mass transfer correlations for packed towers

Journal Identification = CHERD Article Identification = 694 Date: June 6, 2011 Time: 4:14 pm

chemical engineering research and design 8 9 ( 2 0 1 1 ) 1308–1320

Contents lists available at ScienceDirect

Chemical Engineering Research and Design

j ourna l ho me pa ge: www.elsev ier .com/ locate /cherd

Model for the prediction of liquid phase mass transfer ofrandom packed columns for gas–liquid systems�

Jerzy Mackowiak ∗

ENVIMAC Engineering GmbH, Im Erlengrund 27, 46149 Oberhausen, Germany

a b s t r a c t

The following work presents a new, generally applicable model for description of the mass transfer in the liquid

phase for packed columns filled with random dumped non-perforated and lattice-type packing with size between

12 and 90 mm for gas–liquid systems in operating range up to flooding point.

The new equation for evaluation of the volumetric mass transfer coefficient in the liquid phase ˇL·ae was derived

on the basis of the assumption that liquid flows down in packed bed mainly in the form of droplets and that effective

interfacial area ae depends on hold-up in packed bed. The relation between the fluid dynamics and the mass transfer

is shown based on the channel model with a partly open structure.

The experimentally derived values for the effective mass transfer area in different types of random packings ae

are in good agreement with the calculation based on the new model. It is therefore possible to separate the product

ˇL·ae into liquid phase mass transfer coefficient ˇL and effective interfacial area ae.

© 2011 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

Keywords: Random packing; Lattice-type packing; Liquid phase mass transfer coefficient; Separation performance;

Effective mass transfer area; Extended channel model

Mersmann (1984, 1985). Based on the assumption of rivulet

1. Introduction

In the field of separation technology, the use of random,lattice-type packings in addition to structured packings hasbeen gradually increasing in the last 20 years.

The new generation of lattice packings, so called Nor-Pacwas first presented by Billet and Mackowiak (1980) in 1979 ata conference held during the German trade fair Envitec. Con-trary to expectations, initial experimental results (Billet andMackowiak, 1980) showed that the mass transfer behaviourof the 25 mm Nor-Pac with small specific packing area a wassimilar to that of 25 mm plastic Pall rings (1962) with largespecific packing area a, which were analysed for compari-son. The loading capacity of the new lattice packings wassignificantly higher than that of Pall rings, whilst the pres-sure drop �p/H and the specific pressure drop �p/NTUOV ofthe lattice packings was considerably lower, yet they werefound to have the same separation efficiency when applied
under the same operating conditions. As a result, a number
Abbreviations: RSR, Raschig Super ring; PR, Pall ring; BR, Białecki rinRalu, Ralu Flow ring; K, ceramic; M, metal; PP, polypropylene.

� Presented on 9th Distillation & Absorption Conference in Eindhoven∗ Tel.: +49 2089410440; fax: +49 208941044100.

E-mail address: [email protected]/$ – see front matter © 2011 The Institution of Chemical Engidoi:10.1016/j.cherd.2011.01.021

of new lattice-type packing elements of different types suchas IMTP ring (1977), Hiflow ring (1982), Envipac (1984), Flexi-max (1991), Mc-Pac (1991) or Raschig Super Ring (1995) wereproduced by leading packing manufacturers, see Fig. 1. Theselattice packings were initially made of plastic, followed laterby models made of ceramic and metal (Billet and Mackowiak,1980, 1982a, 1985; Mackowiak, 1990, 1999, 2010; Billet et al.,1983).

A comprehensive overview of the methods used to describethe resistance of the mass transfer in the liquid phase is avail-able in the literature (e.g. Onda et al., 1968; Bornhütter andMersmann, 1993; Wang and Yuan, 2005; Kolev, 1976), but thereis no method explaining and correlating the influence of formand geometric data of packing on the volumetric mass transfercoefficient ˇL·ae in liquid phase.

The separation of the product ˇL·ae was first achievedby Zech and Mersmann (1978) (Kolev, 1976) and Shi and

g; CMR, Cascade Mini Rings; RR, Raschig ring; IS, Intalox saddle;

, The Netherlands on 12–15 September 2010.

formation, they derived new correlations for determining

neers. Published by Elsevier B.V. All rights reserved.

http://www.sciencedirect.com/science/journal/02638762

mailto:[email protected]

dx.doi.org/10.1016/j.cherd.2011.01.021


chemical engineering research and design 8 9 ( 2 0 1 1 ) 1308–1320 1309

Nomenclature

a geometric surface area of packing per unit vol-ume [m2/m3]

ae interfacial area per unit volume [m2/m3]Cp constant, Eq. (7a) [–]d packing diameter [m]dh hydraulic diameter [m]dS column diameter [m]dT mean droplet diameter acc. to Sauter [m]DL diffusion coefficient in the liquid phase [m2/s]FV gas load factor in relation to full column cross

section, FV = uV·�V0.5 [Pa0.5]

g acceleration of gravity [m/s2]hL liquid hold-up in relation to total free packing

volume VS, hL = VL/VS [m2/m3]H packing height [m]l mean contact path [m]N packing density [1/m3]p operating pressure [bar]t temperature [◦C]uV linear gas velocity in relation to full column

cross section [m/s]uL specific liquid load in relation to full column

cross section [m/s]VL liquid volume [m3]VS free packing volume, VS = ((� · d2

S)/4) · H [m3]

Greek symbols mass transfer coefficient [m/s]

ϕP form factor [–]� contact time [s]�, �� density, density difference �� = �L − �V [kg/m3]�L surface tension [N/m]� kinematic viscosity [m2/s]

Indicescal calculated valueexp experimentally derived valueL relating to liquidFl relating to operating point at flooding pointS relating to operating point above loading point,

0.65 ≤ FV/FV,Fl ≤ 1V relating to gas

Dimensionless numbersFo = 4 · DL · �/d2

T Fourier numberFrL = u2

L · a/g Froude numberReL = uL/a · �L Reynolds numberShL = ˇL · dT/DL Sherwood numberWe/FrL = �L · g/a2 · �L Weber/Froude numberScL = �L/DL Schmidt number

ts

dBBdd(

in a mass transfer, which is highest at the beginning and

he effective interfacial area per unit volume ae for ceramicpheres, Raschig rings and saddles.

Following on from the correlations for mass transfer pre-iction for liquid–liquid systems derived by Mackowiak andillet (1982/84) (Billet and Mackowiak, 1982b; Mackowiak andillet, 1986), which are based on the model of non-stationaryiffusion for short contact times, it was in the 1990s thatimensionless correlations, developed by Billet and Schultes

1993) as well as Bornhütter and Mersmann (1991, 1993),

were applied to gas–liquid systems, but they required theknowledge of the individual packing constants that must beevaluated from experimental data for each packing type andsize. The correlations are valid in the operating range up toloading line.

The aim of this study is to develop a generally applicablemethod for determining the volumetric mass transfer coeffi-cient in the liquid phase ˇL·ae for gas–liquid systems in wholeoperating range up to flooding, valid for different types of clas-sic, non-perforated as well as for lattice-type packing elementsand that can be used to predict the separation efficiency forany type of packing based only on specific packing-relateddata.

2. Deriving a model for determining thevolumetric mass transfer coefficient in theliquid phase ˇL·a below the loading line

Visual observations and measurements of droplet propor-tions have shown that in packed bed liquid primarily occursin the form of droplets rather than rivulets (Bornhütter andMersmann, 1991, 1993; Charpentier et al., 1968). As the size ofthe packing element increases, the amount of the droplets inthe packed bed also increases, an observation that was con-firmed as early as 1960 by Charpentier et al. (1968) and bystudies carried out by Bornhütter and Mersmann (1991, 1993)in connection with large diameter lattice packings, d ≥ 25–50.For this reason, it can be expected that mass transfer occursnon-stationary and can be described by model that is valid fordisperse systems. Droplets generated in the random packingfall in the gas phase, which constitutes the continuous phase.

The new method is derived on the basis of a model,whereby the liquid in a random packing flows down along thesurface of the individual packing elements in the form of thinrivulets, whereas between the individual packing elementsthe liquid flows down mainly in the form of droplets, providingthe area for mass transfer. In addition, the following assump-tions were made: in the case of droplet fall in the packing,deformed droplets with a Sauter diameter d32 = dT are formedbelow the loading line in accordance with the correlation

dT = CT

√�L

�� · g; CT = 1 [m] (1)

(dT > 1 mm). The validity of this equation for falling dropletshas been confirmed by numerous experimental resultsfor liquid–liquid systems (Billet and Mackowiak, 1982b,1988; Mackowiak and Billet, 1986) and gas–liquid systems(Bornhütter and Mersmann, 1991, 1993).

The effective mass transfer area ae is identical to thedroplet surface, whilst the total liquid hold-up hL correspondsto the liquid hold-up of the droplets. As a result, it is possibleto determine the interfacial area per unit volume using thecorrelation of Eq. (2)

ae = 6 · hL

dT[m2/m3] (2)

which is valid for disperse systems.The liquid flowing down the edges of the packing in the

form of droplets has a composition that is not in equilibriumwith the surrounding gas phase. This disequilibrium results

decreases along the flow length l, which is referred to here as


1310 chemical engineering research and design 8 9 ( 2 0 1 1 ) 1308–1320

king
Fig. 1 – Overview of pac
the contact path. During the formation of rivulets, mass trans-fer is interrupted and only recommences as new droplets areformed. The process is therefore non-stationary, as describedby the well-known model of Higbie (1935)

ˇL = 2√�

√DL

�[m/s] (3)

As a result, the mass transfer coefficient ˇL for mass transfer inthe liquid phase can be determined acc. to Eq. (3) if the contacttime � is known.

The contact time � in Eq. (3) is described by the time thata droplet needs to cover the distance l between two contactpoints within the packing. Hence:

� = l

uL[s] (4)

The absolute droplet velocity uL is expressed by Eq. (5):

uL = uL

hL[m/s] (5)

By substituting Eq. (5) in Eq. (4) we obtain Eq. (6):

� = l · hL

uL[s] (6)

elements investigated.

In order to determine the contact time � acc. to Eq. (6) for agiven specific liquid load, the liquid hold-up hL and the contactpath l must be known.

The contact path l can be determined for random packingsusing the volumetric mass transfer coefficient ˇL·ae derivedfrom measurements, as has been done for liquid–liquid sys-tems (Billet and Mackowiak, 1982b; Mackowiak and Billet,1986). This means that in practice the contact path l can beseen as a mean value that is valid for a whole series of mea-surements.

Acc. to Mackowiak (2010), the liquid hold-up hL in randompackings for turbulent liquid flow ReL ≥ 2 in the range belowloading point FV ≤ 0.65·FV,Fl can be described by Eq. (7a):

hL = Cp · Fr1/3L = Cp ·

(a · u2

L

g

)1/3

for Cp = 0.57 [m3/m3] (7a)

The liquid hold-up hL according to Eq. (7a) decreases as the sizeof the packing is increased, whilst the liquid load uL remainsconstant, see as an example Fig. 2, and hL is equivalent to uL

raised to the power of 2/3.Based on the evaluation of more than 1000 experimental

data points for the liquid hold-up using systems with differentphysical properties (Mackowiak, 2010), the constant Cp in Eq.(7a) was found to have a mean value of Cp = 0.57. The exper-
imental values (Mackowiak, 2010) are reproduced by Eq. (7a)for the operating range below the loading line with a relative



Fig. 2 – Flow structure in random packing: (a) for ceramic packing elements acc. to Charpentier et al. (1968); (b) for differentp 993)

en

t

h

FlF

acking elements acc. to Bornhütter and Mersmann (1991, 1

rror of ±20–25% for different types of plastic packings withominal sizes of 0.015–0.090 m (Fig. 3).

For laminar liquid flow 0.16 < ReL < 2, the Eq. (7b) is valid acc.o Mackowiak (2010):

L = 34

·(

3g

)1/3

a2/3(uL · �L)1/3 [m3/m3] (7b)

ig. 3 – Liquid hold-up hL as a function of the specific liquidoad uL valid for 15–50 mm metal Pall rings in the range

V ≤ 0.65·FV,Fl (Mackowiak, 2010).

; (c) droplet fall in packed column – model.

The product of the mass transfer coefficient ˇL and the inter-facial area per unit volume ae results from Eqs. (2) and (3).Substituting Eqs. (1), (6) and (7a) in Eqs. (2) and (3) leads tothe following correlation for determining the volumetric masstransfer coefficient ˇL·ae (8), valid for turbulent liquid flowReL ≥ 2:

ˇL · ae = 12 ·(

Cp

� · l

)1/2

·(

a

g

)1/6·(

DL · �� · g

�L

)1/2· u

5/6L [1/s]

(8)

where the contact path l must be known for each packing type.

3. Experimental results

Table 1a–d contains a list of technical data for different typesof packings investigated as well as the operating conditionsused in experiments carried out in columns with diametersbetween 0.15 and 1.2 m and a packing height of H = 0.7–4 m,some of which have been published previously (Billet andMackowiak, 1977, 1980, 1982a,b, 1985; Mackowiak, 1990, 2006;Bornhütter and Mersmann, 1991, 1993; Mackowiak, 1975; Billetet al., 1983). In addition, the table contains experimental dataavailable in the literature, e.g. data obtained by Bornhütterand Mersmann (1991, 1993) using a plant with dS = 1 m andH = 1.65–4 m, as well as data provided by Schultes (2001)
for Raschig Super rings, and by Sahay and Sharma (1973),Dharwadkar and Sawant (1985), and Linek et al. (1983).



Table 1 – Overview of technical data of packings used for calculating volumetric mass transfer coefficient ˇL·ae acc. to Eqs.(10) and (12), as well as form factors ϕP, valid for (a) to (d).

Packing Symbol d × 103

(m)ε(m3/m3)

a(m2/m3)

N × 103

(1/m3)dS (m) H (m) uL × 103,

from–to(m/s)

tL (◦C) ϕP (–)

(a) Classic, non-perforated packing elementsRaschig ring ♦ 15 0.626 239.3 – 0.10 1.0 1.7–11 20–40 0Ceramic � 50 0.782 100 6300 0.3 0.75 1–22.5 20 0

Intalox saddleceramic

38 0.757 125.7 18.9 0.3 1.4 1–11 21 0

(b) Packing elements with slightly perforated walls

Pall ring metal

15 0.964 380 243.2 0.3 0.87 1–11 22.5 0.28© 25

s = 0.40.954 223.5 53.9 0.3 1.46 1–11 21.5 0.28

© 25 0.942 232.1 55.6 0.15 1.3 0.79–10 22.5 0.28

35 0.946 150 19.6 0.3 1.4 1.2–8 19.5 0.28

� 38 0.952 149.6 15.8 0.3 1.46 1–11 20 0.28� 50 0.95 115.4 6.4 0.3 1.36 1–12 22.5 0.28

Pall ring plastic(PP)

� 25 0.894 238 55.18 0.3 1.4 1–10 23 0.309

35 0.905 160 18 0.3 1.4 1–10 20 0.309

50 0.93 111 6.85 1.0 1.65 1–18 20 0.309

50 0.92 110 6.7 0.3 1.35 1–15 22 0.309

Pall ring ceramic 50 0.78 120 6.4 0.22 1 1–12 20 0.430

Bialecki ringmetal

12 0.934 403 443 0.3 0.9 1–11 17.5 0.158

25 0.94 238 55 0.15 1.5 0.79–28 20 0.208

25 0.939 227 52.6 0.3 1.4 1–7 22 0.208

35 0.95 155 19 0.3 0.74 2–30 17.5 0.158

50 0.97 111.7 6.7 0.3 1.45 1–11 20 0.158

53.5 0.968 101.5 6 0.3 1.2–1.4 0.8–28 16.5 0.208

(c) Lattice packings with moderately perforated walls

Top-Pak� 45 0.957 104.7 6.8 0.3 1.45 1–11 20 0.474

75 0.979 75.0 2.8 1.0 1.65 1–18 20 0.424

VSP ring metal� 32 0.972 200 33.5 0.3 1.46 1–12 23 0.38 50 0.982 95.3 7.15 0.3 1.46 1–12 20 0.38

Ralu-Flow 58 0.941 98.9 4.7 0.3 1.44 1–12 19 0.705

CMR metal⊕ 1.5 0.974 176.3 60.8 0.3 1.4 0.8–6 19.5 0.475⊗ 1 0.9712 232.5 158.5 0.3 1.4 1–12 22.3 0.475

CMR plastic 1 0.94 200.0 25.6 0.3 1.42 1–11 12.0 0.496

(d) Lattice packings with highly perforated walls

Hiflow ring metal� 27 0.965 198.4

18495.4

37 0.220.30.45

1.21.422

1–15 2422.5

0.509

58 0.977 92.392.390

4.78 0.30.451.00

1.421.7

1–121–121–18

22.522.520

0.63

Hiflow ringplastic (PP)

17 0.91 292 183.8 0.3 1.43 1–11 21 0.54

� 28 0.92 192.5 46.1 0.3 0.9/1.4 1–10 22 0.54� 50 0.935 100.0 7.02 1.0 1.65 1–28 20 0.7� 50 0.932 107.7 6.3 0.3 1.57 1–12 14 0.7

90 0.955 61.0 1.415 1.0 1.65 1–28 20 0.69490 × 65 0.956 64.5 – 0.3 1.5 1–11 20 0.736

Hiflow ringceramic (1985)

20 (A) 0.77 261 110.74 0.3 1.2 2–12 20 0.587



– Table 1 (Continued)

Packing Symbol d × 103

(m)ε(m3/m3)

a(m2/m3)

N × 103

(1/m3)dS (m) H (m) uL × 103,

from–to(m/s)

tL (◦C) ϕP (–)

50(A) 0.815 88.8 5.12 0.3 1.3 1–10 20 0.54

Hiflow ringceramic (1988)

20 (B) 0.696 227 87.1 0.3 1.15 1–7 23.5 0.492

38 (B) 0.788 119.2 13.2 0.3 1.46 1–11 20 0.55

ENVIPAC PP

32 0.941 124 49.2 0.3 1/1.4 1–11 22 0.590

58 0.964 91.7 6.3 0.3 1.45 1–11 22 0.676

800.96 54.2 1.81 0.3 1.45 1–11 23.5

0.6760.954 61.1 2.05 1 1.6 1–12 20

DTNPAC � 70 0.936 112 10.2 0.3 1.45 1–11 20 0.676CMR turbo metal 1.5 0.976 167.7 60.3 0.3 1.4 1–11 21 0.475

Nor-Pac (NSWring) plastic

� 22 × 27 0.914 243 68.8 0.3 0.9 1–11 20 0.694

Φ 17 0.88 332 221.6 0.3 0.9 1–11 20 0.694

28 0.9215 191.7 47.4 0.3 1.4 2–10 17 0.694

� 38 0.932 138 20.5 0.3 1.4 0.8–6 16.5 0.694� 50 0.95 95 7.71 0.3 1.4 1–12 22.5 0.694

Hackette, PP 45 0.932 131 12 0.3 1.4 1–22 15 0.665

3l

FuCwaf1aTpasmdftrl

3t

EFmmt

.1. Effect of the packing form on mass transfer in theiquid phase

ig. 4a shows that the mass transfer coefficient in the liq-id phase ˇL·ae is highly dependent on the type of packing.ontrary to expectation, 17 mm Hiflow rings made of plasticith a smaller specific geometric surface area of a = 292 m2/m3

nd 17 mm Nor-Pac made of plastic with a = 332 m2/m3 wereound to have a considerably higher separation efficiency than2 mm metal Bialecki rings with a specific surface area of

= 403 m2/m3 and metal 15 mm Pall rings with a = 380 m2/m3.his would suggest that in random packings containing latticeacking elements, the geometric surface area of the packingvailable for mass transfer is used more efficiently and theize of the geometric surface area of the packing a is not theainly factor that determines mass transfer. In classic ran-

om packings, not all of the surface area appears to be usedor mass transfer. In addition, Figs. 4, 5a–d, 6a–d and 7 showhe significance of the packing form, i.e. the bigger the perfo-ation of the packing element, the better the mass transfer iniquid phase.

.2. Influence of the packing size and type on massransfer in the liquid phase

q. (8) and the experimental results, shown as an example inigs. 5–7, reveal two parameters that have a main effect onass transfer coefficient ˇL·ae in the liquid phase: the geo-
etric surface area of the packing per unit volume “a” and
he contact path “l”.

3.3. Evaluation of the contact path l for differentpacking forms

This was discussed in a previous study (Mackowiak, 2006,2010) on the modelling of the fluid dynamics of packed columnfilled with lattice packings, where the effect of the individualpacking elements on the fluid dynamics of random packingswas described by an extended “channel model with openstructure” (Mackowiak, 2006, 2010). Acc. to this model, a ran-dom packing is characterised by three parameters, which are:the geometric surface area of the packing “a”, the void fraction“ε” and the form factor “ϕP”, which is defined as the ratio ofthe open area to the total surface area of the packing element(Mackowiak, 2006, 2010).

In the case of classic packing elements with non-perforatedwalls, as Raschig rings and saddles, ϕP is given as ϕP = 0 acc.to Mackowiak (2006, 2010). Fig. 8 shows that for the samehydraulic diameter dh their contact paths are almost twice aslong as those of lattice packings with a very open structureacc. to Fig. 5d with form factors of ϕP = 0.55–0.7.

The numerical values for the contact paths l in Eq. (8) forthe investigated packings were determined on the basis of theexperimental data of this work shown for example in Figs. 4–7.Plotting the contact path l on the hydraulic diameter dh ofthe packing gives the following correlation (9) for the packingsinvestigated acc. to data presented in Figs. 4–7:

l = 0.115 · (1 − ϕP)2/3 · d1/2h

[m] (9)

where ϕP is a parameter relating to a different characteristic
form of packing element, s. Table 1a–d, and dh is hydraulicdiameter of packing.



Fig. 4 – Volumetric mass transfer coefficient ˇL·ae as afunction of the specific liquid load uL, valid for: (a)randomly filled 15 mm Pall rings, 12 mm Bialecki rings and17 mm Hiflow rings as well as 17 mm Nor-Pac made ofplastic. System: CO2–water/air, 293 K, dS = 0.3 m, H = 0.9 m;(b) randomly filled 25 mm Pall rings, Bialecki rings andHiflow rings made of metal. System: CO2–water/air, 1 bar,293 K, dS = 0.3 m, H = 1.36 m.

Fig. 5 – Volumetric mass transfer coefficient ˇL·ae as afunction of the specific liquid load uL, valid for randomlyfilled packing elements made of metal: (a) VSP rings size 1and 25 mm Pall rings; (b) VSP rings size 2 and 38 mm Pall

Fig. 8a–d shows that not only the size and type of the pack-ing element has a significant effect on the contact path. Itcan be noted that the more open the structure of the packingelement, the shorter the contact paths l.

Substituting the relations of Eq. (9) in Eq. (8) leads to thenew, generally valid Eq. (10) for the prediction of volumetricmass transfer coefficient ˇL·ae in columns with random pack-ings below the loading line FV ≤ 0.65·FV,Fl and for turbulentliquid flow ReL ≥ 2:

ˇL · ae = 15.1

(1 − ϕP)1/3 · d1/4h

·(

DL · �� · g

�L

)1/2·(

a

g

)1/6u

5/6L [1/s]

(10)

see Fig. 6.
For laminar liquid flow 0.16 < ReL < 2, the Eq. (11) will be
obtained after substitution of Eqs. (7b) and (9) into Eqs. (2),

rings; (c) 50 mm Pall rings, Bialecki rings and Hiflow rings.System: CO2–water/air, 1 bar, 293 K, dS = 0.3 m, H = 1.36 m.

(3) and (6)

ˇL · ae = 17.3 · a1/3

(1 − ϕP)1/3 · d1/4h

·(

3 · �L

g

)1/6

·(

DL · �� · g

�L

)1/2

· u2/3L [1/s] (11)

Fig. 9a–f shows the comparison between the calculation basedon Eqs. (10) and (11) and the experimental data of this work



Fig. 6 – Volumetric mass transfer coefficient ˇL·ae as a function of the specific liquid load uL, valid for different types ofpacking elements made of plastic (PP): (a) 32, 56 and 80 mm ENVIPAC; (b) 45 mm Hackettes, 45 mm Nor-Pac, Hiflow rings,Hiflow Super rings, Ralu rings and Pall rings; (c) Dtnpac size 2; (d) 58 mm Ralu Flow, 50 mm Pall rings, 50 mm Nor-Pac.S .6 m

pB

mitcwm

H

ystem: CO2–water/air, 1 bar, 295 K, dS = 0.3–1.0 m, H = 1.45–1

lus data collected by Bornhütter and Mersmann (1991, 1993),udzinski and Kozioł (2000) and Schultes (2001).

Eqs. (10) and (11) allow consolidating the information onass transfer in the liquid phase in random packings contain-

ng packing elements of different types and sizes, enabling uso predict the ˇL·ae values for different types of modern andlassic packings sufficiently enough for practical applicationsith a mean error of ±13% in the range below loading line forore then 800 experimental points.
The comparison between experimental data for 50 mm
iflow rings and calculated values according to Eq. (10) as well

.

as to various models available in the literature is shown inFig. 10.

4. Model for determining the volumetricmass transfer coefficient in the liquid phase(ˇL·ae)S above the loading line and below theflooding point

Based on the assumption that in the range above the loading
line, i.e. for high gas velocities FV > 0.65·FV,Fl acc. to Mackowiak(2010), the droplet diameter dT remains acc. to Eq. (2) constant,



Fig. 7 – Volumetric mass transfer coefficient ˇL·ae as afunction of the specific liquid load uL, valid for differentpacking elements with nominal dimensions of 15–75 mmmade of ceramic. System: CO2–water/air, 1 bar, 295 K,

the mass transfer coefficient ˇL

dS = 0.1–0.3, H = 0.75–1.4 m.

the volumetric mass transfer coefficient ˇL·ae acc. to Eq. (14) isequivalent to the liquid hold-up hL raised to the power of 1/2

ˇL · ae∼h1/2L (12)

Fig. 11 shows that in the range above the loading line forFV > 65% of the flooding point, the ratio of liquid hold-up hL,S/hL

for moderate liquid loads is just a function of the relative
column load FV/FV,Fl. This information applies to packing ele-ments of different types, materials and sizes.
Fig. 8 – Effect of hydraulic diameter dh on mean contact path l fonon-perforated packing elements for ϕP = 0; (b) for classic, perforawith perforated walls for ϕP = 0.30–0.55; (d) for lattice packings w

As a result, the quotient (ˇL·ae)S/(ˇL·ae) can be expressed asa function of the relative column load FV/FV,Fl. The experimen-tal values listed in Fig. 12a and b can be described accordingto data presented in Fig. 12 using the following empirical cor-relation (13) for uL = const.:

(ˇL · ae)S = (ˇL · ae) ·[

1 +(

FV

FV,Fl− 0.65

)]uL=const

= (ˇL · ae) ·(

0.35 + FV

FV,Fl

)uL=const

[1/s] (13)

By substituting Eq. (10) in Eq. (13), we obtain Eq. (14):

(ˇL · ae)S = 15.1

(1 − ϕP)1/3 · d1/4h

·(

DL · �� · g

�L

)1/2·(

a

g

)1/6

·(

0.35 + FV

FV,Fl

)uL=const

· u5/6L [1/s] (14)

The evaluation of approx. 40 experimental points in the rangeabove the loading line reveals a congruence between the cal-culation based on Eq. (14) and the experiment, with a relativeerror ı(ˇL·ae)S of less than ±15%. These experimental resultsare also shown in Fig. 9a–d (Table 2).

5. Validation of model

5.1. Dimensionless representation of the correlationfor determining the interfacial area per unit volume and

Eqs. (1), (2) and (7a) lead to Eq. (15) for determining the inter-facial area per unit volume for turbulent liquid flow ReL ≥ 2 in

r types of packings investigated: (a) for classic,ted packing elements ϕP = 0.15–0.30; (c) for lattice packings

ith highly perforated walls for ϕP ≥ 0.55–0.70.



Fig. 9 – Comparison between calculation acc. to Eqs. (10) and (12) and experimental values for: (a) classic, non-perforatedpacking elements, ϕP = 0; (b) packing elements with partly open structure, ϕP = 0.15–0.30; (c) lattice-type packing elementswith open structure, ϕP = 0.30–0.55; (d) lattice-type packing elements with open structure, ϕP = 0.55–0.70; (e) packingelements with highly open structure: Raschig Super rings (RSP), ϕP = 0.28.

t

wF

t1

By substituting Eqs. (7a) and (9) in Eqs. (6) and (3), we obtain

he operating range below loading line:

ae

a= 6 · Cp · Fr

1/3L ·

(We

FrL

)1/2Cp=0.57⇒ 3.42 · Fr

1/3L ·

(We

FrL

)1/2[–] (15)

hich describes the experimental data well, as illustrated inig. 13.

Correlation (16) provides a dimensionless representation ofhe mass transfer coefficient ˇL for short contact times (Higbie,935; Brauer, 1971):

ShL = 2.26 · 1

Fo1/2L

(16)

Eq. (17) for predicting of the mass transfer coefficient in theliquid phase ˇL in random packings of any type and nominaldimension, valid for turbulent liquid flow ReL ≥ 2 below the



Fig. 10 – Volumetric mass transfer coefficient ˇL·ae as afunction of the specific liquid load uL, valid for randomlyfilled 50 mm Hiflow rings made of plastic (PP). System:CO2–water/air, 293 K, dS = 0.3–1.0 m, H = 1.4–1.65 m.Comparison between experimental points [A,7,8] and Eq.(10) (straight line) as well as different literature methods(Billet and Schultes, 1993; Bornhütter and Mersmann, 1993;Kolev, 1976; Zech and Mersmann, 1978; Shi and
Mersmann, 1984; Onda et al., 1968).
loading line:

ˇL = 5.524√�

· a1/12 · D1/2L · g1/6

(1 − ϕP)1/3ε1/4· u

1/6L [m/s] (17)

For laminar liquid flow ReL < 2 below the loading line we obtainfollowing Eq. (18) for determining the interfacial area:

��1/2 · g1/6 · �1/3

1/3
ae = 6.49 · a2/3 · L
�1/2L

· uL [m2/m3] (18)

Fig. 11 – Ratio of liquid hold-up hL,S/hL as a function of therelative gas load, valid for different packing elements acc. toMackowiak (2010).

Fig. 12 – Volumetric mass transfer coefficient (ˇL·ae)S/(ˇL·ae)as a function of the relative gas load FV/FV,Fl in the entireoperating range up to flooding point, valid for: (a) 25 mmmetal Białecki and Hiflow rings, metal CMR rings no. 1.5and 20 mm Hiflow rings made of ceramic; (b) 50 mm Palland Hiflow rings made of plastic.

Table 2 – Experimental conditions and limits of validityof models as per Eq. (14) for ReL ≥ 2.

d = 0.012–0.090 mdS = 0.10–1.4 mdS/d ≥ 6H = 0.71–4 ma = 54.2–403.0 m2/m3

ε = 0.696–0.987 m3/m3

ReL = 2–900FV/FV,Fl ≤ 1FrL = 5.5 × 10−6–1.4 × 10−2

We/FrL = 0.8–4.5ScL = 5100–10,000



Fig. 13 – Effective interfacial area per unit volume ae as a function of the specific liquid load uL, valid for different packingelements. Comparison between Eq. (15) (continuous line) and experimental data of different authors. (a) 28 mm Nor-Pac and25 mm Tellerette made of plastic (Krötsch, 1981 and Krötsch and Kürten, 1979); (b) 35 mm Pall rings and 38 mm Nor-Pacm a, 1

ap

ˇ

6

Otrm(tcet(fe(iv

ade of plastic; (c) 25 mm metal Pall rings (Sahay and Sharm

nd Eq. (19) for the mass transfer coefficient in the liquidhase ˇL:

L = 3.842 · D1/2L

(1 − ϕP)1/3 · d1/4h

· (3/g)1/6 · a1/3 · �1/6L

· u1/3L [m/s] (19)

. Conclusions

n the basis of the presented model, according to the assump-ion that droplet flow occurs in packed columns filled withandom packings, combined with the application of the

odel of non-stationary diffusion for short contact timesMackowiak and Billet, 1986; Higbie, 1935), it has been shown,hat it is possible to calculate the volumetric mass transferoefficient ˇL·ae for packings of any type and size withoutvaluation of specific empirical packing constants which haveo be derived from experiments. The equations according to10) and (11) are valid in the range below the loading lineor turbulent and laminar flow respectively and have beenxtended to the range up to flooding point according to Eq.14). The presented mass transfer correlations as well as the
nterconnected hydraulics correlations have been tested witharious absorption and various distillation systems covering
973).

a large range of physical properties, details are shown in theliterature (Mackowiak, 2010). For the prediction of the masstransfer coefficient ˇL Eq. (17) is derived. Therefore it is nec-essary to determine the effective mass transfer area. It is thearea formed by droplets that determines the interfacial areaper unit volume ae/a in the random packing for laminar andturbulent liquid flow in the range of ReL ≤ 900 acc. to Eqs. (15)and (18).

References

Billet, R., Mackowiak, J., 1977. Chem. Tech. 6, 455–461.Billet, R., Mackowiak, J., 1980. Chem. Tech. (Heidelberg) 9, 219–226.Billet, R., Mackowiak, J., 1982a. vt “verfahrenstechnik” 16 (2),

67–74.Billet, R., Mackowiak, J., 1982b. Inz. Chem. Procesowa (Orig. Engl.)

3 (3/4), 459–482.Billet, R., Mackowiak, J., 1984. Chem. Tech. 12, 37–46 (1985) 4,

91–99 and (1985) 5, 195–206.Billet, R., Mackowiak, J., 1988. Chem. Eng. Technol. 11, 213–227.Billet, R., Schultes, M., 1993. Chem. Eng. Technol. 16, 1.Billet, R., Mackowiak, J., Ługowski, Z., Filip, S., 1983. Fette Seifen

Anstrichmittel 85 (10), 383–389.
Bornhütter, K., Mersmann, A., 1991. Chem. Ing. Tech. 63 (2),
132–133.



Bornhütter, K., Mersmann, A., 1993. Chem. Eng. Technol. 16,46–57.

Brauer, H., 1971. Stoffaustausch einschließlich chemischerReaktionen. Verlag Sauerländer, Aarau.

Budzinski, W., Kozioł, A., 2000. Chem. Eng. Sci..Charpentier, J., van Swaaij, V., Le Goff, 1968. Chemie et industrie –

genie Chemique 99, 6.Dharwadkar, S.W., Sawant, S.B., 1985. Chem. Eng. J. 31, 15–21.Higbie, R.R., 1935. AIChE J., 365–389.Kolev, N., 1976. Chem. Ing. Tech. 48 (12), 1105–1112.Krötsch, P., 1981. Chem. Ing. Tech. 53 (11), 892–893, synopsis 953.Krötsch, P., Kürten, H., 1979. Verfahrenstechnik 13, 939–944.Linek, V., Petricek, P., Benes, P., Krivsky, Z., Braun, R., 1983. vt

“verfahrenstechnik” 17 (6), 382–385.Mackowiak, J., 1975. Einfluss der Führungsflächen in

ringförmigen Füllkörpern auf die Fluiddynamik und
Stoffaustausch im System Gas-Flüssigkeit, Dissertation TUWrocław (Poland).
Mackowiak, J., 1990. Staub–Reinhaltung der Luft 50, 221.Mackowiak, J., 1999. Chem. Ing. Tech. 71 (1+2), 100–104.Mackowiak, J., 2006. Chem. Ing. Tech. 78 (8), 1079–1086.Mackowiak, J., 2010. Fluid Dynamic of Packed Columns.

Springer-Verlag.Mackowiak, J., Billet, R., 1986. German Chem. Eng. 9 (1), 48–64.Onda, K., Takeuchi, H., Okumoto, Y., 1968. J. Chem. Eng. Jpn. 1 (1),

56–61.Sahay, B.N., Sharma, M.H., 1973. Chem. Eng. Sci. 28, 41–47.Schultes, M., 2001. Raschig Super-Ring A New Fourth Generation

Random Packing Paper Presented at AICHE Meeting , Houston,Texas, April 22–26.

Shi, G., Mersmann, A., 1984. Chem. Ing. Tech. (MS 1222/84) 56 (5).Shi, G., Mersmann, A., 1985. German Chem. Eng. 8, 87–96.Wang, G.Q., Yuan, X.G., 2005. Ind. Eng. Chem. Res. 44, 8715–

8729.
Zech, J.B., Mersmann, A., 1978. Chem. Ing. Tech. 50, 7 MS
604/78.

mass transfer correlations for packed towers

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