MODELLING OF THE DRYING PROCESS OF WOOD IN 3-DIMENSIONS

The process of drying parallelepipedic samples of wood is studied, by considering 3-dimensional transport of water along the 3 principal axes of diffusion, as well as evaporation out of the surface. During a large part of the process, the water content is considerably higher than the value associated with the fiber saturation point. A numerical model with finite differences, based on the assumption that the transport of water is controlled by transient diffusion through the sample and evaporation from the surface, is successfully tested with a beam in the following two cases : the initial concentration of water is uniform, or not. The model is capable of predicting not only the kinetics of drying, but also the profiles of concentration developed through the samples at various times. The principal diffusivities are determined by using a short test technique in transient condition.     

Modeling coupled heat and mass transfer during drying in tape casting with a simple ceramics–water system

In many industrial processes such as in tape casting for electronics or in the food industry, drying is one of the determining physical phenomena. In this study, the evaporation of water from a ceramic–water mixture is investigated with the purpose of understanding the drying rate in the drying process of thin sheets produced by the tape casting process. The rate of mass loss in the drying process is a key factor that often is of interest, as it affects the final properties of the tapes. The 1D heat conduction equation is solved numerically to obtain the temperature field in a ceramic sheet. The change in the concentration of the water content is then used as the driving force for diffusive mass transport of the water. Mass–averaged thermal properties are assumed for the ceramic–water mixture in the initial stage. As the water evaporates, the thermal properties of the solid ceramic become more dominant since the fraction of water approaches zero. The developed model is used to simulate a simple test for the drying process. The drying rate is simply calculated by examining the water content in each time step. It is found that the mass loss due to the evaporation is increasing close to linearly with the drying time corresponding to an almost constant drying rate. However, the rate starts to decrease after some time in the simulation. It is also shown that too extensive surface drying results in a slow diffusion rate from the bottom, which in turn reduces the drying rate in general and hence is not favorable from a process viewpoint.     

Drying regime maps for particulate coatings

Key microstructural properties of particulate coatings such as porosity and particle order are established during drying. Therefore, understanding the evolution of particulate distributions during drying is useful for designing coating properties. Here, a 1D model is proposed for the particle distribution through the coating thickness at different drying times and conditions, including Brownian diffusion, sedimentation, and evaporation. Effects of particle concentration on diffusion and sedimentation rates are included. Results are condensed onto a drying regime map which predicts the presence of particle surface accumulation or sediment based on two dimensionless numbers: the Peclet number and the sedimentation number. Cryogenic scanning electron microscopy (cryoSEM) is used to image the transient particulate distributions during the drying of a model system comprised of monodisperse silica particles in water. Particle size and evaporation rates are altered to access various domains of the drying map. There is good agreement between cryoSEM observations and model predictions. © 2010 American Institute of Chemical Engineers AIChE J, 2010     

CONVECTWE DRYING MODEL OF SOUTHERN PINE

A transient one dimensional first principles model is developed for the drying of a porous material (wood is used as an example) that includes both heat and mass transfer. Heat transfer by conduction and convection, mass transfer by binary gas diffusion, pressure-driven bulk flow in the gas and liquid, and diffusion of bound water are included in the analysis. The diffusive mass transfer terms are modeled using a Fickian approach, while the bulk flow is modeled assuming Darcian flow. Depending on the state (pendular or funicular) of the moisture in the wood, appropriate terms are considered in the development of the governing mass equations. The results provide distributions within the material of each moisture phase (vapor, liquid, and bound), temperature, and total pressure. Information regarding the drying rate and evaporation rate is also presented. Average distributions are obtained as a function of time, and compared with experimental data from the literature. It is observed that the total pressure within the material can be considerably above one atmosphere during the drying process.     

THE INFLUENCE OF THE DRYING MEDIUM ON HIGH TEMPERATURE CONVECTIVE DRYING OF SINGLE WOOD CHIPS

High temperature convective drying of single wood chips with air and superheated steam respectively is studied theoretically. The two-dimensional model presented describes the coupled transport of water, vapour, air and heat. Transport mechanisms included are the convection of gas and liquid, intergas as well as bound water diffusion. In the initial part of the drying process, moisture is transported to the surface mainly due to capillary forces in the transversal direction where evaporation occurs, As the surface becomes dry, the drying front moves towards the centre of the particle and an overpressure is simultaneously built up which affects the drying process

The differences between drying in air and steam respectively can be assigned to the physical properties of the drying medium. The period of constant drying rate which does not exist (or is very short) in air drying becomes more significant with decreasing amounts of air in the drying medium and is clearly visible in Dure superheated steam drying. The maximal drying rate is larger in air drying, and shorter drying times are obtained since the heat flux to the wood chip particle increases with increasing amounts of air in the drying medium. The period of falling drying rate can be divided into two parts: in the first, the drying rate is dependent upon the humidity of the drying medium whereas in the second, there is no such correlation.     

CONVECTWE DRYING MODEL OF SOUTHERN PINE

ABSTRACT

A transient one dimensional first principles model is developed for the drying of a porous material (wood is used as an example) that includes both heat and mass transfer. Heat transfer by conduction and convection, mass transfer by binary gas diffusion, pressure-driven bulk flow in the gas and liquid, and diffusion of bound water are included in the analysis. The diffusive mass transfer terms are modeled using a Fickian approach, while the bulk flow is modeled assuming Darcian flow. Depending on the state (pendular or funicular) of the moisture in the wood, appropriate terms are considered in the development of the governing mass equations. The results provide distributions within the material of each moisture phase (vapor, liquid, and bound), temperature, and total pressure. Information regarding the drying rate and evaporation rate is also presented. Average distributions are obtained as a function of time, and compared with experimental data from the literature. It is observed that the total pressure within the material can be considerably above one atmosphere during the drying process.     

THE INFLUENCE OF THE DRYING MEDIUM ON HIGH TEMPERATURE CONVECTIVE DRYING OF SINGLE WOOD CHIPS

ABSTRACT

High temperature convective drying of single wood chips with air and superheated steam respectively is studied theoretically. The two-dimensional model presented describes the coupled transport of water, vapour, air and heat. Transport mechanisms included are the convection of gas and liquid, intergas as well as bound water diffusion. In the initial part of the drying process, moisture is transported to the surface mainly due to capillary forces in the transversal direction where evaporation occurs, As the surface becomes dry, the drying front moves towards the centre of the particle and an overpressure is simultaneously built up which affects the drying process

The differences between drying in air and steam respectively can be assigned to the physical properties of the drying medium. The period of constant drying rate which does not exist (or is very short) in air drying becomes more significant with decreasing amounts of air in the drying medium and is clearly visible in Dure superheated steam drying. The maximal drying rate is larger in air drying, and shorter drying times are obtained since the heat flux to the wood chip particle increases with increasing amounts of air in the drying medium. The period of falling drying rate can be divided into two parts: in the first, the drying rate is dependent upon the humidity of the drying medium whereas in the second, there is no such correlation.     

TWO-FLUID MODEL FOR PNEUMATIC DRYING OF PARTICULATE MATERIALS

The Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a one-dimensional steady-state condition and was applied to the drying process of wet PVC particles in a large-scale pneumatic dryer and to the drying process of wet sand in a laboratory-scale pneumatic dryer. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The drying process is assumed to stop when the moisture content of a particle falls to a predefined value or when the particle riches the exit of the pneumatic dryer. Our developed model was solved numerically and two operating conditions, adiabatic and given pneumatic dryer wall temperature, were simulated. Comparison between the prediction of the numerical models of Rocha and DryPak, (Pakowski, 1996), which were presented by Silva and Correa (1998), with the prediction of our numerical simulation reviled better agreements with DryPak then with the models of Rocha. The results of the developed model were also compared with experimental results of Baeyens et al. (1995) and Rocha.     

TWO-FLUID MODEL FOR PNEUMATIC DRYING OF PARTICULATE MATERIALS

The Two-Fluid model has been used for modeling the flow of particulate materials through pneumatic dryer. The model was solved for a one-dimensional steady-state condition and was applied to the drying process of wet PVC particles in a large-scale pneumatic dryer and to the drying process of wet sand in a laboratory-scale pneumatic dryer. A two-stage drying process was implemented. In the first drying stage, heat transfer controls evaporation from the saturated outer surface of the particle to the surrounding gas. At the second stage, the particles were assumed to have a wet core and a dry outer crust; the evaporation process of the liquid from a particle assumed to be governed by diffusion through the particle crust and by convection into the gas medium. As evaporation proceeds, the wet core shrinks while the particle dries. The drying process is assumed to stop when the moisture content of a particle falls to a predefined value or when the particle riches the exit of the pneumatic dryer. Our developed model was solved numerically and two operating conditions, adiabatic and given pneumatic dryer wall temperature, were simulated. Comparison between the prediction of the numerical models of Rocha and DryPak, (Pakowski, 1996), which were presented by Silva and Correa (1998), with the prediction of our numerical simulation reviled better agreements with DryPak then with the models of Rocha. The results of the developed model were also compared with experimental results of Baeyens et al. (1995) and Rocha.     

Drying Simulation of a Solid Slab with Three Dimensional Shrinkage

ABSTRACT

A mathematical model is developed to simulate the drying of a hygroscopic porous solid. The model, based on the gradient of moisture concentration per unit volume as driving force, takes into account the migration of water within the solid by diffusion and the evaporation at the interface. A mathematical equation for diffusion in a slab with three dimensional shrinkage has been derived, assuming that the magnitude of shrinkage is equal to the volume of water evaporated. The resulting diffusion equation and the heat balance eauation for infinite thermal conductivitv were solved n;merically with temperature dependent diffusion coefficient and convective boundary conditions. The deDendence of the desorption isotherm with temperature is-also considered. corndination of all these factors in a single model provides a tool that is effective in predictinq dryinq behavior and also useful in exploring and understanding the impact of important variables on the drying process.     

Three-Layer Model for Drying of Coating Applied on Silicone-Coated Paper

Upon application of water based coating onto silicone-coated paper and during the subsequent drying process, the water permeates through the silicone layer into the paper substrate. At the same time, water evaporates from both the surface of the coated layer and throughout the paper layer. Initially, the evaporation rate from the wet coating surface may be dominant, but at longer times the bulk evaporation from the paper can dominate. Here a three-layer diffusion model for such a system is developed. Solutions obtained by Galerkin's method with finite element basis functions show that the hygroscopic nature of the paper leads to low drying rates at low moisture contents. Further, the model predicts that initially the coating dries to a moderately low residual moisture concentration faster than a coating applied on an impermeable substrate. However, at longer times, the predicted residual moisture of coatings applied on silicon-coated paper is higher than for a coating applied on an impermeable substrate.     

Multiphase modeling of intermittent drying using the spatial reaction engineering approach (S-REA)

Several schemes of energy minimization of drying process including intermittent drying have been attempted. Intermittent drying is conducted by applying different heat inputs in each drying period. An effective and physically meaningful drying model is useful for process design and product technology. The lumped reaction engineering approach (L-REA) has been shown previously to be accurate to model the intermittent drying In L-REA, the REA (reaction engineering approach) is used to describe the global drying rate. In this study, the REA is used to model the local evaporation/condensation rate and combined with the mechanistic drying models to yield the spatial reaction engineering approach (S-REA), a non-equilibrium multiphase drying model. The accuracy of the S-REA to model the intermittent drying under time-varying drying air temperature is evaluated here. In order to incorporate the effect of time-varying drying air temperature, the equilibrium activation energy and boundary condition of heat balance implement the corresponding drying settings in each drying period. The results of modeling using the S-REA match well with the experimental data. The S-REA can yield the spatial profiles of moisture content, concentration of water vapor, temperature and local evaporation/condensation rate so that better understanding of transport phenomena of intermittent drying can be obtained. It is argued here that the REA can describe the local evaporation rate under time-varying external conditions well. The S-REA is an effective non-equilibrium multiphase approach for modeling of intermittent drying process.     

STEAM DRYING OF SINTERED SPHERES OF GLASS BEADS

Superheated steam drying of sintered spheres of glass beads with different diameters is investigated to reveal the effects of the gravitational force on drying rates. In a previous study, the drying rate curves of small samples with coarse glass beads in which the frictional resistance to flow of water and the effect of the gravitational force are negligible, were predicted by an evaporation zone model.In the present investigation, the drying rate curves of sintered spheres of glass beads with diameters ranging from 1.53×10^-2m to 4.99×lO^-2m are experimentally and theoretically obtained, and also the capillary pressure curves are measured by use of Haines' apparatus. The drying rate curves of large samples in which the effect of the gravitational force can not be negligible, are compared with those for small samples and the difference among these curves is discussed in terms of the moisture distributions which are estimated from the evaporation zone model with the observed capillary pressure curves.     

TEE EFFECIS OF EXTENDED THIN FILM EVAPORATION AND EXPWNAL DIFFUSION RESISTANCE DURING THE CONSTANT DRYING RATE PERIOD

Extended thin film evaporation with external diffusion resistance is analyzed for the constant rate period of the drying process, in which a polar liquid evaporates from porous bodies made of glass. The extended thin film is defined as the Liquid film in which the disjoining pressure dominates the fluid flar field and works as the driving force replenishing the evaporating Liquid. The results of the analysis shows that due to the existence of the evaporating thin Liquid film, the evaporation fran the extended thin film can compensate the reduction of evaporation rate caused by the increase of the dry spots and keep the drying rate the same as or even greater than that of the completely wetted surface. The external diffusion resistance makes the vapor concentration near the porous solid surface remain constant and therefore keeps     

Examining the Suitability of the Reaction Engineering Approach (REA) to Modeling Local Evaporation/Condensation Rates of Materials with Various Thicknesses

The reaction engineering approach (REA) is examined here to investigate its suitability as the local evaporation rate to be used in multiphase drying. For this purpose, REA is first implemented to model the convective drying of materials with various thicknesses. The relative activation energy, as the fingerprint of REA, generated from one size of a material is used to model the convective drying of the same material with different thicknesses. Because the results indicate that REA parameters can model the drying of materials with various thicknesses, REA can be scaled down to describe the local evaporation rate (at the microscale as affected by local composition and temperature). The relative activation energy is used to describe the global drying rate in modeling the local evaporation rate. REA is combined with a system of equations of conservation of heat and mass transfer in order to yield the spatial reaction engineering approach (S-REA) as a nonequilibrium multiphase drying model. By using S-REA, the spatial profiles of moisture content, concentration of water vapor, temperature, and local evaporation rate can be generated, which can assist in comprehending the transport phenomena.     

Three-Layer Model for Drying of Coating Applied on Silicone-Coated Paper

Abstract

Upon application of water based coating onto silicone-coated paper and during the subsequent drying process, the water permeates through the silicone layer into the paper substrate. At the same time, water evaporates from both the surface of the coated layer and throughout the paper layer. Initially, the evaporation rate from the wet coating surface may be dominant, but at longer times the bulk evaporation from the paper can dominate. Here a three-layer diffusion model for such a system is developed. Solutions obtained by Galerkin's method with finite element basis functions show that the hygroscopic nature of the paper leads to low drying rates at low moisture contents. Further, the model predicts that initially the coating dries to a moderately low residual moisture concentration faster than a coating applied on an impermeable substrate. However, at longer times, the predicted residual moisture of coatings applied on silicon-coated paper is higher than for a coating applied on an impermeable substrate.     

STEAM DRYING OF SINTERED SPHERES OF GLASS BEADS

ABSTRACT

Superheated steam drying of sintered spheres of glass beads with different diameters is investigated to reveal the effects of the gravitational force on drying rates. In a previous study, the drying rate curves of small samples with coarse glass beads in which the frictional resistance to flow of water and the effect of the gravitational force are negligible, were predicted by an evaporation zone model.In the present investigation, the drying rate curves of sintered spheres of glass beads with diameters ranging from 1.53×10^-2m to 4.99×lO^-2m are experimentally and theoretically obtained, and also the capillary pressure curves are measured by use of Haines' apparatus. The drying rate curves of large samples in which the effect of the gravitational force can not be negligible, are compared with those for small samples and the difference among these curves is discussed in terms of the moisture distributions which are estimated from the evaporation zone model with the observed capillary pressure curves.     

TEE EFFECIS OF EXTENDED THIN FILM EVAPORATION AND EXPWNAL DIFFUSION RESISTANCE DURING THE CONSTANT DRYING RATE PERIOD

ABSTRACT

Extended thin film evaporation with external diffusion resistance is analyzed for the constant rate period of the drying process, in which a polar liquid evaporates from porous bodies made of glass. The extended thin film is defined as the Liquid film in which the disjoining pressure dominates the fluid flar field and works as the driving force replenishing the evaporating Liquid. The results of the analysis shows that due to the existence of the evaporating thin Liquid film, the evaporation fran the extended thin film can compensate the reduction of evaporation rate caused by the increase of the dry spots and keep the drying rate the same as or even greater than that of the completely wetted surface. The external diffusion resistance makes the vapor concentration near the porous solid surface remain constant and therefore keeps     

THE RELEASE OF MONOTERPENES DURING CONVECTIVE DRYING OF WOOD CHIPS

ABSTRACT

The release of volatile organic components (VOC) during high temperature convective drying of wood chips was studied experimentally and theoretically. The drying medium was superheated steam with a pressure of two bar. Two different temperature levels of the drying medium, 160 and 180 °C, and two different materials, Scots Pine and Norway Spruce, were investigated. It was found that the main components released consist of various types of monoterpenes, with α-pinene dominating in each of the two materials. The amount released is dependent on the drying temperature as well as the time of the drying process.

In order to describe the release rate of monoterpenes during drying, two separate models, called the communicating and the non-communicating model respectively, were developed. The mechanisms included for the transport of monoterpenes are, in the communicating model, transport by diffusion and with the advective gas and liquid flow within the tracheids and, in the non-communicating model, diffusion within the resin canal system.

The results obtained using the communicating model largely overpredict the experimental results. To avoid this rapid release, additional mass transfer resistance for the transport of monoterpenes between the two canal systems could be introduced. The non-communicating model was found to be useful in explaining the release rate when drying spruce. This model, however, can not distinguish between the two temperature levels studied.