Activity Coeff Estimation Methods
Transcript of Activity Coeff Estimation Methods
-
7/28/2019 Activity Coeff Estimation Methods
1/25
Activity Coefficient EstimationMethods
Bharat Chandramouli
February 5, 2002
-
7/28/2019 Activity Coeff Estimation Methods
2/25
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
-
7/28/2019 Activity Coeff Estimation Methods
3/25
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
-
7/28/2019 Activity Coeff Estimation Methods
4/25
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
-
7/28/2019 Activity Coeff Estimation Methods
5/25
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
-
7/28/2019 Activity Coeff Estimation Methods
6/25
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)
-
7/28/2019 Activity Coeff Estimation Methods
7/25
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
-
7/28/2019 Activity Coeff Estimation Methods
8/25
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
-
7/28/2019 Activity Coeff Estimation Methods
9/25
UNIFAC Methods Interaction parameters are fit from
experimental data
This work is still ongoing and manyparameters still not available
-
7/28/2019 Activity Coeff Estimation Methods
10/25
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
-
7/28/2019 Activity Coeff Estimation Methods
11/25
Hansen Activity Coefficient The activity coefficient is given by
dARTVomiomii
om
i ,,
)/(ln
Molar VolumeCohesive energy density
Size effect term
Enthalpy Entropy
-
7/28/2019 Activity Coeff Estimation Methods
12/25
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(,
-
7/28/2019 Activity Coeff Estimation Methods
13/25
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
-
7/28/2019 Activity Coeff Estimation Methods
14/25
Solubility parameters are measures ofcohesive energy
2/12/1 )/()( VEe icohcoh
solubility parameter
coh. energy density
cohesive energy
Solubility parameter
-
7/28/2019 Activity Coeff Estimation Methods
15/25
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
-
7/28/2019 Activity Coeff Estimation Methods
16/25
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
-
7/28/2019 Activity Coeff Estimation Methods
17/25
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
-
7/28/2019 Activity Coeff Estimation Methods
18/25
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
-
7/28/2019 Activity Coeff Estimation Methods
19/25
Activity Coefficient Putting the two components together
RTbbV hi
homi
pi
pomi
di
domi /])()()[( 222
VVVV omiomi /1)/ln(
+
lniom
=
-
7/28/2019 Activity Coeff Estimation Methods
20/25
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
-
7/28/2019 Activity Coeff Estimation Methods
21/25
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
-
7/28/2019 Activity Coeff Estimation Methods
22/25
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
-
7/28/2019 Activity Coeff Estimation Methods
23/25
Gas/Particle Partitioning
What happens when a semivolatile organic(SOC) encounters a particle??
particle
gas
Particle type
CompoundTemperature
Humidity
Thermodynamic Equilibrium?
partK
gas CparticleCp
-
7/28/2019 Activity Coeff Estimation Methods
24/25
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
-
7/28/2019 Activity Coeff Estimation Methods
25/25
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