Chemical Engineering Science 59 (2004) 2705–2713www.elsevier.com/locate/ces

Gas-holdup distribution and energy dissipation in an ejector-induceddown(ow bubble column: the case of non-Newtonian liquid

Ajay Mandal∗, Gautam Kundu, Dibyendu MukherjeeDepartment of Chemical Engineering, Indian Institute of Technology, Kharagpur 721 302, India

Received 23 June 2003; received in revised form 5 December 2003; accepted 14 April 2004

Abstract

A precise knowledge of gas-holdup distribution and energy dissipation is essential for designing gas–liquid contactors. A semi-theoreticalapproach has been presented to obtain the axial distribution of gas holdup through the column for gas-non-Newtonian liquid two-phase(ow system. The whole column is distinguished to have three zones based on gas holdup, viz. top, middle and bottom. The middlesection where signi9cant accumulation of bubbles takes place, contributes higher gas holdup towards the total compared to the other twosections. Energy dissipation in the column have been calculated from two-phase gas–liquid frictional losses. A comparative study showsthat substantial gas holdup are observed in the present system with considerably lower energy losses. The experimental data of gas holduphave been correlated in terms of pressure drop by the modi9ed Lockhart–Martinelli equation.? 2004 Elsevier Ltd. All rights reserved.

Keywords: Two-phase (ow; Gas-holdup distribution; Energy dissipation; Cocurrent down(ow; Pressure drop; Bubble column; Non-Newtonian

1. Introduction

The e=cient dispersion of gases in liquids is of major im-portance in many chemical engineering operations and itssigni9cance continues to grow with the development of pol-lution control, fermentation and waste treatment problems.This has initiated a wide interest amongst researchers anddesigners to develop e=cient systems for the dispersion ofgases in liquids. A review of the literature on the design anddevelopment of (uid–(uid contacting equipment shows thatcontactors or reactors belonging to the jet-mixing categorywith cocurrent or countercurrent contacting of phases such asejectors, venturies and other similar devices are gaining im-portance because of the high interfacial area and mass trans-fer coe=cients available in such systems. On the other hand,a co-current down(ow system (Ohkawa et al., 1986; Bandoet al., 1988; Kundu et al., 1995) possesses some uniqueadvantages viz. higher residence time of the gas bubblesand the extensive back mixing particularly in the plungingzone.

∗ Corresponding author. Tel.: +91-3222-281380;fax: +91-3222-282250.

E-mail address: mandal ajay@hotmail.com (A. Mandal).

Signi9cant works have been done on radial distributionof gas holdup in a bubble column. In recent papers, Chenet al. (1998) and Parasu Veera and Joshi (1999) have inves-tigated the radial distribution of gas holdup by tomographymethod. However, the literature on axial distribution of gasholdup through the column is scanty. Further, there is a lotof publication on gas–liquid bubble columns, but most ofthe experiments have been carried out with gas-Newtonianliquid system, though the processing media for many chem-ical industries are often non-Newtonian in nature.A comparative study on variations of gas entrainment and

holdup due to diGerent operating and geometric conditionshas been discussed with Newtonian and non-Newtonian liq-uids in our earlier paper (Mandal et al., 2003). In this study,experiments on gas–liquid two-phase (ow were conductedin a down(ow bubble column with non-Newtonian liquidto obtain axial distribution of gas holdup. The performanceof the present system was examined by the measured gasholdup and energy dissipation (E) per unit volume of liq-uid of the gas–liquid bed. The results were compared withother gas–liquid contacting systems. An attempt was alsomade to correlate the experimental results of gas holdupin terms of pressure drop by modi9ed Lockhart–Martinelliequation.

0009-2509/$ - see front matter ? 2004 Elsevier Ltd. All rights reserved.doi:10.1016/j.ces.2004.04.012

2706 A. Mandal et al. / Chemical Engineering Science 59 (2004) 2705–2713

2. Experimental

2.1. Model systems

Aqueous solution of carboxy methyl cellulose (CMC)was used as non-Newtonian (uid and atmospheric airwas used as gas phase for the present system. It is wellknown that CMC solution in water is a time-independentnon-Newtonian pseudo-plastic (uid and its rheology isdescribed by Ostwald–Dewaele model or power law model:

�= K(−dudr

)n; (1)

where K and n are constants for a particular (uid and thevalue of n is less than one. The constant K is known asthe consistency of the (uid; the higher the value of K , themore viscous the (uid. The constant n is called (ow indexand gives a measure of degree of departure from Newtonianbehaviour.The viscosity of CMC solution reported is the eGective

viscosity, �EL which is de9ned as the ratio of the shear stressat the wall to the average shear rate at the boundary. Forpipeline viscometer, on the basis of Poiseuille’s equation, itis given as

�EL = 8n−1Vn−1Dn−1K ′; (2)

where

K ′ = K(3n+ 14n

)n; (3)

where D and L are the diameter and length of the pipe, re-spectively, and V is the average velocity through the pipe.A logarithmic plot between �w and 8V=D shows linear rela-tionship (Skelland, 1967) and the slope of the line shouldgive the value of n and intercept K[(3n + 1)=4n]n i.e. K ′.Therefore, the eGective viscosity, �EL can be evaluated fromthe measured value of K and n (Khatib and Rechardson,1984; Das et al., 1992). The rheological properties of CMCsolution at diGerent concentrations are given in Table 1. Sur-face tension and density of the liquids were measured by theStalagmometer and Gravity method, respectively.

2.2. Flow pattern

Depending on the (ow conditions there are mainly fourtypes of (ow as shown in Fig. 1, they are homogeneous

Table 1Physical properties CMC solutions measured at 29± 1◦C

Fluid Concentration Flow behaviour Consistency index, Density, �L Surface tension(kg=m3) index, n K (Pa sn) (kg=m3) �L (N/m)

CMC-1 1.0 0.948 0.00218 1000.8 0.0735CMC-2 1.5 0.910 0.00419 1001.2 0.0745CMC-3 2.0 0.871 0.00588 1001.3 0.0750CMC-4 2.5 0.850 0.00692 1001.5 0.0755

bubbly (ow, heterogeneous churn (ow, slug (ow and annu-lar (ow though other types like froth, mist, etc. have beenreported in some cases. Although, (ow regime primarily de-pends upon the gas super9cial velocity and column diameter,liquid viscosity sometimes takes the prime role. In bubbly(ow, the bubbles are quite uniform in size; and they movein an orderly fashion with little collision among bubbles andthe liquid is mildly stirred by the bubbles. Yamagiwa et al.(1990) reported that for cocurrent down(ow, with increasingliquid velocity in the column, (ow behaviour changed fromnon-uniform bubbling (ow to uniform bubbling (ow, andthen to churn—turbulent (ow. But with further increase ofliquid velocity, a uniform bubbling (ow was again obtained.Kendoush and Al-khatab (1989) showed that the transitionfrom bubbly to slug (ow occurs when �G = 0:3 and slug(ow occurs in the range 0:3¡�G ¡ 0:7 in 3:8 cm I.D. pipewith air–water (ow. In the present system of ejector-inducedcocurrent down(ow system, where gas (owrate is primarilycontrolled by liquid (owrate for a particular gas–liquid mix-ing height, it has been found that if liquid velocity increasessigni9cantly the gas bubbles coalesce to form larger bub-bles which move upward rapidly due to increased buoyantforce and churn (ow, slug (ow, etc. However, for co-currentdown-(ow system homogeneous bubbly (ow regime is thebetter selection, otherwise it is rather di=cult to move thebubbles in the downward direction. The operating range ofthe liquid (owrate for bubbly (ow of the present system was2:0×10−4–3:53×10−4 m3=s and the corresponding air en-trainment rate varied from 0:40× 10−5 to 9:0× 10−5 m3=s.

2.3. Experimental set-up

The experimental set-up used is as shown in Fig. 2. Theexperiments were carried out in a Perspex cylindrical bub-ble column of 51:6 mm i.d. and 1:9 m height. An ejectoris placed at the top of the column as gas–liquid distributorand bottom section is connected with a gas–liquid separator.The gas–liquid separator is a rectangular mild steel vesselof 320 × 320 mm2 size and 910 mm height and was largeenough to minimize the eGect due to liquid leaving the sys-tem or air–liquid separation. There is a gas outlet at the topof the separator and a liquid outlet at the bottom. Other ac-cessories e.g. centrifugal pump, rotameter, gas (owmeter,pressure gauge, manometers, control valves, etc. are shownin Fig. 2. A number of U tube manometers (M1–M7) are

A. Mandal et al. / Chemical Engineering Science 59 (2004) 2705–2713 2707

Fig. 1. Flow pattern of vertical column [(a) homogeneous bubbly (owand heterogeneous (b) churn (ow, (c) slug (ow and (d) annular (ow].

Fig. 2. Schematic diagram of experimental set-up. Legends: AI, Air inlet;C, Contactor; E, Ejector assembly; GM, Gas (owmeter; hm, hl, liquidlevel in arm L, Gas–liquid mixture height in the column; M1–M11,Manometers; N, Forcing Nozzle, PG, Pressure Gauge; PU-1, 2, Pump;R, Rotameter; SE, Separator; SV1–SV3, Solenoid Valves; T, Circulatingtank; V1–V5, Valves; VS, Collector vessel.

connected to the column at diGerent heights for measuringthe column pressure. In the present set-up, the optimum di-mensions of the ejector were used as reported by Mukherjeeet al. (1988). The forcing nozzle, N , is of straight type andis precision-bored to obtain a smooth passage and to avoidany undue shock or losses. The dimensions of diGerent sec-tions and the diameter of nozzles used are given in Table 2.

2.4. Experimental method

The column and ejector assembly were 9tted with perfectalignment to obtain an axially symmetric jet. The nozzle was

Table 2Dimensions of the ejector–contactor assembly

Description Dimension (in mm)

Height of the suction chamber, hs 50.0Diameter of suction chamber, ds 60.0Diameter of throat, dt 19.0Length of the throat, Lt 184.0Length of the diGuser, Ld 204.0Diameter of the contactor, dc 51.6Diameter of gas inlet, di 10.0Length of the contactor 1900.0Diameter of the nozzle used, dn 5, 6, 7, 8

9xed at the optimum position at a distance of one throat di-ameter from the entry of the throat, which was decided fromearlier experiments (Datta, 1976). At start, a high-velocityliquid jet was produced through the nozzle, which travelledstraight through the ejector and vertical column and got ac-cumulated in the gas–liquid separator. When a certain heightof the separator was 9lled with liquid, the valve, V5, wasadjusted to maintain the liquid height in the separator. It wasfound that the liquid jet plunged into the accumulated liq-uid, which entrained air along with it, and there was a zoneof intense mixing of gas and liquid. The gas–liquid mix-ture moved downward to a certain distance depending onthe jet momentum and then gas bubbles moved up and gotreleased from the liquid. This was simply a case of plungingjet system. The manometers attached to the system did notshow any change in this case, because the air in the systemgot recirculated in the separator. These phenomena contin-ued until the liquid level increased and touched the bottompart of the extended vertical contactor attached to the ejec-tor. As soon as the liquid height in the separator touched thebottom part of the column, the secondary air got entraineddue to arresting of jet inside the column. The column wasthen 9lled with gas–liquid mixture by proper adjustment ofpressure and liquid level inside the separator by valves V4and V5, respectively. At this condition, there was a suctionof air from the secondary inlet of the ejector, as air was notgetting recirculated and manometers connected to the ejec-tor showed positive de(ection.The experiments were conducted at diGerent liquid and

gas entrainment rates. At constant liquid (owrate (QL), gasentrainment rates (QG) were varied by controlling the pres-sure inside the separator by the valve V4 and maintainingconstant liquid level by valve V5. Pressure readings werenoted from the manometers connected to the column atsteady (ow of gas and liquid in the column.Gas holdup for the present system were measured by two

diGerent techniques, viz. pressure-drop method and isolatingmethod. According to second method, when a steady-statecondition of the system was attained, the total height of gas–liquid mixture in the column was noted. Then the threesolenoid valves, SV1, SV2 and SV3 (Fig. 2) were switchedoG simultaneously. This caused an immediate termination

2708 A. Mandal et al. / Chemical Engineering Science 59 (2004) 2705–2713

Fig. 3. Distribution of gas bubbles and manometer positions.

of (ow of both the (uids. The liquid–gas mixture insidethe column got arrested and was allowed to settle for sometime whereby all the gases got separated. The clear liquidheight inside the column was then noted. The diGerence be-tween the gas–liquid mixing height and the correspondingclear liquid height gave the integral gas holdup in the col-umn. Whereas, pressure-drop technique was used to obtaingas-holdup distribution in the column. The average bub-ble sizes along the column were measured by the capillarymethod.

2.4.1. Gas-holdup distributionEstimation of gas holdup in two-phase gas–liquid system

by measuring the column pressure is a well-known method(Marchese et al., 1992). To obtain a cumulative gas-holdupthroughout the column, pressures at diGerent positions ofthe column were measured by manometers as shown inFig. 3. An assumption has been made to incorporate thismethod that, the dynamic pressure component is negligiblecompared to the hydrostatic pressure. Further, for a partic-ular gas and liquid (owrate frictional loss is assumed to beconstant throughout the column.Under steady operation, the overall gas holdup can be

obtained by measuring the total gas–liquid mixing height(hm) and the corresponding clear liquid height (hl) in thearm L (Fig. 3), and it can be expressed as

�G = �G1 =hm − hlhm

: (4)

Now a pressure balance between the points M1 (i = 1) andM2 (i = 2) gives

P1 − P2 = hm(1− �G1)�Lg− hm2(1− �G2)�Lg: (5)

Similarly pressure balance between points 1 and 3 gives

P1 − P3 = hm(1− �G1)�Lg− hm3(1− �G3)�Lg: (6)

Thus, in general a pressure-balance equation between thebottom part of the column and at any position, i, can bewritten as

P1 − Pi = hm(1− �G1)�Lg− hmi(1− �Gi)�Lg; (7)

where Pi is the pressure at point i (1; 2; 3; : : : ; 7) (Fig. 3) and�Gi is the overall gas-holdup from point i to the top of thegas–liquid mixture. By measuring the pressures at diGerentpositions of the column and hmi, the height of a gas–liquidmixing zone from position i to the upper point of the gas–liquid mixture in the column, the gas holdup values for thatparticular zone can be obtained.

3. Results and discussion

In the present system of gas-non-Newtonian liquidtwo-phase (ow, the experiments were carried out in the freesuction regime, i.e. air was sucked through the secondaryentrance of the ejector by the high-velocity liquid jet.Fig. 4 shows the air entrainment rate (QG) with primaryliquid (owrate (QL) for air–CMC solution system at aparticular gas–liquid mixing height (hm) and nozzle diam-eter. It may be seen from Fig. 4, that higher entrainmentoccurs at lower gas–liquid mixing height in the columndue to lower resistance experienced by the gas bubblesto move downward. Besides, nozzle geometry has a lit-tle eGect on gas entrainment rate (Mandal et al., 2003).Fig. 5 shows variation of overall gas holdup with gas(owrate at constant liquid (owrate. For the same liquid(owrate gas holdup increases with increase in gas (owratebecause of increased bubble population. Fig. 5 also showsthat for same gas (owrate gas holdup decreases with increasein liquid (owrate due to increase in momentum imparted

2.0x10-4 2.2x10-4 2.4x10-4 2.6x10-4

0.0

1.0x10-5

2.0x10-5

3.0x10-5

4.0x10-5

5.0x10-5

6.0x10-5

7.0x10-5

8.0x10-5

System: Air-CMC-2 (1.5kg/m3)d

n: 6 mm

Symbol hm

1.00 mm 1.25 mm

QG(m

3 /s)

QL(m

3/s)

Fig. 4. Variation air entrainment rate with the volumetric (owrate of themotive (uid.

A. Mandal et al. / Chemical Engineering Science 59 (2004) 2705–2713 2709

0.0 2.0x10-5 4.0x10-5 6.0x10-5 8.0x10-5 1.0x10-40.30

0.35

0.40

0.45

0.50

0.55

0.60

System: Air-CMC-3 soln. (2 kg/m3)d

n: 6 mm

Symbol QL

(m3/s)

2.10x10-4

2.45x10-4

2.62x10-4

2.79x10-4

2.95x10-4

ε G

QG(m3/s)

Fig. 5. Variation of overall gas holdup with gas (owrate.

0 20 40 60 80 100 120 1400.40

0.44

0.48

0.52

0.56

0.60

0.64

Symbol QL(m3/s) dn(mm)

0.264x10-3

6.0

0.200x10-3

7.0

0.247x10-3

6.0

0.214x10-3

7.0

ε Gi

hmi

(cm)

Fig. 6. Variation �Gi with gas–liquid mixing height (hmi) air-CMC-2solution (1:5 kg=m3) system.

by liquid on the gas bubbles and results in lower residencetime of the bubble in the column.

3.1. Gas-holdup distribution

Characteristic pictures showing the variation of �Gi withhmi are presented in Figs. 6 and 7. Analysis of the plots givesan axial distribution of local integral gas holdup along thecolumn, as shown in Figs. 8 and 9. The whole column maybe roughly divided into three diGerent sections viz. A, B andC. From Figs. 8 and 9, it is clear that Section B contributesmaximum gas holdup to the overall. Whereas, top and bot-tom sections show decreasing trend of gas holdup towardsthe end. Experimental observations also show that there arethree distinct zones in the column at steady state. At the

0 20 40 60 80 100 120 140

0.30

0.35

0.40

0.45

0.50

0.55

0.60

Symbol QL(m3/s) dn(mm)

0.258x10-3 5

0.262x10-3

6

0.313x10-3 7

0.279x10-3

8

e Gi

hmi

(cm)

Fig. 7. Variation �Gi with gas–liquid mixing height (hmi) air-CMC-3solution (2:0 kg=m3) system.

0 20 40 60 80 100 120 140 1600.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8 CBA

QL: 0.264x10-3 m3/s

dn : 6.0 mm

gas-

hold

up,ε

G

hmi

(cm)

Fig. 8. Distribution of local integral gas holdup with gas–liquid mixingheight (hmi) for air-CMC-2 solution (1:5 kg=m3) system.

top, there is an intense gas–liquid mixing zone where the jetpenetrates the liquid, releases its energy and disperses thegas. A signi9cant back mixing and hence, regeneration ofgas bubbles occur in this section. This is followed by a uni-form bubble zone with substantial bubble population. Thebubble sizes in this section are relatively higher than theprevious section. The bottom section consists of bubbleswhose sizes permit them to move downward by the impartedmomentum of liquid (ow, which prevail over the upwardbuoyant force. Bubble population in this section is relativelylower than the previous section and consequently lower gasholdup was observed. An increase in bubble population al-ways leads to higher gas holdup. An increase in bubble sizeand hence, slip velocity also leads to higher gas holdup forcocurrent down(ow, since the bubbles then spend more timein the column. In the intense mixing zone, there is signi9cant

2710 A. Mandal et al. / Chemical Engineering Science 59 (2004) 2705–2713

0 20 40 60 80 100 120 140 1600.0

0.1

0.2

0.3

0.4

0.5

0.6

CBA

Gas

-hol

dup,

ε G

hmi

(cm)

QL: 0.313x10-3 m3/s

dn : 7.0 mm

Fig. 9. Distribution of local integral gas holdup with gas–liquid mixingheight (hmi) for air-CMC-3 solution (2:0 kg=m3) system.

0.35 0.40 0.45 0.50 0.55 0.600.35

0.40

0.45

0.50

0.55

0.60

Symbol System QLx104(m3/s)

Air-CMC-2 2.00-2.64 Air-CMC-3 2.10-2.95

ε G-P

ress

ure

drop

met

hod

εG -Isolating method

Fig. 10. Comparison of overall gas holdup data obtained by pressure dropmethod with that obtained by isolating method.

bubble population but bubble sizes are much smaller com-pared to the following section and thus a lower gas-holdupresult.Overall gas holdup data obtained by (ow isolation tech-

nique at diGerent operating conditions were compared withthe same as obtained from the pressure-drop method asshown in Fig. 10. It may be seen from the 9gure that overallgas holdup data obtained by two diGerent methods are closeenough with standard deviation 0.72%.

3.2. Energy dissipation

In order to compare the performance of the present sys-tem with other gas–liquid contactors, the e=ciency of dif-ferent systems have been evaluated on the basis of energydissipation. The energy dissipation in gas–liquid two-phase(ow basically occurs from the frictional losses. The rate of

1.0x102 1.5x102 2.0x102 2.5x102 3.0x1020.35

0.40

0.45

0.50

0.55

ε G

E (w/m3)

Symbol dn(mm) Q

L(m3/s)

6 2.10x10-4

6 2.45x10-4

6 2.62x10-4

Fig. 11. Variation overall gas holdup with energy dissipation at diGerentliquid (owrate for air-CMC-3 solution (2:0 kg=m3).

100 150 200 250 3000.45

0.50

0.55

0.60ε G

Symbol dn(mm) QL(m3/s)

6 2.00x10-4

6 2.14x10-4

7 2.00x10-4

7 2.14x10-4

E (w/m3)

Fig. 12. Variation overall gas holdup with energy dissipation at diGerentliquid (owrate for air-CMC-2 solution (1:5 kg=m3).

energy dissipation (E) per unit volume of liquid of the gas–liquid bed can be expressed as (Zahradnik et al., 1982)

E =SPf(QL + QG)(!=4)d2chm�L

: (8)

However, in the present system, as gas is sucked by theliquid jet, no extra energy is required for gas pumping andhence Eq. (8) can be written as

E =SPfQL

(!=4)d2chm�L: (9)

The dispersion e=ciency of diGerent gas–liquid contactorscan be obtained from the knowledge of gas holdup andenergy dissipation. The dependence of �G on energy dissi-pation are shown in Figs. 11 and 12. Graphical presentation

A. Mandal et al. / Chemical Engineering Science 59 (2004) 2705–2713 2711

Table 3Comparison of energy dissipation for diGerent gas–liquid contacting systems

Author Type VL (m/s) VG (m/s) �G E(kw=m3)

Zahradnik et al. (1982) Ejector bubble column 0.008–0.028 0.004–0.067 0.05–0.25 1–12Chandraker et al. (1985) Vertically upward 0.023–0.10 0.02–1.0 0.15–0.40 0.05–9.2Akagawa et al. (1989) Vertically up(ow 0.01–0.10 7.7–12.8 0.005–0.01 2.3–13Das et al. (1992) Horizontal tube 0.14–1.0 0.25–1.5 0.1–0.40 0.9–20Iliuta and Thyrion (1997) Down(ow-packed bed 0.005–0.012 0.04–0.40 0.15–0.30 0.7–20Badie et al. (2000) Horizontal pipe 0–0.03 15–25 0.01–0.10 0.80–10.5Meikap (2000) Multi-stage bubble column 0.003–0.005 0.11–0.20 0.21–0.65 0.25–1.0Present work Down(ow bubble column 0.095–0.16 0.004–0.043 0.40–0.57 0.1–0.50

0.04 0.05 0.06 0.07 0.08 0.09 0.1 0.210

100

1000

Symbols : Experimental values------ : Theoretical values from correlation (Eq.11)

Symbol Solutions CMC-1 CMC-2 CMC-3 CMC-4

E (

w/m

3 )

∆P (Pa)

Fig. 13. Variation of energy dissipation on pressure drop.

con9rms the existence of an unambiguous relation of �G onthe rate of energy dissipation for the gas–liquid two-phase(ow in the column. For same dissipation energy gas holdupis higher at lower liquid (owrate. Table 3 shows that a sig-ni9cantly higher gas holdup was obtained in the present sys-tem compared with the other reported works at the cost ofvery low-dissipation energy.Energy dissipation calculated by Eq. (9) was correlated

as a function of two-phase frictional pressure drop and canbe expressed as

E = c[SPf]b: (10)

The multiple linear regression analysis of the data yieldedthe following correlation:

E = 0:316× 104[SPf]1:104: (11)

Eq. (11) has been statistically tested. The correlation coef-9cient and standard deviations of the above correlation are0.914 and 13.3, respectively. The experimental results arein excellent agreement with the predicted values as shownin Fig. 13.

3.3. Analysis of the holdup

Lockhart–Martinelli (1949) proposed a graphical correla-tion for the analysis of the liquid holdup data for horizontalgas-Newtonian liquid systems. They made a graphical re-lation between the liquid holdup, �L and the parameter X ,de9ned by the following equation:

X 2 =(SpfSz

)L

/(SpfSz

)G: (12)

To take into account the eGect of (ow patterns,Lockhart–Martinelli (1949) presented separate correlationsfor four diGerent (ow combinations of continuous and dis-perse phases, namely, laminar–laminar, laminar–turbulent,turbulent–laminar and turbulent–turbulent. The frictionalpressure drop for single-phase non-Newtonian liquid (owcan be evaluated by the following expression:(SpfSz

)L=2fLV 2L �Ldc

; (13)

where the friction factor is the fanning’s friction factor cal-culated by the usual friction factor-Reynolds number rela-tionship for laminar (ow as follows:

fL =16ReL

(14)

and the Reynolds number of the non-Newtonian (uid isgiven by

ReL =V 2−nL dnc�L8n−1K ′ : (15)

Whereas the friction factor for turbulent (ow has been takenas 0.005 (Wallis, 1969). The frictional pressure drop for thegas phase has been evaluated by the usual technique.Davis (1963) extended the applicability of the Lockhart–

Martinelli approach for vertical (ow through the modi9ca-tion of the parameter, X by incorporating the Froude num-ber, Fr to allow the eGects of gravity and velocity. Thus,the modi9ed parameter, X ′ is expressed as

X ′ = 0:19Fr0:185X: (16)

The experimental liquid holdup data obtained in the presentsystem and the modi9ed Lockhart–Martinelli parameter, X ′,

2712 A. Mandal et al. / Chemical Engineering Science 59 (2004) 2705–2713

11 2 3 4 5 6 7 8 9 1010 200.10.1

0.2

0.3

0.4

0.5

0.60.70.80.9

11

2

System: Air-CMC solutionSymbol Solutions

CMC-1 CMC-3 CMC-4

Liq

uid-

hold

up,

ε L

X /

Fig. 14. Typical comparison of liquid holdup data with Davis parameter.

calculated from Eq. (16) have been plotted in Fig. 14. How-ever, it may be seen from Fig. 14 that the experimentaldata satisfy the Lockhart–Martinelli correlation very quali-tatively and the liquid holdup in the present case is higher.The deviation is due to non-Newtonian behaviour of liquidphase and the enhanced gas–liquid mixing in the column.Further, it has been found that at higher values of X ′ the ex-perimental data tend to merge with the Lokharat–Martinellicurve due to limiting eGect at turbulent (ow regime.

4. Conclusion

Gas-holdup distribution is obtained by measuring pres-sure in a down(ow bubble column at diGerent points alongthe column height. The quantitative experimental results arefound to be in agreement with the visual observation.Three principle dispersion zones are distinguished: (1) a

top mixing zone where liquid jet plunges with simultaneousformation and breaking up of gas bubbles, (2) a homoge-neous bubble (ow middle zone with bubble size somewhathigher than the one of the top zone, and (3) zone at thebottom section corresponding to a decrease in bubble pop-ulation and gas hold up.The results for diGerent gas–liquid contacting equipment

based on the available gas hold up and energy dissipationdata are compared. High-dispersion e=ciency is found forthe present modi9ed down(ow bubble column.The results are correlated in terms of pressure drop by the

modi9ed Lockhart–Martinelli equation.

Notation

b exponent of Eq. (10)c coe=cient of Eq. (10), (w=m3)=Pab

dc diameter of the column, mm

dn diameter of the nozzle, mmE dissipation energy per unit volume of liquid of

gas–liquid bed, w=m3

fL friction factor for liquid (ow only, dimension-less

Fr Froude number, (V 2m =gdc), dimensionlessg acceleration due to gravity, m=s2

hl height of clear liquid in arm L (Fig. 3), mhm height of gas–liquid mixture in the column, mhmi diGerent positions of gas–liquid mixture height

in the column, mK; K ′ (ow consistency index of the (uid, Pa sn

n (ow behaviour indexP pressure of the column, PaSP pressure drop, PaQG gas (owrate, m3=sQL liquid (owrate, m3=sr radial position from centre of the pipe, mReL Reynolds number of liquid, dimensionlessu velocity, m/sV super9cial velocity based on column diameter,

m/sX Lockhart–Martinelli parameter, dimensionlessX ′ modi9ed Lockhart–Martinelli parameter,

dimensionlessSz distance between two pressures tapping over

which the pressure drop has been measured, m

Greek letters

�G overall gas holdup, dimensionless�Gi overall gas holdup from point i to the top of the

gas–liquid mixture (Fig. 3), dimensionless�L overall liquid holdup, dimensionless�EL eGective viscosity of liquid, kg/m s�L density of liquid, kg=m3

�L surface tension of the liquid, N/m� shear stress, Pa�w shear stress at wall, Pa

Subscripts

f frictionalG gasi 1; 2; 3; : : : refers diGerent position of the column

(Fig. 3)L liquidm gas–liquid mixture

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