An Electrolyte NLF-HB Equation of State Applicable to … · 2004-11-09 · Applicable to Concentrated Electrolyte systems Kim, Yong Sooand Lee, Chul Soo* Chemical & Biological Engineering

An Electrolyte NLF-HB Equation of State Applicable to Concentrated Electrolyte systems

Kim, Yong Soo and Lee, Chul Soo*

Chemical & Biological Engineering

Korea University

Thermodynamics & Properties Laboratory

Contents

Introduction

Theory

Results

Conclusions


Introduction

Electrolyte solutions

– Wastewater treatment, extraction, distillation, seawater desalination, salt-added bioseperation…

– Need for understanding of thermodynamics

– For engineering purposesExperimental work

A good model capable of describing the phase behavior


Introduction

More difficult to model than most other solutions

– Ions : Interaction both each other and with solvents

– Charged particlesLow concentration : dominant electrostatic force

High concentration : Short-range forces become important.

– The chemistry of solutions changes at different conditions such as temperature and density.


Introduction

Excess Gibbs function– Debye-Hückel, Pitzer model, electrolyte NRTL …– Useful for non-idealities of electrolyte solutions– Not adequate to high pressure applications

Equation of state approch

– Applicable to wide range of pressure– Description of phase equilibria using unified model


Electrolyte NLF-HB Equation of State

Development of an equation of state for electrolyte systems

– Fully ionized electrolyte solutions

– Electrostatic interactions => Mean spherical approximation(MSA) model

– Association(or hydration) => Veytsman statistics



Helmhlotz free energy

– Athermal contributionGuggenheim-Huggins-Miller approximation

– Residual contributions Quasi-chemical approximation

– Association contributionsNormalized Veytsmann statistics

– Long-range contributionsMean spherical approximation

lrassresathm AAAAA +++=



Helmhlotz free energy

[ ]rrrfqqqirathm NNNNNNzNNA +−−⎟⎠⎞

⎜⎝⎛−+−= ∑ lnln

2!ln!lnβ

⎥⎦

⎤⎢⎣

⎡−−+⎟

⎠⎞

⎜⎝⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛−= ∑∑ ∑∑∑∑ )(

22 jkikklijijlkjiijjiq

resNz

A εεεεεθθθθβεθθβ

β

∑ ∑ −+−−=m

i

m

iiiid

id

id

ir

HBass NNNNNNNNA )ln()ln(ln 000β

∑ ∑ −+−−n

i

m

jjjja

ia

ia

i NNNNNN )ln()ln( 000

∑∑ −++m

i

HBij

HBij

HBij

n

j

HBij

HBij NNNAN )ln(β

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛Γ+Γ

−Γ

=ions

k

kklr

zNVAσπ

απ

β143

223



Chemical potential : PvrNA

kTNRT Hii

C

aii ββµµ +⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

==

⎟⎟⎠

⎞⎜⎜⎝

⎛+−−

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−++=

i

ii

M

Miii q

rrqlr θρρβµ ln)1ln(11ln)(

⎥⎥⎦

⎤

⎢⎢⎣

⎡ −−++−−×⎟

⎠⎞

⎜⎝⎛+ ∑ ∑∑∑

22 )22(2

12 θε

εεεεεθθθβεθθεβ

M

ikjkklijijlkjikk

i

iMi q

rqz

∑∑ −−=j j

jak

ji i

idk

iass NNa

NNd

00lnlnβµ

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛Γ+Γ

⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

+Γ+Γ

−=ions

k

k

NVTii

ilri

zND

Dz

jσπ

ασπ

αβµ14)1(4

2

,,

22

,



Pressure

ρνθεβρρρ HBMMM

MH zrr

qzRT

PV−−+−−

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−+= 2

2)1ln(11ln

2

⎥⎦

⎤⎢⎣

⎡−−+⎟

⎠⎞

⎜⎝⎛+= ∑∑ ∑∑∑∑ )223(

21

2 jkikklijijlkjiijjiM εεεεεθθθθβεθθθ

ε

∑ ⎟⎟⎠

⎞⎜⎜⎝

⎛Γ+Γ

⎟⎠⎞

⎜⎝⎛∂∂

−Γ

−=ions

k

kk

NTlr

zNVD

DP

σπα

πβ

143

2

,

23

Athermal and residual contributions

Association contribution



Parameters for solvent

– energy and size parameters

– Hydrogen bonding energy and number of donor and acceptor

– Obtained by fitting saturated vapor pressure and density

)]()/ln([)(/ 000 TTTTTTTk cbaii −++−+= εεεε

)]()/ln([)( 000 TTTTTrTTrrr cbai −++−+=



Three parameters for salts

– Interaction energy and segment numberMean values of cation and anion

Size in MSA term

– Hydration energy and donor number for cationsFixed to 7 for donor number

– Obtained by fitting mean activity coefficients and osmotic coefficients

and anioncationsaltanioncationsalt rrr ==== εεε

πσ /63iHci rVf=


Thermodynamic properties

Mean ionic chemical potential and mole fractions

Molal mean activity coefficient and osmotic coefficient

where

iiiiiii −−++−+± +=+ νµνµννµ )( iiii

i ii xxx −+−+

± −++ = νννν )(

∞±±

∞±±± ×−= i

li

li

li

li xxRT /]/)exp[(* µµγ

∑−=ions kSSS xRTxx γφ ln

⎟⎟⎠

⎞⎜⎜⎝

⎛+−= ∑∑

==±±±

solvent

jj

salt

kkk

li

mi xx

11

** /1lnlnln νγγ


Parameters for salts


Parameters for salts


Results

Molality

0 1 2 3 4 5 6

Osm

otic

coe

ffici

ent

0.8

1.0

1.2

1.4

NaCl NaBr NaI NaF NaClO4 NaNO3 NaClO3 NaBrO3 Electrolyte NLF-HB

Molality

0 1 2 3 4 5 6

Mea

n ac

tivity

coe

ffici

ent

0.4

0.6

0.8

1.0

1.2NaCl NaBr NaI NaF NaClO4 NaNO3 NaClO3 NaBrO3 Electrolyte NLF-HB

Comparison of experimental mean activity coefficient and osmotic coefficient and calculated results


Results

Molality

0 1 2 3 4 5 6

Mea

n ac

tivity

coe

ffici

ent

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

KCl KBr KI KF KCNS KNO3 KClO3 KBrO3 Electrolyte NLF-HB

Molality

0 1 2 3 4 5 6

Osm

otic

coe

ffici

ent

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

KCl KBr KI KF KCNS KNO3 KClO3 KBrO3 Electrolyte NLF-HB

Comparison of experimental mean activity coefficient and osmotic coefficient and calculated results


Results

Molality

0 5 10 15 20

Mea

n ac

tivity

coe

ffici

ent

0

100

200

300

400

500

600

HClHClO4LiClLiBrElectrolyte NLF-HB EOS

Molality

0 5 10 15 20

Mea

n ac

tivity

coe

ffici

ent

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

NH4NO3

CsCl AgNO3

Electrolyte NLF-HB EOS

Comparison of experimental mean activity coefficients and calculated results for concentrated electrolyte solutions


Comparison of Models

Electrolyte NRTL model(based on GE model)

– Chen et al. (1999)– Two adjustable parameters and hydration number

Myers and Sandler (2002)

– Equation of state approach– Three adjustable parameters for each salts– The Born contribution for hydration process and MSA model for electrostatic interaction


Results


Results


Results : Summary

a : calculated up to 6 molal


Conclusion

Development of electrolyte NLF-HB equation of state

– Electrostatic interactions by mean spherical approximation

– Hydration(association) contribution by Veytsmannstatistics

Mean activity coefficients, osmotic coefficients, and densities were calculated for 60 electrolyte solutions

Documents

An Electrolyte NLF-HB Equation of State Applicable to … · 2004-11-09 · Applicable to Concentrated Electrolyte systems Kim, Yong Sooand Lee, Chul Soo* Chemical & Biological Engineering