Transcript CBE_417
CBE 417 “Unit Operations” Lecture: 3 7 Sep 2012 1 Overview • Introduction • UO course overview • Equilibrium Stage separations • What are “Unit Operations” • Brief thermodynamics review • Binary flash with energy balance • Multicomponent flash 2 V L fˆi fˆi Vapor Liquid Equilibrium (VLE) Vapor phase: good; liquid phase: good for HC or moderate – high pressures (compressible liquid phase) V L y i P ˆi x i P ˆi V sat sat y i P ˆi x i i Pi i P .C . V y i P ˆi x i H i Typical simplifications: Ideal vapor phase Ideal liquid phase Typically used for liquid phase fugacity calculations Used for special cases (like gases dissolving into liquid phase) ˆi 1 y i P x i i Pi i 1 y i P x i Pi V sat sat Raoult’s Law 3 Phase Equilibrium (Alternate Form VLE) Historically, when estimates were done by hand: y i K i xi •Seader & Henley (2006) 4 Phase Equilibrium (Recommendations) 5 Phase Equilibrium (Alternate Form VLE) Historically, when estimates were done by hand: y i K i xi K i K i T , P , all x i Sometimes the K values are nearly composition independent “hand” techniques of design/solution have used DePriester Charts (hydrocarbons): 6 DePriester Chart P = 2 bar T = 100 oC Isobutane others…. 7 ln K aT 1 T 2 aT 2 T a T 6 a P 1 ln P aP2 P 2 aP3 DePriester P (equation fit) with T [ ] R & P [ ] psia o 8 V L fˆi fˆi Vapor Liquid Equilibrium (VLE) V L y i P ˆi x i P ˆi V sat sat y i P ˆi x i i Pi i P .C . V y i P ˆi x i H i Vapor phase: good; liquid phase: good for HC or moderate – high pressures (compressible liquid phase) Typically used for liquid phase fugacity calculations Used for special cases (like gases dissolving into liquid phase) Equations of state models Activity coefficient models 9 Equations of State Models 10 Phase Equilibrium (Recommendations) 11 Activity Coefficient Models 12 Activity Coefficient Models 13 Activity Coefficient Models 14 Activity Coefficient Models 15 CBE 417 “Unit Operations” Lecture: 4 10 Sep 2012 16 Overview • Introduction • UO course overview • Equilibrium Stage separations • What are “Unit Operations” • Brief thermodynamics review • Binary flash with energy balance • Multicomponent flash 17 Activity Coefficient Models 18 Phase Equilibrium (Recommendations) Mixtures to model: • • • • • • • • MeOH – water EtOH – water propanol – water n-butanol – water n-butane – n-pentane benzene – toluene acetic acid – propionic acid CO2 – toluene (high P) 19 Other Equilibrium Diagrams: P – T diagram 20 PT Equilibrium Diagram: http://www.dlr.de/vt/en/Portaldata/29/Resources/dokumente/CO2GasphaseDiagrams_Goos_Riedel_Zhao_Blum2010_GHGT_webnew.pdf 21 Other Equilibrium Diagrams: P = 1.013 bar T = various oC Benzene - Toluene Y vs X diagram T vs X or Temp vs Composition 22 Other Equilibrium Diagrams: 23 Y vs X Diagram (LLE) 24 Effect of Pressure: 25 Effect of Pressure: •Seader & Henley (2006) 26 Other Equilibrium Diagrams: 27 Overview • Brief thermodynamics review • Binary Flash with energy balance •Sequential solution •Simultaneous solution • Multicomponent Flash 28 Binary Flash F V L Overall mole balance mole balance on a mole balance on b equilibrium eqn for a ya V Z a F y aV x a L Za & F Z b F y bV x b L xa L ya P xa P sat a sat mole balance on a xa ZaF Za sat a V L P F F P x a Pa P by F & solve for x a V xa L xb Zb sat V L P F F Pb 29 x Flash separation: i Binary Flash ya 1 V Za 1 sat a V L P F F P Specify: a = n-pentane b = n-hexane Z a 0 .5 T 90 C sat V L P F F Pb Za & F xa L Find: V frac , x a , y a T ,Za & P sat 4 . 707 bar V frac , ?? sat 1 . 888 bar Vfrac 0.471 V/F P 3.000 bar functi 1.89Eon 08 Xa 0.394 Xb 0.606 Ya 0.619 Yb 0.381 Pa Pb V frac V F L frac L F P 3 bar Zb f 1 V frac q 30 Binary Flash ya F V L Overall mole balance V Z a F y aV x a L mole balance on a mole balance on b Z b F y bV x b L equilibrium eqn for a y a P xa a P Za & F xa L sat a x a a Pa sat mole balance on a xa ZaF Za aP sat a P V L F F P by F & solve for x a V xa L xb Zb b Pb sat P V L F F 31 x Flash separation: 1 i Binary Flash ya 1 V Za aP sat a P Specify: a = n-pentane b = n-hexane Z a 0 .5 T 90 C P 3 bar V L F F Zb b Pb sat P T ,Za & P sat 4 . 707 bar sat 1 . 888 bar Pa Pb V L F F Find: V frac , x a , y a a f x a , xb , T b f x a , xb , T Za & F xa L V frac , ?? a Pasat V L Z a xa 0 P F F y a P x a a Pa sat 0 32 Binary Flash ya Graphical Solution: V Z a F y aV x a L mole balance on a ya xa solve for ya V F f or L F q L V Za Za & F F xa V L (1 f ) 1 ya xa Z a f f “Operating Line” 33 Binary Flash Graphical: 1 ya (1 f ) 1 ya xa Z a f f V Za & F Equilibrium curve 0.9 xa y=x 0.8 L 0.7 Solution! Ya 0.6 0.5 0.4 What if f is unknown, but T is known? Za 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Xa 1 Limits: f =0 f =1 34 Binary Flash Energy Balance Q flash ya T feed V P feed T in HV P&T QH Pin F , Z a Za & F xa hf hL L EB on CV: F h f Q flash V H V L h L h f Z a C Pa T Feed T ref Z b C Pb T Feed T ref L L h L x a C Pa T T ref x b C Pb T T ref L L H V y a a (T ref ) C Pa T T ref V y b (T ref ) C Pb T T ref b V 35 Other Equilibrium Diagrams: 36 Alternative Thermodynamics Older (hand methods): ya K a xa yb K b xb Relative Volatility (VLE): ya ab Ka Kb ya / xa yb / xb Raoult’s law * Pa * Pb ab x a 1 x a ab 1 Aside (couple with MB) 1 f f ab 1 f Za Za 1 x ab ab 1 0 xa f f f 2 a 37 Separation Factor or Relative Volatility * ab Pa * Pb 38 Effect of Pressure: •Seader & Henley (2006) 39 Constant Relative Volatility? 1 0.9 0.8 Y MeOH 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 0.2 0.4 0.6 0.8 1 X MeOH 40 Alternative Thermodynamics Ki with multicomponent flash: y i K i x i xi Into MB: x i 1 1 Zi V L Ki F F Zi V L Ki F F Zi K f 1 f i Sequential solution: suggestions p 35-37 (Rachford-Rice Eqn) Simultaneous solution technique: suggestions p 40-43 41 Sizing Flash Drums u perm K drum h total L V L 3 to 5 D V V ( mol ) u perm Ac V Mw V 42 Simulators Flash input: Sensitivity Analysis: Design Spec: 43 Questions? 44