Thermodynamic Consistency Test of Vapor-Liquid Equilibrium Data for Mixtures

Containing Ionic Liquids

José O. ValderramaUniversity of La Serena- Chile

Properties of Ionic LiquidsExperimental Data and Property Estimation

International Workshop

Testing data for consistency means to check whether the data fulfill or not certainthermodynamic requirements

Why published data shouldbe analyzed for their

consistency?

0

1

2

3

4

5

6

50 150 250 350

P(bar)

Y*E+

07

CO2+β-Carotene, 313K

The high pressure phase equilibrium data correspond to PX data at a given T, or solubility

Aki, A.; Mellein, B. R.; Saurer, E. M.; Brennecke, J. F. High-Pressure Phase Behavior of Carbon Dioxide with Imidazolium-Based Ionic Liquids. J. Phys. Chem. B 2004, 108, 20355-20365.

Analysis of experimental setup

Believe data from Reliable Labs

Still… this is not enough

We need to know which set to use in a given application

The independent test is the Gibbs-Duhem Equation

↓Thermodynamic consistency

We need an independent test

The Gibbs-Duhem equation

[ ] dPRTVdT

RTHGdx

R

2

RRii +−=∑

( )R N

i ii 1

V d P x d L nR T =

= γ∑

For isothermal cases

( )Nii

j ji 1

d Lnx1 dPP dx Z 1 dx=

ϕ=

−∑

P jj

1A d PP x

= ∫

( ) ( )N N

ij i j i

i ji 1 i 1

xA {A } dZ 1 xϕ ϕ

= == = ϕ

− ϕ∑ ∑ ∫

For multicomponent mixtures…

For binary mixtures…

AP = Aϕ

( )1

12

22

2φ φ d

φ)1Z(xx-1φ d

φ)1Z(1A ∫∫ −

+−

=

∫= dPPx

1A2

P

AP from P-x data

Aϕ from an EoS

How we do calculate AP and Aϕ ?

data for AP

good modeling for and Aϕ

So, we need…

Equation of state Mixing rules Peng-Robinson equation Wong-Sandler

)bV(b)bV(Va

bVRTP

mmmm

m −++−= -

)T(PTR

42748.0ac

2c

2α=

c

cP

RT08664.0b =

α(Tr) = [1 + F(1 – Tr

0.5)]2

F = 0.48 + 1.574 ω - 0.176 ω2

34657.0RT/)y(g

RTbay

1

RTabyy

be

iii

ijji

m−

Σ−

⎟⎠⎞

⎜⎝⎛ −ΣΣ

=

( )

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛+

Σ=

34657.0yg

bayba

E

iii

mm

[ ] ( )ijji

jiij

k1RT

aa)bb

21

RTab −−+=⎟

⎠⎞

⎜⎝⎛ −

( )

2

N

jjijii

N

jijji

N

jijji

i

N

jijjN

ii

E

Lyyy1Lyy

Lyy

1.y1

Ly

yRTg

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−+

−−

=

∑∑

∑∑∑

%ΔAi=100[(Aϕ-AP)/ AP]

%ΔAav=100Σ[(Aϕ-AP)/ AP]/(N-1)

%Δx2=100Σ[(xcal-xexp)/xexp] /N

MainMain EquationsEquations......

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Thanks to:Thanks to:

ConicytConicyt--Fondecyt 1070025Fondecyt 1070025

University of La SerenaUniversity of La Serena--ChileChile

and to all of you, for your presence…