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A review on empirical correlations estimating gas holdup for shear-thinning non-Newtonian fluids in bubble column systems with future perspectives

  • Ajay Sujan

    Ajay Sujan is a PhD scholar under the supervision of Dr. Raj K. Vyas, Chemical Engineering Department, MNIT (Jaipur, India). He was a lecturer at the Chemical Engineering Department, Anand Engineering College (Agra, India) from 2010 to 2013. He completed his Master’s degree at MNIT Jaipur. He is currently working on hydrodynamic and mass transfer parameters in a bubble column. He has published a number of articles related to international conferences.

    and Raj K. Vyas

    Raj K. Vyas is an Associate Professor at the Chemical Engineering Department, MNIT (Jaipur, India). He obtained his PhD from the former University of Roorkee, Roorkee (now IIT Roorkee). The major areas of his research are separation processes, environmental engineering, catalysis and biotechnology. He has published/presented over 70 research papers in various international/national journals and conferences of repute, guided five PhDs and 14 Master’s theses. He has received several academic awards including a “Khosla Commendation Certificate” from the University of Roorkee, Roorkee in 1996.

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Published/Copyright: September 26, 2017
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Abstract

Gas holdup is one of the most important parameters for characterizing the hydrodynamics of bubble columns. Modeling and design of bubble columns require empirical correlations for precise estimation of gas holdup. Empirical correlations available for prediction of gas holdup (εG) in various non-Newtonian systems for both gas-liquid and gas-liquid-solid bubble columns have been presented in this review. Critical analysis of correlations presented by different researchers has been made considering the findings and pitfalls. As the magnitude of gas holdup depends on many factors, such as physicochemical properties of gas and/or liquid, column geometry, type and design of gas distributors, operating conditions, phase properties, and rheological properties, etc., all of these have been discussed and examined. In order to emphasize the significance, relative importance of parameters such as flow behavior index, consistency index, column diameter, gas flow rate, and density of aqueous carboxymethylcellulose (CMC) solution on gas holdup has been quantified using artificial neural network and Garson’s algorithm for an experimental data set of air-CMC solution from the literature. Besides, potential areas for research encompassing operating conditions, column geometry, physical properties, modeling and simulation, rheological properties, flow regime, etc., have been underlined, and the need for developing newer correlations for gas holdup has been outlined. The review may be useful for the modeling and design of bubble columns.

About the authors

Ajay Sujan

Ajay Sujan is a PhD scholar under the supervision of Dr. Raj K. Vyas, Chemical Engineering Department, MNIT (Jaipur, India). He was a lecturer at the Chemical Engineering Department, Anand Engineering College (Agra, India) from 2010 to 2013. He completed his Master’s degree at MNIT Jaipur. He is currently working on hydrodynamic and mass transfer parameters in a bubble column. He has published a number of articles related to international conferences.

Raj K. Vyas

Raj K. Vyas is an Associate Professor at the Chemical Engineering Department, MNIT (Jaipur, India). He obtained his PhD from the former University of Roorkee, Roorkee (now IIT Roorkee). The major areas of his research are separation processes, environmental engineering, catalysis and biotechnology. He has published/presented over 70 research papers in various international/national journals and conferences of repute, guided five PhDs and 14 Master’s theses. He has received several academic awards including a “Khosla Commendation Certificate” from the University of Roorkee, Roorkee in 1996.

Nomenclature

Ar

Archimedes number, dimensionless

AC

Acceleration number, dimensionless

CD

Drag coefficient, dimensionless

d

Impeller diameter, m

d0

Sparger hole diameter, mm

dP

Diameter of particle, mm

d32

Sauter mean bubble diameter, m

de

Volume equivalent bubble diameter, m

ds

Sparger diameter, m

DL

Diffusivity, m2/s

DC

Column diameter, m

E

Elasticity or bubble aspect ratio, dimensionless

Eo

Eötvös number, dimensionless

Ga

Galilei number, dimensionless

g

Acceleration of gravity, m/s2

Gʹ

Storage modulus, dimensionless

Gʺ

Loss modulus, dimensionless

H0

Initial liquid height in column, m

HL

Liquid height in column, m

Hc

Height of the column, m

H

Height of measurement location from the sparger, m

k

Consistency index, Pa·sn

Mo

Morton number, dimensionless

n

Flow behavior index, dimensionless

N

Impeller speed, rev/s or rev/min

NH

Number of hidden layer

Nμr

Viscosity ratio

OA

Open area, m2

Pg

Mechanical agitation power input in gas-liquid dispersion, W

P

Pressure, bar or atm

ΔPH

Pressure drop per unit height, kPa/m

Ret

Terminal Reynolds number, dimensionless

ReM

Reynolds number based on the Carreau model, dimensionless

Re

Reynolds number, dimensionless

s

Carreau model parameter, dimensionless

S

Fractional plate free area, dimensionless

T

Temperature, °C or K

uG

Superficial gas velocity, m/s

uL

Superficial liquid velocity, m/s

U

Bubble rise velocity, m/s

VL

Volume of liquid, m3

Wi

Weissenberg number, dimensionless

We

Weber number, dimensionless

x

Largest horizontal dimension

y

Largest vertical dimension

z

Axial location from the sparger level, m

Greek letters
λ

Carreau model parameter, s

λt

Fluid characteristic time, s

εG

Gas holdup, dimensionless

εF

Holdup of floating bubble breakers, dimensionless

μeff

Effective viscosity of liquid, Pa·s

μa

Apparent viscosity, Pa·s

μ0

Zero shear rate viscosity, Pa·s

μ

Infinite shear rate viscosity, Pa·s

μL

Liquid-phase viscosity, Pa·s

ρs

Density of solid particle, kg/m3

ρL

Liquid-phase density, kg/m3

σL

Liquid phase surface tension, N/m

σ

Surface tension, N/m

θ

Taper angle, degree

Subscripts
G

Gas phase

L

Liquid phase

S

Solid phase

Abbreviations
CBDT

Concave bladed disc turbine

CMC

Carboxymethyl cellulose

DT

Flat bladed disc turbine

MOC

Material of construction

MAPE

Maximum average percentage error

OCENOL

A mixture of saturated and unsaturated alcohol from the fraction C16–C18

PPG

Polypropylene glycol

PAA

Polyacrylamide

PVP

Polyvinyl pyrrolidone

PAM

Polyacrylamide

RMSE

Root mean square error

SAG

Silicone antifoam emulsion

SOKRAT

A water-soluble liquid polymer based on acrylonitrile and acrylic acid in ratio 2:1

SS

Stainless steel

References

Abdelrahim KA, Ramaswamy HS. High temperature/pressure rheology of carboxymethyl cellulose (CMC). Food Res Int 1995; 28: 285–290.10.1016/0963-9969(94)00045-ASearch in Google Scholar

Acharya A, Mashelkar RA, Ulbrecht J. Mechanics of bubble motion and deformation in non-Newtonian media. Chem Eng Sci 1977; 32: 863–872.10.1016/0009-2509(77)80072-9Search in Google Scholar

Ahmed Zeki NS. Prediction of bubble size in bubble columns using artificial neural network. Iraqi J Chem Pet Eng 2009; 10: 1–8.10.31699/IJCPE.2009.1.1Search in Google Scholar

Al-Masry WA, Abdennour A. Gas hold-up estimation in bubble columns using passive acoustic waveforms with neural networks. J Chem Technol Biotechnol 2006; 81: 951–957.10.1002/jctb.1475Search in Google Scholar

Alvarez E, Correa JM, Riverol C, Navaza JM. Model based in neural networks for the prediction of the mass transfer coefficients in bubble columns. Study in Newtonian and non-Newtonian fluids. Int Commun Heat Mass Transf 2000; 27: 93–98.10.1016/S0735-1933(00)00087-7Search in Google Scholar

Amiri S, Mehrnia MR, Barzegari D, Yazdani A. Determination of bubble size distribution in a bubble column reactor using artificial neural network. Asia Pac J Chem Eng 2011a; 7: 613–623.10.1002/apj.615Search in Google Scholar

Amiri S, Mehrnia MR, Barzegari D, Yazdani A. An artificial neural network for prediction of gas holdup in bubble columns with oily solutions. Neural Comput Appl 2011b; 20: 487–494.10.1007/s00521-011-0566-xSearch in Google Scholar

Anastasiou AD, Passos AD, Mouza AA. Bubble columns with fine pore sparger and non-Newtonian liquid phase: prediction of gas holdup. Chem Eng Sci 2013; 98: 331–338.10.1016/j.ces.2013.05.006Search in Google Scholar

Baawain MS, Gamal El-Din M, Smith DW. Artificial neural networks modelling of ozone bubble columns: mass transfer coefficient, gas hold-up, and bubble size. Ozone Sci Eng 2007; 29: 343–352.10.1080/01919510701549236Search in Google Scholar

Balamurugan V, Subbarao D, Roy S. Enhancement in gas holdup in bubble columns through use of vibrating internals. Can J Chem Eng 2010; 88: 1010–1020.10.1002/cjce.20362Search in Google Scholar

Bar N, Das SK. Comparative study of friction factor by prediction of frictional pressure drop per unit length using empirical correlation and ANN for gas-non-Newtonian liquid flow through 180 degree circular bend. Int Rev Chem Eng 2011; 3: 628–643.Search in Google Scholar

Bar N, Bandyopadhyay TK, Biswas MN, Das SK. Prediction of pressure drop using artificial neural network for non-Newtonian liquid flow through piping components. J Pet Sci Eng 2010a; 71: 187–194.10.1016/j.petrol.2010.02.001Search in Google Scholar

Bar N, Biswas MN, Das SK. Prediction of pressure drop using artificial neural network for gas non-Newtonian liquid flow through piping components. Ind Eng Chem Res 2010b; 49: 9423–9429.10.1021/ie1007739Search in Google Scholar

Behkish A, Lemoine R, Sehabiague L, Oukaci R, Morsi BI. Prediction of the gas holdup in industrial-scale bubble columns and slurry bubble column reactors using back-propagation neural networks. Int J Chem React Eng 2005; 3: 1;35.10.2202/1542-6580.1193Search in Google Scholar

Benchabane A, Bekkour K. Rheological properties of carboxymethyl cellulose (CMC) solutions. Colloid Polym Sci 2008; 286: 1173–1180.10.1007/s00396-008-1882-2Search in Google Scholar

Benyounes K. Investigation of the influence of molecular weight of polymer on the rheological behavior of carboxymethylcellulose solutions. International Multi disciplinary Scientific GeoConference: SGEM: Surveying Geology & mining Ecology Management 2013; 2: 951–958.10.5593/SGEM2013/BA1.V2/S06.002Search in Google Scholar

Bhunia K, Kundu G, Mukherjee D. Prediction of gas holdup in a flotation column by artificial neural network. Int J Coal Prep Util 2015; 35: 165–175.10.1080/19392699.2014.916701Search in Google Scholar

Buchholz H, Buchholz R, Lucke J, Schugerl K. Bubble swarm behaviour and gas absorption in non-Newtonian fluids in sparged columns. Chem Eng Sci 1978; 33: 1061–1070.10.1016/0009-2509(78)85011-8Search in Google Scholar

Bulsari AB, Saxen H. Application of artificial neural networks for filtering, smoothing and prediction for a biochemical process. Expert Syst 1994; 11: 159–166.10.1111/j.1468-0394.1994.tb00322.xSearch in Google Scholar

Cancela MA, Alvarez E, Maceiras R. Effects of temperature and concentration on carboxymethylcellulose with sucrose rheology. J Food Eng 2005; 71: 419–424.10.1016/j.jfoodeng.2004.10.043Search in Google Scholar

Chen BH, Yang NS. Characteristics of a cocurrent multistage bubble column. Ind Eng Chem Res 1989; 28: 1405–1410.10.1021/ie00093a020Search in Google Scholar

Chen Z, Liu H, Zhang H, Ying W, Fang D. Oxygen mass transfer coefficient in bubble column slurry reactor with ultrafine suspended particles and neural network prediction. Can J Chem Eng 2013; 91: 532–541.10.1002/cjce.21663Search in Google Scholar

Chhabra RP. Bubbles, drops, and particles in non-Newtonian fluids. Boca Raton, FL: CRC Press, 2006: 17.10.1201/9781420015386Search in Google Scholar

Clift R, Grace JR, Weber ME. Bubbles, drops, and particles. Mineola, NY: Dover Publications, 1978.Search in Google Scholar

Craig VS. Bubble coalescence and specific-ion effects. Curr Opin Colloid Inter Sci 2004; 9: 178–184.10.1016/j.cocis.2004.06.002Search in Google Scholar

Deckwer WD, Schumpe A. Improved tools for bubble column reactor design and scale-up. Chem Eng Sci 1993; 48: 889–911.10.1016/0009-2509(93)80328-NSearch in Google Scholar

Deckwer WD, Nguyen-Tien K, Schumpe A, Serpemen Y. Oxygen mass transfer into aerated CMC solutions in a bubble column. Biotechnol Bioeng 1982; 24: 461–481.10.1002/bit.260240215Search in Google Scholar

Deng Z, Wang T, Zhang N, Wang Z. Gas holdup, bubble behavior and mass transfer in a 5 m high internal-loop airlift reactor with non-Newtonian fluid. Chem Eng J 2010; 160: 729–737.10.1016/j.cej.2010.03.078Search in Google Scholar

Devine WD, Shah YT, Morsi BI. Liquid phase axial mixing in a bubble column with viscous non-Newtonian liquids. Can J Chem Eng 1985; 63: 195–201.10.1002/cjce.5450630204Search in Google Scholar

Dewsbury K, Karamanev D, Margaritis A. Hydrodynamic characteristics of free rise of light solid particles and gas bubbles in non-Newtonian liquids. Chem Eng Sci 1999; 54: 4825–4830.10.1016/S0009-2509(99)00200-6Search in Google Scholar

Edali M, Esmail MN, Vatistas GH. Rheological properties of high concentrations of carboxymethyl cellulose solutions. J Appl Polym Sci 2001; 79: 1787–1801.10.1002/1097-4628(20010307)79:10<1787::AID-APP70>3.0.CO;2-2Search in Google Scholar

Eickenbusch H, Brunn PO, Schumpe A. Mass transfer into viscous pseudoplastic liquid in large-diameter bubble columns. Chem Eng Process Process Intensif 1995; 34: 479–485.10.1016/0255-2701(95)00626-5Search in Google Scholar

El-Temtamy SA, Khalil SA, Nour-el-din AA, Gaber A. Oxygen mass transfer in a bubble column bioreactor containing lysed yeast suspensions. Appl Microbial Biotechnol 1984; 19: 376–381.10.1007/BF00454372Search in Google Scholar

Elgozali A, Linek V, Fialova M, Wein O, Zahradnık J. Influence of viscosity and surface tension on performance of gas-liquid contactors with ejector type gas distributor. Chem Eng Sci 2002; 57: 2987–2994.10.1016/S0009-2509(02)00165-3Search in Google Scholar

Esmaeili A, Guy C, Chaouki J. The effects of liquid phase rheology on the hydrodynamics of a gas-liquid bubble column reactor. Chem Eng Sci 2015; 129: 193–207.10.1016/j.ces.2015.01.071Search in Google Scholar

Esmaeili A, Farag S, Guy C, Chaouki J. Effect of elevated pressure on the hydrodynamic aspects of a pilot-scale bubble column reactor operating with non-Newtonian liquids. Chem Eng J 2016; 288: 377–389.10.1016/j.cej.2015.12.017Search in Google Scholar

Fransolet E, Crine M, Marchot P, Toye D. Analysis of gas holdup in bubble columns with non-Newtonian fluid using electrical resistance tomography and dynamic gas disengagement technique. Chem Eng Sci 2005; 60: 6118–6123.10.1016/j.ces.2005.03.046Search in Google Scholar

Franz K, Buchholz R, Schuerl K. Comprehensive study of the gas holds up and bubble size distribution in highly viscous liquids II. CMC solutions. Chem Eng Commun 1980; 5: 187–202.10.1080/00986448008935963Search in Google Scholar

Funfschilling D, Li HZ. Effects of the injection period on the rise velocity and shape of a bubble in a non-Newtonian fluid. Chem Eng Res Des 2006; 84: 875–883.10.1205/cherd.01229Search in Google Scholar

Gandhi AB, Joshi JB. Unified correlation for overall gas hold-up in bubble column reactors for various gas-liquid systems using hybrid genetic algorithm‐support vector regression technique. Can J Chem Eng 2010; 88: 758–776.10.1002/cjce.20296Search in Google Scholar

Gandhi AB, Joshi JB, Jayaraman VK, Kulkarni BD. Development of support vector regression (SVR)-based correlation for prediction of overall gas hold-up in bubble column reactors for various gas-liquid systems. Chem Eng Sci 2007; 62: 7078–7089.10.1016/j.ces.2007.07.071Search in Google Scholar

Garakani AK, Mostoufi N, Sadeghi F, Fatourechi H, Sarrafzadeh M, Mehrnia M. Comparison between different models for rheological characterization of activated sludge. Iran J Environ Health Sci Eng 2011; 8: 255;264.Search in Google Scholar

Garcia-Ochoa F, Castro EG. Estimation of oxygen mass transfer coefficient in stirred tank reactors using artificial neural networks. Enzym Microb Technol 2001; 28: 560–569.10.1016/S0141-0229(01)00297-6Search in Google Scholar

Garson GD. Interpreting neural-network connection weights. AI Expert 1991; 6: 47–51.Search in Google Scholar

Ghannam MT, Esmail MN. Rheological properties of carboxymethyl cellulose. J Appl Polym Sci 1997; 64: 289–301.10.1002/(SICI)1097-4628(19970411)64:2<289::AID-APP9>3.0.CO;2-NSearch in Google Scholar

Ghosh UK, Upadhyay SN. Gas holdup and solid-liquid mass transfer in Newtonian and non-Newtonian fluids in bubble columns. Can J Chem Eng 2007; 85: 825–832.10.1002/cjce.5450850604Search in Google Scholar

Godbole SP, Honath MF, Shah YT. Holdup structure in highly viscous Newtonian and non-Newtonian liquids in bubble columns. Chem Eng Commun 1982; 16: 119–134.10.1080/00986448208911090Search in Google Scholar

Godbole SP, Schumpe A, Shah YT, Carr NL. Hydrodynamics and mass transfer in non-Newtonian solutions in a bubble column. AIChE J 1984; 30: 213–220.10.1002/aic.690300207Search in Google Scholar

Gómez-Dıaz D, Navaza JM. Rheology of aqueous solutions of food additives: effect of concentration, temperature and blending. J Food Eng 2003; 56: 387–392.10.1016/S0260-8774(02)00211-XSearch in Google Scholar

Grace JR. Shapes and velocities of bubbles rising in infinite liquids. Trans Inst Chem Eng 1973; 51: 116–120.Search in Google Scholar

Gupta R, Wanchoo RK. Motion of a single Newtonian liquid drop through quiescent immiscible visco-elastic liquid: shape and eccentricity. ASME J Fluids Eng 2009; 131: 1;11.10.1115/1.3054284Search in Google Scholar

Hamed MM, Khalafallah MG, Hassanien EA. Prediction of wastewater treatment plant performance using artificial neural networks. Environ Model Softw 2004; 19: 919–928.10.1016/j.envsoft.2003.10.005Search in Google Scholar

Haque MW, Nigam KDP, Joshi JB. Hydrodynamics and mixing in highly viscous pseudo-plastic non-Newtonian solutions in bubble columns. Chem Eng Sci 1986; 41: 2321–2331.10.1016/0009-2509(86)85082-5Search in Google Scholar

Haque MW, Nigam KDP, Joshi JB, Viswanathan K. Studies on gas holdup and bubble parameters in bubble columns with (carboxymethyl) cellulose solutions. Ind Eng Chem Res 1987; 26: 86–91.10.1021/ie00061a016Search in Google Scholar

Hecht-Nielson R. Neurocomputing. Reading, MA: Addison-Wesley, 1990.Search in Google Scholar

Heijnen JJ, Riet K, Wolthuis AJ. Influence of very small bubbles on the dynamic KLa measurement in viscous gas–liquid systems. Biotechnol Bioeng 1980; 22: 1945–1956.10.1002/bit.260220912Search in Google Scholar

Henzler HJ. Begasen hoherviskoser kltissigkeiten. Cbem.rlng – Techn 1980; 52: 643–652.10.1002/cite.330520807Search in Google Scholar

Ibrehem AS, Hussain MA. Prediction of bubble size in bubble columns using artificial neural network. J Appl Sci 2009; 9: 3196–3198.10.3923/jas.2009.3196.3198Search in Google Scholar

Jamialahmadi M, Zehtaban MR, Müller-Steinhagen H, Sarrafi A, Smith JM. Study of bubble formation under constant flow conditions. Chem Eng Res Des 2001; 79: 523–532.10.1205/02638760152424299Search in Google Scholar

Jana SK, Biswas AB, Das SK. Gas holdup in tapered bubble column using pseudoplastic non-Newtonian liquids. Korean J Chem Eng 2014a; 31: 574–581.10.1007/s11814-013-0205-6Search in Google Scholar

Jana SK, Biswas AB, Das SK. Pressure drop in tapered bubble columns using non-Newtonian pseudoplastic liquid-experimental and ANN prediction. Can J Chem Eng 2014b; 92: 578–584.10.1002/cjce.21838Search in Google Scholar

Jana SK, Biswas AB, Das SK. ANN applicability in gas holdup prediction in tapered bubble columns using non-Newtonian pseudoplastic liquids. ChemXpress 2015; 8: 102–111.Search in Google Scholar

Jhawar AK, Prakash A. Bubble column with internals: effects on hydrodynamics and local heat transfer. Chem Eng Res Des 2014; 92: 25–33.10.1016/j.cherd.2013.06.016Search in Google Scholar

Joshi JB. Axial mixing in multiphase contactors;a unified correlation. Trans Inst Chem Eng 1980; 58: 155;165.Search in Google Scholar

Joshi JB, Veera VP, Prasad Ch V, Phanikumar DV, Deshphande NS, Thakre SS, Thorat BN. Gas hold-up structure in bubble column reactors. Pinsa 1998; 64: 441–567.Search in Google Scholar

Kang Y, Min BT, Nah JB, Kim SD. Mass transfer in continuous bubble columns with floating bubble breakers. AIChE J 1990; 36: 1255–1258.10.1002/aic.690360815Search in Google Scholar

Kang Y, Cho YJ, Woo KJ, Kim SD. Diagnosis of bubble distribution and mass transfer in pressurized bubble columns with viscous liquid medium. Chem Eng Sci 1999; 54: 4887–4893.10.1016/S0009-2509(99)00209-2Search in Google Scholar

Kantak MV, Hesketh RP, Kelkar BG. Effect of gas and liquid properties on gas phase dispersion in bubble columns. Chem Eng J Biochem Eng J 1995; 59: 91–100.10.1016/0923-0467(94)02922-9Search in Google Scholar

Kantarci N, Borak F, Ulgen KO. Bubble column reactors. Process Biochem 2005; 40: 2263–2283.10.1016/j.procbio.2004.10.004Search in Google Scholar

Kawalec-Pietrenko BT. Time-dependent gas hold-up and bubble size distributions in a gas—highly viscous liquid—solid system. Chem Eng J 1992; 50: B29–B37.10.1016/0300-9467(92)80017-5Search in Google Scholar

Kawase Y, Moo-Young M. Influence of non-Newtonian flow behaviour on mass transfer in bubble Columns with and without draft tubes. Chem Eng Commun 1986; 40: 67–83.10.1080/00986448608911691Search in Google Scholar

Kawase Y, Moo-Young M. Theoretical prediction of gas holdup in bubble columns with Newtonian and non-Newtonian fluids. Ind Eng Chem Res 1987; 26: 933–937.10.1021/ie00065a014Search in Google Scholar

Kawase Y, Umeno S, Kumagai T. The prediction of gas holdup in bubble column reactors: Newtonian and non-Newtonian fluids. Chem Eng J 1992; 50: 1–7.10.1016/0300-9467(92)80001-QSearch in Google Scholar

Kelkar BG, Shah YT. Gas holdup and backmixing in bubble column with polymer solutions. AIChE J 1985; 31: 700–702.10.1002/aic.690310424Search in Google Scholar

Khare AS, Niranjan K. Mechanically agitated contactors: gas hold up in highly viscous media. IChemE Res Event Proc 1994; 1: 120–122.Search in Google Scholar

Khare AS, Niranjan K. Impeller-agitated aerobic reactor: the influence of tiny bubbles on gas hold-up and mass transfer in highly viscous liquids. Chem Eng Sci 1995; 50: 1091–1105.10.1016/0009-2509(94)00474-6Search in Google Scholar

Khare AS, Niranjan K. The effect of impeller design on gas holdup in surfactant containing highly viscous non-Newtonian agitated liquids. Chem Eng Process Process Intensif 2002; 41: 239–249.10.1016/S0255-2701(01)00139-8Search in Google Scholar

Kojima E, Akehata T, Shirai T. Rising velocity and shape of single air bubbles in highly viscous liquids. J Chem Eng Jpn 1968; 1: 45–50.10.1252/jcej.1.45Search in Google Scholar

Kulkarni AA, Joshi JB. Bubble formation and bubble rise velocity in gas-liquid systems: a review. Ind Eng Chem Res 2005; 44: 5873–5931.10.1021/ie049131pSearch in Google Scholar

Lahiri SK, Ghanta KC. Development of an artificial neural network correlation for prediction of hold-up of slurry transport in pipelines. Chem Eng Sci 2008; 63: 1497–1509.10.1016/j.ces.2007.11.030Search in Google Scholar

Lakota A. Effect of highly viscous non-Newtonian liquids on gas holdup in a concurrent upflow bubble column. Acta Chim Slovenica 2007; 54: 678.Search in Google Scholar

Lee DH, Kim JO, Kim SD. Mass transfer and phase holdup characteristics in three-phase fluidized beds. Chem Eng Commun 1993; 119: 179–196.10.1080/00986449308936115Search in Google Scholar

Lemoine R, Morsi BI. An algorithm for predicting the hydrodynamic and mass transfer parameters in agitated reactors. Chem Eng J 2005; 114: 9–31.10.1016/j.cej.2005.08.015Search in Google Scholar

Lemoine R, Fillion B, Behkish A, Smith AE, Morsi BI. Prediction of the gas–liquid volumetric mass transfer coefficients in surface-aeration and gas-inducing reactors using neural networks. Chem Eng Process Process Intensif 2003; 42: 621–643.10.1016/S0255-2701(02)00211-8Search in Google Scholar

Lemoine R, Behkish A, Sehabiague L, Heintz YJ, Oukaci R, Morsi BI. An algorithm for predicting the hydrodynamic and mass transfer parameters in bubble column and slurry bubble column reactors. Fuel Process Technol 2008; 89: 322–343.10.1016/j.fuproc.2007.11.016Search in Google Scholar

Leonard C, Ferrasse JH, Boutin O, Lefevre S, Viand A. Bubble column reactors for high pressures and high temperatures operation. Chem Eng Res Des 2015; 100: 391–421.10.1016/j.cherd.2015.05.013Search in Google Scholar

Li S, Ma Y, Fu T, Zhu C, Li H. The viscosity distribution around a rising bubble in shear-thinning non-Newtonian fluids. Braz J Chem Eng 2012a; 29: 265–274.10.1590/S0104-66322012000200007Search in Google Scholar

Li S, Zhu C, Fu T, Ma Y. Study on the mass transfer of bubble swarms in three different rheological fluids. Int J Heat Mass Transf 2012b; 55: 6010–6016.10.1016/j.ijheatmasstransfer.2012.06.011Search in Google Scholar

Li S, Ma Y, Jiang S, Fu T, Zhu C, Li HZ. The drag coefficient and the shape for a single bubble rising in non-Newtonian fluids. J Fluids Eng 2012c; 134: 1–4.10.1115/1.4007073Search in Google Scholar

Mandal A, Kundu G, Mukherjee D. Gas holdup and entrainment characteristics in a modified downflow bubble column with Newtonian and non-Newtonian liquid. Chem Eng Process Process Intensif 2003; 42: 777–787.10.1016/S0255-2701(02)00134-4Search in Google Scholar

Mitra T, Singha B, Bar N, Das SK. Removal of Pb (II) ions from aqueous solution using water hyacinth root by fixed-bed column and ANN modeling. J Hazard Mater 2014; 273: 94–103.10.1016/j.jhazmat.2014.03.025Search in Google Scholar PubMed

Mok YS, Kim YH, Kim SY. Bubble and gas holdup characteristics in a bubble column of CMC solution. Korean J Chem Eng 1990; 7: 31–39.10.1007/BF02697339Search in Google Scholar

Moo-Young M, Kawase Y. Gas holdup and mass transfer in a bubble column with visco-elastic fluids. Can J Chem Eng 1987; 65: 113–118.10.1002/cjce.5450650118Search in Google Scholar

Muller FL, Davidson JF. On the contribution of small bubbles to mass transfer in bubble columns containing highly viscous liquids. Chem Eng Sci 1992; 47: 3525–3532.10.1016/0009-2509(92)85066-KSearch in Google Scholar

Nakanoh M, Yoshida F. Gas absorption by Newtonian and non-Newtonian liquids in a bubble column. Ind Eng Chem Process Des Dev 1980; 19: 190–195.10.1021/i260073a033Search in Google Scholar

Nishikawa M, Kato H, Hashimoto K. Heat transfer in aerated tower filled with non-Newtonian liquid. Ind Eng Chem Process Des Dev 1977; 16: 133–137.10.1021/i260061a607Search in Google Scholar

Olden JD. An artificial neural network approach for studying phytoplankton succession. Hydrobiologia 2000; 436: 131–143.10.1023/A:1026575418649Search in Google Scholar

Olden JD, Jackson DA. Illuminating the “black box”: a randomization approach for understanding variable contributions in artificial neural networks. Ecol Model 2002; 154: 135–150.10.1016/S0304-3800(02)00064-9Search in Google Scholar

Olden JD, Joy MK, Death RG. An accurate comparison of methods for quantifying variable importance in artificial neural networks using simulated data. Ecol Model 2004; 178: 389–397.10.1016/j.ecolmodel.2004.03.013Search in Google Scholar

Olivieri G, Russo ME, Simeone M, Marzocchella A, Salatino P. Effects of viscosity and relaxation time on the hydrodynamics of gas–liquid systems. Chem Eng Sci 2011; 66: 3392–3399.10.1016/j.ces.2011.01.027Search in Google Scholar

Ozturk SS, Schumpe A. The influence of suspended solids on oxygen transfer to organic liquids in a bubble column. Chem Eng Sci 1987; 42: 1781–1785.10.1016/0009-2509(87)80182-3Search in Google Scholar

Pandit AB, Joshi YK. Mixing time studies in bubble column reactor with and without internals. Int J Chem React Eng 2005; 3: 1–25.10.2202/1542-6580.1182Search in Google Scholar

Pareek VK, Brungs MP, Adesina AA, Sharma R. Artificial neural network modeling of a multiphase photodegradation system. J Photochem Photobiol A Chem 2002; 149: 139–146.10.1016/S1010-6030(01)00640-2Search in Google Scholar

Passos AD, Voulgaropoulos VP, Paras SV, Mouza AA. The effect of surfactant addition on the performance of a bubble column containing a non-Newtonian liquid. Chem Eng Res Des 2015; 95: 93–104.10.1016/j.cherd.2015.01.008Search in Google Scholar

Philip J, Proctor JM, Niranjan K, Davidson JF. Gas hold-up and liquid circulation in internal loop reactors containing highly viscous Newtonian and non-Newtonian liquids. Chem Eng Sci 1990; 45: 651–664.10.1016/0009-2509(90)87008-GSearch in Google Scholar

Pilizota V, Subaric D, Lovric T. Rheological properties of CMC dispersions at low temperatures. Food Technol Biotechnol 1996; 34: 87–90.Search in Google Scholar

Pirdashti M, Curteanu S, Kamangar MH, Hassim MH, Khatami MA. Artificial neural networks: applications in chemical engineering. Rev Chem Eng 2013; 29: 205–239.10.1515/revce-2013-0013Search in Google Scholar

Pradhan AK, Parichha RK, De P. Flow behavior and gas holdup in two-phase bubble column. Inst Eng (India) 1991; 72: 6–9.Search in Google Scholar

Pradhan AK, Parichha RK, De P. Gas hold-up in non-Newtonian solutions in a bubble column with internals. Can J Chem Eng 1993; 71: 468–471.10.1002/cjce.5450710319Search in Google Scholar

Reisener J, Reuter MA, Kruger J. Modelling of the mass transfer in gas-sparged electrolysers with neural nets. Chem Eng Sci 1993; 48: 1089–1101.10.1016/0009-2509(93)81039-XSearch in Google Scholar

Rodrigue D. Drag coefficient;Reynolds number transition for gas bubbles rising steadily in viscous fluids. Can J Chem Eng 2001; 79: 119;123.10.1002/cjce.5450790118Search in Google Scholar

Roy S, Parichha RK, De P, Ray P, Barman B. Gas holdup in bubble column with immersed tubes. Proc Indian Chem Eng Cong 1989; 1: 72–77.Search in Google Scholar

Rumelhart DE, Hinton GE, Williams RJ. Learning internal representation by error propagation. In: Rumelhart DE, McClelland JL, editors. Parallel distributed processing, Vol. 1, Chapter 8. Cambridge, MA: MIT Press, 1986.10.7551/mitpress/5236.001.0001Search in Google Scholar

Ryu HW, Chang YK, Kim SD. Gas holdup and mass transfer characteristics of carboxymethyl cellulose solutions in a bubble column with a radial gas sparger. Bioprocess Eng 1993; 8: 271–277.10.1007/BF00369840Search in Google Scholar

Saxena SC, Vadivel R. Heat transfer from a tube bundle in a bubble column. Int Commun Heat Mass Transf 1988; 15: 657–667.10.1016/0735-1933(88)90056-5Search in Google Scholar

Schumpe A, Deckwer WD. Gas holdups, specific interfacial areas, and mass transfer coefficients of aerated carboxymethyl cellulose solutions in a bubble column. Ind Eng Chem Process Des Dev 1982; 21: 706–711.10.1021/i200019a028Search in Google Scholar

Schumpe A, Deckwer WD. Organic liquids in a bubble column: holdups and mass transfer coefficients. AIChE J 1987a; 33: 1473–1480.10.1002/aic.690330907Search in Google Scholar

Schumpe A, Deckwer WD. Viscous media in tower bioreactors: hydrodynamic characteristics and mass transfer properties. Bioprocess Eng 1987b; 2: 79–94.10.1007/BF00369528Search in Google Scholar

Schumpe A, Deckwer WD, Nigam KD. Gas-liquid mass transfer in three-phase fluidized beds with viscous pseudoplastic liquids. Can J Chem Eng 1989; 67: 873–877.10.1002/cjce.5450670523Search in Google Scholar

Schwarz S, Kempe T, Fröhlich J. An immersed boundary method for the simulation of bubbles with varying shape. J Comput Phys 2016; 315: 124–149.10.1016/j.jcp.2016.01.033Search in Google Scholar

Shah YT, Kelkar BG, Godbole SP, Deckwer WD. Design parameters estimations for bubble column reactors. AIChE J 1982; 28: 353–379.10.1002/aic.690280302Search in Google Scholar

Shaikh A, Al-Dahhan M. Development of an artificial neural network correlation for prediction of overall gas holdup in bubble column reactors. Chem Eng Process Process Intensif 2003; 42: 599–610.10.1016/S0255-2701(02)00209-XSearch in Google Scholar

Sharma R, Singh K, Singhal D, Ghosh R. Neural network applications for detecting process faults in packed towers. Chem Eng Process Process Intensif 2004; 43: 841–847.10.1016/S0255-2701(03)00103-XSearch in Google Scholar

Suh IS, Schumpe A, Deckwer WD, Kulicke WM. Gas-liquid mass transfer in the bubble column with viscoelastic liquid. Can J Chem Eng 1991; 69: 506–512.10.1002/cjce.5450690215Search in Google Scholar

Takahashi T, Miyahara T, Izawa H. Drag coefficient and wake volume of single bubbles rising through quiescent liquid. Kagaku Kogaku Ronbunshu 1976; 2: 480–487.10.1252/kakoronbunshu.2.480Search in Google Scholar

Tripathi MK, Sahu KC, Govindarajan R. Dynamics of an initially spherical bubble rising in quiescent liquid. Nat Commun 2015; 6: 1–9.10.1038/ncomms7268Search in Google Scholar

Utomo MB, Sakai T, Uchida S, Maezawa A. Simultaneous measurement of mean bubble diameter and local gas holdup using ultrasonic method with neural network. Chem Eng Technol 2001; 24: 493–500.10.1002/1521-4125(200105)24:5<493::AID-CEAT493>3.0.CO;2-LSearch in Google Scholar

Utomo MB, Sakai T, Uchida S. Use of neural network–ultrasonic technique for measuring gas and solid hold‐ups in a slurry bubble column bubble colum. Chem Eng Technol 2002; 25: 293–299.10.1002/1521-4125(200203)25:3<293::AID-CEAT293>3.0.CO;2-XSearch in Google Scholar

Valente GFS, Mendonça RCS, Pereira JAM, Felix LB. Artificial neural network prediction of chemical oxygen demand in dairy industry effluent treated by electrocoagulation. Sep Purif Technol 2014; 132: 627–633.10.1016/j.seppur.2014.05.053Search in Google Scholar

Vatai GY, Tekic MN. Gas holdup and mass transfer in bubble columns with pseudoplastic liquids. Chem Eng Sci 1989; 44: 2402–2407.10.1016/0009-2509(89)85178-4Search in Google Scholar

Veera UP, Joshi JB. Measurement of gas holdup profiles in bubble column by gamma ray tomography: effect of liquid phase properties. Chem Eng Res Des 2000; 78: 425–434.10.1205/026387600527329Search in Google Scholar

Vinaya M, Varma YBG. Some aspects of hydrodynamics in multistage bubble columns. Bioprocess Eng 1995; 13: 231–237.10.1007/BF00417633Search in Google Scholar

Wanchoo RK, Sharma SK, Bansal R. Rheological parameters of some water-soluble polymers. J Polym Mater 1996; 13: 49–55.Search in Google Scholar

Wanchoo RK, Sharma SK, Gupta R. Shape of a Newtonian liquid drop moving through an immiscible quiescent non-Newtonian liquid. Chem Eng Process Process Intensif 2003; 42: 387–393.10.1016/S0255-2701(02)00059-4Search in Google Scholar

Wellek RM, Agrawal AK, Skelland AHP. Shape of liquid drops moving in liquid media. AIChE J 1966; 12: 854–862.10.1002/aic.690120506Search in Google Scholar

Wenyuan F, Youguang M, Shaokun J, Ke Y, Huaizhi L. An experimental investigation for bubble rising in non-Newtonian fluids and empirical correlation of drag coefficient. J Fluids Eng 2010; 132: 1–7.10.1115/1.4000739Search in Google Scholar

Wenyuan F, XiaoHong Y. A laser imaging-LDV coupling measurement of single bubble forming and rising in shear-thinning fluid. J Thermal Sci 2014; 23: 233;238.10.1007/s11630-014-0700-zSearch in Google Scholar

Yamashita F. Effects of vertical pipe and rod internals on gas holdup in bubble columns. J Chem Eng Jpn 1987a; 20: 204–206.10.1252/jcej.20.204Search in Google Scholar

Yamashita F. Effect of shape of baffle plates and mesh and cross-sectional area of wire gauges on gas hold-up and pressure drop in a bubble column. J Chem Eng Jpn 1987b; 20: 201–204.10.1252/jcej.20.201Search in Google Scholar

Yang H, Fang B, Reuss M. kLa Correlation established on the basis of a neural network model. Can J Chem Eng 1999; 77: 838–843.10.1002/cjce.5450770508Search in Google Scholar

Youssef AA, Al-Dahhan MH. Impact of internals on the gas holdup and bubble properties of a bubble column. Ind Eng Chem Res 2009; 48: 8007–8013.10.1021/ie900266qSearch in Google Scholar

Yuanxin W, Xianghua L, Qiming C, Dinghuo LI, Shirong L, Al-Dahhan MH, Dudukovic MP. Prediction of gas holdup in bubble columns using artificial neural network. Chin J Chem Eng 2003; 11: 162–165.Search in Google Scholar

Zhang L, Yang C, Mao ZS. An empirical correlation of drag coefficient for a single bubble rising in non-Newtonian liquids. Ind Eng Chem Res 2008a; 47: 9767–9772.10.1021/ie8010319Search in Google Scholar

Zhang L, Yang C, Mao ZS. Unsteady motion of a single bubble in highly viscous liquid and empirical correlation of drag coefficient. Chem Eng Sci 2008b; 63: 2099–2106.10.1016/j.ces.2008.01.010Search in Google Scholar

Received: 2016-12-07
Accepted: 2017-08-02
Published Online: 2017-09-26
Published in Print: 2018-11-27

©2018 Walter de Gruyter GmbH, Berlin/Boston

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