prediction of hetp for randomly packed towers operation ... technology 33 2003 145.pdf · a steady...

Prediction of HETP for randomly packed towers operation:integration of aqueous and non-aqueous mass transfer

characteristics into one consistent correlation

Simon Piche, Stephane Levesque, Bernard P.A. Grandjean, Faıcal Larachi *

Department of Chemical Engineering and CERPIC, Laval University, Laval, Que., Canada G1K 7P4

Received 1 October 2002; received in revised form 2 December 2002; accepted 9 December 2002

Abstract

Height equivalent to a theoretical plate (HETP) calculations, essential for the design of randomly packed distillation

columns were extracted from the open literature to generate a working database including over 2350 measurements

(only total molar reflux data). The merging of mass transfer characteristics from non-aqueous and aqueous separation

experiments has instigated the generation of a consistent correlation predicting HETP. Based on results presented

elsewhere for absorption and stripping conditions (Ind. Eng. Chem. Res. 41 (2002) 4911), a set of artificial neural

network (ANN) correlations for the gas�/liquid interfacial area (aw) and the pure local mass transfer coefficients (kg,

g�/G or L) was proposed with the following dimensionless structures: aw/aT�/f (ReL, FrL, EoL, I , x , K ) and Shg�/

f (Reg, Frg, Scg, x ). The gas�/liquid interfacial area and the pure local mass transfer coefficients were extracted using a

reconciliation procedure which combined actually measured interfacial areas with pseudo-interfacial areas inferred

from the actually measured volumetric mass transfer coefficients (kLaw, KLaw, kGaw, KGaw*/absorption and stripping)

and HETP (distillation). The neural network weights of the two aw and kg correlations were adjusted using a least-

squared composite criterion simultaneously over the six mass transfer parameters’ databases. The optimized set of

ANN correlations yielded an average absolute relative error (AARE) of 21.3% for the 2357 HETP measurements

available. Likewise, the measured interfacial area and volumetric mass transfer coefficients (3770 data) were correlated

with an AARE of approximately 26.5%, which undeniably proves the intimate correspondence of absorption and

distillation mass transfer characteristics in randomly packed towers. HETP predictions remain as well in accordance

with the physical evidence reported in the literature.

# 2003 Elsevier B.V. All rights reserved.

Keywords: Random packed bed; Distillation; Absorption; Stripping; HETP; Mass transfer; Neural network; Database

1. Introduction

Randomly packed bed technology intended for

non-aqueous mixtures separation has been the

ground of intense research for the last 30 years

or so. Fundamentally, packed beds are used to

* Corresponding author. Tel.: �/1-418-656-3566; fax: 1-418-

656-5993.

E-mail address: [email protected] (F. Larachi).

Separation and Purification Technology 33 (2003) 145�/162

www.elsevier.com/locate/seppur

1383-5866/03/$ - see front matter # 2003 Elsevier B.V. All rights reserved.

doi:10.1016/S1383-5866(03)00005-4

mailto:[email protected]

Nomenclature

AARE average absolute relative error, AARE�1

NaN

i�1j yexp(i) � ypred(i)

yexp(i) j/aT bed specific surface area (m�1)aw gas�/liquid interfacial area (m�1)CL, CG packing-specific constants for Billet and Schultes correlation (�/)CPK packing-specific constant for Wagner et al. correlation (�/)Da a phase diffusion coefficient (m2 s�1)DC column diameter (m)dN packing nominal diameter (m)dpv sphere diameter equivalent with particle volume, 6(1�/o )aT

�1f�1 (m)

EoL liquid phase Eotvos numberFra a phase Froude numberg gravitational acceleration (m s�2)G gas mass flow rate (kg m�2 s�1)G ? gas molar flow rate (mol s�1)HETP height equivalent to a theoretical plate (m)Hj hidden neuronshT operating liquid holdup per bed volumeHTUOG gas-phase overall height of a transfer unit (m)I modified relative stabilizing indexK bed characterizing numberka a phase-film mass transfer coefficient (m s�1)Ka overall a phase-side mass transfer coefficient (m s�1)L liquid mass flow rate (kg m�2 s�1)L ? liquid molar flow rate (mol s�1)m thermodynamic partition coefficientMa a phase molecular weight (g mol�1)P pressure (Pa)Q optimized cost functionRea a phase Reynolds numberS normalized output variableSca a phase Schmidt numberSha

O overall a phase Sherwood numberSha a phase-film Sherwood numberSh� a a phase volumetric film Sherwood number, kaawaT

�2Da�1

T temperature (K)Ua a phase superficial velocity (m s�1)Ui normalized input variablesxi molar fraction of specie i in liquid phase

z bed height coordinate (m)Z bed height (m)

a interfacial area per bed specific surface areax Lockhart�/Martinelli parametero bed porosityf particle sphericityl stripping factor

Greek letters

S. Piche et al. / Separation and Purification Technology 33 (2003) 145�/162146

promote gas�/liquid contacting which can be

translated into higher inter-phase volumetric

mass transfer and better column efficiency. It is

actually well-employed in many industrial opera-

tions involving absorption and stripping processes.

Modern random packings creating sufficiently

high surface area and high throughput environ-

ments will often render this technology more

attractive for distillation processes compared to

tray columns, for example Ref. [2]. As a rule of

thumb, packed towers should be selected when a

liquid mixture hosts inconvenient properties for

tray columns (i.e. high stripping factor, high gas

density) [3]. Although structured packings are

more convenient for distillation, their actual costs

still prevent their proliferation over random pack-

ings. Therefore, based on the current market

status, the progress of inquiring tools for the

assessment of distillation randomly packed towers

remains essential for the well-being of this tech-

nology.

Performance analysis, scale-up and tower design

revolves on the understanding of macroscopic

gas�/liquid hydraulic behaviour as well as inter-

phase mass transfer and thermodynamic funda-

mentals. The overall efficiency defined in terms of

height equivalent to a theoretical plate (HETP)

adheres to the fudging of separate variables

emanating from those engineering fields (Eq.

(1)). Gas�/liquid interfacial area (aw), the most

intriguing variable in distillation, depends entirely

on the gas�/liquid flow behaviour across the solid

medium while the interface-sensitive mass transfer

coefficients (kG, kL), also affected by the hydro-

dynamics, remains bound to molecular diffusivity

drive in the gas and liquid films. Such variables

(aw, kG, kL) can be evaluated using previously

published sets of correlations/models allowingknowledge of the operating conditions (i.e. pres-

sure, liquid loading rate). On the other hand,

involvement of thermodynamics consolidated into

the stripping factor (l�/mG/L) remains rather

peculiar since the gas�/liquid equilibrium con-

stantly changes along the liquid flow path down-

stream of the column. This fact implicitly suggests

a steady change in the HETP as well. Forsimplification, equimolar composition of the bin-

ary mixture is used as the main premise for the

evaluation, or rather the approximation, of the

partition coefficient (m ) as well as the gas and

liquid physical properties (i.e. rG, mL, etc.). Un-

fortunately, it renders the HETP approach more a

rule of thumb concept rather than an exact science.

HETP�lnl

l� 1HTUOG

�ln(mG?=L?)

mG?=L? � 1

�UG

kGaw

�mUL

kLaw

�(1)

Nevertheless, the procurement of separate cor-

relations for aw, kG and kL emerging from the two-

film resistance concept is still accepted to be quite

useful for extracting the areal effect from the inter-

phase transfer effect in the volumetric masstransfer coefficient (kgaw). In doing so, several

investigators attempted the split by proposing

correlations for the interfacial area (aw) and local

mass transfer coefficients (kL and kG) apart,

resulting thus in three structurally different corre-

lations, eventually estimating not only overall

ma a phase viscosity (kg m�1 s�1)ra a phase density (kg m�3)s standard deviation, s�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiaN

i�1½j yexp(i) � ypred(i)

yexp(i) j�AARE�2=(N�1)

s/

sC packing criticalsurface tension (N m�1)

sL surface tension (N m�1)vi j, vj neural network fitting parameters

g gas or liquidG gasL liquidvol volatile compoundint interface

Subscripts

S. Piche et al. / Separation and Purification Technology 33 (2003) 145�/162 147

Table 1

Summary of important correlations predicting the HETP

Onda et al. [4]a

kL�0:0051

�rLUL

awmL

�2=3� mL

rLDL

��1=2� rL

mLg

��1=3

(aTdN)4=10 (2) kG�2

�rGUG

aTmG

�7=10� mG

rGDG

�1=3� DG

aTd2N

�(3)

aw

aT

�1�exp

��1:45

�sC

sL

�3=4�rLUL

aTmL

�1=10�aTU 2L

g

��1=20�rLU2L

aTsL

�2=10�(4)

Bravo and Fair [5]a

aw

aT

�6:249s0:5

L

Z0:4

�mLUL

sL

�0:392�rGUG

aTmG

�0:392

(5)kG, kL are computed from the Onda et al. correlation (Eqs. (2) and

(3))

Billet and Schultes [6]a

kL�CL

�rLg

mL

�1=6�aTDL

4o

�1=2�UL

aT

�1=3

(6) kG�CG

aTDG

(4o2 � 4ohT)1=2

�rGUG

aTmG

�3=4� mG

rGDG

�1=3

(7)

�aw

aT

�O

�1:5(4o)1=2

�rLUL

aTmL

��2=10�rLU 2L

aTsL

�3=4�aTU2L

g

��0:45

(8)For absorption, desorption and distillation with dsL/dzE/0

aw

aT

��

aw

aT

�O

��

1�2:4�10�4j dsL

dxvol

(x � xint)

aTDLmLj0:5� (9)

For distillation with dsL/dzB/0

Wagner et al. [10]

HETP�CPK

Z0:5

aT

�p(o � hT)UG

4DG

�0:5�1�

�hTDGMLrG

(o � hT)DLMGrL

G?

L?

�0:5��1 � o � hT

1 � o

�0:66

�1

��1

(10)

Norton Chemicals [2,12]

Atmospheric distillation (0.4�/4 atm) RestrictionsHEPT�exp(C1�0:187lnsL�0:213lnmL) (11) sL�/4�/36 dynes/cm

C1�/1.13 (dN�/25 mm), 1.35 (dN�/38 mm), 1.65 (dN�/50 mm) mL�/0.08�/0.83 Cp

Pressure distillation (�/4 atm)HEPT�C2�0:213ln(ML) (12) ML�/22�/72 g/mol

i.e. C2�/1.49 (IMTP #40), 1.35 (IMTP #25), 1.65 (IMTP #50)

a HETP are calculated with Eq. (1).

S.

Pich

eet

al.

/S

epa

ratio

na

nd

Pu

rificatio

nT

echn

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33

(2

00

3)

14

5�

/16

21

48

mass transfer coefficients (Kgaw) for absorption/stripping separation but HETP as well [4�/6]. As a

matter of fact, the first known three-equation

structure from Onda et al. work [4] suggests

similarities, allowing reasonable error, in the

mass transfer response for both aqueous and

non-aqueous separation processes although some

antagonistic arguments can be noted. Indeed, the

Onda et al. correlations (Table 1), althoughdeveloped on grounds of gas absorption, deso-

rption and vaporization experiments, remain gen-

erally applicable for the prediction of HETP [7].

Bravo and Fair [5] identifying a lack in Onda’s aw

equation proposed another empirical aw correla-

tion based on over 200 experiments while using

Onda’s kL and kG equations to complete HETP

predictions (Table 1). Yet, some disagreementswere noted by Yang and Chuang [3] as for the

validity of this correlation which presupposed a

disputable effect of bed height (aw8/Z�0.4) and an

increasing effect of surface tension (aw8/sL0.108) on

interfacial area, a relationship that is opposite to

the low wettability (sL�/) low interfacial area (aw¡/)

expectation.

Recently, Billet and Schultes [6] proposed an-other three-equation semi-empirical procedure

(Table 1) which requires, besides the usual operat-

ing conditions, the theoretical liquid hold-up value

and also two packing-specific constants account-

ing for shape, material and size. It has been

successfully tested over a wide range of aqueous-

type experiments [8]. Based on their own database

reportedly spanning over 50 test system (aqueousand non-aqueous) and 70 types of dumped and

structured packings, the correlation yielded a

relative average deviation of 12% for absorption/

stripping experiments and 14% for rectification

systems [9]. Billet and Schultes set of equations

was actually the first to explicitly link aqueous and

non-aqueous mass transfer characteristics alto-

gether while applying appropriate distinctions fordistillation type experiments. The main distinction

resides on the Marangoni factor (dsL/dz) encoun-

tered for ever changing surface tension due to

varying liquid compositions along the liquid flow

path (z ). The relevance of this concept in distilla-

tion will be thoroughly discussed in a later section.

Wagner et al. [10] also derived a model predicting

HETP using the Higbie’s penetration theory tocalculate the mass transfer rate (kL and kG) and

considerations from the hydrodynamics model

(pressure drop, liquid hold-up) of Stichlmair et

al. [11] to evaluate the interfacial area. The

combination of those premises has led to the

explicit formulation of HETP expressed in Table

1.

Simplified HETP correlations have also beendeveloped as a loophole out of more complex

calculations. Understandingly, packed towers effi-

ciency is said to be mainly influenced by the size

and shape of the packing rather than the fluids

physical properties. For a gross estimation of the

HETP, several potential factors can be omitted.

Norton Chemicals correlations [2,12] which only

use packing size constants, liquid viscosity andsurface tension represent good examples (Table 1).

In a previous work, a set of neural network

correlations predicting the interfacial area (ANN-

aw) and the pure local mass transfer coefficients

(ANN-kg, kg�/kL or kG) was developed using a

comprehensive database (3770 measurements) of

gas�/liquid interfacial area and volumetric mass

transfer coefficients (kgaw, Kgaw) retraced in theopen literature [1]. The database was exclusive to

absorption and stripping. The modeling approach

was revolving around the use of a reconciliation

procedure which combines actually measured

interfacial areas with pseudo-interfacial areas

intuited from the actually measured volumetric

mass transfer coefficients. Fig. 1a exposes the

various steps undertaken throughout the modelingprocess which have resulted into the following

artificial neural network (ANN) correlations

[Shg�/f(Reg, Frg, Scg, x ) and aw/aT�/f(ReL, FrL,

EoL, x , K )]. Having demonstrated good level of

precision and robustness in terms of phenomen-

ological consistency, this empirical modeling ap-

proach could easily be extended to HETP

prediction allowing appropriate discriminatoryparameters for non-aqueous systems as adopted

by Billet and Schultes with the Marangoni term.

Furthermore, HETP modeling using a neural

network approach has already been conducted

for trayed [13] and structured packing [14] distilla-

tion columns confirming thus the potentiality of

this method for the present case in hand.


2. Mass transfer correlation development

2.1. Databases overview

The cited literature pertaining to the absorption/stripping database was divulged in a previous

publication [1]. It regroups 325 measurements on

the interfacial area, 1100 measurements on the

liquid-film coefficient (kLaw), 361 measurements

on the gas-film coefficient (kGaw), 1242 measure-

ments on the liquid-overall coefficient (KLaw) and

742 measurements on the gas-overall coefficient

(KGaw). Table 2 (1st column) summarizes thebreadth of operating variables characteristic to

these five mass transfer characteristics. The dis-

tillation database is constituted of 2357 HETP

measurements taken from 22 references spanning

between 1960 and 2001 [7,10,15�/34]. All experi-

ments were conducted at total molar reflux (G?�/

L?) with standard binary mixtures (chlorobenzene/

ethylbenzene, ethylbenzene/styrene, benzene/tolu-

ene, methanol/ethanol, trans -decalin/cis -decalin,

ethanol/water, n-hexane/cyclohexane, n-hexane/

n-heptane, isopropanol/water, iso-octane/toluene,

toluene/methylcyclohexane, cyclohexanone/cyclo-

hexanol, o -xylene/p -xylene, benzene/1,1-dichlor-

oethylene, trichloroethylene/n -heptane, n -

heptane/toluene). The liquid physical properties

were established on an equimolar composition

basis. If information on the liquid physical proper-

ties were not explicitly given by the author, the

following methods were employed to estimate the

liquid density (weighted average), liquid viscosity

(Grunberg and Nissan method), surface tension

(Macleod�/Sugden method) and liquid diffusion

coefficient (Siddiqi�/Lucas correlation) [35]. The

resulting gas phase equilibrium composition was

also used as basis for the calculation of gas density

Fig. 1. Modeling organization charts for (a) the ANN-awI and ANN-kg

I correlations developed from absorption and stripping

experiments [1] (b) the actual ANN-awII and ANN-kg

II correlations developed from absorption, stripping and distillation experiments.


(ideal gas law), gas viscosity (Wilke correlation),

gas diffusion coefficient (Chapman�/Enskog the-

ory) and equilibrium constant (m ). Operating

variables pertaining to the distillation database

are displayed in Table 2 (2nd column). Both

databases also exhibit results on 24 packingvarieties, summarized in Table 3, spanning from

classical packings (e.g. Pall ring) to modern high-

porosity, low-pressure drop packings (e.g. IMTP

ring).

2.2. Artificial neural network optimisation

procedure

A four-step procedure similar to the one advo-cated previously [1] was implemented to develop

the ANN-awII and ANN-kg

II correlations (Fig. 1b).

The general strategy surrounding the implementa-

tion of ANNs (NNFIT software [36]) and the

identification of the Buckingham P dimensionless

input groups best correlated with the output mass

transfer dimensionless group is similar to the one

discussed in several past works [37�/39].

In a first step, the ANN-awI and ANN-kg

I

correlations developed for predicting mass transfer

coefficients in aqueous solutions [1] was tested

over the HETP database. It has demonstrated a

fairly good sense of predictability (average abso-

lute relative error (AARE)�/76%) allowing that it

was not specifically developed for non-aqueous

liquid separation. At some extent, it also confirms

the compatibility of the chosen dimensionless

numbers predicting mass transfer parameters for

both aqueous and non-aqueous liquid separation.

Yet, modifications of the interfacial area correla-

tion have to be made in order to take the

Marangoni factor into account. Accordingly, a

customized relative stability index (I) (Eq. (13))

was added to the ANN-aw correlation architecture

(Table 4). It represents the ratio between the rate

of surface tension change per molar fraction of the

most volatile component and the mixture surface

Table 2

Anatomy of the absorption/stripping and distillation databases

Absorption/stripping experiments (3770 data) Distillation experiments (2357 data)

flow rate range: 0.1�/0.5

Operating pressure, P [atm] 0.9�/13.6 0.026�/2.0

Operating temperature, T (K) 276�/316 258�/408

Liquid mass flow rate, L [kg m�2 s�1] 0.07�/76 0.1�/5.0

Gas mass flow rate, G [kg m�2 s�1] �/0�/5.55

Packing nominal diameter, dN [mm] 6.0�/76.2 9.5�/88.9

Bed porosity, o [%] 40.0�/98.0 62.4�/98.7

Bed surface area, aT [m�1] 87�/764 62�/553

Tower diameter, DC [m] 0.04�/1.40 0.09�/1.22

Bed height, Z [m] 0.1�/5.9 0.8�/10.7

Liquid density, rL [kg m�3] 802�/1190 600�/969

Liquid viscosity, mL�/103 [Pa s] 0.61�/26 0.23�/1.40

Surface tension, sL�/102 [N m�1] 2.2�/7.7 1.1�/2.9

Marangoni effect, dsL/dxvol�/102 [N m�1] 0 �/1.0�/2.7

Liquid diffusion coefficient, DL�/109 [m2 s�1] 0.1�/6.3 1.2�/6.2

Gas density, rG [kg m�3] 0.18�/16.1 0.12�/5.5

Gas viscosity, mG�/105 [Pa s] 1.3�/2.1 0.2�/1.2

Gas diffusion coefficient, DG�/105 [m2 s�1] 0.7�/8.4 0.2�/7.2

HETP [m] 0.09�/1.48

Interfacial area, aw [m2 m�3] 7�/244

Liquid-film coefficient, kLaw�/103 [s�1] 0.81�/83

Gas-film coefficient, kGaw [s�1] 0.95�/15

Global liquid-side coefficient, KLaw�/103 [s�1] 0.23�/82

Global gas-side coefficient, KGaw [s�1] 0.02�/23


tension. The Marangoni effect (dsL/dxvol) wasevaluated using a simple finite difference method

around xvol�/0.5 (i.e. [sL(0.6)�/sL(0.4)]/0.2). For

binary non-aqueous solutions, the index will be

either negative or positive depending on the liquids

to be separated while aqueous solutions does not

create any Marangoni effect (I�/0).

I �1

sL(0:5)

�dsL

dxvol

(0:5)

�(13)

It is conceived here that the ANN-kg correlation

structure requires no adjustment for accurate

prediction of either kG or kL in aqueous andnon-aqueous conditions. Therefore, a decision was

made to use the ANN-kgI input/output structure as

the basis of further improvements. The ANN-kgarchitecture and its general expression are given in

Table 5. It leads to the second modeling step where

pseudo-film mass transfer coefficients (kg) were

calculated for all HETP and mass transfer coeffi-cient measurements using the ANN-kg

I correlation

(Fig. 1b). This in turn allowed the extraction of

pseudo-interfacial areas which were merged with

actually measured interfacial areas and used for

the development of the new ANN-aw correlation

(third step). Both ANN-aw and ANN-kg correla-

tions obtained up to this stage remain initiatory

correlations requiring further optimizationthrough a refined tuning of their weights. A

postulation is made that the inputs intervening in

the initiatory ANN-aw and ANN-kg correlations

still remain the best explicatory inputs after the

ANN weights have been tuned. This implicitly

assumes that the initiatory ANNs accomplished

already a sufficient representational level of the

mass transfer parameters.The fourth step consisted in reconciling between

the six mass transfer characteristics. This was

accomplished through minimization of a cost

function Q (Eq. (14)) which includes the predic-

tion errors on the HETP, interfacial area and all

four volumetric mass transfer coefficients. Simul-

taneous optimization of ANN-aw and ANN-kgweights (vi j,vj) was achieved using Powell’s algo-rithm [40] by minimization of:

Q�X325

i�1

(logaexp� logacal)2

�X361

i�1

(logSh+G;exp� logSh+

G;cal)2

�X1100

i�1

(logSh+L;exp� logSh+

G;cal)2

�X742

i�1

(logShO+G;exp� logShO+

G;cal)2

�X1242

i�1

(logShO+L;exp� logShO+

L;cal)2

�X2357

i�1

(logHETPexp� logHETPcal)2 (14)

For each iterative step during minimization, the

local volumetric mass transfer coefficients (kgaw)

were calculated by multiplying the predictions for

Table 3

Database summary of ANN-awII and ANN-kg

II correlations

effectiveness (in terms of AARE, %) relative to the packing

elements

Packing type

data # (aw�/kgaw�/Kgaw/HETP) aw kgaw Kgaw HETP

Raschig ring (1630/439) 21.7 23.9 33.1 26.5

Pall ring (491/1225) 26.6 16.5 17.1 19.5

Intalox saddle (347/79) 34.8 19.5 26.4 18.3

Berl saddle (358/60) 19.8 33.7 47.7 42.9

Hiflow ring (167/198) 19.1 14.6 16.1

IMTP ring (0/154) 20.0

Tellerette (143/0) 45.6 13.6

Cascade mini-ring (26/87) 19.8 15.2

Nor-Pac (NSW) ring (86/14) 14.1 17.6 24.6

Super Intalox saddle (96/0) 19.1

Hedgehog (95/0) 18.9

Jaeger Hackettes (18/67) 8.2 14.4

Sphere (68/0) 16.0 30.1

Jaeger Top-Pak (42/17) 26.1 31.0 22.4

Nutter ring (22/36) 14.4 16.4

Bundle ring (48/0) 10.0

Spiral tile (18/28) 27.7 56.2

Oblique triangle (30/0) 28.9

VSP ring (0/24) 34.9

Hy-Pak ring (15/0) 25.2

Flat triangle (15/0) 104.0

Glitsch 30Pmk ring (0/14) 17.5

Fleximax (0/10) 16.1

Ralu ring (6/0) 52.3


Table 4

ANN-awII normalized inputs, output, schematic diagram and optimized weights

S.

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/S

epa

ratio

na

nd

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33

(2

00

3)

14

5�

/16

21

53

Table 5

ANN-kgII normalized inputs, output, schematic diagram and optimized weights

S.

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/S

epa

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na

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(2

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54

aw and kg while comparing them with theirexperimental counterparts. Using a similar pro-

cess, overall volumetric mass transfer coefficients

(Kgaw) were calculated and compared in conjunc-

tion with the two-film theory and knowledge of

partition coefficient. HETP was calculated using

Eq. (1). Tables 4 and 5 contain the final optimized

weights for ANN-awII and ANN-kg

II, respectively. A

‘downloadable’ simulator is also made available atthe following web addresses: http://www.gch.ula-

val.ca/grandjea or http://www.gch.ulaval.ca/flara-

chi.

3. Performance analysis

3.1. Statistical evaluation

Statistical comparison between the Piche et al.

ANN correlations [1] developed from absorptionand stripping experiments and the new ANN-aw

II

and ANN-kgII correlations is summarized in Table

6. As mentioned previously, Piche et al. ANN

correlations display rather imprecise results over

the HETP measurements (AARE�/76%) while

keeping good track of the aw, kgaw and Kgaw

experiments (AARE�/9/23%). In contrast, the

new ANN correlations, while predicting goodHETP (AARE�/21%), also offer good results

over the aqueous-type experiments although it is

not as accurate as the Piche et al. correlations

(AARE�/9/27%). Of course, this particular in-

congruity comes from the inherent difficulty of

modeling, in the same framework, two databases

which exhibit very different operating positions.Added to the fact that HETP measurements are

only approximations from the real mass transfer

coefficients, it should be understood that predic-

tion of volumetric mass transfer coefficients for

absorption and stripping with the latter correla-

tion will be less effective. Nonetheless, homogene-

ity of the optimized correlations (ANN-awII, ANN-

kgII) for predicting mass transfer in both aqueous

and non-aqueous environments remains well illu-

strated in Fig. 2. Interfacial area (Fig. 2b) and

local coefficients (Fig. 2c) present good consis-

tency within the 9/2s scope (40% envelopes) while

HETP (Fig. 2a) and overall coefficients (Fig. 2d)

reported as KLaw values (KLaw�/mKGaw) manifest

slightly more scatter which seems logical consider-

ing the fact that the inaccuracy comes from threedifferent sources: aw, kG and kL.

The statistical performance on account of pack-

ing elements (Table 3) exposes the ability of the

new set of equations to predict, generally success-

fully, the HETP (4th column) over a wide range of

packing physical properties. Needless to say,

exceptions will always take place in such empirical

correlation (i.e. Berl saddle, VSP ring) which inthis case does not create much of an issue since

these packings involve a small fraction of the

experimental database.

3.2. Influence of physical properties on predicting

HETP

ANN correlations ability to provide good

phenomenological representations over wide

Table 6

Statistical comparison between the Piche et al. [1] correlation (based on aqueous systems) and the new correlation (based on aqueous

and non-aqueous systems)

No. of data AARE (%) AARE s (%)

Piche et al. This work Piche et al. This work

HETP 2357 75.7 21.3 99.9 18.4

Interfacial area, aw 325 22.5 23.6 16.1 18.1

Liquid-film coefficient, kLaw 1100 22.5 22.1 19.0 19.4

Gas-film coefficient, kGaw 361 21.8 26.9 15.6 18.6

Global coefficients, KLaw and KGaw 1984 26.2 29.4 24.6 33.5

TOTAL 6127 44.1 24.5 51.6 23.5


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ranges of operating conditions can be verified with

the help of a sensitivity analysis on physical

properties. Several ANN-awII, ANN-kL

II and

ANN-kGII simulations combined into HETP that

were performed by ascribing different values for

one studied variable while the others holding

constant, providing thus more insights on the

influence of operating variables on the HETP.

For this study, the corresponding physical proper-

ties of 1 in. metal Cascade mini-ring and equimo-

lar chlorobenzene/ethylbenzene mixture at

atmospheric pressure were used for the simulations

(Figs. 3�/6) unless otherwise stated. Other default

values are: column diameter (0.5 m), bed height (3

m) and liquid mass flow rate (5 kg m�2 s�1) with

total molar reflux. A summary of the following

parametric study findings is presented in Table 7.

3.2.1. Operating conditions

Simulations expressed in Fig. 3a adhere clearlyto the general behaviour of HETP against the

liquid loading rate [41]. At very low flow rates (i.e.

L B/0.5 kg m�2 s�1, Fig. 3a), the packing remains

partially wetted resulting into very low interfacial

area and sky-high HETP. As the liquid load

increases, the wetted packing fraction is progres-

Fig. 2. Parity plots of the ANN correlations (a*/ANN-awII and ANN-kg

II coupled prediction on the HETP; b*/ANN-awII prediction on

the interfacial area database; c*/ANN-awII and ANN-kg

II coupled prediction on the film coefficients (kLaw, kGaw); c*/ANN-awII and

ANN-kgII coupled prediction on the overall coefficients (KLaw)). Dotted lines represent 9/40% envelopes.


sively enhanced until extensive wetting is achieved

(i.e. aw$/aT). A sharp decrease in the HETP is

observed in this region. It is believed that an

additional increase of the flow rate in the pre-

loading zone will continuously decrease the HETP

through enhanced liquid�/vapour mixing until the

loading point is reached (see Fig. 3a, loading point

predicted by Billet and Schultes correlation [42]).

From this point on, the HETP reaches a plateau

all through the loading regime where maximum

separation efficiency is achieved. Packed towers

are usually designed in this region. This high-

efficiency plateau will end next to the flooding

regime which is characterized by instability, en-

trainment and thus poor efficiency. It must be

Fig. 3. Simulations representing the effect of operating vari-

ables on HETP (a*/effect of liquid mass flow rate; b*/effect of

operating pressure). Loading and flooding capacities were

calculated from Billet and Schultes correlation [42].

Fig. 4. Simulations representing the effect of important liquid

and gas physical properties on HETP (a*/effect of gas density;

b*/effect of gas and liquid diffusion coefficients; c*/effect of

liquid viscosity).


emphasized that the current scheme presented in

Fig. 3a can vary from case-to-case, especially in

the pre-loading zone. Several reasons have been

advanced going from liquid maldistribution to the

varying liquid�/vapour mixing intensity within the

packed bed structure [2]. Still, the pre-wetted zone

(high HETP), loading zone (lowest HETP, best

performance) and flooding zone (increasing

HETP) normally follow the characteristic scheme

described above.

Under vacuum conditions, HETP significantly

increases as the pressure decreases (Fig. 3b). This

trend is confirmed for every flow environment

(pre-loading to flooding) even though the overall

consequence seems less important for low flow

inputs. Several explanations could be advanced to

interpret this tendency since the absolute value of

HETP is dependent on the physical properties

which in turn are dependent of the equilibrium

temperature and pressure. It finally comes to a

case-to-case analysis. However, it could be ex-

pected that a decrease of pressure which results in

lower interfacial area [1] is one major reason for

the high HETPs in the vacuum region. Under high

pressure conditions (P�/1�/5 atm), different trends

can be observed for each flow regime. In the pre-

loading zone (i.e. L�/1 kg m�2 s�1, Fig. 3b),

HETP seems to reach a minimum at some critical

pressure where after it starts to slowly increase.

This observation was also confirmed by Yang and

Chuang [3]. Yet, as the flooding point is ap-

proached, a pressure increase neither improve

Fig. 5. Simulations representing the effect of (a) packing type

and (b) column diameter on HETP.Fig. 6. Simulations representing the effect of (a) absolute

surface tension and (b) surface tension gradient on HETP.


nor it reduce mass transfer efficiency in the

column. Again a combination of several factors

could only explain this observation. It should at

least be suspected that for low gas�/liquid flow

rates (i.e. less interfacing gas and liquid fluxes) asubstantial increase of the operating pressure will

not improve the interfacial area potentiality (aw�/

as P �/) as it will rapidly reach a quasi-maximum

while pure mass transfer coefficients will progres-

sively decline (kG¡/ as P �/), thus resulting into an

increasing HETP (kGaw¡/ at high P ), see circle

symbol in Fig. 3b. On the other hand, greater gas�/

liquid flow rates will improve the interfacial areawhich should ultimately push back the critical

pressure where HETP starts to increase.

3.2.2. Physical properties

The influence of vapour density which is closely

related to the operating pressure is shown in Fig.

4a. Two distinct simulation curves are sketched.

The first one (empty circles) describes the pure

hydraulic influence of vapour density on HETP.

Logically, an increase of vapour density results in

a sharp decrease on HETP due to increasinginterfacial area. Yet, an antagonistic factor where

molecule gas diffusivity decreases with density (i.e.

DG¡/ and kG¡/ as mG�/, see dotted line in Fig. 4a)

neutralizes the hydrodynamic improvement of

high vapour density on the overall efficiency.

This is well represented by the second simulation

curve (empty triangles) which combines variation

of vapour density with appropriate values ofvapour diffusion coefficient (Chapman�/Enskog

theory). Note that the right-side vertical axis in

Fig. 4a is oriented downwards. Regarding mole-

cular diffusivity, Fig. 4b illustrates how systems

maintaining high diffusion coefficients achieve

better separation results. This state of affair is

apparent at high vapour diffusion coefficients

(empty circles). The fact that the vapour diffusion

coefficient has more weight on the absolute HETP

in contrast to the liquid diffusion coefficient

implicitly suggests that the mass transfer resistance

for distillation is concentrated in the vapour film.

Liquid viscosity is also considered as a matter of

high interest for distillation. Generally, the mass

transfer efficiency is hampered by high liquid

viscosity which knowingly produces poor inter-

facial area (empty circles, Fig. 4c). Furthermore,

the Stokes�/Einstein dependence that usually pre-

vails between viscosity and diffusivity (see dotted

line, Fig. 4c) suggest a further reduction of the

overall efficiency (high HETP) for high viscosity

systems (empty triangles, Fig. 4c) [35]. Still, the

hydrodynamics effect of liquid viscosity is more

significant on the absolute HETP in contrast to the

mass transfer resistance factor in the liquid film

(see Fig. 4b, empty triangles). Other fluid proper-

ties such as liquid density and vapour viscosity

only slightly influence the HETP and are not

represented here. Yang and Chuang [3] however

made the following observations: a) HETP very

slightly decreases with liquid density, b) HETP

moderately increases with vapour viscosity.

It is widely recognized that packing properties

plays a pre-dominant role in defining the HETP.

Most rule of thumbs analyses are based on the

packing type and size [2]. Norton Chemical

simplified correlations are good examples (Table

1). In this case, the lowest HETP (in the loading

zone) directly depends of the packing nominal size

with some adjustments on account of liquid

viscosity and surface tension. Fig. 5a demonstrates

the validity of these assertions as 1 in. packings

(higher surface area) produce lower HETP than 3

in. packings for example. In such a case, the final

Table 7

Summary of the parametric study (variation of HETP with increment of the parameter)

L rG mL DL DG aT DC sL dsL/dz

Pre-loading regime ¡/¡/¡/ ¡/¡/-�/ �/�/ ¡/ ¡/¡/¡/ ¡/¡/¡/ �/ �/�/ �/�/-¡/¡/

Loading regime ¡/-�/ ¡/

Flooding regime �/�/�/ ¡/

�/*/slightly increases, �/�/*/increases, �/�/�/*/largely increases, ¡/*/slightly decreases, ¡/¡/*/decreases, ¡/¡/¡/*/largely decreases.


decision on the choice of a packing (i.e. 1 in. CMRvs 1 in. Pall ring) resides on the hydrodynamic

efficiency (i.e. flooding capacity, pressure drop).

Column diameter plays a rather limited role on the

tower’s efficiency. As shown in Fig. 5b, the HETP

barely decreases for small columns (respectively

higher effective packing surface area, aT ?�/aT�/4/

DC).

3.2.3. Surface tension and the Marangoni effect

The significance of the absolute surface tension

on the HETP, although contained in several

correlations remains minor for the normal area

of operation (i.e. loading regime). As shown in

Fig. 6a, an increase of the surface tension causing

the liquid to contract itself only slightly reduces

the interfacial area (HETP�/ as sL�/) at high liquid

flow rates. In this state of operation, tricklingliquid film conditions is quasi-inexistent which

obviously lessens the influence of surface tension.

On the other hand, the liquid film dependence on

such an interface-sensitive constituent is more

significant at lower flow rates (i.e. L�/1

kg m�2 s�1, Fig. 6a). For this instance, the

simulated HETP increases by approximately 10

cm between 15 and 30 dynes cm�1 while it onlyincreases by 4�/5 cm for the higher simulated flow

rates.

Surface tension is also known to vary from top

to bottom of the column due to the ever changing

mixture composition. This in turn induces a

Marangoni effect (dsL/dz) which is known to

influence the interfacial area [42,43]. Systems

with increasing surface tension along the liquidflow path (i.e., downwards) are referred to as

positive systems (dsL/dz �/0) whereas, for negative

systems, surface tension decreases (dsL/dz B/0)

liquid streamwise. With supporting test results,

Billet and Schultes [6] observed a reduction of the

interfacial area for negative systems whereas the

Marangoni effect becomes minor for neutral and

positive systems. These observations were trans-posed into their interfacial area equation (see Eq.

(9) in Table 1). Equilibrium between the surface

tension gradient shear stress and liquid film shear

stress is their main reason to explain this beha-

viour. If the surface tension decreases across the

flow path, the liquid film becomes unstable and

tends to break up thus reducing the interfacial

area. While agreeing with these terms, Xu et al.

[43] still considered that positive systems should

reinforce the liquid film and increase the interfacial

area, an aspect that was not taken into considera-

tion by Billet and Schultes. Yet these explanations

do not totally sit with the simulations expressed in

Fig. 6b. This is especially the case for the pre-

loading zone.

A possible explanation could reside on the

combination of two antagonist sub-factors from

the Marangoni behaviour: (a) film stability effect

and (b) film recession/spread effect. The latter

notion rests on the fact that a reduction of surface

Fig. 7. Schematic diagram representing the possible influence

of Marangoni sub-factors (film stability and expansion effects)

on the interfacial area.


tension should result, at some extent, into spreadof the liquid film, and thus an increase of the

interfacial area. This being said, the liquid film

spread is expected to be more influential at lower

liquid flow rates, where the liquid film structure is

pre-dominant. This is illustrated in Fig. 7 where

the relative consequence of the film spread effect

on interfacial area (aw�/ as dsL/dz ¡/ by film

spreading) is considered linear for simplification.As for the film stability factor, it could be expected

to follow a trend similar to the one alleged by

Billet and Schultes and Xu et al. Negative systems,

being more prone to film instability, would exhibit

decreasing interfacial areas (aw¡/ as dsL/dz ¡/) at

varying degree (Fig. 7). Here again, the film

stability factor is expected to be lessened as the

liquid flow rate increases. The summation of bothMarangoni sub-factors presents different out-

comes depending of the flow regime. In the pre-

loading zone, the interfacial area is shown to

follow a parabolic-like trend with respect to dsL/

dz (Fig. 7a) whereas the film spreading factor can

be lumped into the film stability factor for higher

flow rates (Fig. 7b). Knowing that HETP8/1/aw,

the tendencies exposed in Fig. 7a and b come inagreement with the simulations presented in Fig.

6b. However, keep in mind that Fig. 7 is only a

schematic diagram and do not represent real

values.

4. Conclusion

A set of ANN correlations for the gas�/liquidinterfacial area and the pure local mass transfer

coefficients was proposed for predicting HETP in

distillation packed towers. The modeling approach

revolved around the use of a reconciliation proce-

dure which combines measured interfacial areas

with pseudo-interfacial areas intuited from the

actually measured HETP and volumetric mass

transfer coefficients. As a matter of fact, the useof non-aqueous and aqueous mass transfer results

from the open literature has strengthened the mass

transfer phenomenology in packed towers whether

absorption, stripping or distillation is considered.

Although this set of ANN correlations presents

good statistical results over aqueous systems, it

would yet be recommended to use the previousANN correlations published elsewhere [1] for

stripping and absorption process design or analy-

sis. It is more precise, more robust and does not

include the obvious modeling pitfalls from mixing

precise aqueous mass transfer coefficients with

approximate HETP values.

Acknowledgements

Financial support from the Natural Sciences

and Engineering Research Council of Canada

(NSERC) and the Fonds Quebecois de la Re-

cherche sur la Nature et les Technologies is grate-

fully acknowledged. We also express our

appreciation to Andre Normandin from Mesar-Environnair for helpful discussions and the tech-

nical literature he made available to us.

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