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Thermodynamic Lab. Korea University 1
Equations of State for Electrolytes
Kim Yong SooThermodynamic Lab.
Chemical Engineering, Korea Univ.
Thermodynamic Lab. Korea University 2
1. Introduction Activity Coefficient Model
An inconsistency when electrostatic terms are im-properly superimposed on convential Gibbs model. Cardoso and O’Connell(1987)
The systems containing supercritical components at high pressures
• Not possible to select a truly useful standard state for the supercritical components(Pausnitz et al., 1986)
Thermodynamic Lab. Korea University 3
Equation of State(Helmholtz energy framework)
To calculate the fugacity(of chemical potential) of each species in each phase
To be successful for nonelectrolyte systems
The problem is to superimpose properly the electro-static effects in an EOS for nonelectrolyte systems.
Thermodynamic Lab. Korea University 4
2. Review on Electrolyte Equation of States
Raatschen’s model(1987)Debye-Huckel, Born and Pitzer term for ionic
contributionsNot to be in a form suitable for extension to systems
containing supercritical gases Copeman and Stein(1987)
To use MSA model to describe ion-ion interactionsTo be limited to pressures near atmosphericTo need second parameter for highly concentrated
systems
Thermodynamic Lab. Korea University 5
Jin and Donohue(1988, 1991)PACT model for short-range molecule-molecule
interactionsThe perturbation expansion for long-range
Coulombic interactionsAdjustable parameter
• One parameter for each electrolyte(1988)• The ionic radii for each ion(1991)
To apply the supercritical gases and the salt systems
Thermodynamic Lab. Korea University 6
Harvey and Prausnitz(1989)
• is the “nonelectrolyte” contribution from Barker-Henderson perturbation theroy.
• is the ion-charging contribution.
–
– To produce the effect on the fugacities of the uncharged species through the composition dependence of the dielectric constant
– To account for long-range portions of the ion-solvent interacions
IIIIII AAAA Δ+Δ+=IA
IIAΔ
−+=Δ
i iciiicii
AII
Dzx
RTeNA
,,
22 111
σσσ
Thermodynamic Lab. Korea University 7
Harvey and Prausnitz(1989) (II)• accounts for charge-charge interactions
– To approximate the Blum’s MSA model for iterative equation of state calculations
Binary parameter( )• To consider the solvent/ion interactions• To correct the salting-out effect
– Utilization of Setchenow-constant data
IIIAΔ
ρπσ
A
mixIII
NA
12)5.11()2( 3 Γ+Γ−=Δ
ijk
Thermodynamic Lab. Korea University 8
Harvey and Prausnitz(1989) (Result)
Thermodynamic Lab. Korea University 9
Harvey and Prausnitz(1989) (Discussion)The MSA is the lowest-order term in seriesThe ion/water interaction is not described correctly
at high salt concentrationsThe salt/water and salt/gas binary parameters may
be dependent on temperatureThe nonelectrolyte portion of the EOS would
improve the salt-free systems.(hydrogen-bonding and structural effects in water)
Thermodynamic Lab. Korea University 10
Aasberg-Petersen et al(1991)
The EOS part (Cubic EOS) is evaluated by using the salt-free mole fractions.
Activity coefficients are calculated by Debye-Huckel model.(Macedo et al., 1990)
•
• binary parameter, (water/salt, salt/gas)
ELi
EOSii γφφ lnlnln +=
)(2ln 2/13 BIf
BMAh misEL
i =γ
ish
Thermodynamic Lab. Korea University 11
Aasberg-Petersen et al(1991)(Result)
Thermodynamic Lab. Korea University 12
LRSRSRRF RTaa
RTaa
RTaa
RTaa
RTaa
−+
−+
−+
−=
− 0
2
0
1
000
Furst and Renon(1993)(Theory)
• Schwartzentruber et al.(1989)
• Repulsive forces(RF) and the first attractive short-range forces term(SR1)
• Wong-Sandler mixing rule using UNIQUAC or NRTL
+++
++
−=
−+
−k
SRk
kSRRF cbv
cvcbRT
abvP
RTxxRT
aaRT
aa2
ln)()(
ln01
00
Thermodynamic Lab. Korea University 13
Furst and Renon(Theory)
• A short-range term specific to interactions involving ionic species
• where the shielding parameter is obtained from
• The long-range interaction term in the form used by Ball
−−=
−k l
kllk
SR vWxx
RTaa
)1( 32
0
ξ =k
kk
vxN 3
3 6σπξ
NvZx
RTaa
k i
iiLR
RF πσπα
314
3220 Γ+Γ+
Γ−=
−
Γ
Γ+
=Γi i
iiLR
ZvxN
222
14
σα
Thermodynamic Lab. Korea University 14
Furst and Renon(Theory) Ionic parameters( )
•
•
•
•
– Adjustable parameter :
klii Wb ,,σ
36
πσ
Nbi
i =
( ) ( ) 23
123
1 , λσλλσλ +=+= Paa
Scc bb
43 λσλ += SccwW
( ) 64
5 λσσλ ++= Pa
SccaW
65 ,λλ
Thermodynamic Lab. Korea University 15
Furst and Renon(1997)Apply to the nonaqueous solvent-salt systemsPredict the vapor pressures and the mean ionic
activity coefficients
Zuo and Renon(1998)Apply to the calculation of VLE and mean ionic
activity coefficients for mixed solvent electrolyte system
Thermodynamic Lab. Korea University 16
Thermodynamic Lab. Korea University 17
Thermodynamic Lab. Korea University 18
Zuo et al(FPE, 2000)Extension to mixed solvent halide electrolyte
systems Zuo et al(Energy and Fuels, 2000)
Represent hydrate phase equilibria in aqueous solutions of methanol and electrolytes using the Furst and Renon model
Thermodynamic Lab. Korea University 19
Thermodynamic Lab. Korea University 20
Thermodynamic Lab. Korea University 21