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Transport Coefficients during Drying of Solids containing Multicomponent Mixtures
KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena.
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

This study investigated the transport coefficients involved in mass and heat transfer during the drying of a porous solid partially saturated with multicomponent mixtures.  It included the coefficients governing liquid transport through the solid, the matrix of multicomponent diffusion coefficients in the liquid phase, and the effective thermal conductivity.  As it is not possible to determine these coefficients by theoretical considerations alone and considerable experimental work is required to determine them in a broad range of process conditions, the principle of this study has been the use of mathematical models complemented with some empirical parameters.  These empirical parameters were determined by comparison between measurements in specially designed experiments and the results of mathematical models that describe the process.  In addition, the application of the multicomponent diffusion coefficients is described in two cases where liquid diffusion is important: convective evaporation of a multicomponent stationary liquid film and a falling film.

To study liquid transport through the solid, isothermal drying experiments were performed to determine the transient composition profiles and total liquid content of sand samples wetted with ternary liquid mixtures with different initial compositions and temperatures.  A mathematical model including mass transfer by capillary movement of the liquid and interactive diffusion in both the gas and liquid phases was developed.  To simulate the capillary movement of liquid mixtures, parameters experimentally determined for single liquids were weighed according to liquid composition. A fairly good agreement between theoretical and experimental liquid composition profiles was obtained considering that axial dispersion was included in the model.

To study the matrix of multicomponent diffusion coefficients in the liquid phase, the redistribution of liquid composition in a partially filled tube exposed to a longitudinal temperature gradient was analysed.  Experimental work was carried out using two main ternary mixtures with different initial compositions and temperature gradients.  Experimental data were compared with the results of a theoretical model that describes the steady-state liquid composition distribution in a partially filled non-isothermal tube to find the empirical exponent that modifies the matrix of thermodynamic factors.  Correlations for the exponents as a function of temperature were determined for each particular multicomponent mixture.

The effective thermal conductivity of a porous solid containing multicomponent liquid mixtures was studied by measuring the liquid composition, liquid content and temperature distributions in a cylindrical sample dried by convection from the open upper side and heated by contact with a hot source at the bottom side.  Simulations performed at a quasi steady state were compared with experiments to estimate the adjusting geometric parameter of Krischer’s model for effective thermal conductivity, which includes the contribution of the evaporation-diffusion-condensation mechanism. The results revealed that a resistance corresponding to a parallel arrangement between the phases seems to dominate in this case.

In the study of the convective drying of a multicomponent stationary liquid film, the equations describing interactive mass transfer were decoupled by a similarity transformation and solved simultaneously with a conduction equation by the method of variable separation.  Variations of physical properties along the process trajectory were taken into account by a stepwise application of the solution in time intervals with averaged coefficients from previous time steps.  Despite simplifications, the analytical solution gives a good insight into the selectivity of the drying process and is computationally fast.  On the other hand, numerical simulations of the convective evaporation of the multicomponent falling liquid film into an inert gas with a co-current flow arrangement of the phases almost always revealed a transition from liquid-phase-controlled conditions to a process in which neither the gas nor the liquid completely controls the evaporation.

The results obtained in this work would be useful in implementing models to improve the design, process exploration and optimisation of dryers by incorporating the solid-side effects to describe the drying of liquid mixtures along the whole process.

Place, publisher, year, edition, pages
Stockholm: KTH , 2011. , xii, 85 p.
Series
Trita-CHE-Report, ISSN 1654-1081 ; 5
Keyword [en]
capillary, conduction, convection, diffusion, evaporation, heat transfer, hydraulic conductivity, liquid film, liquid transport, mass transfer, Maxwell-Stefan diffusion coefficients, molar fluxes, phase equilibrium, temperature gradient, ternary mixture, thermodynamic factors
National Category
Chemical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-28897ISBN: 978-91-7415-850-2 (print)OAI: oai:DiVA.org:kth-28897DiVA: diva2:390497
Public defence
2011-02-11, E3, entréplan, Lindstedtsvägen 3, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20110124Available from: 2011-01-24 Created: 2011-01-21 Last updated: 2012-03-23Bibliographically approved
List of papers
1. Internal mass transfer during isothermal drying of a porous solid containing multicomponent liquid mixture
Open this publication in new window or tab >>Internal mass transfer during isothermal drying of a porous solid containing multicomponent liquid mixture
2005 (English)In: Drying Technology, ISSN 0737-3937, E-ISSN 1532-2300, Vol. 23, no 9-11, 1939-1951 p.Article in journal (Refereed) Published
Abstract [en]

Internal mass transfer in a porous solid partially saturated with multicomponent liquids has been experimentally and theoretically studied. Isothermal drying experiments were performed using a jacketed wind tunnel where the transient composition profiles and total liquid content of a cylindrical sample were determined. Sand samples wetted with the ternary liquid mixtures watermethanol-ethanol and 2-propanol-methanol-ethanol were dried at two different initial compositions and temperatures. A mathematical model including mass transfer by capillary movement of the liquid and interactive diffusion in both gas and liquid phase was developed. To simulate the capillary movement of liquid mixtures, parameters experimentally determined for single liquids where weighed according to liquid composition. A fairly good agreement between theoretical and experimental liquid composition profiles was obtained provided that axial dispersion is included in the model.

Place, publisher, year, edition, pages
Taylor & Francis, 2005
Keyword
liquid transport, hydraulic conductivity, capillary, diffusion coefficients
National Category
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-28889 (URN)10.1080/07373930500210390 (DOI)000232422200014 ()2-s2.0-27144524913 (Scopus ID)
Note

QC 20110124

Available from: 2011-01-21 Created: 2011-01-21 Last updated: 2017-12-11Bibliographically approved
2. Study of Heat and Mass Transfer to Determine Multicomponent Liquid Diffusion Coefficients in Partially Saturated Capillaries
Open this publication in new window or tab >>Study of Heat and Mass Transfer to Determine Multicomponent Liquid Diffusion Coefficients in Partially Saturated Capillaries
2007 (English)In: Experimental heat transfer, ISSN 0891-6152, E-ISSN 1521-0480, Vol. 20, no 2, 147-157 p.Article in journal (Refereed) Published
Abstract [en]

A study of simultaneous heat and mass transfer in partially saturated capillaries has been performed in order to develop a method that determines the matrix of multicomponent diffusion coefficients in liquid phase. The literature provides a semi-empirical formula developed by Bandrowski and Kubaczka [4] to calculate the matrix of multicomponent diffusion coefficients. The method separates the kinetic and thermodynamic contributions to mass transfer, and it contains an empirical exponent to improve the calculations. The present work attempts an estimation of the empirical exponent by studying the redistribution of compositions in an unsaturated nonisothermal capillary, taking into consideration the nonideality described by the matrix of thermodynamic factors. Two different ternary mixtures were tested at different temperature gradients and saturation degrees. The results reveal that the method is effective since specific values of the empirical exponent that modifies the matrix of thermodynamic factors were obtained for each system. In addition, the exponent seems to be dependent on temperature.

Keyword
liquid mixture, Maxwell-Stefan diffusion, saturation, temperature gradient
National Category
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-28891 (URN)10.1080/08916150601091464 (DOI)000245351000006 ()2-s2.0-33947374335 (Scopus ID)
Note

QC 20110124

Available from: 2011-01-21 Created: 2011-01-21 Last updated: 2017-12-11Bibliographically approved
3. Determination of Multicomponent Diffusion Coefficients in Liquid Phase from the Liquid Composition Distribution in a Partially Filled Non-Isothermal Tube
Open this publication in new window or tab >>Determination of Multicomponent Diffusion Coefficients in Liquid Phase from the Liquid Composition Distribution in a Partially Filled Non-Isothermal Tube
(English)Manuscript (preprint) (Other academic)
National Category
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-28893 (URN)
Note
QC 20110124Available from: 2011-01-21 Created: 2011-01-21 Last updated: 2011-01-24Bibliographically approved
4. The use of drying experiments in the study of the effective thermal conductivity in a solid containing a multicomponent liquid mixture
Open this publication in new window or tab >>The use of drying experiments in the study of the effective thermal conductivity in a solid containing a multicomponent liquid mixture
2012 (English)In: Chemical engineering research & design, ISSN 0263-8762, E-ISSN 1744-3563, Vol. 90, no 11, 1765-1778 p.Article in journal (Refereed) Published
Abstract [en]

The effective thermal conductivity of a porous solid containing multicomponent liquid mixtures has been studied. To achieve this, the liquid composition, liquid content and temperature distributions have been measured in a cylindrical sample dried by convection from the open upper side and heated by contact with a hot source at the bottom side. A quasi-steady state reached at high source temperatures permits to calculate the total heat flux from temperatures measured on the surface and the gas stream. The simulations performed and compared with experimental data made it possible to estimate the adjusting geometric parameter of Krischer's model for the effective thermal conductivity. The effective thermal conductivity has been widely studied for two-phase systems, mostly with regard to thermal insulation elements. The calculation of this transport parameter includes the contribution to heat transfer of the evaporation–diffusion–condensation mechanism undergone by the multicomponent mixture. The influence of liquid composition and temperature on the thermal conductivity due to the evaporation–diffusion–condensation mechanism and the effective thermal conductivity is described. The results reveal that in this case the resistance to heat transfer seems to correspond to a parallel arrangement between the phases.

Keyword
Diffusion, Evaporation, Heat transfer, Phase equilibrium, Temperature gradient
National Category
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-28894 (URN)10.1016/j.cherd.2012.04.003 (DOI)000312431400008 ()2-s2.0-84868354876 (Scopus ID)
Note

QC 20121214

Available from: 2011-01-21 Created: 2011-01-21 Last updated: 2017-12-11Bibliographically approved
5. AN ANALYTICAL SOLUTION OF THE CONVECTIVE DRYING OF A MULTICOMPONENT LIQUID FILM
Open this publication in new window or tab >>AN ANALYTICAL SOLUTION OF THE CONVECTIVE DRYING OF A MULTICOMPONENT LIQUID FILM
2006 (English)In: DRYING 2006 / [ed] I. Farkas, Gödöllo, Hungary: Szent István University Publisher , 2006, 516-523 p.Conference paper, Published paper (Refereed)
Abstract [en]

Analytical solutions of the diffusion and conduction equations applied to liquid-side-controlled convective drying of a multicomponent liquid film are developed. Assuming constant physical properties of the liquid, the equations describing interactive mass transfer are decoupled by a similarity transformation and solved simultaneously with conduction equation by the method of variable separation. Variations of physical properties along the process trajectory are taken into account by a stepwise application of the solution in time intervals with averaged coefficients from previous time steps. Despite simplifications, the analytical solution gives a good insight into the selectivity of the drying process and is computationally fast.

Place, publisher, year, edition, pages
Gödöllo, Hungary: Szent István University Publisher, 2006
Keyword
Evaporation, Mass transfer, Multicomponent diffusion, Selectivity, Ternary mixture
National Category
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-34195 (URN)963-9483-58-3 (ISBN)
Conference
15th International Drying Symposium (IDS 2006)
Note
QC 20110708Available from: 2011-07-08 Created: 2011-05-30 Last updated: 2012-03-23Bibliographically approved
6. Convective Drying of a Multicomponent Falling Film
Open this publication in new window or tab >>Convective Drying of a Multicomponent Falling Film
2006 (English)In: DRYING 2006: IDS 2006 / [ed] István Farkas, 2006, 243-250 p.Conference paper, Published paper (Refereed)
National Category
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-28896 (URN)963-9483-58-3 (ISBN)
Conference
15th International Drying Symposium, Budapest, August 20-23, 2006
Note
QC 20110124Available from: 2011-01-21 Created: 2011-01-21 Last updated: 2011-01-24Bibliographically approved

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