Ind. Eng. Chem. Res. 1993,32, 2247-2253
2247
Pressure Drop in Ceramic Structured Packings Juana Uresti-Melhdez and J. Antonio Rocha' Znstituto Tecnolbgico de Celaya, Auenida Tecnolbgico y Garcia Cubas, Celaya Gto. 38010, Mexico
Three correlations to predict irrigated pressure drop in ceramic structured packings are proposed and compared. These are based on the open-channel model. First dry pressure drop is correlated, and then the pressure drop increment due to the liquid is taken into account. Data reported for aidwater in one commercial structured ceramic packing (Flexeramic) of three sizes, plus experimental data developed in this project for the system cyclohexane saturated vapor/cyclohexane saturated liquid were used for the development of the correlations. The average deviations for the three methods range between 25 and 31% .
Introduction One of the more important new developments for separation processes in the past decade has been the gradual displacement of plates by high-efficiencypacking in gas-liquid contacting columns. These packings may be random or structured packings. The packing material selection is based on the corrosionresistance. Carbon steel packings are usually the first choice for noncorrosive services, because stainless steel packings cost approximately4 times as much as carbon steel. Ceramic packings are specified when resistance to high temperature and inertness between the chemicals and the packing are required (e.g., in sulfuric acid absorption). The advantage of structured packings is that they eliminatemuch of the form drag associated with traditional dumped packings. This causes low-pressure drop without sacrificingefficiency or capacity. The high superficialarea per volume gives structured packings a high efficiency. Large spacing between adjacent parallel sheets provides high capacity, along with very low pressure drop. Fair and Bravo (1990)report that structured packings or packings with an ordered geometry evolved before 1940, but the credit for the specific geometry goes to Sulzer Brothers in Switzerland in 1965. The Sulzer packing was fabricated first from metal gauze and later from sheet metal. Actually there are packings made from carbon and stainless steel, ceramics, and various plastics. The objective of this article is to present, and discuss the development of, several correlations to predict the pressure drop through ceramic structured packings. We have used the pressure drop versus F,factor data reported for the packing Flexeramic on three different sizes, using the air/water system taken from Bulletin KCP-1 of Koch (1989)and experimental points measured in our laboratory for the system cyclohexane saturated vapor/cyclohexane saturated liquid for the Flexeramic 48. Previous Work Methods for estimating maximum hydraulic capacity and pressure drop for a packing are extremely valuable because in many cases they provide a basis for design. Previous methods have been developed following one of three approaches: (a) a generalized pressure drop correlation (GPDC) based on the original work of Sherwood et al. (1938); (b) empirical flow parameter vs capacity parameter plots; (c) friction factor/dry pressure drop correction methods. The first approach has been used for a long time, and several updates and modifications have been made over the years. The modification by Eckert (1970)is representative of the versions used today. O~SS-58S5/93/2632-2247$04.QQIQ 0
The Eckert diagram is designed to provide both limiting capacity and pressure drop predictions. A single constant, the packing factor, is presumed to account for differences between packing sizes and types. Fair and Bravo (1990)discuss several methods for the prediction of the flood point and pressure drop in structured packings and emphasize the usefulness of empirical capacity plots. The main disadvantage of this approach is that a particular plot is needed for each size and type of packing. This approach is used by the structured packing vendors to estimate capacity, based on a limited amount of data. It is important to note that, in many cases, significant anomalies have been found in the prediction of the maximum capacity of a structured packing when the prediction was based on the extensions of these empirical plots, especially at high liquid loads and gas densities. A novel approach for estimating pressure drop and flooding point for random as well as structured packings has been presented by Stichlmair et al. (1989). This method is more fundamental in nature and should be more general. The approach is based on the pressure loss in a dry bed of particles and how it is affected by the presence of the liquid. The derivation of the model follows an analogy to a fluidized bed where the change in void fraction is caused by the presence of irrigating liquid. A very important feature of this work is that it takes into account the direct effect of holdup on pressure drop and vice versa. The prediction of holdup is key to the implementation of the model. Two additional methods, applicable to random as well as structured packings, have been presented by Robbins (1990)and by Kister and Gill (1991).These methods are more empirical than that of Stichlmair et al. but have been validated with a very extensive data bank that includes most of the commercially available random and structured packings. In many cases the data used in the development of the correlations were obtained from vendor literature. A method specifically developed for the prediction of pressure drop in structured packings is that of Bravo et al. (1986). This method has proven to be very reliable at low pressure drops, those typically found in structured packing applications, but is not reliable at pressure drops above 600 Palm. The reason for this is that the original model was developed specificallyfor pressure drops below the loading point. Rocha et al. (1993)present a general model for structured packings that is an extension of the Bravo et al. (1986) model. It can be used to predict pressure drop above the loading point and up to flooding.
1993 American Chemical Society
2248 Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993
Model Development Although the models discussed in the previous section have been developed for metallic structured packings, the model of Rocha et al. (1993) has provisions for including the effect of different materials of construction as well as inclination angles for the parallel sheets. The fundamental equation relating friction factor and gas velocity under dry pressure drop conditions has been discussed extensively in the literature. The more recent general models for pressure drop in irrigated packed beds are based on the correction of the dry pressure drop by the presence of liquid holdup. The works of Bravo et al. (19861, Bemer and Kalis (1978), Billet and Mackowiak (19841, and Buchanan (1969) all proposed the same general equation for the irrigated pressure drop based on the channel model: hp _
( U / U ) d
- (1- C3hLI6
of geometry, sizes,surfaces, and flow conditions commonly encountered in metallic structured packing applications. For irrigated pressure drop, eq 1 is used:
In this paper, three correlations to predict AP/U are studied; they differ in the form of the term C3h~.The bases of these correlations are as follows: Method I. Method I is based on the article of Bravo et al. (1986). Liquid holdup is taken as proportional to the liquid Froude number: C3h, = alFrLaa Method 11. Method I1 is based on the article of Rocha et al. (1993). Liquid holdup is a function of liquid and vapor flow rates, by means of the following equation:
(1)
( f l / u ) d is the “dry bed pressure drop”, for the flow of gas through the packing without any flow of liquid. The term hL represents liquid holdup (volumetric fraction of the liquid phase), and C3 is an adjustable constant. The exponent in eq 1takes different values according to the authors, from 3.0 for Billet and Mackowiak (1984) to 4.65 for Stichlmair et al. (1989) to 5.0 for Bemer and Kalis (1978). The first two papers use the particle model, while Bemer and Kalis use the channel model. Stichlmair et al. (1989) proposed a slightly different form of eq 1 based on the particle model. Since the geometry of structured packings approximates more closely with the channel model, eq 1with an exponent of 5 will be used as the basis for the development of the new pressure drop correlation for ceramic packings. Equation 1 is fundamentally correct and can be arrived at theoretically with few assumptions. Bemer and Kalis (1978) and Buchanan (1969) explain the development of the equation in detail. The dry pressure drop is calculated using a conventional friction factor equation, as proposed by Bravo et al. (1986) and by Rocha et al. (1993):
where the friction factor f is a linear function of the inverse of the gas Reynolds number: (3)
and the effective Reynolds number for the gas, is defined as (4) As proposed earlier by Bravo et al. (1986), and more recently by Rocha et al. (19931, the definition of the equivalent diameter of the structured packing is taken as the side of the corrugation. Combining eqs 2-4 provides a final expression for dry pressure drop:
Previous work (Bravo et al., 1986; Rocha et al., 1993) proved that a single expression for the friction factor (similar values for C1 and C2)covered the complete range
Ft is a correction factor for partial wetting that depends only on liquid properties and velocity. Shi and Mersmann (1985) propose b( We ~ r ) ~ l 3 ~~ ’ s O Ft = 02 06 (8) Re, . e * (1- 0.93 cos y)(sin I ~ ) O * ~ where 0 is a constant and the terms WeL,FQ, and Re, are the dimensionless (liquid) Weber, Froude, and Reynolds numbers respectively. The contact angle y takes into account the wettability of the packing material by the working fluids using the surface tension of the liquids and the material of the packing. For example, Rocha et al. (1993), on the basis of the work of Shi and Mershmann (1985), report for stainless steel: cos y = 0.9 for CT < 0.055 N/m (9) cos y = 5.211 X 10-16.8S6efor Q > 0.055 N/m (10) The term geffin eq 7 is the effective gravity introduced in the article of Rocha et al. (1993):
This effective gravity accounts for the influence of gas velocity (through the term hp/U)on liquid holdup h ~ ; high values of h~ produce high incrementa of pressure drop above the load point and below the flooding point. The term ( f l / A , Z ) f l dis the pressure drop at flooding and is taken as the value of the pressure drop when the slope of f l l Uversus F, factor approaches infinity. From the analysis of the curves reported in the Koch Bulletin (1989) a value of 2050 Pa/m (2.5 in. of liquid/ft of packing) was taken as the value for (hp/A,Z)flood,for the three sizes of Flexeramic packing. Equations 1,7, and 11show an interrelationship between liquid holdup and pressure drop and imply that the solution method for these parameters must be an iterative one. Method 111. Method I11is based on the thesis of Uresti (1993). Liquid holdup is considered proportional to liquid and gas flow rates in direct form: C3h, = a$rLa4Reg,? (12) This method intends to account for the influence of gas velocities, but in a simpler form than method 11.
Data Bank Pressure drop data (dry and irrigated) using the system air/water, for the ceramic structured packing Flexeramic
Ind. Eng. Chem. Res., Vol. 32,No. 10,1993 2249 Table I. Geometric Characteristics of Flexeramic Structured Packing and Operational Parametere for Irrigated Pressure Drop with the System Air/Water Flexeramic type 28 type 48 Geometric Parameters 0.018 S (m) 0.009 € 0.70 0.74 45.0 0 (ded 45.0 157.0 up (m2/m8) 282.0 Operational Parameters UL, (m/s) 0.0034 0.0034 0.0068 0.0068 0.0136 0.0136 0.0204 0.0204 0.0272 0.0272 0.0340 F, (m/s)(kg/m~)o~5 0.509-2.607 0.868-3.168
3
PWexp PDd =I-28
+
PDd cab4
A
PDd calc-86
type 88
0.036 0.85 45.0 102.0 0.0034 0.0068 0.0136 0.0204 0.0272 0.0340 0.716-4.678
,o
..L
0.1
1
10
M, (mk) ( k g / m 3 ) 0 ' 5 [*0.82=( f tl.)( I blt t
)O*
1
-
I
0
mew
A
u
8
U b.0272
u
~.0094 m.0136
0 0 0
loo0
t
F 0.1
1
Fa, ( d o )
(kglm
[*0.82=( f t/r)(Iblf t
i
t
10 10
3 0.5 0.1
) 0 * 5I
10
H,(mh) (kglm
Figure 1. Comparisonof experimental and calculated values of dry pressure drop for Flexeramic types 28,48,and 88.Equation 14 was wed. Air/water, atmospheric pressure.
in three different sizes, has been published by Koch (1989). From the same reference and from direct measurement, the geometric characteristics of the different packings are shown in Table I. The range for the irrigated pressure drop was taken from 25to 2050Pa/m (0.03-2.5in. of liquid/ f t of packing). The data bank also includes experimental points measured in this project for dry and irrigated pressure drop for the system cyclohexane saturated vapor/cyclohexane saturated liquid.
1
3 0.6
-
[ *0.82r(t t h ) (I blt I
)Os ]
Flexeramk O M h d 1
100
Correlation Development And Results Dry Pressure Drop. By analogy with metallic structured packing, the dry pressure drop for the ceramic structured packing was calculated by eqs 2-4. When these equations were applied to the experimental data, different values for the friction factor were obtained for the different sizes of the ceramic structured packing. Because the material is the same, it is assumed that the friction factors should be the same, independent of the size. In order to get this result, the original expression for the friction factor was affected for several combinations of the void fraction. The best fit was obtained with eq 13:
The best values for C1 and CZwere 0.0453 and 6.6441, respectively. The final expression for the prediction of
0.1
10
1
F8, (mh)
(kglm
[*0.62-(ffh)(Iblft
Figure 2. Comparison of experimental and calculated values of irrigated pressure drop for Flexeramic types 28,48,and 88.Method I with eq 16. Air/water, atmospheric pressure.
dry pressure drop for Flexeramic is given by
The calculated and experimental dry pressure drop for the three types of Flexeramic packing are shown in Figure 1. The mean average absolute deviation is 10% This
.
2250 Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993
the best fit gives
0
+
C3hL= 2.5113Fr>m (15) The complete expression for predicting irrigated pressure drop for method I is
PDexp PDcal
6.644lp, U,, + -AP - se2(1- e)(sin el2 S2a(1- €)(sine) Az 1-2.5113 (,,),m)s 0 . 0 4 5 3U ~,, ~"
(16)
gs
10
L-
o. 1
1 Fs (mh) (Kglm ')'" [*0.82=(ftl~)(lbltt
-=loo0
i
0
+
10
3 )0 . 6 I
Method II
PDexp PDcal
Figure 2 shows the fit of the calculated pressure drop for method I. The deviation is 31 % . Figure 3 shows a comparison of measured and calculated irrigated pressure drop for the system cyclohexane saturated vapor/cyclohexane saturated liquid. Method 11. In order to calculate hL and C3, several parameters must be determined; hL is obtained from eq 7. The Ft factor is taken from the work of Rocha et al. (1993) with the value of cas y adapted for ceramic packings. The cosine of the contact angle for ceramic packings is calculated. From Figure 6 of the paper of Shi and Mersmann (19851, cos y = 0.9 for u C 0.065 N/m (17) cos y = 1.5209 X 103.s1&4r for
Ft =
i
L L.J. i
0.1
10
Method 111 0
PDexp PDcal
i
i
29.12(WeFr)21ss0.369 Re22co.e(l- 0.93 cos y)(sin e)'.
10
1 Fs ( m h )
(Kglm 3 ) 0 ' 5
'
['O. 8 2 4 ttlS)( 1 blft )O' I Figure 9. Comparison of experimental and calculated values of irrigated pressure drop for Flexeramic type 48. Me&& I, 11, and 111. System cyclohexane Saturated vapor/cyclohexane eaturated liquid, atmospheric pressure.
deviation is calculated by % deviation abs(calculated value - experimental value) experimental value Irrigated Pressure Drop. Method I. The values for a1and a2 for eq 6 were calculated by linear regression, and
(18) (19)
Constant C3 for eq 1 was calculated by linear regression with the same points of the data bank. It was found that C3 is a function of packing size or corrugation size according to eq 20: C3 = 0.626 + 32.6699 (20) Then the final correlation in method I1 is
The recommended procedure is summarized in Table 11. It is an iterative method that has only two iterations. Figure 3 shows the comparison between experimental and calculated irrigated pressure drops for method 11,using the system cyclohexane saturated vapor/cyclohexane saturated liquid, for Flexeramic 48. Figure 4 shows the fit of this method 11,for the system aidwater. The deviation is 25%. Method 111. The values for a3, ad,and a5 in eq 12 were calculated by linear regression. The best fit gives C3hL= 0.381Fr2"'Re
0.1
u > 0.065 N/m
(22) Then, the complete expression for predicting irrigated pressure drop with method I11 is 0.0453pgUg,"
,*e 0.257
6.6441pgUg,
Figures 3 and 5 show the fit of method 111. The deviation is 26%, for the system air/water.
Analysis of Results Based on Average Deviation. The analysis of Figures 2-5 may provide some insight into the performance of
Ind. Eng. Chem. Res., Vol. 32, No.10,1993 2251 Table 11. Method I1 To Predict Irrigated Pressure Drop for Flexeramic Structured Paclrings 1. Calculate dry pressure drop:
i
I
2. Calculate the first value for effective gravity, with ( A P / h z ) a= 2050 Palm, and (hp/m (u/Wd:
1
3. Calculate the first value for liquid holdup, using Ft from eq 1 9
10
-
0.1
10
1
(T-3)
8 0.5
Fs, (rnh) (kglm )
s)O's]
['0.82=(ttl~)(lbMt
4. Calculate the first estimate of the irrigated pressure drop: (u/hz)d
[l- (0.626
+ 32.669S)hL116
(T-4)
5. Calculate the second effective gravity; WlWnood =
2050 Palm:
.
1
-
gc
c
==p
1000
0
.
PDap
u u
u
Flexeramk 48Mthod II
w.0136
0 0 0
c . 0 2 7 2 0
0. 100
:
8 0
-
8A{A
a#
08
A
-
-
8 0
=g
!3
...&&*
oo
2 s
6. Calculate the second liquid holdup:
i
w.0034
0 I
10
7. Calculate the final irrigated pressure drop:
each one of the three proposed methods, but a comparison of the average absolute deviation may prove useful. The average deviations for the 134 data points were classified in different forms: (A) by method (I,11,111);(B) by packing size (28,48,88); (C)by range of pressure drop, (1)hp < 410 Pa/m (0.5 in. of liquid/ft) and (2) 410 < M/AZ C 820 Pa/m, and (3) hp/AZ > 820 Pa/m (1.0 in. of liquid/ft). All these values are shown in Tables I11and
IV. Based on Their Mechanisms. Method I, taken from Bravo et al. (1986),considers the liquid holdup as a function only of liquid flow rate. Thus, this model will theoretically be good only for pressure drop below loading. However, this model has the advantage of being the most simple method proposed. Method 11, taken from Rocha et al. (1993), is more rigorous because it takes into account the effect of both vapor and liquid flow rates. This procedure predicts well the pressure drop within the loading region and provides a great deal of insight into the determination of maximum hydraulic capacity of ceramic structured packings. One possible disadvantage is that more equations need to be solved in order to get the predicted value. The method presented in this paper requires only two iterations to provide a good prediction of irrigated pressure drop for Flexeramic structured packings. Method I11 is introduced as a means of taking into account the effect of vapor flow rate, but in a simpler form than method 11. The overall result seems to be good.
I
1 -
ge
==" 1000 6% 2
:
0
P D q
A
u u
.
u
Fiexerarnlc Whkthod II :
w.0034 w.0136 k.0272
go
O t
2%
?
Zr
Q
100
:
66
e 6
-
Q *O
P .o
s i gg
-t
-
e%?@@ 0 6 6
0
10
I
Conclusions Three methods to predict irrigated pressure drop in structured ceramic packings have been proposed. All the methods use the same general equations for dry pressure drop and then correct for the presence of liquid flow rate by means of the liquid holdup h ~ . The three methods vary in the way they calculate liquid holdup:
2262 Ind. Eng. Chem. Res., Vol. 32, No. 10, 1993
0 A
WePCP u !s=o.0034
u u
Table 111. Average Absolute Deviations for the Prediction of Irrigated Pressure Drop for Flexeramics
Flexerarnlc PSlMethod 111
w.0136 k.0272
9
0
size
0
Flexeremic 28 Q
@
1
@
@@ @@
@ (3
Flexeramic 48 Flexeramic 88 three sizes
average absolute deviation ( % ) method I method I1 method I11 41 22 11 31 34 24 20 18 39 31 25 26
Table IV. Average Absolute Deviations for the Prediction of Irrigated Pressure Drop for Flexeramics averme absolute deviation ( % method I method II method I11 APIA2 < 410 Palm 27 25 22 (45% of data) 410 < APIA2 < 820 Palm 29 20 26 (42% of data) APIA2 > 820 Palm 46 39 35 (13% of data) three APIA2 ranges 31 25 26
This method gives an average deviation of 31% for 134 data points and is recommended only for pressure drop below loading. Method I1 is more mechanistic. It uses the effective gravity, a partial wetting correction factor, and contact angle for packing material and process fluids to calculate liquid holdup. Consequently it should stand the best chance of predicting the irrigated pressure drop for systems other then air/water. Method I1uses the equations shown in Table 11,and is recommended because it gives the lowest overall average deviation. Method I11considers the effect of vapor and liquid flow rate for the calculation of liquid holdup. It uses the dimensionless Reynolds and Froude numbers for gas and liquid, respectively. Equation 23 shows the parameters of this correlation: 0 . 0 4 5 3U ~,~,"
-I-
6 . 6 4 4 1Uga ~~
This method is simple but takes into account the effect of gas flow rate.
-
10
'
I
0.1
10
1
Fs. ( m h ) (kglm ['O.S2=(ttl8)(l blft
]
Figure 1. Comparison of experimental and calculated values of irrigated pressure drop for Flexeramic types 28,48,and 88. Method I11 with eq 23. Airlwater, atmospheric pressure.
The first method considers hL only a function of liquid flow rate, using the dimensionless Froude number in the final correlation, given by eq 16: M--
Az
0.0453pgUg,2 + 6.6441pgUg, S E ~-( E)(sin I el2 S2e(1 - e)(sin e) 1-2.5113
(&?s
uL:)o*m)s
(16)
Acknowledgment We gratefully acknowledge Koch Engineering Company for the donation of Flexeramic packing to our Institute, the financial aid of CONACYT and COSNET for the Scholarship for the J.U. and one Research Project, respectively. Also we truly appreciate the contribution of Jose L. Bravo and Dr. James Fair from the Separations Research Program at The University of Texas. Nomenclature CI,CZ= constants in eqs 3, 5, and 13, dimensionless f = friction factor, dimensionless Ft =correction factor for partial wetting in eqs 8 and 19, dimensionless FrL = Froude number, dimensionless g = acceleration of gravity = 9.81 m/s2 g, = conversion factor = 1.0 in SI units gee = effective gravity in eqs 11, T-2 and T-5, m/e2 h~ = liquid holdup, dimensionless A P / U = irrigated pressure drop per height of packing, Pa/m ( h P / u ) d = dry pressure drop per height of packing, Pa/m
Ind. Eng. Chem. Res., Vol. 32,No. 10, 1993 2253
Rer = gas Reynolds number based on effective velocity, imensionless ReL = Reynolds number for liquid, dimensionless S = side dimension of corrugation, m Vg,e= effective gas velocity (=Ugd(esin e)), m/s Vg,@= superficial velocity of gas, m/s ULr = superficial velocity of liquid, m/s n = number of points Dimensionless Numbers FrL = ULe2/Sg = Froude number for liquid Reg,s= Ug,eSpg/pg = Ug,&3pg/e(sin8)pg= Reynolds number for
gas
ReL = U ~ , s p d /=p Reynolds ~ number for liquid We= = UL,s2pLS/ag,= Weber number for liquid Greek Letters al,a2 = constants in eq 6, dimensionless as,a4,a5 = constants in eq 12, dimensionless 0 = constant in eq 8, dimensionless y = contact angle, degrees t = void fraction of packing, dimensionless 8 = angle with horizontal for corrugation channel, degrees p = viscosity, kg/(m e) p = density, kg/m3 Q = surface tension, N/m (1 N/m = 1000 dynlcm)
Subscripts eff = effective
flood = conditions at flooding g = gas phase L = liquid phase s = superficial
Billet, R.;Mackowiak,J. How to Use the Absorption Data for Design and Scale-up of Packed Columns. Fette Seifen Anstrichm. 1984, 86,349. Bravo, J. L.; Rocha, J. A,; Fair, J. R. Pressure Drop in Structured Packings. Hydrocarbon Process. 1986,56,45. Buchanan, J. E. Pressure Gradient and Liquid Holdup in Irrigated Packed Towers. Znd. Eng. Chem. Fundam. 1969,8,502. Eckert, J.S.Selecting the Proper Distillation Column Packing. Chem. Eng. B o g . 1970,66 (3),39. Fair, J. R.;Bravo, J. L. Distillation Columns Containing Structured Packings. Chem. Eng. h o g . 1990,86 (11,19. Kister, H.;Gill, D. R. Predict Flood Point and Pressure Drop for Modern Random Packings. Chem. Eng. Prog. 1991,87,32. Koch. “Flexeramic Structured Ceramic Packing”; Bulletin KCP-1, Koch Engineering Company Inc., Knight Division, 1989. Robbins, L. A. Improve Pressure-Drop Prediction with a New Correlation. Chem. Eng. Prog. 1991,5,87. Rocha, J. A.; Bravo, J. L.; Fair, J. R. Distillation Columns Containing Structured Packings: A Comprehensive Model for Their Performance. 1.Hydraulic Models. Znd. Eng. Chem. Res. 1993,32,641. Sherwood,T. K.; Shipley,G. H.; Holloway,F. A. L. Flooding Velocities in Packed Columns. Znd. Eng. Chem. 1938,30,765. Shi, M. G.; Mersmann, A. Effective Interfacial Area in Packed Columns. Ger. Chem. Eng. 1985,8,87. Stichlmair, J. G.; Bravo, J. L.; Fair, J. R.General Model for Prediction of Pressure Drop and Capacity of Countercurrent Gas/Liquid Packed Columns. Gas Sep. Purif. 1989,3,19. Uresti-MelendBz,J.EmpaqueEstructurado de CerWca. M.S. Thesis, Instituto Tecnol6gico de Celaya, 1993. Received for review January 12, 1993 Revised manuscript received June 10, 1993 Accepted June 15, 1993.
Literature Cited Bemer, G. G.; Kalis, G. A. J. A new Method to Predict Holdup and PressureDrop in Packed Columns. Trans. Inst. Chem. Eng. 1978, 56,200.
~
~~
~
Abstract published in Advance ACS Abstracts, September 1, 1993.
