Hydrodynamics in spray and packed liquid-liquid extraction columns: A review

Milan N. Sovilj, Branislava G. Nikolovski, Momčilo Đ. Spasojević


This work provides a review of hydrodynamic characteristics such as the slip velocity, the dispersed-phase holdup, mean drop size, and axial dispersion of non-mechanically agitated liquid-liquid (L-L) extractors, with special reference to spray and packed bed columns. The complexity and importance of hydrodynamic behavior in designing and scaling up L-L extractors was a driving force to analyze, compare and discuss some important experimental findings available in the literature. The effects of phase velocities and the dispersed-phase holdup on the slip velocity, the mean drop size and the axial dispersion coefficient were studied and presented. Empirical correlations for slip velocity, the Sauter mean drop diameter and the axial dispersion coefficient, which were taken from the literature, were commented in terms of their applicability.


spray and packed bed columns; slip velocity; Sauter mean drop diameter; axial dispersion coefficient

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L. A. Robbins, R. W. Cusack, Liquid-liquid extraction operations and equipment. In: Perry's Chemical Engi-neers' Handbook R. H. Perry, D. W. Green (Eds.), Sev-enth Edition. McGraw-Hill Companies, Inc., 1997, pp. 1–47.

J. D. Thornton, Extraction, liquid-liquid. In: Thermo-pedia; A-to-Z Guide to Thermodynamics, Heat & Mass Transfer, and Fluids Engineering(Authors) A. A. Ale-ksandrov, D. J. Archer, D. Arcoumanis, B. J. Azzopardi, Begell House, Begell Digital Portal, 2011.

DOI: 10.1615/AtoZ.e.extraction_liquid-liquid, accessed July 2018.

S. Mohanty, Modelling of Liquid-Liquid Extraction Col-umn: A Review, Rev. Chem. Eng., 16 (3), 199–248 (2000). DOI: https://doi.org/10.1515/REVCE.2000.16.3.199

N. N. Hidayah, S. Z. Abidin, The evolution of mineral processing in extraction of rare earth elements using liq-uid-liquid extraction: A review, Miner. Eng., 121, 146–157 (2018).

DOI: https://doi.org/10.1016/j.mineng.2018.03.018

D. F. Gerson, Liquid-Liquid Separations in Biotechnolo-gy. In: Biotechnology Research and Applications, J. Ga-vora, D. F. Gerson, J. Luong, A., Storer, J. H., Woodley (Eds), Springer, Dordrecht,1988.

DOI: https://doi.org/10.1007/978-94-009-1371-4_10

H. R. C. Pratt, G. W. Stevens. Design procedures for extractors with axial dispersion. In Science and Practice of Liquid Extraction, J. D. Thornton (Ed.), Oxford Uni-versity Press. Oxford. Ch. 8, 1992.

H. Zheng, W. Ren, K. Chen, Y. Gu, Z. Bai, S. Zhao, Influence of Marangoni convection on mass transfer in the n-propyl acetate/acetic acid/water system, Chem. Eng. Sci., 111, 278–285 (2014).

DOI: https://doi.org/10.1016/j.ces.2014.02.015

Koch Modular Process Systems, LLC. Typical Industrial Applications for Separation by Extraction, Liquid-Liquid Extraction Equipment and Chemical Separation Solutions, https://kochmodular.com/liquid-liquid-extrac¬tion, ac-cessed July 2018.

J. Rauber, Design Practice for Packed Liquid/Liquid Extraction Columns, Sulzer Chemtech Ltd., Winterhtur, 2003, http://folk.ntnu.no/skoge/prost/proceedings/aiche-2006/data/papers/P73337.pdf, accessed July 2018.

R. M. Sá, L. M. N. Góis, C. F. Cavalcanti, Dispersed phase holdup in a liquid-liquid extraction column, Lat. Am. Appl. Res., 40, 373–376 (2010), ISSN 0327-0793. http://www.scielo.org.ar/pdf/laar/v40n4/v40n4a12.pdf, accessed July 2018.

A. F. Seibert., J. R. Fair, Hydrodynamics and mass trans-fer in spray and packed liquid-liquid columns. Ind. Eng. Chem. Res., 27 (3), 470–481 (1988).


J. Maćkowiak, Basic principles of packed column design for liquid/liquid systems. In: Fluid Dynamics of Packed Columns, Springer, Berlin Heidelberg, 2010, pp.315–350. DOI:10.1007/b98397_7.

G. A. Hughmark, Liquid-liquid spray column drop size, hold-up, and continuous phase mass transfer, Ind. Eng. Chem. Fund., 6 (3), 408–413 (1967).


R. Letan, E. Kehat, The mechanics of a spray column, AIChE J. 13 (3), 443–449 (1967).


L. Steiner, S. Hartland, Neues zur mathematischen model-lierung von flüssig/flüssig-extraktions kolonnen, Chem. Ing. Tech., 55 (3), 194–201(1983).

DOI: https://doi.org/10.1002/cite.330550305

M. Diaz, A. T. Aguayo, R. Alvarez, Hydrodynamics of liquid-liquid countercurrent extraction column with up-flow gas agitation, Chem. Ing. Tech., 58 (1), 74–75 (1986). DOI: https://doi.org/10.1002/cite.330580127

M. Sovilj, G. Knežević, Gas-agitated liquid-liquid extrac-tion in a spray extraction column, Collect. Czech. Chem. Commun., 59, 2235–2243 (1994).

DOI: https://doi.org/10.1135/cccc19942235.

M. Sovilj, Axial dispersion in a three-phase gas-agitated spray extraction column, Collect. Czech. Chem. Com-mun., 63, 283–292 (1998).

DOI: https//doi.org/10.1135/19980283.

J. Xiong, L. Zhang, Effects of gas-agitation and packing on hydrodynamics and mass transfer of extraction col-umn, Can. J. Chem. Eng. , 82 (5), 1076–1080 (2004). DOI: https://doi.org/10.1002/cjce.5450820526

Y. Cheng, L. Wang, Sh. Lü, Y. Wang, Zh. Mi, Gas−liquid−liquid three-phase reactive extraction for the hydrogen peroxide preparation by anthraquinone process, Ind. Eng.Chem. Res., 47(19), 7414–7418 (2008). DOI:10.1021/ie800500y.

L. Steiner, M. Horvath, S. Hartland, Mass transfer be-tween two phase in a spray column at the unsteady state, Ind. Eng. Chem. Process Des. Dev., 17 (2), 175–182 (1978). DOI:10, 1021/i260066a011.

M. Sovilj, Slip velocity and hydrodynamic parameters in liquid-liquid spray columns, Collect. Czech. Chem. Commun., 54, 990–995 (1989).


M. N. Sovilj, Diffusion Operations, University of Novi Sad, Faculty of Technology, Novi Sad, 2004, pp 156–192. (in Serbian).

W. Batey, J. D. Thornton, Partial mass transfer coeffi-cients and packing performance in liquid-liquid extraction, Ind. Eng.Chem. Res., 28 (7), 1096–1101 (1989). DOI: 10.1021/ie00091a032.

Ch. E. Wicks, R. B. Beckmann, Dispersed-phase holdup in packed, countercurrent liquid-liquid extraction col-umns, AIChE J., 1 (4), (1955).

DOI: 10.1002/aic.690010408.

F. J. Appel, J. O. Elgin, Countercurrent extraction of ben-zoic acid between toluene and water – performance of spray and packed columns, I. E. C., 29, 451 (1937). DOI:10.1021/ie50328a022.

A. Salimi-Khorshidi, H. Abolghasemi, A. Khakpay, Z. Kheirjooy, M. Esmaieli, Spray and packed liquid-liquid extraction columns: drop size and dispersed phase mass transfer, Asia-Pacific J. Chem. Eng., 8 (6), 940–949 (2013). DOI: https://doi.org/10.1002/apj.1739

Z. Azizi, A. Rahbar, H. Bahmanyar, H. Abolghasemi, Mass transfer model for a single dropflow of two liquid phases in a structured packed column. In: Separation Processes: Emerging Technologies for Sustainable De-velopment, P. K. Mishra, M. K.Mondal, P. Srivastava (Eds), Allied Publishers Pvt. Ltd., New Delhi, India 2009, pp. 291–299.

S. A. Ghorbanian, H. Abolghasemi, S. R. Radpour, Modelling of mean drop size in an extraction spray col-umn and developing a new model, Iran. J. Chem. Chem. Eng. Research., 30 (4), 89–96 (2011).

www.ijcce.ac.ir/article_6094_b6b4ff3cbec22aa9d8bfbc84b51bfb88.pdf, accessed July 2018.

M. Fourati, V. Roig, L. Reynal, Liquid dispersion in packed columns: experiments and numerical modelling. 11th International Conference on Gas-Liquid & Gas-Liquid-Solid Reactor Engineering, Séoul, South Korea, 2013, pp.266–278. https://hal.archives-ouvertes.fr/hal-00911059, accessed July 2018.

F. W. Keith, A. N. Hixson, Liquid-liquid extraction spray columns - drop formation and interfacial transfer area, Ind. Eng. Chem., 47 (2), 258–267 (1955). DOI:10.1021/ie50542a030.

M. N. Sovilj, B. G. Nikolovski, M. Đ. Spasojević, Hy-drodynamics of a pilot plant spray extraction column, APTEFF, 49, 159–168 (2018).

M. Horvath, L. Steiner, S. Hartland, Prediction of drop diameter, hold-up and back mixing coefficients in liquid-liquid spray columns, Can. J. Chem. Eng., 56 (1), 9–18 (1978). DOI:10.1002/cjce.5450560102.

V. L. Pebalk, B. G. Varfolomeev, K. Sh. Chigogidzeet, Hydrodynamics and mass transfer in spray extractors with closely packed drops, Khim. Prom–st. (Moscow), 8, 496 (1985).

S. Samdavid, T. Renganathan, K. Krishnaiach, Hydrody-namics of a cocurrent downward liquid-liquid extraction column, RSC Adv., 6, 12439–12445 (2016).

DOI: 10.1039/C5RA23649E.

J. C. Godfrey, M. J. Slater, Slip velocity relationships for liquid-liquid extraction columns, Chem. Eng. Res. Des., (Part A), 69a, 130–142 (1991).

J. D. Thornton, Spray liquid-liquid extraction columns: Prediction of limiting holdup and flooding rates, Chem. Eng. Sci., 5 (5), 201–208 (1956).

DOI: https://doi.org/10.1016/0009-2509(56)80031-6.

B. G. Varfolomeev, V. L. Pebalk, K. Sh. Chigogidzet, N. N. Lan, R. S. Fernando, Spray extraction columns: drop size and dispersed phase holdup, Theor. Found. Chem. Eng., 34(6), 556–561 (2000).

DOI: https://doi.org/10.1023/A:100522092

T. Pilhofer, Hydrodynamik von tropfenschwärmen in flüssig/flüssig-sprühkolonen, Chem. Ing. Tech., 46 (18), 783, MS 133/74 (1974) (in German).

A. Kumar, D. K. Vohra, S. Hartland, Sedimentation of drop dispersion in counter-current spray columns, Can. J. Chem. Eng. , 58, 154–159 (1980).


A. Kumar, S. Hartland, Gravity settling in liquid/liquid dispersions, Can. J. Chem. Eng., 63 (3), 368–376 (1985). DOI:10.1002/cjce.5450630303

A. Kumar, S. Hartland, Independent prediction of slip velocity and holdup in liquid-liquid extraction columns, Can. J. Chem. Eng., 67 (1), 17–25 (1989).


A. Kumar A., S. Hartland, Empirical prediction of operat-ing variables. In: Liquid–Liquid Extraction Equipment, J. C. Godfrey, M. J. Slater (Eds), John Wiley & Sons,1994, pp. 625–735.

A. Kumar, S. Hartland, A unified correlation for the pre-diction of dispersed phase hold-up in liquid–liquid extrac-tion columns, Ind. Eng. Chem. Res., 34, 3925–3940(1995). DOI:10.1021/ie00038a032.

H. C. Peterson, Effect of flow rates on holdup in a liquid-liquid extraction spray column for the system hexane-water, Ames Laboratory ISC Technical Reports. 6., Iowa State University, USA, (1950).

https://lib.dr.iastate.edu/cgi/viewcontent.cgi?article=1009&context=ameslab_iscreports, accessed July 2018.

R. Gayler, H. R. C. Pratt, Hold-up and pressure drop in packed columns, Trans. Inst. Chemical Engrs,. (Lon-don), 29, 110 (1951).

R. Gayler, N. W. Roberts, H. R. C. Pratt, Liquid-liquid extraction: Part IV. A further study of hold-up in packed columns, Chem. Eng. Res. Des., 31a, 57–68 (1953).

T. Sitamarayya, G. S. Laddha, Hold-up in packed liquid-liquid extraction columns, Chem. Eng. Sci., 13, 263 (1960).

G. Venkatamaran, G. S. Laddha, Limiting velocities, hold-up and pressure drop at flooding in packed extrac-tion columns, Am. Inst. Chem. Engrs J., 6, 355 (1960).

P. Chandrasekaran, G. S. Laddha, Counter-current two-phase flow in packed liquid-liquid extraction towers – es-timation of hold-up at and below flooding. In: Hydraulics and Fluid Mechanics, Proceedings of the First Australa-sian Conference held at the University of Western Aus-tralia, 6–13th December 1962, R. Silvester (Ed.), Elsevier Ltd., 1964, pp.243–257.

DOI: https://doi.org/10.1016/C2013-0-01769-0

A. Kumar, Droplet behavior in liquid/liquid extraction, Ph D. Thesis, ETH, Zürich, 1983.

E. Barnea, J. Mizrahi, A generalized approach to the fluid dynamics of particulate systems: Part 1. General correla-tion for fluidization and sedimentation in solid multiparti-cle systems, Chem. Eng. J., 5, 171–189 (1973).

DOI: https:// doi.org/10.1016/0300-9467(73)80008-5.

M. Perrut, R. Loutaty, Drop size in a liquid-liquid disper-sion: formation in jet break-up, Chem. Eng. J., 3, 286–293 (1972).

DOI: https://doi.org/10.1016/0300-9467(72) 85032-9.

S. Vedaiyan, T. E. Degaleesan, G. S. Laddha, Mean drop size & characteristic velocity of drop swarm in spray col-umn, Indian J. Technol., 12, 135 (1974).

A. Kumar, S. Hartland, Unified correlations for the pre-diction of drop size in liquid−liquid extraction columns, Ind. Eng. Chem. Res., 35, 2682–2695 (1996).


D. W. Marquardts, An algorithm for least-squares estima-tion of nonlinear parameters, J. Soc. Ind. Appl. Math., 11, 431–441 (1963).


B. S. Chun, G. T. Wilkinson, Drop size and hold-up in countercurrent extraction with supercritical CO2 in spray column, Ind. Eng. Chem. Res., 39 (12), 4673–4677 (2000). DOI:10.1021/ie000255l.

A. Salimi-Khorshidi, H. Abolghasemib,A. Khakpaya, N. Younes-Sinakia, Maximum Sauter mean diameter and terminal velocity of drops in a liquid-liquid spray extrac-tion column, Chem. Biochem. Eng. Q., 27 (3), 279–287 (2013), https://hrcak.srce.hr/108944.

S. GhaffariTooran, H. Abolghasemi, H. Bahmanyar, M. Esmaeili, A. Safari, A new correlation for overall Sher-wood number in packed liquid-liquid extraction column, World Academy Sc. Eng. Tech., 55, 137–139 (2009).

T. Miyauchi, T. Vermeulen, Longitudinal dispersion in two-phase continuous-flow operations, Ind. Eng. Chem. Fund., 2 (2), 113–126 (1963).

DOI: 10.1021/i160006a006

D. E. Hazlebeck, C. J. Geankoplis, Axial dispersion in a spray-type extraction tower, Ind.Eng. Chem. Fund., 2(4), 310–315 (1963). DOI: 10.1021/i160008a013.

D. R. Brutvan, Ph.D. Thesis, Rensselaer Polytechnic Institute, Troy, New York, 1958.

J. E. Henton, Back-mixing in liquid-liquid extraction spray columns. Ph.D. Thesis, University of British Co-lumbia, Vancouver, 1967.

J. E. Henton, S. D. Cavers, Continuous-phase axial dis-persion in liquid-liquid spray towers, Ind. Eng. Chem. Fund., 9 (3), 384–392 (1970).

M. Hozawa, H. Kono, T. Tadaki, S. Maeda, Axial disper-sion in a spray type liquid-liquid extraction column, Kagaku Kogaku, 34 (5), 533–538 (1970).

A. S. Zheleznyak, A. M. Landau, Calculation of longitu-dinal-mixing coefficients in two-phase systems with a continuous liquid phase, Theor. Fund. Chem. Eng., 7, 525 (1973).

J. E. Henton, L. W. Fish, S. D. Cavers, Liquid-liquid spray towers: continuous phase Peclet numbers, Ind. Eng. Chem. Fund., 12(3), 365–372 (1973).

DOI: 10.1021/i160047a016.

G. S. Laddha, T. R. Krishnan, S. Viswanathan, S. Vedai-yan, T. E. Degaleesan, H. E. Hoelscher, Some perfor-mance characteristics of liquid phase spray columns, AIChE J., 22 (3), 456–462 (1976).


C. J. Geankoplis, J. B. Sapp, F. C. Arnold, G. Marro-quin, Axial dispersion coefficients of the continuous phase in liquid-liquid spray towers, Ind. Eng. Chem. Fund., 21 (3)306–311 (1982).


J. S. Moon, A. Hennico, T. Vermeulen, Longitudinal dispersion in packed extraction columns with and without pulsation, Lawrence Berkley National Laboratory, Uni-versity of California, USA, Report UCRL-10928, 1963. https://esholarship.org/uc/item/0bj2q2vx, accessed July 2018.

K. W. McHenry, R. H. Wilhelm, Axial mixing of binary gas mixtures flowing in a random bed of spheres, AIChE J., 3 (1), 83–91 (1957). DOI: 10.1002/aic.690030115.

A. Hennico, G. Jacques, T. Vermeulen, Segmented lami-nar flow and other models for packed-bed longitudinal dispersion, Lawrence Berkley National Laboratory, Uni-versity of California, USA, Report UCRL-10696, 1964.

J. M. P. Q. Delgado, A critical review of dispersion in packed beds, Heat Mass Transfer., 42 (4), 279–310 (2006). DOI:10.1007/s00231-005-0019-0.

N. W. Han, J. Bhakta, R. G. Carbonell, Longitudinal and lateral dispersion in packed beds: Effect of column length and particle size distribution, AIChE J., 31 (2), 277–288 (1985), DOI: 10.1002/aic.690310215.

S. F. Chung, C. Wen, Longitudinal dispersion of liquid flowing through fixed and fluidized beds, AIChE J., 14 (6), 857–866 (1968),DOI: 10.1002/aic.690140608

C. L. De Ligny, Coupling between diffusion und convec-tion in radial dispersion of matter by fluid flow through packed beds, Chem. Eng. Sci., 25 (7), 1177–1181 (1970).

DOI: https://doi.org/10.1016/0009-2509(70)85007-2.

S. O. Rastegar, T. Gu, Empirical correlations for axial dispersion coefficient and Peclet number in fixed-bed col-umns, J. Chromatogr. A., 1490, 133–137 (2017). DOI: org/10.1016/j.chroma.2017.02.026.

DOI: http://dx.doi.org/10.20450/mjcce.2019.1519


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