Express estimation of crude oil TBP curves only from the viscosity
of the crude oil
G. Argirov, S. Ivanov, G. Cholakov
Bulgaria, 8104 Bourgas, Lukoil Neftochim Bourgas AD, Heavy Residue
Upgrading Complex-Project, e-mail: [email protected]
Key words: crude oil, distillation, TBP prediction, viscosity.
Abstract
Crude oil TBP curves are well recognized as an important characteristic, needed to
determine the potential of fractions obtained by distillation, to monitor distillation
units, to verify the identity of crude oil samples, etc. They can be obtained
experimentally or calculated by a variety of methods, which have different precision.
The precision of the particular method determines the applicability of the obtained
TBP data. Riazi’s two-parameter distribution model and experimental crude assay
data for 117 crudes from all over the world have been used to derive a model for
prediction of true boiling point (TBP) curves from the kinematic viscosity of the
samples at 37,8 oC. The model was tested by prediction of the cumulative mass
fractions of all studied crude samples. It was found that the TBP distribution for
fractions boiling up to 340 oC could be predicted with an average relative deviation of
the order of 6 %. This is higher than the respective deviation of previously proposed
models, e.g. - Riazi’s model, with an average deviation of 3.3 %. However, these
models require experimental data for several properties, while in practical terms the
precision of our model is sufficient to detect any significant upsets in the operation of
refinery crude distillation units (CDUs), so its computerized procedure may be used
as a quick tool for monitoring of the CDU operation.
INTRODUCTION
For modern refineries frequent crude oil switching and disturbances in crude
distillation unit (CDU) operations often propagate into bigger issues
downstream. Managing the change of crudes and diminishing disturbances
require regulatory control of the daily performance necessary to respond
quickly and adequately to setpoint changes. The quality and value of a crude
oil significantly depend on its TBP (“true” boiling point) distillation curve.
Unfortunately, the experimental determination of TBP curves is costly and
time consuming, so it is impractical to use them as a tool for daily monitoring
of CDUs. This calls for the development of TBP calculation methods, requiring
a minimum of experimental data, but having sufficient precision for daily
monitoring of CDU operations. Riazi developed a three-parameter distribution
model, which is widely used for estimation of the boiling points and other
properties of C7+ fractions of petroleum fluids [1, 2]. It predicts TBP
distributions with high precision, when at least three experimental points of the
TBP curve of the crude are available [3]. Moreover, it can be used for
predictions of the rest of the distillation curves, needed in petroleum
processing (ASTM D 86, EFV, CD, etc.)
If distillation data are not available, the values of at least three crude oil
properties (molecular mass, density and refraction index) have to be known.
Riazi’s method can not be used directly for daily monitoring of CDU
operations, because of the need of significant amount of tests, but it gives the
general lines along which this can be achieved. Stratiev et al. [4, 5] developed
further Riazi’s ideas and showed that the boiling temperature and other
property distributions can be calculated when experimental density and
distillation data up to 300 oC are an available. The Lukoil Neftochim Bourgas
AD (LNB) refinery has developed a data base of potential feedstocks - 117
crude oil assays, characterized by TBP curves, density, sulphur, viscosity,
metals, Conradson carbon, and asphalthene content of crude oils and TBP
cuts. The crude oils originate from different parts of the world .
The aim of this work is to use the LNB database and Riazi’s ideas, for
development of a model for crude oil TBP curve prediction from one routine
measurement – the crude oil’s kinematic viscosity at 37.8 oC.
EXPERIMENTAL
The TBP distillation of all 117 investigated crude oil samples has been carried
out in the AUTODEST 800 Fisher column apparatus, according to АSTM-D
2892 - for the atmospheric part of the test, and according to АSTM-D 5236 for the vacuum one. The TBP distillation has been performed in the
AUTODEST
800
Fisher
column
at
pressure
drop
from 760 to 2 mm Hg and in the AUTODEST 860 Fisher column from 1 to 0. 2
mm Hg.
The sulphur content has been analyzed according to АSTM-D 4294. Density
at 20 oC has been determined according to АSTM-D 1298. The viscosity has
been measured according to АSTM-D 445. Table I characterizies the range of
variation of the properties of the crude oils.
Table I. Characterization of the properties of the crude oils in the database.
Property or TBP range
Total sulfur, %
Specific
gravity
@150C
range per group
Viscosity, 37.8 oC, mm2/s
TBP yields, %
IBP – 70 oC
70 - 100 oC
100 – 150 oC
150 – 190 oC
190 – 235 oC
235 - 280 oC
280 – 343 oC
343 – 565 oC
Above 565 oC
Number of crude samples in group/range of values in group
I
II
III
IV
64/≤ 0.5
44/0.51 – 2.0
4/2.01 – 2.5
5/>2.5
0.7883-0.8886
0.8095-0.8970
0.8685-0.9047
0.8581-0.9024
88/≤ 10.00
I
9/1 - 2 incl.
62/3 - 5 incl.
16/6 - 8 incl.
1/9 - 10 incl.
5/1 - 2 incl.
73/3 - 5 incl.
10/6 - 8 incl.
23/5 - 7 incl.
50/8 - 10 incl.
15/11-13 incl.
47/5 - 7 incl.
38/8 - 10 incl.
3/10 - 12 incl.
42/6 - 8 incl.
42/9 - 11 incl.
4/12 - 14 incl.
62/7 - 9 incl.
17/10-12 incl.
6/13-15 incl.
3/16-17 incl.
54/10 -12 incl.
20/13 -15 incl.
6/16 -18 incl.
4/19 -21 incl.
2/22 -23 incl.
1/26
1/20
4/21 - 23 incl.
7/25 - 27 incl.
25/28 -30 incl.
33/31 -33 incl.
10/34 -36 incl.
4/37 -39 incl.
1/40
2/41
1/48
37/1 – 10 incl.
44/11 –20 incl.
7/21 –24 incl.
17/10.01 – 20.0
II
9/1 - 2 incl.
8/3 - 5 incl.
7/20.01 – 30.00
III
2/1 - 2 incl.
5/3 - 5 incl.
5/30.01 – 40.00
IV
4/1 - 2 incl.
1/3
8/1 - 2 incl.
9/3 - 5 incl.
2/1 - 2 incl.
5/3 - 5 incl.
5/1 - 2 incl.
7/3 - 5 incl.
10/6 - 7 incl.
4/3 - 5 incl.
3/6
5/4 - 5 incl.
1/3
16/5 - 6 incl.
7/4 - 6 incl.
5/3 - 4 incl.
1/4
16/6 - 8 incl.
7/6 - 7 incl.
5/4 - 6 incl.
14/6 - 8 incl.
3/9
1/5
6/6 - 7 incl.
1/8
1/5
4/6 - 7 incl.
14/10 - 12 incl.
2/13
1/15
6/9-11 incl.
1/12
1/7
4/9-11 incl.
6/30 – 33 incl.
10/35 – 41 incl.
1/50
6/25 – 35 incl.
1/41
5/33 – 40 incl.
12/13 – 23 incl.
12/13 – 23 incl.
6/24 – 30 incl.
1/35
4/30 – 31 incl.
1/34
As would be shown later, we needed data also for the volume average boiling
points (VABP) and the viscosities at 38 oC of the discrete fractions of the
crude oils, presented in Table I. Some of these data were measured
experimentally, others had to be calculated or approximated to known values.
Table II summarizes the origin of the data.
Table II. Estimation of the volume average boiling points (VABP) and data
for the viscosity at 38 oC (V38) of the crude oil cuts.
TBP range,
o
C
VABP,
K
V38,
mm2/s
Viscosity at 38 oC, mm2/s
IBP - 70
326.15*
0.32
estimated as decribed in [6]
70 - 100
358.15
0.46
estimated as decribed in [6]
100 - 150
398.39
0.64
estimated as decribed in [6]
150 - 190
442.57
0.96
estimated as decribed in [6]
190 - 235
485.85
1.47
measured at 38 oC
235 - 280
529.96
2.47
measured at 38 oC
280 - 343
584.29
5.11
measured at 38 oC
343 - 565
716.67
52.83
measured at 38 oC
565 +
949.47**
1.2x109
measured at 60 and 99 oC; converted to
viscosity at 38 oC as described in [7]
*The initial boiling point, IBP was assumed to be 36 oC (the boiling point of n-pentane).
**For calculation of the 565 0C+ range, the mass average boiling points were
calculated by Riazi’s two parameter method [3], and the VABP of the cuts
was assumed to be approximately equal to the mass one.
Methodology
Riazi’s three-parameter distribution model for the absolute boiling points can
be presented in the following form [3]:
1
⎡
⎛ 1 ⎞⎤ B
A
log
⎜
⎟
− To + T ⎢
1− x ⎠ ⎥
⎝
⎢
⎥
=
To
B
⎢
⎥
⎢⎣
⎥⎦
(1),
in which T is the temperature on the distillation curve in kelvin and x is the
cumulative volume or mass part of the respective distillate, obtained up to that
temperature. In order to distinguish cumulative concentrations of distillates in
the crude oil from discrete concentrations, we shall further denote the former
as “xC”, and the latter – as “xD”.
A, B, and To are the three parameters, which have to be determined by
regression of available distillation data. For atmospheric and vacuum residues
the parameter B can be considered a constant with a value of 1.5.
To is the initial boiling point (IBP, T at xC = 0). However, it should be lower
than the experimentally determined IBP and can be determined by regression
of experimental distillation data for xC > 0 and iterations for its value [3].
Alternatively, as shown by Stratiev et al. [5], To might successfully be replaced
by the normal boiling point of isobutane (-11.6 0C), the lowest-boiling
component in the crude.
For our calculations it is convenient to transform equation (1) into:
⎡
⎢ A log
U = ⎢
⎢
⎢
⎣⎢
⎛ 1
⎜⎜
⎝ 1 − xC
B
⎞⎤
⎟⎟ ⎥
⎠⎥
⎥
⎥
⎦⎥
1
B
(2),
in which U is a normalized temperature, defined by:
− To + T
=U
To
(3)
Solving equation (2) for xC (the cumulative mass fraction distilled up to
temperature T, CDM) leads to the following relationship:
xc [ A, B , U ] = 1 − e
−
BU B
A
(4)
For a complex continuous mixture, such as a crude oil, equation (4) can be
represented as:
U
xC [A, B, U ] = ∫ xD [A, B , U ]dU
(5),
0
where the function xD [A, B, U] represents the mass of a pseudocomponent,
distilled within a certain infinitely small temperature range (dU).
The function xC [A, B, 0] is equal to zero for To = T, and Riazi’s two-parameter
model can be differentiated in terms of the normalized temperature U:
x D [A _, B _,U ] = ∂ U xC [ A, B,U ]
(6)
The output of (6) gives a relation between the concentration of a discrete
pseudocomponent, distilled within a narrow temperature range (which for
practical purposes can be represented by its average boiling point) and the
parameters of Riazi’s equation:
xD [ A, B,U ] =
2
Be
−
BU B −1+ B
U
A
A
(7)
The parameters of (7) can be calculated from experimental data for discrete
fractions (pseudocomponents) by an algorithm, described in [3], if the
temperatures in U (To and T) are defined for the respective discrete yields of
distillate (xD). However, for achieving the aim of this article, namely development of a model for crude oil TBP prediction from crude viscosity, a
combined approach including (7) and other suitable correlations needs to be
developed.
Development of a correlation between average boiling point and
viscosity
A basic concept of the proposed model is that the properties of a petroleum
mixture are built-up by a linear or non-linear (depending on the particular
property) contribution of the pseudocomponents, contained in that mixture.
The viscosity contribution of a pseudocomponent can be expressed by its
viscosity blending number (VBN), thereby applying the equation of Refutas
[6]. According to this equation the crude oil viscosity could be calculated,
knowing the viscosity of its constituent hydrocarbon fractions. The calculations
are carried out in three steps:
1. Calculation of the VBN of each pseudocomponent (discrete fraction) of the
crude oil at the same temperature by:
VBNDi = 14.534 xDi ln [ln (vDi+0.8)]+10.975
(8),
where vDi is the kinematic viscosity of the crude oil pseudocomponent in
mm2/s, and xDi – its mass %.
2. Additive calculation of the viscosity number of the crude oil, VBNcrude by:
VBNcrude = (xD1 VBND1) + (xD2 VBND2) +…+ (xDn VBNDn)
(9),
where xDi is the percentage mass part of each hydrocarbon fraction of the
crude oil.
3. Once the viscosity blending number of a crude oil is obtained from equation
(9), the viscosity of the crude oil, vcrude, can be determined by using the invert
of equation (8):
VBNcrude−10.975
vcrude = e
e
14.534
− 0.8
(10)
where VBNcrude is the viscosity blending number of the crude oil, determined
by (9).
Our next task was to develop a correlation for prediction of viscosity blending
numbers of the discrete fractions of the crudes from their volume average
boiling points. For this purpose the data, presented in Table II were used. For
our next steps in the algorithm, it was convenient to present the VABPs of the
discrete cuts (Table II) as normalized temperatures (U), calculated by eq. (2)
above. Like in [4], the Riazi’s IBP of the crude - To, was assumed to be equal
of the isobutane boiling point (261 K) – the lowest-boiling component in the
crude.
The viscosities at 38 oC, determined as described in Table II, were used to
calculate the VBNs of the respective discrete fractions of each of the 117
crude oil samples. Then the desired correlation, giving the dependence of
pseudocomponent’s VBN from its normalized boiling point, was obtained by
regression of the VBN and U data, in the following form:
(11)
VBNDi [U]=14.8567 (0.919903U+ln(0.919903U))
Table III summarizes the data for the volume average boiling points (VABPs,
their transformation into normalized temperatures (U) and the viscosity
blending numbers of the discrete fractions (VBN), calculated by (11).
Table III. Volume average boiling points, normalized
temperatures (U) and viscosity blending numbers of
the discrete fractions.
Discrete
fraction
boundaries,
TBP range,
0C
IBP - 70
70 - 100
100 - 150
150 - 190
190 - 235
235 - 280
280 - 343
343 - 565
565 +
Discrete
fraction
boundaries,
TBP
range,
normalized
temperature
0.0003 – 0.314
0.314 – 0.429
0.429 – 0.621
0.621 – 0.774
0.774 – 0.946
0.946 – 1.119
1.119 – 1.360
1.360 – 2.211
2.211 – 3.887
VABP, K
U,
(normalized
VABP)
VBNcalc
0.25
0.37
0.52
0.70
0.86
1.03
1.24
1.75
2.64
-20.04
-10.25
-3.58
2.76
8.17
13.48
19.41
30.90
49.05
326.15
358.15
398.39
442.57
485.85
529.96
584.29
716.67
949.47
The average absolute deviation of the resulting model was an acceptable
2,69%, and the R2 correlation coefficient was higher than 0.999.
The right hand side of (11) can be decomposed as:
VBNDi1[U]=14.8567x0.919903U= 13.6667U
VBNDi2[U]=14.8567(ln(0.919903U)) = 14.8567ln(0.919903U)
(12)
(13)
In continuation of our study, we used Riazi’s two-parameter model (with To
fixed at 261 K), as transformed above for for discrete pseudocomponents,
distilled up within a certain temperature range, eq. (7) and eq. (9) – for the
linear calculation of the VBN of a blend, with the aim to define a dependence
necessary for evaluation of Riazi’s model parameters AT (A) и BT (B). The
mathematical notation is as follows:
b
b
a
a
VBN Di [ A, B, a , b ] = ∫ x Di [ A, B ,U ]VBN Di 1[U ]dU + ∫ x Di [ A, B,U ]VBN Di 2[U ]dU (14),
where a, b are temperature boundaries of the discrete fraction distilled up
within temperature range, expressed by normalized temperatures.
The definite integral output gave the following expression for VBN of a
discrete pseudocomponent, VBNDi in (9) :
Ba
Ba
Bb
Bb
⎡ ⎛
−
−
−
−
14.8567 ⎢ B ⎜ − 0.0834867 e A + ln( a ) e A + 0.0834867 e A − ln(b ) e A
⎢⎣ ⎜⎝
B
B
B
B
B
B
B
⎞
⎟ − Ei ⎛⎜ − a B ⎞⎟ + Ei ⎛⎜ − b B ⎞⎟
⎜
⎜
⎟
A ⎟⎠
A ⎟⎠
⎝
⎝
⎠
⎤
⎥
1
⎥⎦
⎛
1 aB B ⎞
1 bB B ⎞ ⎤
⎛ A⎞B ⎡ ⎛
⎟ − 1. Γ ⎜⎜1 + ,
⎟⎥
+ 13 .6667 ⎜ ⎟ ⎢Γ ⎜⎜1 + ,
B
B
A ⎟⎠
B
A ⎟⎠ ⎦
⎝ ⎠ ⎣ ⎝
⎝
(15),
where Γ is Riazi’s gamma function and Ei is ExpIntegral – gives the
exponential integral function Ei (z).
However, in the definite integral output (15), both parameters A and B are
unknown. Therefore, we used the relation obtained for a VBN of fraction
(VBNDi) with AT (A) and BT (B) originating from Riazi’s model and the
pseudocomponent’s boiling temperature range (expressed as VABP) to form
a system of two equations:
VBNDi [A, B, 0.000001, 3.877394]=VBNcrude
(16)
VBNDi [A, B, 0.000001, 1.360153]=2.905
(17)
The first equation (16) is in fact equation (9) applied to equalize the VBN of
the whole crude to the VBN of a pseudocomponent, obtained within the
boiling range from IBP to 1000 oC (0 to 3.87, expressed as normalized
temperature, U), which covers the crude distillation range up to T98% , as
suggested in [4, 5]. The second equation (17) does the same, equalizing to
the constant 2.905, the VBN of a fraction distilled up to 343 oC (1.36
expressed as normalized temperature).
The above system empirically allows for the determination of Riazi’s
coefficient. The fraction distilled up to 343 oC for equation (17) was chosen
because it provided best agreement of the model with the available
experimental data. Hence, with the known values of A and B, the prediction of
a crude TBP yields for discrete pseudocomponets expressed with normalized
VABPs, as shown in Table III mathematically is as follows:
FractionsTemperatureBoundaries={0.0003,0.314,0.429,0.621,0.774,0.946,1.119,1.360,2.211,3.877}
(18)
FractionMass[A,B,n]=XC[A,B,FractionsTemperatureBoundaries[[n+1]]]–XC[A,B, FractionsTemperatureBoundaries[[n]]]
(19),
where an equation (18) defines the discrete fraction temperature boundaries
in normalized temperature (U) while an equation (19) gives the mass of each
discrete fraction. n is equal of the sum of the boundaries covering each
discrete fractions (in this case n equals of 9 and it varies between 1 and 9).
Further, the obtained mass concentrations of the discrete fractions (i.e., in oС):
IBP - 70; 70 - 100; 100 - 150; 150 - 190; 190 - 235; 235 - 280; 280 - 343; 343 565; 565+, can be readily summed up for cumulative fractions: IBP - 70; IBP 100; IBP - 150; IBP - 190; IBP – 235, etc.
RESULTS AND DISCUSSION
In order to test the validity and accuracy of the new proposed model (15), its
predictions for discrete fractions were recalculated into predictions for the TBP
yields of cumulative fractions of the 117 crude oil assays in the data base.
They were compared with the measured TBP yields and with those predicted
by Riazi’s model. The results are summarized in Table IV.
Table IV. Comparison of absolute deviations
TBP
cumulative
fraction, oC
IBP - 70
IBP - 100
IBP - 150
IBP - 190
IBP - 235
IBP - 280
IBP - 343
IBP - 565
Average absolute deviation of the TBP yields (%) from the 117 crudes,
estimated by New model and Riazi’s model per group crude sample
I
Riazi’s
model
0.39
0.33
1.03
1.02
0.80
0.96
1.63
1.42
II
New
model
1.09
1.57
2.29
2.23
2.08
1.95
2.74
2.83
Riazi’s
model
0.17
0.16
0.49
0.50
0.56
0.65
0.90
2.06
III
New
model
1.00
1.59
2.35
2.74
2.96
2.97
2.80
1.81
Riazi’s
model
0.19
0.22
0.46
0.45
0.41
0.63
0.85
1.57
IV
New
model
1.57
2.72
4.18
4.88
5.14
4.83
3.88
3.32
Riazi’s
model
0.11
0.10
0.45
0.18
0.57
0.87
0.90
2.08
New
model
0.67
1.23
2.27
2.23
3.62
4.10
4.63
3.49
Table IV shows that the average absolute deviations of the yields, predicted
by Riazi’s method are several times closer to the experimental values than
those estimated by the new method. This not surprising since the parameters
of the Riazi model have been calculated from all available TBP data, while
the parameters of new model involve estimated data. The calculated average
relative deviation was reasonably well for white oil fractions distilled up to
3430С, amounting of 5.95% against 3.30% - calculated through Riazi’s model.
On the other hand, the deviations of the obtained by calculation by any
method yields cannot be less than those which can be reproduced
experimentally. For instance, the reproducibility of experimental yields,
obtained by the ASTM D 2892 method is 1.2 % for atmospheric and 1.4 % for vacuum fractions [9]. So, the deviations of the new method are comparable
to the experimental and thus acceptable for its declared practical applications.
Moreover, there are possibilities to improve the new method if more
experimental data are available and/or other routinely determined properties
of the crudes are used.
The adequacy of the model was verified, also for predicting the TBP
distribution of a test set of three crude oil samples, not included among the
117 samples used to develop the model. The results obtained are given in
Table V.
Table V. Absolute deviations of the predictions with the new method for the
test set
Properties
Mellitah
Visc. at 38 oC, mm2/s
Specific
gravity
@150C
TBP range, oC
IBP - 70
IBP - 100
IBP - 150
IBP - 190
IBP - 235
IBP - 280
IBP - 343
IBP - 565
2.07
0.8132
0.50
3.72
1.42
1.70
0.77
1.68
1.10
5.00
Crude oil
Western
Desert
2.51
0.8200
REBCO
8.25
0.8680
Absolute deviation, %
1.64
3.44
4.08
2.87
1.58
1.12
3.62
3.48
0.58
1.04
1.25
1.07
0.34
0.05
0.51
0.96
The deviations with the test set fall within those for the 117 samples used in
the development of the model.
CONCLUSIONS
The main aim of this work was to develop a method for express prediction of
crude true boiling point (TBP) curves, that would be suitable for daily
monitoring of the operarion of crude oil distillation units (CDUs). The main
results achieved in the realization of this aim can be summatrized as follows:
- The developed new model requires only data from the routine laboratory
analysis of the kinematic viscosity of crude oil at 38 oС. In its development
assay data for 117 crude oils from different parts of the world have been used.
The precision of the predictions of the new model, though somewhat worse
than those of the original Riazi model, are comparable to the experimental
reproducibility of the standard methods for laboratory distillation. The
adequacy of the model was verified, also for predicting the TBP distribution of
a test set of three crude oil samples, not used in the development of the
model. The results of this test showed the consistency of the model
predictions.
- In practical terms the reported deviation is sufficient to detect any upsets in
the operation of refinery CDUs. The method requires only data for the
viscosity of crude oil at 38 oС, and uses a computerized calculation algorithm,
easily realized in Excel or other popular statistical software.
- An integral part of the new model is a sub model describing the dependence
of the viscosity blending numbers (VBNs) of crude oil pseudocomponents
from their average boiling boiling points. The submodel allows for subsequent
calculation of other integral parameters for each narrow cut of crude oil, such
as: molecular mass, specific gravity and refractive index, including proxy on
TBP-distillation curve at known VBNs.
- In terms of mathematics, it can be assumed that Riazi’s model can be
reduced to an essentially one-parameter model, taking into account eq. (17)
which allows to estimate its property parameters from only one laboratory
measurement. The Riazi’s model, which is originally in integral form, can be
subjected to differentiation in order to identify the properties of
pseudocomponent.
REFERENCES
[1] Riazi, M., “Distribution Model for Properties of Hydrocarbon-Plus
Fractions”, Ind. Eng. Chem. Res., Vol.28 (1989), pp.1831-35.
[2] Riazi, M.,”A Continuous Model for C7+ Fraction Characterization of
Petroleum Fluids”, Ind. Eng. Chem. Res., Vol. 36 (1997), pp 4299-4307
[3] Riazi, M. “Characterization and properties of petroleum fractions”, ASTM
Manual Series: MNL 50, 2005. ASTM
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