Explicit equation for determination of overall mass transfer coefficient in a hollow fiber membrane contactor


Membrane separation procedures, which are based on hollow low fiber membrane contactors, come with a number of benefits including high interfacial area as well as a dispersion-free operation. For these units, the porous membrane operates as a barrier and fortifies the aqueous-organic interface. The hollow fiber contactors have the advantage of being versatile and easy to operate. They also have a straightforward extrapolation from the laboratory to industrial conditions and flow rates. This is possible by raising the number of modules applied  due to the fact that the same fibers as well as fluid velocities can be implemented in both environments.

The concept of hollow fiber based  non-dispersive solvent extraction method has gained a lot of popularity. This concept has been investigated for a number of applications including organic acid separation from fermentation broths, metal and rare earth elements recovery, and recovery of aroma compounds from natural resources.

Yaidelin Manrique, Ana Ribeiro, and José Loureiro at University of Porto in Portugal in collaboration with Ahmet Özdural at Hacettepe University in Turkey and Dominique Trébouet CNRS in France developed an explicit equation for determining the overall mass transfer coefficient in the hollow fiber membrane modules while considering the unsteady state conditions within the membrane contactor and measuring the transient profiles of the inlet concentration in the aqueous phase. Their research work is published in journal, Chemical Engineering Science.

The authors computed the mass transfer coefficient measuring only the transient profiles of the inlet aqueous concentration. This was possible without the need of an optimization procedure. They obtained the explicit equation by the solution of the model equations of a membrane contactor when the concentration of the solute in the organic extractant phase could be assumed as zero in the system operation.

The authors then applied the characteristics method to solve the partial differential equation representing the mass balance to the aqueous phase in the fibers. They introduced a linear combination between the solutions in the two physical directions in a bid to combine the evolution of the solute concentration in the reservoir.

The researchers then used the numerical solution of the membrane contactor model in a bid to validate the approximation and define its validity region. The proposed explicit equation gave reasonable estimations of the mass transfer coefficient even when it was applied when the concentration in the organic phase could not be assumed to be zero. For example, when there was a recirculation of the organic phase from its reservoir, through the casing of the contactor and back to its reservoir.

The authors then proposed a method that allowed them to apply the explicit equation in the approximation of the overall mass transfer coefficient in the unit with recirculation of the organic phase and in the single pass units. This method was then applied to approximate the overall mass transfer coefficient from experimental data published in literature and the experimental outcomes were simulated. This indicated that the developed equation was capable of estimating the number of mass transfer units with appreciable precision even when the units were operated far a bit from the conditions for which the equation was derived.

Explicit equation for determination of overall mass transfer coefficient in a hollow fiber membrane contactor

About the author

Dr. Ana Mafalda Ribeiro graduated in Chemical Engineering at the Faculty of Engineering of the University of Porto (FEUP) in 1999. She completed her Ph.D. Thesis, entitled “Impregnated activated carbon filters. Their application in the removal of toxic gases and vapours by simultaneous adsorption and reaction”, at LSRE in April 2006. From 2006 to 2012, she was a Post-Doctoral Researcher and since July 2012, she is an Associate Researcher at LSRE-LCM. Her main field of expertise is in cyclic adsorption/reaction processes.

About the author

Prof. Dr. Dominique TREBOUET  received his Ph.D. degree on the topic of the landfill leachates treatment by membrane processes from the University of Nantes in 1998. He joined the University of Strasbourg and the Institut Pluridisciplinaire Hubert Curien in 2000. First, he was as an associate professor and he is as full professor since 2014. He teaches environmental chemistry, wastewater treatment, life cycle analysis, environmental management system at the Louis Pasteur University Institute of Technology.

His research is focused on the membrane engineering to respond to the valorization of ingredients from agro-resources (bio-based compounds) and urban mines (metal).

About the author

Dr. Yaidelin Manrique graduated in Chemical Engineering at the University Simón Bolívar in Venezuela in 2007. In 2009, she came to the Faculty of Engineering of University of Porto (FEUP) and obtained her Integrated Master in Chemical Engineering in 2010 with the thesis “Modeling and Simulation of Water-Gas Shift Reactors: from Conventional Packed-Bed to Membrane Reactor”. In 2017, she received her Ph.D. degree in Chemical and Biological Engineering from the FEUP with the Ph.D. thesis entitled “Supercritical fluid extraction and fractionation of bioactive natural products from cork”. Since September 2017, she has been working as a post-doctoral researcher at the LSRE-LCM participating in several research projects.

About the author

José Miguel Loureiro  graduated in Chemical Engineering in 1975 and obtained his PhD in Chemical Processes in 1986 from the University of Porto, Portugal. He was enrolled as a “monitor” before graduating (in 1974) and is currently Associate Professor of Chemical Engineering (with “agregação”) at the University of Porto. His research interests are mainly related with Adsorption, Chemical Reaction Engineering and Process Intensification. He published more than 140 scientific research papers in peer reviewed Journals with more than 2800 citations and an h-index of 30.

About the author

Professor Ahmet R. Özdural is Visiting Academic Staff at Hacettepe University, Chemical Engineering Department, Turkey. He received his Dipl. Chemical Engineer degree from University of Ankara in 1970 and his PhD degree from Hacettepe University in 1976. He entered academics at Hacettepe University as lecturer, and later transferred to pharmaceuticals industry and undertook several technical and administrative ranks until 1988, when he re-joined the Department of Chemical Engineering at Hacettepe University as a full professor.

He has lectured and published in biochemical engineering, modeling separation processes, chromatographic separation processes. Dr. Özdural is the recipient of several awards and fellowships including incentive award of Turkish Scientific and Technical Research Council, Fulbright fellowship (USA), Heinrich Hertz-Stiftung fellowship (Germany). He is serving as “Japan Prize” official nominator since 1996. He was inducted as honorary member of Ankara Industrialists and Businessmen Association.


Yaidelin A. Manrique, Ahmet R. Özdural, Dominique Trébouet, Ana M. Ribeiro, José M. Loureiro. Explicit equation for the determination of the overall mass transfer coefficient in a hollow fiber membrane contactor. Chemical Engineering Science, volume 166 (2017), pages 210–219.


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