Lecture 5. Single Equilibrium Stages ()(1) [Ch. 4] • Phase Separation • Degree of Freedom Analysis - Gibbs phase rule F CP2 -General analysis • Binary Vapor-Liquid Systems - Examples of binary system - Phase equilibrium diagram -q-line - Phase diagram for constant relative volatility • Azeotropic Systems Phase Separation

• Simplest separation processes V - Two phases in contact  physical equilibrium  phase separation - If the separa tion fac tor is large, a single contact stage may be sufficient V/L -If the seppg,aration factor is not large, multiple stages are required

• Seppparation factor for vapor-liqqquid equilibrium

KLK  LK, HK ()relative volatility  KHK L  = 10,000 : almost perfect separation in a single stage  = 1.10 : almost perfect separation requires hundreds of stages • Calculation for separation operations : material balances, phase equilibrium relations, and energy balance Gibbs Phase Rule

• Variables - Intensive variables : Do not depend on system size; temperature, pressure, phase compositions - EtExtens ive var ibliables :D: Depend on sys tem si;ize; mass, moles, energy; mass or molar flow rates, energy transfer rates

• Degree offf freed om, F Number of independent variables (variance) • Gibbs phase rule Relation between the number of independent intensive variables at equilibrium F CP2

C : Number of components at equilibrium P : Number of phases at equilibrium Degree of Freedom Analysis (1)

• Gibbs phase rule : consider equilibrium intensive variables only Variables

yi T, P : 2 variables

xi, yi, … : C×P variables Equations T, P CC P equations  xandyii11  ii11

LV y ff or K  i C  (P-1) equations x ii i i xi F = (()2 + CP) – P – C(P - 1) = C – P + 2

For a binary VLE system (F=2) : given T, P  determine x and y Degree of Freedom Analysis (2)

• General analysis: consider all intensive and extensive variables Variables V T, P : 2 zi, TF, PF, C+P+4 in general yi + FQF, Q, x , y ,… : C×P (C+6 for VLE) i i [V, L,…] Equations

T,P P + C(P-1) equations F + z Q i Fz Vy Lx TF iii C+1 equations P F Fh Q Vh  Lh L FVL

xi F = (2+CP) + (C+P+4) – [P+C(P-1)] - (C+1) = C + 5 C If we consider  zi 1  F = C + 4 i1 Binary VaporVapor--LiquidLiquid Systems

• Experimental vapor-liquid equilibrium data for binary systems (A and B) are widely available e.g. Perry’s handbook • Types of equilibrium data - Isothermal : P-y-x -Isobaric : T-y-x • If P and T are fi xed  phhiiase compositions are compllletely defined ⇒ separation factor (relative volatility for vapor-liquid) is also fixed K (/)yx (/) yx  AAA  AA A is the more-volatile AB, component (y > x ) KB (/)(1)/(1)yxBB y A x A A A Examples of Binary System

• Water + Glycerol - Normal boiling point difference : 190 ℃ - Relative volatility : very high ⇒ Good separation in a single equilibrium stage • Methanol + Water - Normal boiling point difference : 35.5 ℃ - Relative volatility : intermediate ⇒ About 30 trays are required for an acceptable separation • p-xylene + m-xylene - Normal boiling point difference : 0.8 ℃ -Relative volatility : close to 1.0 - Distill a tion separa tion is imprac tica l : a bou t 1, 000 trays are requ ire d ⇒ Crystallization or adsorption is preferred Equilibrium Data for Methanol-Water System (1) T = 50 ℃ T = 150 ℃ 9 250 8 7 200 6 psia psia

150 5 ure, ure, ss ss 4 100 3 Pres Pres 2 50 1 0 0 0 0.2 0.4 0.6 0.8 1 0 0.2 0.4 0.6 0.8 1 Composition Composition T = 250 ℃ 1400 1200 • As T becomes higher, relative 1000 sia volatility becomes smaller pp 800 600  Separation becomes difficult

Pressure, 400 o 200 • At 250 C  no seppyaration by 0 distillation when x ≥ 0.772 0 0.2 0.4 0.6 0.8 1 Composition Equilibrium Data for Methanol-Water System (2)

•  (relative volatility) = 1.0  The separation by distillation is not possible ∵ The compositi ons o f the vapor and liquid are identical and two phases become one phase

yA = xA Tc (℃) Pc (psia) 0.000 374.1 3,208 0.772 250 1,219 1.000 240 1,154

In industry, distillation columns operate at pressures

below Pc Phase Equilibrium Diagram

Methanol-water system n hexane-n octane system y-x diagram a t 1 a tm T-y-x diagram at 1 atm

Dew point

Tie line

P-x diagram at 150 ℃ Bubble point qq--lineline

n hexane-n octane system FzHHH Vy  Lx y-x phase diagram at 1 atm FVL  (/)1VF 1 yH xzHH (/)VF (/) VF Feed mixture, F with overall

composition zH = 0.6 F60l%For 60 mol% vapor itiization, slope = (0.6-1)/0.6 = -2/3 ⇒ Eqqpuilibrium composition from equilibrium curve

: yH = 0.76 and xH = 0.37

Slope=0, (V/F)=1 : vapor only Slope=∞, (V/F)=0 : liquid only yy--xx Phase Diagram for Constant Relative Volatility • Relative volatility

yxAA// yx AA  AB,  yxB /(1)/(1)BAA y x

If A,B is assumed constant over the entire composition range, the y-x phase equilibrium curve can be determined using A,B

 A,B xA yA  1 xA ( A,B 1)

For an ideal solution, A,B can be approximated with Raoult’s law

sat sat K A PA / P PA  A,B   sat  sat K B PB / P PB Azeotropic systems (1)

• Azeotropes : formed by liquid mixtures exhibiting minimum- or maximum-biliboiling po itints - Homogeneous or heterogeneous azeotropes

Isopropyl ether-isopropyl alcohol Acetone-chloroform at 101 kPa at 101 kPa

• Identical vapor and liquid compositions at the azeotropic composition  all K-values are 1  no separation by ordinary distillation Azeotropic systems (2)

• Azeotropes limit the separation achievable by ordinary distillation ⇒ Changing pressure sufficiently : shift the equilibrium to break the azeotrope or move it • Azeotrope formation can be used to achieve difficult separations An entrainer (MSA) is added  combining with one or more of the components in the feed  forming a minimum-boiling azeotrope  recover as the distillate e. g. heterogeneous azeotropic distillation: addition of benzene to an alcohol-water mixture