Activity Coeff Estimation Methods

7/28/2019 Activity Coeff Estimation Methods

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Activity Coefficient EstimationMethods

Bharat Chandramouli

February 5, 2002


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Activity Coefficient The activity coefficient is a measure of

the non-ideality of mixing

Two components, Enthalpic andEntropic

idealnonideal

lnln

esmix G

w

G

ws RTxRTG


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Estimation/MeasurementActivity coefficients in single

component/simple mixtures easy to

measure

Activity coefficients in water or octanolcan be calculated from solubility givensufficiently sensitive methods

sat

satx

1


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Need for estimation What about complex mixtures?

What about dynamic systems withchanging compositions?

It becomes more practical to useestimation methods to approximate in

these cases


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Estimation Methods Group contribution methods are most

common because they have predictive

ability

There are two group contributionmethods commonly used for i

om

calculation from solubility parameters

UNIFAC calculation


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UNIFAC the UNIversal Functional

group Activity Coefficient model The activity coefficient is calculated

from two components

RiCii lnlnln

Combinational

(V, SA)

Residual (interactions)

(Experiment Fit)


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UNIFAC The group contribution components consist of

volume contributor -Rk

surface area contribution -Qk

interaction parameter between functional groupsAmk

To calculate interactions, similar sub-groupsare assigned to groups and interactions arebetween these groups

Calculate activity coefficients by summing allcontributions and interactions


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UNIFAC-Simple example Ethanol CH3-CH2-OH

Main Group. Subgroup Rk (vol) Qk(SA) Amk

CH3 CH3 CH3 (1) 0.9011 0.848 0, 0

CH2

CH2 CH

2(2) 0.6744 0.540 0, 0

OH OH OH (2) 1.000 1.200 986.5, 156.4


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UNIFAC Methods Interaction parameters are fit from

experimental data

This work is still ongoing and manyparameters still not available


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Hansen Solubility Parameter This method calculates activity

coefficients from the solubility

parameter Theory of cohesive energy developed

by Hildebrand for dispersive systems

and extended by Hansen for polar andhydrogen bonding


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Hansen Activity Coefficient The activity coefficient is given by

dARTVomiomii

om

i ,,

)/(ln

Molar VolumeCohesive energy density

Size effect term

Enthalpy Entropy


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The Size Effect Term

i,omdis a measure of the effect ofdiffering sizes of i and om on their

entropy of mixing This was derived by Flory and Huggins

using statistical thermodynamics

For an infinitely dilute solution

VVVVd iiomi /1)/ln(,


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Cohesive Energy (Ecoh) Closely linked to the heat of evaporation

It is a measure of a the ability of a liquid

molecule to stay together

Theory of cohesive energy developed byHildebrand for dispersive systems andextended by Hansen for polar and hydrogenbonding

)()()( ydrogenhi

olarpi

ispersivedi

cohi EEEE


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Solubility parameters are measures ofcohesive energy

2/12/1 )/()( VEe icohcoh

solubility parameter

coh. energy density

cohesive energy

Solubility parameter


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Calculating solubility

parameters Hansen and others compiled molar

attraction constants for functional

groups, which are additive contributionsto the solubility parameter

2/1

,

2/12,

,

)/(

/)(

/

VE

VF

VF

i

khh

i

ikpp

i

i

kdd

i


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Attraction Constants (F) The product ofVwas found to vary

linearly across homologous series

Additivity of structural sub-groups

F=Vvalues compiled for dispersionand polar components of

Hansen later compiled additivecontributions to Eh


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Multi-component Mixtures How are om parameters calculated?

Parameters weighted using component

mole fraction and molar volume to getaverage om

2/1,

2/12,

,

]/)([

/)]([

/)(

omkhi

hom

omkpi

pom

omkdi

dom

VEx

VFx

VFx


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Cohesive Energy Density

i,omAcan be derived as

ibis a weighting factor based ondispersive forces, has been tabulated

for a variety of compounds

ibcorrects for the fact that polar and Hbonding forces are localized

222

)()()( hi

h

omi

p

i

p

omi

d

i

d

om

bb


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Activity Coefficient Putting the two components together

RTbbV hi

homi

pi

pomi

di

domi /])()()[( 222

VVVV omiomi /1)/ln(

+

lniom

=


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Calculation First, calculate group contributions for

each component in the mixture

Calculate om parameters by weightingwith mole fraction and molar volume

Calculate parameters for compound of

interest Calculate activity coefficient


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Hansen or UNIFAC? UNIFAC more powerful interaction

UNIFAC not universalmissing parameters

Hansen has certain inconsistencies as certainparameters have to be culled from differentsources. Very sensitive to parameter choice

i

bnot widely available for many compounds,so estimation may be difficult


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Where do you use this?1. Water solubility estimation

2. Solvent-Water partitioning (Kow)

sat

w

sat

wx

1

sssat

w

swVLC

K 11),1(

1


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Gas/Particle Partitioning

What happens when a semivolatile organic(SOC) encounters a particle??

particle

gas

Particle type

CompoundTemperature

Humidity

Thermodynamic Equilibrium?

partK

gas CparticleCp


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Partitioning Modes Mode of SOC-particle interaction depends on

the particle Adsorption Solid particle, no organic liquid layer

(dust, inorganic salts)

Absorption Particle either liquid, or has substantialliquid layer (combustion particles, secondaryorganic aerosol)

SOCs such as PAHs, and alkanes primarilypartition to organic or carbonaceous aerosolsrather than to mineral-based aerosols


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Predictive Partitioning models Pankow (1994) for absorptive

partitioning

0910

501.7

Lomi

om

omp

pMW

RTfK

fom- fraction extractable organic matteriom - activity coefficient of SOC in om

MWom-molecular weight ofom

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Activity Coeff Estimation Methods