Journal of Chemical Engineering of Japan, Vol. 38, No. 1, pp. 1–11, 2005 Research Paper

Copyright © 2005 The Society of Chemical Engineers, Japan 1

The Effect of Superficial Gas Velocity and Aerated Liquid Height onthe Spatial Distribution of Local Liquid-Phase Axial DispersionCoefficients in a Bubble Column

Stoyan NEDELTCHEV*, Shinichi OOKAWARA

and Kohei OGAWADepartment of Chemical Engineering, Graduate School of Scienceand Engineering, Tokyo Institute of Technology,12-1, Ookayama 2, Meguro-ku, Tokyo 152-8552, Japan

Keywords: Bubble Column, Absorption, Regime Transition, Axial Dispersion Coefficient, Spatial Distribu-tion

The spatial liquid-phase concentrations were measured by means of an electrical conductivity probein a 0.289-m ID bubble column operated at superficial gas velocities (ug) of 0.018, 0.031 and 0.038 m/s, re-spectively. The column was equipped with a perforated plate gas distributor (0.002 mø ××××× 31 holes).Carbon dioxide was used as a tracer gas, whereas deionized water was used as a liquid phase. The localliquid-phase axial dispersion coefficient EL was derived from the local liquid-phase concentrations bymeans of the graphical method developed by Khang and Kothari (1980). It was found that the spatialdistribution of the local EL coefficients becomes radially non-uniform as a function of ug. At the regimetransition velocity (Utrans = 0.031 m/s) between bubbly and transition flow regimes the mean, EL coeffi-cient for the upper zone (UZ) becomes identical to the one for the lower zone (LZ). At both lower andhigher ug values EL(UZ) is systematically higher than EL(LZ). The same result also holds if the overallbubble bed (BB) is divided into core and annulus regions. It was proven that, in the bubbly flow regime(ug < Utrans), EL (core region) ≈ EL (annulus region), whereas in the transition flow regime (ug >Utrans), EL (annulus region) > EL (core region). The effect of the aerated liquid height L on the spatialdistribution of the local EL coefficients was studied, as well. Three different BBs, viz. L = 0.64 m (shal-low BB), 1.28 m (medium BB) and 2.1 m (deep BB) were examined at ug = 0.038 m/s. The spatial distri-bution of the local EL coefficients was most scattered in the shallow BB (L = 0.64 m). In a medium BBwith an aerated liquid height L = 1.28 m the existence of a well-developed helical flow structure wasdetected.

It was shown that the graphically determined mean EL coefficient (for the overall BB) increases as afunction of both the superficial gas velocity ug and aerated liquid height L, and a useful empirical corre-lation was derived. It covers the following range of bed aspect ratios: 2.1 ≤ L/Dc ≤ 7.3.

Introduction

Operations in bubble column reactors (BCRs) inwhich one or more components of a gas phase are ab-sorbed into a liquid phase are common throughout thechemical process industries. These reactors are fre-quently used in chemistry, petrochemistry and mineralprocess industries because of their simple construction,ease of operation and their flexibility with respect tothe liquid phase residence time.

The liquid-phase backmixing is unavoidable ran-dom process. According to Shah et al. (1978) thebackmixing has a negative effect on the performance

Received on February 25, 2004. Correspondence concerningthis article should be addressed to K. Ogawa (E-mail address:kogawa@chemeng.titech.ac.jp).

* Present address: Institute of Chemical Engineering, BulgarianAcademy of Sciences, “Acad. G. Bonchev” Str. Bl. 103, 1113Sofia, Bulgaria.

of a gas–liquid BCR. The authors define it as a spe-cific case of axial mixing in which the random move-ment of the fluid is superimposed on and is in the di-rection of the main flow stream and where the trans-verse mixing (i.e., mixing in the direction perpendicu-lar to the flow) is complete. The extent of backmixingin each phase is, in general, different and should betreated individually. In a BCR, the backmixing in thefast moving gas phase is rather smaller than in the slowmoving liquid phase. In small scale BCRs, the gasphase is usually assumed to move in a plug flow.

In a BCR, significant liquid-phase backmixing iscaused by the gas flow. Furthermore, the backmixingincreases as a function of D

c. For the sake of a proper

BCR design the liquid-phase backmixing should bealways considered. Liquid-phase backmixing reducestemperature and concentration gradients and thusstrongly affects the heat and mass transfer processes.

The backmixing in BCRs has been largely char-acterized in terms of the axial dispersion model (ADM).

2 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

It is the simplest and the most frequently used model.The ADM quantifies the mixing in the respective phaseby a single parameter (so-called axial dispersion(backmixing) coefficient). It is the fundamental dif-ferential mixing model developed for the descriptionof axial (longitudinal) mixing. The ADM is based uponthe analogy between the axial mixing and the diffu-sion. This model characterizes the backmixing by asimple, one-dimensional Fick’s law type diffusionequation. The constant of proportionality in this equa-tion is identical with the axial dispersion (backmixing)coefficient. The assumption that all mixing processesfollow Fick’s law type diffusion equation regardlessof the actual mechanism becomes increasingly dubi-ous for the large extents of backmixing. However, themodel is still widely used in practice.

The literature data on the liquid-phase axial dis-persion coefficient E

L in BCRs is extensive. Especially

for the air–water system at an atmospheric pressurenumerous single-point measurements have been done,and both theoretical (Baird and Rice, 1975; Joshi andSharma, 1978; Joshi, 1980; Field and Davidson, 1980;Riquarts, 1981; Walter and Blanch, 1983; Kawase andMoo-Young, 1986) and empirical (Ohki and Inoue,1970; Gondo et al., 1973; Deckwer et al., 1974; Hikitaand Kikukawa, 1974; Dobby and Finch, 1985) equa-tions have been developed for the sake of E

L predic-

tion. Many interesting papers devoted to liquid mix-ing in BCRs have been published in the last four dec-ades (Aoyama et al., 1968; Reith et al., 1968; Katoand Nishiwaki, 1972; Eissa and Schügerl, 1975; Koniget al., 1978; Khang and Kothari, 1980; Rice et al., 1981;Wendt et al., 1984; Tinge and Drinkenburg, 1986; Riceand Littlefield, 1987; Myers et al., 1987; Schmidt etal., 1992; Yang et al., 1992, 1993; Wilkinson et al.,1993; Ityokumbul et al., 1994; Kantak et al., 1994;Millies and Mewes, 1995; Groen et al . , 1996;Degaleesan et al., 1996; Zahradnik and Fialova, 1996;Degaleesan and Dudukovic, 1998; Hebrard et al., 1999;Moustiri et al., 2001).

Particularly interesting is the paper by Khang andKothari (1980) which introduces a new graphicalmethod for estimation of the E

L coefficient. As men-

tioned above, most of the previous studies on liquidmixing were based on single-point E

L measurements.

However, these one-point measurements give ambigu-ous results. Only numerous (spatial) in situ measure-ments in the bubble bed (BB) lead to sufficient infor-mation. That is why, in the present paper we shallpresent spatial distributions of the local E

L coefficients

(derived by means of the graphical method by Khangand Kothari (1980)) at several operating conditions. Itis worth noting that the method is not sensitive to themeasurement position. This fact allows us to performmultiple measurements at different radial and axialpositions. Our paper provides extensive backmixingdata from all regions of the BB. Most literature data

were obtained in the bubble-dominated bulk zone andthus led to the erroneous conclusion that the E

L coeffi-

cient is essentially independent of the measurementposition. Our new E

L data reveal that this is not cor-

rect.The liquid-phase axial dispersion coefficient E

L

takes part in the dimensionless gas–liquid Pecletnumber (Pe

GL = (u

gL)/E

L). The Pe

GL value character-

izes the degree of backmixing. If PeGL

= 0, backmixingis complete, whereas for Pe

GL = ∞, a plug flow pre-

vails. According to Lee and Tsui (1999) the completebackmixing is an idealized scenario in which concen-tration is uniform throughout the BB. At the other ide-alized extreme (plug flow), absolutely no backmixingoccurs. It is conceivable that the gas and liquid phasespossess opposite backmixing characteristics. In the caseof the plug flow, the axial mixing is nonexistent. How-ever, owing to the complete radial mixing, all fluid el-ements within the system have identical velocities andhence identical residence times. In a completely mixedsystem, the residence time distribution of the fluid fol-lows an exponential decay, i.e. the exit stream compo-sition is identical to that within the system. In reality,however, BCRs deviate considerably from the aboveextreme cases of macromixing. These deviations maybe the result of non-uniform velocity profiles, shortcircuiting, bypassing and channeling, velocity fluctua-tions due to molecular and turbulent diffusion, reactorshape, backflow of fluid due to velocity differencesbetween the phases, and by recycling due to agitation.

One of the objectives of this paper is to identifythe transition gas velocity U

trans between bubbly and

transition flow regimes by comparing the ug-depend-

ent profiles of EL(LZ) and E

L(UZ) not only for the over-

all BB but also for both core and annulus regions ofthe column. The regime transition identification is avery important issue because when scaling up a BCR,it is essential to maintain the same flow regime. In ad-dition, the accurate prediction of the transition gas ve-locity U

trans from bubbly to transition flow regime is

crucial for the reliable estimation of the design param-eters in gas–liquid BCRs. It is well-known that thehydrodynamics and the rates of heat and mass transferin BCRs are substantially different in the bubbly andtransition flow regimes.

Another important objective is to study the effectof u

g on the spatial distribution of the local E

L coeffi-

cients. In addition, the effect of the aerated liquid heightL on the spatial distribution of the local E

L coefficients

will be researched at ug = 0.038 m/s. The change of the

helical nature of the flow pattern as a function of Lwill be examined, as well.

Nedeltchev et al. (1999, 2000, 2003a, 2003b) havealready reported what are the effects of u

g and L on the

spatial distributions of the local liquid-phase concen-trations and volumetric liquid-phase mass transfer co-efficients. The effect of u

g on the spatial distribution

´

VOL. 38 NO. 1 2005 3

of the local volumetric liquid-phase mass transfer co-efficients was used even for an identification of theregime transition velocity U

trans (see Nedeltchev et al.,

2003b). Nedeltchev et al. (2003c) identified the Utrans

location based on the number of the appearances of asingle radioactive particle in the different regions ofthe BB.

1. Theoretical Background

As was mentioned above, Khang and Kothari(1980) have developed a new graphical method forfinding the axial dispersion (backmixing) coefficientE

L in a BCR. This method requires only the area above

the experimental profile of the normalized liquid con-centration, thus it is simpler than the conventionalmethod of curve fitting. The graphical method is basedon a moment method for the mean residence timedistribution in a BCR. The liquid-phase mixing inBCRs is related to the axial concentration gradient inthe liquid phase. Khang and Kothari (1980) plottedthe normalized concentration measured at the top ofthe BB against the operational time, and proved thatthe area above the response curve is proportional toL2/(6E

L). Thus, the E

L coefficient in a given BCR can

be obtained from the tracer response curve by measur-ing the area between the normalized concentration re-sponse curve and the horizontal line of unity height.According to Khang and Kothari (1980) the newgraphical method gives accurate measurements of theE

L coefficient without any numerical curve fitting tech-

nique.Khang and Kothari’s (1980) method is not sensi-

tive to the selection of the measurement position. Insuch a way, the graphical method enables us to derivethe local E

L coefficient in every region of the BB where

we have measured the liquid concentration profile.Therefore, the spatial distribution of the local E

L coef-

ficients can be examined at various operating condi-tions. The local time-dependent liquid concentrationprofile (measured by an electrical conductivity probe)was normalized by dividing it to its maximum (equi-librium) value which was different in each region ofthe BB.

2. Experimental Setup

The local liquid-phase concentration measure-ments were performed in a semi-batch cylindrical BCRof 0.289 m in ID made from acrylic resin and workingat ambient pressure. The column was equipped with aperforated plate gas distributor of 0.005 m thicknessconsisting of 31 holes of 0.002 m diameter arrangedon an equilateral triangular pitch of 0.05 m. The col-umn was installed to be perfectly vertical in order toavoid the effect of the reactor tilt on the E

L coefficient.

The true verticality has a profound effect in reducingliquid circulation and dispersion in the bubbly flowregime.

Three different clear liquid heights L0 of 0.56, 1.12

and 1.84 m were used. As shown in Table 1, the BBwith L

0 = 0.56 m (shallow BB) was aerated at three

different superficial gas velocities (ug) of 0.018, 0.031

and 0.038 m/s, respectively. The BBs with L0 = 1.12 m

(medium BB) and 1.84 m (deep BB) were aerated onlyat u

g = 0.038 m/s. The corresponding aerated liquid

heights L and bed aspect ratios L/Dc are given in Table

1. The BBs were imaginarily divided into 4 (L = 0.6,0.63 and 0.64 m), 8 (L = 1.28 m) and 12 (L = 2.1 m)layers, respectively. Each layer consisted of eight semi-cylindrical shells.

Figure 1 shows schematically the division of ashallow BB (L = 0.6, 0.63 and 0.64 m) into LZ, UZ,core and annulus regions. The annulus region consistsof the outer semi-cylindrical shells adjacent to the col-umn wall, while the other inner semi-cylindrical shellsconstitute the core region. Therefore, the annulus re-gion for the overall BB consists of 8 semi-cylindricalshells, whereas the annulus region for both LZ and UZconsists of 4 semi-cylindrical shells. Likewise, the coreregion for the overall BB consists of 24 semi-cylindri-cal shells, whereas the core region for both LZ and UZconsists of 12 semi-cylindrical shells. This definitionalways keeps the volume ratio of the core region to theannulus region constant and equal to 0.78 regardlessof the aerated liquid height L of the BB. Therefore, themixing properties of these regions can be compared.

The overall gas holdup εg was estimated visually

as follows:

Air [l/min] 50 70 100 100 100CO2 [l/min] 20 50 50 50 50

ug [m/s] 0.018 0.031 0.038 0.038 0.038L0 [m] 0.56 0.56 0.56 1.12 1.84L [m] 0.60 0.63 0.64 1.28 2.1L/Dc [—] 2.1 2.2 2.2 4.4 7.3

εg [—] 0.067 0.111 0.125 0.125 0.124

PeGL [—] 11.201 15.895 18.159 10.074 6.614

Table 1 Specification of the operating conditions examined

4 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

εg0= ( )L L

L

–1

The εg values under the different operating conditions

examined are given in Table 1. Deionized water con-stituted the continuous phase and carbon dioxide (CO

2)

was used as a tracer gas. The latter was added to theoil-free compressed air which was used as a carriergas. The dynamic method for studying liquid mixingcomprehensively described by Deckwer (1992) andKastanek et al. (1993) was applied, i.e. the tracer wascontinuously fed into the filtered air supply line pro-ducing a stepwise change of the liquid concentrationprofiles. Before introducing the CO

2 tracer, the

deionized water was thoroughly purged by nitrogen(N

2) for about 5 min with a flow rate of 1.7 × 10–3

m3/s. Following that procedure, the system was allowedto come to equilibrium over a period of 2 min duringwhich time the desired CO

2 flow rate in the filtered air

was substituted by an equal flow rate of N2. The data

acquisition was started simultaneously with the com-puterized solenoid valve opening of the CO

2 supply

line.The local liquid concentration profiles in the BB

were routinely measured three times (at the positionsindicated by the circles in Figure 1) by an electricalconductivity probe (the output signal was in volts) andthen averaged. Only one liquid concentration measure-ment was performed at a time since a single probe was

used. The average relative error was always less than10%. The probe was always mounted vertically down-wards. It consisted of two platinum tips 0.002 m inlength, separated by a distance of 0.001 m. The sam-pling frequency was adjusted at 100 Hz. A chemicaltitration method was employed for the sake of the probecalibration.

3. Results and Discussion

3.1 The effect of the superficial gas velocity ug

on the spatial distribution of the local EL co-

efficients in a shallow BB (L = 0.6, 0.63 and0.64 m)The influence of the superficial gas velocity u

g on

the spatial distribution of the local EL coefficients was

examined in a shallow BB with a clear liquid heightL

0 = 0.56 m which was aerated at u

g = 0.018, 0.031 and

0.038 m/s as shown in Figures 2(a), (b) and (c), re-spectively. The column central axis is indicated by thedotted line in these figures. It is worth pointing outthat the local E

L coefficients at u

g = 0.018 m/s are

radially uniform from a practical viewpoint, while theinhomogeneities increase as a function of u

g. In the

captions of Figures 2(a)–(c) are given the comparisonsamong the mean E

L coefficients for each axial posi-

tion. In addition, the comparisons between EL(UZ) and

EL(LZ) are provided, as well. In Figures 2(a)–(c) the

maximum and minimum local EL coefficients are prop-

erly indicated by a set of circles and arrows. The maxi-mum local E

L coefficient corresponds to the highest

local ug value, and vice versa.

In Figure 3 it is shown that at ug = 0.018 m/s the

mean EL coefficient for the UZ is higher than the one

for the LZ. However, at ug = 0.031 m/s E

L(UZ) be-

comes practically equal to EL(LZ). Further increase of

ug leads again to E

L(UZ) > E

L(LZ). At u

g = 0.018 m/s

EL(UZ) = 1.24 E

L(LZ), whereas at u

g = 0.038 m/s

EL(UZ) = 1.08 E

L(LZ). According to Deckwer et al.

(1973) the ug value at which E

L(UZ) becomes practi-

cally equal to EL(LZ) should be considered as a re-

gime transition velocity Utrans

from bubbly to transi-tion flow regime. Therefore, our results lead to theconclusion that at u

g = U

trans = 0.031 m/s occurs the

physical transition from bubbly to transition flow re-gime.

Chen et al. (1994) argue that for an air–tap watersystem and a tube-orifice type of sparger, the regimetransition velocity U

trans occurs at 0.03 m/s because the

pitch of the spiral motion of the central bubble streamexhibits a maximum therein. Rice and Littlefield (1987)also showed that the regime transition between bubblyand transition flow regimes occurs at about 0.03 m/sfor a perforated latex membrane. Zehner and Schuch(1985) proved based on the profiles of the gas phasemixing coefficient and gas holdup that the regime tran-sition occurs at 0.03 m/s. Lee and Tsui (1999) presented

Fig. 1 Schematic representation of the lower zone (LZ),upper zone (UZ), core and annulus regions of a0.289-m-ID bubble column with aerated liquidheights L = 0.6, 0.63 and 0.64 m

VOL. 38 NO. 1 2005 5

a flow regime transition diagram according to whichin a 0.289-m-ID column the transition occurs at about0.04 m/s.

Higher EL coefficients in the UZ have been also

reported by Deckwer et al. (1973). According to theseauthors, at 0.004 ≤ u

g ≤ 0.062 m/s two mixing zones

exist with different degrees of backmixing. It was foundthat E

L(UZ) was always two times larger than E

L(LZ).

The point of separation between both mixing zones liesapproximately in the middle of the BB. At u

g ≤ 0.004

m/s the BB is characterized with a single EL coeffi-

cient. At ug ≥ 0.062 m/s the splitting into two mixing

zones disappears again and one constant backmixingcoefficient is obtained.

The equations derived by Reilly et al. (1994)

Upsmall

L

G

= ( )0 352 20 12

0 04..

.σ

ε ρρ

σtransG

LL= ( )4 457 3

0 960 12.

..

U Utrans small trans trans= ( ) ( )ε ε1 4–

also confirm the above conclusion. They show that forthe CO

2–water system the regime transition should

Fig. 2 (a) Spatial distribution of the local liquid-phase axial dispersion coefficients EL in a shallow bubble bed, u

g = 0.018

m/s, L = 0.6 m, EL (z = 0.4 m) = 1.188 × 10–3 m2/s > E

L (z = 0.54 m) = 1.052 × 10–3 m2/s > E

L (z = 0.08 m) = 0.982 ×

10–3 m2/s > EL (z = 0.24 m) = 0.828 × 10–3 m2/s; (b) u

g = 0.031 m/s, L = 0.63 m, E

L (z = 0.4 m) = 1.344 × 10–3 m2/s ≈ E

L

(z = 0.08 m) = 1.304 × 10–3 m2/s > EL (z = 0.24 m) = 1.167 × 10–3 m2/s ≈ E

L (z = 0.56 m) = 1.149 × 10–3 m2/s; (c) u

g =

0.038 m/s, L = 0.64 m, EL (z = 0.4 m) = 1.469 × 10–3 m2/s > E

L (z = 0.24 m) = 1.367 × 10–3 m2/s > E

L (z = 0.56 m) =

1.251 × 10–3 m2/s > EL (z = 0.08 m) = 1.144 × 10–3 m2/s

(b)

(a) (c)

6 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

occur at Utrans

= 0.034 m/s. Therefore, from a theoreti-cal viewpoint the data shown in Figure 2(c) shouldbelong to the transition flow regime. In Eq. (3) is takeninto account the constant 3.85 as suggested by Krishnaand Ellenberger (1996).

In Figure 3 it is shown that the profile of the meanE

L coefficient for the overall BB is an increasing func-

tion of ug. Since the E

L coefficient depends on u

g it is

obvious that the maxima and minima in Figures 2(a)–(c) correspond to higher and lower u

g values at these

particular local positions. Therefore, the superficial gasvelocity u

g is variable throughout the BB. The same

conclusion was reached by Deckwer (1976).Figure 4 shows that in the bubbly flow regime

the EL(UZ)-to-E

L(LZ) ratios for both core and annulus

regions of the column are practically the same (EL(UZ)

> EL(LZ) in both core and annulus regions of the col-

umn). At the regime transition velocity (Utrans

= 0.031m/s) E

L(UZ) becomes practically equal to E

L(LZ) in

both core and annulus regions. According to Deckweret al. (1973) this is a typical indicator for regime tran-sition. Therefore, Figure 4 can be used for the sake offlow regime identification, as well. Once the operat-ing regime is changed into the transition flow regime,the E

L(UZ)-to-E

L(LZ) ratio for the annulus region be-

comes higher than the one for the core region (againE

L(UZ) > E

L(LZ) in both core and annulus regions).

Figure 5 shows that in the bubbly flow regimethe mean E

L coefficients for both core and annulus re-

gions are identical from a practical viewpoint. There-fore, the dimensionless gas–liquid Peclet numbers Pe

GL

for both regions are practically the same and thus thedegrees of liquid mixing are identical. At u

g ≥ 0.031

m/s EL(annulus) becomes higher than E

L(core) which

Fig. 3 Regime transition identification between bubbly and transition flow regimes based on the liquid-phase axial disper-sion coefficient E

L profile as a function of u

g in the lower zone (LZ), upper zone (UZ) and overall bubble bed (BB),

L0 = 0.56 m

Fig. 4 Regime transition identification between bubbly and transition flow regimes based on the profile of the EL(UZ)-to-

EL(LZ) ratio for both core and annulus regions of the column as a function of the superficial gas velocity u

g

VOL. 38 NO. 1 2005 7

in terms of the gas–liquid Peclet number PeGL

meansthat the liquid mixing in the annulus region is better.3.2 The effect of the aerated liquid height L on the

spatial distribution of the local EL coefficients

The influence of the aerated liquid height L onthe spatial distribution of the local E

L coefficients was

examined at ug = 0.038 m/s as shown in Figures 2(c),

Fig. 5 Regime transition identification between bubblyand transition flow regimes based on the profile ofthe E

L(core)-to-E

L(annulus) ratio as a function of

the superficial gas velocity ug

Fig. 6 Spatial distribution of the local EL coefficients at

an aerated liquid height L = 1.28 m and superficialgas velocity: u

g = 0.038 m/s; E

L (z = 0.08 m) =

7.75 × 10–3 m2/s > EL (z = 1.03 m) = 6.3 × 10–3 m2/s

> EL (z = 0.40 m) = 6.0 × 10–3 m2/s > E

L (z = 0.72 m)

= 5.8 × 10–3 m2/s ≈ EL (z = 0.88 m) = 5.7 × 10–3

m2/s > EL (z = 0.56 m) = 4.9 × 10–3 m2/s > E

L (z =

0.24 m) = 4.65 × 10–3 m2/s > EL (z = 1.11 m) = 4.4 ×

10–3 m2/s; EL (LZ) = 5.8 × 10–3 m2/s > E

L (UZ) =

5.6 × 10–3 m2/s

Fig. 7 Spatial distribution of the local EL coefficients at

an aerated liquid height L = 2.1 m and superficialgas velocity: u

g = 0.038 m/s; E

L (z = 1.52 m) =

1.47 × 10–2 m2/s > EL (z = 1.20 m) = 1.37 × 10–2

m2/s > EL (z = 1.04 m) = 1.27 × 10–2 m2/s = E

L (z =

0.40 m) = 1.27 × 10–2 m2/s = EL (z = 1.82 m) =

1.27 × 10–2 m2/s ≈ EL (z = 0.08 m) = 1.26 × 10–2

m2/s = EL (z = 0.88 m) = 1.26 × 10–2 m2/s > E

L (z =

0.56 m) = 1.19 × 10–2 m2/s ≈ EL (z = 0.24 m) =

1.13 × 10–2 m2/s ≈ EL (z = 0.72 m) = 1.12 × 10–2

m2/s > EL (z = 1.68 m) = 1.05 × 10–2 m2/s > E

L (z =

1.36 m) = 0.93 × 10–2 m2/s; EL (UZ) = 1.23 × 10–2

m2/s ≈ EL (LZ) = 1.21 × 10–2 m2/s

6 and 7 for L = 0.64, 1.28 and 2.1 m, respectively. Whenthe aerated liquid height is L = 1.28 m (see Figure 6),the radial E

L distribution is not so inhomogeneous in

comparison with the BB with an aerated liquid heightL = 0.64 m (see Figure 2(c)).

Figure 6 shows that, for L = 1.28 m, the radial EL

profile at z = 0.08 m is much higher than the rest of theradial E

L profiles. This means that at the gas distribu-

tor zone the ug value is the highest. In Figure 3 and

Eqs. (5) and (6) it is shown that the EL coefficient is a

function of ug. Therefore, a higher u

g value will lead to

a higher EL coefficient, and vice versa. It is worth not-

ing that the radial EL values at one axial position are

higher, whereas at the next axial position they becomelower. Therefore, the fluctuation of the radial E

L pro-

files is associated with the variable superficial gas ve-locity u

g due to the typical absorption–desorption tran-

sitions occurring in the BB in the axial direction z (seeDeckwer, 1976). The mean E

L coefficient for the LZ is

slightly higher than the one for the UZ (see the cap-tion of Figure 6). The comparison among the mean E

L

coefficients at the different axial positions (see the

8 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

caption of Figure 6) reveal that the local ug value is

maximum at the bottom (z = 0.08 m) and minimum atthe top (z = 1.11 m) of the medium BB.

When the aerated liquid height L is 2.1 m (seeFigure 7), most of the radial E

L distributions lie close

to each other. The radial EL non-uniformity is espe-

cially pronounced at z = 1.20 m where several peaksare observable. The maximum mean E

L coefficient at

z = 1.52 m (see the caption of Figure 7) reveals thatthe local u

g value is the highest therein. On the other

hand, the minimum mean EL coefficient at z = 1.36 m

shows that the local ug value is the lowest therein. Since

z = 1.36 m and z = 1.52 m are neighbouring axial posi-tions, it is clear that the lowest and highest local u

g

values are associated with the typical absorption–desorption transitions occurring throughout the deepBB. Deckwer (1976) argues that the superficial gasvelocity u

g throughout the BB may vary considerably

as absorption proceeds. According to the author, theoptimal design of BCRs should take account of the vari-able u

g since it influences almost all fluid dynamic

properties. It is notable that in the bulk of the BB mostof the mean E

L values are very close to each other. The

mean EL coefficients for both LZ and UZ are practi-

cally the same (see the caption of Figure 7).As was already mentioned, the operating condi-

tion at ug = 0.038 m/s falls within the transition flow

regime. According to Franz et al. (1984), Drahos et al.(1992), Chen et al. (1994), Fischer et al. (1994) andLin et al. (1996) the flow follows a zigzag or helicalupward path in this hydrodynamic flow regime. Thelocal maximum E

L value at a particular axial position z

is expected to identify the local region through whichmost of the gas flow passes during its rise at this z.This identification is possible since the local maximumE

L value corresponds to the highest local u

g value. Fig-

ures 8–10, which pinpoint the radial positions of thelocal maximum E

L coefficients at the different axial

positions, could confirm the existence of such a heli-cal flow pattern.

It seems that the BB at L = 0.64 m is too shallowfor the formation of a well-developed helical flowstructure (see Figure 8). In addition, a local maximumE

L coefficient in the right part of the BB is not ob-

served. On the other hand, the results shown in Figure9 confirm the existence of a well-developed helicalflow structure in a medium BB with an aerated liquidheight L = 1.28 m. It is notable that at z = 0.08 m thelocal maximum E

L coefficient is not located close to

the column wall (at other axial positions z) but it islocated at a radial position 0.198 m. In Figure 10 it isshown that the predominant part of the gas flow ispushed towards the right zone of the deep BB (L =2.1 m, u

g = 0.038 m/s) and rises upwards in a zigzag

way. A local maximum EL coefficient close to the left

wall of the column is not observed.

Fig. 8 Radial positions of the maximum local EL coeffi-

cients at different axial positions, L0 = 0.56 m, u

g =

0.038 m/s

Fig. 9 Radial positions of the maximum local EL coeffi-

cients at different axial positions, L = 1.28 m, ug =

0.038 m/s

Fig. 10 Radial positions of the maximum local EL coeffi-

cients at different axial positions, L = 2.1 m, ug =

0.038 m/s

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VOL. 38 NO. 1 2005 9

3.3 The effect of the aerated liquid height L on themean E

L coefficient for the overall BB

In Figure 11 it is shown that the mean EL coeffi-

cient for the overall BB is an increasing function ofthe aerated liquid height L provided that the superfi-cial gas velocity u

g is kept constant at 0.038 m/s. Based

on our data shown above, the mean EL coefficient for

the overall BB can be successfully correlated to bothsuperficial gas velocity u

g and aerated liquid height L:

E L uL g= × ( )7 64 10 53 1 85 0 28. – . .

The average relative error is 4.3%, whereas the maxi-mum relative error is 14.5% (at L = 1.28 m). Equation(5) is applicable in the following range of bed aspectratios: 2.1 ≤ L/D

c ≤ 7.3. The parity plot of the calcu-

lated EL coefficients by means of Eq. (5) vs. the ex-

perimental mean EL coefficients (for the overall BB)

determined by the graphical method of Khang andKothari (1980) is shown in Figure 12. The data arefitted reasonably well. It is worth pointing out that the

Fig. 11 Dependence of the mean EL (BB) coefficient on the

aerated liquid height L

Fig. 12 Parity plot of the experimental EL (BB) coefficients

vs. the theoretically calculated ones by means ofEq. (5)

prediction of our EL correlation in a deep BB (u

g =

0.038 m/s, L = 2.1 m) is close to the EL value calcu-

lated by means of the correlation of Kantak et al. (1994)(the absolute error is 7.1%). Under the rest of the op-erating conditions, i.e. in shallow and medium BBs,the deviations are considerable since the correlationof Kantak et al. (1994) does not take into account theeffect of the aerated liquid height L. It is worth notingthat the exponent of u

g in Eq. (5) is very close to the

one derived by Deckwer et al. (1974):

E D uL c g= ( )0 678 61 4 0 3. . .

Equation (6) is widely endorsed and cited in Shah etal. (1978), Joshi and Sharma (1978), Kastanek et al.(1993), Rubio et al. (1999) and Hebrard et al. (1999).

In the literature hitherto are available only twocorrelations between E

L and L reported by Joshi and

Sharma (1978, 1979) and Field and Davidson (1980).Shah et al. (1978) reported Schugerl’s results that thedispersion increases with the column height. Field andDavidson (1980) cited the results of Katz andRozenberg which show that the E

L coefficient is a func-

tion of the aerated liquid height L provided that theaspect ratio is less than 7–10 as is usually the case forindustrial BCRs. The authors concluded that equationsexcluding L are unsuitable for industrial design.

Our future objective will be to verify what is theeffect of the column diameter D

c on the mean E

L coef-

ficient for the overall BB determined by the graphicalmethod of Khang and Kothari (1980). Therefore, thefinal form of Eq. (5) will incorporate the effect of thecolumn diameter D

c.

The increase of the degree of heterogeneity in thespatial distribution of the local E

L coefficients with the

increase of ug (see Figures 2(a)–(c)) can be explained

in terms of the dimensionless gas–liquid Peclet numberPe

GL which incorporates the mean E

L coefficient de-

fined by Eq. (5). The gas–liquid Peclet number PeGL

can also be used for an explanation of the increaseddegree of homogeneity in the spatial distribution ofthe local E

L coefficients with the augmentation of the

aerated liquid height L (see Figures 2(c), 6 and 7).As was mentioned in the beginning of this paper,

the gas–liquid Peclet number PeGL

can be defined asfollows:

Peu L

EGLg

L

= ( )7

The substitution of Eq. (5) into Eq. (7) yields:

Peu

LGLg= ( )130 89 80 72

0 85..

.

10 JOURNAL OF CHEMICAL ENGINEERING OF JAPAN

According to Shah et al. (1978) PeGL

= 0 corre-sponds to a complete liquid mixing state, whereasPe

GL = ∞ corresponds to no mixing state. In Table 1

are given the PeGL

values calculated by means ofEq. (8) under the different operating conditions exam-ined. It is obvious that the Pe

GL value increases with u

g

augmentation, which means that the degree of liquidmixing decreases and thus the spatial distribution ofthe local E

L coefficients become more heterogeneous.

On the other hand, the results in Table 1 show that thePe

GL value decreases with the increase of the aerated

liquid height L, which means that the degree of liquidmixing increases and thus the spatial distribution ofthe local E

L coefficients becomes more homogeneous.

Conclusions

The effect of the superficial gas velocity ug on the

spatial distribution of the local liquid-phase axial dis-persion coefficients E

L (derived by a graphical method)

was investigated. It was shown that in the bubblyflow regime (u

g = 0.018 m/s) the spatial distribution

of the local EL coefficients is more homogeneous. Once

the superficial gas velocity ug is increased beyond

0.031 m/s (the regime transition velocity Utrans

betweenbubbly and transition flow regimes), the spatial distri-bution of the local E

L coefficients changes consider-

ably and the degree of heterogeneity increases. Fur-thermore, it was shown that at u

g = 0.031 m/s E

L(UZ)

becomes identical to EL(LZ). Based on this finding it

was concluded that at Utrans

= 0.031 m/s occurs the re-gime change from bubbly to transition flow regime.At both lower and higher u

g values E

L(UZ) becomes

systematically higher. It was shown that in the bubblyflow regime the degree of liquid mixing is the same inboth core and annulus regions (E

L(core) ≈ E

L(annulus)),

whereas in the transition flow regime the annulus re-gion is characterized with a higher degree of liquidmixing (E

L(annulus) > E

L(core)).

The effect of the aerated liquid height L on thespatial distribution of the local E

L coefficients was stud-

ied, as well. Three different BBs, viz. L = 0.64 m (shal-low bed), 1.28 m (medium bed) and 2.1 m (deep bed)were examined. The superficial gas velocity u

g was kept

constant at 0.038 m/s. It was observed that the spatialdistribution of the local E

L coefficients is most scat-

tered in the shallow BB (L = 0.64 m). In a medium BBwith an aerated liquid height L = 1.28 m the existenceof a well-developed helical flow structure was detected.It was shown that the graphically determined mean E

L

coefficient (for the overall BB) increases as a functionof both the superficial gas velocity u

g and aerated liq-

uid height L and a useful empirical correlation wasderived. It covers the following range of bed aspectratios: 2.1 ≤ L/D

c ≤ 7.3.

AcknowledgmentDr. Stoyan Nedeltchev expresses his gratitude to the Japan

Society for the Promotion of Science (JSPS) for providing him witha two-year postdoctoral fellowship.

NomenclatureADM = axial dispersion model [—]BB = bubble bed [—]BCR = bubble column reactor [—]D

c= column diameter [m]

EL

= liquid-phase axial dispersion (backmixing) coeffi-cient [m2/s]

ID = inner diameterL = aerated liquid height [m]L/D

c= bed aspect ratio [—]

L0

= clear liquid height [m]LZ = lower zonePe

GL= gas–liquid Peclet number, Eq. (7) [—]

Usmall

= small-bubble velocity [m/s]U

trans= superficial gas velocity at a transition point [m/s]

UZ = upper zoneu

g= superficial gas velocity [m/s]

z = axial position [m]

εg

= gas holdup [—]ε

trans= gas holdup at transition [—]

µL

= liquid viscosity [Pa·s]ρ

G= gas density [kg/m3]

ρL

= liquid density [kg/m3]σ

L= surface tension [N/m]

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