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AN ANALYTICAL SOLUTION OF THE CONVECTIVE DRYING OF A MULTICOMPONENT LIQUID FILM
KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena.
KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena. (Drying)
KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena.
KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena. (Drying)
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. 516-523 p.
Keyword [en]
Evaporation, Mass transfer, Multicomponent diffusion, Selectivity, Ternary mixture
National Category
Chemical Engineering
Identifiers
URN: urn:nbn:se:kth:diva-34195ISBN: 963-9483-58-3 (print)OAI: oai:DiVA.org:kth-34195DiVA: diva2:419846
Conference
15th International Drying Symposium (IDS 2006)
Note
QC 20110708Available from: 2011-07-08 Created: 2011-05-30 Last updated: 2012-03-23Bibliographically approved
In thesis
1. Transport Coefficients during Drying of Solids containing Multicomponent Mixtures
Open this publication in new window or tab >>Transport Coefficients during Drying of Solids containing Multicomponent Mixtures
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
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:nbn:se:kth:diva-28897 (URN)978-91-7415-850-2 (ISBN)
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
2. An Analytical Solution Applied to Heat and Mass Transfer in a Vibrated Fluidised Bed Dryer
Open this publication in new window or tab >>An Analytical Solution Applied to Heat and Mass Transfer in a Vibrated Fluidised Bed Dryer
2011 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

A mathematical model for the drying of particulate solids in a continuous vibrated fluidised bed dryer was developed and applied to the drying of grain wetted with a single liquid and porous particles containing multicomponent liquid mixtures. Simple equipment and material models were applied to describe the process. In the plug-flow equipment model, a thin layer of particles moving forward and well mixed in the direction of the gas flow was regarded; thus, only the longitudinal changes of particle moisture content and composition as well as temperature along the dryer were considered. Concerning the material model, mass and heat transfer in a single isolated particle was studied. For grain wetted with a single liquid, mass and heat transfer within the particles was described by effective transfer coefficients. Assuming a constant effective mass transport coefficient and effective thermal conductivity of the wet particles, analytical solutions of the mass and energy balances were obtained. The variation of both transport coefficients along the dryer was taken into account by a stepwise application of the analytical solution in space intervals with non-uniform inlet conditions and averaged coefficients from previous locations in the dryer. Calculation results were verified by comparison with experimental data from the literature. There was fairly good agreement between experimental data and simulation but the results depend strongly on the correlation used to calculate heat and mass transfer coefficients.

 

For the case of particles containing a multicomponent liquid mixture dried in the vibrated fluidised bed dryer, interactive diffusion and heat conduction were considered the main mechanisms for mass and heat transfer within the particles. Assuming a constant matrix of effective multicomponent diffusion coefficients and thermal conductivity of the wet particles, analytical solutions of the diffusion and conduction equations were obtained. The equations for mass transfer were decoupled by a similarity transformation and solved simultaneously with conduction equation by the variable separation method. Simulations gave a good insight into the selectivity of the drying process and can be used to find conditions to improve aroma retention during drying.

 

Also, analytical solutions of the diffusion and conduction equations applied to liquid-side-controlled convective drying of a multicomponent liquid film were 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 and the ordinary differential equation that describes the changes in the liquid film thickness. Variations of physical properties along the process trajectory were taken into account as in the previous cases. Simulation results were compared with experimental data from the literature and a fairly good agreement was obtained. Simulations performed with ternary liquid mixtures containing only volatile components and ternary mixtures containing components of negligible volatility showed that it is difficult to obtain an evaporation process that is completely controlled by the liquid-side mass transfer. This occurs irrespective of the initial drying conditions.

 

Despite simplifications, the analytical solution of the material model gives a good insight into the selectivity of the drying process and is computationally fast. The solution can be a useful tool for process exploration and optimisation. It can also be used to accelerate convergence and reduce tedious and time-consuming calculations when more rigorous models are solved numerically.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2011. x, 54 p.
Series
Trita-CHE-Report, ISSN 1654-1081 ; 2011:44
Keyword
Analytical solution, Heat and mass transfer, Temperature and moisture distribution, Drying modelling, Multicomponent drying, Drying selectivity, Volatile retention, Ternary mixture, Drying of particulate materials, Vibrated fluidised bed dryer
National Category
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-34241 (URN)978-91-7501-038-0 (ISBN)
Presentation
2011-06-15, D41, KTH, Lindstedtsvägen 17, 1 tr, Stockholm, 10:00 (English)
Opponent
Supervisors
Note
QC 20110614Available from: 2011-06-14 Created: 2011-05-30 Last updated: 2012-03-23Bibliographically approved

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