Thermodynamic Property Methods

Thermodynamic Property Methods

VLE, LLE and VLLE in ASPEN PLUS Mohammad Ali Fanaei, Ferdowsi University of Mashhad EOS Method 1- Vapor-Liquid Equilibrium v fi fi At Equilibrium: Where Therefore v v i f i yi Pt , l l f i x P l i v i yi k xi vl

i l i i t EOS Method 2- Liquid-Liquid Equilibrium l1 fi fi At Equilibrium: Where Therefore l1 l1 l1 i i t f i x P k l1l 2 i , l1 i l2 i l2 l2

l2 i l2 i f i x Pt l2 i l1 i x x EOS Method 3- Vapor-Liquid-Liquid Equilibrium At Equilibrium: l1 l1 l2 fi fi fi l1 l1 i i t v i v l2 l2

i l2 i f i x P , f i x Pt v f i yi Pt Where Therefore k vl1 i l1 i v i yi l1 xi , k vl2 i l2 i v i yi

l2 xi EOS Method 4- Fugacity Coefficient Formula 1 ln i RT V P RT dV ln Z m ni T ,V ,n j V Cubic Equations of State in the Aspen Physical Property System Redlich-Kwong(-Soave) based Peng-Robinson based Redlich-Kwong (RK) Standard Peng-Robinson(PENGROB) Standard Redlich-Kwong-Soave(RK-SOAVE ) Peng-Robinson(PR-BM) Redlich-Kwong-Soave (RKS-BM) Peng-Robinson-MHV2 Redlich-Kwong-ASPEN(RK-ASPEN) Peng-Robinson-WS Schwartzentruber-Renon Redlich-Kwong-Soave-MHV2

Predictive SRK (PSRK) Redlich-Kwong-Soave-WS EOS Method 5- Standard RK-SOAVE RT a P Vm b Vm (Vm b) Where a xi x j (ai a j ) 0.5 (1 kij ), b xi bi i j i R 2Tci2 RTci ai i 0.42747 , bi 0.08664 Pci Pci i (T ) [1 mi (1 Tri0.5 )]2 , mi 0.48 1.57i 0.176i2 EOS Method 6- Standard PENG-ROB RT a P Vm b Vm (Vm b) b(Vm b) Where a xi x j (ai a j ) 0.5 (1 kij ), b xi bi i

j i R 2Tci2 RTci ai i 0.45724 , bi 0.07780 Pci Pci i (T ) [1 mi (1 Tri0.5 )]2 , mi 0.37464 1.54226i 0.26992i2 EOS Method 7- Advantages and Disadvantages Equations of state can be used over wide ranges of temperature and pressure, supercritical regions. including subcritical and Thermodynamic properties for both the vapor and liquid phases can be computed with a minimum amount of component data. For the best representation of non-ideal systems, you must obtain binary interaction parameters from regression of experimental VLE data. Binary parameters for many component pairs are available in the Aspen databanks. EOS Method 7- Advantages and Disadvantages

Equations of state are suitable for modeling hydrocarbon systems with light gases such as CO2 , N2 and H2 S . The assumptions in the simpler equations of state (SRK, PR, Lee-Kesler , ) are not capable of representing highly non-ideal chemical systems, such as alcohol-water systems. Use the activity-coefficient options sets for these systems at low pressures. At high pressures, use the predictive equations of state. Activity Coefficient Method 1- Vapor-Liquid Equilibrium v fi fi At Equilibrium: Where Therefore f i v iv yi Pt , l f i l i xi f i *,l *,l yi i f i k v xi i Pt vl i

F0r ideal gas and liquid * y P v vl i 1, i 1 ki i i Raoult' s Law xi Pt Activity Coefficient Method 2- Liquid-Liquid Equilibrium l1 fi fi At Equilibrium: Where l1 l1 l1 i i f i x f i Therefore k l1l 2 i *,l , l1 i

l2 i l2 l2 l2 i l2 i f i x f i l2 i l1 i x x *,l Activity Coefficient Method 3- Vapor-Liquid-Liquid Equilibrium At Equilibrium: Where l1 l1 l2

fi fi fi l1 l1 i i v l2 *,l l2 i l2 i f i x f i , f i x f i v v f i i yi Pt Therefore k vl1 i l1 i *,l yi f i l1 v xi i Pt

, k vl2 i *,l l2 i *,l yi f i l2 v xi i Pt Activity Coefficient Method 4- Liquid Phase Reference Fugacity For solvents: The reference state for a solvent is defined as pure component in the liquid state, at the temperature and pressure of the system. fi *,l *,v i *,l *,l *,l i (T , Pi ) Pi , (i 1 as xi 1)

i*,v = Fugacity coefficient of pure component i at the system temperature and vapor pressures, as calculated from the vapor phase equation of state i*,l = Poynting factor *,l i 1 exp RT P *,l V dP Pi*,l i Activity Coefficient Method 4- Liquid Phase Reference Fugacity For dissolved gases: Light gases (such as O2 and N2 ) are usually supercritical at the temperature and pressure of the solution. In that case pure component vapor pressure is meaningless and therefore it cannot serve as the reference fugacity. l * *,l i i f i xi f where

f i *,l H i and i* 1 as xi 0 Activity Coefficient Method 5- NRTL (Non-Random Two-Liquid) The NRTL model calculates liquid activity coefficients for the following property methods: NRTL, NRTL-2, NRTL-HOC, NRTL-NTH, and NRTL-RK. It is recommended for highly nonideal chemical systems, and can be used for VLE, LLE and VLLE applications. x G x G j ln i ji j k k ki ji x j Gij j xk Gkj k

ij x G x G m mj mj m k k kj Activity Coefficient Method 5- NRTL (Non-Random Two-Liquid) x G x G j ln i ji j k

k ki ji x j Gij j xk Gkj k ij x G x G m mj mj m k k kj

Where Gij exp( ij ij ) , Gii 1 ij aij bij T eij ln T f ijT , ii 0 ij cij d ij (T 273.15) The binary parameters aij, bij, cij, dij, eij and fij can be determined from VLE and/or LLE data regression. The Aspen Physical Property System has a large number of built-in binary parameters for the NRTL model. Activity Coefficient Method 6- Advantages and Disadvantages The activity coefficient method is the best way to represent highly non-ideal liquid mixtures at low pressures. You must estimate or obtain binary parameters from experimental data, such as phase equilibrium data. Binary parameters are valid only over the temperature and pressure ranges of the data. The activity coefficient approach should be used only at low pressures (below 10 atm). Principle Steps in Selecting the Appropriate Thermodynamics Package 1. Choosing the most suitable model/thermo method. 2. Comparing the obtained predictions with data from the literature. 3. Estimate

or obtain binary experimental data if necessary. parameters from 4. Generation of lab data if necessary to check the thermo model. Eric Carlsons Recommendations Figure 1 Polar Non-electrolyte E? Electrolyte NRTL Or Pizer Electrolyte Real All Non-polar Peng-Robinson, Redlich-Kwong-Soav Lee-Kesler-Plocker R? Polarity R? Real or pseudocomponents P?

Pressure E? Electrolytes See Figure 2 Pseudo & Real P? Vacuum Chao-Seader, Grayson-Streed or Braun K-10 Braun K-10 or ideal Yes Figure 2 P < 10 bar (See also Figure 3) Yes LL? No ij? P? No

No Yes LL? Liquid/Liquid Pressure P > 10 bar ij? Interaction Parameters Available WILSON, NRTL, UNIQUAC and their variances Yes UNIFAC LLE LL? Polar Non-electrolytes P? NRTL, UNIQUAC and their variances ij? No UNIFAC and its extensions Schwartentruber-Renon PR or SRK with WS PR or SRK with MHV2

PSRK PR or SRK with MHV2 Hexamers Figure 3 Yes DP? Dimers VAP? Wilson NRTL UNIQUAC UNIFAC Wilson, NRTL, UNIQUAC, or UNIFAC with special EOS for Hexamers No Wilson, NRTL, UNIQUAC, UNIFAC with Hayden OConnel or Northnagel EOS Wilson, NRTL, UNIQUAC, or UNIFAC* with ideal Gas or RK EOS VAP? Vapor Phase Association DP? Degrees of Polymerizatiom UNIFAC* and its Extensions Eric Carlsons Recommendations for 1-Propanol ,H2O mixture Figure 1

Non-electrolyte Polar E? Polarity R? Real or pseudocomponents P? Pressure E? Electrolytes See Figure 2 Figure 2 P < 10 bar (See also Figure 3) P? Polar Non-electrolytes LL? Liquid/Liquid P? Pressure ij? Interaction Parameters

Available Yes LL? WILSON, NRTL, UNIQUAC and their variances No ij? No LL? No UNIFAC and its extensions

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