Fahim M.A., Sahhaf T.A., Elkilani A.S. Fundamentals of Petroleum Refining
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Based on the distillation curve, five different average boiling points can be
estimated. Among these, the volume average boiling point (VABP) and the
mean average boiling points (MeABP) are the most widely used in property
estimation and design. The MeABP is utilized in the definition of an
important parameter, the Watson characterization factor K given by:
K ¼
ðMeABPÞ
1=3
SG
ð3:5Þ
where MeABP is in degrees Rankin.
Given the ASTM D86 distillation the VABP can be calculated as the
average of the five boiling temperatures at 10, 30, 50, 70 and 90 percent
distilled.
VABP ¼
T
10
þ T
30
þ T
50
þ T
70
þ T
90
5
ð3:6Þ
where all temperatures are in
F.
The MeABP is calculated using the following equation:
MeABP ¼ VABP D ð3:7Þ
where D is given by:
ln D ¼0:94402 0:00865ðVABP 32Þ
0:6667
þ 2:99791 SL
0:333
SL ¼
T
90
T
10
90 10
As mentioned before, ASTM and TBP distillation can be performed
on crude oils and petroleum products. The petroleum fractions are
‘‘cuts’’ from the crude oil with specific boiling point range and with
special properties such as API gravity and viscosity. Each of these cuts
can be further defined by dividing them into narrow boiling fractions,
called pseudo- (not real) component s. For these pseudo-compone nts, the
average boiling point can be estimated a s either mid-boiling point or
mid-percentage boiling poin t. The TBP curve is div ide d i nto an arbi-
trary number of pseudo-components or narrow boiling cuts. The mid
boiling point is the average between t he IBP and the EP of that pseudo-
component. The mid percentage boiling point is the temperature at t he
arithmetic average of the volumes dis tilledatIBPandEPofthatpseudo-
component. Since the boili ng range is small, both mid points are close to
each other and can be considere d as the VABP or t he MeABP for that
pseudo-component.
Thermophysical Properties of Petroleum Fractions and Crude Oils 39
Example E3.2
Calculate the MeABP of the petroleum fraction of example E3.1. If the API
gravity of this fraction is 62, calculate the Watson’s characterization factor.
Solution:
The D86 distillation temperatures are converted to
F. The VABP is obtained
from equation (3.6)
VABP ¼
129:2 þ 170:6 þ 214:7 þ 267:8 þ 339:8
5
¼ 224:4
F
SL ¼ 2:6325
D ¼ 18:279
MeBP ¼ 224:4 18:3 ¼ 206:1
For96:7
C
From equation (3. 2) SG can be calculated as:
SG ¼
141:4
62 þ 131:5
¼ 0:7313
Watson characterization factor from equation (3.5)
K ¼
ð206:1 þ 460Þ
1=3
0:7313
¼ 11:94
3.3. Pseudo-Components
Calculations involving crude oil and petroleum fractions require the
composition of each process stream. Since most of the actual components
are not known, the petroleum fractions are characterized as a mixture of
discrete pseudo-components with defined boiling point ranges or cut points
on the TBP distillation curve. Each pseudo-component corresponds to
several unknown actual compounds (e.g. paraffins, naphthenes and aro-
matics) which boil in a given temperature range.
Usually each pseudo-component is characterized by an average normal
boiling point, specific gravity and molecular weight. The first two properties
are obtained experimentally from the TBP curve and gravity versus volume
distilled curve. In some cases, only the overall specific gravity of the fraction is
measured. The molecular weight is usually calculated through a correlation.
Once these parameters are determined, the pseudo-components can be treated
as any defined component for the calculation of thermophysical and
40 Chapter 3
thermodynamic property like enthalpy, entropy, and transport properties such
as viscosity, thermal conductivity and diffusivity. Some properties, like pour
point, depend on the chemical nature of the compounds represented in the
pseudo-components. Then the information on the chemical compositions in
terms of percentage of paraffins, naphthenes and aromatics becomes necessary.
3.3.1. Breakup of TBP Curve into Pseudo-components
The TBP for the crude oil or the petroleum fraction has to be available, either
by direct laboratory measurements through ASTM D1160 distillation or
through the conversion of ASTM D86 distillation into TBP distillation
curve. TBP cut point ranges are used to define pseudo-components with
the average temperature of the cut or the mid point NBP. If the petroleum
fraction contains components lighter than pentanes, the composition of the
lighter ends has to be available experimentally through chromatographic
analysis of the vapours. Otherwise the lighter ends are lumped with the lightest
pseudo-component. The number of such pseudo-components depends on
the boiling point range of the whole petroleum fraction. This number is a
trade off between producing a smooth calculated property curve and having
too many components which both leads to excessive computation time.
The following cut-point ranges are reasonable for most refining
calculations:
TBP range Numbe r of cuts
< 37.8
C (100
F) Use actual components (pentanes and
lighter)
37.8–427
C (100–800
F) 28
427–649
C (800–1200
F) 8
649–871
C (1200–1600
F) 4
A general guideline for determining the number of pseudo-components is
as follows:
10
C(50
F) for light fractions with boiling points less than 200
C (392
F)
15
C (59
F) for fractions with boiling points between 200 and 400
C
(392–752
F)
20
C (68
F) for fractions with boiling points between 400 and 600
C
(752–1112
F)
30
C(86
F) for fractions with boiling points beyond 600
C (1112
F)
The number of pseudo-component depends on the application. In distilla-
tion calculations, more NBP cuts might be needed to represent narrow
boiling products. Figure 3.1 shows how the TBP curve is cut into several
pseudo-components.
Thermophysical Properties of Petroleum Fractions and Crude Oils 41
Example E3.3
Divide the TBP curve of the petroleum cut as calculated from API method in
example E3.1 into 20 pseudo-components. Calculate the liquid volume percentage
of each pseudo-component.
Solution:
The TBP curve obtained in example E3.1 extends to 95 volume percent distilled
only. In order to obtain the average boiling point of the last cuts, the curve is
extrapolated to the final point of the distillation (100%) by fitting the curve to a
suitable polynomial function and extrapolating the results. An Excel spreadsheet
program was used to fit a fifth order polynomial function, as shown Figure E3.3 for
TBP temperature versus volume% .
Atmospheric TBP Distillation Curve
Liquid Volume % 0 100
Boiling Point
Defined components
x
x
x
x
x
O
X = pseudo components average normal
boiling point
O = Defined components NBP
O
O
x
x
x
x
x
x
x
x
x
Figure 3.1 Representation of TBP curve by pseudo-components
TBP Curve
y = 0.0000001x
5
− 0.0000287x
4
+ 0.0027144x
3
−
0.1208156x
2
+ 4.2608778x − 5.3573689
R
2
= 0.9999966
−50
100
50
0
150
200
250
300
0
Vol%
TBP, C
TBP Curve
ASTM D86
Poly. (TBP Curve)
10 20 30 40 50 60 70 80 90 100
Figure E3.3 Extrapolation of TBP curve
42 Chapter 3
The end point of the cut is 218.2
C (425
F) and the IBP is 5.4
C (22
F).
Therefore each pseudo-component has a temperature interval of (218.2 þ 5.4)/20
or 11.2
C. Then the curve can be cut as follows. The EBP of the first cut is IBP þ
11.2
Cor5.8
C. The average boiling point for the first pseudo-component is
(5.4 þ 5.8)/2 or 0.2
C. The vol% is 2.84 as read from the TBP curve. The
second cut has an end boiling point of 17
C and an end volume percent of 6.19.
Therefore, the vol% of this cut is 6.19 2.84 or 3.36 vol%. The average boiling
point for the second cut is (17 þ 5.8)/2 or 11.4
C. For the subsequent cut, the
results are shown in Table E3.3.
3.3.2. Breakup of TBP Curve into Pseudo-components
Using Generalized Form
Laboratory crude assay reports provide TBP for the whole crude as explained
in Section 3.2.3. The maximum temperature that can be measured with this
test is in the range of 496–526
C (925–975
F), depending on the crude oil.
The actual end point of the crude oil can be as high as 790
C(1455
F). This
Table E3.3 Pseudo-components
EBP of cut (
C) NBP of cut (
C) Volume % at end of cut Cut vol%
5.8 0.2 2.84 2.84
17.0 11.4 6.19 3.36
28.2 22.6 10.22 4.03
39.4 33.8 15.09 4.87
50.5 44.9 20.82 5.73
61.7 56.1 27.15 6.34
72.9 67.3 33.68 6.52
84.1 78.5 40.10 6.42
95.3 89.7 46.36 6.26
106.4 100.8 52.53 6.17
117.6 112.0 58.69 6.16
128.8 123.2 64.89 6.21
140.0 134.4 71.09 6.20
151.1 145.6 77.07 5.98
162.3 156.7 82.53 5.45
173.5 167.9 87.25 4.73
184.7 179.1 91.25 4.00
195.9 190.3 94.63 3.37
207.0 201.5 97.51 2.88
218.2 212.6 100.00 2.49
Thermophysical Properties of Petroleum Fractions and Crude Oils 43
means that a substantial portion of the TBP curve is not defined by laboratory
data. Extrapolation of the measured portion of the TBP curve to a volume
percent approaching the end point is required. While probability distillation
graph paper can be used for extrapolation, a computer method will be used in
this section.
The TBP curve can be fitted to the following generalized equation
(Riazi, 2005):
P
∗
¼
A
B
ln
1
x
∗
1=B
ð3:8Þ
where
P
∗
¼
T
b
T
b0
T
b0
and x
∗
¼ 1 x
c
The boiling point T
b
is in Kelvin. x
c
is the cumulative weight, volume or
mole fraction. T
b0
corresponds to the boiling point at x
c
¼ 0. Therefore, it
should be equal or lower than the IBP given in the assay data. The parameters
A and B are obtained by fitting the equation to available assay data. Since in
this equation P
∗
!1as x
∗
! 1, an arbitrary point can be added to the
measured TBP data to limit the actual TBP end point. The same equation can
be used to fit data for molecular weight and specific gravity. The above
generalized equation can be converted to the following linear form:
Y ¼ C
1
þ C
2
X ð3:9Þ
where
Y ¼ ln P
∗
and X ¼ ln ln
1
x
∗
From equations (3.8) and (3.9):
B ¼
1
C
2
ð3:10Þ
A ¼ B expðC
1
BÞ
The fitting procedure is to calculate P
∗
, knowing T
b0
and plot Y versus X.
This means the correlation parameter R
2
is calculated. If T
b0
is not known,
the value of T
b0
is assumed and varied until a good fit is obtained (R
2
¼
0.99). This fitting procedure can be easily done using the linear regression fit
of a Microsoft Excel spreadsheet.
T
b0
represents the initial boiling point. It can be estimated for cases
where T
b0
is not available. Nonlinear regression of equation (3.8) is applied
to find T
b0
as well as A and B.
44 Chapter 3
Example E3.4
The following TBP data for a crude oil sample is available with an IBP of 17
C.
Fit the data to the generalized equation and compare with the polynomial fit.
Volume % TBP (
C)
540
10 85
30 215
50 340
70 495
Repeat the generalized fit if the initial boiling point is not known.
Solution:
Plotting the data of equation (3.9) on a Microsoft Excel spreadsheet with linear
fitting, we obtain the following parameters:
C
1
¼ 0.452 and C
2
¼ 0.936, which gives a correlation parameter of R
2
¼
0.998. The constant A and B for the generalized equation are then calculated to
be:
A ¼ 1:732 and B ¼ 1:069
A comparison between the experimental and calculated TBP curve is shown
in Figure E3.4. The % error calculated for the generalized equation is 3.6%,
while the polynomial fit is 2.4%.
100
0
200
300
400
500
600
0 1020304050607080
Volume % Distilled
Temperature,⬚C
Generalized
Polynomial
Experimental
Figure E3.4 TBP curve for Kuwait export crude sample
Thermophysical Properties of Petroleum Fractions and Crude Oils 45
This example can be solved again to estimate the value of IBP, T
b0
.
C
1
and C
2
are calculated using linear regression as follows:
Y ¼ ln P
∗
¼ ln
T
b
T
b0
T
b0
and X ¼ ln ln
1
x
∗
Y ¼ C
1
þ C
2
X
R
2
¼
nSðXiYiÞSXiSYi
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
nSX
2
i
ðSXiÞ
2
q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
nSY
2
i
ðSYiÞ
2
q
2
6
4
3
7
5
2
C
2
¼
nSðXiYiÞSXiSYi
nSX
2
i
ðSXiÞ
2
"#
C
1
¼
SYi
n
C
2
SXi
n
Excel solver is used to determine the value of T
b0
. The target is to set the value
of R
2
close to 1.0 by changing the value of T
b0
. The solution is shown in the
table below which shows the values of C
1
and C
2
that result in T
b0
= 8.03
C
(281.03K).
n
xc cum
vol%
T
b
(
C) Y
x* ¼
1 xc
X ¼
ln (ln(1/x*)) XY x
2
y
2
15402.1738 0.9500 2.9702 6.4567 8.8221 4.7256
210 851.2951 0.9000 2.2504 2.9145 5.0642 1.6774
3 30 215 0.3059 0.7000 1.0309 0.3154 1.0628 0.0936
4 50 340 0.1666 0.5000 0.3665 0.0610 0.1343 0.0277
5 70 500 0.5599 0.3000 0.1856 0.1039 0.0345 0.3135
sum 3.0484 6.4324 9.7295 15.1178 6.8378
C
2
0.8488
C
1
0.4822
R 0.9950
R
2
0.9900
T
b0
¼ 8.0349
C
46 Chapter 3
3.3.3. Calculation of Pseudo-components Specific Gravities
As pointed out earlier, the distillation test might include the measurement of
gravity versus volume distilled. Sometimes this is not available and only the
average gravity of the whole petroleum fraction is measured. In this case,
the following procedure is used to obtain the gravity for each pseudo-
component. This step is necessary to calculate the molecular weight of
the pseudo-component and hence to convert volume fractions into mass
fractions or mole fractions.
Any petroleum fraction or NBP cut can be characterized by the Watson
Characterization (K) factor defined in equation (3.5). For the petroleum
cut comprising the pseudo-components, the K factor for the pseudo-
components is assumed constant and equal to its value for the whole
petroleum cut. Hence the definition of the K factor is used to calculate
the gravity of each pseudo-component given its average NBP.
Example E3.5
Calculate the specific gravity of each pseudo-components of the crude assay
attached, knowing that K ¼ 11.94.
Volume % TBP (
C)
540
10 85
30 215
50 340
70 495
Plot the API gravity versus vol% and fit it to the pro per polynomial.
Solution:
The K factor for this cut is 11.94. Using this value for each of the pseudo-
components and the TBP of each cut, the specific gravity of the pseudo-
components is generated and then the API is calculated.
TBP is calculated at the extended vol% up to 95% from the generalized
equation from Example E3.4.
The polynomial fit of the API versus vol% is
API ¼0:0002 vol%
3
þ 0:0238 vol%
2
1:7637 vol% þ 80:471 with R
2
¼ 0:9994
Figure E3.5 shows the API-TBP versus vol% curves.
Thermophysical Properties of Petroleum Fractions and Crude Oils 47
3.4. Thermophysical Properties Calculation
3.4.1. Molecular Weight
Any material or energy balance calculations would certainly require the
estimation of molecular weight of a petroleum fraction. Experimentally, the
average molecular weight can be determined by several methods, such as
freezing point depression osmometry, or gel permeation chromatography.
Most oil fractions have molecular weights in the range of 100–700. The
method most suitable for determining molecular weights within this range is
that based on freezing point depression.
Prediction of the molecular weight of petroleum fractions is achieved
through the following equation (Pedersen et al., 1989):
M ¼ 42:965½expð2:097 10
4
T
b
7:78712 SG þ 2:08476
10
3
T
b
SGÞT
1:26007
b
SG
4:98308
ð3:11Þ
where M is the molecular weight of the petroleum fraction, T
b
is the mean
average boiling point of the petroleum fraction in K, and SG is the specific
gravity, 60
F/60
F.
200
0
400
600
800
1000
1200
1400
0 102030405060708090100
Liquid Vol%
TBP (⬚C)
−10
10
0
20
30
40
50
60
70
80
API
TBP
API
Figure E3.5 TBP and API versus vol%
48 Chapter 3