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An Analytical Solution Applied to Heat and Mass Transfer in a Vibrated Fluidised Bed Dryer
KTH, School of Chemical Science and Engineering (CHE), Chemical Engineering and Technology, Transport Phenomena. (Drying)
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 [en]
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: urn:nbn:se:kth:diva-34241ISBN: 978-91-7501-038-0OAI: oai:DiVA.org:kth-34241DiVA: diva2:419855
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
List of papers
1. Mathematical Modeling of a Continuous Vibrating Fluidized Bed Dryer for Grain
Open this publication in new window or tab >>Mathematical Modeling of a Continuous Vibrating Fluidized Bed Dryer for Grain
2012 (English)In: Drying Technology, ISSN 0737-3937, E-ISSN 1532-2300, Vol. 30, no 13, 1469-1481 p.Article in journal (Refereed) Published
Abstract [en]

A mathematical model for the drying of grain in a continuous vibrating fluidized bed dryer was developed. 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 examined. Mass and heat transfer within a single wet particle was described by effective transport coefficients. Assuming constant effective mass transport coefficient and thermal conductivity, analytical solutions of the mass and energy balances were obtained. The variation in both transport coefficients along the dryer was taken into account by a stepwise application of the analytical solution in space intervals with averaged coefficients from previous locations in the dryer. Calculation results were in fairly good agreement with experimental data from the literature. However, the results depend strongly on relationships used to determine heat and mass transfer coefficients; because the results from correlations found in the literature vary considerably, the correlations should be adapted to the specific equipment in order to obtain reliable results.

Keyword
Continuously worked dryer, Dryer simulation, Drying modeling, Drying of particulate materials, Heat and mass transfer
National Category
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-34630 (URN)10.1080/07373937.2012.690123 (DOI)000308982400010 ()2-s2.0-84866644596 (ScopusID)
Note

QC 20121106

Available from: 2011-06-10 Created: 2011-06-10 Last updated: 2012-11-06Bibliographically approved
2. 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 (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
3. Simulation of a Vibrated Fluidised Bed Dryer for Solids containing a Multicomponent Moisture
Open this publication in new window or tab >>Simulation of a Vibrated Fluidised Bed Dryer for Solids containing a Multicomponent Moisture
2006 (English)In: IACChE 2006 / [ed] Oscar Pagola, Buenos Aires, Argentina: Argentine Association of Chemical Engineers (AAIQ) , 2006, 01d-301 p.Conference paper (Refereed)
Abstract [en]

The drying of solids in a continuously worked vibrated fluidised bed dryer is studied by simulations. A model considering the drying of a thin layer of particles wetted with a multicomponent mixture is developed. Particles are assumed well mixed in the direction of the airflow and only the longitudinal changes of liquid content, liquid composition and particle temperature are considered. Interactive diffusion and heat conduction are 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 are obtained. The variation of both the diffusion coefficients and the effective thermal conductivity of the particles along the dryer is taken into account by a stepwise application of the analytical solution in space intervals with averaged coefficients from previous locations in the dryer. The analytical solution gives a good insight into the selectivity of the drying process and can be used to estimate aroma retention during drying. The solution is computationally fast; therefore, the experimental verification of this approximate model would introduce an important computational economy since the rigorous treatment of multicomponent drying involves tedious and time-consuming calculations.

Place, publisher, year, edition, pages
Buenos Aires, Argentina: Argentine Association of Chemical Engineers (AAIQ), 2006
Keyword
Aroma retention; Drying selectivity; Multicomponent drying
National Category
Chemical Engineering
Identifiers
urn:nbn:se:kth:diva-28898 (URN)
Conference
22nd Inter-American Congress of Chemical Engineering. Buenos Aires, Argentina. October 1-4, 2006.
Note

QC 20110124

Available from: 2011-01-21 Created: 2011-01-21 Last updated: 2016-08-16Bibliographically approved

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