CFD modelling of gas-sparged ultraﬁltration in tubalr membranes

8/4/2019 CFD modelling of gas-sparged ultrafiltration in tubalr membranes

1/15

Journal of Membrane Science 210 (2002) 1327

CFD modelling of gas-sparged ultrafiltrationin tubular membranes

Taha Taha, Z.F. Cui

Department of Engineering Science, Oxford University, Parks Road, Oxford OX1 3PJ, UK

Received 16 August 2001; received in revised form 15 July 2002; accepted 22 July 2002

Abstract

In ultrafiltration processes, injecting gas to create a gasliquid two-phase crossflow operation can significantly increase

permeate flux and, moreover, can improve the membrane rejection characteristics. It has been shown that controlled pulse

injection to generate slug flow is more advantageous than uncontrolled gas sparging, especially when the gas flow rate is

low. The slug size and frequency affect the performance of ultrafiltration, and there exits an optimal slug size and frequency

to achieve high permeate flux. Previous studies have been based on the analysis of the experimental data and mass-transfer

correlations. In this work, an attempt is made to model the slug flow ultrafiltration process using the volume of fluid (VOF)

method with the aim of understanding and quantifying the details of the permeate flux enhancement resulting from gas

sparging. For this numerical study, the commercial CFD package, FLUENT, is used. The first part of the model uses the

VOF method to calculate the shape and velocity of the slug, the velocity distribution and the distribution of local wall shear

stress in the membrane tube (neglecting the wall permeation effect). The second part links the local wall shear stress to the

local mass-transfer coefficient that is then used to predict the permeate flux. In order to validate the model, experimental data

reported in the literature over a wide range of gas and liquid velocities, slug frequencies, and transmembrane pressures are

compared with the CFD predictions. Good agreement is obtained between theory and experiment.

2002 Elsevier Science B.V. All rights reserved.

Keywords: Ultrafiltration; Gas sparging; Enhancement; CFD; Hydrodynamics

1. Introduction

Ultrafiltration has become an established unit op-

eration with a great potential in various applicationsin the dairy, water, chemical and pharmaceutical in-

dustries. However, its practical use has been limited

by the high process cost, including both capital and

operational costs. A relatively high energy cost is

associated with the high crossflow velocities that are

necessary to control concentration polarisation and

Corresponding author. Tel.: +44-1865-273-118/017;

fax: +44-1865-283-273.

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

membrane fouling, thereby maintaining an acceptably

high permeate flux. The need for frequent cleaning

with chemicals and detergents also contributes signifi-

cantly to the operational cost of membrane processes.Gas sparging, i.e. injecting air bubbles into the liquid

feed to generate a two-phase flow stream, has proved

to be an effective, simple and low-cost technique for

enhancing ultrafiltration processes [1,2].

Gas and liquid flowing together in a pipe distribute

in an annular flow pattern when gas rate is high. At

low gas rates in vertical flow, the pattern observed

is bubbly. Over a wide range of flow rates between

these two limits, the slug flow pattern exists. Such flow

pattern is characterised by a quasi-periodic passage

0376-7388/02/$ see front matter 2002 Elsevier Science B.V. All rights reserved.

P I I : S 0 3 7 6 - 7 3 8 8 ( 0 2 ) 0 0 3 6 0 - 5


2/15

14 T. Taha, Z.F. Cui / Journal of Membrane Science 210 (2002) 1327

Nomenclature

C concentration of solute (kg/m3)

Cb bulk concentration of solute (kg/m3)Cw wall concentration of solute (kg/m

3)d diameter of the tubular membrane (m)dh equivalent hydraulic diameter (m)

D diffusion coefficient (m2/s)F external body forces (N)

g acceleration due to gravity (m/s2)

Jv permeate flux (kg/(m2 h))

k mass-transfer coefficient (m/s)L length of the tubular membrane (m)n normal vector to the bubble surface

p static pressure (Pa)ps surface tension induced pressure

difference (Pa)

P transmembrane pressure (Pa)

QL liquid flow rate (l/min)

QG gas flow rate (l/min)

Rc cake resistance (Pa s/m)Rm membrane resistance (Pa s/m)Re Reynolds numbert time (s)Uinlet inlet velocity (m/s)

UL liquid velocity (m/s)

UTB Taylor bubble velocity (m/s)

Uwall wall velocity (m/s)

v velocity vector (m/s)

x axial tube coordinate (m)y perpendicular tube coordinate (m)

Greek letters

G volume fraction of the gas phase

in the computational cell

L volume fraction of the liquid phase

in the computational cell

osmotic pressure difference (Pa) shear rate (l/s) free surface curvature molecular viscosity (kg/(m s))

G gas density (kg/m3)

L liquid density (kg/m3)

surface tension (N/m)

of long round-nosed bubblesusually referred to as

Taylor bubbles or slugsseparated by liquid plugs.

Slug flow, which has proved advantageous over

bubbly flow in enhancing membrane filtration [3], canbe achieved even at low gas flow rates by injecting

the gas in a controlled manner with a timer and a

solenoid valve in order to give the desired slug size

and frequency. In particular, for ultrafiltration, it was

found, firstly, that the gas flow rate required to effect

substantial improvements in permeate flux is very

small. Secondly, that the liquid crossflow velocity has

little effect on the permeate flux in gas-sparged ul-

trafiltration. The combination of these two particular

aspects of this technique provides the possibility of a

significant saving on energy costs [1,2].

Yet, published literature in this field so far has

mainly dealt with performance assessment of exper-

imental methods. Suggestions for flux enhancement

have failed to be quantitative and, at times, have been

merely speculative. Ghosh and Cui [4] used approxi-

mated hydrodynamic models [5,6] to calculate the

average velocities in the film and the wake regions.

Adopting the Dittus and Boelter correlation [7], they

calculated the mass-transfer coefficient from the veloc-

ity values to predict the permeate flux. Otherwise, sev-

eral mechanisms involved in flux enhancement have

been identified and qualitatively described. For tubularmembranes, it was postulated that the two-phase flow

generated complex hydrodynamic conditions inside

the filtration module that limited the accumulation

of particles or molecules by creating local velocity

and pressure fluctuations related to intermittence [8].

Cui and Wright [1,2] speculated that the mixing zone

in the bubble wake induced secondary flows that are

responsible for enhancing the permeate flux. Bellara

et al. [9] hypothesised that physical displacement

of the mass-transfer boundary layer is responsible

for the enhancement in the hollow fibre membranesystems. High shear stresses were thought to be the

main reasons for the observed flux improvement

[3].

In order to optimise the process efficiency, it is

essential to understand and quantify the details of

slug flow dynamics and to identify their effect on

ultrafiltration performance. In this paper, an attempt

is made to explain permeate flux enhancement due

to gas sparging by examining the hydrodynamics

of gasliquid two-phase flow and the increase in


3/15

T. Taha, Z.F. Cui / Journal of Membrane Science 210 (2002) 1327 15

mass-transfer, in the special case of upward slug flow

in a tubular membrane module. All the published

numerical methods to model slug flow in vertical

tube assume either the shape of the bubble or a func-tional form for the shape [10,11]. These assumptions

constrain the nature of the solution while the ap-

proach adopted here (VOF method) lays no such a

priori foundations. The solution domain in the present

model not only includes the field around the bubble,

as in the study of Mao and Duckler [12], but also

extends behind the bubble, allowing field information

to be obtained in the wake region.

2. Formulation of the problem and the

solution strategy

The first part of the proposed model uses the VOF

method to calculate the Taylor bubble shape and ve-

locity, the velocity and the pressure fields and the

wall shear rate around the slug unit in a vertical

closed-wall pipe. The second part uses a polarisation

and osmotic model to predict the permeate flux using

the output data from the first part, namely the wall

shear rate, to evaluate the mass-transfer coefficient

with a standard correlation [13]. Wang et al. [14]

proved that the existence of realistic wall fluxes doesnot alter the bulk flow fields. This justifies the use of

the previous consecutive steps.

The CFD software FLUENT (Release 5.4.8, 1998)

was used to simulate the motion of a single Taylor

bubble rising in a flowing liquid through a tube of

a circular cross-section. In FLUENT, the control

volume methodsometimes referred to as the finite

volume methodis used to discretize the transport

equations. The movement of the gasliquid interface

is tracked based on the distribution of G, the volume

fraction of gas in a computational cell, where G = 0in the liquid phase and G = 1 in the gas phase [15].Therefore, the gasliquid interface exists in the cell

where G lies between 0 and 1. The geometric re-

construction scheme that is based on the piece linear

interface calculation (PLIC) method [16] is applied to

reconstruct the bubble-free surface. The surface ten-

sion is approximated by the continuum surface force

model of Brackbill et al. [17]. Turbulence is intro-

duced by the Renormalization Group based k-epsilon

zonal model.

2.1. Governing equations

2.1.1. The continuity equation

t

() + ( v) = 0 (1)

2.1.2. The momentum equation

A single momentum equation is solved throughout

the domain, and the resulting velocity field is shared

among the phases. The momentum equation, shown

later, is dependent on the volume fractions of all phases

through the properties and .

t( v) + ( v v)

= p + [( v + vT

)] + g + F (2)

2.1.3. The volume fraction equation

The tracking of the interface between the gas and

liquid is accomplished by the solution of a continuity

equation for the volume fraction of gas [15].

t(G) + v G = 0 (3)

The volume fraction equation will not be solved for

the liquid; the liquid volume fraction will be computed

based on the following constraint:

G + L = 1 (4)

2.1.4. Surface tension

The surface tension model in FLUENT is the

continuum surface force (CSF) model proposed by

Brackbill et al. [17]. With this model, the addition

of surface tension to the VOF calculation results in

a source term in the momentum equation. In the

gasliquid free surfaces, the stress boundary condition

follows the LaplaceYoung equation as

ps = (5)

where ps is the surface tension induced pressure

difference, the surface tension, and is the free

surface curvature defined in terms of the divergence

of the unit normal, n as [17]

= n =1

|n|

n

|n|

|n| ( n)

(6)

where

n =n

|n|, n = G (7)


4/15


2.2. Differencing schemes

The solution of the momentum equation is ap-

proximated by the second order up-wind differencingscheme in order to minimise numerical diffusion.

The pressure-implicit with splitting of operators

(PISO) pressurevelocity coupling scheme, part of

the SIMPLE family of algorithms, is used for the

pressurevelocity coupling scheme [18]. Using PISO

allows for a rapid rate of convergence without any

significant loss of accuracy. As large body forces

(namely, gravity and surface tension forces) exist in

multiphase flows, the body force and pressure gra-

dient terms in the momentum equation are almost

in equilibrium, with the contributions of convective

and viscous terms small in comparison. Segregated

algorithms converge poorly unless partial equilibrium

of pressure gradient and body forces is taken into ac-

count. FLUENT provides an optional implicit body

force treatment that can account for this effect, mak-

ing the solution more robust [19]. Eq. (3) is solved

using an explicit time-marching scheme and the maxi-

mum allowed Courant number is set to 0.25. A typical

value of 103 was used as the time step. A total time

run of 1.0 s was used for each run of the simulations.

2.3. Phyiscal properties

The properties of liquid or gas are used in the

transport equations when the computational cell is in

the liquid or the gas phase, respectively. When it is

in the interface between the gas and liquid phases,

the mixture properties of the gas and liquid phases on

the volume fraction weighted average are used. If the

volume fraction of the gas being tracked, the density

and viscosity in each cell are given by

= GG + (1 G)L (8)

= GG + (1 G)L (9)

2.4. Interface tracking

To overcome the problem of diffusion which most

standard differencing schemes suffer, the geometric

reconstruction scheme is used [16]. It assumes that the

interface between two fluids has a linear slope within

each cell, and uses this linear shape for calculation of

the advection of fluid through the cell faces.

The first step in this reconstruction scheme is

calculating the position of the linear interface rela-

tive to the centre of each partially filled cell, based

on information about the volume fraction and itsderivatives in the cell. The second step is calculating

the adverting amount of fluid through each face us-

ing the computed linear interface representation and

information about the normal and tangential velocity

distribution on the face. The third step is calculating

the volume fraction in each cell using the balance of

fluxes calculated during the previous step [19].

2.5. Model geometry

A two-dimensional coordinate system assuming ax-

ial symmetry about the centreline of the pipe was used.The grid used to generate the numerical results was

uniform and contained 26 280 quadrilateral controlvolume. Thus, the length of the domain is 11d, where

d is the pipe diameter. The grid was refined until the

shape and terminal velocity of the bubble no longer

varied with additional grid refinement. The grid was

refined near to the wall with the intention of resolving

the laminar sublayer. The simulation was initialised

with an arbitrarily shaped bubble and allowed to run

until a steady bubble shape was established.

In Fig. 1, the boundary conditions used in the sim-ulation are displayed. The no-slip wall condition is

applied to the walls. The fluid mass flux at the inlet

is specified using a profile for a fully developed flow

through a pipe. The previous equations are solved for

a domain surrounding a Taylor bubble in a frame of

reference attached to the rising Taylor bubble (Fig. 1).

With these coordinates, the bubble becomes stationary

and the pipe wall moves with a velocity Uwall, equal

to that of the Taylor bubble rise velocity, UTB. The

liquid is fed at the inlet with a velocity Uinlet, which

is equal to UTB

UL

.

2.6. Permeate flux evaluation

In this work, the local shear stress was evaluated

by the CFD simulation and its absolute value was

averaged over the length of the membrane module.

The average mass-transfer coefficient can then be

estimated as follows:

k = 1.62

d D

dhL

0.33(10)


5/15


Fig. 1. Taylor bubble rising in a vertical pipe in a moving coor-

dinate.

It should be pointed out that the previous equation

was developed under steady shear rates [14]. In this

calculation, the absolute values of the wall share rate

are averaged over the length of the membrane. The

transient behaviour of the wall shear rate is to be consi-

dered in our future investigation. For the special case

of total solute rejection, the permeate flux is calculated

by using the concentration polarisation equation for to-

tal rejection, together with the osmotic pressure model:

Jv = k ln

Cw

Cb

(11)

Jv =(P )

(Rm + Rc)(12)

The previous correlations are based on steady-state

ultrafiltration. Rc is significant only when gel layerformation takes place. In ultrafiltration of a macro-

molecule such as dextran, the value of Rc is expected

to be negligible in comparison to Rm and hence may

be neglected. The experimental results reported by Li

et al. [20] and Sur et al. [21] are simulated here in

order to test the proposed model. They used dextran

167 and 283 kDa, respectively. The osmotic pres-

sure for dextran is calculated using the correlations

[22]

log (150 kDa) = 0.248 + 0.2731C0.35 (13)

log (283 kDa) = 0.1872 + 3.343C0.3048 (14)

3. Results and discussion

3.1. Hydrodynamics and mass-transfer

In vertical pipes, Taylor bubbles are axisymmetric

and have round noses, while the tail is generally as-

sumed to be nearly flat (Fig. 2). The Taylor bubble

occupies most of the cross-sectional area of the tube.When the bubble rises through a moving liquid, the

liquid that is flowing ahead of the nose of the bubble is

picked up and displaced as a liquid filmit begins to

flow downwards in the annular space between the tube

wall and the bubble surface. Alongside the bubble,

the liquid film accelerates until it reaches its terminal

velocity under the condition of a long enough bubble.

At the rear of that bubble the liquid film plunges into

the liquid plug behind the bubble as a circular wall

jet and produces a highly agitated mixing zone in the

bubble wake. This mixing zone is generally believedto have the shape of a toroidal vortex [23]. This wake

region is believed to be responsible for mass- and

heat-transfer enhancement.

Fig. 3 shows the wall shear stress around a slug unit

(Taylor bubble + liquid plug) together with the liquidfilm thickness. The wall shear stress sign changes

twice in a slug unit. The first change takes place near

the nose of the Taylor bubble and the second near

the top of the liquid plug. The negative shear stress,

indicating upflow, exists over the liquid plug ahead of


6/15


Fig. 2. Calculated velocity field around a Taylor bubble with

a frame of reference moving with the bubble: membrane

length = 1.18m; D = 12.7 mm; dextranair system; Cb = 10 g/l;

QL = 1.0 l/min; Vb = 8.3 ml; TMP = 1.0 bar.

the bubble and persists beyond the nose of the Taylor

bubble, before becoming positive as the downflow is

established in the liquid film around the bubble. The

inverse transition from the downward film to an up-ward one in the liquid plug is of a burst-like type. The

brief fluctuations of the wall shear stress in the film

region correspond to the wavy nature of the bubble

surface. Near the slug tail, the wall shear stress starts

to fluctuate. The previous features were observed ex-

perimentally [24]. The predicted permeate flux of the

earlier case study was found to be 13.31 kg/(m2 h)

comparing to 14.47 kg/(m2 h), the value reported in

literature with 8.0% error.

3.2. Effect of TMP

The variation of permeate flux with the transmem-

brane pressure (TMP) is shown in Fig. 4. Experiments

were performed for ultrafiltration of industrial grade

dextran having average molecular weight of 283 kDa

using a tubular PVDF membrane having a molecu-

lar cut-off of 100 kDa [21]. The length of the tubular

membrane was 1.18 m and the diameter was 12.7 mm.

The slug frequency was controlled using a solenoid

valve and set to 1.0 Hz. It can be seen that at a fixed

liquid flow rate the permeate flux increases with TMP.

The CFD predicted values clearly capture the sametrend. The predicted values underestimate the exper-

imental ones due to the fact that the model does not

consider the transient nature of the shear stress.

3.3. Effect of liquid flow rate

The response of the permeate flux to increasing

liquid velocity, observed experimentally [21] and

calculated theoretically is shown in Figs. 5 and 6,

respectively. The permeate flux decreases with an in-

creased liquid flow rate from 1.5 l/min (Re = 2494) to4.0 l/min (Re = 6651) but increases when the liquidflow rates increases to 6 l/min (Re = 9978). This be-haviour is repeated for all the TMP values examined.

The theoretically calculated values follow the same

trend with reasonable accuracy. Cui and Wright [1]

also observed the same trend experimentally when

using uncontrolled gas sparging. Explanations to this

phenomenon can be found in a closer examination

of the hydrodynamics of a rising slug in a flowing

liquid.


7/15


Fig. 3. Wall shear stress distribution around a slug unit and the liquid film thickness: membrane length = 1.18m; D = 12.7 mm; dextranair

system; Cb = 10 g/l dextran (100 kDa MW); QL = 1.0 l/min; Vb = 8.3 ml; TMP = 1.0 bar.

Fig. 4. Effect of TMP on permeate flux: membrane length = 1.18m; D = 12.7 mm; dextranair system; Cb = 10 g/l dextran (283 kDa

MW); QL = 0.6 l/min; QG = 0.6 l/min; slug frequency = 1.0 l/s.


8/15


Fig. 5. Effect of liquid flow rate on permeate flux [21]: membrane length = 1.18m; D = 12.7 mm; dextranair system; Cb = 10 g/l dextran

(283 kDa MW); QG = 0.6 l/min; slug frequency = 1.0 l/s.

Fig. 6. Effect of liquid flow rate on permeate flux (Theory): membrane length = 1.18m; D = 12.7 mm; dextranair system; Cb = 10g/l

dextran (283 kDa MW); QG = 0.6 l/min; slug frequency = 1.0 l/s.


9/15


Fig. 7. Wall shear stress distribution around a slug unit: (1) QL = 1.5 l/min; (2) QL = 4.0 l/min; (3) QL = 6.0 l/min; membrane

length = 1.18m; D = 12.7 mm; dextranair system; Cb = 10 g/l dextran (283 kDa MW); QG = 0.6 l/min; slug frequency = 1.0 l/s;

TMP = 1.0 bar.

Figs. 7 and 8 illustrate the calculated wall shear

stress around a slug unit and the liquid film axial

velocity around the gas slug respectively for threedifferent liquid rates. The character of the wall shear

stress distribution is similar for all cases. The wall

shear stress rapidly decreases to zero and attains the

maximum positive value near the slug bottom (Fig. 7).

In the liquid plug, the wall shear stress recovers. As

the liquid flow increases, the portion of downward

flow becomes shorter (Fig. 8). The previous trend was

also reported in the literature [24].

Fig. 9 shows the calculated mass-transfer coeffi-

cient for three different mass-transfer zones: the film

region, surrounding the bubble; the wake zone, ahighly agitated region behind the bubble tail; and the

liquid plug zone, the region separating two bubbles.

In the film zone, increasing the liquid flow rate causes

a decrease in the mass-transfer coefficient which is

attributed to the decrease in the average shear rate.

The mass-transfer coefficient in the wake region show

the same response of the permeate flux (Fig. 5). In-

tuitively, since the film velocity just before plunging

into the liquid behind the bubble actually decreases

by increasing the flow rate (Fig. 8), one expects the

mass-transfer coefficient in the wake region to increase

with the liquid flow rate. Fig. 10 shows the turbulence

intensity in the wake, defined as ratio of the magni-tude of the rms of turbulent fluctuations to the mean

velocity. The contribution from the turbulent intensity

in the wake region is more significant for higher liquid

flow rates. It can be deduced that the turbulent inten-

sity in the wake depends on the relative velocities of

the circular jet of liquid film and the flowing liquid

behind the bubble [20]. As far as the optimisation of

gas-sparged ultrafiltration processes is concerned, one

should consider the contribution from the three distinct

zones of the slug unit in permeate flux enhancement.

3.4. Effect of the gas flow rate and slug frequency

Li et al. [20] used a solenoid valve to generate

slug flow with defined frequency and bubble size.

They carried out their experiments for ultrafiltration

of industrial grade dextran having average molecular

weight of 167 kDa using a tubular PVDF membrane

having a molecular cut-off of 100 kDa. The length of

the tubular membrane was 1.18 m and the diameter

was 12.7 mm. Their experimental results are modelled


10/15


Fig. 8. Axial liquid film velocity: (1) QL = 1.5 l/min; (2) QL = 4.0 l/min; (3) QL = 6.0 l/min; membrane length = 1.18m; D = 12.7mm;

dextranair system; Cb = 10 g/l dextran (283 kDa MW); QG = 0.6 l/min; slug frequency = 1.0 l/s; TMP = 1.0 bar.

here. Fig. 11 illustrates the bubble shapes calculated

for the parameters in their experiments. It can be

seen that the shape of the nose of the bubble does

not change with a change in the bubble length which

Fig. 9. Mass-transfer coefficient in the different zone: membrane length = 1.18m; D = 12.7 mm; dextranair system; Cb = 10 g/l dextran

(283 kDa MW); QG = 0.6 l/min; slug frequency = 1.0 l/s; TMP = 1.0 bar.

agrees with observations in the literature [2528].

The bubble interface becomes wavy in nature near to

the tail when the bubble is long. This phenomenon

was observed by Nakoryacov et al. [24].


11/15


Fig. 10. Turbulence intensity: (1) QL = 1.5 l/min; (2) QL = 4.0 l/min; (3) QL = 6.0 l/min; membrane length = 1.18m; D = 12.7mm;

dextranair system; Cb = 10 g/l dextran (283 kDa MW); QG = 0.6 l/min; TMP = 1.0 bar.

The calculated wall shear stress is presented in

Fig. 12. There is a smooth transition from the upward

to the downward flow, occurring in the film zone.

The reverse transition, however, from the downward

to the upward flow is rather sudden. For the longer

bubble, fluctuations in the wall shear stress near to

Fig. 11. Liquid film thickness: () QG = 0.66 l/min; () QG = 1.0 l/min; (+) QG = 1.5 l/min; () QG = 2.5 l/min; QL = 1.0 l/min;

membrane length = 1.18m; D = 12.7 mm; dextranair system; Cb = 10 g/l dextran (100 kDa MW); TMP = 1.0 bar.

the bubble tailcorresponding to the wavy bubble

surface (Fig. 11)and in the wake can be clearly

seen in Fig. 12.

Fig. 13 shows experimental and theoretically cal-

culated values for permeate flux as a function of gas

flow rate for a fixed sparging frequency. The response


12/15


Fig. 12. Wall shear stress distribution around a slug unit: (1) QG = 66.7 ml/min; (2) QG = 100ml/min; (3) QG = 150 ml/min;

4-QG = 250 ml/min; QL = 1.0 l/min; membrane length = 1.18m; D = 12.7 mm; dextranair system; Cb = 10 g/l dextran (100 kDa MW);

TMP = 1.0 bar.

Fig. 13. Effect of gas flow rate on permeate flux: membrane length = 1.18m; D = 12.7 mm; dextranair system; Cb = 10 g/l dextran

(100 kDa MW); QL = 1.0 l/min; slug frequency = 0.5 l/s; TMP = 1.0 bar.


13/15


Fig. 14. Effect of slug frequency on permeate flux: membrane length = 1.18m; D = 12.7 mm; dextranair system; Cb = 10 g/l dextran

(100 kDa MW); QL = 1.0 l/min; Vb = 8.3 ml; TMP = 1.0 bar.

of the increase in the permeate flux, which is its re-

sponse to an increase in sparging frequency with a

fixed gas flow rate, is shown in Fig. 14. The calcu-

lated values by Ghosh and Cui [4] are also included.

Fig. 15. Parity plot of permeate flux.

A good agreement between the experimental and pre-

dicted data is obtained. As has been already noted,

the model generally underestimates the experimental

values. The experimental results obtained by Sur et al.


14/15


Table 1

Measured permeate flux (Jv, kg/(m2 h)) data [21]

QL (l/min) TMP (bar)

0.5 1.0 1.5 2.0

1.5 10.17 11.51 13.33 13.91

2.0 9.93 11.14 12.23 13.04

3.0 8.90 11.16 11.62 12.10

4.0 9.62 11.31 12.23 13.12

6.0 12.23 14.71 16.42 17.35

Gas flow rate: 0.6 l/min; dextranair system, Cb = 10 g/l (283 kDa

MW); slug frequency: 1.0 l/s.

[21] and modelled in this work are summarised in

Table 1. Fig. 15 shows a parity plot of the permeate

flux measured by Li et al. [20] and Sur et al. [21] andthe calculated permeate flux. The agreement between

experiment and theory is quite encouraging and the

model may be improved by considering the transient

behaviour of the wall shear stress.

4. Conclusion

The CFD software FLUENT with the method of

volume of fluid (VOF) was adopted to model the mo-

tion of a Taylor bubble rising in a flowing liquid insidea tubular membrane module. The shape of the Taylor

bubble can be predicted by the VOF method with rea-

sonable accuracy. The shear stress behaviour in a slug

unit was calculated and agreed qualitatively with the

published experimental findings.

The permeate flux enhancement due to gas-sparged

ultrafiltration with tubular membranes can be pre-

dicted with reasonable accuracy. The agreement be-

tween the values calculated by the previous model and

experimental data reported in literature is quite en-

couraging. The enhancement can be explained by theincrease in the mass-transfer coefficient. The turbu-

lence just behind the air bubble, caused by the annular

film flowing downward, is of significant intensity; and

it plays a pivotal role in permeate flux enhancement in

tubular membranes. Contribution from the film region

and the liquid plug region has also been discussed.

Based on the present model, guidance for the design,

operation, and control of gas-sparged ultrafiltration

can be prepared for achieving optimal design, as well

as safe and economical operation.

Acknowledgements

T. Taha is grateful to the Karim Rida Said Founda-

tion for financial support.

References

[1] Z.F. Cui, K.I.T. Wright, Gasliquid two-phase crossflow

ultrafiltration of BSA and dextran solutions, J. Membr. Sci.

90 (1994) 183.

[2] Z.F. Cui, K.I.T. Wright, Flux enhancements with gas sparging

in downwards crossflow ultrafiltration: performance and

mechanism, J. Membr. Sci. 117 (1996) 109.

[3] C. Cabassud, S. Laborie, J.M. Lain, How slug flow can

enhance the ultrafiltration flux in organic hollow fibres, J.

Membr. Sci. 128 (1997) 93.[4] R. Ghosh, Z.F. Cui, Mass-transfer in gas-sparged ultrafil-

tration: upward slug flow in tubular membranes, J. Membr.

Sci. 162 (1999) 91.

[5] G.B. Wallis, One-dimensional Two-phase Flow, McGraw-Hill,

New York, 1969.

[6] Y. Taitel, D. Barnea, A.E. Duckler, Modelling flow pattern

transition for steady upward gasliquid flow in vertical tubes,

AICHE J. 26 (1980) 345.

[7] F.W Dittus, L.M. Boelter, Publication in Engineering, vol. 2,

University of California, Berkeley, 1930, p. 443.

[8] M. Mercier, C. Maranges, C. Fonade, C. Lafforgue-Delorme,

Flux enhancement using an upward gas/liquid slug flow

application to continuous alcoholic fermentation with cellrecycle, Biotechnol. Bioeng. 58 (1998) 47.

[9] S.R. Bellara, Z.F. Cui, D.S. Pepper, Gas sparging to enhance

permeate flux in ultrafiltration using hollow fibre membranes,

J. Membr. Sci. 121 (1996) 175.

[10] D.T. Dumitrescu, Stromung an einer Luftblase im senkrechten

Rohr, Z. Angew. Math. Mech. 23 (1943) 139.

[11] R.M. Davies, G.I. Taylor, The mechanics of large bubbles

rising through extended liquids and through liquid in tubes,

Proc. R. Soc. London Ser. A 200 (1949) 375.

[12] Z.-S. Mao, A.E. Duckler, The motion of Taylor bubbles in

vertical tubes I. A numerical simulation for the shape and

the rise velocity of Taylor bubbles in stagnant and flowing

liquids, J. Computat. Phys. 91 (1990) 132.

[13] M.C. Porter, Concentration polarisation with membrane

ultrafiltration, Ind. Eng. Prod. Res. Dev. 11 (1972) 234.

[14] Y. Wang, J.A. Howell, R.W. Field, D. Wu, Simulation of

crossflow filtration for baffled tubular channels and pulsatile

flow, J. Membr. Sci. 95 (1994) 243.

[15] C.W. Hirt, B.D. Nichols, Volume of fluid (VOF) method

for the dynamics of free boundaries, J. Computat. Phys. 39

(1981) 201.

[16] L. Young, Time-dependent multi-material flow with large fluid

distortion, in: K.W. Morton, M.J. Baibnes (Eds.), Numerical

Methods for Fluid Dynamics, Academic Press, New York,

1982.


15/15


[17] J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method

for modeling surface tension, J. Computat. Phys. 100 (1992)

335.

[18] R.I. Issa, Solution of implicity discretized fluid flow equations

by operator splitting, J. Computat. Phys. 62 (1986) 40.[19] FLUENT/UNS Users guide, Fluent Incorporated, Lebanon,

New Hampshire, 1998.

[20] Q.Y. Li, Z.F. Cui, D.S. Pepper, Effect of bubble size and

frequency on the permeate flux of gas-sparged ultrafiltration

with tubular membranes, J. Membr. Sci. 67 (1997) 71.

[21] H.W. Sur, Q. Li, Z.F. Cui, Gas sparging to enhance crossflow

ultrafiltration in tubular flow, IChemE Research Event,

1998.

[22] Osmotic Stress website: http://mecko.nichd.nih.gov/Lpsb/

docs/OsmoticStress.html.

[23] J.B.L.M. Campos, J.R.F. Gueded de Carvalho, An experi-

mental study of the wake of gas slugs rising in liquids, J.

Fluid Mech. 196 (1988) 27.

[24] V.E. Nakoryacov, A.V. Kashinsky, R.S. Petukhov, R.S.

Gorelik, Study of local hydrodynamic characteristics ofupward slug flow, Exp. Fluids 7 (1989) 560.

[25] D.J. Nicklin, J.O. Wilkes, J.F. Davidson, Two-phase flow in

vertical tubes, Trans. Inst. Chem. Engs. 40 (1962) 61.

[26] W. Ahmad, J.M. DeJesus, M. Kawaji, Falling film hydro-

dynamics in slug flow, Chem. Eng. Sci. 53 (1998) 123.

[27] Z.-S. Mao, A. Duckler, An experimental study of gasliquid

slug flow, Exp. Fluids 8 (1989) 169.

[28] S. Polonsky, D. Shemer, D. Barnea, The relation between the

Taylor bubble motion and the velocity field ahead of it, Int.

J. Multiphase Flow 25 (1999) 957.
http://ttp//http://mecko.nichd.nih.gov/Lpsb/docs/OsmoticStress.htmlhttp://ttp//http://mecko.nichd.nih.gov/Lpsb/docs/OsmoticStress.htmlhttp://ttp//http://mecko.nichd.nih.gov/Lpsb/docs/OsmoticStress.html

Documents

CFD modelling of gas-sparged ultraﬁltration in tubalr membranes