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Drying of Solid Materials 1 Drying of Solid Materials See also Solids Technology, Introduction Evangelos Tsotsas, Institut fur¨ Thermische Verfahrenstechnik, University of Karlsruhe, Karlsruhe, Federal Republic of Germany Volker Gnielinski, Institut fur¨ Thermische Verfahrenstechnik, University of Karlsruhe, Karlsruhe, Federal Republic of Germany Ernst-Ulrich Schlunder¨ , Institut fur¨ Thermische Verfahrenstechnik, University of Karlsruhe, Karlsruhe, Federal Republic of Germany 1. Theoretical Fundamentals of the 2.2.2. Low-Viscosity Materials ........ 26 Drying Process .............. 2 2.2.3. Pasty Materials .............. 27 1.1. Concepts, Definitions .......... 2 2.2.4. Granular Materials ............ 28 1.2. Characteristics of Moist Solids ... 3 2.3. Radiant Heat or Infrared Drying .. 29 1.3. Drying Rate Curves for Convection 2.4. Dielectric Heating ............ 30 ................... Drying 6 2.5. Vacuum and Freeze Drying ..... 30 1.4. Drying Rate Curves for Contact 3. Selecting, Sizing, and Energy Re- ................... Drying 11 quirements of Dryers .......... 31 1.5. Drying Rate and Moisture- 3.1. Choosing the Type of Dryer ..... 31 Composition Curves for Solids Wet- 3.1.1. The Role of the Material Properties of ted by Liquid Mixtures ........ 13 the Solid .................. 31 2. Drying Methods and Dryer Types . 15 3.1.2. Production Rate .............. 31 2.1. Convection Drying ........... 15 3.1.3. Dryer Ventilation ............. 32 2.1.1. Flowing Gas ................ 15 ............. 2.1.2. The Solid is Aerated ........... 18 3.2. Sizing the Dryer 33 ................ 2.1.3. Large-Scale Agitation of the Solid .. 21 3.2.1. Batch Dryers 33 ............ 2.1.4. The Solid Moves in the Drying Agent 23 3.2.2. Continuous Dryers 34 2.1.5. The Material is Sprayed ......... 24 3.3. Heat and Driving Power Require- 2.2. Contact Drying ............. 25 ments .................... 35 2.2.1. Flat and Strip Materials ......... 25 4. References ................. 36 Symbols R gas constant, J kg−1 K−1 2 s A surface area of the drying solid, m width of sample, m T C excess air factor in Eq. (38) temperature, K −2 −4 t C radiation coefficient, W m K time, s −1 −1 u velocity of drying agent, m/s c specific heat, J kg K v d particle diameter, m velocity of liquid in capillaries, m/s W˙ h enthalpy, J/kg power, W X L dryer length, m moisture content in solid, kg moisture/kg l modified mean free path, m dry solid x˜ M mass, kg mole fraction in the liquid phase Y M˙ mass flow rate, kg/s humidity of the drying agent, kg mois- M˜ molecular mass, kg/kmol ture/kg drying agent −2 −1 y˜ m˙ drying rate, kg m s mole fraction in the gas phase z N number of moles, kmol axial coordinate in a dryer, m z P pressure, Pa distance from the free surface of sample, ˙ m Q heat transfer rate, W α −2 −1 q˙ heat flux, W/m2 heat-transfer coefficient, W m K c 2005 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim 10.1002/14356007.b02 04 2 Drying of Solid Materials β mass-transfer coefficient, m/s 1. Theoretical Fundamentals of the γ accommodation coefficient Drying Process δ diffusion coefficient, m2/s δ surface roughness, m 1.1. Concepts, Definitions ζ dimensionless axial coordinate in a dryer Λ mean free path, m Drying denotes the separation of volatile liq- −1 −1 λ thermal conductivity, W m K uids from solid materials by vaporizing the liq- µ ratio of molecular masses uid and removing the vapor. The liquid that is to ν˙ normalized drying rate, Eq. (23) be removed is usually water, but it could also be ξ normalized moisture content, Eq. (24) a solvent such as alcohol or acetone, or a mixture 3 density, kg/m of such solvents. The solid material that is to be τ dimensionless time dried can be a natural product such as wood, a Φ dimensionless number, Eq. (29) semifinished or a finished good (such as paper). ϕ relative humidity The removal of water from other fluids such as ϕ surface coverage refrigerants or from gases, such as natural gas, is ψ porosity also considered a drying process, but this topic is not treated in this article. The vaporization of liquids requires the supply Subscripts of heat. Accordingly, drying can be considered a a ambient thermal separation process. The removal of liq- bed bed uids from solids without the application of heat, crit at the critical point which is the case in a centrifuge, does not come eq in equilibrium under the strict definition of drying. f final, at the outlet The product that is to be dried is denoted as g gas (drying agent) the moist solid, or simply as the solid. The sub- h maximum hygroscopic moisture content stance that carries the necessary heat is called heat from the heater the drying agent. This substance could be air, an i initial, at the inlet inert gas, or superheated steam. Heat could also l liquid (moisture) be supplied by radiation, by hot surfaces, or by lost heat losses to the surroundings microwaves. The moisture content of the solid max maximum is denoted by X and measured in kg liquid per p at constant pressure kg of dry solid. For the humidity of a gaseous r radiation drying agent the symbol Y is used (in kg vapor s dry solid per kg of dry gas). The saturation humidity is v vapor denoted by Y ∗. The mass flux of the vapor leav- vent ventilator ing the surface of the solid per unit time is called W wall the drying rate, and is denoted by the symbol m˙ w wetting (in kg m−2 s−1). The drying rate is usually de- 1 component index (isopropyl alcohol) termined by measuring the change of moisture I in the first period of drying content with time dX/dt. It follows that M dX m˙ = − s Superscripts A dt 0 effective coefficient, Eqs. (15), (17) Ms is the mass of the dry solid, and A is the por- ∗ saturated tion of its surface area that is in contact with the ∼ molar quantities drying agent. The drying rate m˙ depends on the conditions of drying and on the moisture con- tent X. The drying conditions are specified by factors such as the air pressure, temperature, and humidity, the radiator temperature, the temper- ature of a heating surface, or the strength of the microwaves. The relationship of the drying rate Drying of Solid Materials 3 m˙ and the moisture content X under constant In most practical cases the total pressure P is drying conditions – this is m˙ (X) – is called the prescribed. The partial pressure of the inert gas drying rate curve. can be obtained from Eq (1): ∗ Pg =P −Pv (T ) (2) 1.2. Characteristics of Moist Solids The ratio of the partial pressure to the total pres- sure is equal to the mole fraction of the respective Almost all industrial products have to be dried component. It follows: one or more times in the course of their manu- ∗ ∗ Nv Pv facture. Consequently, the variety and charac- y˜v (T )= = (3) teristics of moist solids are manifold. However, Nv +Ng P only two of these characteristics have a direct and correspondingly influence on the drying rate curve m˙ (X). They Ng Pg relate to the questions: y˜g= = (4) Nv +Ng P 1) Is the liquid in the solid freely mobile or is it bonded to the solid by sorption? The number of moles N (expressed in kmol), is related to the mass of the respective component 2) Does vaporization take place at the surface ˜ or in the interior of the solid? M (expressed in kg) by the molecular mass M (which is given in kg/kmol) by The first characteristic is described by the ther- ˜ ˜ modynamic equilibrium (sorption isotherms), Mv =Nv Mv Mg =Ng Mg (5a,b) the second by the kinetics of liquid migration (M˜ v= 18.01 kg/kmol for water and M˜ g= in the interior of the solid (capillarity, diffu- 28.96kg/kmol for air) From Eqs. (1) – (5) the sion). Both topics will be treated thoroughly saturation humidity of the inert gas [Y ∗ (T )in subsequently. In any case it should be borne in kg vapor per kg inert gas] can be obtained: mind that drying is not only a thermal separa- M˜ P ∗ (T ) tion process; it is also a means to manufacture Y ∗ (T )= v v ˜ ∗ (6) specified products and to influence their quality. Mg P − Pv (T ) Paper is an example of such a specified prod- The humidity of the unsaturated inert gas is given uct whose quality is controlled by the choice of by the relationship drying conditions. Further, the risk of possible product damage during drying must be reduced. M˜ ϕP∗ (T ) Y = v v ˜ ∗ (7) This is particularly important for sensitive prod- Mg P − ϕPv (T ) ucts such as foodstuffs. In this context, a large number of product characteristics differing from where ϕ is the relative humidity, defined as material to material should be accounted for. ϕ=P /P ∗ (T ) Some remarks on the handling of temperature- v v (8) sensitive materials are given in Section 3.1 The limits of ϕ are 0 and 1, which corre- spond to completely dry air and vapor-saturated Free and Bonded Moisture in Solids. If air, respectively. In summary, the thermody- free (unbound) liquid is in contact with its own namic equilibrium between the unbound mois- vapor, then the vapor pressure is equal to the sat- ture within a solid that is in contact with a gas – uration pressure for the respective temperature vapor atmosphere is characterized by ϕ = 1 and ◦ Pv∗ (T ), e.g., Pv∗ = 0.1 MPa for water at 100 C.
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