Norwegian University of Science and Technology (NTNU) 1 Outline - PowerPoint PPT Presentation

Thermodynamic consistency in modeling of SLE and VLE in aqueous alkanolamine solutions Ardi Hartono and Hallvard F Svendsen PCCC2 Conference Bergen, September 17-20, 2013 Norwegian University of Science and Technology (NTNU) 1

Outline  Introduction  Theory  VLE (Vapor-Liquid Equilibrium)  SLE (Solid-Liquid Equilibrium)  Modeling : NRTL Framework as an example  Results  MEA+H 2 O  DEEA+H 2 O  AMP+H 2 O  Conclusions 2

Introduction  Rigorous thermodynamic models based on excess Gibbs energy (eNRTL and eUNIQUAC) are capable of representing both Solid-Liquid-Equilibria (SLE) and Vapor-Liquid-Equilibria (VLE) in aqueous alkanolamine solutions  A robust and accurate modeling relies on the quality and type of data used to regress the parameters to get the best representation of the data.  Different apparatuses provide different equilibrium data:  Ebulliometer experiments usually generate PTxy data which can be used to determine the activity coefficient for both amine and water.  A calorimetric measurement can provide excess enthalpy of mixing and reaction as well heat capacity  Freezing point depression measurements provide SLE and water activity data .  When comparing activity coefficients of water from VLE and SLE data often inconsistencies are seen: e.g.  the excess enthalpies calculated were slightly skewed toward higher amine concentrations when a best fit to freezing point depressions was achieved .  the minimum value of the excess enthalpy was fitted optimally but the freezing point depression was found to be under-predicted, in particular at higher concentrations. 3

 Examples: MEA +H 2 O Posey, 1996 VLE (P-T-x and P-T-x-y), Excess Enthalpy and Freezing Point. 1.1 2 0 0 10 γ MEA 25 ° C (Touhara, et al., 1982) Fosbøl, et al., 2011 1 Cheng, et al., 1992 γ H2O -5 0.9 -0.5 0.8 -10 1 10 0.7 H E (kJ/mol) -1 P (kPa) Θ 1 ( ° C) γ i (-) 0.6 -15 0.5 -1.5 -20 0.4 0 10 0.3 -2 -25 0.2 0.1 -2.5 -30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 x 1 (-) x 1 ,y 1 (-) x 1 (-) x 1 (-) Fits Overpredict Schmidt, et al., 2007 VLE (P-T-x and P-T-x-y) and Excess Enthalpy. 1.1 2 0 0 10 γ MEA Fosbøl, et al., 2011 25 ° C (Touhara, et al., 1982) 1 Cheng, et al., 1992 γ H2O -5 0.9 -0.5 0.8 -10 1 10 0.7 H E (kJ/mol) -1 P (kPa) Θ 1 ( ° C) γ i (-) 0.6 -15 0.5 -1.5 -20 0.4 0 10 0.3 -2 -25 0.2 0.1 -2.5 -30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 x 1 (-) x 1 ,y 1 (-) x 1 (-) x 1 (-) 4 Skewed Overpredict Underpredict

 Examples: Hessen, et al., 2010 VLE (P-T-x and P-T-x-y), Excess Enthalpy and Freezing Point. 2 1.1 0 0 10 γ MEA 25 ° C (Touhara, et al., 1982) Fosbøl, et al., 2011 1 Cheng, et al., 1992 γ H2O -5 0.9 -0.5 0.8 -10 1 10 0.7 H E (kJ/mol) -1 P (kPa) Θ 1 ( ° C) γ i (-) 0.6 -15 0.5 -1.5 -20 0.4 0 10 0.3 -2 -25 0.2 0.1 -2.5 -30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 x 1 (-) x 1 ,y 1 (-) x 1 (-) x 1 (-) Fits Overpredict Overpredict Underpredict Zhang, et al., 2011 VLE (P-T-x and P-T-x-y), Excess Enthalpy and Heat Capacity. 1.1 2 10 0 0 γ MEA 25 ° C (Touhara, et al., 1982) Fosbøl, et al., 2011 1 γ H2O Cheng, et al., 1992 -5 0.9 -0.5 0.8 1 -10 10 0.7 H E (kJ/mol) -1 P (kPa) γ i (-) Θ 1 ( ° C) 0.6 -15 0.5 -1.5 -20 0.4 0 10 0.3 -2 -25 0.2 0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -2.5 -30 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2 x 1 (-) x 1 ,y 1 (-) x 1 (-) x 1 (-)  AIM: To find the origin of the discrepancy between measured data used for the thermodynamic modeling of the activity 5 coefficient of water.

Theory VLE SLE D = D - D = = m m m ( , ) T p m ( , ) T p G H T S ( , ) T p ( , ) T p   s v =  +  =  +  T m m m ( , ) T p m ( , ) T p RT ln f ( , ) T p ( , ) T p RT ln f ò  D = D  + D  i i   H H C dT f P = + =  +  s v m m m ( , ) T p m ( , ) T p RT ln f ( , ) T p ( , ) T p RT ln f Tf s i v i s v  T  = D v f f f C ò D = × × = - D = D  + i i i P G R T ln RT ln a S S dT i s f f × ×  = × × F T g x P P y i Tf i i i i i D = -  s C C C  - = D g P P P RT ln x G ì ü ï ï  -  f ï V ( P P ) ï i i F º × - » i í i ì ý exp 1 ï ï f ° i ï RT ï î þ i D  D  T T D H S 1 1 C ò ò - = - + D - f f g P ln x C dT dT é ù ¶ E i i P ( nG RT ) RT R RT R T ê ú = ê g ln T T ú f f i ¶ n ë û i T P ni , , D  = D  H T S f f ` f é ù ¶ E E H ( G RT ) ê ú - = ê ú D  T T ¶ D 2 H RT T 1 1 C ë û ( ) ò ò - = - + D - f P g P x , ln x T 1 C dT dT i i R P RT RT R T f T T é ù f f ¶ E H ê ú = ê E C ú P ¶ T ë û P x , 6 Prausnitz, et al., 1999, Molecular Thermodynamics of Fluid-Phase Equilibria Hojjati and Rohani, 2006, Measurement and prediction solubility of Paracetamol in Water-Isopopanol solution

D  T T D H 1 1 C ( ) ò ò - = - + D - f P g ln x T 1 C dT dT i i R P RT RT R T f T T f f Case 1 D  T T T D H 1 1 C = f ò ò ( ) D º = f - T P g C dT dT ln x 1 T R T P i i R RT R T RT f T T f f  Posey (1996), Cheng et al. (1993) and Hessen, et al. (2010) Case 2 D  H - = f D @D S  ln g ln x T C i i R P f RT f Case 3 D  D H C D @ ( ) ( ) - = f - + + - C k P g ln x T 1 1 ln T T P Tf i i R R R RT RT f 7

D  T T D H 1 1 C ( ) ò ò - = f - + D - P g ln x T 1 C dT dT i i R P RT RT R T f T T f f Case 4 D  æ ö H bT a ( ) ( ) ÷ ç D = + - = f - + + - + f - - 1 ln x g T 1 1 ln T T 2 T ÷ C a bT ç ÷ è ø T P i i R R R R RT R 2 R R f  Ge and Wang (2009) and Hartono, et al. (2013) Case 5 c D = + + C a bT P - ( T T Q ) ì ü ï ( ) ï D  - - H bT T 1 a ï T T ï ( ) 2 ( ) ( ) - = f - + + - + f - + Q - í ý ln x g T 1 1 ln T T T T c ln ln T ï ï i i R R R f - R RT R 2 RT T T T ï ï î þ Q f f  Fosbøl, et al. (2009 and 2011) 8

Thermo physical property of water as solvent 100 ∆ Cp=Cp l -Cp s 90 Cp l Heat Capacity, Cp (J ⋅ mol -1 ⋅ K -1 ) 80 70 J D  = H 6009.4 ∆ Cp= a + b.*T 60 f mol ∆ Cp 50 J D = C 37.97 P × K mol 40 J 30 Cp s D = - × C 75.929 0.1405 T K mol P × 20 T f =273.15K - × 4 2.45634 10 J D = - × - 10 C 75.929 0.1405 T ( ) P - × T 200 K mol 0 0 50 100 150 200 250 300 350 400 450 500 550 T (K) 9 DIPPR-Design Institute for Physical Properties (2004)

Modeling æ ö æ ö æ ö æ ö 2 2 2 2 - - - Q - Q n Exp calc n Exp calc n E Exp E calc n F Exp F calc g g ÷ P P ÷ ( H ) ( H ) ÷ ( ) ( ) ÷ ç ç ç ç å å å å ÷ ÷ ÷ ÷ = + + + ç ç ç ç i i Sol Sol Sol Sol Sol Sol OF ÷ ÷ ÷ ÷ ç ç ç ç ç ÷ ç ÷ ç ÷ ç ÷ Q è Exp ø è Exp ø è E Exp ø è F Exp ø g P ( H ) ( ) = = = = i 1 i i 1 Sol i 1 Sol i 1 Sol  -  n 1 å model exp = AARD  n = 1 i exp Melting/ Freezing Point ( ° C) Species Water 0 MEA 10.3 AMP 67 DEEA -70 10 Hertzberg, T and Mejdell, T., 1998, MODFIT for Matlab: Parameter Estimation in a General Nonlinear Multiresponse Model.