Towards asphaltenes characterization by simple measurements
Transcript of Towards asphaltenes characterization by simple measurements
Towards asphaltenes characterization by simple measurements
Sylvain Verdier1, Frédéric Plantier2, David Bessières2,
Simon Ivar Andersen1,*, Hervé Carrier2
1IVC-SEP, Institut for Kemiteknik, Danmarks Tekniske Universitet, 2800 Lyngby,
Denmark
2Laboratoire des Fluides Complexes – Groupe Haute Pression,
Université de Pau BP 1155, 64013 Pau, France
* corresponding author: [email protected]
Phone: (45) 45 25 28 67
Fax: (45) 45 88 22 58
Abstract
Behaviour of asphaltenic fluids are hardly understood and explained. Nonetheless,
aggregation, precipitation and deposition, the three steps leading to problems in the
petroleum industry, are being modelled. This work is an attempt to determine important
parameters (such as the critical constants or the solubility parameter of asphaltenes) in
order to help modelling asphaltene phase behaviour.
Partial volumes were measured in three solvents at 303.15 K and 0.1 MPa. The regular
solution theory enabled the calculation of solubility parameters of two asphaltenes and a
cubic equation of state was used to determine their critical constants.
All the results are within the expected ranges. These simple experiments will be
completed later on by calorimetric and optical measurements.
Keywords: Asphaltene, critical properties, solubility parameter, density, partial volume.
1. Introduction
Ongoing and intensive research about asphaltenes has been carried out intensively since
the 50’s. And, surprisingly, little certitude can be drawn from the massive literature
dedicated to this issue. Even “simple” questions like “what is the asphaltene molecular
weight?”, “when does aggregation start?” or “how come no model can predict
asphaltene precipitation if there is no extensive fitting procedure?” are sources of serious
and harsh discussions between experts. However, advances are regularly done, such as
the recent and more or less general agreement that there is no critical micellization
concentration phenomena in asphaltene solutions [1].
In 2003, Porte et al. [2] published an article compiling many properties and ideas related
to asphaltenes so as to find relevant and trustable facts such as the moderate molecular
weight, the reversibility of the precipitation in most cases or the independence of dilution
on the onset of precipitation of asphaltenes solutions. Obviously, there is still a great need
of robust experimental facts regarding asphaltene structure, the types of forces that are
predominant, precipitation caused by various solvents including gases and the influence
of pressure and temperature as well as the molar weight determination to name a few of
the crucial pending questions.
The petroleum industry is of course interested in prediction tools to avoid cases similar to
the Hassi Messaoud’s reservoirs, where asphaltenes precipitated and made oil extraction
impossible for years. The number of models and theories is quite impressive (Flory-
Huggins theory [3-8], micellization models [9-10], scaling equations [11] or advanced
equations of state such as SAFT [12-14] for instance). Nonetheless, most models remain
a fitting exercise and, as Porte et al. reported it [2], their capacities to predict the
behaviour of asphaltenic fluids is generally poor. What could be the reasons?
If we have a closer look to the models using the Flory-Huggins or the Scatchard-
Hildebrand approaches, the determination of the solubility parameters of asphaltenes
remains doubtful in many cases. Hirschberg et al. [5] used titration experiments to
determine asphaltene solubility parameters, assuming a molar volume. They found a
value of 19.50 MPa1/2 and small temperature dependence when fitting their data. Wang
and Buckley [6] use asphaltene molar volume and solubility parameter as adjustable
parameters in their asphaltene solubility model. Yarranton and Masliyah [8] determined it
by fitting the model to one set of asphaltene-n-heptane-toluene titration curve. Obviously,
accurate methods to determine asphaltene’s solubility parameters are still necessary. In
this work, a method, based on density measurements of asphaltene dilutions, enable its
determination.
As for the determination of critical parameters of asphaltenes, Alexander’s correlations
based on NMR data [15] is used most of the time. Amongst others, Gupta [16] and
Thomas et al. [17] employed this technique to model asphaltene precipitation. However,
this technique is heavy and time-consuming. In this work, a method based on partial
volume is investigated and might open new possibilities.
2. Theory
2.1. Determination of the solubility parameter of asphaltene
The solubility parameter, δ, was defined by Hildebrand and Scott [1] as follows:
12E
vδ −⎛ ⎞= ⎜ ⎟
⎝ ⎠ (1)
where E− is the cohesive energy of the liquid and V the molar volume.
A recent article summarized the various definitions and approximations present in
literature [18]. Cohesive energy is actually equal to the residual internal energy : rU−
( ) ( ) ( ), , 0 ,vap liq rE T P U T P U T P U− = = − = − (2)
As a result, the definition used in this work is:
( ) ( ) ( )( )
12, 0 ,
,,
vap liq
liq
U T P U T PT P
v T Pδ
⎛ ⎞= −= ⎜⎜⎝ ⎠
⎟⎟ (3)
Heat of vaporization is often used as an approximation at ambient conditions to evaluate
cohesive energy. Unfortunately, asphaltenes are not volatile. Nevertheless, several
techniques are available to determine this parameter for asphaltenes. They are based on
miscibility [19], titration ([5] and [20]), inverse gas chromatography [21] or correlations
[22]. In this work, a simple and fast technique, based on density measurements of
asphaltenes dissolved in several solvents, is explained. The input parameters are the
internal and solubility parameters of the pure solvents at 0.1 MPa and the desired
temperature. This procedure had been used by Liron and Cohen [23] for compounds of
pharmaceutical relevance such as cholesterol in various solvents (toluene, carbon
tetrachloride, chlorobenzene, chloroform and nitrobenzene).
Let us consider a binary constituted of a solvent 1 and a solute 2. According to
Hildebrand and Dymond [24], introducing molecules of solute in the solvent causes
microscopic regions of weakness and expansion until enough energy has been absorbed
to restore the local internal pressure to the bulk internal pressure. Accordingly, it can be
written:
( ) 0221
022 EEvv −=− π (4)
where 2v is the partial molar volume, is the molar volume of the pure solute, 02v 1π the
internal pressure of the solvent 1 and 022 EE − is the partial molar energy of transferring a
mole of liquid solute 2 from pure liquid to solution.
The definition of internal pressure should be mentioned here since it is often confused
with solubility parameter. The fundamental differences between these two concepts were
explained earlier and will not be detailed here [18].
P
T V T
U PT P Tv T
απκ
∂ ∂⎛ ⎞ ⎛ ⎞= = − =⎜ ⎟ ⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠P− (5)
where 1P
P
vv T
α ∂⎛ ⎞= ⎜ ⎟∂⎝ ⎠ is the thermal expansivity and 1
TT
vv P
κ ∂⎛ ⎞= − ⎜ ⎟∂⎝ ⎠ the isothermal
compressibility. It is assumed that internal pressure is unchanged by the small amount of
solute introduced [25].
This equation has no theoretical background but, quoting Hildebrand and Dymond [24],
“the best we have been able to do is to rely somewhat upon intuition to produce a rough-
and-ready relation that withstands the test of experiment amazingly well”.
The regular solution theory can be applied and it gives:
( 221
212
022 δδϕ −=− vEE ) (6)
where iδ is the solubility parameter of the compound i and 1φ is the volume fraction of
the solvent. The key assumption in the regular theory is that, in a regular solution, there is
no entropy change when a small amount of one of its components is transferred to it from
an ideal solution of the same composition, the total volume remaining unchanged [25],
i.e. there is no excess entropy when mixing occurs at constant volume.
Since the solutions are highly diluted (mass fractions of solute below 10-2), 1ϕ is
approximately equal to 1. Thus, combining Eq 4 and Eq 6, we obtain:
( )1
221
2
022
πδδ −
=−v
vv (7)
This expression is the one presented by Hildebrand and Dymond in 1967. However,
Hildebrand et al. [25] write the following version of Eq 3:
( )1
221
02
022
πδδ −
=−v
vv (8)
Indeed, in the equivalent of Eq 6, the volume of solute 2 was written with no more
details. Nonetheless, we do think that refers to the molar partial volume
2v
2v 2v . Actually,
Hildebrand et al. [25] write in chapter 6:
2211 vnvnVm += (9)
where is the volume of the mixture. Thus, we do believe that Eq 7 is the correct one. mV
After dividing each member of Eq 7 by the molecular weight of the solute 2 , one
can write:
2wM
( )1
221
2
022
πδδ −
=−
s
ss
VVV
(10)
The partial specific volume of a liquid can be determined experimentally as explained
later on. Thus, if its pure molar volume is known, its solubility parameter can easily be
determined.
Nevertheless, when dealing with non-crystalline solids (like asphaltenes), two solvents
are necessary [23]. Indeed, if the solvents are named 1 and 3 and the solute 2, Eq 10 can
be written:
( )
1
221
21
0221
πδδ −
=−
s
ss
VVV
(11)
( )3
223
23
0223
πδδ −
=−
s
ss
VVV
(12)
where isV 2 is the partial specific volume of 2 in solvent i and is the specific volume of
the pure solute (i.e. the reciprocal of its pure density). After rearrangement, a 2nd order
polynomial is obtained:
02sV
0222 =++ CBA δδ (13)
where 1
21
3
23
ππss VVA −= , ⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
3
233
1
2112
πδ
πδ ss VVB and ⎟⎟
⎠
⎞⎜⎜⎝
⎛−−⎟⎟
⎠
⎞⎜⎜⎝
⎛−=
3
23
231
21
21 11πδ
πδ
ss VVC
Two roots are obtained and the most relevant one is chosen (within the usual range).
Liron and Cohen [23] used this technique but with Eq 8 instead of 7. The difference is
relatively small but, in our case, it can reach up to 0.6 MPa1/2 for the solubility parameter
of asphaltenes.
2.2. Determination of critical parameters of asphaltenes
The main idea is to use partial volume measurements combined with a cubic equation of
state (EOS) and to determine the critical coordinates.
The partial molar volume is defined as:
, , j
ii T P n
VVn
⎛ ⎞∂= ⎜ ⎟∂⎝ ⎠
(14)
where V is the volume and the mole numbers of component i. in
It can also be written as follows:
, ,
,
ji T V n
i
T n
Pn
VPV
⎛ ⎞∂−⎜ ⎟∂⎝ ⎠
=∂⎛ ⎞
⎜ ⎟∂⎝ ⎠
(15)
Each term of this ratio is function of the reduced residual Helmholtz energy,
( ), ,rF A T V n RT= .
2
, , ,j ji iT V n T n
P FRTn V n
⎛ ⎞ ⎛ ⎞∂ ∂= − +⎜ ⎟ ⎜ ⎟∂ ∂ ∂⎝ ⎠ ⎝ ⎠
RTV
(16)
2
2, ,T n T n
P F nRTRTV V
⎛ ⎞∂ ∂⎛ ⎞ = − −⎜ ⎟⎜ ⎟∂ ∂⎝ ⎠ ⎝ ⎠2V
(17)
Each of this derivative is easily determined analytically if the method developed by J.
Møllerup is followed (Michelsen and Møllerup, 2004). Thus, knowing iV should enable
the determination of , and CT cP ω suitable for a defined equation.
2.3. Determination of the partial molar volume
Figure 1 is a schematic representation of the specific volume of a binary mixture as a
function of the mass fraction . 2y
In this plot, for a point M ( , ) , one can write: 2y SV
01 2
1
2
2
2 −−
=−−
=y
VVyVV
dydV SSSSS (18)
where iSV is the partial specific volume of component i.
Thus, we have:
221 dy
dVyVV SSS −= (19)
212 dy
dVyVV SSS += (20)
Since we are interested in determining 2SV , only small mass fractions of solute are
required, corresponding to a point on the curve at 02 =y . In practice, a tangent can be
drawn at this point from a series of points having values smaller than 10-2 [23]. Once
this tangent is obtained, its linear equation
2y
2 2sV ay b= + should be determined and the
partial specific volume is obtained by choosing 2 1y = .
3. Experimental part
3.1. Principle
An Anton-Paar densimeter DMA 58 was used. This high-precision densimeter contains a
U-shaped sample tube electromagnetically excited. The period of oscillation T is related
to the density of the sample by the following relationship:
BAT −= 2ρ (21)
Precision of the temperature-controlled system is better than ± 0.005°C and the display
resolution is 0.01°C. The sample volume is approximately 0.7 cm3.
The constants were calculated with solvent itself and air. The DIPPR correlations were
used. Table 1 presents the origin of the compounds and their respective purities.
3.2. Calibration
The method was first tested with known compounds. Densities of several dilutions of n-
heptane and n-decane in methanol were measured. Then, partial molar volumes were
calculated and compared to literature [27] (table 2). The maximum deviation is 2.2%,
which is found acceptable.
3.3. Application to asphaltene solutions
The asphaltenes used were obtained with a modified IP 143 method from the oils OLEO
D and A95. The mixtures were prepared by mass using the balance Sartorius Analytic
A210P (accuracy: 0.0005 g, display resolution: 0.0001 g). These asphaltenes were mixed
with the different solvents (toluene, m-xylene and carbon disulfide) by 15 minutes of
ultrasonication. Each sample was injected in the oscillating tube with a 2 mL-syringe.
Excess fluid was overflowed past the vibrating tube. Once the thermal equilibrium was
reached, the measurement was made, the cell was cleaned with toluene, then ethanol and
finally dried with air (by means of the small pump included in the densimeter) until the
period reached the one of the empty tube. Each sample was measured twice. The
dilutions were prepared between 0 and 0.3 wt. %. Table3 give the different specific
partial volumes with respect to the various solvents.
4. Results and discussion
4.1. Solubility parameter of asphaltenes
According to Eq 13, the internal pressure and the solubility parameter of each solvent is
required. Internal pressure was calculated using thermal expansivity and isothermal
compressibility (Eq 5). As for the solubility parameter, cohesive energy was
approximated with heat of vaporization. DIPPR correlations were used for both molar
volumes and heats of vaporization (Eq 1). These values and the relevant references are
presented in table 4. Note that the calculations were performed at 303.15 K and 0.1 MPa.
Table 5 presents the solubility parameters of the asphaltenes under investigation, as well
as their densities (deduced from Eq 11 and 12). The solubility parameters for each
asphaltene are close to the range reported in the literature, i.e. between 19 and 22 MPa1/2
[20], except for the solvent pair toluene/m-xylene. The second root of Eq 13 is also
mentioned for this last pair of solvents (in brackets). In this case, the solubility parameter
is too small but the density is in the expected order of magnitude. The deviations between
m-xylene/CS2 and toluene/CS2 are within 3.5% for the solubility parameter and within
1% for the density.
It turns out that the internal pressure of toluene is a key parameter for the solvent pair
toluene/m-xylene. Table 6 shows the different results (for the asphaltene OLEO D)
according to the value chosen amongst literature data. The results are outside the general
accepted range for the solubility parameter. However, other values from literature might
give decent results. The values in brackets are the second solutions of Eq 13. As for the
other pair toluene/carbon disulfide, the influence is smaller (within 0.3 MPa1/2 for the
solubility parameter and 3 kg/m3 for the density). Thus, it is advised to use the solvent
pairs toluene/carbon disulfide or carbon disulfide/m-xylene.
As for the density, Rogel and Carbognani [33] measured the densities of 13 different
asphaltenes at 298.15 K and they vary between 1.17 and 1.52 g/cm3. Thus, the values of
1.09 g/cm3 and 1.16 g/cm3 (respectively for OLEO D and A95) seem relevant, though
smaller.
4.2. Critical constants of asphaltenes
As explained in paragraph 2.2, partial molar volumes can be calculated by cubic EOS. In
this work, the Peng-Robinson was chosen. Details about this equation will not be detailed
here but can be found in most of text books related to thermodynamics ([34] for
instance). This method was first tested with two pure and heavy compounds (n-
tetradecane and n-octadecane) mixed in the solvents of interest (toluene, m-xylene and
carbon disulfide) at 298.15 K and 0.1 MPa. Partial volumes are given in table 7. The
partial molar volumes calculated with the EOS are then compared to experimental values
and the deviation is as follows (for n-tetradecane and n-octadecane, respectively): -12.8%
and 8.5% in toluene, -10.1% and -26.1% in m-xylene, 12.3% and-7.8% in carbon
disulfide. The absolute average deviation is 13%.
A major issue rises when dealing with asphaltenes: the molecular weight. Indeed, specific
volumes are determined and a molecular weight has to be measured or assumed. Table 8
present the critical parameters calculated with two assumed molecular weights (1000 and
4000 g/mol). As expected, the bigger the molecule, the higher Tc and the smaller Pc.
However, the acentric factor has a very small influence on the calculated partial volume.
Conclusion
Attempts to determine physical parameters related to asphaltenes (such as the solubility
parameter and critical constants) were tested on two asphaltenes by means of density
measurements. The following solubility parameters were found: 21.2 ± 0.3 MPa1/2 for
OLEO D and 22.4 ± 0.4 MPa1/2 for A95 at 303.15 K and 0.1 MPa (the solvent pair
toluene/m-xylene is not taken into account). As for the critical parameters, the method
based on partial volumes was tested with two pure compounds in three solvents and the
absolute average deviation is 13%. When applied to asphaltene dilutions, acceptable
critical constants were found but the influence of molecular weight is significant. It is
believed that other simple measurements (such as refractive index or calorimetry) can
give important pieces of information as well and bring relevant data for modelling the
behaviour of asphaltenic fluid.
List of symbols
Latin letters
E Cohesive energy
H Enthalpy
wM Molar weight
n mole number
P Pressure
T Temperature
U Internal energy
V Volume
v Molar volume
v Partial molar volume
sV Specific volume
sV Partial specific volume
Greek letters
Pα Isobaric thermal expansivity
δ Solubility parameter
Tκ Isothermal compressibility
π Internal pressure
ω Acentric factor
Subscripts
c critical
liq liquid phase
r residual
vap vapour phase
Superscript
° pure phase
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Figure 1: Relation between the specific volume and the mass fraction SV 2y
M
y2 = 0 y2 = 1 y2
VS2
VS10
VS20
Table 1: Origin and purity of the chemical compounds
Compound Origin compounds Purity (wt. %)
methanol JT Baker > 99.8
n-heptane Rathburn Chemicals > 99
n-decane Aldrich Chemie > 99
toluene Riedel de Haën > 99
carbon disulfide Rathburn Chemicals
m-xylene Merck-Schuchardt > 99
Table 2: Partial molar volumes of n-decane and n-heptane in methanol at 298.15 K
and 0.1 MPa (in cm3/mol)
Solute ( )sv this work ( )sv literature [27] Deviation (%) a
n-heptane 156.01 152.63 2.2
n-decane 205.54 203.88 0.8
a: ( )this work literature literaturedeviation ρ ρ ρ= −
Table 3: Partial specific volumes of the asphaltenes at 303.15 K (m3/kg)
Toluene Carbon disulfide m-xylene
OLEOD 9.48.10-4 9.20.10-4 9.42.10-4
A95 9.22.10-4 8.78.10-4 9.14.10-4
Table 4: Internal pressures and solubility parameters of the solvents at 303.15K and
0.1 MPa
Toluene m-Xylene
Internal pressure (MPa) 322.0 a 343.4 b
Solubility parameter (MPa1/2) 18.20 17.94
a: Verdier et al. [28]
b: Taravillo et al. [29] for thermal expansivity; Weast and Selby [30] for isothermal
compressibility.
Table 5: Solubility parameter and densities of the asphaltenes OLEO D and A 95
(303.15 K and 0.1 MPa)
Solubility parameter
(MPa1/2)
Density
(kg/m3) Solvents
OLEO D A 95 OLEO D A 95
Toluene/m-xylene
Toluene/Carbon disulfide
Carbon disulfide/m-xylene
28.2 (15.2)
21.5
20.8
28.7 (14.5)
22.81
22.03
1533 (1085)
1092
1088
1657 (1134)
1162
1150
Table 6: Influence of the internal pressure of toluene on the solubility parameter of
OLEOD (303.15 K and 0.1 MPa)
Toluene/m-xylene Toluene/carbon disulfide
tolueneπ
(MPa)
asphalteneδ
(MPa1/2)
asphalteneρ
(kg/m3)
asphalteneδ
(MPa1/2)
asphalteneρ
(kg/m3)
307.1 a
322.0 b
347.1 c
24.90 (15.60)
28.22 (15.21)
13.76
1236 (1079)
1533 (1085)
1119
21.38
21.49
21.69
1091
1092
1094
a: from the Tait equation of state (Cibulka and Takagi, [31])
b: from density measurements and microcalorimetry (Verdier et al., [28])
c: from speed of sound measurements (Sun et al., [32])
Table 7: Partial molar volumes of pure compounds in the various solvents at 298.15 K and 0.1 MPa (m3/mol)
Toluene Carbon disulfide m-xylene
n-C14 2.70.10-4 4.70.10-4 2.68.10-4
n-C18 3.35.10-4 5.50.10-4 3.33.10-4
Table 8: Critical parameters of asphaltenes calculated from partial volume measurements and with PR EOS
Tc (K) Pc (atm) omega Mw (g/mol)
OLEOD 980 7.2 2.90 1000
OLEOD 1650 3.1 2.90 4000
A95 947 7.0 2.98 1000
A95 1500 3.0 3.07 4000