VLE, LLE and VLLE in ASPEN PLUS

Mohammad Ali Fanaei, Ferdowsi University of Mashhad

EOS Method1- Vapor-Liquid Equilibrium

At Equilibrium:

Where

Therefore

li

vi ff

tili

liti

vi

vi PxfPyf ,

vi

li

i

ivli x

yk

EOS Method2- Liquid-Liquid Equilibrium

At Equilibrium:

Where

Therefore

21 li

li ff

tli

li

lit

li

li

li PxfPxf 222111 ,

1

2

2

121

li

li

li

lill

i xxk

EOS Method3- Vapor-Liquid-Liquid Equilibrium

At Equilibrium:

Where

Therefore

vi

li

li fff 21

tivi

vi

tli

li

lit

li

li

li

PyfPxfPxf

222111 ,

vi

li

li

ivliv

i

li

li

ivli x

ykxyk

2

2

21

1

1 ,

EOS Method4- Fugacity Coefficient Formula

m

V

nVTii ZdV

VRT

nP

RTj

ln1ln,,

Cubic Equations of State in the Aspen Physical Property SystemRedlich-Kwong(-Soave) based Peng-Robinson basedRedlich-Kwong (RK) Standard Peng-Robinson(PENG-ROB)Standard Redlich-Kwong-Soave(RK-SOAVE ) Peng-Robinson(PR-BM)Redlich-Kwong-Soave (RKS-BM) Peng-Robinson-MHV2Redlich-Kwong-ASPEN(RK-ASPEN) Peng-Robinson-WSSchwartzentruber-RenonRedlich-Kwong-Soave-MHV2Predictive SRK (PSRK)Redlich-Kwong-Soave-WS

EOS Method5- Standard RK-SOAVE

)( bVVa

bVRTP

mmm

Where

i

iii j

ijjiji bxbkaaxxa ,)1()( 5.0

ci

cii

ci

ciii P

RTbPTRa 08664.0,42747.0

22

225.0 176.057.148.0,)]1(1[)( iiiriii mTmT

EOS Method6- Standard PENG-ROB

)()( bVbbVVa

bVRTP

mmmm

Where

i

iii j

ijjiji bxbkaaxxa ,)1()( 5.0

ci

cii

ci

ciii P

RTbPTRa 07780.0,45724.0

22

225.0 26992.054226.137464.0,)]1(1[)( iiiriii mTmT

EOS Method7- Advantages and Disadvantages

Equations of state can be used over wide ranges of temperature and pressure, including subcritical and supercritical regions.

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 Method7- 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

At Equilibrium: Where Therefore

F0r ideal gas and liquid

li

vi ff

liii

liti

vi

vi fxfPyf *,,

tvi

lii

i

ivli P

fxyk

*,

LawsRaoultPP

xyk

t

i

i

ivli

vii '1,1

*

Activity Coefficient Method 2- Liquid-Liquid Equilibrium

At Equilibrium:

Where

Therefore

21 li

li ff

li

li

li

li

li

li

li

li fxffxf *,*, 222111 ,

1

2

2

121

li

li

li

lill

i xxk

Activity Coefficient Method 3- Vapor-Liquid-Liquid Equilibrium

At Equilibrium:

Where

Therefore

vi

li

li fff 21

tivi

vi

li

li

li

li

li

li

li

li

Pyffxffxf

*,*, 222111 ,

tvi

li

li

li

ivli

tvi

li

li

li

ivli P

fxyk

Pf

xyk

*,*, 2

2

21

1

1 ,

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.

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

)11(,),( *,*,*,*,*, iil

il

il

iv

il

i xasPPTf

P

P

li

li l

i

dPVRT *,

*,*, 1exp

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.

01**,

*,*

iiil

i

liii

li

xasandHfwhere

fxf

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.

jk

kjk

mmjmjm

ij

kkjk

ijj

kkik

jjijij

i Gx

Gx

GxGx

Gx

Gx

ln

Activity Coefficient Method 5- NRTL (Non-Random Two-Liquid)

Where

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.

jk

kjk

mmjmjm

ij

kkjk

ijj

kkik

jjijij

i Gx

Gx

GxGx

Gx

Gx

ln

)15.273(

0,ln

1,)exp(

Tdc

TfTeTba

GG

ijijij

iiijijijijij

iiijijij

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).

1. Choosing the most suitable model/thermo method.

2. Comparing the obtained predictions with data from the literature.

3. Estimate or obtain binary parameters from experimental data if necessary.

4. Generation of lab data if necessary to check the thermo model.

Principle Steps in Selecting the Appropriate Thermodynamics Package

Eric Carlson’s Recommendations

E?

R?

P?

Polar

Real

Electrolyte

Pseudo & Real

Vacuum

Non-electrolyte

Braun K-10 or ideal

Chao-Seader,Grayson-Streed or Braun K-10

Peng-Robinson,Redlich-Kwong-Soave,Lee-Kesler-Plocker

Electrolyte NRTLOr Pizer

See Figure 2Figure 1

Polarity

R?Real or pseudocomponents

P? Pressure

E? Electrolytes

All Non-polar

P?

ij?

ij?

LL?

(See alsoFigure 3)

P < 10 bar

P > 10 bar

PSRKPR or SRK with MHV2

Schwartentruber-RenonPR or SRK with WSPR or SRK with MHV2

UNIFAC and its extensions

UNIFAC LLE

PolarNon-electrolytes

No

Yes

Yes

LL?No

No

Yes

Yes

NoWILSON, NRTL,UNIQUAC and their variances

NRTL, UNIQUACand their variances

LL? Liquid/Liquid

P? Pressure

ij? Interaction Parameters Available

Figure 2

VAP?

DP?Yes

No Wilson, NRTL,UNIQUAC, or UNIFAC* with ideal Gas or RK EOS

Wilson NRTLUNIQUACUNIFAC

Hexamers

Dimers Wilson, NRTL, UNIQUAC, UNIFAC with Hayden O’Connell or Northnagel EOS

Wilson, NRTL, UNIQUAC, or UNIFAC with special EOS for Hexamers

VAP? Vapor Phase Association

Degrees of PolymerizatiomDP?UNIFAC* and its Extensions

Figure 3

Eric Carlson’s Recommendationsfor 1-Propanol ,H2O mixture

E?Polar

Non-electrolyteSee Figure 2

Figure 1

Polarity

R?Real or pseudocomponents

P? Pressure

E? Electrolytes

P?

ij?

LL?

(See alsoFigure 3)

P < 10 bar

UNIFAC and its extensions

PolarNon-electrolytes

Yes

LL?No

No

NoWILSON, NRTL,UNIQUAC and their variances

LL? Liquid/Liquid

P? Pressure

ij? Interaction Parameters Available

Figure 2