Solids drying is generally understood to follow two distinct drying zones, known as the constant-rate period and the falling-rate fa lling-rate period. The T he two zones are demarcated by a break point called the critical moisture content.
drying rate curves experimentally determined air conditions ( P , T, RH) kept RH) kept constant sample weighed at specified intervals of time Δt , the reduction of mass ΔW is calculated (ΔX = ΔW/W s), and the drying rate is obtained:
2
R is drying rate in kg H 20/h.m , L s kg of dry solid 2 used, and A and A exposed surface area for drying in m .
Constant rate drying period Layer of saturated air on solid surface Rate (R c) determined by the capacity and properties of the inlet vapor Solid temperature = wet bulb temperature Free water drying Evaporation rate per unit drying area is constant Governed by rates of external heat and mass transfer since a film of free water at the surface. Rate independent of the material being dried.
Critical moisture content, X c At X c drying rate first begins to drop R begins to fall with decrease in X since water cannot migrate at the rate Rc to the surface due to internal transport limitations - depends on material and drying conditions. Drying surface becomes first partially unsaturated and then fully unsaturated until it reaches the EMC X*.
Falling rate period Begins when surface or free water is removed Solid temperature increases from wet bulb temp to that approaching the inlet air temperature Rate falls continuously in time Interior moisture must travel to reach the surface Moisture fails to reach surface fast enough to maintain a constant drying rate, transition to falling-rate period occurs.
TIME FOR DRYING Constant-rate period
During the period from initial moisture content X1 to the CMC Xc, rate is constant, and time of drying tc is given by:
A 100 kg batch of granular solids containing 30 per cent moisture is to be dried in a tray drier to 15.5 per cent of moisture by passing a current of air at 350 K tangentially across its surface at a velocity of 1.8 m/s. If the constant rate of drying 2 under these conditions is 0.0007 kg/s m and the critical moisture content is 15 per cent, calculate the approximate drying time. Assume the drying surface to be 0.03 m2/kg dry mass.
Rc calculated using empirical or analytical techniques to estimate the external heat/mass transfer rates
where q sum of heat fluxes due to convection, conduction and/or radiation λ s latent heat of vaporization at solid temperature. In the case of purely convective drying, drying surface saturated with water in constant rate period - liquid film attains wet-bulb temperature, T w T w is independent of geometry of the drying object Heat transfer and mass transfer are critical aspects in drying processes. Heat transferred to product to evaporate liquid, and mass transferred as a vapour into the surrounding gas. Drying rate is determined by set of factors that affect heat and mass transfer. During constant-rate period drying rate per unit area Rc estimated with fair precision from correlations developed for evaporation from a free liquid surface. The calculations may be based on mass transfer or on heat transfer
q rate of convective heat transfer in Watts (J/s) from air at T°C to the surface of the solid at T w °C, 2 h is the heat-transfer coefficient in W/m K 2 A is the exposed drying area in m λ w is the latent heat at T w in J/kg 2 k y is the mass-transfer coefficient in kg mol/s m M B is the molecular weight of air H is the humidity of the air, kg water vapour/kg dry air Hw is the humidity of the air at the solid surface, kg water vapour/kg dry air Substituting for R c in
CaCO3 filter cake in a tray is to be dried by crosscirculation from the top surface. Each tray is 2.5 2 cm high, with an area of 1.5 m , and is filled with 73 kg of wet filter cake having a water content of 30% on a dry basis. The heating medium is air at 1 0 atm and 77 C with a relative humidity of 10%. The velocity of air passing across the wet solid is 4 m/s. Estimate time in hours needed to reach the experimentally determined, critical moisture content of 10% on a dry basis, if the preheat period is neglected.
Effect of Process Variables on R c theoretical equations helpful to predict effect of changing drying process variables Effect of air velocity. R c is proportional to h and 0.8 hence to G for air flow parallel to the surface. Effect of air humidity, If air humidity H is decreased for a given T of air, T w will decrease. Then Rc will increase e.g., if original conditions are Rc1 , T 1 , T w1 , H 1 , and H w1 , then if H 1 is changed to H 2 and H 1 is changed to H 2 , Rc2 becomes
Effect of air temperature. If air temperature T is increased, T w also increases, but not as much as the increase in T. Hence, Rc increases as follows:
Effect of thickness of solid being dried. For heat transfer by convection only, Rc is independent of the thickness x1 of the solid. However, the time t for drying between fixed moisture contents X1 and X2 will be directly proportional to the thickness x 1. as increasing the thickness with a constant A will directly increase the amount of L s kg dry solid.
1 Mg of dry mass of a non-porous solid is dried under constant drying conditions in an air stream flowing at 0.75 m/s. The area of surface drying is 55 m2. If the initial rate of drying 2 is 0.3 g/m .s, how long will it take to dry the material from 0.15 to 0.025 kg water/kg dry solid? The critical moisture content of the material may be taken as 0.125 kg water/kg dry solid. If the air velocity were increased to 4.0 m/s, what would be the anticipated saving in time if the process were surfaceevaporation controlled?
Falling-rate period
idealized theories for capillary flow and diffusion can be used to estimate drying rates. Alternatively, estimates could be made by a strictly empirical approach - experimental determination of drying rate as a function of average moisture content for a particular set of conditions. Drying rate in the falling rate period is a function of X (or X f ) determined experimentally for a given material dried in a given type of dryer. If the drying rate curve ( R versus X ) is known, the total drying time required to reduce the solid moisture content from X 1 to X 2 can be simply calculated by:
Analytical expressions obtained for drying times t depend on the functional form of R or the model used to describe the falling rate, e.g., liquid diffusion, capillarity, evaporation-condensation.
Rate is a linear function of X. if both X1 and X2 are less than Xc and the rate R is linear in X over this region, R=aX+b
Rate is a linear function through origin. In some cases a straight line from the critical moisture content passing through the origin adequately represents the whole falling-rate period. Often for lack of more detailed data, this assumption is made. R = aX
A wet solid is dried from 25 to 10 % moisture under constant drying conditions in 4.17 h. If the critical and the equilibrium moisture contents are 15 and 5 % respectively, how long will it take to dry the solid from 30 to 8 % moisture under the same conditions? Assume rate of drying in falling rate period is proportional to the free moisture content
Falling rate period, diffusion control
where X = average free moisture content at time h, X1 = initial free moisture content at t = 0, X = equilibrium free moisture content, x1 = - the thickness of the slab when drying occurs from the top and the bottom parallel faces, and x 1 = total thickness of slab if drying only from the top face. when internal diffusion controls R is directly proportional to the free moisture X and the liquid diffusivity and that the rate of drying is inversely proportional to the thickness squared Falling rate period, capillary movement control
When capillary flow controls R is inversely proportional to the thickness. The time of drying between fixed moisture limits varies directly as the thickness and depends upon the gas velocity, temperature, and humidity.
A piece of hemlock wood measuring 15.15X14.8X0.75 cm is to be dried from the two large faces from an initial total moisture content of 90% to a final average total moisture content of 10% (both dry basis), for drying taking place in the falling-rate period with liquid-diffusion controlling. The moisture diffusivity has been -6 2 experimentally determined as 1.7x10 cm /s. Estimate the drying time if bone-dry air is used.
Heat Requirements of Dryers
1. Heating the feed (dry material and moisture) to evaporation temperature 2. Evaporation of water 3. Heating the material to exit temperature 4. Heating the evaporated liquid to exit temperature The heat consumption is determined from an energy and mass balance of the system. Figure shows the situation for a batch dryer. Mass balance is
In these equations, hi and hf are the entering (initial) and exiting (final) enthalpies of the moist drying agent, respectively; hs is the enthalpy of the dry solid and hl the enthalpy of the liquid. Qheat is the heat requirement from the heaters; W vent is the power required by the ventilation unit; and Q lost is the heat lost to the surroundings.
Material and Heat Balances for Continuous Dryers
the drying gas flows counter-currently to the solids flow. The solid enters at a rate of Ls kg dry solid/h, having a free moisture content X1 and a temperature Ts1. It leaves at X2 and Ts2. The gas enters at a rate G kg dry air/h, having a humidity H2 kg H20/kg dry air and a temperature of TG2. The gas leaves at TG1 and H1. material balance on the moisture,
heat balance on the dryer is
where Q is the heat Loss in the dryer in kJ/h. For an adiabatic process Q = 0, and if heat is added, Q is negative.
enthalpy of the wet solid = enthalpy of the dry solid + enthalpy of the Liquid as free moisture. enthalpy of the gas H’G in kJ/kg dry air is
λ 0 is the latent heat of water at T 0°C= 2501 kJ/kg at 0°C, and cs is the humid heat kJ/kg dry air K. cs = 1.005 + 1.88H The enthalpy of the wet solid H in kJ/kg dry solid, where
c pS heat capacity of the dry solid kJ/kg dry solid•K c pA heat capacity of liquid moisture kJ/kg H 20•K.
A granular material containing 40 per cent moisture is fed to a counter-current rotary dryer at a temperature of 295 K and is withdrawn at 305 K, containing 5 per cent moisture. The air supplied, which contains 0.006 kg water vapour/kg dry air, enters at 385 K and leaves at 310 K. The dryer handles 0.125 kg/s wet stock. Assuming that radiation losses amount to 20 kJ/kg dry air used, determine the mass flowrate of dry air supplied to the dryer and the humidity of the exit air. The latent heat of water vapour at 295 K = 2449 kJ/kg, specific heat capacity of dried material = 0.88 kJ/kg K, the specific heat capacity of dry air = 1.00 kJ/kg K, and the specific heat capacity of water vapour = 2.01 kJ/kg K.
