Property Scaling Relations for Nonpolar Hydrocarbons
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1
Property Scaling Relations for Nonpolar Hydrocarbons
Sai R. Panuganti1, Francisco M. Vargas1, 2, Walter G. Chapman1
1 Chemical and Biomolecular Engineering Department, Rice University, Houston, USA
2 Department of Chemical Engineering, The Petroleum Institute, Abu Dhabi, UAE
February, 2013
2
Outline
• One-Third Rule
• Electronic polarizability
• Dielectric constant
• Critical temperature and pressure
• Surface tension
• Conclusion
3
One-Third Rule• Specific Refractivity: independent of the temperature and pressuren, refractive index and ρ, mass density (g/cc)
• For nonpolar hydrocarbons and their mixtures
1
2
12
2
n
n Constant
3
11
2
12
2
D
D
n
n
2
12
2
n
n True volume of the molecules in unit volume
2
12
2
n
n
True density of the molecules
• But strictly speaking, it is a function of the mass density and can be expressed as 2
2
2
2314.03951.05054.01
2
1
n
nL-L Expansion
4
One-Third Rule
Increase
Temperature
V increases, ρ decreases
n increases
Volume occupied by molecules without considering space
between molecules
3
11
2
12
2
D
D
n
n
Vargas FM, Chapman WG; Fluid Phase Equilibria, 2010; 290:103-108
For nonpolar hydrocarbons
5
Electronic Polarizability Lorentz–Lorenz equation:
where, N – Number of molecules per unit volume α – Polarizability
Refractive index and Polarizability are independent of the amount of material
where, Na – Avogadro number v – Molar Volume (v = MW/ρ)
With the help of One-Third Rule the above expression simplifies as
The above equation is independent of the state of the substance and its polarizability can be computed by just knowing the molecular weight
N
n
n
3
4
2
12
2
v
N
n
n a
3
4
2
12
2
aN
MW
4
6
Predicted Polarizability
0 5 10 15 20 25 30 35 40 450
5
10
15
20
25
30
35
40
45 Mean Electronic Polarizability (cm3 x 10-24)
Experiment
Pred
icte
d fr
om O
ne-T
hird
Rul
e + 4 % De-viation
• Data shown is for 80 different nonpolar hydrocarbons belonging to different homologues series
0 5 10 15 20 25 30 35 40 450
5
10
15
20
25
30
35
40
45 Mean Electronic Polarizability (cm3 x 10-24)
X=Y
ExperimentPr
edic
ted
from
L-L
Exp
ansi
on + 2.5 %
Deviation
• Using One-Third Rule• Average absolute deviation is 4.16 %
• Using Lorentz-Lorenz Expansion• Average absolute deviation is 2.72 %
7
Dielectric Constant It is well established that for weakly magnetic materials
εr , relative permitivity
For low-loss materials like nonpolar hydrocarbons,
k, dielectric constant
Substituting dielectric constant in the One-Third Rule and solving for dielectric constant
The dielectric constant expression can handle operational variations in temperature and pressure
It is independent of the knowledge of individual constituents of a mixture or the composition allowing the use for complex fluids
such as crude oils and polydisperse polymers
rn
krr )0()(
3
32k
8
Predicted Dielectric Constant
1.4 1.6 1.8 2 2.2 2.4 2.6 2.81.4
1.6
1.8
2
2.2
2.4
2.6
2.8Dielectric Constant
Se...
Experiment
Pred
icte
d fr
om O
ne-T
hird
Rul
e
+ 2 % Deviation
X=Y
• Data shown is for 260 nonpolar hydrocarbons, including polymers, mixtures with varying temperatures and pressures
Panuganti SR, Vargas FM, Chapman WG; IEEE Transactions on Dielectrics and Electrical Insulation, 2013; Submitted
1.4 1.6 1.8 2 2.2 2.4 2.6 2.81.4
1.6
1.8
2
2.2
2.4
2.6
2.8Dielectric Constant
Series11
ExperimentPr
edic
ted
from
L-L
Exp
ansi
on
+ 1 % Deviation
X=Y
• Using One-Third Rule• Average absolute deviation is 1.98 %
• Using Lorentz-Lorenz Expansion• Average absolute deviation is 1.0 %
9
Critical Temperature and Pressure From literature we have,
Thus, the following expression holds good
Applying One-Third Rule
also
904.22
104.52 2
25.0
D
D
n
n
v
a
Hildebrand and Scott Buckley et al.
),( 202/1MWfunction
P
T
C
C
2020
2
22/1 904.2
2
1042.52
MWMW
n
na
D
D
),( 20
2/1
MWfunctionP
TT
C
BC
2020 1674.0),(
MW
MWMWf
Let,
Hildebrand JH, Scott RL; The Solubility of Nonelectrolytes, 1950 Buckley et al; Petroleum Science and Technology, 1998; 16:251-285
10
Critical Temperature and Pressure
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
350
f(x) = 0.612962186296466 x + 24.8584279807217R² = 0.997304082632775
f(MW,ρ20)
Tc/P
c0.5
{K/
atm
0.5}
0 50 100 150 200 250 300 350 400 450 5000
50
100
150
200
250
300
f(x) = 0.57775397294106 x + 11.1206773684791R² = 0.99839713029832
f(MW,ρ20)
(Tb*
Tc/P
c)0.
5 {K
/atm
0.5}
85.24),(613.0 202/1 MWf
P
T
C
C 12.11),(577.0 20
2/1
MWf
P
TT
C
BC
Panuganti SR, Vargas FM, Chapman WG; Industrial and Engineering Chemistry Research, 2013; Accepted
11
Predicting Critical Properties
100 300 500 700 900 1100100
300
500
700
900
1100Critical Temperature (K)
X = Y
Experiment
Pred
icte
d
0 10 20 30 40 50 60 700
10
20
30
40
50
60
70 Critical Pressure (atm)
X = Y
Experiment
Pred
icte
dAverage absolute deviation
is 2.2 %Average absolute deviation
is 4.5 %
• Data shown is for 80 different nonpolar hydrocarbons belonging to different homologues series. The applicability to mixtures is limited to nonpolar hydrocarbons
composed of similar sized molecules
Surface Tension from Hole Theory
12
Volume of hole = Volume of liquid - Volume of solid
Heat of fusion = Energy required for the formation of all the holes
Solving the Schrodinger wave equation for a hole in a liquid,
Using the correlation of a/v2 from the previous section, at a given temperature we have
For example at 20oC we have
2
2
1
22223
22
)(4)(
3
4
m
P
m
PPPrpprEEE rzyx
oPq
509.7)(39.34 2020 h
21 )( ChC 8/1141674.0
)(
h
7/1
7/2
27/8
4.2 h
V
a
where,
Furth R; Proc. Phys. Soc., 1940; 52:768-769 Auluck FC, Rai RN; Journal of Chemical Physics, 1944; 12:321-322
13
Predicted Surface Tension
Average absolute deviation is 1.8 %
The practical application of equation can improved further by incorporating the temperature variation of surface tension
With reference temperature as 20°C, surface tension at any other temperature can be calculated as
)( hTTC
)(
)(
293509.7)(39.34
2020
h
h
T
TTh T
c
cT
The parameter of critical temperature can be eliminated using the equation
obtained in the critical properties section.
0 10 20 30 400
10
20
30
40 n-Xylene
Ethylbenzene
Methylcy-clohexane
Cyclopentane
n-Hexane
Experiment
Pred
icte
d
14
ConclusionInput Parameters
Property Density MW Boiling Point Function of Temperature
Mixtures
Critical Temperature Y Y Y - Y
Critical Pressure Y Y Y - YSurface Tension Y Y Y Y N
Electronic Polarizability N Y N - -
Dielectric Constant Y N N Y Y
• Polarizability of an asphaltene molecule of molecular weight 750 g/mol will be 99.16x10-24 cc
• Polydispere asphaltene system with density between 1.1 to 1.2 g/cc at ambient conditions will have a dielectric constant
between 2.737 and 3
Panuganti SR, Vargas FM, Chapman WG; IEEE Transactions on Dielectrics and Electrical Insulation, 2013; Submitted
Panuganti SR, Vargas FM, Chapman WG; Industrial and Engineering Chemistry Research, 2013; Accepted
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