Chapter 6.,Ficks first law of diffusion Relations between diffusivities,Equimolal diffusion,For equimolal diffusion in gases, the net volumetric and molar flows are zero,The concentration gradient for A is linear in the film, and the gradient for B has the same magnitude but the opposite sign,one-way diffusion,only component A is transferred through the interface,or,6.2 Prediction of Diffusivities,Diffusivities are best estimated by experimental measurements they are also estimated from published correlations,Diffusion in gases,A simple theory for gases shows that D is proportional to the product of the average molecular velocity and the mean free path .,The mean free path for ideal gases varies inversely with pressure and increases with T1.0 The mean molecular velocity depends on T0.5,D for ideal gases varies with T1.5 and varies inversely with pressure,The Chapman-Enskog equation for binary diffusion,Diffusion in liquids,The diffusivities in liquids are generally 4 to 5 orders of magnitude smaller than in gases, but the fluxes for a given mole fraction gradient in liquid or gas may be nearly the same because of the much greater liquid densities.,Two-Film Theory,In the two-film theory, equilibrium is assumed at the interface, and the resistances to mass transfer in the two phases are added to get an overall resistance, just as is done for heat transfer. The reciprocal of the overall resistance is an overall coefficient.,Chapter7.,7.1 Equilibrium Relations,Equilibrium data can be shown in tables, equations, or graphs.,7.1.1 gas-liquid equilibrium,Henrys law,The equilibrium relation between partial pressure in the gas phase and xA,The equilibrium relation between mole fraction in the gas phase and mole fraction in the liquid xA,7.1.2 Vapor-Liquid Equilibrium Relations,Raoults Law,Equilibrium relation,At low pressure the vapor of mixture approaches ideal behavior and follows the ideal gas law. Raoults law applies to each component over entire concentration range, such mixtures are called ideal.,Relative Volatility of VaporLiquid Systems,Definition,For a separation process in which =1, the compositions of component A would be the same in both phases, separation is not possible when this occurs since the driving force for mass transfer is zero. When the value of is above 1, a separation is possible. The value of may change as concentration and total pressure change.,Boiling-Point Diagrams and x-y Plots,the boiling-point diagram x-y diagram,maximum boiling azeotrope minimum boiling azeotrope,7.2. Equilibrium-Stage Operations,rectifying section Stripping Reboiler and vapor stream Reflux Total condenser and partial condenser Vapor enriched in boiler Liquid enriched in heavier boiler,Material balances and operating line,Total material balance Material balance on component Operating line,Ideal contact stages,In an ideal stage, the V phase leaving the stage is in equilibrium with the L phase leaving the same stage.,Determining the number of ideal stages,Absorption factor method for calculating the number of ideal stages,When the operating and equilibrium lines are both straight over a given concentration range xa to xb, the number of ideal stages can be calculated directly,(7.2-22),(7.2-24),When the operating line and the equilibrium line are parallel,Chapter 8,8.1 Principles of Absorption,8.1.1 Material balances,Total material balance Material balance on component Operating lines,In many instances more convenient expressions can be derived for evaluating the absorption process if a solute-free basis is used for compositions rather than mole fractions.,8.1.2 Limiting and Optimum Gas-liquid Ratio,Limiting liquid-gas ratio,In general, the liquid rate for the absorber should be between 1.1 and 2.0 times the minimum rate, unless the liquid is to be discarded and not regenerated,8.1.3. Rate of absorption in packed towers,Individual coefficient and overall coefficient,controlling resistance gas phase is controlling liquid phase is controlling,8.2 Calculation of tower height,8.2.2 Number of transfer units and height of a transfer unit,height of a transfer unit HOy,number of transfer units NOy.,For straight operating and equilibrium lines, the number of transfer units is the change in concentration divided by the logarithmic mean driving force:,A different forms of the equations for absorption with NOy,8.4 Desorption or stripping,Chapter 9,9.1 Flash Distillation Flash distillation consists of vaporizing a definite fraction of the liquid in such a way that the evolved vapor is in equilibrium with the residual liquid, separating the vapor from the liquid, and condensing the vapor.,Flash distillation is used most for separating components that boil at widely different temperatures.,9.2. Simple Batch or Differential Distillation,In differential distillation, liquid is first charged to a heated kettle. The liquid charge is boiled slowly and the vapors are withdrawn as rapidly as they form to a condenser, where the condensed vapor is collected.,9.4 Continuous Distillation with Reflux,9.4.1 Action on an Ideal Plate Partial vaporization and partial condensation,9.4.2 Combination Rectification and Stripping,9.4.3 Material Balances in Plate Columns,Overall material balance and material balance for the component,Operating lines,the operating line for rectifying section is,the operating line for rectifying section is,9.4.4 Number of Ideal Plates; McCabe-Thiele Method,Constant molal overflow This results from nearly equal molar latent heats of vaporization, heat loss and sensible heat were neglected,Reflux ratio,Condenser and top plate,Total condenser condenses all vapor from the column and supplies both reflux and product. When a partial condenser is used, the liquid reflux does not have the same composition as the overhead product; that is, xc xD. The partial condenser is therefore equivalent to an additional theoretical stage,Bottom plate and reboiler,The vapor leaving the reboiler is in equilibrium with the liquid leaving as bottom product.,Condition of feed,Effects of different conditions of feed on distillation process,Then q has the following numerical limits for the various conditions: Cold feed, q 1 Feed at bubble point (saturated liquid), q = 1 Feed partially vapor, 0 < q < 1 Feed at dew point (saturated vapor), q = 0 Feed superheated vapor q < 0,Feed line,Construction of operating lines,Feed plate location,The optimum position of feed plate, the triangle representing the feed plate straddles the intersection of the operating lines.,Minimum number of plates,Total reflux and minimum number of plates,Minimum reflux,At a minimum value, called the minimum reflux ratio, the number of plates becomes infinite. Concave downward Concave upward,Optimum reflux ratio,It is a minimum at a definite reflux ratio not much greater than the minimum reflux. This is the point of most economical operation, and this ratio is called the optimum reflux ratio.,In ordinary situations, the minimum on the total cost curve will generally occur at an operating reflux ratio of from 1.1 to 1.5 times the minimum.,Number of ideal plates at operating reflux,9.4.5 Special Cases for Rectification Using McCabe Thiele Method,Stripping distillation Enriching distillation Rectification with direct steam injection Multiple feeds and sidestreams,Azeotropic Distillation,Differences between the azeotropic distillation and extractive distillation,9.6 Plate Efficiencies,Overall plate efficiency Murphree efficiency,Chapter 11.,11.1.1. Purposes of Drying 11.1.2. General Methods of Drying 11.2. EQUIPMENT FOR DRYING 11.2.1. Tray Dryer 11.2.2. Vacuum-Shelf Indirect Dryers 11.2.3.ContinuousTunnel Dryers 11.2.3. Rotary Dryers 11.2.4. Drum Dryers 11.2.5. Spray Dryers 11.2.6.Flash Dryer,VAPOR PRESSURE OF WATER AND HUMIDITY,Humidity and Humidity Chart,1. Definition of humidity,2. Percentage humidity,3. Percentage relative humidity,The percentage humidity is nearly equal to the relative humidity if the partial pressure of vapor in air is very low,4. Dew point of an airwater vapor mixture,The temperature at which a given mixture of air and water vapor would be saturated is called the dew-point temperature,5. Humid heat of an airwater vapor mixture,(11.3-6),6. Humid volume of an airwater vapor mixture,7. Total enthalpy of an airwater vapor mixture,8. Humidity chart of airwater vapor mixtures,Adiabatic Saturation Temperatures,This means that the total enthalpy of the entering gas mixture = enthalpy of the leaving gas mixture.,Wet Bulb Temperature,This means that the adiabatic saturation temperature is approximately equal to wet bulb temperature.,EQUILIBRIUM MOISTURE CONTENT OF MATERIALS,After exposure of the solid sufficiently long for equilibrium to be reached, the solid will attain a definite moisture content.,Effect of temperature,Often, for moderate temperature ranges, the equilibrium moisture content will be assumed constant when experimental data are not available at different temperatures.,Bound and Unbound Water in Solids,Free and Equilibrium Moisture of a Substance,Free moisture content in a sample is the moisture above the equilibrium moisture content.,Free and Equilibrium Moisture of a Substance,Free moisture content in a sample is the moisture above the equilibrium moisture content. Free moisture can be removed by drying under the given percent relative humidity.,RATE-OF-DRYING CURVES,11.5.2. Rate of Drying Curves for Constant-Drying Conditions,Drying in the Constant-Rate Period,In the constant-rate drying period, the surface of the solid is initially very wet and a continuous film of water exists on the drying surface. This water is entirely unbound water and it acts as if the solid were not present.,The rate of evaporation under the given air conditions is independent of the solid and is essentially the same as the rate from a free liquid surface.,The surface temperature is approximately the same as the wet bulb temperature,Drying in the Falling-Rate Period,3. Effect of shrinkage,It is desirable to dry with moist air. to decrease the temperature of air This decreases the rate of drying so that the effects of shrinkage on warping or hardening at the surface are greatly reduced.,CALCULATION METHODS FOR CONSTANT-RATE DRYING PERIOD,Drying time for constant rate period,Effect of Process Variables on Constant-Rate Period,1. Effect of air velocity 2. Effect of gas humidity 3. Effect of gas temperature 4. Effect of thickness of solid being dried,CALCULATION METHODS FOR FALLING-RATE DRYING PERIOD,Rearranging,The drying rate in the falling-rate period is controlled by the rate of internal movement of the liquid by liquid diffusion or by capillary movement.,Material and Heat Balances for Continuous Dryers,A wet material containing moisture content of 50wt% on a wet basis is dried to 6wt% in a continuous countercurrent drier. The moist air leaves the drier at t2=38 and H2=0.034kgH2O/ kg dry air and part of it recirculated and mixed with the fresh air having the temperature t0=25, humidityH0=0.005kgH2O /kg dry air before entering a preheater. The ratio of recirculated dry air to the mixed dry air is 0.8. Calculate the amount of fresh air and rate of heat transfer in the preheater when the wet material is fed to the dryer at rate of 1000kg/h on assumption that the dryer operates under the condition of isenthalpic process.,