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Biochemical Engineering Journal 39 (2008) 405–429

Review

Oxygen transfer in hydrocarbon–aqueous dispersions and itsapplicability to alkane bioprocesses: A review

K.G. Clarke ∗, L.D.C. Correia

DST-NRF Centre of Excellence in Catalysis (c* change), Department of Process Engineering, University of Stellenbosch, South Africa

Received 13 June 2007; received in revised form 31 October 2007; accepted 25 November 2007

Abstract

Accumulation of alkane by-products fromgas to liquidfuel processespresents an attractive feedstock opportunitywith potentialfor bioconversion

to a wide variety of valuable commodity products. This review highlights the need to address the complexities of the oxygen transfer rate andoverall volumetric oxygen transfer coefficient (K La) in hydrocarbon bioprocesses so that this potential can be realised.

Three markedly different K La behavioural trends have been identified in hydrocarbon–aqueous dispersions and characterised according to the

hydrocarbon type and concentration, operating conditions and geometric constraints. A fundamental conceptual understanding of the mechanisms

which define the exact behaviour of K La in response to changes in turbulence and fluid properties is provided. Further, the behaviour is quantified

in terms of the parameters which underpin this response viz. bubble diameter, gas–liquid interface rigidity, gas hold up, surface tension, viscosity

and diffusivity.

Consideration is given to existing predictive correlations for interfacial transfer area, bubble diameter, gas hold up, oxygen transfer coefficient

and K La. It is envisaged that through the elucidation and quantification of the parameters which shape the behaviour of K La, these correlations may

be successfully extended to predict the complex behavioural K La trends in hydrocarbon-based bioprocesses.

© 2007 Elsevier B.V. All rights reserved.

Keywords: Alkane bioconversion; Aerobic processes; Gas–liquid transfer; Oxygen transfer; Agitation; Fluid properties

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

1.1. Alkanes as an attractive feedstock opportunity for bioconversion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

1.2. Adequacy of oxygen supply to alkane-based bioprocesses . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407

2. Oxygen transfer rate and overall volumetric oxygen transfer coefficient in hydrocarbon–aqueous dispersions . . . . . . . . . . . . . . . . . . . . . 408

2.1. Oxygen solubility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 408

2.2. Trends in overall volumetric oxygen transfer coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409

3. Factors influencing overall volumetric oxygen transfer coefficient in hydrocarbon–aqueous dispersions . . . . . . . . . . . . . . . . . . . . . . . . . . 412

3.1. Influence of turbulence on interfacial area and oxygen transfer coefficient. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

3.1.1. Influence of turbulence on interfacial area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

3.1.2. Influence of turbulence on oxygen transfer coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

3.2. Influence of fluid properties on interfacial area and oxygen transfer coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

3.2.1. Influence of fluid properties on interfacial area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4193.2.2. Influence of fluid properties on oxygen transfer coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

4. Prediction of the overall volumetric oxygen transfer coefficient and oxygen transfer rate in hydrocarbon–aqueous dispersions . . . . . . 421

5. Concluding remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425

∗ Corresponding author at: Department of Process Engineering, University of Stellenbosch, Private Bag X1, Stellenbosch 7602, South Africa.

Tel.: +27 21 8084421; fax: +27 21 8082059.

E-mail address: [email protected] (K.G. Clarke).

1369-703X/$ – see front matter © 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.bej.2007.11.020

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406 K.G. Clarke, L.D.C. Correia / Biochemical Engineering Journal 39 (2008) 405–429

Nomenclature

a gas/liquid interfacial area per unit volume

(m2 /m3)

A function of flow index {280(n +1)/

39(3/2)2}1/(n+1)

As area of sieve plate (m2

)C constant

C a additive concentration (mol/L)

C G concentration of the solute in the gas phase

(mol/m3)

C N carbon number

C o concentration of dissolved oxygen in bulk liquid

(mol/m3)

C o,sat saturation concentration of dissolved oxygen

(mol/m3)

Crk 2 / σ parameter of bubble coalescence proposed by

Marrucci [145]

C s average solid concentration gas-free slurry

(ρSεS /(εL + εS)) (kg/m3)

C x biomass concentration (g/L)

d b gas bubble diameter (m)

D32 Sauter mean diameter (m)

Dd inner diameter of draught tube (m)

DG gas phase diffusivity (m2 /s)

Di impeller diameter (m)

DL liquid phase diffusivity (m2 /s)

DS orifice diameter (m)

Dt reactor/column diameter (m)

E t total power input (W)

g gravitational constant (m2 /s)

H Henry’s law constant (Pa m3 /mol) H t dispersion height (m)

H WO partition coefficient of oxygen in water–oil sys-

tem

L length parameter (m)

k consistency index in a power law model (Pa s)

k e local mass transfer coefficient (m/s)

k 1 −(dσ /dC a)(3V sld b /4V B)/(d b RT /2)

K L liquid phase oxygen transfer coefficient

(m/s)

(K L)GO K L through the hydrocarbon film surrounding the

gas bubbles (m/s)

(K L)GW K L through the aqueous film surrounding the gasbubbles (m/s)

(K L)OW K L through the aqueous film surrounding the

hydrocarbon droplets (m/s)

K La overall volumetric oxygen transfer rate (s−1)

K LaGW K La through the aqueous film surrounding the gas

bubbles (s−1)

K LaOW K La through the aqueous film surrounding the

hydrocarbon droplets (s−1)

K Lamax maximum overall volumetric oxygen transfer rate

(s−1)

M {(εGT,o / GH,o)− 1}at U GC

M v molecular volume (m3 /mol)

n flow index in a power law model

N impeller speed (rpm)

N G number of holes in gas distributor

N s number of holes on sieve plate

N VD Van Dierendonck speed (rpm)

OTR oxygen transfer rate (mg/L s) po partial pressure of oxygen (Pa)

P power dissipated by impeller (W)

P / V power per unit volume of liquid phase (W/m3)

Pe / V effective power per unit volume of liquid phase

(W/m3)

q height of the agitator blades (m)

Q volume air per volume liquid per minute (vvm)

QG gassed volumetric flow rate (m3 /s)

R universal gas constant (Pa m3 /mol K)

t time (s)

T absolute temperature (◦C)

T +

dimensionless time period

U G gas velocity based on cross section of column and

based on average static pressure in column (m/s)

U GC gas velocity where maximum value of

{(εGT,o / εGH,o)− 1} is observed (m/s)

V volume of liquid (m3)

V B bubble rise velocity (m/s)

V D drift flux (m/s)

V gel volume of gels (m3)

V L superficial liquid velocity (m/s)

V s superficial gas velocity (m/s)

V s mean superficial gas velocity at H t /2 (m/s)

V sl slip velocity (m/s)

V t terminal gas bubble velocity in free rise (m/s) X n aqueous phase xanthan concentration (kg/m3)

Greek letters

α, β & γ exponent constants

αr apparent yield stress to shear stress ratio

δN nozzle diameter (m)

ε power rate per unit mass (W/kg)

εG gas holdup; fraction of total volume of aerated

liquid

εGH,o gas holdup for heterogeneous flow regime

εGT,o gas holdup for transition regime

εL

liquid holdup

εS solid holdup

εS/L V gel /(Vgel + V) = partical concentration

λ characteristic material time (s)

μa apparent viscosity (Pa s)

μc continuous phase viscosity (Pa s)

μd dispersed phase viscosity (Pa s)

μG gas viscosity (Pa s)

μL liquid viscosity (Pa s)

νL kinematic viscosity of liquid phase (m2 /s)

Π ∞ surface pressure, −C a(dσ /dC a)

ρa density of air at operating conditions (kg/m3)

ρd density of dispersed phase (kg/m3)



K.G. Clarke, L.D.C. Correia / Biochemical Engineering Journal 39 (2008) 405–429 407

ρg gas density (kg/m3)

ρL liquid density (kg/m3)

ρS solid density (kg/m3)

φ volume fraction of dispersed phase

φW volume fraction of aqueous phase

φWO water to oil phase volume ratioσ surface tension (mN/m)

1. Introduction

1.1. Alkanes as an attractive feedstock opportunity for

bioconversion

Gas-to-liquid and solid-to-liquid fuels processes are expand-

ing globally, resulting in an accumulation of associated alkane

by-products. Currently, alkanes are marketed at their fuel value,

but increasingly have been viewed as an exciting feed stock opportunity for the production of a broad range of commod-

ity products. In particular, attention has been focused on the

potential of alkane feed stocks for commercial biotechnology

ventures. The large range of bacteria and fungi which can

efficiently biofunctionalise these hydrocarbons under moderate

temperatures and pressures, and the considerable variety of fine

chemicals and versatile chemical intermediates which can be

produced, make the bioconversion route exceptionally attrac-

tive [1–3]. Chemicals which have been successfully produced

biologically from alkane substrates include amino acids, organic

acids, carbohydrates, lipids, nucleic acids, vitamins, enzymes,

co-enzymes and antibiotics [2], polyhydroxyalkanoates [4–6],

biosurfactants [7] and dioic acids [8,9]. Developments in genet-

ically modified organisms which carry out these bioconversions

[10,11] f urther promote the biological route as an option with

extensive commercial potential.

In addition to itswideranging suitability as a substratefor bio-

products in general, the alkane moiety confers specific process

advantages. Alkanes promote the accumulation of hydropho-

bic products (e.g. biosurfactants), products which require an

enhanced pool of acetyl-CoA as precursor (e.g. co-enzyme

Q) and products which are converted directly from the alkane

molecular structure and cannot be produced from a carbohy-

drate substrate alone (e.g. dioic acids, polyhydroxyalkanoates)

[2]. Moreover, the immiscible nature of the alkane substrateprovides prospects for in situ extraction of products that are

preferentially soluble in the organic phase. This is particularly

advantageous for processes in which the microbial growth is

inhibited by the product formed. For instance, in situ extraction

was used to decrease the alcohol concentration around the cell

in the aqueous phase [12–14].

These considerations, together with the numerous microor-

ganisms well capable of converting alkanes to valuable products,

ranks biofunctionalisation of alkanes as a leading route to alkane

conversion, and further, emphasises the need to address engi-

neering complexities associated with process operation, so that

its potential can be optimised.

1.2. Adequacy of oxygen supply to alkane-based

bioprocesses

Current interest in the development of alkane-based biopro-

cesseshas raised thequestion of an adequate supply of oxygen in

these media. Sufficient oxygen to satisfy the organisms’ demand

is crucial in any aerobic bioprocess if successful process oper-

ation is to be realised. Further, the role of the oxygen transfer

rate in ensuring optimal yields and productivities becomes pro-

portionately more important as the scale of operation increases

and a change in the limiting regime from kinetic to transport

control is likely [15]. Accordingly, the oxygen transfer rate has

traditionally been cited as the key criterion in the design and

scale up of aerobic bioprocesses [16].

In alkane-based bioprocesses, the difficulty in supplying

adequate oxygen is exacerbated by the deficiency of oxy-

gen in the molecular structure of the substrate. This means

that the oxygen requirement has to be met solely by trans-

fer to the culture, contrary to carbohydrate-based bioprocesses

where the substrate supplies approximately 66% of the oxy-gen demand [1,17]. The proportionately higher requirement for

oxygen transfer, relative to carbohydrate processes, remains a

common feature of alkane metabolism and is likely to influ-

ence all alkane bioprocesses, irrespective of the chain length of

the alkane. This has been known since early studies showed

that the oxygen requirement for equivalent yeast growth on

hydrocarbon was almost triple that on carbohydrate [17–19].

A 2.5-fold higher oxygen requirement per unit of biomass

of Candida petrophilum for growth on n-hexadecane relative

to growth on glucose provides further support [20]. Simi-

larly, a 2.5-fold higher oxygen requirement was evident for

Pseudomonas oleovorans growing on octane compared with Escherichia coli growing on glucose at the same specific growth

rate [21].

The importance of an adequate oxygen transfer rate in

hydrocarbon-based bioprocesses for the enhancement of the

organisms’ potential for biofunctionalisation has been widely

recognised. The oxygen transfer rate, and especially the overall

volumetric oxygen transfer coefficient (K La), have been exten-

sively documented in hydrocarbon-based systems. Nonetheless,

the response of K La to changes in fluid dynamics and fluid

properties in hydrocarbon–aqueous dispersions is still not well

understood.

Further, the prediction of K La in hydrocarbon–aqueous dis-

persions is complex. This highlights the importance of thedevelopment of a fundamental understanding of the behaviour

of K La in these systems, and the identification and quantification

of the parameters which underpin this behaviour so that exist-

ing predictive models may be successfully extended to provide

reliable estimates of K La for hydrocarbon bioprocesses.

This review focuses on the oxygen transfer rate and K La

in hydrocarbon–aqueous dispersions and provides a basis for

the development of a knowledge platform for oxygen transfer

in alkane-based bioprocesses. Three types of K La behavioural

trends in hydrocarbon–aqueousdispersions have beenquantified

over a wide range of operating conditions, reactor geometries

and hydrocarbon types and concentrations.




The keyfactors whichunderpin these behavioural trends have

been identified and their relative impact on oxygen transport in

these systems has been assessed. Particular attention has been

given to the influence of hydrocarbon on bubble diameter, gas

hold up, gas–liquid interfacial transfer area and liquid phase

oxygen transfer coefficient. Finally, consideration is given to

existing models and how these could be modified or extrapo-

lated to predict K La for the design, operation and scale up of

hydrocarbon-based bioprocesses.

2. Oxygen transfer rate and overall volumetric oxygen

transfer coefficient in hydrocarbon–aqueous dispersions

The two-film model defining oxygen transfer in aqueous sys-

tems (Eq. (1)) is well documented [22,23]

OTR= dCo

dt = KLa(Co,sat − Co) (1)

Here the oxygen transfer rate is quantified in terms of the con-

centration driving force, or oxygen solubility, and K La. K La, acomposite parameter comprising the liquid phase oxygen trans-

fer coefficient (K L) and the gas–liquid interfacial area per unit

volume (a) is frequently highlighted as the key criterion in

design, operation and scale up of aerobic bioprocesses [24]. In

aqueous systems, K La is predicted according to Eqs. (2) or (3)

for stirred tank reactors (STRs) and bubble columns, or airlift

reactors, respectively [25] where the empirical constants α, β

and γ vary with physicochemical properties [26–28] and scale

[24].

KLa

=α

P

V β

V γ s (2)

KLa = αV βs (3)

2.1. Oxygen solubility

Typically, oxygen solubilities in aqueous solutions are usu-

ally less than 10 mg/L [29]. On the other hand, oxygen

solubilities in hydrocarbon–aqueous dispersions are signifi-

cantly higher, due to the increased saturation level of oxygen

in pure hydrocarbon. There is, however, some lack of consensus

in the literature with respect to the actual values of the oxygen

solubility in hydrocarbons (Fig. 1). For instance, oxygen solu-

bility in n-C12 alkane is generally reported as 260 mg/L [30],324 mg/L [31] and 305 mg/L [32] at similar temperatures. Oxy-

gen solubility in the longer chain n-C16 alkane was reported

as 322 mg/L [33], 190 mg/L [30], 340 mg/L [29], 255 mg/L

[32] and 271 mg/L [31] over a temperature range of 22–30 ◦C.

Nevertheless, when considering alkanes of chain lengths char-

acteristically employed in bioprocesses, the oxygen solubility

in the pure alkanes is more than 20 times that in water. At

chain lengths of n-C8, possibly the level below which substrate

inhibition would make any bioprocess impracticable, a 40-fold

increase in oxygen solubility over that in water is reported.

It should be noted, however, that the oxygen solubility in

n-dodecane does not follow the general trend. While oxygen

Fig. 1. Solubility of oxygen in pure alkanes at 1 atm and 22–30◦C. () Ju and

Ho [29]; () Ho et al. [33]; () Makranczy et al. [30]; (᭹) Blanc and Batiste

[32]; (♦) Wilcock et al. [34]; () Thomsen and Gjaldbaek [42]; () Hesse et al.

[31]; () Rols et al. [35], Jia et al. [36] and Galaction et al. [38].

solubility in this chain length had been reported to lie between

260 mg/L and 324 mg/L, at temperatures ranging from 10 ◦C to40 ◦C [30–32,34], more recent studies have reported the solu-

bility of a commercially purchased n-dodecane as 54.9 mg/L at

35 ◦C [35–41]. It is not known why the latter should differ so

widely from the solubility data reported in the earlier literature

studies.

In hydrocarbon–aqueous dispersions, the effect of increased

oxygen solubility in hydrocarbons on the oxygen transfer rate

may be considerable. Assuming applicability of the volumetric

relationship for oxygen solubility in hydrocarbon–aqueous dis-

persions proposed by Ju and Ho [29], the increase in oxygen

solubility of a 10% n-hexadecane–aqueous suspension may be

three to fourfold that in an aqueous solution. This phenomenonhas prompted the modification of aqueous carbohydrate-based

media to carry more oxygen by hydrocarbon addition, thus ele-

vating the maximum oxygen transfer attainable. Ho et al. [33]

were one of the first groups to propose the use of hydrocarbon

droplets as an enhancer of oxygen transfer in carbohydrate-based

bioprocesses. Oxygen transfer has been successfully enhanced

in Aspergillus niger cultures through addition of n-dodecane,

n-hexadecane and soybean oil during glucose oxidase produc-

tion [43] and through addition of n-dodecane during citric acid

production [44]. Oxygen transfer in Saccharomyces cerevisiae

cultures has similarly benefited from addition of n-C12-16 alka-

nes, n-dodecane and perfluorocarbon [36,45].

Although the strategy of using hydrocarbons to function asoxygen vectors has wide appeal, and has been used to good

effect in bioprocesses utilising carbohydrate substrates, this does

not imply that bioprocesses which utilise hydrocarbon sub-

strates are invariably unlikely to be oxygen limited. Firstly,

the hydrocarbon-based process is compromised by the defi-

ciency of oxygen in the molecular structure which leads to

a higher requirement for oxygen transfer, relative to that in

carbohydrate-based bioprocesses in which oxygen is also con-

tributed directly by the substrate. Secondly, the hydrocarbon

substrate may depress K La. Regimes of depressed (less than

that in water) and enhanced (greater than that in water) K La have

been defined according to agitation rate and alkane concentra-




tion [46]. In regions of depressed K La, the resultant variation in

oxygen transfer rate will depend directly on the relative magni-

tudes of the K La and the transfer driving force (i.e. the oxygen

solubility), andindirectly on theprocess conditions which define

these magnitudes. Under conditions of depressed K La, the ele-

vated oxygen solubility does not always compensate for the

increased requirement for oxygen transfer. Clarke et al. [46]

have reported a plateau in the oxygen transfer rate from 10%

n-C12-13 alkane, when depressed K La was observed, despite an

increase in the oxygen solubility with increasing alkane con-

centration. This study also showed that at lower agitation rates,

K La depression was more likely, suggesting that the increased

solubility was less likely to offset the depression of K La at the

lower agitation.

On the other hand, in regions of enhanced K La, the higher

K La coupled with the increased oxygen solubility in the hydro-

carbon doubly benefits the oxygen transfer rate. Ho and Ju [47]

report both an increase in the K La and the oxygen solubility

in n-hexadecane relative to water. Under these conditions, the

increased oxygen transfer rate is likely to compensate for thegreater requirement for oxygen transfer.

Consequently, despite the superior oxygen solubility in

hydrocarbons, and the effective use of hydrocarbons as oxy-

gen vectors in carbohydrate-based bioprocess, oxygen transfer

may still be suboptimal in hydrocarbon-based bioprocess. These

considerations underline the critical importance of the quantifi-

cation of K La behaviour in hydrocarbon–aqueous dispersions,

andthe development of a model to predict optimal transport rates

for the successful operation and scale up in these systems.

2.2. Trends in overall volumetric oxygen transfer

coefficient

In aqueous systems, where the behaviour of K La is well

understood, the quantification and prediction of the oxygen

transfer rate has been established. The behaviour of K La in

hydrocarbon containing systems, on the other hand, is consider-

ably less well understood, notwithstandingthe numerous studies

conducted in hydrocarbon–aqueous dispersions in systems with

differing reactor and impeller geometries, over a wide range of

operating conditions, hydrocarbon moieties and concentration

ranges.

These studies have invariably shown that the hydrocarbon

fraction impacts markedly on K La, although paradoxically, not

always in the same manner (Tables 1a–1c). The manner in whichthe hydrocarbon affects K La differed widely, and depended on,

inter alia, the reactor type and the fluid properties of the aqueous

and hydrocarbon phases. Three distinct trends in K La behaviour

in hydrocarbon–aqueous dispersions can be defined. Firstly, a

K La trend with an increase on hydrocarbon addition to a max-

imum value, and subsequently, a decrease on further addition

of hydrocarbon, has been firmly established (type 1 behaviour).

Secondly, a K La increase on hydrocarbon addition but with no

subsequent decline has also been frequently reported (type 2

behaviour). Thirdly, no increase in K La has with been observed

with hydrocarbon addition, with K La either being maintained

constant or decreasing (type 3 behaviour).

Those studies which exhibit type 1 behaviour, report a char-

acteristic K La peak associated with a specific system-dependent

hydrocarbon concentration (Table 1a). In STRs, where the aque-

ous phase comprised either pure water or a salt solution, peak

K La was observed at 5% n-C12–13 alkane [46], 10% n-C10–13

alkane [48], 10% n-hexadecane [49], 1% silicone oil and 2%

soybean oil [50].

Similar trends were observed in this reactor type when the

aqueous phase contained cells. K La peaks were reported in S.

cerevisiae cultures at 1% or 2% lard oil, depending on the agi-

tation rate, and 1% olive oil [51]. In E. coli cultures, peak K La

occurred at 30% PFC-40 [52]. Aerobacter aerogenes cultures

exhibited peak K La at 23% n-dodecane [35] and 15% soybean

oil [53].

Type 1 behaviour was also observed in airlift and bub-

ble column reactors in both cell-culture and cell-free systems.

K La peaks were reported in S. cerevisiae cultures at 3% n-

dodecane [36], 2% PFC-40 [36] and 4% n-C12–16 [45], and

in A. niger cultures, at 5% n-dodecane [37]. In cell-free bub-

ble columns K La peaks were reported at 0.5% hexanol [54]and 6% silicone oil [55]. A K La peak was even reported in

soybean oil–water dispersion at 2% in a shake flask culture

[56].

Although a hydrocarbon concentration associated with peak

K La can be identified, this concentration varies considerably

between studies. For instance, in STRs, the hydrocarbon con-

centration associated with the K La peak was lower (1–2%) in

silicone oil [50], soybean oil [50], lard oil [51] and olive oil [51]

than that (5–30%) in n-C12–13 [46], n-C10–13 [48], n-hexadecane

[49], PFC-40 [52] and n-dodecane [35]. In the studies where the

peak occurred at a lower hydrocarbon concentration, the viscos-

ity of the hydrocarbon phase was relatively high at 5–10 cP forsilicone oil [55,64], 41 cP for soybean oil [53], 53 cP for lard oil

[51] and 58 cP for olive oil [51]. In the studies where the peak

occurred at a comparatively higher hydrocarbon concentration,

the viscosity of the hydrocarbon phase was about a order of

magnitude lower, viz. 3 cP for n-hexadecane [55,64,65], 3–4cP

for PFC-40 [52,65] and 1.3–1.5 cP for n-dodecane [55,59,65],

with the viscosities of n-C12–13 and n-C10–13 likely to be in a

similar range. This suggests that the hydrocarbon concentration

at which the K La will peak depends on the dispersion viscosity

such that an increased dispersion viscosity will tend to decrease

the K La, resulting ina decline in the K La at a lower concentration

of hydrocarbon.

It is unlikely, however, that a variation in fluid propertiesbrought about by hydrocarbon addition is the sole contributing

factor accounting for the discrepancy in hydrocarbon concentra-

tions at peak K La. Clearly, system geometry also plays a major

role. In STRs, K La was observed to peak at both 2% soybean oil

and 15% soybean oil [53], notwithstanding the same viscosity

of 41 cP. Further, K La peaked at significantly lower hydrocar-

bon concentrations in column reactors than in STRs with the

same hydrocarbon type. For example, when comparing cell cul-

tures in different reactor configurations, K La peaked at 3–5%

n-dodecane [36,37] and 2% PFC-40 [36] in column reactors,

compared with 23% n-dodecane [35] and 30% PFC-40 [52] in

STRs.




Type 2 behaviour was also demonstrated in numerous studies

(Table 1b). Here one of two trends was evident. Either K La

continued to increase up to the last hydrocarbon concentration

examined, or increased to a maximum value at which a plateau

was reached. In both of these trends, no K La peak was observed.

The absence of a peak K La may be explained in part by the lack

of K La data at hydrocarbon concentrations where the peak value

could conceivably occur.

In the first case, where K La continued to increase to that at the

maximum hydrocarbon concentration examined, it is possible

that the K La peak may yet have occurred at a higher hydro-

carbon concentration where data had not been acquired. These

studies include STR configurations where the maximum K La

was observed at 1% castor oil [51], 20% toluene [57,58] as well

as bubble column configurations where the maximum K La was

observed at 10% n-decane, 10% n-heptane and 10% n-dodecane

Table 1a

Behaviour of K La in aerated hydrocarbon–aqueous dispersions: type 1 behaviour (K La peak)

Reactor type Aqueous phase Hydrocarbon phase Hydrocarbon

concentration (v/v)

Hydrocarbon

concentration (v/v)

at maximum K La

Reference

STR Distilled water n-C12–13 0–20% 5% Clarke et al. [46]

STR Distilled water n-C10–13 0–20% 10% Correia et al. [48]

STR Distilled water n-Hexadecane 0–33% 10% Nielsen et al. [49]

STR 0.2 M Na2SO4 Silicone oil 1–10% 1% Morao et al. [50]

STR 0.2 M Na2SO4 Soybean oil 1–10% 2% Morao et al. [50]STR Saccharomyces cerevisiae Lard oil 0–4% 1–2% Liu et al. [51]

STR S. cerevisiae Olive oil 0–3% 1% Liu et al. [51]

STR Escherichia coli K12 wild type PFC-40 0–40% 30% McMillan and Wang [52]

STR Aerobacter aerogenes NRRL B199 n-Dodecane 0–33% 23% Rols et al. [35]

STR A. aerogenes NRRL B199 Soybean oil 0–30% 15% Rols and Goma [53]

Airlift reactor S. cerevisiae AY-12 n-Dodecane 0–15% 3% Jia et al. [36]

Airlift reactor S. cerevisiae AY-12 PFC-40 0–7% 2% Jia et al. [36]

Airlift reactor Aspergillus niger n-Dodecane 0–14% 5% Jianlong [37]

Tower reactor S. cerevisiae AY-12 n-C12–16 0–8% 4% Jia et al. [45]

Bubble column Distilled water Hexanol 0–1.5% 0.5% Koide et al. [54]

Bubble reactor Distilled water Silicone oil 47V5 0–10% 6% Dumont et al. [55]

500 mL flask Distilled water Soybean oil 0–4% 2% Jia et al. [56]

Table 1b

Behaviour of K La in aerated hydrocarbon–aqueous dispersions: type 2 behaviour (K La increase)


concentration (v/v)

Hydrocarbon

concentration (v/v)

at maximum K La

Reference

STR S. cerevisiae Castor oil 0–1% 1% Liu et al. [51]

STR Carboxymethyl cellulose/salt solutions n-Dodecane 0–20% 20% Cascaval et al. [39]

STR Carboxymethyl cellulose/salt solutions n-Dodecane 0–20% 20% Galaction et al. [38]

STR Distilled water Toluene 0–20% 20% Cents [57]

STR Distilled water Toluene 1–20% 20% Yoshida et al. [58]

Bubble column Distilled water n-Decane 0–10% 10% Kundu et al. [59]

Bubble column Distilled water n-Dodecane 0–10% 10% Kundu et al. [59]

Bubble column Distilled water n-Heptane 0–10% 10% Kundu et al. [59]

Bubble reactor Distilled water n-Hexadecane 0–10% 10% Dumont et al. [55]Bubble reactor Distilled water PFC-40 0–4% 4% Dumont et al. [55]

Bubble reactor Distilled water Silicone oil 0–10% 10% Dumont et al. [55]

STR Carboxymethyl cellulose/salt solutions n-Dodecane 0–20% 10%a Cascaval et al. [39]

STR Carboxymethyl cellulose/salt solutions n-Dodecane 0–20% 10%a Galaction et al. [38]

STR Distilled water Ethanol 0–0.8% 1%a Bi et al. [60]

STR Tap water n-Dodecane 0–10% 1%a da Silva et al. [40]

STR Distilled water/salt solutions n-Dodecane 0–10% 6%a Hassan and Robinson [61]

STR Distilled water/salt solutions n-Hexadecane 0–10% 6%a Hassan and Robinson [61]

STR Distilled water n-Dodecane 0–5% 5%a Wong and Shiuan [24]

STR Distilled water Oleic Acid 0.01–22% 8%a Yoshida et al. [58]

Bubble column Distilled water Toluene 0–10% 10%a Kundu et al. [59]

Bubble column Distilled water 2-Ethyl-1-hexanol 0–10% 10%a Kundu et al. [59]

Bubble reactor Distilled water n-Dodecane 0–10% 6%a Dumont et al. [55]

a Plateau reached.




Table 1c

Behaviour of K La in aerated hydrocarbon–aqueous dispersions: type 3 behaviour (K La decrease or K La constant)


concentration (v/v)

K La constant

or decreased

Reference

STR Distilled water Ethanol 0–0.8% Constant Bi et al. [60]

STR Distilled water PFC-40 0–10% Decreased Cesario et al. [62]

STR Distilled water n-C12-13 0–20% Decreased Clarke et al. [46]

STR Distilled water n-C10-13 0–20% Decreased Correia et al. [48]STR S. cerevisiae Olive oil 0–3% Constant Liu et al. [51]

STR S. cerevisiae Castor oil 0–1% Constant Liu et al. [51]

STR Distilled water n-Hexadecane 0–33% Decreased Nielsen et al. [63]

STR Distilled water n-Hexadecane 0–33% Decreased Nielsen et al. [49]

STR Distilled water Paraffin 1–21% Decreased Yoshida et al. [58]

Bubble column Distilled water Heptanol 0–1% Decreased Koide et al. [54]

Bubble column Distilled water Octanol 0–0.5% Decreased Koide et al. [54]

[59] and 10% n-hexadecane, 4% PFC-40 and 10% silicone oil

[55].

In the second case, where a plateau has been defined, a K La

peak may not have been detected if there were large intervalsbetween data points. For example, da Silva et al. [40] report

a maximum K La at 1% n-dodecane, and essentially the same

value at 10% n-dodecane. However, the lack of data between

1% and 10% n-dodecane means it cannot be said with certainty

that a peak K La would not have been obtained at an intermediate

hydrocarbon concentration.

Nevertheless, the lack of data at critical hydrocarbon con-

centrations does not necessarily account for the absence of the

characteristic K La peak in all cases. In several studies, a K La

plateau was rigorously demonstrated, with no evidence of a

subsequent K La decrease. Moreover, even in studies where a

plateau was not detected, the absence of a peak cannot invari-

ably be attributed simply to insufficient data, as evidenced by the

K La maximum in a dispersion of n-dodecane and carboxymethyl

cellulose (CMC)/salt solution [38,39]. Here, maximal K La was

observed at 20% n-dodecane, the highest concentration exam-

ined, when the dispersion viscosity was 100–330 cP. However,

at a reduced viscosity of 10–40cP, a K La plateau was reached

at 10% n-dodecane.

In addition, K La plateaux where also recognised in water at

6% n-dodecane [61], 6% n-hexadecane [61], 5% n-dodecane

[24] and 8% oleic acid [58] in STRs. In bubble columns, K La

plateaux were similarly documented at 10% toluene and 10%

2-ethyl-1-hexanol [59] and at 6% n-dodecane [55]. As with the

studies in which K La peak was reported, these studies show adependence of the hydrocarbon concentration at which maximal

K La was attained and on the type of hydrocarbon and reactor

configuration used. A maximal K La at 6% n-dodecane both in

a STR [61] and a bubble column [55], however, suggests a less

marked influence of the reactor configuration and operation in

these studies.

In yet other studies, type 3 behaviour occurred, where no

increase in K La was observed, and a decrease often reported

(Table 1c). In STRs this trend may be partly ascribed to a low

agitation rate. Bi et al. [60] reported a constant K La in an aque-

ous ethanol solution at 135 rpm, while at 300–600 rpm, K La

increased to reach a plateau at 1% ethanol. Similarly, Clarke

et al. [46] and Correia et al. [48] report a decrease in K La in

n-C12–13 alkane and n-C10–13 alkane, respectively, at 600 rpm,

although K La peaks at 5–10% were defined at agitation rates

between 800 and 1200 rpm, over the same hydrocarbon concen-tration range. Similarly, Liu et al. [51] document an essentially

K La constant at 200 rpm, while K La increased to 1% olive oil

and castor oil at 400 rpm.

Nielsen et al. [49], on the contrary, showed a decrease in

K La with increasing n-hexadecane to 33% at agitation rates of

600 and 800rpm, and a K La peak at 10% n-hexadecane at the

comparatively lower agitation of 400 rpm. Earlier studies by this

group [63] reported a decreased K La at400 rpm as wellas at 600

and 800 rpm. This suggests that, in addition to lower agitation

rates, K La will be negatively influenced by other parameters.

Certainly, K La behaviour has been influenced by hydrocarbon

type. K L

a was observed to decrease with paraffin addition at an

agitation rate of 500 rpm, but increase with toluene and oleic

acid addition at the relatively lower agitation rate of 350 rpm

[58]. Further support for the influence of hydrocarbon type is

provided by the increased K La with n-hexanol addition, while

n-heptanol and n-octanol addition both resulted in a decreased

K La under the same conditions [54].

Notwithstanding the importance of defining the trend of K La

behaviour with hydrocarbon addition, consideration should also

be given to the absolute value of K La in these systems, relative

to that in the absence of hydrocarbon, i.e. whether hydrocar-

bon addition results in K La depression or enhancement relative

to that in water. Generally, where K La decreases with hydro-

carbon addition, depression is observed and correspondingly,where K La increases with hydrocarbon addition, enhancement

occurs.

The latter, however, does not always hold, and depres-

sion may occur even when K La increases with hydrocarbon

addition. It has been found, in both stirred tank and bubble

reactors, that the addition of hydrocarbon at low concentra-

tions (less than 2.5%) sometimes yields an initial decrease in

K La to below the level attained in the absence of hydrocar-

bon (K La*) (Figs. 2 and 3). A subsequent increase in K La on

further hydrocarbon addition may compensate for the initial

decrease, leading to an enhanced K La at higher hydrocarbon

concentrations (Fig. 2). However, this increase is not invariably




Fig. 2. Depression and subsequent enhancement of overall volumetric oxygen

transfer coefficient by hydrocarbon. () Cents [57], toluene; () Yoshida et al.

[58], toluene; () Dumont etal. [55], n-dodecane; (᭹) Kundu etal. [59], toluene;

(+) Kundu et al. [59], 2-ethyl-1-hexanol.

sufficient to offset the initial decrease, when a depressed K Laresults (Fig. 3). Depression appears to be influenced by both

the agitation and the hydrocarbon moiety; depression occurred

with silicone oil but not n-dodecane [55] and with agitation at

800 rpm but not 1000 rpm or 1200 rpm [48].

The behaviour of K La in these studies suggests that the

fluid properties (as determined by the type and concentra-

tion of the hydrocarbon) as well as the reactor geometry

and operating parameters (especially agitation) strongly influ-

ence K La behaviour in hydrocarbon–aqueous dispersions. It

is likely that these parameters do not act independently, but

that multiple causative factors relate to K La behaviour and fur-

ther, that the predominance of each of these factors varies,depending on the prevailing process conditions. If a predictive

model to define locales of optimum K La is to be developed in

hydrocarbon–aqueous dispersions, it is essential to acquire a

fundamental understanding of the factors which underpin the

behaviour of K La, and the complex interaction of the factors, in

these systems.

Fig. 3. Depression of overall volumetric oxygen transfer coefficient by hydro-

carbon. () Correia et al. [48], n-C10–13; () Dumont et al. [55], silicone oil

47V5; () Dumont et al. [55], silicone oil 47V10; (᭹) Wong and Shiuan [24],

n-dodecane; (+) Yoshida et al. [58], oleic acid.

3. Factors influencing overall volumetric oxygen

transfer coefficient in hydrocarbon–aqueous dispersions

In hydrocarbon–aqueous dispersions, K La is significantly

influenced by turbulence and fluid properties, the extent of this

influence being ultimately defined by the operating conditions

and hydrocarbon type and concentration. Here the influences of

turbulence and fluid properties on interfacial area and K L are

discussed separately; nevertheless, cognisance is taken of their

interactive influence on both these parameters.

3.1. Influence of turbulence on interfacial area and oxygen

transfer coefficient

Turbulence is essentialin promoting oxygen transfer and with

its positive effect both on the interfacial area and K L, is the

key to supplying adequate oxygen. Traditionally, turbulence has

been promoted through increased energy input, as defined by

power input per unit volume (P / V ), increased impeller speed

( N ) or increased aeration rate (V s). Turbulence is often furtherenhanced by the modification of vessel and impeller geometries.

3.1.1. Influence of turbulence on interfacial area

The influence of turbulence on interfacial area has been doc-

umented in a wide variety of fluids and over a broad range

of operating conditions in systems with differing reactor and

impeller geometries. Empirical models defining the contribu-

tion made by turbulence, through the parameters P / V , N and V s,

to the interfacial area are listed in Table 2.

These correlations exhibit a range of dependencies of inter-

facial area on P / V , N and V s. The exponents of P / V varied from

a low of 0.25 in water [70] to highs of 0.9 and 1.06 in elec-trolyte solutions [69,71,72] and electrolyte/polymer solutions

[82]. In fluids containing hydrocarbons, the exponent was rela-

tively small at 0.4 [26,75]. Similarly, a wide range of exponents

of N and V s is reported, with exponents of N from 0.7 in an

electrolyte solution [66] to 2.55 in a polymer solution [79] and

exponents of V s from 0.06 in a polymer solution [79] to 0.9 in a

hydrocarbon solution [27].

The influences of P / V , N and V s on interfacial area are, how-

ever, not independent. When comparing the interaction of P / V

and V s for instance, the influence of V s is generally less at high

P / V [71,72,76,78], than at comparatively lower P / V [70]. Conse-

quently, whenassessing the influence of turbulence on interfacial

area, the interaction between P / V , N and V s, as well as theirindividual influences, needs to be considered.

The positive exponents on P / V , N and V s in these correla-

tions nevertheless confirm the beneficial impact of turbulence

on the interfacial area in all fluids and systems examined. Turbu-

lence increases the interfacial area available for transfer through

increased shear which modifies the coalescence and break up of

the gas bubbles, thereby reducing the bubble size. The reduced

bubble size results in an increased residence time of the gas in

the liquid, thus concomitantly increasing the gas hold up. The

effect of bubble size and bubble hold up on interfacial area is

defined by Eq. (4) which relates interfacial area per unit volume

to the volume-surface mean diameter, or Sauter mean diameter



Table 2

Empirical correlations for the prediction of interfacial area

System Operating conditions Liquid phase(s) Equation

STR N = 200–1200rpm; V s = 0.305–0.61 cm/s Aqueous: ethanol, methanol, i-propanol,

n-butanol, ethylene glycol, CCl4; ethyl

acetate, nitrobenzene; toluene

a = 1.44

(P/V )0.4ρ0.2

L

σ 0.6 V sV t

0.5

Sieve plates V s = 6.1–60.1 cm/s Aqueous: aliphatic alcohols, glycol a = 0.38V sV t

0.775 V sρL(N s/As)DsμL

0.125 ρLgDsσ

1/3

STR N = 60–400 rpm;

V s = 0.1693–0.762cm/s

Aqueous:

NaOH

a ∝ (NDt)1.1V 0.75

s

STR a ∝ (NDt)0.7−0.9

STR N = 255, 325 & 455rpm; QG =0.68m3 /h Aqueous: NaCl, sodium dodecyl

sulphate, dow corning antifoam C

a∝ N 1.75

Bubble column V s = 0.925–4.28 cm/s Aqueous: glycol, methanol, CCl4 a = 13Dt

gD2

tρL

σ

0.5gD3

t

v2L

0.1

ε1.13G

STR N = 800–2000rpm; V s = 0.457 cm/s Aqueous: Na2SO3, KOH, K2CO3 a∝ (P / V )0.89–1.06

STR N = 250–500rpm; V s =0.634–1.27cm/s Aqueous a = 593(P/V )0.25V 0.75s

STR N = 732–1900rpm; V s =0.37–1.11cm/s Aqueous: Na2SO4; KOH; KCl; K2SO4 a ∝ (P/V )0.85−0.9V 0.39s

STR N = 732–1900rpm; V s =0.37–1.11cm/s Aqueous: Na2SO4, KOH, KCl, K2SO4 a ∝ (P/V )0.85−0.9V 0.39−0.42s

Review a = 3.00 ρLg

σ 1/2QG

NV 5/12 N 2D4

t

gqV 2/30.658 ρLd bN

σV 2

Bubble column V s = 0–20 cm/s Aqueous: CMC a = 4.65× 10−2V 0.51s μ−0.51

L

STR N = 480–1800rpm; V s = 1–5 cm/s Cyclohexane a = 1.44

(P/V )0.4ρ0.2

L

σ 0.6

V sV t

0.5 EtP

ρg

ρa

0.16

STR N = 400–850rpm; QG = 0.12–0.48 m3 /h Aqueous: NaCl a ∝ (P/V )0.62V 0.45s

Bubble column V s = 2–7 cm/s Aqueous: CMC 7H4,

carboxypolymethylene;

a = 6C

ε0.4ρ0.6

L

σ 0.6

ε1−α

G

μdμc

0.25

Stirred slurry reactor P / V = 300–10000 W/m3; V s = 0.34–4.6cm/s Aqueous: CMC, Na2SO3-glass beads a = 2.87(P/V )0.76V 0.34s μ−0.18

L

a = 3.17(P/V )0.39V 0.48s μ−1.11

L

STR N = 750–1500rpm; QG = 0.12–7.26 m3 /h Aqueous a = 0.14N 0.77Q0.28G

Aqueous: PGME a = 1023.9N 2.55Q0.06G σ −15.4

STR N =180rpm; QG = 5.904–24.7 m3 /h Aqueous: NaCl a ∝ N 0.85(P/V )0.3V 0.4−0.5s

Prediction models a ∝ N 1.6(P/V )0.5V 0.65s μ−0.3L

STR N = 0–1130 rpm; V s = 18–54 cm/s Aqueous: Na2SO3 a∝ (P / V )0.863

Aqueous: Na2SO3, Sokrat a∝ (P / V )0.913

Aqueous: Na2SO3, CMC TS.5 a∝ (P / V )0.632

Aqueous: Na2SO3, CMC TS.20 a∝ (P / V )0.689

Aqueous: Na2SO3, ocenol a∝ (P / V )0.492

Aqueous: Na2SO3, PEG 100 a∝ (P / V )0.903




( D32), through the fractional gas hold up (εG).

a = 6εG

D32(4)

Empirical equations relating turbulence to D32 (Table 3) and

εG (Table 4), similar to those relating turbulence to interfacial

area, have been proposed.

Turbulence, induced through P / V and N , both resulted

in decreased d b or D32. d b or D32∝ (P / V )−0.4 has been

found to be similar in systems containing hydrocarbons

[26,83,84,85,89,91,92] and electrolytes [84]. Alves et al. [95]

found the effect of P / V on D32 to differ in the turbine and bulk

regions of the reactor. In electrolyte solutions (or noncoalescing

systems) D32 correlated with (P / V )−0.52 in the turbine region

and (P / V )−0.37 in the bulk region, which corresponds well with

the hydrocarbon and electrolyte systems in which a correlation

with (P / V )−0.4 was observed. On the other hand, D32 was pro-

portional to (P / V )−0.24 in the turbine region and (P / V )−0.14 in

the bulk region suggesting a relatively greater influence of tur-

bulence on D32 in a hydrocarbon system relative to an aqueoussystem.

The effect of agitation on D32 varied, with exponents of N

of −0.76 to −1.4 [96] in hydrocarbon containing systems com-

pared with −0.1 to −0.3 in electrolyte solutions [66]. Overall,

increased agitation shifted the bubble size distribution towards

a smaller D32, and further, improved the uniformity of bubble

size distribution, particularly at the lower gas flow rates [114].

The mechanism by which N influences D32 is attributed to the

increase in entrainedgas bubbles whichreach the impeller blades

[100].

Hu et al. [96] used various dispersed phases to bring about

different flow regimes in a stirred reactor under constant aerationand agitation. Addition of decanol, diethylene glycol and cyclo-

hexanol as solutes resulted in D32 proportional to N −1.4D−2.8i .

Use of butanol and propanol caused turbulent flow resulting in

D32 proportional to N −0.76D−1.52i , i.e. with a comparatively

lesser dependence of bubble size on impeller speed.

The influence of agitation on D32, however, reaches a maxi-

mum after which D32 remains constant with further increases in

agitation. Calderbank [26] and Westerterp et al. [115] showed

that, in their system, D32 reached a constant minimum value

between 1200 rpm and 2300 rpm. The value of the minimum

D32 has been found to be dependent on the solute. Bi et al.

[60] observed a minimum D32 around 1.8 mm with pure water,

whereas, the addition of more than 1 g/L ethanol lowered thisvalue to 0.8 mm. An analogous influence of agitation on inter-

facial area has been observed where N corresponding to the

maximum interfacial area correlated well with that correspond-

ing to the minimum D32 [28,75,116].

The effect of V s on D32, on the contrary, is generally opposite

to that of P / V and N . D32 ∝ V 0.1−0.4s holds in stirred agitators

[90], flotation cells [88] and bubble columns [87]. Only Akita

and Yoshida [68], working in three different bubble columns,

found the bubble size to decrease with increasing V s. The

increase in D32 with increased V s is a probable consequence of

the reduction in turbulence as aeration reduces the mechanical

power dissipation in the liquid through the growth of gascavities

behind the impeller blades, and through the dampening of veloc-

ityfluctuationsin thefluid [114]. In addition, a higher probability

of bubble collision and coalescence because of greater gas hold

up is likely to lead to an increase in D32 [114,117,118].

In contrast, gas hold up is positively influenced by increased

V s (Table 4), which probably accounts for the increase in inter-

facial area with increased V s, despite the frequent decrease

in D32. Hold up is enhanced in STRs with both increasing

P / V and V s [26,70,76,85,100,109,110,111]. In these reactors,

similar dependencies on P / V and V s were reported in water

[70,100,111], electrolyte solutions [76,110], cyclohexane [85]

and in hydrocarbon–aqueous dispersions [26,109]. The expo-

nents of P / V and V s varied from 0.25 to 0.85 and 0.2 to

1 respectively, over widely differing impeller geometries and

scale, suggesting a lesser role of system geometry in defining

hold up. The dependence on P / V (exponent 0.8) in an air-lift

reactor is by comparison, considerably larger [112]. Increased

hold up similarly results from increased agitation [66,98,103]

and exponents of N ranging from 0.6 to 1.04 have been reported.

The improved gas hold up, through increased P / V and N ,results from an increased dispersion of small bubbles within

the system, with slower bubble rise velocities [79]. The longer

residence time of smaller bubbles allows more time for the oxy-

gen to transfer to the liquid phase [116]. On the other hand, a

larger V s increases the bubble collision frequency leading to a

higher coalescence [117] with correspondingly larger bubbles.

The preferential release of larger bubbles may result in greater

proportion of smaller bubbles in the fluid and consequently, a

larger gas hold up.

In bubble columns, the fluid dynamic characterization has a

significant effect on the operation and performance. Here the

exponents depend strictly on the flow regime prevailing in thecolumn. Three types of flow regimes are commonly observed

and are classified according to the prevailing V s, viz. the homo-

geneous (bubbly flow), the heterogeneous (churn-turbulent) and

the slug flow regimes. The bubbly flow regime and churn turbu-

lent regimes are observed at low and high V s, respectively. The

slug flow regime is of lesser importance, being limited solely to

small diameter columns at high V s. The transition from bubbly

to churn-turbulent flow depended, inter alia, on the liquid phase

and reactor type. Transitional phases were reported at V s values

of 0.1–0.2 m/s in a slurry bubble column with an paraffin oil-

silica suspension [119], 0.2–0.7 m/s in water and cyclohexane

[120] and 0.08–0.2 m/s in water, tetradecane, paraffin and tellus

oil [121].The bubbly flow regime is characterised by relatively small

uniform bubbles sizes and slow rise velocities. There is neg-

ligible bubble coalescence or break up, thus bubble size is

essentially dictated by the sparger design and system proper-

ties. Generally it is found that hold up in this regime increases

with increasing V s with the exponent varying from 0.7 to

1 in both electrolyte solutions and hydrocarbon dispersions

[99,105,107,113]. Kelkar et al. [104] reported an exponent of

0.58 in alcohol dispersions but show that hold up increased with

increasing carbon chain length.

The churn-turbulent regime exhibits unsteady flow patterns

with enhanced turbulent motion of the bubbles and high liq-



Table 3

Empirical correlations for the prediction of bubble diameter


Theoretical models D32 = 2 σ 0.6

(P/V )0.4ρ0.2L

STR N = 200–1200rpm; V s = 0.305–0.61 cm/s Aqueous: ethanol, methanol, i-propanol,

n-butanol, ethylene glycol, CCl4, ethyl

acetate, nitrobenzene, toluene

D32 = 4.15

σ 0.6

(P/V )0.4ρ0.2L

ε0.5

G + 0.09

STR N = 60–400 rpm;

V s = 0.1693–0.762cm/s

Aqueous:

NaOH

D32 ∝ N −0.3

STR D32 ∝ N −0.1

STR N = 30–600 rpm; V s =0.36–0.91cm/s Aqueous: NaCl, Na2SO4 d b = 4.25 σ 0.6

[(P/V )(1/(1−εG))]0.4ρ0.2L

ε0.5G

Bubble column V s = 0 .925–4.28 c m/s Aqueous: glycol, methanol, CCl4D32Dt

= 26

gD2

tρL

σ

−1/2gD3

t

v2L

−0.12V s√ gDt

−0.12

STR N = 480–1800rpm; V s = 1–5 cm/s Cyclohexane D32 ∝ (P / V )−0.4

Bubble column V s = 0.26–6.7 cm/s Aqueous: glycerol-glass beads D32 = 0.59(V D/εG)2

g

Bubble column V s = 8cm/s Aqueous: sucrose, ethanol-Ca alginate D32 = 0.87

gD

2

t ρLσ −0.44

gD

3

tv2

L

0.1V s√ gDt

0.39

Flotation cell QG =0.096m3 /h Aqueous D32 ∝ V 0.4s

STR N = 125–800 rpm; V s = 0.025–0.125cm/s Aqueous: 4-methyl 2-pentanol D32 = 2.0 σ 0.6

(P/V )0.4ρ0.2L

STR Aqueous D32 ∝ N −0.5V 0.1(region of the impeller)s

STR N = 125–1000rpm; V s = 0.025–0.125cm/s Aqueous: 4-methyl 2-pentanol D32 ∝ (P / V )−0.4

STR N =770rpm; Q = 1.1 vvm Aqueous: Na2SO4, ethanol, n-butanol D32 ∝ N −1.2(P / V )−0.4

STR D32 ∝ (ε)−0.4(σ )0.6(ρL)−0.6

STR N = 300–450rpm; Q =0.25 and 5vvm Aqueous: Na2SO4, PEG D32 = C

σ 0.6

(P/V )0.2ρ0.6L

STR N = 300–450rpm; Q =0.25 and 5vvm Aqueous: Na2SO4, PEG D32 ∝ (P / V )−0.52 (turbine) and −0.37 (bulk)

Tap water D32 ∝ (P / V )−0.24 (turbine) and −0.14 (bulk)

Prediction models d b

∝σ 0.6

(P/V )

0.4

ρ

0.2

L

STR ε = 17− 47 W/kg Aqueous: decanol, diethylene glycol,

cyclohexanol

D32 = 2.72Di

ρLN 2D3

iσ

−0.70

(transitional flow)

Aqueous: propanol, butanol D32 = 0.113Di

ρLN 2D3

iσ

−0.38

(turbulent flow)




uid recirculation. High gas throughputs encourage coalescence

leading to large bubbles with short residence times. A wide bub-

ble size distribution is attained. The effect of V s in this regime

on hold up is less pronounced than in the bubbly flow regime,

with the exponent varying between 0.2 and 0.7. Koide et al.

[105] noted that moving from the transition regime to the churn-

turbulent regime by increasing the superficial velocity increases

the overall gas hold up.

3.1.2. Influence of turbulence on oxygen transfer

coefficient

In addition to its effect on the interfacial transfer area, inten-

sified fluid turbulence impacts on K L by decreasing the width of

the stagnant boundary layer, according to the two-phase theory.

This results in a decreased resistance to molecular diffusion and

a consequent increase in K L and increased overall rate of oxygen

transfer. This effect has been noted in a bubble column where

an enhancement of K La on increased aeration was concluded to

result from increased disturbance of the concentration boundary

layer by neighbouring bubbles [122]. Thus an increase in turbu-lence will increase K La macroscopically through the increases in

the interfacial transfer area available for oxygen transfer, as well

and microscopically by increasing the effectiveness of transfer

across these interfaces.

Enhanced K L with increased turbulence has been empirically

demonstrated through the effect of P / V and N on K L and a num-

ber of correlations are available (Table 5). K L proportional to

(P / V )0.09–0.531 has been observed in a variety of systems con-

taining hydrocarbons, similar to systems containing electrolytes

or polymers [28,66,70,82,123,124,125,126,127]. K L is similarly

enhanced with increasing turbulence through increased N as

observed in other several publications [66,125,128].

K L has been found to be only slightly dependent on V s over

a range of tank geometries [100] and for both aqueous and

aqueous-solid suspensions [134]. These results have been con-

firmed by Prasher and Wills [126], Schumpe and Deckwer [74]

and Sun and Furusaki [87]. Schumpe and Deckwer [74] f ound

KL ∝ V 0.8s with K L constant at V s over 8 cm/s. Hassan and

Robinson [71,72] and Ho et al. [76] f ound K L to be indepen-

dent of V s for all practical purposes. Similarly, K L was found to

be independent of V s in several otherstudies [28,70,81,123,130].

The lesser effect of V s on K L suggests that the influence of V son coalescence is diluted by its effect on K L through increased

turbulence.

In addition to enhancing K L through reduced resistance tooxygen transfer, turbulence also alters K L through its influ-

ence on bubble size. K L associated with large (>2.5 mm)

bubbles was greater than K L associated with small (<2.5 mm)

bubbles by as much as fivefold [132]. A transition zone

between the large and small bubble regimes has been observed

where K L decreased uniformly with decreasing bubble size

[28,67,100,124,131,135,136,137,138,139]. In this transition

zone, K L has been found to be proportional to D1.0432 [28] and

D0.81332 [69] in non-viscous electrolyte solutions.

The dependence of K L on bubble size has been attributed

to the different characteristics in the hydrodynamic regimes

of the rigid spherical surfaces of the small bubbles and the

deformable, mobile surfaces of the large bubbles [27,69,70].

Bubbles with mobile oscillating surfaces have an internal gas

circulation that promotes oxygen transfer by regenerating the

gas–liquid surface at the interface. Bubbles with rigid surfaces,

on the other hand, have no internal circulation, but behave

as rigid spheres, resulting in relatively lower oxygen trans-

fer. Further, oscillating bubbles are able to wobble and move

in spirals during free rise, movements which generate con-

vective motions that greatly enhance the oxygen transfer rate

[139], with rates from oscillating bubbles 7–70 times larger

than those from rigid bubbles [140]. The enhanced transfer

rates are suggested to result from a marked effect of surface

rigidity on K L for which a value of 4.56× 10−2 cm/s is gener-

ally accepted for oscillating bubbles [28] while K L values for

rigid bubbles are 3.6-fold lower at 1.27× 10−2 cm/s [28,135].

Robinson and Wilke [69] and Akita and Yoshida [68] also

observe a decrease in K L with decreasing bubble size corre-

sponding to the transitional zone between oscillating and rigid

bubbles.

Calderbank [27], Calderbank and Moo-Young [28], Midouxand Charpentier [141] and Schmitz et al. [78] have shown that

while K L decreased in the transition regime from oscillating

to rigid bubbles, K L remained constant with changing bubble

diameter for either large oscillating bubbles or small rigid bub-

bles. This suggests that in discrete bubble regimes of rigid and

oscillating bubbles, turbulence has no effect on K L. Hassan

and Robinson [71,72] found K L to be independent of P / V for

P / V < 2000 W/m3 corresponding to the rigid regime. However,

for P / V > 2000 W/m3, K L decreased with increasing P / V in the

transitional zone, being proportional to (P / V )−0.56. Ho et al.

[76] likewise found no dependence of K L on P / V in the rigid

regime.These authors developed semi-theoretical equations for rigid

and oscillating bubbles based on turbulence having no effect on

K L in these regimes. For bubbles with a rigid interface, K L is

obtained by the following equation [132,137]:

KL ∝

V sl

d bD

2/3G v

−1/6L (5)

For bubbles with a mobile interface, K L is obtained by the

following equation [132]:

KL ∝ V sl

d b D

1/3

G (6)

A constant K L in each of the rigid and oscillating regimes is

not, however, supported by Linek and Mayrhoferova [138] and

Linek et al. [124], who found that K L decreased with increasing

bubble size outside the transition zone.

3.2. Influence of fluid properties on interfacial area and

oxygen transfer coefficient

The fluid properties influence the characteristics of K La

through their influence on the interfacial transfer area or on K L.

Hydrocarbons may enhance K La by increasing the gas–liquid



Table 5

Empirical correlations for the prediction mass transfer coefficient


KL = 1.13

V sld bD0.5

G

Sieve plates V s = 6.1–60.1cm/s Aqueous: aliphatic alcohols, glycolKLD32DL

=

μLρLDL

0.5D32V slρLμL

0.766

Review KL

vLDL

1/2 = 0.42

(ρG−ρL)μLg

ρ2L

1/3

KL

vLDL

2/3 = 0.31

(ρG−ρL)μLg

ρ2L

1/3

KL

vLDL

2/3

= 0.13

(P/V )μLρ2

L

1/4

STR N = 60–400 rpm;V s = 0.1693–0.762cm/s

Aqueous: NaOH KL ∝ N 0.6(P/V )0.2D−0.432

Bubble columns V s =4–45cm/s Aqueous: kerosene, glycerol, lightoil, Na2SO3, ZnCl2

KLD32DL

= 2+ 0.0187

d bV slρL

μL

0.484 vLDL

0.339

d bg1/3

DL

1.61

Prediction models KL = 0.4

(P/V )vLρL

1/4DLvL

1/2

STR N = 250–550 rpm Aqueous: Na2SO3, KI, Na2SO4 K L ∝ (P / V )0.19

STR N = 255, 325 and 455rpm;QG =0.68m3 /h

Aqueous: NaCl, sodium dodecylsulphate, Dow Corning antifoam

KL ∝ D0.532

STR N = 180–780 Aqueous: NaCl K L ∝ (P / V )0.3

STR N = 180–780 Aqueous: NaCl KL = 3.25× 10−4

N 3D5

i

D3t

0.3DiDt

0.7 1Dt

0.35

STR N = 150–350rpm;

V s = 0.29–1.2cm/s

Aqueous: NaOH KL

=0.592 (P/V )vL

ρL 1/4DLvL 1/2

Bubble column Aqueous: glycol, methanol, CCl4KLD32DL

= 0.5

vLDL

0.5

gD332

v2L

0.25gD2

32ρL

σ

0.375

STR N = 100–500rpm;V s = 0.162–0.466cm/s

Aqueous: carbopol KL = 5.11× 10−3

11n−1

3n+14n

n−0.426D0.5(k/ρL)−0.426N 1.352−0.42

STR N = 250–500rpm;V s = 0.634–1.27 cm/s

Aqueous K L ∝ (P / V )0.33

STR N = 732–1900rpm;V s = 0.37–1.11 cm/s

Aqueous: Na2SO4, KOH, KCl,K2SO4

K L ∝ (P / V )−0.56

STR N = 732–1900rpm;V s = 0.37–1.11 cm/s

Aqueous: Na2SO4, KOH, KCl,K2SO4

K L ∝ (P / V )−0.56

ReviewKLμL= α

LV LvL

β vLDL

γ Bubble column V s = 0–20 cm/s Aqueous: CMC KL = 4.5× 10−3V

0.08s μ−0.32

L

Bubble column V s = 2 –7 c m/s Aqueous: CMC, carbopol KL =2

√ π√ DL V sρLg

k1/2(1+n)

Bubble column V s = 8 c m/s Aqueous: sucrose, ethanol-Caalginate

KLD32DL

= 0.13

μLDLρL

1/2

gD232ρL

σ

0.1gD3

32ρ2

L

μ2L

0.43d pDt

0.2

Bubble column V s = 0.8–7 cm/s Aqueous: CMC-C. cellulolyticum KL = 0.301εvLρL

1/4DLvL

1/2

KL =

4√ π

21/n

1T +D

1/2L

kρL

−1/2(1+n)ε1/2(1+n)

Theoretical models KL =0.42

9(n+1)

2(2n+1)

30A(n+1)

(2n+1)

−1/3D

2/3L

kρL

−1/(n+2)g(4−n)/3(n+2)ε

−2(n−G

KL = 0.42

2√ π

D

1/2L

kρL

−1/2(n+2)

g1/(n+2)ε(n−1)/3(n+2)G




T

a b l e 5 ( C o n t i n u e d )

S y s t e m

O p e r a t i n g c o n d i t i o n s

L i q u i d p h a s e ( s )

E q u a t i o n

R e f e r e n

c e

S T R

N = 2 0 0 –

6 0 0 r p m

A q u e o u s : i - p r o p a n o l , a m y l a l c o h o l

K L =

0 . 1

3 2

g μ L

ρ L

1 / 3 D

G ρ L

μ L

1

/ 2 P V 0

. 1 5

P a n j a a n d P h a n e s w a r a R a o [ 1 2 7 ]

S T R

N = 2 5 0 –

6 0 0 r p m ;

Q G = 0

. 6 a n d 1

. 2 m

3 / h

A q u e o u s : N a 2 S O 4 ,

P E G

K L =

0 . 6

V

s l d

b

D 2 / 3

G v

1 / 6

L

A l v e s e t a l . [ 1 3 2 ]

S T R

N = 2 5 0 –

6 0 0 r p m ;

Q G = 0

. 6 a n d 1

. 2 m

3 / h

A q u e o u s : N a 2 S O 4 ,

P E G

K L =

1 . 1

3

V s l

d b

D 0

. 5 G

A l v e s e t a l . [ 1 3 2 ]

S T R

N = 2 5 0 –

8 5 0 r p m ;

V s

= 0

. 2 1 2 –

0 . 8

4 8 c m / s

A q u e o u s : N a 2 S O 4

K L =

0 . 5

2 3 ( P / V ) v

L

ρ L

1 / 4 D

L v L

1 / 2

L i n e k e t a l . [ 1 1 1 ]

T h e o r e t i c a l m o d e l s

A q u e o u s : g l u c o s e , x a n t h a n g u m ,

s i l i c o

n e

a n t i f o a m ; b i o s u r f a c t a n t - X a n t h o m o n a s

c a m p e s t r i s

N R R L B - 1

4 5 9

, C a n d i d a b o m b i c o l a

N R R L Y - 1

7 0 6 9

K L =

2 √ π

√ D

L ˜ ε

ρ L

k

1 / 2 ( 1 + n

)

G a r c i a - O c h o a a n d G o m e z [ 1 3 3 ]

K L =

2 √ π

√ D

L

˜ ε ρ L

( 1 − √

α r ) 2

μ L

0

. 2 5

S T R

N = 0 –

1 1 3 0 r p m ;

V s

= 1 8 –

5 4 c m / s


K L =

0 . 4

4 8 ( P / V ) v

L

ρ L

0 . 2

5 D

L v L

0 . 5

L i n e k e t a l . [ 8 2 ]


K L ∝ ( P / V ) 0 . 2

3 8

A q u e o u s : N a 2 S O 3 ,

S o k r a t

K L ∝ ( P / V ) 0 . 2

4 3

A q u e o u s : N a 2 S O 3 ,

C M C T S

. 5

K L ∝ ( P / V ) 0 . 2

7 6

A q u e o u s : N a 2 S O 3 ,

C M C T S

. 2 0

K L ∝ ( P / V ) 0 . 0

9

A q u e o u s : N a 2 S O 3 ,

o c e n o l

K L ∝ ( P / V ) 0 . 1

8 8

A q u e o u s : N a 2 S O 3 ,

P E G 1 0 0

K L ∝ ( P / V ) 0 . 2

4 6

interfacial area. Alternatively, hydrocarbon may decrease K La

by increasing the resistance to oxygen transfer.

3.2.1. Influence of fluid properties on interfacial area

The interfacial area is highly dependent on the liquid phase

physicochemical properties, such as surface tension and vis-

cosity, which define bubble size through their influences on

bubble break up and coalescence. Hydrocarbons change these

fluid properties, and hence the bubble size, gashold up and inter-

facial area available for transfer. The type of hydrocarbon plays

a major role in the degree to which it affects the fluid properties

of the dispersion [142].

Hydrocarbons have been demonstrated to decrease the

surface tension. Bi et al. [60] reported surface tensions of

71.4 mN/m, 70.2 mN/m and 67.7 mN/m with ethanol con-

centrations of 1 g/L, 3 g/L and 8 g/L, respectively. Likewise,

surface tension was lowered from 73 mN/m to 66 mN/m when

polypropylene glycol methyl ether (PGME) concentration was

increased from 0 ppm to 100 ppm [79] and by almost two thirds

on addition of cyclohexane to an air–aqueous system [117].The surface active effect of the hydrocarbon is a con-

sequence of the coexistence of a hydrophilic functional

group (e.g. –OH; –CO–; –COOH) and a hydrophobic struc-

tural group. The hydrocarbon molecules orientate at the

gas–liquid interface with the hydrophobic group directed

towards the gas phase and the hydrophilic group towards

the liquid phase. The positioning of the hydrophilic group

around the surface of the gas bubbles results in surface

polarization and repulsive forces which inhibit coalescence

when the bubbles come into close contact [127,143]. Sur-

face charges have similarly been implicated in coalescence

inhibition by hydrocarbons [92,143]. Other mechanisms of coa-lescence inhibition proposed include spatial blocking by the

oil drops between the bubbles, restricting bubble movement

and bubble–bubble contact [36,45,61,144] and a decrease in

the force available to rupture the film for coalescence to occur

[117,145].

Increased hydrocarbon concentration has been shown exper-

imentally to result in enhancement of interfacial area. Dodecane

addition up to 25% (v/v) increased theinterfacialarea by approx-

imately 15% [35]. Zieminski et al. [146] found increases in

interfacial area of 1100% for alcohols, 1100% for monocar-

boxylic acids and 500% for dicarboxylic acids upon addition

of additives of 90 ppm, 500 ppm and 50 ppm, respectively. Al

Taweel and Cheng [79] obtained a 45-fold increase in interfa-cial area when increasing the additive concentrations of PGME

(>20 ppm).

The interfacial area relates inversely to the bubble size

through the gas hold up, according to Eq. (4). The bub-

ble size is determined by the balance of surface tension

and viscous forces [29] and, as hydrocarbon concentration

increases, bubbles become smaller with decreasing surface ten-

sion [50,68,79,117,127,146,147]. Thus the surface tension has

been related to the interfacial area through its effect on bubble

size.

The link between surface tension and bubble size has been

established in a study using diethylene glycol and decanol




whose fluid properties differ significantly only in their surface

tension [96]. Here D32 was considerably smaller in decanol

which had a correspondingly lower surface tension. The cor-

relation of decreased surface tension and reduced bubble size

is further supported by an observed decrease in D32 due to

addition of ethanol [60,117,148], propanol [96], i-propanol

[127], n-hexanol [54], 2-ethyl hexanol [142], n-heptanol [54],

n-octanol [54], amyl alcohol [127], n-diols [149,150], alkanes

[35], ketones [149,150], castor oil [144], silicone oil [50,55,64],

toluene [142] and monocarboxylic acids [146,149,150].

The magnitude of the effect of reduced surface tension on

bubble size is marked. Keitel and Onken [149,150] reported that

addition of a variety of hydrocarbons, including n-alcohols (n-

C1–8), n-diols (n-C2–5), ketones (C3–4, C7) and monocarboxylic

acids (C1–3), decreased the average diameter of 4.1–2.5 mm.

Zieminski et al. [146] and Zieminski and Whittemore [151]

added mono- and dicarboxylic acids and observed a decrease

in average bubble diameter of 300% with addition of 100 ppm

organic solutes. Galindo et al. [144] f ound that in a simulated

fermentation broth containing castor oil, bubble size decreasedfrom 2 mm to 0.8 mm as the oil content was increased to 15%

(v/v). Calderbank and Moo-Young [28] f ound the mean bubble

size reduced with an increase in oil concentration up to 15% in a

salt rich aqueous solution. Rols et al. [35], using a photographic

method, reported a 15% reduction in D32 when n-dodecane was

added up to 25% (v/v).

The reduction of surface tension and inhibition of bub-

ble coalescence by hydrocarbons promotes gas dispersions

with slower rising velocities and, thus, an increased gas

hold up [89,152]. Increased gas hold up was reported with

ethanol addition [60,107,148], butanol [153] and oleic acid

concentrations [58]. Addition of alcohols methanol, ethanol,butanol, hexanol and octanol to water also increased the

gas hold up by 70–100% [154]. i-Propanol at concentra-

tions ranging from 0.01 to 1% (v/v) increased the gas hold

up with increasing alcohol concentration [155]. Al Taweel

and Cheng [79] found gas hold up to increase up to five-

fold with increasing concentration of PGME. Chaumat et al.

[120] observed 30–75% greater gas hold up in cyclohexane

compared with water. The degree to which the hydrocarbon

affected gas hold up was dependent on its chain length. Long

chain alcohols affected gas hold up considerably more than

short chain alcohols. The gas hold up increased with chain

length in the following order: water > methanol > ethanol > i-

propanol > n-propanol > n-butanol [104].In addition to their influence on surface tension, hydrocar-

bons also significantly influence the viscosity of the dispersion,

but in an opposite manner. As the hydrocarbon concentration is

increased, so is the viscosity, with a correspondingly decreased

interfacialarea. Viscosity is proposed to decrease interfacialarea

according to one or more of several mechanisms influencing

break up, coalescence or formation of the bubbles. Firstly, an

increased viscosity decreases the turbulence in the liquid. This

results in a reduction in the energy of the eddies, with concomi-

tant damped bubble break up [117]. The damped bubble break

up is likely to be exacerbated by an increased boundary layer

thickness around the bubbles which would require eddies with

high energy for penetration and break up to occur [156]. Sec-

ondly, increased viscosity enhances bubble coalescence [155].

Thirdly, increased viscosity results in a slower formation of the

liquid film at the point of bubble formation thereby trapping a

larger amount of air in each bubble, and thus larger but fewer

bubbles [88].

The negative influence of viscosity on interfacial area has

been demonstrated experimentally through its effect on bub-

ble size. In dispersions containing propanol and decanol, where

decanol is more viscous than propanol but has a comparable sur-

face tension, D32 was significantly larger in the decanol than in

the propanol dispersion [96]. Similar results were demonstrated

by these authors for viscous alcohols where the bubbles in the

more viscous dispersions were relatively larger. Several other

studies have confirmed an increase in average bubble size with

increasing viscosity [88,113,115,117,144,157,158].

The interfacial area is further decreased due to a decreased

gas hold up in viscous fluids, as a result of the formation of larger

bubbles under these conditions. The larger bubbles pass more

quickly through the reactor with high bubble rise velocities andlow residence times [113,156,159,160,161]. As much as a 30%

decrease in gas hold up in viscous liquids has been attributed to

these large bubbles.

Since larger bubbles have a shorter residence time relative to

smaller bubbles, increased viscosity may result in an increased

proportion of smaller bubbles in thepopulation. A positive effect

of viscosity on gas hold up due to an increased proportion of

smaller bubbles in the population [162] is suggested to balance

the negative effect of viscosity on gas hold up as a result of

the generation of larger bubbles [113]. The behaviour of rising

bubbles inevitably becomes restricted with increasing viscos-

ity, however, due to the increase of drag force on the bubbles[155,163], even in the case of large bubbles.

The resultant effect of increased hydrocarbon fraction on

the interfacial area and gas hold up of the dispersion will ulti-

mately depend on the relative predominance of the influences of

decreased surface tension and increased viscosity in the system

under consideration. Studies which report a minimum constant

bubble size, irrespective of an increase of hydrocarbon concen-

tration, suggest that under the conditions of these studies, the

negative effect of increased viscosity on interfacial area with

hydrocarbon addition was compensated by a coincident posi-

tive effect of reduced surface tension. A minimum bubble size

was observed at 3–4% octane in an octane–aqueous suspension

[164] and at ethanol concentrations above 1 g/L [60]. Keitel andOnken [149,150] related specific critical concentrations to a con-

stant bubble size for each of a wide variety of additives. Other

authors who have found similar observations of critical con-

centrations include Albal et al. [116] and Machon et al. [92].

Yamamoto et al. [165] f ound the bubble size to be almost inde-

pendent of volume fraction of PFC-43 less that 60% (v/v). This

trend is also evident in the study of PFC-40 addition to 15%

(v/v), in which no effect on the interfacial area was observed

[65].

A cancellation of these two effects is supported by the obser-

vation of a constant maximum gas hold up with addition of

glycerol [160], addition of PGME [79], perfluorotributylamine




[165], 2-ethyl hexanol [142] and toluene [142]. A maximum

gas hold up was similarly observed at a liquid viscosity of 4 cP

[155]. However, Das et al. [142] also noted that at concentra-

tions above 10% in both 2-ethyl hexanol and toluene, increasing

hydrocarbon concentration resulted in bubble size increase. This

suggeststhat over a critical hydrocarbon concentration, the effect

of increased viscosity may outweigh that of decreased surface

tension.

The empirical models which define the influence of P / V ,

N and V s on interfacial area (Table 2) also incorporate the

influence of viscosity and surface tension on this parameter.

Calderbank [26] first described the influence of the surface

tension on the interfacial area by assessing the effect of 10

different aqueous–hydrocarbon emulsions at the 5 L and 100 L

scale. This model and its extensions by Sridhar and Potter

[75] and Kawase et al. [77] predict an increase in interfacial

area with a decrease in surface tension according to a∝ σ −0.6.

Similar dependencies of interfacial area on surface tension,

namely a

∝σ −0.5 and a

∝σ −0.33, were formulated by Akita

and Yoshida [68] and Calderbank [27], respectively. Al Taweeland Cheng [79] observed a substantially higher dependency of

interfacial area on surface tension with PGME, according to

a∝ σ −15.4.

The influence of viscosity on interfacial area was incorpo-

rated by Kawase et al. [77]. Examination of CMC solutions

showed the interfacial area to be inversely proportional to con-

tinuous phase viscosity (μc) according to (μd / μc)0.25. Negative

influence of viscosity on the interfacial area was also noted in by

Calderbank [27], Schmitz et al. [78], Garcia-Ochoa and Gomez

[81] and Schumpe and Deckwer [74] who reporteda ∝ μ−0.125L ,

a ∝ μ−0.18L , a ∝ μ−0.3

L and a ∝ μ−0.51L , respectively. Akita and

Yoshida [68] f ound a similar effect on kinematic viscosity oninterfacial area in a bubble column, namely a ∝ v−0.2L .

The influence of surface tension and viscosity on bubble size

and gas hold up is similarly incorporated into these equations

(Tables 3 and 4) such that a decreased surface tension is related

to a smaller bubble size and increased gas hold up. Increased

viscosity may be related to increased or decreased bubble size

and generally a decreased gas hold up, depending on the system.

3.2.2. Influence of fluid properties on oxygen transfer

coefficient

The influence of hydrocarbon on the oxygen transfer coeffi-

cient (K L) has generally been found to be negative. Further, thedegree to which the hydrocarbon decreases K L depends on the

hydrocarbon type. Koide et al. [54] reported a 44%, 50% and

62.5% decrease in K L upon addition of n-hexanol, n-heptanol

and n-octanol, respectively, suggesting a more marked effect of

alcohols with a long chain length when compared with those

of a comparatively shorter chain length. Similar results have

been found by Raymond and Zieminski [135] who report a

K L decrease of 53.8% for n-hexanol and 700% for n-octanol,

attributing the larger drop in K L to the increased chain length of

the hydrocarbon.

A major mechanism through which the hydrocarbon influ-

ences K L is through its effect on the bubble mobility. Calderbank

and Moo-Young [28] ascribed a steady decrease in K L with

increasing oil concentration from 14 to 69.5% (v/v) to the

adsorption of the hydrocarbon at the gas–liquid interface and

reduced surface tension. A reduction in surface tension results

in a decrease in the bubble surface mobility [135] and the bub-

ble behaves as a rigid sphere. Consequently internal motion is

retarded and K L is reduced [26,166].

The link between reduced surface tension and decreased K Lis supported experimentally. Linek et al. [82] added substances

that inhibit surface tension (ocenol, polyethylene glycol (PEG),

CMC and TS.20) and observed a reduction in K L of up to 80%.

Yagi and Yoshida [167] also observed a decreased K L on the

addition of 0.1% of surfactant. Further,a decrease in K L hasbeen

observed on the addition of antifoam agents such as silicone oil

and soybean oil [50].

In addition to the surfactant effect of the hydrocarbon, the

increased viscosity also impacts negatively on K L. Several stud-

ies suggest that the comparatively more viscous nature of the

hydrocarbon increases the liquid phase’s resistance to transfer

[82,133,156,168,169,170]. This may be due to the decrease ininternal recirculation of bubbles or depression of the diffusivity

of dissolved gas in the liquid.

The oxygen transfer coefficient has been shown to be highly

dependent on the liquid-phase diffusion coefficient. This rela-

tionship has been found for a wide variety of process conditions

and additives for both rigid (Eq. (7)) and oscillating bubbles (Eq.

(8)).

KL = D2/3L (7)

KL = D1/2L (8)

Eq. (7) was found applicable for rigid bubbles inboth single and mixed electrolyte solutions [76,132], and

hydrocarbon–aqueous [28] and CMC-aqueous suspensions

[131]. Similarly, Eq. (8) for oscillating bubbles has been

found true for hydrocarbons [28,68,87,127,133], electrolyte

[27,82,111,132] and aqueous solutions [77,123,126,130,131].

4. Prediction of the overall volumetric oxygen transfer

coefficient and oxygen transfer rate in

hydrocarbon–aqueous dispersions

Prediction of K La in hydrocarbon–aqueous dispersions is

complicated. In addition to the fluid turbulence, the physic-

ochemical properties of the hydrocarbon–aqueous dispersion,defined mostly by the hydrocarbon concentration and its molec-

ular structure and chain length, strongly influence the behaviour

of K La. The difficulty of defining a predictive model for K La

is exacerbated by the complex interactions between the hydro-

carbon and the operating variables, particularly agitation rate,

which may result in different K La trends over similar hydrocar-

bon concentration ranges and comparable hydrocarbon types.

K La prediction in hydrocarbon–aqueous dispersions has

been restricted almost exclusively to empirical correlations

(Tables 6 and 7). K La in these systems, in common with K La

behaviour in aqueous systems, exhibits a dependence on the tur-

bulence generated by agitation and aeration, the fluid properties




Table 6

Empirical correlations for the prediction of overall volumetric oxygen transfer coefficient

System Liquid phase(s) Equation Reference

STR; N = 240–570; V s = 0.2–0.8 cm/s Aqueous n-C10–21 solution (KLa)GW = (1.75× 10−2 e0.115φ − 0.8×10−3 e−46.9φ)NV

1/3s

Matsumura et al.

[171]

STR; N = 240–570; V s = 0.2–0.8 cm/s Aqueous n-C10–21 solution (KLa)OW = 11+H WO(1/(φ−1)) (KLa)GW Matsumura et al.

[171]

STR; two 6-blade turbines; Dt =17.6cm;

V L = 4 L ; N = 600 rpm; Q = 0.5 vvm

Xanthan solution/vegetable oil (KLa)GOH ∝ (P/V )0.36V 0.59s φWXn−0.26 Zhao et al. [172]

STR; two 6-blade Rushton turbines; four

baffles; Dt =11cm; V = 1 L ;

N = 200–800rpm; Q = 0.5–2vvm

n-Hexadecane/nutrient medium KLa = 650(P/V )0.31V 0.7s (1− φ)1.7 Nielsen et al. [63]

STR; two 4-blade turbines; three baffles;

Dt = 17.5 cm; V = 4 L ; N = 0–700 rpm;

V s = 0–0.5cm/s

n-Dodecane/simulated broths

(CMC/sodium salt solution)

KLa = 5.6× 10−3

(P/V )1.54V 2.30

s

μ3.78a

φGalaction et al. [38],

Cascaval et al. [39]

STR; two 4-blade turbines; three baffles;

Dt = 17.5 cm; V = 4 L ; N = 0–700rpm

V s = 0–0.5cm/s

n-Dodecane/ Propionibacterium

shermanii broths

KLa = 0.714

V 0.97

s

(P/V )0.40C1.22x

φCascaval et al. [39]

n-Dodecane/ S. cerevisiae broths KLa

=6.72

×10−2 (P/V )2.74V 0.75

s

C0.03

xφ

N = 325–1200 rpm CO2 and propene in

toluene/water; acetylene in

sulphur(s)/water

(KLa)φ(KLa)φ=0

=

(DL)φ(DL)φ=0

1/2(μL)φ=0 (ρL)φ (ε)φ

(μL)φ(ρL)φ=0(ε)φ=0

1/4

Zhang et al. [173]

of the aqueous phase and the geometric constraints. Accord-

ingly, the conventional generalised empirical correlations for

non-viscous aqueous solutions (Eqs. (2) and (3)), which relate

K La to superficial gas velocity and power per unit volume (or

agitation rate), have frequently been used as a basis for the devel-

opment of the more complex empirical correlations proposed

for hydrocarbon–aqueous dispersions by additionally account-

ing for the influences of the physical properties of a secondimmiscible phase. These adaptations usually comprise either

incorporation of a term or terms relating to the hydrocarbon

fraction or the physical properties of the dispersion (Table 6).

An empirical correlation to predict the observed behaviour

of K La at discrete n-hexadecane concentrations up to 33% in a

hydrocarbon–aqueous dispersion incorporated a term contain-

ing the alkane fraction [63]. In this study, K La was maximal

at the lowest alkane concentration and decreased consecutively

at each subsequent concentration examined. Consequently,

this correlation is limited to use where the influence of the

hydrocarbon is negative over the entire range of hydrocarbon

concentrations.

Zhao et al. [172] similarly developed an empirical correlation

whichdescribedthe behaviourof K La in a vegetable oil–aqueous

dispersion where the properties of the aqueous phase was var-

ied, here by altering the concentration of xanthan gum in the

aqueous phase. In this study, though, both the influence of the

change in the properties of the aqueous phase as well as the

change in oil fraction was assessed. The predicted decrease in

K La with increased xanthan gum concentration and increased

oil fraction, described their data. This correlation will, as with

that proposed by Nielsen et al. [63], be limited to use where the

influence of the hydrocarbon is negative over the entire range of

hydrocarbon concentrations. Further, since this correlation was

developed from data obtained in a system where oil comprised

the continuous phase, its validity in hydrocarbon–aqueous dis-

persions, where the hydrocarbon is the dispersed phase, remains

questionable.

Empirical correlations which predict an increased K La on

hydrocarbon addition have also been developed in terms of the

ratio of K La in the presence of hydrocarbon relative to that

without hydrocarbon [173]. Although these authors validatedtheir model with data from CO2 and propene absorption in

a toluene–water dispersion, and absorption of acetylene in a

sulphur–water suspension, Dumont et al. [64] have suggested it

is applicability to enhanced oxygen absorption in the presence

of hydrocarbon droplets.

These correlations have all assumed that oxygen transfer in

a hydrocarbon–aqueous dispersion can be represented by a sin-

gle rate-limiting K La. In an aqueous solution, where the oxygen

transport takes place directly from the gas to the aqueous phase

and the major resistance to oxygen transfer is considered to

reside in the stagnant aqueous layer at the gas–liquid interface,

this is generally held to be reasonable. However, in a system

containing gas bubbles and hydrocarbon droplets, oxygen trans-

port from the gas to the aqueous phase may take place by one of

several mechanisms, and the assumption of a single rate-limiting

K La may not be valid.

An important consideration in ascertaining the most likely

oxygen transport mechanism is the adsorption of hydrocarbon

droplets to the bubble surface, and whether the hydrocarbon

adsorbs as beads or forms a continuous film around the surface.

This will depend on the relative gas bubble and hydrocarbon

droplet sizes as well as the intensity of turbulence. Generally

the average bubble diameters are approximately two orders of

magnitude larger than that of the hydrocarbon droplets, suggest-




T

a b l e 7

E

m p i r i c a l c o r r e l a t i o n s f o r t h e p r e d i c t i o n o f o v e r a l l v o l u m e t r i c o x y g e n t r a n s f e r c o e f fi c i e n t ( d e r i v e d f r o m d i m e n s i o n l e s s a n a l y s i s )

S y s t e m

L i q u i d p h a s e ( s )

E q u a t i o n

R e f e r e n c e

B u b b l e c o l u m n ; D

t = 1 5

. 2 –

6 0 c m ;

V s

= 3 –

4 0 c m / s

A q u e o u s : g l y c o l , m e t h a n o l , C C l 4

,

N a C l , N a 2 S O 3

K

L a

D 2 t

D L

2 =

0 . 6

μ L

ρ L

D L

0 . 5

g D

2 t ρ L

σ

0

. 6 2

g D

3 t ρ L

μ 2 L

0

. 3 1

ε 1

. 1 G

A k i t a a n d Y o s h i d a [ 9 9 ]

S T R ; o n e 6 - b

l a d e t u r b i n e ; f o u r b a f fl e s ;

D t = 2 5 c m ; N = 3 0 0 –

6 0 0 r p m ; V

s = 0

. 3 8 1 c m / s

A q u e o u s : g l y c e r o l , m i l l e t - j e l l y ,

p o l y a c r y l a t e ( P A N a ) , C M C

K L a

D 2 i

D L

=

0 . 0

6

D 2 i N ρ L

μ L

1

. 5

D i N

2

g

0

. 1 9

μ L

ρ L

D L

0 . 5

μ L

V s

σ

0 . 6 N D

i

V s

0 . 3

2[ 1 + 2 ( λ N ) 0 . 5

] − 0

. 0 7

Y a g i a n d Y o s h i d a [ 1 6 7 ]


t = 1 4

. 5 5 c m ; V

s = 2

. 7 8 c m / s

A q u e o u s : s u c r o s e , C M C

, s o d i u m

p o l y a c r y l a t e

K L a

D t

D L

=

0 . 0

9

v L

D L

0 . 5

g D

3 t v

2 L

0

. 3 9

g D

2 t ρ L

σ

0

. 7 5

V s

√ g

D t

1

. 0

1 + α V

B λ

D 3 2

β −

1

N a k a n o h a n d Y o s h i d a

[ 1 7 4 ]


t = 1 0 a n d 1 9 c m ;

V s

= 4

. 2 –

3 8 c m / s

A q u e o u s : s u c r o s e , m e t h a n o l ,

n - b u t a n o l

K L a

V s

g

=

1 4

. 9 V

s μ L

σ

1 . 7

6

μ 4 L

g

ρ L σ

3 −

0 . 2

4 8

μ G

μ L

0 . 2

4 3

μ L ρ L D

L − 0

. 6 0 4

H i k i t a e t a l . [ 1 7 5 ]

S T R ; f o u r b a f fl e s ; V = 2 L ; N = 1 0 0 –

1 3 0 0 r p m

A q u e o u s : g l y c e r i n e , C M C

, t r i t o n

C F - 3

2 - g

l a s s b e a d s

K L a

D 2 i

D L

=

1 . 4

1 × 1 0 −

3

μ L

ρ L

D L

0 . 5

D 2 i N ρ L

μ L

0

. 6 7

ρ L

N 2 D

3 i

σ

1

. 2 9

A l b a l e t a l . [ 1 1 6 ]


t = 1 0

, 1 4

, 2 1

. 8 a n d 3 0 c m ;

V s

= 0

. 9 8 –

1 5

. 6 c m / s

A q u e o u s : g l y c e r o l , g l y c o l , B a C l 2

,

N a 2 S O 4

K L a σ

D L g ρ L =

2 . 2

5

μ L

ρ L

D L

0 . 5

ρ L σ

3

g μ

4 L

0

. 1 3 6 δ

N D t

− 0

. 0 9 0 5

ε 1

. 2 6 G

K o i d e e t a l . [ 1 0 5 ]


t = 2 3 a n d 7 6 c m ; V = 4 0 a n d

1 0 0 0 L

A q u e o u s : C M C ; c a r b o p o l

K L a

D 2 t

D L

=

1 2 C

1 √ π

√ 1

. 0 7 n

1 / 3

k / ρ L

D 1 − n

t

D V

1 − n

s

1 / 2

D n t V

2 − n

s

k / ρ L

( 2 + n

) / 1 ( 1 + n

) V

s

√ g

D t

2 ( 1 1

n −

4 ) / 3 9 ( 1 + n

) g

D 2 t

ρ L

σ

3 / 5

K a w a s e e t a l . [ 7 7 ]


t = 1 4

, 2 1

. 8 a n d 3 0 c m

A q u e o u s : m e t h a n o l , e t h a n o l ,

b u t a n o l , h e x a n o l , o c t a n o l - c a l c i u m

a l g i n a t e g e l p a r t i c l e s , p o l y s t y r e n e

p a r t i c l e s

K L a σ

ρ L

D L g =

1 2

. 9 ( v

L / D

L ) 0

. 5 ( g

μ 4 L / ρ L σ

3 ) −

0 . 1

5 9

( g D

2 t ρ L

/ σ

) − 0

. 1 8 4

ε 1

. 3 G

[ 0 . 4

7 + 0

. 5 3 e x p

( − 4 1

. 4

∞ k

1 / μ L

V s l ( d b

V s l ρ L

/ μ L

) − 1 / 2 ) ]

1 + 0 . 6 2

ε S / L

S a l v a c i o n e t a l . [ 1 5 4 ] ing that in the case of a continuous hydrocarbon film, a large

number of hydrocarbon droplets coalesce and spread around

the gas bubble [35,53]. Hydrodynamic instabilities can lead to

the disruption or removal of this superficial hydrocarbon film

[35,38,39]. Oil has also been observed to trap air bubbles under

conditions of particularly low agitation rates of 300–700 rpm

[144].

For beading hydrocarbons, the pathway from gas to water

may occur in series with no direct gas to hydrocarbon trans-

fer taking place [61,171,176]. For spreading hydrocarbons, on

the other hand, direct gas to hydrocarbon contact is likely to

occur. Linek and Benes [176] and Das et al. [142] suggest,

however, that transfer takes place from the gas bubble into the

aqueous and hydrocarbon phases in both spreading and beading

hydrocarbons.

Matsumura et al. [171] developed correlations to predict

interphasic K La in a dispersion containing discrete gas bubbles

and hydrocarbon droplets for transport through the aqueous film

surrounding the gas bubbles (K LaGW) and the aqueous film sur-

rounding the hydrocarbon droplets (K LaOW). These correlationspredicted increased K La values with n-C14–18 alkane addition up

to 10%, the maximum concentration examined, to within 15%

of their experimental data.

Interphasic K La was also considered by Rols and Goma

[177] and Rols et al. [35] who proposed several possible

alternate mechanisms for oxygen transport. They present the

most probable scenario as that in which the hydrocarbon is

adsorbed onto the bubble surface and oxygen transport takes

place from the gas to the aqueous phase via the hydrocarbon,

either directly to an organism adsorbed on the hydrocarbon

droplet, or indirectly through the aqueous phase. Roles et al.

[35] measured the resistances to oxygen transfer between thegas, hydrocarbon and water phases for n-dodecane and forane

F66E and report transfer coefficients as (K L)GO = 1.29 (K L)GW;

(K L)OW = 0.97 (K L)GW for n-dodecane and (K L)GO =2.02

(K L)GW; (K L)OW = 0.95 (K L)GW for forane F66E. These results

suggest that the main resistance to oxygen transfer is located

in the aqueous boundary layer at the hydrocarbon–aqueous

interface.

Empirical correlations for K La prediction have also been

obtained by dimensional analysis (Table 7). Here the physi-

cal properties of the gas and liquid, which could conceivably

influence K La, namely surface tension, viscosity, diffusivity

and density, were considered in the development of the cor-

relations. These have found application mainly in viscousaqueous solutions or dispersions of polymers or short chain

hydrocarbons such as carboxymethyl cellulose [77,116,174],

Na-polyacrylate [174], Ca-alginate glycol [154], glycerine

[116], glycol [99,105], glycerol [105]; carbopol [77], methanol

[99,154,175], butanol [154,175] and hexanol and octanol [154].

These correlations invariably predict an improvement in K La

with decreased surface tension and viscosity. Dimensional anal-

ysis has been shown to be a feasible option for the incorporation

of the effect of the physical properties conferred the hydro-

carbon and has potential for extension into K La prediction

in hydrocarbon–aqueous dispersions of longer chain hydrocar-

bons.




In addition to empirical correlations, several mechanisms

have been modelled for systems containing two immisci-

ble liquid phases. These models have been classified into

homogeneous [178,179,180] and heterogeneous [52,180–184]

models. Homogeneous models ignore bubble–droplet geome-

try. In addition, the fraction of the dispersed phase is assumed

to be equally uniform at the gas–liquid interface and in

the bulk liquid. Heterogeneous models consider the geome-

try such as the bubble–droplet distance and droplet–droplet

distance. Heterogeneous models are generally preferred from

a physical perspective. However, homogeneous models are

numerically simpler requiring less detailed parameter values,

and with their shorter computation times are preferred for sim-

ple cases where they describe the experimental data equally

well.

However, to date, both homogeneous and heterogeneous

models are valid only for the process conditions relevant to the

study under consideration. Further, these models involve the use

of a number of physical parameters which can neither be accu-

rately predicted nor measured and for which insufficient datahave been reported in literature [180]. Consequently, the use of

these models for the quantification of K La behaviour is limited

and further research is required for the development of a uni-

fied model to explain oxygen transfer in hydrocarbon–aqueous

systems.

5. Concluding remarks

In hydrocarbon–aqueous dispersions, the hydrocarbon

impacts markedly on K La, but in widely differing manners

depending on the hydrocarbon type and concentration, the

process conditions and the geometric constraints under consid-eration. This gives rise to three distinct K La behavioural trends

which have been classified as type 1 behaviour (K La increase to

a maximum, with subsequent decease), type 2 behaviour (K La

increase to a maximum with no decrease) and type 3 behaviour

(no increase in K La or K La decrease). Under conditions where

K La is depressed, the enhanced oxygen solubility in hydrocar-

bons may not be able to compensate for the greater oxygen

transfer rate required in hydrocarbon-based bioprocesses due

to the absence of oxygen in the molecular structure. In view

of the importance of an adequate oxygen transfer rate for the

optimisation of the organisms’ performance and its potential

for hydrocarbon bioconversion, the need for predictive models

to provide reliable estimates of K La in hydrocarbon–aqueousdispersions has been realised.

Currently, models for K La prediction in the presence of

hydrocarbons are empirically derived and based either on a cor-

relation of K La with power input and gasvelocity in non-viscous

aqueous solutions, or on dimensional analyses applied to vis-

cous aqueous solutions and dispersions. The correlation of K La

to power input and gas velocity is made applicable to a range

of hydrocarbon dispersions, including the potentially impor-

tant bioconversion substrates n-hexadecane and n-dodecane, by

the incorporation of the hydrocarbon concentration or its fluid

properties into the equation. However, these correlations pre-

dict solely a K La increase or a K La decrease, depending on

the behavioural trend in the K La data used to formulate the

correlation. Further, correlations based on dimensional analy-

sis procedures are limited to only a few hydrocarbons, none of

which is generally considered suitable for bioconversion pur-

poses.

The K La trends in hydrocarbon–aqueous dispersions are

shaped by the pressures imposed by fluid turbulence and physic-

ochemical properties of the dispersion, through alteration of a

number of parameters such as Sauter mean diameter, gas–liquid

interface rigidity, gas hold up, surface tension, viscosity and

diffusivity. The K La behaviour is further complicated by the

interactions between the pressures imposed by the turbulence

and fluid properties, which may result in different K La trends

under similar conditions of agitation and system geometry, or

over similar hydrocarbon concentration ranges and comparable

hydrocarbon types.

Enhanced turbulence has a positive influence on K La in all

hydrocarbon–aqueous dispersions by increasing the interfacial

area available for transfer and decreasingthe resistanceto molec-

ular diffusion. The interfacial area available increases directlythrough a shear-induced decrease in the Sauter mean bubble

diameter and indirectly through an increased gas hold up as a

result of the smaller bubbles. The resistance to molecular diffu-

sion decreases due to a reduction in the thickness of the stagnant

fluid layer surrounding the bubble.

The fluid properties, surface tension and viscosity, are strong

influences in K La behaviour through their effect on bubble

break up and coalescence, albeit with opposite consequences.

Hydrocarbons tend to decrease surface tension, resulting in a

smaller Sauter mean bubble diameter with a lower rise veloc-

ity and, therefore, an increase in gas hold up, both of which

serve to amplify K La through increased available transfer area.On the other hand, hydrocarbons also increase the viscosity

which damps turbulence, thereby reducing K La macroscopi-

cally through attenuated bubble break up, and microscopically

through increased resistance to molecular diffusion. Viscos-

ity also enhances bubble coalescence and the entrapment of

a greater amount of air per bubble during formation, which

together with attenuatedbubble breakup, decreases K La through

a decrease in interfacial area. The effect on gas hold up is not

always negative, however, since the larger bubbles leave the dis-

persion more rapidly and a shift in size distribution to smaller

bubbles may occur.

The positive response of K La to enhanced turbulence and

lower surface tension is limited by the effect of these parameterson the gas–liquid interface rigidity. As the Sauter mean diameter

decreases, so does the bubble surface mobility, until a threshold

minimum diameter is reached at which the bubble behaves as a

rigid sphere with no internal circulation. So although the inter-

facial area is maximal, K La may be decreased through a decline

in effective transfer across the interface. This is exacerbated

by an increased resistance to molecular diffusion imposed by

the concomitant increase in viscosity with a decrease in surface

tension.

This review provides a fundamental conceptual understand-

ing of the mechanisms which define the exact behaviour of

K La in response to changes in turbulence and fluid properties,




and quantifies this behaviour in terms of the parameters which

underpin the response. It is envisaged that through the eluci-

dation and quantification of the parameters which are directly

responsible for the behaviour of K La in hydrocarbon–aqueous

dispersions, current knowledge of existing models may be suc-

cessfully extended in order to predict the criteria for optimal

oxygen transfer in hydrocarbon-based bioprocesses.

Acknowledgements

The authors gratefully acknowledge the DST-NRF Centre

of Excellence in Catalysis (c*change) and the University of

Stellenbosch for funding of this research. LDC Correia also

acknowledges bursary funding from and DST-NRF Centre of

Excellence in Catalysis (c*change).

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