, s
Literature Cited Argo, W. B.; Smith, J. M. Chem. Eng. Prog. 1953. 4 9 , 443. Byrne. G. D.; Hindmarsh, A. C. Report UCRL-75868, 1975; Lawrence Livermore Laboratory, Livermore, CA; Report UCID-30312. 1976; Lawrence Livermore Laboratory, Livermore, CA. Coberly, C. A.; Marshall, W. R., Jr. Chem. Eng. hog. 1951. 4 7 , 141. Deissler, R. G.; Eian. C. S. National Advisory Committee for Aeronautics: RM-E52c05, Washington, DC, 1952. Falconer, J. L.; Schwarz, J. A. Catal. Rev.-Sci. Eng. 1983, 2 5 , 141. Finlayson, B. A. Nonllnear Analysis in Chemical Engineering; McGraw-Hill: New York, 1980; p 117. Froment. G. F.; Bischoff, K. B. Chemical Reactor AnafLsls and Des@n; Wiiey: New York, 1979; p 532. Heydweiller, J. C.; Patel, H. S. Comput. Chem. Eng. 1982. 6 , 101. Hill, C. G., Jr. An Intrductlon to Chemical Engineering Kinetics & Reactor Design; Wiiey: New York, 1977; p 496. Kreyszig, E. Advanced Engineering Mathematics; Wiiey: New York, 1979; p 195. Kunii, D.; Smith, J. M. AIChE J . 1980, 6 , 71. Lee, P. 1.; Schwarz. J. A. J . Catal. 1982, 73, 272. Leva, M. Ind. Eng. Chem. 1950, 4 2 , 2498. Polizzotti, R. S.; Schwarz, J. A. J . Catal. 1982, 77, 1. Vannlce, M. A. J . Catal. 1975, 3 7 , 449. Zehner, P.; Schiunder, E. U. Chem.-Ing.-Tech. 1970, 42, 333. Zehner, P.; Schlunder, E. U. Chem.-Ing.-Tech. 1972, 44, 1303.
Receiued for review September 25, 1984 Revised manuscript receiued September 11, 1985 Accepted October 10, 1985
Packed Column Efficiency Fundamentals Gordon A. Hughmark Ethyl Corporation, Baton Rouge, Louisiana 7082 1
Turbulent liquid-film hydrodynamics are used with experimental liquid-film data for dumped and structured packings to develop relationships for liquidfilm thickness and gas-phase pressure drop analogous to vertical gas-liquid flow in a circular pipe. The turbulence contribution to liquid-phase mass transfer is found to be represented by the shear velocity of the liquid film. The analysis can be extended to the flooding point as experimental flooding data show a consistent relationship of the dimensionless film thickness and the hydraulic radius for flow in the packing.
A reliable design method for packed column masstransfer efficiencies should logically depend upon the two-resistance model with a vapor-liquid interfacial area and calculated vapor- and liquid-phase mass transfer
coefficients based upon fundamentals. Such a design method would be more likely to extrapolate correctly to systems outside the range of experimental efficiency data than methods based upon empirical models. Packed 0 1986 American Chemical Society
406
Ind. Eng. Chem. Fundam., Vol. 25, No.
3, 1986
column efficiencies should be more readily modeled from fundamentals than tray column efficiencies because the two phases represent nearly countercurrent flow through packing with minimal back-mixing. The vapor-liquid contacting and liquid back-mixing that occur on crossflow trays make a fundamental model of efficiency extremely difficult if not impossible to develop. Bolles and Fair (1982) note the lack of a reliable, generalized design method for packed column efficiency and report the development of an improved model for the empirical estimation of the heights of a vapor-phase transfer unit and a liquid-phase transfer unit. This model combines the interfacial area with the mass transfer coefficient €or each phase. Hughmark (1980) attempted to separate interfacial areas and the mass transfer coefficients so as to apply fundamental models to the latter. This work indicated that the liquid-phase mass transfer could be represented by the behavior of a turbulent falling film. The vapor-phase mass transfer for a turbulent flow system was found to be related to the behavior of a free interface, the shear velocity contribution corresponding to a fraction of the pressure drop in the packing. The vapor velocity for the calculations was that relative to the falling liquid film rather than to the packing. This paper presents an extension of the prior work and suggests a design method for estimation of packing efficiencies. Interfacial Area Published vendor data are often available for C02 absorption from air into aqueous NaOH for each of several packings. The standard system is 1% C02ill air, absorbed in 4% NaOH (25% carbonate) at about 15 "C,so that K 6 is obtained as a function of liquid rate. At these conditions, the liquid-phase mass transfer coefficient, KL,is enhanced by the chemical reaction and is calculated as 0.0042 m/s in accordance with kinetic and other data summarized by Danckwerts and Sharma (1966). The two-resistance equation applicable to packing is H -RT = - + RT K,a k,a kLa
For K 8 in units of s-' and the Henry's law coefficient, H, of 2225 kPa/(kg-mol m3) for COz-water, eq 1 is 2225 -RT- - -RT K,a k,a 0.0042~
+-
Only about 10% of the total mass transfer resistance is generally represented by the gas phase in this system. The gas-phase mass transfer coefficient can be calculated by the method presented in the next section. Solution for interfacial area is by trial and error. Even though there may be considerable error in the calculated gas-phase mass transfer coefficients, this will have a relatively small effect on the interfacial area calculated from K,a data. Vapor-Phase Mass Transfer Coefficients The prior paper (Hughmark, 1980) presented a model for vapor-phase mass transfer in packings. The model is applicable to packings when the flow in the vapor phase is turbulent and, therefore, is restricted to packing sizes of 2.54 cm and larger. As the background for the model was presented in the prior paper, only the method is presented here. The mass transfer coefficient is a function of the shear velocity of the vapor stream in the packing. The shear velocity for a turbulent fluid is u(f/2)'l2. The vapor velocity for a packing, UG, is estimated as the velocity of the gas in the free cross section of the wetted packing, relative
to the velocity of the countercurrent liquid falling film. The difference is the vapor velocity at the free interface between the vapor and liquid. A method for estimating the liquid-film velocity is presented in the next section. The equation for the relative vapor velocity is UG
= uGs/c
+ UL
(3)
where E is the void fraction of the wetted packing. The friction factor for vapor flow in the packing is obtained from the pressure drop at the flow conditions:
f=
2 (@/ 2)
(4) apuG2 A fraction, a,of the pressure drop represents shear drag and is applicable to mass transfer. Vapor shear velocity is then uG(Y(f/2)'/2. The equation for mass transfer is (f/2)'I2
kG =
l/kT+
+ 1/[a(f/2)'/2]
(5)
The term kT+ is the dimensionless maas transfer coefficient for the transition region of turbulent flow and as shown by the previous paper is kT+
= (0.097/Ns,,)(a tan [34.6(0.0094Ns,)'/2] a tan [5.5(0.0094Ns,)'/2]}-1 (6)
The term 2c~(f/2)'/~ is the dimensionless mass transfer coefficient for the core region, within which mostly turbulent diffusion and negligible molecular diffusion occur. Liquid-Phase Mass Transfer Coefficients The prior paper suggested the Kapitsa equation to represent the liquid film on packing when the vapor-phase resistance is negligible. A less restrictive model is obtained, however, from consideration of a turbulent liquid film with a vapor-phase contribution to the wall shear stress of the liquid film. Kosky (1971) developed a film thickness correlation for annular gas-liquid flow with the dimensionless film thickness y+ as a function of the liquid-film Reynolds number. Kosky used the wall shear stress for the shear velocity term in the dimensionless film thickness. Henstock and Hanratty (1976) suggested a characteristic shear stress that is a weighted average of the wall and interface shear stresses. This provides a good correlation of film thickness data for vertical, annular,gas-liquid flow. The equation for the wall and interface shear stresses for vertical, annular, gas-liquid flow can be modified to represent packing.
7w = [Pea - PG(1-
e)
- ~W/Z)I:
(7)
The Henstock and Hanratty characteristic shear stress, T,, is approximated by 7, = (2/3)7w (1/3)~i (9) Data from the Norton Engineering Co. (1977) provide experimental liquid holdup values for various random packings as a function of the gas-phase pressure drop. McNulty and Hsieh (1982) report similar data for the "Flexipac" structured packings. All of these data are with water as the liquid. The holdup data of Shulman et al. (1955) on 2.54-cm Raschig rings are reported for water, benzene, methanol, and aqueous calcium chloride. Holdup data for negligible gas-phase pressure drop were used with interfacial areas from the COz-aqueous NaOH data to
+
Ind. Eng. Chem. Fundam., Vol. 25, No. 3, 1986 407
estimate the film thickness and then the shear velocity from the shear stress equations (7) and (9) with q = 0. The calculated values of y+ = yu*/v were then correlated with the Reynolds number, 4L/uv. A single linear correlation was found to represent the data for 2.54-, 3.81-, and 5.08-cm Raschig rings and 5.08-cm Intalox saddles.
y+ = 7.9
+ 0.07(4L/uv)
(loa)
For 34 data seta including the data for liquids other than water, the average absolute deviation between experimental and calculated values of y+ is 6.0%, so this model appears to be a good representation of the data. Similar equations were obtained for 5.08-cm Pall rings
y+ = 5.5 + 0.04(4L/uv)
0 NORTON (19771 C02-aq. NaOH A NORTON PR-16 i80-oclano/tobo~
(lob)
and Flexipac Type 2
y+ = -0.3
+ 0.0264(4L/uv)
(10c)
The wetted interfacial area was assumed equal to the dry surface area for Flexipac Type 2 because this is a structured packing. Data for liquid holdup in the presence of gas flow, providing a significant pressure drop, can then be used with eq 7-9 and one of the equations for y+ as a function of Reynolds number to calculate the fraction of the pressure drop causing shear, a. This assumes that y+ is a function only of Reynolds number and does not vary with gas-phase pressure drop. Averages of calculated values for a are 0.17 for 2.54-cm Raschig rings, 0.30 for 5.08-cm Pall rings, and 0.57 for Flexipac Type 2. These values are consistent with values of a from my previous paper, obtained from the shear contribution from pressure drop for the vapor-phase mass transfer coefficients. The prior paper shows a correlation of the liquid-phase mass transfer data for packing as
k+NSc;l2 = O.O!27( 4L vu ) I 3 The constant for eq 11 was obtained from a different equation for shear velocity than from eq 9. Calculation of a constant for eq 11from the oxygen-water desorption data of Sherwood and Holloway (1940) with interfacial areas from the C02-aqueous NaOH data for 2.54-, 3.81-, and 5.Wcm Raschig rings shows an average value of 0.0168 with a standard deviation of 0.0035. Water flow rates were in the range of 0.0014-0.042 m/s. Echarte et al. (1984) show mass transfer data for COS desorption from water and 25-50 w t 9% glycerol in water with 5.8-cm Raschig rings. Interfacial areas are also shown for this packing with water as the liquid. The water data represent a flow range of L = 0.0025-0.0135 m/s. The average value of the coefficient for eq 11for the water and glycerol-water and glycerol-water data is 0.0102 with a standard deviation of 0.0011. The interfacial areas for the 5.8-cm Raschig rings were considerably higher than would be estimated from the normal interfacial areas for 2.54-, 3.81-, and 5.08-cm packings. The correction for estimated areas is consistent with the smaller packing results in a coefficient of 0.012. This coefficient is used in succeeding calculations in this paper.
Interfacial Area Comparison Norton Bulletin PR-16 shows Kcu data for C02 and aqueous NaOH and HETP data for distillation of isooctane-toluene mixtures a t total reflux and atmospheric pressure with 5.08-cm Pall rings. Data for both systems are available over the same range of liquid superficial velocities. The C02-aqueous NaOH data are from a 76-
40
*I
I I
-i 01 0
1
I
2
3
4
5
6
L, m/r I 10-2
Figure 1. Calculated interfacial areas (5.08-cm Pall rings).
cm-diameter by 3.05-m-deep packed bed. Isooctanetoluene data are from a 38-cm-diameter by 0.05-m-deep bed. These data provide an opportunity to calculate interfacial areas for aqueous and organic liquid systems at the same superficial liquid velocities. Equations 2 and 5 were used to calculate interfacial areas from the CO,-aqueous NaOH system data. Figure 1 shows the interfacial areas as a function of liquid superficial velocity. Equations for vaporand liquid-phase mass transfer coefficients were used by trial and error with assumed interfacial areas to match the experimental HETP for the isooctane-toluene system. Figure 1 shows two calculated interfacial areas. These appear to be nearly the same as for the COB-aqueous NaOH system at the same superficial liquid velocity. The COz-aqueous NaOH system efficiency contains a major contribution from the interfacial area and a minor contribution from the gas-phase mass transfer coefficient. The isooctane-toluene efficiency contains a large contribution from the vapor-phase mass transfer coefficient and a minor contribution from the liquid-phase mass transfer coefficient. This comparison indicates that the model and the equations for interfacial area and the vapor-phase mass transfer coefficient are consistent with experimental data. The liquid-phase mass transfer coefficient does not enter into calculations with the C02-aqueous NaOH system and influences the efficiency of the isooctane-toluene system in a minor way, so these data do not provide a test of the liquid-phase mass transfer coefficient model and the equations. The interfacial area shown by Figure 1for 5.08-cm Pall rings is the typical response to liquid rate for a random packing. Interfacial area is observed to increase rapidly with increased liquid rate a t low liquid rates and to be relatively constant at high liquid rates. The dry surface area for this packing is 102 m2/m3so that interfacial area at high liquid rates exceeds the dry surface area. Equivalent interfacial areas are indicated for the aqueous and organic liquid system at liquid rates less than 0.005 m/s. As this is an extrapolation of interfacial areas calculated from experimental data, it is not known whether
408
Ind. Eng. Chem. Fundam., Vol. 25,
No. 3, 1986 IO
interfacial areas are equal for different systems with the same volumetric flow rate at the very low liquid flow rates. McNulty and Hsieh (1982) report results for heat transfer from heated water to air for 5.08-cm slotted-ring packing. Data for three liquid rates and a range of air rates for each liquid rate are presented, including liquid holdup and pressure drop values. Gas-phase transfer coefficients were estimated from eq 3-5. Average interfacial areas obtained with the calculated gas-phase transfer coefficients at the three liquid rates are as follows: L = 0.0034 m/s, a = 53 m-l; L = 0.0068 m/s, a = 103 m-l; and L = 0.0135 m/s, a = 126 m-l. The interfacial areas at the higher liquid rates are somewhat greater than values shown in Figure 1. The difference in interfacial areas may result from end effect contributions because a very short length of the column, 0.6 m, was used for active heat transfer. Surface Tension Effects Koshy and Rukovena (1982) report data for the methanol-water and water-dimethylfuran (DMF) systems using Norton’s No. 25 IMTP packing. These fluid systems were selected because the surface tension of the light component is less than that of the heavy component in the methanol-water system, and the reverse is true in the waterDMF system. This difference could possibly have an effect on the film flow characteristics. Interfacial areas were calculated from the C02-aqueous NaOH K a data in Norton Bulletin MI-80 for this packing. Interfacial areas were calculated from the methanol-water and water-DMF data for total reflux. These HETP values should represent minimum error. Liquid holdup data are not published for the packing, so film characteristics were assumed equivalent to 5.08-cm Pall rings. Calculated interfacial areas for the methanol-water and water-DMF systems were found to be essentially equal to the interfacial areas calculated from the C02-aqueous NaOH system at the same superficial liquid velocity. This indicates that the liquid films in these systems have about the same interfacial area for mass transfer. The relatively small contribution of the liquid-phase mass transfer coefficient to the calculated area does not rule out the possibility of an effect from the uncertainty in the mass transfer coefficient. Pressure Drop and Flooding The prior paper showed that the friction factor from eq 4 is relatively constant below the load point of the packing. Extension of a pressure drop model into the load region and to flooding is desirable. Hughmark (1973) showed that the friction factor for the gas phase in vertical upward annular flow increases as the ratio of the film thickness to the pipe radius increases. Figure 2 shows friction factors calculated from eq 4 from the Norton Engineering Co. (1977) data for pressure drop and liquid holdup with 5.08-cm Pall rings. The friction factors are plotted as a function of ya/2t, the equivalent of the y/(pipe radius) ratio for annular flow. For high liquid flow rates, the interfacial area is the wetted surface area. For low liquid flow rates and in the extreme for no liquid flow, an effective interfacial area is required for eq 4. This is apparently about 80 m-l for 5.08-cm Pall rings. Figure 2 shows the factor increases with increasing film thickness. Flooding could be expeded to occur when the wall shear stress of the liquid film is zero. From eq 7, flooding should occur when p ~ y a+ pc(t - 1)= abp/Z. Extensive flooding data are provided by Billet (1967) for 5.08-cm Pall rings. The data represent flooding at different liquid and vapor rate combinations for the four systems listed under this reference in the section Interfacial Area Comparison. The friction factor for each data set was fit to the curve of
0
f
0 5.0Ocm
PALL RI NOS
I
A
-
FLEXIPAC TYPE 2
A A
a A
0 FLOODING DATA
0.1
I
0.01
0.I
0.2
y0/2e
Figure 2. Friction factors calculated from eq 4 (5.08-cm Pall rings).
Figure 2 by variations in a. For 14 data sets, the values of a ranged from 0.50 to 0.88 with an average of 0.72. Thus, the shear fraction of vapor-phase pressure drop is higher at flooding conditions, about 0.72, than below the load point, where the value of about 0.30 was found. This indicates a greater interaction between the liquid and the vapor above the load point, as shown by the increase in friction factor and the increase in the shear fraction of the vapor-phase pressure drop. Flooding data shown by Figure 2 indicate that this occurs when ya/2c is greater than about 0.08.
Figure 2 also shows the friction factor for Flexipac Type 2 from the data of McNulty and Hsieh (1982). Friction factors are observed to be much lower than with 5.08-cm Pall rings. The indicated load point is at ya/2c about 0.06; the flood point is at ya/2e about 0.1. The fraction shear of the gas-phase pressure drop approaches unity, in comparison to a fraction of about 0.4 below the load point. Similar responses of the friction factor and the fraction of pressure drop producing shear occur with both random and structured packings. HETP Calculations Computer programs were written to calculate HETP and pressure gradient for various random and structured packings using the model concepts described in this paper. Strigle and Rukovena (1979) reported HETP data for the isooctane-toluene system at atmospheric pressure with 5.08-cm Pall rings. These total reflux data represent a range from about 30% of flood to near the flood point. Comparison of experimental HETP data with values calculated from the computer program shows a 7% average absolute deviation for 11 data sets and a maximum deviation of 20%. Norton Engineering Company data (1977) for 5.08-cm Pall rings show pressure gradients for the air-water system as a function of gas and liquid rates. Sixteen data sets were selected to cover the range of the data from a liquid rate of 0.007 to 0.028 m/s. The average
Ind. Eng. Chem. Fundam., Vol. 25, No.
absolute deviation between reported pressure gradients and values calculated with the computer program is 8.6%. As pressure gradient and HETP calculations both require the fraction of the vapor pressure gradient that represents shear, this fraction can be obtained from either type of data. Thus, an entire computer program for a random packing can be obtained from the following data: (1) K from C02-NaOH(aq); (2) pressure gradient from liqui and gas combinations such as for the air-water system; (3) liquid holdup as a function of liquid rate and pressure gradient as from the air-water system. Computer programs were written for several packings with these data and were then tested with HETP data. The agreement was surprisingly good.
c$
Sample Calculation Data are from Strigle and Rukovena (1979) for isooctanetoluene at atmospheric pressure with 5.08-cm Pall rings: mass velocity a t a total reflux = 3.4 kg/(m2/s); HETP = 0.7 m; physical property data: pL = 657 kg/m3, pv = 3.36 kg/m3, vL = 3 X lo-’ m2/s, Nsc, = 51, N9 = 0.7 and m = 0.85; L = 3.4/657 = 0.00518 m/s, a = 79 m (from Figure l), 4L/(va) = 874, y+ = 5.5 + 0.04(874) = 40.5 (from m2/s; e for dry packing eq lo), yu* = y+vL= 1.215 X = 0.96, e for wetted packing = 0.96 - ya; f = 3 . 2 3 ( y ~ / 2 e ) ~ . ~ (from Figure 2) for low liquid rates. A solution for y is obtained from the above values of yu* and e with eq 3,4, and 7-9 by using uL = L / y a and a = 0.29 for eq 7 and 8 y = 0.00040 m, ya = 0.0316, e = 0.928, f = 0.8; U L = L / y a 0.164 m/s, UGS = 3.4/3.36 = 1.01 m/s, UG+= 1.25m/s (from eq 3), a = 0.29 (for 5.OScm Pall rings), kT = 0.171 (from eq 6), k~ = 0.026 m/s (from eq 5), and u* = 1.215 X 10-5/0.0004 = 0.0304 m/s. From eq 11 with the 0.012 coefficient, kL = 0.012 X (874)0.333X 0.0304/(51)0.5,kL-= 0.00049 m/s, I?L= (mass velocity)/(KLad = 0.134 m, HG = (maas velocity)/(kGapv) = 0.493 m, X =-m (ma_ssvelocity vapor)/(mass velocity liquid), I?% = HG AHL = 0.607 m, and HETP = R%(h X ) / ( l - A) = 0.66 m. This compares with 0.70 m from the experimental data.
+
Nomenclature a = interfacial area between gas or vapor and liquid phases, f = friction factor g = acceleration due to gravity, m/sz H = Henry’s law coefficient, kPa/ (kg-mol m3)
3, 1986 409
H = height of an individual transfer unit, m K = overall mass transfer coefficient, m/s
k = mass transfer coefficient, m/s k+ = k/u* L = superficial liquid velocity, m/s m = slope of equilibrium curve AP = packing pressure drop, Pa Ns, = Schmidt number R = gas constant, kPa m3/(kg-molK) T = temperature, K u = phase velocity, m/s u* = shear velocity, m/s y = film thickness, m y+ = dimensionless film thickness 2 = depth of packing, m
Greek Letters a = fraction of pressure drop producing shear drag e = packing void fraction v = kinematic viscosity, m2/s p
= density, kg/m3
T
= shear stress, Pa
Subscripts
G , V = gas or vapor phase GS = gas superficial L = liquid phase OG = overall gas phase T = transition region Literature Cited Billet, R. Chem. Eng. Frog. 1967, 63, 53. Bolles, W. L.; Fair, J. R. Chem. Eng. ( N . Y . ) 1982, 8 9 , 109. Danckwerts, P. V.; Sharma. M. M. Trans. Insf. Chem. Eng. 1968, 4 4 , CE 244. Echarte, R.; Campana. H.; Brlgnole, E. A. Ind. Eng. Chem. Process Des. Dev. 1964. 23. 349. Henstock, W. H.; Hanratty, T. J. A I C K J . 1978, 22, 990. Hughmark, 0. A. A I C M J . 1973, 19, 1062. Hughmark, 0. A. Ind. Eng. Chem. Fundam. 1960, 19, 385. Koshy, T. D.; Rukovena, F. Presented at the Annual Meeting of the American Institute of Chemlcal Engineers, Los Angeles, CA, Nov. 1982. Kosky, P. G. I n t . J . Heat Mess Transfer 1971, 14, 1220. ”Metal Intalox Tower Packing”; Bulletin MI-80;Norton Company: Akron, OH, 1977. McNulty, K. J.; Hsleh, C. Presented at the Annual Meeting of the American Instltute of Chemical Engineers, Los Angeles, CA, Nov. 1982. “Norton Englneerlng Data”; Norton Company: Akron, OH, 1977. “Norton Pall Rings in Mass Transfer Operations”; Bulletin PR-16; Norton Cornpany: Akron, OH, 1976. Sherwocd, T. K.; Holloway, F. A. L. Trans. A I C M 1940, 36, 39. Shulman. H. L.; Ulhlch, C. F.; Wells, N.; Proulx, A. 2. AIChE J . 1955, 1 , 259. Strigle, F. R., Jr.; Rukovena. F., Jr. Chem. Eng. Rag. 1979, 75, 86.
Received for review September 28, 1984 Revised manuscript received June 19,1985 Accepted July 25, 1985
