1Efficiency of vapour/liquid contactors a) Overall Murphree gas phase efficiency 1 * 1 n n OG n n y y E y y + + ÷ = ÷ a) Overall Murphree liquid phase efficiency 1 * 1 n n OL n n x x E x x ÷ ÷ ÷ = ÷ b) Local or point efficiency - Murphree local (point) efficiency 2 1 * 1 ' n v n y y E y y + + ÷ = ÷ ' 1 * 1 n L n x x E x x ÷ ÷ ÷ = ÷ c) ideal o real Column Efficiency N E N = Factors affecting Point Efficiency - , L V - , , ... x y k k m - interfacial area - residence time 1. Determination of Point Efficiency From Overall Number of Transfer Unit OG N 1 ' n y OG e y dy N y y + = ÷ } 1 ' ln e OG e n y y N y y + ÷ = ÷ ÷ Hence: 1 ' OG N e e n y y e y y ÷ + ÷ = ÷ 1 1 1 1 1 ' ' ' 1 1 OG N e e n e n e n e n e n y y y y y y y y e y y y y y y ÷ + + + + + ÷ ÷ ÷ + ÷ / / ÷ = ÷ = = ÷ ÷ ÷ 1 1 ' The group : is n v e n y y E y y + + ÷ ÷ Hence 1 OG v N E e ÷ = ÷ But as 1 1 1 : OG G L mV N N L N = + × Then: 1 1 1 1 ln(1 ) v OG G L mV E N N L N ( = ÷ = ÷ + × ( ÷ ¸ ¸ 3 AIChE Method 0.5 3 0.776 4.57 10 0.24 105 G w v p v N h F L Sc ÷ ÷ ( = + × ÷ + ¸ ¸ ( ) ( ) 0.5 8 4.13 10 0.21 0.15 L L v L N D F t = × + 2- Relationship between v E and OG E Depends on degree of mixing - For complete mixing v OG L OL E E E E = = - For Liquid flow on tray streamline, gas phase complete mixing ( ) 1 1 v E OG v v E e E E ì ì = ÷ - For other degrees of mixing , mixing is indicated by Peclet Number , graphs below are used Pe N Peclet Number defined as 2 L Pe e L Z N D t = The Eddy Diffusivity e D - ( 2 / m s ) is obtained from the empirical relationship: 3 2 (0.0038 0.017 3.86 0.18 10 ) e a p w D u L h ÷ = + + + × v E , OG E , Pe N , mV L ì = 4 (Gerster, 1985, Coulson and Richardson, vol.6, 1983) 3- The relationship between OG E and o E - Lewis Relationship log 1 1 log OG o mV E L E mV L + ÷ = | |( | ( ¸ \ .¸ | | | \ . Efficiencies from Empirical Equations 1. O'Connell's equation o E modified as shown below: Eduljee: 51 32.5log( ) o L a E µ o = ÷ Lockett: 0.245 0.492( ) o L a E µ o ÷ = 5 (O'Connell,1946) 2. Van Winkle OG E - Bubble cap trays - Sieve or perforated trays 0.14 0.25 0.08 0.07 Re OG E Dg Sc = - Re Reynolds Number Re w v v L h u F µ µ = - Sc Schmidt Number L L LK Sc D µ µ = - Dg Surface tension Number L L v Dg o µ µ = 3- Relationship between OG E and 0 E Lewis relationship: log 1 1 log OG o mV E L E mV L ( | | + ÷ | ( \ . ¸ ¸ = | | | \ . 6 Example: A tray in a distillation column receives liquid from the tray above at a rate of 150 moles per hour and vapor from the tray below at a rate of 200 moles per hour. The equilibrium between the liquid and vapor phases leaving the tray is given by the following relationship: 1.5 n n y x = . For the conditions of the operation and the type of tray used, the Number of the individual transfer unit is: 2.4 L N = and 3.6 G N = . Calculate: a) Local efficiency of the tray V E . b) Overall tray efficiency OG E for the case of complete mixing. c) Tray efficiency when the degree of mixing is such that : Peclet Number = 5 d) Use Lewis relationship to find the column efficiency 0 E for case ( C ) Solution: - Data: 150 200 1.5 2.4 3.6 L G L V m N N = = = = = - mass transfer parameter: 150 1.5 200 2 mV L ì ì = × = ¬ = - Number of overall transfer units: 1 1 1 1 1.5 200 1 0.9 3.6 150 2.4 OG OG G L mV N N N L N × = + × = + × ¬ = - Efficiencies: a) Local efficiency: 0.9 1 0.593 1 OG N v e E e ÷ ÷ ÷ = = ÷ = b) For complete mixing of both phase 0.593 OG v E E = = c) From Fig at 2 0.593 1.186 v E ì = × = and 5 Pe N = it is found that 1.45 OG v E E = hence: 1.45 0.593 0.86 86% OG OG E E = × = = d) Using Lewis relationship log 1 1 log OG o mV E L E mV L ( | | + ÷ | ( \ . ¸ ¸ = | | | \ . for the column efficiency 0 E ( ) ( ) log 1 0.86 2 1 0.895 log 2 o E + × ÷ ( ¸ ¸ = = ¬ 89.5% o E =