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Transcript of Thermodynamic Consistency Test of Vapor-Liquid … grupo chil/JOV...Thermodynamic Consistency Test...
![Page 1: Thermodynamic Consistency Test of Vapor-Liquid … grupo chil/JOV...Thermodynamic Consistency Test of Vapor-Liquid Equilibrium Data for Mixtures Containing Ionic Liquids José O. Valderrama](https://reader031.fdocuments.us/reader031/viewer/2022022008/5ae5f5fe7f8b9a08778c645b/html5/thumbnails/1.jpg)
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
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Testing data for consistency means to check whether the data fulfill or not certainthermodynamic requirements
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Why published data shouldbe analyzed for their
consistency?
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0
1
2
3
4
5
6
50 150 250 350
P(bar)
Y*E+
07
CO2+β-Carotene, 313K
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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.
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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
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The independent test is the Gibbs-Duhem Equation
↓Thermodynamic consistency
We need an independent test
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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
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( )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…
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For binary mixtures…
AP = Aϕ
( )1
12
22
2φ φ d
φ)1Z(xx-1φ d
φ)1Z(1A ∫∫ −
+−
=
∫= dPPx
1A2
P
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AP from P-x data
Aϕ from an EoS
How we do calculate AP and Aϕ ?
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data for AP
good modeling for and Aϕ
So, we need…
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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
⎥⎥⎥⎥⎥⎥⎥⎥
⎦
⎤
⎢⎢⎢⎢⎢⎢⎢⎢
⎣
⎡
−+
−−
=
∑∑
∑∑∑
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%ΔAi=100[(Aϕ-AP)/ AP]
%ΔAav=100Σ[(Aϕ-AP)/ AP]/(N-1)
%Δx2=100Σ[(xcal-xexp)/xexp] /N
MainMain EquationsEquations......
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Congress Presentations
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In press
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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…