Theo Drying.docx

PERRY (Perry & Green, 2008) Drying is the process by which volatile materials, usually water, are evaporated from a material to yield a solid product. Drying is a heat and mass-transfer process. Heat is necessary to evaporate water. The latent heat of vaporization of water is about 2500 J/g, which means that the drying process requires a significant amount of energy. Simultaneously, the evaporating material must leave the drying material by diffusion and/or convection. MASS AND ENERGY BALANCES The most basic type of calculation for a dryer is a mass and energy balance. This calculation only quantifies the conservation of mass and energy in the system; by itself it does not answer important questions of rate and quality.

Overall mass and energy balance diagram Figure 12-10 shows a simple sheet drying system. Hot air enters the dryer and contacts a wet sheet. The sheet leaves a dryer with a lower moisture content, and the air leaves the dryer with a higher humidity. Mass Balance The mass balance is given by the following equations:

Fdry sheet in = Fdry sheet out

(12-15)

Fliquid water in = Fliquid water out + Fevaporated

(12-16)

Gdry air in = Gdry air out Gwater vapor in + Fevaporated = Gwater vapor out

(12-17) (12-18)

The wet-basis moisture contents of the incoming and outgoing sheet are given by 𝐹𝑙𝑖𝑞𝑢𝑖𝑑 𝑤𝑎𝑡𝑒𝑟 𝑖𝑛

𝑥𝑖𝑛 = 𝐹

𝑙𝑖𝑞𝑢𝑖𝑑 𝑤𝑎𝑡𝑒𝑟 𝑖𝑛 +𝐹𝑑𝑟𝑦 𝑠ℎ𝑒𝑒𝑡 𝑖𝑛

𝑥𝑜𝑢𝑡 = 𝐹

𝐹𝑙𝑖𝑞𝑢𝑖𝑑 𝑤𝑎𝑡𝑒𝑟 𝑜𝑢𝑡

𝑙𝑖𝑞𝑢𝑖𝑑 𝑤𝑎𝑡𝑒𝑟 𝑜𝑢𝑡 +𝐹𝑑𝑟𝑦 𝑠ℎ𝑒𝑒𝑡 𝑜𝑢𝑡

(12-19) (12-20)

The relationship between the total airflow, the dry airflow, and the absolute humidity is given by 1

𝐺𝑑𝑟𝑦 𝑎𝑖𝑟 = 𝐺𝑎𝑖𝑟 1+𝑌

(12-21)

The absolute humidity of each airstream is given by 𝑌𝑖𝑛 =

𝐺𝑤𝑎𝑡𝑒𝑟 𝑣𝑎𝑝𝑜𝑟 𝑖𝑛

𝑌𝑜𝑢𝑡 =

𝐺𝑑𝑟𝑦 𝑎𝑖𝑟 𝑖𝑛 𝐺𝑤𝑎𝑡𝑒𝑟 𝑣𝑎𝑝𝑜𝑟 𝑜𝑢𝑡 𝐺𝑑𝑟𝑦 𝑎𝑖𝑟 𝑜𝑢𝑡

(12-22) (12-23)

Energy Balance The general energy balance is given by the following equation: ΔHdry air + ΔHwater vapor+ ΔHevaporated + ΔHdry sheet + ΔHliquid water = 0

(12-29)

The enthalpy change due to evaporation ∆Hevaporation is given by Fevaporatedλw. To evaluate λw rigorously, a decision has to be made on the calculational path of the evaporating water since this water is both heating and evaporating. Typically, a two-step path is used—isothermal evaporation and heating of either phase. The incoming liquid water can all be heated to the outlet temperature of the sheet, and then the heat of vaporization at the outlet temperature can be used; or the evaporation can be calculated as occurring at the inlet temperature, and the water vapor is heated from the inlet temperature to the outlet temperature. Alternatively a three-step path based on latent heat at the datum (0°C) may be used. All these methods of calculation are equivalent, since the

enthalpy is a state function; but in this case, the second method is preferred since the outlet temperature is unknown. THERMODYNAMICS The thermodynamic driving force for evaporation is the difference in chemical potential or water activity between the drying material and the gas phase. For a pure water drop, the driving force for drying is the difference between the vapor pressure of water and the partial pressure of water in the gas phase. The rate of drying is proportional to this driving force. 𝑠𝑎𝑡 𝑅𝑎𝑡𝑒 ∝ (𝑝𝑝𝑢𝑟𝑒 − 𝑝𝑤,𝑎𝑖𝑟 )

The activity of water in the gas phase is defined as the ratio of the partial pressure of water to the vapor pressure of pure water, which is also related to the definition of relative humidity. 𝑣𝑎𝑝𝑜𝑟 𝑎𝑤 =

𝑝𝑤 %𝑅𝐻 = 𝑠𝑎𝑡 100 𝑝𝑝𝑢𝑟𝑒

The activity of water in a mixture or solid is defined as the ratio of the vapor pressure of water in the mixture to that of a reference, usually the vapor pressure of pure water. In solids drying or drying of solutions, the vapor pressure (or water activity) is lower than that for pure water. 𝑠𝑜𝑙𝑖𝑑 𝑎𝑤 =

𝑠𝑎𝑡 𝑝𝑚𝑖𝑥𝑡𝑢𝑟𝑒 𝑠𝑎𝑡 𝑝𝑝𝑢𝑟𝑒

Therefore, the water activity value equals 1 for pure water and <1 when binding is occurring. This is caused by thermodynamic interactions between the water and the drying material. In many standard drying references, this is called bound water. When a solid sample is placed into a humid environment, water will transfer from the solid to the air or vice versa until equilibrium is established. At thermodynamic equilibrium, the water activity is equal in both phases. 𝑣𝑎𝑝𝑜𝑟 𝑠𝑜𝑙𝑖𝑑 𝑎𝑤 = 𝑎𝑤 = 𝑎𝑤

MECHANISMS OF MOISTURE TRANSPORT WITHIN SOLIDS

Drying requires moisture to travel to the surface of a material. There are several mechanisms by which this can occur: 1. Diffusion of moisture through solids. Diffusion is a molecular process, brought about by random wanderings of individual molecules. If all the water molecules in a material are free to migrate, they tend to diffuse from a region of high moisture concentration to one of lower moisture concentration, thereby reducing the moisture gradient and equalizing the concentration of moisture. 2. Convection of moisture within a liquid or slurry. If a flowable solution is drying into a solid, then liquid motion within the material brings wetter material to the surface. 3. Evaporation of moisture within a solid and gas transport out of the solid by diffusion and/or convection. Evaporation can occur within a solid if it is boiling or porous. Subsequently vapor must move out of the sample. 4. Capillary flow of moisture in porous media. The reduction of liquid pressure within small pores due to surface tension forces causes liquid to flow in porous media by capillary action. DRYING KINETICS Drying Curves and Periods of Drying The most basic and essential kinetic information on drying is a drying curve. A drying curve describes the drying kinetics and how they change during drying. The drying curve is affected by the material properties, size or thickness of the drying material, and drying conditions. In this section, the general characteristics of drying curves and their uses are described.

FIG. 12-13 Several common representations of a typical drying curve. Several representations of a typical drying curve are shown in Fig. 12-13. The top plot, Fig. 1213a, is the moisture content (dry basis) as a function of time. The middle plot, Fig. 12-13b,is the drying rate as a function of time, the derivative of the top plot. The bottom plot, Fig. 12-13c,is the drying rate as affected by the average moisture content of the drying material. Since the material loses moisture as time passes, the progression of time in this bottom plot is from right to left. Some salient features of the drying curve show the different periods of drying. These are common periods, but not all occur in every drying process. The first period of drying is called the induction period. This period occurs when material is being heated early in drying. The second period of drying is called the constant-rate period. During this period, the surface remains wet enough to maintain the vapor pressure of water on the surface. Once the surface dries sufficiently, the drying

rate decreases and the falling-rate period occurs. This period can also be referred to as hindered drying. Figure 12-13 shows the transition between constant- and fallingrate periods of drying occurring at the critical point. The critical point refers to the average moisture content of a material at this transition. Introduction to Internal and External Mass-Transfer Control—Drying of a Slab The concepts in drying kinetics are best illustrated with a simple example—air drying of a slab. Consider a thick slab of homogeneous wet material, as shown in Fig. 12-14.

In this particular example, the slab is dried on an insulating surface under constant conditions. The heat for drying is carried to the surface with hot air, and air carries water vapor from the surface. At the same time, a moisture gradient forms within the slab, with a dry surface and a wet interior. The curved line is the representation of the gradient. At the bottom the slab (z = 0), the material is wet and the moisture content is drier at the surface. The following processes must occur to dry the slab: 1. Heat transfer from the air to the surface of the slab. 2. Mass transfer of water vapor from the surface of the slab to the bulk air. 3. Mass transfer of moisture from the interior of the slab to the surface of the slab Depending on the drying conditions, thickness, and physical properties of the slab, any of the above steps can be rate-limiting. Figure 12-15 shows two examples of rate-limiting cases.

FIG. 12-15 Drying curves and corresponding moisture gradients for situations involving external heat and mass-transfer control and internal mass-transfer control. The top example shows the situation of external rate control. In this situation, the heat transfer to the surface and/or the mass transfer from the surface in the vapor phase is slower than mass transfer to the surface from the bulk of the drying material. In this limiting case, the moisture gradient in the material is minimal, and the rate of drying will be constant as long as the average moisture content remains high enough to maintain a high water activity (see the section on thermodynamics for a discussion of the relationship between moisture content and water vapor pressure). External rate control leads to the observation of a constant-rate period drying curve. The bottom example shows the opposite situation: internal rate control. In the case of heating from the top, internal control refers to a slow rate of mass transfer from the bulk of the material to the surface of the material. Diffusion, convection, and capillary action (in the case of porous media) are possible mechanisms for mass transfer of moisture to the surface of the slab. In the internal rate control situation, moisture is removed from the surface by the air faster than moisture is transported to the surface. This regime is caused by relatively thick layers or high values of the

mass- and heat-transfer coefficients in the air. Internal rate control leads to the observation of a falling-rate period drying curve. Generally speaking, drying curves show both behaviors. When drying begins, the surface is often wet enough to maintain a constant-rate period and is therefore externally controlled. But as the material dries, the mass-transfer rate of moisture to the surface often slows, causing the rate to decrease since the lower moisture content on the surface causes a lower water vapor pressure. However, some materials begin dry enough that there is no observable constant-rate period.