Chapter 6. Multiphase Systems. Dr. M. A. A. Shoukat Choudhury Website:
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1 Chapter 6 Multiphase Systems Dr. M. A. A. Shoukat Choudhury shoukat@buet.ac.bd Website: Multiphase Systems Why Study? - Phase change operations such as freezing, melting, evaporation, condensation Example: 1. brewing a cup of coffee or tea, 2. absorption of SO2, 3. distillation to recover methanol or ethanol from aqueous solution 4. L-L extraction 5. Adsorption 10/17/2012 ChE 201/shoukat@buet.ac.bd 2 ChE 201/shoukat@buet.ac.bd 1
2 6.1 Single Component Phase Equilibrium Phase diagram A plot of one system variable against another that shows the conditions at which the substance exists as solid, liquid and gas. Phase Diagram of water - Boiling point - normal boiling point - melting/freezing point - sublimation point - triple point - critical temperature and pressure above which two phases (liquid-vapor) never coexist. 10/17/2012 ChE 201/shoukat@buet.ac.bd 3 Phase Diagram of water Gas 10/17/2012 ChE 201/shoukat@buet.ac.bd 4 ChE 201/shoukat@buet.ac.bd 2
3 Difference of vapor and gas Vapor: - Gaseous substance below its critical temperature which can be condensed by compressing or increasing the pressure Gas : - Gaseous substance above its critical temperature which cannot be condensed by compressing or increasing the pressure 10/17/2012 ChE 201/shoukat@buet.ac.bd 5 Vapor Pressure Definition: Vapor pressure (also known as equilibrium vapor pressure) is the pressure of a vapor in equilibrium with its nonvapor phases. All liquids and solids have a tendency to evaporate to a gaseous form, and all gases have a tendency to condense back into their original form (either liquid or solid). At any given temperature, for a particular substance, there is a pressure at which the gas of that substance is in dynamic equilibrium with its liquid or solid forms. This is the vapor pressure of that substance at that temperature. The equilibrium vapor pressure is an indication of a liquid's evaporation rate. It relates to the tendency of molecules and atoms to escape from a liquid or a solid. Higher the vapor pressure, the more volatile the compound is. 10/17/2012 ChE 201/shoukat@buet.ac.bd Source : wikipedia 6 ChE 201/shoukat@buet.ac.bd 3
4 Estimation of Vapor Pressure Clapeyron Equation / Clausius-Clapeyron Equation Antoine Equation Cox s Chart Clapeyron Equation / Clausius-Clapeyron Equation Example Vapor Pressure Estimation using Clausius -Clapeyron Equation: If the vapor pressure of benzene is 40 mm Hg at 7.6 o C and 60 mm Hg at 15.4 o C, find the vapor pressure at 42.2 o c using Clausius-Clapeyron Equation 10/17/2012 ChE 201/shoukat@buet.ac.bd 7 Antoine Equation log 10 p * = A - B/ (T + C) p * = 10^(A - B/ /(T + C)) T is in o C p * is in mm Hg 10/17/2012 ChE 201/shoukat@buet.ac.bd 8 ChE 201/shoukat@buet.ac.bd 4
5 Cox s Chart for Vapor Pressure Estimation 10/17/2012 ChE 201/shoukat@buet.ac.bd 9 Water Vapor Pressure Table 10/17/2012 ChE 201/shoukat@buet.ac.bd 10 ChE 201/shoukat@buet.ac.bd 5
6 Water Vapor Pressure Table 10/17/2012 ChE 11 Gibbs Phase Rule How many intensive variables must be specified to define a system? DOF = 2+C P, C=number of components, P=number of phases intensive variables do not depend on the size of the system. Example: molar volume, density Extensive variables depend on the size of the system. Example: mass, volume Calculate DOF for various regions of water phase diagram. 10/17/2012 ChE 201/shoukat@buet.ac.bd 12 ChE 201/shoukat@buet.ac.bd 6
7 Gas-Liquid Systems One Condensable Components Examples evaporation, drying, humidifications, condensations, dehumidifications BDA Bone + water dry air Water P, T Raoult s Law: p i = y i P = p * i Saturated: pi= yi P = pi* Superheated: pi= yi P < pi*(t) Dew point: if the superheated vapor is cooled at constant pressure, the temperature at which the first dew forms Degrees of superheat: T i -T dp 10/17/2012 ChE 201/shoukat@buet.ac.bd 13 Example A stream of air at 100 o C and 5260 mm Hg contains 10% water by volume. a) Calculate the dew point and the degree of superheat of the air b) Calculate the percentage of vapor that condenses and the final composition of the gas phase if the air is cooled to 80 o C at constant pressure. c) Calculate the percentage of vapor that condenses and the final composition of the gas phase, if the air is compressed isothermally to 8500 mm Hg. 10/17/2012 ChE 201/shoukat@buet.ac.bd 14 ChE 201/shoukat@buet.ac.bd 7
8 Gas-Liquid Systems Multi-Component systems A, B, C P, T A + B + C Raoult s Law:p A = y A P = x A p A * - works good for x A is close to 1 (i.e., the solution is almost pure A) - mixtures of structurally similar liquids (straight-chain alcohols, aromatic hydrocarbons,...) 1. pentane, hexane, heptane, 2. methanol, ethanol, propanol 3. benzene, toluene, xylene Henry s Law: p A = y A P = x A H A (T) -H A is Henry s constant for A at temp. T - works good for x A is close to 0 (i.e., the dilute solution of A) 10/17/2012 ChE 201/shoukat@buet.ac.bd 15 Bubble Point Temperature (for solution) Bubble point: When a liquid solution is slowly heated at constant pressure, the temperature at which the first bubble forms is the bubble point of the solution at the given pressure. 10/17/2012 ChE 201/shoukat@buet.ac.bd 16 ChE 201/shoukat@buet.ac.bd 8
9 Dew Point Temperature Dew point: When a vapor is slowly cooled at constant pressure, the temperature at which the first liquid droplet forms is the dew point temperature at the given pressure. 10/17/2012 ChE 201/shoukat@buet.ac.bd 17 Graphical Representations of VLE 10/17/2012 ChE 201/shoukat@buet.ac.bd 18 ChE 201/shoukat@buet.ac.bd 9
10 Solubility The solubility of a solid in a liquid is the maximum amount of that substance that can be dissolved in a specified amount of the liquid in the equilibrium. The solubility strongly depends on temperature. Saturated Supersaturated Solubility curve 10/17/2012 ChE 201/shoukat@buet.ac.bd 19 Figure (p. 266) Solubilities of inorganic solutes. Elementary Principles of Chemical Processs, 3/E by Richard M. Felder and Ronald W. Rousseau Copyright 2005 by John Wiley & Sons, Inc. All rights reserved. ChE 201/shoukat@buet.ac.bd 10
11 Solubility Curves o C 10/17/2012 ChE 201/shoukat@buet.ac.bd 21 Problem 6.78 A solution containing 100 lbm KNO 3 / 100 lbm H 2 O at 80 o C is fed to a cooling crystallizer operated at 25 o C. Slurry from the crystallizer is fed to a filter where the crystals are separated from the solution. Determine the production rate of crystals (lbm crystals/ lbm of feed) and the solid-liquid mass ratio (lbm crystals/ lbm of liquid) in the slurry leaving the crystallizer. The solubility of KNO 3 is 40 g KNO 3 / 100 g H 2 O at 25 o C. 10/17/2012 ChE 201/shoukat@buet.ac.bd 22 ChE 201/shoukat@buet.ac.bd 11
12 6.78 solution 10/17/2012 ChE 23 Weather Report What kind of humidity? What is its meaning? Courtesy: The Daily Star, April 27, /17/2012 ChE 24 ChE 12
13 Gas-Vapor Systems 10/17/2012 ChE 25 Definitions of Various Humidity - Saturation refers to any gas - vapor system - Humidity refers to air water system % relative saturation/humidity s r or h r = p i X 100% p i* (T) Molal saturation p s m or h m = i P - p i Absolute Saturation or humidity P s a or h a = i M i (P- p i )M dry 10/17/2012 ChE 201/shoukat@buet.ac.bd 26 ChE 201/shoukat@buet.ac.bd 13
14 Definitions of Various Humidity Percentage saturation/humidity s p or h p = s m s * X 100% m p i P - p i p * = i x 100% P p * i 10/17/2012 ChE 201/shoukat@buet.ac.bd 27 Problem 6.27 On a hot summer day the temperature is 35 o C, and barometric pressure is 103 kpa, and the relative humidity is 90%. An air conditioner draws in outside air, cools it to 20 o C, and delivers it at a rate of L/h. Calculate the rate of moisture condensation (kg/h) and the volumetric flow rate of the air drawn from the outside 10/17/2012 ChE 201/shoukat@buet.ac.bd 28 ChE 201/shoukat@buet.ac.bd 14
15 6.27 Solution 10/17/2012 ChE 29 Problem 6.38 Stack gas is emerging from a furnace at 300 o C and 105 kpa. It contains CO 2 at a partial pressure of 80 mm Hg and no CO, O 2 2, methane or ethane. The fuel gas fed to the furnace containing methane and ethane is burned with air. Calculate the mole fraction of methane in the fuel and the dew point temperature of the stack gas. 10/17/2012 ChE 201/shoukat@buet.ac.bd 30 ChE 201/shoukat@buet.ac.bd 15
16 10/17/2012 ChE 31 Example Do Yourself 10/17/2012 ChE 32 ChE 16
17 Problem 6.44 Sulfur trioxide (SO 3 ) dissolves in and reacts with water to form an aqueous solution of sulfuric acid (H 2 SO 4 ). The vapor is in equilibrium with the solution contains both SO 3 and H 2 O. If enough SO 3 is added, all of the water reacts and the solution becomes pure H 2 SO 4. If still more SO 3 is added, it dissolves to form a solution of SO 3 in H 2 SO 4, called oleum or fuming sulfuric acid. The vapor in equilibrium with oleum is pure SO 3. A 20% oleum by definition contains 20 kg of dissolved SO 3 and 80 kg of H 2 SO 4 per hundred kg of solution. Alternatively oleum composition can be expressed as % SO 3 by mass, with constituents of the oleum considered to be SO 3 and H 2 O. a) Prove that a 15.0% oleum contains 84.4% SO 3 b) Suppose a gas stream at 40 o C and 1.2 atm containing 90 mol% SO 3 and 10% N 2 contacts a liquid stream of 98% H 2 SO 4 (aq), producing 15% oleum at the tower outlet. Tabulated equilibrium data indicate that the partial pressure of SO 3 in equilibrium with this oleum is 1.15 mm Hg. Calculate i) the mole fraction of SO 3 in the outlet gas if this gas is in equilibrium with the liquid product at 40 o C and 1 atm, and ii) the ratio of (m 3 gas feed)/(kg liquid feed). 10/17/2012 ChE 201/shoukat@buet.ac.bd 33 10/17/2012 ChE 201/shoukat@buet.ac.bd 34 ChE 201/shoukat@buet.ac.bd 17
18 Who is he? 10/17/2012 ChE 35 ChE 18
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