Application of Crossover Theory to the SAFTVR Equation of State

1
Application of Crossover Theory to the SAFT-VR
Equation of State

• Clare McCabe
• Department of Chemical Engineering,
• Colorado School of Mines, Golden CO, USA

Molecular Thermodynamics and Molecular Simulation
03 Hotel New Mitoya, Akiu,Sendai, Japan 28th May
2003
2
Acknowledgements

• Collaborators
• Sergei Kiselev
• Eric Whitebay
• Research Support
• Division of Chemical and Thermal Systems,
  Directorate for Engineering, National Science
  Foundation

• Heather Langmack

3
Outline

• Motivation
• Application of SAFT-VR to real fluids
• Failure of classical equations of state in
  critical region
• Theory
• SAFT-VR approach
• Models
• Critical scaling of Kiselev
• Results
• SAFT-VRX
• Non-associating fluids
• Hydrocarbons
• Associating and polar fluids
• Water, alcohols and carbon dioxide
• Conclusions

4
Motivation

• Numerous EOS models exist to describe phase
  behavior
• Simple cubic engineering equations of state
• Predictive models based on thermodynamic
  perturbation theory
• SAFT approach very versatile and powerful EOS for
  modeling associating fluids and their mixtures
• SAFT-VR successfully applied to a wide range of
  industrially important fluid systems
• Major drawback of classical EOSs is poor
  description of critical region
• Incorporation of crossover into the SAFT-VR EOS
  enables an accurate representation of the whole
  phase diagram

5
SAFT Statistical Associating Fluid Theory

• Molecular based equation of state (EOS)
• Originally developed for chains of Lennard-Jones
  segments with association sites
• Explicitly takes into account non-sphericity
• Unlike simple cubic EOS such as Peng-Robinson and
  Redlich-Kwong
• Ideal for modelling chain molecules

Chapman, Gubbins, Jackson, Radosz, Fl. Ph. Eq.,
52, 31 (1989). Chapman, Gubbins, Jackson, Radosz,
Ind. Eng. Chem. Res., 29, 1709 (1990).
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SAFT-VR
A. Gil-Villegas, et al., J. Chem. Phys., 106,
4168 (1997). A. Galindo, et al., Mol. Phys., 93,
241 (1998).

• Monomer Contribution
• Monomer free energy per segment

7

• Chain contribution

Chapman, W. G., 1990, J. Chem. Phys., 93, 4299.
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Model

• United Atom
• Alkanes
• United Atom m (C-1)/31
• 3 adjustable parameters
• fit to experimental pure component saturated
  liquid density and vapour pressure data
• Water
• 4 site model
• 5 adjustable parameters
• fit to experimental pure component saturated
  liquid density and vapour pressure data

9
Alkanes

• Vapour pressures

ln (p /MPa)
p /MPa
C. McCabe, A. Galindo, A. Gil-Villegas, and G.
Jackson, Int. J. Thermophys., 19, 1511 (1998).
10
Alkanes

• Vapour pressures

ln (p /MPa)
p /MPa
11
Methane (1) Butane (2)
C. McCabe, et al., Int. J. Thermophys., 19, 1511
(1998).
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Butane (1) n-Alkanes (2)

• Critical lines

C. McCabe, A. Galindo, A. Gil-Villegas, and G.
Jackson, Int. J. Thermophys., 19, 1511 (1998).
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Problem with re-scaling

• Original parameters

• Rescaled parameters

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Critical Exponents

• Classical vs. non-classical critical behavior

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Crossover SAFT-VR SAFT-VRX

• Recast Helmholtz free energy
• where

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SAFT-VRX

• Replace ?T and ?v in critical term
• Where,
• the critical exponents
• the critical shifts

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SAFT-VRX

• Crossover function
• where
• 3 additional parameters obtained by fitting to
  experimental data

18
Alkane Results

• Methane - Octane

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Alkane Results

• Close to critical region

and far from the critical region
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Alkane Results

• Methane coexisting densities

SAFT-VR
SAFT-VRX
Crossover SAFT-HR
rescaled SAFT-VR
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Alkane Results

• Ethane - octane coexisting densities

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Alkane Results Prediction

• Parameters
• Fitted VLE data for C2 - C6, C8, C10, C20
• Obtained simple expressions for parameters as a
  function of molecular weight
• Example for m
• Similar simple expressions obtained for all
  parameters

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Alkane Results Prediction

• Longer alkanes

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Alkane Results Prediction

• Enthalpy of Vaporization

25
Alkanes Prediction

• PVT behaviour
• C30

• C40

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Alkanes

• Critical constants
• Experimental data from Nikitin, High Temp., 36,
  305-318 (1998).

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Associating Fluids

• Water

p /MPa
T /K
r /molcm-3
28
Associating Fluids

• Propanol

T /K
p /MPa
29
Carbon dioxide
30
Conclusions

• Application of crossover to SAFT-VRX
• SAFT-VRX shows significant improvement in
  theoretical description of phase diagram over
  SAFT-VR
• Non-associating
• Associating and polar fluids
• Parameters retain physical meaning and allow
  prediction of phase behavior for other members of
  homologous series
• Extension to mixtures underway