Contribution to Design and ScaleUp of Packed Columns

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Verbindungen zeigten unter den gewalten Bedingungen entweder keine oder aber eine nur schwach ausgepragte antioxidative Wirkung, so daB praktisch nur wenig Aus sicht besteht, durch diese Vorstufen der MaillardReaktion, wie sie im Rahmen des Trocknungsprozesses in Lebensmit teln gebildet werden konnen, eine antioxidative Wirkung zum Schutze von Lipiden zu erzielen.
L i t e r a t u r 1 W Grosch, Z. LebensmittelUnters. u. Forsch. 157, 70 [1975]. 2 P. Schieberle u. W Grosch, J. Amer. Oil Chemists' SOC. 58, 602
3 K. E. Peers et al., J. Sci. Food Agric. 35, 813 [1984]. 4 C. M. Houlihan, J. Amer. Oil Chemists' SOC. 61, 1036 [1984]. .5 H. P. KauJinann, Die Ernihrungsindustrie 120 [1973]. 6 A. Seher u. D. Loschner, Fette Seifen Anstrichmittel 88, 1
7 R. Yamauchi et al., Agric. Biol. Chem. 46, 2997 [1982]. 8 R. S. Farag et al., Can. Inst. Food Sci. Technol. J. 15,174 [1982]. 9 K. Eichner, Prog. Fd. Nutr. Sci. 5, 441 [1981].
[1981].
[ 19861.
10 H. Lingnert, SIK Rapport No. 458, 45 [1979]. 1 1 L. B. Rockland, Analyt. Chem. 32, 1375 [1960]. 12 J. E. Hoke, Agr. Food Chem. 1, 928 [1953]. 13 K. H ns, G. Miiller u. H. Pauhen, Liebigs Ann. Chem. 703,202
l4 W Butte, J. Chromatogr. 261, 261 [1983]. 15 E. SchuZte u. K. Weber, Fat Sci. Technol. 91, 181 [1989]. 16 W Grosch, Z. LebensmittelUnters. u. Forsch. 160, 371 [1976]. 17 S. S. Chng et al., J. Food Sci. 42, 1102 [1977]. 18 J. C. Uhl, Dissertation Universit;it Miinster, 1989. 19 A. GolanGoldhirsch, Z. LebensmittelUnters. u. Forsch. 182,29
20 M. Tokati u. M. Morita, Agric. Biol. Chem. 49, 3545 [1985].
D anks agung
[196$
[1986].
Die Untersuchungen wurden im Rahmen der industriellen Gemeinschaftsforschung aus Mitteln des Bundesministers fiir Wirtschaft (BMWi) gefordert. Hierfiir sei an dieser Stelle verbind lich gedankt.
Eingegangen am 10. Mai 1990.
Contribution to Design and ScaleUp of Packed Columns* By R B i l l e t * *
Institute for Tharmo and Fluid Dynamics, RuhrUniversiq, Bochum, Federal Republic of Germany
The demand for high accuracy in packed column design for countercur rent thermal separation processes, such as rectification, absorption and desorption, has been stepped up research in scaling of packed column efficiency in response to the growing application of packings for various systems in the chemical and allied industries. The investigations confmed the suitability of relationships for describing the performance, the validity of which was proved with differing systems and packings. This equations takes due account of geometric, hydrodynamic and systemrelated parameters that govern mass transfer and the fluiddynamics in packed columns.
In response to the growing application of packings for various systems in the chemical and allied industries the demand for high accuracy in packed column design for countercurrent thermal separation processes, such as rec tification, absorption and desorption, has been stepped up research in scaling of packed columns on the basis of fundamental studies of the fluid dynamics and mass trans fer.
These investigations confirmed the suitability of theo retically developed relationships, the validity of which was proved with differing systems and packings. The equations take due account of geometric, hydrodynamic and system related parameters that govern the fluidity behaviour and mass transfer.
F u n d a m e n t a l r e l a t i o n s h i p s The correlation, defining the specific column volume v,
* Summary of papers presented at 38'h Canadian Chem. Eng. Confer., Edmonto, AlbertaXanada, 1988; at XIIP Inter american Congress of Chem. Eng. PACHEC, Acapulco/Mex ico, 1988; at Intern. Confer., on Chem. Eng. and Petroleum Technology, New Delhi, India, 1989.
** Author's address: Prof. Dr.Ing. R Billet, RuhrUniversity Bochum, Institute for Thermo and Fluid Dynamics, Depart ment of Thermal Separation Processes, P. 0. Box 10 21 48, D4630 Bochum.
Fat Sci. Technol 92. Jahrgang Nr. 9 1990
Berechnung und Beitrag zur Auslegung von Fiillktirperkolonnen Die Forderung nach hoher Genauigkeit bei der Auslegung von Fullkor
perkolonnen fiir GegenstromTrennprozesse wie Rektifiation, Absorption und Desorption fiihrte zu einer verstirkten Forschung auf dem Gebiete der Beschreibung der Wirksamkeit dieser Apparate bei ihrem steigenden Einsatz f i r Prozesse der chemischen und verwandten Industrien. Es werden Berech nungsmodelle zur Beschreibung der Leistungsfihigkeit von Fiillkorperko lonnen vorgestellh die gleichermal3en konstruktiven, hydrodynamischen und stomichen Parametem Rechnung tragen, und ihre Gultigkeit und Eignung fiir die praktische Anwendung wird durch Ergebnisse experimen teller Untersuchungen mit verschiedenen Stoffsystemen bestiitigt.
per unit efficiency and per unit gas throughput according to Eqn. (11,
with nJH being the number of theoretical stages per unit packing height and u, the vapour or gas load, is a criterion for the investment costs of the packings applied in the column. The relationship expressed by Eqn. (2) between nJH and the height equivalent to an overall transfer unit in the gas or vapour phase HTUOv is valid for the separation of mixtures with mass transfer predominantly in the gas or vapour phase. The stripping factor I. is fixed by the vapour/ liquid ratio U Vand the slope myx of the equilibrium curve according to Eqn. (3).
"I;. 1 x1 H HTU,, Inh
( 2 I
(31
In the light of the HTU/NTU model, Eqn. (4) applies for the height HTUov of an overall transfer unit on the gas side.
1 IV
I 4 1
Its evaluation requires the knowledge of the volumetric
361
mass transfer coefficients pv . a,,h in gas or vapour phase and PL * a+ in liquid phase which are principally dependent on gas load uv respectively on liquid load uL. Therefore the efficiency of a packed column and consequently its specific column volume are closely related to the fluid dynamics under operating conditions.
Based on a theoretical model, recently developed by the author, a description of the fluiddynamics and mass transfer takes into account the great diversity in the geometry, structure and materials for packings in industrial columns, which normally entails differences in the fluiddynamics under operation conditions and thus in the packing
performance. The model correlations were checked against the results of comprehensive and systematic experimental studies performed in the Chair for Thermal Separation Processes in the RuhrUniversity and figures taken from the literature. The number of measurements performed in the fluiddynamic tests was 500; in the tests to determine mass transfer on the liquid side, 1050; and in the tests to deter mine mass transfer on the gas side 1100. The measurements were made on about 60 packings of different designs and dimensions, some of which are shown in Fig. 1 as examples for dumped packings and in Fig. 2 as representatives for regular packings.
Packing main size 50 mm
metal ceramic plastic
CMR No. 1.5 Pall ring 
Pall ring Hake t te
N = 19350 a = 120 E = 0.978
N = 6400 a = 120 E = 0.78
N = 6700 a = 110 6 = 0.92
N = 12400 a = 135 E = 0.93
Hiflow ring Hiflow ring Hiflow ring DINPAC
N = 5000 a = 97.3 E = 0.973
N = 4950 a = 86.7 E = 0.815
N = 6400 a = 112 E = 0.93
N = 29000 a = 135 E =0.92
VSP ring Intalox saddle ~ ~~
Norpac ring ENVI PAC
N = 7800 a = 104 E = 0.98
N = 9300 a = 120 E = 0.77
N = 7300 a = 90 E = 0.952
N = 6800 a = 98 E = 0.961
Dimensions: N [ 1 /m3 I , a [ m2 /m3 I , E Im3 /m3 1 ~ ~~~
Fig. 1. Examples for fillings of dumped packed columns, investigated in this work
Fat Sci. Technol. 92. Jahrgang Nr. 9 1990 362
Mellapak 250Y
a=250, ~=0.96
Montz packing B1  300
a=300, ~ = 0 . 9 3
Ralupak 250Y
a=250, ~ = 0 . 9 6 3
Montz C1300
a=300, &=0.90
Sulzer BX”’
a=500, &=0.90
Gempak A2T
a=202, E = 0.978
Dimensions a [m2 /m3 1 , E [m3 /m3 1 
Fig. 2. Examples for regular packings, investigated in this work
M o d e l l i n g of c o u n t e r c u r r e n t f l o w i n p a c k  i n g s
The void space in the bed can be simplified regarded as a network of numerous channels, having the void fraction E
and the specific area a of the packing, through which the liquid passes downwards in the form of a film or in lamell flow. The gas flows upwards through the bed, countercur rent to the liquid. Under stationary conditions, the force of gravity and the shear forces in the liquid film of the density
pL and the dynamic viscosity qL are assumed to be in equilibrium at a point representing any given thickness s in a coaxial layer within the liquid film, and the fnctional force exerted by the vapour of the density pv acts at the surface of the film. Operating magnitudes are the liquid load uL and the gas velocity u,, which effects also the liquid hold up h,. The solution of the differential equation describing this flow model gives rise to Eqn. (5) where the index n and the flow factor 4 depend on the flow pattern.
Fat Sci. Technol. 92. Jahrgang XI. $1 1990 363
151
Eqn. (5) can be quahtatively described in accordance with the experimental investigations by the diagrams of Fig. 3, which is selfexplanatory and which shows the conditions, under which loading and flooding occur.
Vapour velocily uv
r a
s
I I
h,= f(UY)u,.cmrl
c loading line  llmding line
"1 = f ( h l ) u " m s t
o loading point a flwding paint
Flooding condilions :
 hl.FI
uV.FI Holduph, % * o 
dh,
du,  = 0  U1.J
dhl r 2
v z
a8
   2 uv = f(~L'Ul,,,",t
0 loading point 0 flooding point
B >
Hold UP hl
Fif 3. Qualitative describing of the fluiddynamic in packed co umns, operated in countercurrent phase flow of gas or vapour
liquid systems
Loading can be defined as the load at which the frictional force exerted by the gas prevents downflow of the inner coaxial layer of liquid in a flow channel, i.e. the load at which the liquid velocity becomes zero. Thus the gas velocity uv,s at the loading point is an important design criterion. It can be derived from the equations in the mathematical model resulting in Eqn. (6)
and in Eqn. (7)
161
(71
which describes the liquid holdup h,, at the loading point. If the flow of the liquid film is laminar and vertically downwards the following values apply to C , and n: C, = 12" and n = 1/3. Finally Eqn. (8) is derived by combining Eqn. (6) and Eqn. (7).
The flow factor ts in Eqn. (8) depends according to Eqn. (9) on the phase ratio W e the densities pL and pv and the
dynamic viscosities qL and qv of the phases, and a factor C , that characterizes the geometry and surface area of the packing.
191
All that is required for its application is a knowledge of the packing constants C,, which has to be determined by experiment. The index n, is a constant for the system. Below the phase inversion point, corresponding to (Wq . (pV/p3O.5 < 0.4, it is given by n, = 0.326. Above the phase inversion point, it has a value of n, = 0.723.
If the gas velocity is higher than u., = uv, s, the liquid hold up increases rapidly above the value at the loading point, i. e. hL > hL, until the flood point is reached, i. e. h, = hL,n. At this point, all the liquid is theoretically forced upwards by the stream of gas in the bed. According to the model the gas velocity at the flood point is given by Eqn. (10)
and the liquid holdup at the flood point is defined by Eqn. (11), which mathematically satisfies the boundary condi tions in Fig. 3.
(11 I
These equations are theoretically derived correlations, which can be used for practical estimation of the flooding conditions.
The application demands a knowledge of the flow factor in, which .is related to the main parameters by Eqn. (12). Below (Wq . (pv/pJJ.5 S 0.4, nn has an average value of nR = 0.194; and above this point, nF1 = 0.708.
This flow model was the subject of comprehensive experi mental studies to determine whether is could be applied in general to all kinds of packed columns with countercurrent liquid/* or vapour systems. The correlation between all the measurements and the theoretically derived relation ships for the loading and flood points was very good. The liquid loads varied between uL = 4.88 and 144 m3/m2h; the densities of the gases or vapours, between p, = 0.3 and 1.37 kg/m3; the dynamic viscosities, between qv = 7.14 .
and 18.19 * 106kg/m . s; the liquid densities, between pL = 750 and 1026kg/m3; and the dynamic viscosities between qL = 0.36 . 103 and 92.6 103 kg/m * s. Detailed figures on the evaluation of the model parameters are dealt with in Tables 1 to 2. They allow application of Eqns. (6) to
The Reynolds number for film flow in the liquid phase is defined by Eqn. (13). The evaluation of the experimental results has also revealed that if this Rqrnolds number is higher than 10, Eqn. (14) will apply for the relationship between the index n in Eqn. (7) and the number of packings N, their area a per m3 and their main dimension d. For regular packings n was found to be n = 213.
(12).
Fat Sci. Technol. 92..Jahrgdng Nr. 9 1990 364
Table 1
Constants for holdup, loading and flooding conditions Dumped Packings Material Size d Ch CS C,,,
Metal 50 rnm 51.70 2.725 1.580 Pall ring Plastic 50 rnm (i7.95 2.816 1.757
Ceramic 50 mrn 70.29 2.84(j l.!)l:3
Metal 50 rnrn 81.71 2.702 1.62ti Hiflow ring Plastic 50 rnrn 73.03 2.8!/4 1 ,871
Ceramic 50 mm 2.81!) l.6!)4 Hiflow ring; Super Plastic 50 mm 2.86ti 1.7W NOR PAC ring Plastic 5 0 mm 143.96 2.!).5!) 1.786 Raschig ring Ceramic 50 rnm 2.482 1.574 VSP ring, No. 2 Metal 50 rnm 94.17 2.806 1 .M!) Glitsch, CMR ring Metal 38 mm 121.M 2.6!)7 1.841
Ralu ring Plastic 5 0 mm 2.843 1.812
Envipac ring, No. 2 Plastic 60 mm 115.50 2.!)87 1.864 Dinpac ring, No. 1 Plastic 4.5 mm 2.!U!) 1 .w 1
Intalox saddle; grid Plastic 50 mm 2.675 1.657 Intalox saddle Plastic 50 mrn 2.382 1.548
Hackette Plastic 4.5 mm 59.!) 1
Table 2
Constantsfor holdup, loading and flooding conditions
Regular Packings Material Size C h CS c I 1
Ralu pack YC
Montz packing
Mellapak Y Gempak A2 T304
Metal 250 mz/rn:{ 3.178 2.558 B1100 mz//m.' 97.0.5 3.08!) 1 . 9 1 1
Metal B1200 rnVm' 52.3Y 3 . 1 16 2.33!) B1300 mVm1 34.80 3.098 2.464
Plastic CZ1100 m2/m+ 2.653 1.973 Plastic 250 m2/m,' 43.!)7 3.1Fi7 2.464 Metal 2012 rn2/m'' (j0.40 2.!)8(i 2.0!)!)
M o d e l l i n g of m a s s t r a n s f e r i n p a c k i n g s A relatively new model not only describes the systems
investigated quite accurately but is also just as valid for conventional as for modem packing. This model thus allows mass transfer to be described in terms of the packing geometry and the physical magnitudes that influence the gasliquid system. The relationships derived from it can be applied to all countercurrentflow columns, regardless whether the beds of packing have been dumped at random or arranged in a geometric pattern. As a rule, the direction in which the two phases flow through the channels in a bed of packing changes continuously. Thus the path followed by the one phase can be imagined to be split up into zones of mass transfer and mixing zones. In other words, after the phases have flowed through a mass transfer zone, the areas of contact are renewed. The average duration of contact of the phases T~ respectively 'cV in the individual zones of mass transfer in an element of length 1, is comparatively short in packed columns. It is governed by the effective void fraction e of the packing and the liquid holdup h, under operating conditions. At a liquid load uL, tL can be described by Eqn. (15) and if the vapour load is u, tv is given by Eqn. (16).
Fat SCI. Technol. 92. Jahrgang Nr. 9 1990
1 tL = h .I . "1
L r
Hence it assumed that mass transfer follows the law of instationary diffusion valid for brief periods of contact between the phases and described by the Eqn. (17), formu lated by Higbie,
P:&.(< (17)
i.e. the mass transfer coefficient p as function of the diffusion coefficient D and the theoretical duration t required for renewal of the area of contact.
If Eqn. (17) is applied and the terms of Eqns. (15) and (7) are substituted, the volumetric mass transfer coefficient pL
in the liquid phase can be derivated with 5 h being the z a s e contact area, Eqn. (18).
Likewise, the volumetric mass transfer coefficient p,. aph in the gas phase was found to be given by Eqn. (19).
In the derivation of Eqn. (19) was taken into consideration that the volumetric mass transfer coefficient on gas side
365
could be determined most accurately if the gas flow were described by the Reynolds number instead of the gas veloc ity and the influence of the system by the Schmidt number instead of the diffusion coefficient only, according to the terms in the brackets having the exponents 3/4 and Y3.
The magnitudes that affect the phase contact area in the uv < u,, range are the liquid load uL, dynamic viscosity qL, density pL and surface tension oL and the geometric area a and the length of the path of contact 1,. If these magnitudes are subjected to a dimensional analysis, Eqn. (20) will be obtained for ratio aph/a of the phase contact area aPh to the geometric area a,
in which the characteristic length of the path of contact 1, were to be described in terms of the hydraulic diameter dh, defined by Eqn. (21).
The model parameters CL and C, for application of Eqns. (18) and (19) are listed in Tables 3 to 4. They were determined from experimental studies carried out with 28 gashquid systems with different mass transfer resistances and directions.
Table 3
Constants for mms transfer in liquid and gas Dumped Packing Material Size C, C,
Metal 50 mm 1.1% 0.410 Pall ring Plastic 50 mm 1.239 0.368
Ceramic 5 0 mm 1.227 0.415 Plastic 50 mm 1.520 0.303 Metal 50 mm 1.168 0.408 Ralu ring
Hiflow ring Plastic 50 mm 1.487 0.345 Ceramic 5 0 mm 1.377 0.37!)
Hiflow ring, Super Plastic 50 mm 1.2 l!) 0.341 NOR PAC ring Plastic .50 mm 1.080 0.322 Raschig ring Ceramic 50 mm 1.116 0.210 VSP ring, No. 2 Metal 50 mm 1.222 0.328 Envipac ring, No. 2 Plastic f i0 mm 1.522 0.296
Table 4
Constantsfor m a s t r a g e r in liquid and gas
Regular Packings Material Size c, C" Ralu pack YC Metal 250 m'?/mi 1.334 0.385
Metal 2.50 mVmi 0.983 0.270 55 m2/m.+ 0.039
Impulse packing Ceramic 100 mz/m'+ 1.317 1 12 mZ/m'+ 1.170 250 m2/m"
BI200 m 2 / d 0.971 0.390 Metal B I 300 my/m:+ I . 1 fi5 0.422
C1200 m2/m5 1.006 0.412 'Iastic C2200 mZ/m+ 0.739
Montz packing
C o n v e r s i o n of mass t r a n s f e r When considering Eqn. (4), (19) and (20) for systems with
mass transfer resistance mainly but not exclusively located in gas side the simplified version of Eqn. (22) according to the correlation of Shemood can also be used for describing the mass transfer in terms of HTU,,,
HIU,, = q Re;.Sc:'' (22 )
which is interconnected with the equivalent number of stages nJH by Eqn. (2). In this case the Reynolds number is defined by Eqn. (23)
(231
and the Schmidt number in the usual form by Eqn. (24).
scv ' 3 Ov. Pv
The product of the geometrical area a of the packing and the specific column volume v,, defined by Eqn. (l),
0 ' . 0 . v y (25 )
can now be considered as a measure for the geometric efficiency a' of the packing, which is defined as the geomet rical area per unit volumetric gas flow uv and per unit efficiency nJH according to Eqn. (2). Thus, a dimensionless correlation can be obtained from the equations above mentioned. It can be derived from the main factors that affect the efficiency, i. e. those connected with the system to be separated, the load and the properties of the gas. It assumes the form expressed by Eqn. (26), in which Re, is the mohfied Reynolds number for the gas as defined by Eqn. (23)
and expressed in terms of the particle diameter d for packing with a relative void fraction E and specific surice a as expressed by Eqn. (27).
I  € dp: 6.
0 I271
The dimensionless I in Eqn. (26) is a paclung performance rating that connects specific magnitudes for the design, efficiency, load and system in the form of Eqn. (28)
for investigations of the efficiency in terms of nJH and Eqn. (29) for those in terms of HTU,,
(291
For constant ratio i/Vbetween liquid and gas or vapour, the factor q is a magnitude that is characteristic for the packing. It is practically constant for an individual packing at loads less than 70% of the flooding load point. The exponental index m, however, is more or less independent on the packing and system. This can be shown by evaluat ing the results of experiments on rectification and absorp tion systems with resistance to mass transfer predominantly in the vapour or gas phase. When correlating on the basis of Eqn. (30)
130)
as shown for two rectification systems in Fig. 4 for a dumped packing, consisting of CMR 1.5 Turbo rings, straight correlation lines are received in the double log arithmic plot. They thus allow the determination of the quantities for q and m in Eqn. (26), on the basis of which the
Fat Sci. Technol. 92. Jahrgang Nr. 9 1990 366
s % > 3.0 U v? 31s 2.0 I
L W n
1.0 0.8
0.6 b a 0.4
2 0.3
0  v) v1
0 v) .
g 0.2 a 1 2 3 4 6 8 1 0
Vapor Reynolds number Re;lO'
Fig. 4. Dimensionless correlating of packing efficiencies
(? N
9 5 u
s c 5
efficiencies of the test systems can be converted into those of other systems. Furthermore the investigations confirmed that Eqn. (26) can also be applied for absorption systems with resistance mainly on gas side. Examples are dealt with in Fig. 5 indicating that the efficiencies for vacuum rectifica
Correlollon line of pilot plont lest system
\;(\I.ic plot
8 50mm Hillow Ring. PVOF. hydroph. dS:0.ZZm.H*l.47m.N= 7163 l/m3 ChlorobenzenelElhyl benzene p, ~50mmHg. L I V = I
0 50mm Hiflow Ring.PP d, d 3 m . H1137m. N.6997 IIm3 NH,AirIti$. p =Ibor, 1 : 293 K l
L = *: a6 G
&. 0.4
0.3 5 2 s a2 .5 & 0.15
 5
am
ZIP L w
0  .s 0.1
b z 3 6 a 1 0 20 Vopor Reyndds number Rev.103
Fig. 5. Dimensionless correlating of packing efficiencies
tion and those for normal pressure absorption can be described by one and the same correlation line, provided the liquidgas ratio WVis in both operations the same. It also follows from this diagram that only in the range of Reynolds numbers Re, < Re,,, which correspond to gas loads uv < uv, the correlation lines for constant liquidgas ratio W Vdiverse from those for constant liquid load up For Reynolds numbers, corresponding to gas loads uv, < uv < uv, F1 however, i. e. in the loading zone, both operating conditions can be correlated by more or less one common line.
The knowledge of the interrelationship expressed by Eqn. (30) thus provides also the basis for scale up the evaluating of the efficiencies obtained in a pilot plant to a commercial scale packed column. For this purpose a dia gram, according to the qualitative presentation of Fig. 6 can be developed for the individual packing considered. The
I
Gos Reynolds number Re,
Fig. 6. Qualitative diagram for correlating the dimensionless efficiency
dotted lines indicate qualitatively the conditions of the operating point where loading of the packings is to be expected. It allows the estimation of the packing efficiency for the separation of a system, the gas viscosity qv of which is known and the gas load u, corresponding to the Reynolds number Rev to be applied is determined. With the knowl edge of the dependency of Fig. 6 expressed by Eqn. (30), which must be found by experiment in a pilot plant with'a proper defined test system, the efficiency can thus be determined with the equations indicated in the diagram.
C o n v e r s i o n of p r e s s u r e d r o p Experimental data for the pressure drop per unit of
efficiency were correlated in the literature in the form of Eqn. (31)
which takes into account the interrelationship of Eqn. (22) and that of Eqn. (24). It represents a modified specific pressure drop Ap per transfer unit NTUov for a system, the resistance to mass transfer of which is predominantly in the gas or vapour phase, i. e. the Schmidt number Sc, represents the only means of reflecting the properties of the system. Since the expression of Eqn. (31) is independent of the system, it is ideally suited for comparing column packing. It was thus revealed that a common curve can be drawn to represent the results obtained on various mixtures rectified in test runs under total reflux or under constant liquid vapour ratio WVand those obtained in the absorption, for example of ammonia from air under constant liquid load uL by means of water.
However this corrqlation does not apply generally under both conditions, i. e. WV= const. and uL = const., and must be treated with reserve concerning the exponent m. In this case a modified expression is taken for the pressure drop per unit of efficiency. It is described by Ep.. (32) and allows for the difference in the phase ratios WVin the various separation processes.
(321
In rectification experiments under total reflux, d t i s equal to 1; in rectification processes with a finite reflux ratio r, WY
Fat Sci. Technol. 92. Jahrgang Nr. 9 1990 367
is given by Eqn. (33) in the enrichment section,
i r _    Y r + l
(331
and in absorption experiments with constant liquid flow rate uL and variable gas capacity factors F, or vice versa, by Eqn. (34).
Thus the modified pressure drop per unit efficiency in absorption experiments in which the liquid flow rate uL is constant but the gas capacity factor F, is variable can be correlated by Eqn. (35).
(351
The curves reproduced in Fig. 7 confirm the expediency of this method. They were plotted from the results of experi ments on rectification with total reflux, i. e. U V = 1, and on absorption with a constant liquid flow rate uI. = 10 m3/m2h and a variable gas capacity factor F,
0.6 0.8 1 2 3 4 capacity factor F, [m''2.s!kg"z]
Fig. 7. Modified specific pressure drop as function of load in rectification and absorption test
Hence the results of rectification and absorption experi ments cannot be generally correlated by means of a com mon function in form of Eqn. (31) valid for both, unless Eqn. (36)
i i = m . n (361
is satisfied. However this is mathematically impossible until n is negligibily small, i. e. zero in the limiting case; only in
this case the correlations described by Eqns. (31), (32) and (35) are identical. If the conditions stated above does not apply, as shown in Fig. 7, Eqns. (32) and (35) must apply for correlating the results of rectification respectively absorp tion experiments, which thus can be applied for scaling up.
In Fig. 7 values measured in rectification are compared with f ieres for absorption calculated from Eqn. (32) for the case WV= 1. In this example there is a very good agree ment between the values for the systemindependent mod ified specific pressure drop.
The specific pressure drop Ap/NTU,, is interconnected with the pressure drop Ap/H per unit height of packing by Eqn. (37).
137)
In line with a recent proposal the pressure drop Ap/H of a wetted packing can be described in analogy to that of a dry packing by Eqn. (38)
AplNTUo, HTUov = 
A p l H
138)
in the derivation of which the hydraulic diameter dh of the gas flow channels of the wetted packing with the effective void fraction (E  hJ is expressed by Eqn. (39)
1391
Equ. (38) becomes identical with the well known correla tion for a dry packing, i. e. for which h, = 0. The wall factor K takes into account the influence of the column diameter d, according to Eqn. (40).
d h ' 4 . T EhL
From Eqns. (38) to (40), whereby F, defines the gas or vapour capacity factor according to Eqn. (41)
Fv=u,.q% (41)
can now be derived the correlation for the related pressure drop per unit height Ap/H of the wetted packing resulting in Eqn. (42).
It contains the resistance coefficient sL of the gas flow in the wetted packing channels which is related to the flow of liquid according to the Eqns. (43) and (44), which were found by testing of various packings, such as in Figs. 1 and 2. Values for the packing constant C, are listed together with the characteristic data on various types of packing in Tables 5 to 6.
Thus the Eqns. (32) and (42) allow conversion and scaling of pressure drops, but also of efficiencies, because in
Fat Sci. Techno]. 92.Jdhrgang Nr. 9 1990 368
Table 5
Geometrical data and pressure drop constant fo r dumped packmgs Dumped Packmgs Material Size d N a E CP
l /m ' mL/m? m{/m'
Pall ring
Ralu ring
Hiflow ring
Hiflow ring, Super NOR PAC ring VSP ring, No. 2 Envipac ring, No. 2 Toppak Bialecki ring
Italox saddle
Hiflow saddle Hackette
Metal Plastic Ceramic Plastic Metal Plastic Ceramic Plastic Plastic Metal Plastic Alu Metal Plastic Ceramic Plastic Plastic
50 mm 50 mm 50 mm 50 mm 50 mm 50 mm 50 mm 50 mm 50 mm 50 mm ti0 mm 50 mm 50 mm 50 mm 50 mm 50 mm 45 mm
fi242 fi7fi.i (ill 15 5770 5000 ti815 5 I20 605 0 7330 784 1 6800 (i!J47 6278 Rti i i t i 8882 9939
12252
112.6 111.1 116.5 !I52 !12.3
117.1 89.7 82.0 86.8
104.6 !)8.4
1 O6.fi 121.0 122.1 114.6 86.4
133.4
0.95 I 0.!1 I!) 0.783 0.1138 0.9 7 7 0.!125 0.809 ().!I42 0.947 0.!)80 ().!)ti 1 0.956 0.!M 0.!)08 0.7fi1 0.938 0.!)3 1
Table f j
Geometrical data and pressure drop constant for regular packing.
m2/m.? m?/m" Regular Packings Material Size a E
0.7fi3 O.fi98 O.ti62 0.468 0.42 I 0.327 0.538 0.4 14 0.350 0.773 () .33 8 0.604 0. 7 I!) 0.758 0.747 0.454 0.39!)
CP
Ralu pack Metal YC250 250.0 0.!)45 0 . I!) 1 Impulse packing Ceramic I00 Y(i.7 0.828 0.417 
B 1200 200.0 0.!)7!1 0.355 B 1300 300.0 0.930 0.295 c 1200 200.0 0 .!I5 4 (1.453 c 2 2 00 200.0 0.!100 0.48 1
Metal
Plastic Montz packing
connection with Eqn. (37) they form Eqn. (45), which is valid for the main loading range.
F ina l C o n s i d e r a t i o n s It is general knowledge that columns with randomly
oriented or geometrically arranged beds of packing have much lower pressure drops per theoretical stage than plate columns and thus permit lower reflux ratios, particularly in vacuum rectification. Thus column internals with low pres sure drops per theoretical stage are an advantage in realiz ing all energysaving measures in thermal separation pro cesses ranging from product vapour compression to multiplecolumn operation. Furthermore in significant industrial applications, such as the vacuum rectification of ethylbenzene/styrene mixtures or the recovery of fatty acids, avoidance of thermal decomposition is an important factor in favour of columns with low pressure drops. Therefore most of the packings in common use today have been the subjects of systematic studies. The results obtained permit a comprehensive review of the main relationships that exist between the degree of mass transfer and the column hydrodynamics, which themselves depend on the operating conditions, the system, and the packing's geome try and texture. Based on the numerous results a new correlating of these relationships was developed for process
calculation and design, but the results of laboratory or pilot plant experiments can be adopted direct for scaleup, if resistance to mass transfer is predominantly in gas or vapour phase, e. g. in most rectification and many absorp tion processes.
As far as scaling effect of height and diameter of packed columns is concerned the common literature gives quite useful1 information. In this connection, it is worth noting that latticework packing permits hardly any maldistribu tion, as was determined some time ago in systematic studies on Nor Pac packing in columns of 0.3 to 1.5 diameter. It is also worth mentioning, that the critical liquid distribution density, above which no further improvement can be expected in efficiency of a bed of packing, is 400 liquid distribution points per square meter of column cross sectional area. All the liquid distribution points of the feed and top distributor must function uniformly to ensure utmost accuracy and thus a constant W Vin all coaxial flow paths in order to maintain the column efficiency.
If the distributor causes an initial liquid maldistribution of M [O/o], the packed column efficiency may be reduced by AE, the amount of which depends on the ratio d,/d between the column diameter d, and the main size d of the individ ualpacking element and of the liquidvapour or gas ration L / y Fig. 8.
This work is mainly based on own studies and experi mental research carried out in the laboratories of the author. The list of references therefore contains only some of his own publications.
Fat Sci. Iechnol. 92. Jahrgang Nr. 9 l Y Y 0
50
E u40 a g
5
P z a a 0
c
u
g a
10 is is 22 m x1 34 38 P 6 M Ratio Column OiomeierPocking Element Size dS/d
Fig. 8. Decrease of packed column efficienc caused by mal distribution according to Huber and Ifriltbrunner
G r e e k L e t t e r s
E m3/m3 tl kg/ms a
kg/kmol
kg/m3 E P
S u b s c r i p t s Fl Flooding point L Liquid S Loading point V Vapor or gas W Water
Void fraction Dynamic viscosity Stripping factor = my,. hi Molar mass Resistance coefficient Density
N o m e n c l a t u r e a Geometrical area of packing, mVm3 a' Geometrical area per unit volumetric vapor or gas
rate per theoretical stage, m2dm3 aph Interfacial area for mass transfer, mVm3 C Constant Cm Packing factor for flooding capacity C, Packing constant for holdup CL Packing constant for liquid phase mass transfer Cp Packing factor for pressure drop Cs Packing factor for loading capacity C, Packing constant for vapor phase mass transfer d Nominal packing size, mm or m d, H draulic diameter of a packing, m dp Ciaracteristic packing dimension, m d, Column diameter, m D, Diffusion coefficient for vapor, mVs DL Diffusion coefficient for liquid, mVs Fr Froude number F, Ffactor for vapor or gas = qp,1/2, m%lkg1/2 g Gravitational constant, 9.8 m/s2 hL Liquid holdup, m3/rn3 packing volume H Packed height, m HTU,, Height of an overall transfer unit, m I Dimensionless separation magnitude K Wall effect factor L my. Slope of equilibrium curve m Exponent iii Exponent n Exponent n, Number of theoretical stages N NTU,, Number of overall transfer units in vapor or gas pT r Reflux ratio Re Reynolds number Sc Schmidt number uL uv Superficial vapor velocity, m/s \I, Specific column volume, s V W Wettingfunction WG Water column X Mole fraction in liquid Y Mole fraction in vapor Z
Liquid throughput, kg moles/s or kg/s
Number of packings per unit volume, l/m3
Pressure at top of packed bed, mbar
Liquid load, mVm2s or rnVrn2h
Vapor throughput, kg moles/s or kg/s
Number of liquid pour points
flow
L i t e r a t u r e 1 R Billet, Fluiddynamisches Verhalten und Wirksamkeit von
Gegenstromapparaten fiir GasFliissigSysteme bei fliissig keitsseitigem Stoffiibergangswiderstand, Contribution in Fest schrift, Lennings, Fakultiit fiir Maschinenbau der RuhrUniver sit5t Bochum, 1983.
2 R Billet, Operation of Thermal Separation Plants under the Aspect of Environmental Protection, Congress Book 4th Intern. Symp. on Environmental Techniques Development, DongA University, Pusa.n/Korea, pp. 163182, 1984.
3 R Billet, Modelling of Fluiddynamics in Packed Columns, I. Chem. E. Symp. Ser. No. 104, A171 [1987].
4 R Bill&, Performance of Low Pressure Drop Packings, Chem. Eng. Comm. 54, 93 [1987].
5 R. Billet, Relationship between Residence Time, Fluid dynamics and Efficiency in Countercurrent Flow Equipment, Chem. Eng. Technol. 11, 139 [1988].
6 R Billet, J. H. Kim and A. Qaghouri, High Performance Absorption Columns, Proceedings: The First Korea Japan Symposium on Separation Technology, KyongjdKorea, 1987.
7 R. Billet u. J. Mackowiak, Neuartige Fiillkorper aus Kunststoffen fiir thermische Stofftrennverfahren, Chem. Techn. 5, 219 [1980].
8 R Billet and M. Schultex Determination of Liauid HolduD in GasLi uid TwoPhase 'Countercurrent Mas: Transfer h l  umns, ?. Chem. E. S
9 R Billet and M. Schg Capacity Studies of GasLiquid Two Phase CountercurrentFlow Columns, I. Chem. E. Symp. Ser. No. 104, B255 [1987].
I 0 R Billet u. M. Schultes, Vorausberechnung des Stoffaustausches bei GasFliissigsystemen mit gasseitigem Stoffiibergangs widerstand, Paper presented at the Symposium of T.U. Wroclaw/Poland, 1988.
11 R BiUet and M. Schultes, Mass Transfer in Gas/Liquid Systems with resistance in the Liquid Phase, Paper presented at AIChE Spring National Meeting, New Orleans, M S A , 1988.
12 R Billet and M. Schultcs, Modelling pressure drop in packed columns, Paper presented at AIChE Spring National Meeting, Houston, T W S A , 1989.
Received 14th December 1989.
p. Ser. No. 104, A159 [1987].
3 70 Fat Sci. Technol. 92. Jahrgang Nr. 9 1990