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: sia@kt.dtu.dk

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