Energy & Fuels 2004, 18, 667-673
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Solubility Parameters of Crude Oils and Asphaltenes F. Mutelet,† G. Ekulu,‡ R. Solimando,† and M. Rogalski*,‡ Laboratoire de Thermodynamique des Milieux Polyphase´ s, Ecole Nationale Supe´ rieure des Industries Chimiques, Institut National Polytechnique de Lorraine, 1 rue Grandville, BP 451, F-54001 Nancy Cedex, France, and Laboratoire de Thermodynamique des Milieux Polyphase´ s, Universite´ de Metz, 1, Boulevard Arago, CP 87811, 57078 Metz Cedex 3, France Received September 18, 2003. Revised Manuscript Received January 23, 2004
Results obtained with flocculation threshold experiments and with inverse gas chromatography were used to validate the use of the solubility parameter approach to asphaltene flocculation phenomena. It was found that values of solubility parameters obtained with both methods are in good agreement. The global solubility parameter of the crude oils was factorized in terms of Linear Solvation Energy Relationship (LSER) coefficients corresponding to a given fluid. Results confirm the validity of the three-dimensional solubility parameter proposed by Hansen to deal with petroleum fluids.
Introduction Crude oil asphaltenes are compounds classified by their solubilities in n-alkanes. Asphaltene precipitation causes damage in producing reservoirs and wellbores. The deposits can clog tubings and reduce effective hydrocarbon permeability by blocking the pore throats. Asphaltene precipitation has been considered to be a very serious problem facing the oil industry for many years. The economic recovery of the oil of many oil fields around the world has been threatened considerably. Nevertheless, due to the complexity of the asphaltene aggregation processes, trustworthy methods to predict the flocculation onset are still lacking. The best results were obtained with various versions of the method initially proposed by Hirschberg et al.1 and based on the concept of Hildebrand’s solubility parameters. Hildebrand’s theory of nonelectrolyte solubility2 has been frequently used to elaborate thermodynamic models predicting asphaltene precipitation.3,4 Hildebrand stated that the maximum solubility is observed when the solute and solvent cohesive energy densities are identical. He defined the solubility parameter indicating the relative solvency behavior of a specific solvent. This solubility parameter is derived from the cohesive energy density of the solvent and is given by
δ)
1/2
(∆EV)
(1)
where ∆E denotes the difference between the internal energy of the condensed material and that of an ideal * Corresponding author. E-mail:
[email protected]. † Institut National Polytechnique de Lorraine. ‡ Universite ´ de Metz. (1) Hirschberg, A.; deJong, L. N.; Schipper, B. A.; Meijer, J. G. Soc. Pet. Eng. J. 1984, 24, 283-293. (2) Hildebrand, H. J.; Scott, R. L. The Solubility of Nonelectrolytes; van Nostrand: Princeton, NJ, 1950. (3) Wang, J. X.; Buckley, J. S. Energy Fuels 2001, 15, 1004-1012. (4) Mannistu, K. D.; Yarranton, H. W.; Masliyah, J. H. Energy Fuels 1997, 11, 615-622.
gas of the same material at the same temperature, and V is the molar volume of the solute. ∆E of volatile compounds may be derived from the heat of vaporization. It was shown that the onset of flocculation occurs when the solvent solubility parameter overcomes the value characteristic for a given crude oil.3-5 The use of the Hildebrand model is justified when interactions are dominated by dispersive forces. Nevertheless, this model was often used to predict solubility of polar and associating compounds. In this case, the solubility parameter should take into account other types of interactions. The concept of dissociating the attractive intermolecular potential into several parts corresponding to nonpolar and different types polar interactions is based on perturbation theories, but an empirical use of it may be justified by the quality of results obtained only. Indeed, a single molecule, because of its structure, may exhibit interactions that are an additive result of two or three different kinds of polar contributions. The practical importance of this concept appears while dealing with the phase equilibria of multicomponent systems. Indeed, phase equilibria are dependent not only on these global intermolecular interactions between components but also on the sums of composite polar interactions. While the total cohesive energy densities of two compounds are similar, the addends that make up those individual totals may be different. These slight disparities in polar contributions result in considerable differences in phase behavior. If these component differences are taken into account, quantified, and included in solubility theory, the prediction of solubility behavior is more accurate. The most used extension of the multicomponent solubility parameter was introduced by Hansen et al.6,7 The Hildebrand parameter was divided into three (5) Teixeira, M. A. G. Prepr. Pap.sAm. Chem. Soc., Div. Pet. Chem. 2001, 46, 114-116. (6) Hansen C. M. J. Paint Technol. 1967, 39, 505-511. (7) Hansen, C. M.; Beerbower; A. Encyclopedia of Chemical Technology; Wiley: New York, 1971; pp 889-910.
10.1021/ef0340561 CCC: $27.50 © 2004 American Chemical Society Published on Web 03/09/2004
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components with accounting for the dispersive forces, the polar interactions, and hydrogen bonding. The value of each component was determined empirically on the basis of a number of experimental observations. In this paper, we propose an alternative approach. We divide global solubility parameters into contributions accounting for different intermolecular forces using the Linear Solvation Energy Relationship (LSER) concept.8-11 The LSER model was mostly used to represent the solute transfer between two phases and supposes that the corresponding free energy changes may be partitioned using the following linear form:
log SP ) constant + F(effective dispersion interactions) + F(effective dipolarity/polarizability) + F(effective hydrogen bond basicity) + F(effective hydrogen bond acidity) (2) For transfer processes occurring between the liquid and gas phase, Abraham and al.8-11 proposed an empirical form of eq 2:
∑RH2 + b∑ βH2 +
log SP ) c + rR2 + sπH 2 + a
l log L16 (3)
The independent variables in eq 3 are the solute excess molar refraction (R2), the effective solute dipolarity/ polarizability (πH 2 ), the effective solute hydrogen bond acidity (∑RH 2 ), the effective solute hydrogen bond basicity (∑βH 2 ), and the solute gas-liquid partition coefficient on n-hexadecane at 25 °C (log L16). The coefficients c, r, s, a, b, and l are not simply fitting coefficients, because they reflect complementary properties of the solvent phase. The r-coefficients reflect the tendency of the phase to interact with gaseous solutes through dispersive-type interactions via electron pairs and π electrons. The coefficient s is a measure of the phase dipolarity/polarizability. The coefficient a represents the complementary property to solute hydrogen bond acidity and it is a measure of the hydrogen bond basicity. Likewise, the coefficient b is a measure of the phase hydrogen bond acidity. Finally, the coefficient l is a combination of the work needed to create a cavity in the phase and the general dispersion interaction energy between solute and solvent phase. Descriptors used in eq 3 are appropriately scaled and may be assessed by relatively easy experiment.12,13 Some recent studies confirmed that the partitioning of molecular interactions proposed in LSER can by justified on the ground of the quantum chemistry calcula(8) Abraham, M. H.; Grellier, P. L.; McGill, R. A. J. Chem. Soc. Perkin Trans. 2 1987, 797-803. (9) Abraham, M. H. Chem. Soc. Rev. 1993, 110, 73-83. (10) Abraham, M. H.; Whiting, G. S. J. Chem. Soc., Perkin Trans. 2 1990, 1451-1460. (11) Abraham, M. H.; Whiting, G. S.; Dohertu, R. M.; Shuely, W. J. J. Chromatogr. 1991, 587, 213-228. (12) Mutelet, F.; Rogalski, M. J. Chromatogr. A 2003, 988, 117126. (13) Mutelet, F.; Rogalski, M. J. Chromatogr. A 2001, 923, 153163. (14) Murray, J. S.; Politzer, P.; Famini, G. R. J. Mol. Struct. (Theochem) 1998, 454, 299-306. (15) Rassamdana, H.; Dabir, B.; Nemati, M.; Farhani, M.; Sahimi, M. AIChe J. 1996, 42, 10-22. (16) Donaggio, F.; Correra, S.; Lockhart, T. P. 3rd International Conference on Petroleum Phase Behavior and Fouling, 2002.
tions.14 We assumed that the LSER decomposition is adequate for representing the solubility parameter of crude oils and petroleum fractions. The LSER model applied to petroleum systems makes it possible to factorize the global interaction potential and to quantify contributions due to various molecular forces. Thus, it allows comparing not only the dispersion interactions of various oils but also their polarity and the basicity/ acidity balance. When a set of solutes with well characterized polarity, basicity/acidity, and dispersion interactions is used in chromatographic experiments, retention times of solutes may be used to determine c, a, b, r, s, and l coefficients in eq 3. This method was used to determine LSER coefficients of asphaltenes and of the crude oils. On the other hand, solubility parameters of these materials were determined using the methods described below. Solubility parameters of simple compounds can easily be calculated from the physical and chemical properties of a pure liquid. Solubility parameters of defined mixtures may be calculated on the basis of data for the single components. For solid materials and complex mixtures, it is not possible to determine solubility parameters directly, and they should be obtained by indirect methods. The usual method is to dissolve a material in different solvents with known solubility parameters and record the solubility. Another method, often used with polymer materials, is based on the inverse chromatography experiments. In this case, the investigated material is deposited in the chromatographic column as a stationary phase. Retention times of solutes, the solubility parameters of which are known, are recorded and are used to determine the solubility parameter of the stationary phase. In the present study, both methods were used to determine solubility parameters of asphaltenes and of crude oils. A comparison of results obtained with two different methods makes it possible to validate the use of the solubility parameter approach to asphaltene flocculation phenomena. Next, correlation in terms of LSER descriptors was performed with the view to establish a multidimensional characterization of solubility parameters. The LSER characterization of the material makes it possible to determine more precisely the nature of molecular interactions than the Hansen method does, and offers a new method to establish solubility parameters of complex materials. Experimental Section Materials. All experiments were carried out using two crude oils supplied by the TotalFinaElf. These oils, called here F1(West Africa) and F2 (Europe), contained, respectively, 11% and 10.4% of asphaltenes. Asphaltenes F1 and F2 were precipitated with n-heptane at a solvent-to-oil ratio of 40 mL/ g. Asphaltenes were allowed to settle for 16 h and separated on sintered glass filters by vacuum filtration. Precipitated asphaltenes were extracted with toluene. Then the solvent was evaporated, and the precipitate was dried at 60 °C. The asphaltenes so obtained were further washed with aliquots of n-heptane until the supernatant liquid was colorless. This procedure is believed to remove most coprecipitated nonasphaltene components. Molecular weight of both crude oils was estimated using results of chromatographic analysis assuming that the molec-
Solubility Parameters of Crude Oils and Asphaltenes
Energy & Fuels, Vol. 18, No. 3, 2004 669 cyclohexane solution. After evaporation of the cyclohexane under vacuum, the support was equilibrated at 323 K during 6 h. The columns prepared in this way were coated with the part of crude oils less volatile than C9 fractions. The weight of the packing material was calculated from the weight of the packed and empty column and was checked during experiments. The injected volumes of the sampled vapor were 0.1 µL. All other chemicals were obtained from commercial sources and used as received. All support materials used in the packed column studies were purchased from Supelco.
Results and Discussion Figure 1. Flocculation threshold data of crude oils F1, F2, F3, and F4.
Figure 2. Asphaltenes recovery (masph./mcrude oil) as a function of the amount of n-heptane (mn-heptane/mcrude oil). ular weight of asphaltene is 1000 g/mol. Densities of F1 and F2 oils were measured at 298.15 K using the Anton Paar DMA 602 density meter and were 0.95510 and 0.95201 g/cm3, respectively. Flocculation Experiments. The flocculation threshold of crude oils F1 and F2 was determined using the usual optical method. Measurements were performed for a series of toluene/ crude oil mixtures using n-heptane as precipitant. Results are presented in Figure 1. Asphaltenes F1 were fractionated by precipitation with an increasing ratio of n-heptane. The fractions obtained were treated in the same way as described above. Figure 2 illustrates the percentage recovery of asphaltenes as a function of the amount of n-heptane per one gram of the crude oil. The asymptotic character of this relationship indicates that the effect of the n-heptane/crude oil ratio on the amount of deposited asphaltenes is strong at the early flocculation stage and weakens with increasing amount of the flocculent. It was shown by Rassamdana et al.15 that the size and the properties of deposited asphaltene aggregates obtained on the sharp part of the flocculation curve depend on the amount of n-heptane. In this study, we worked with asphaltenes obtained within the flat part of this curve, using a significant excess of n-heptane. Almost all amounts of asphaltenes are deposited at these conditions, and the global composition of asphaltenes should be nearly identical in all samples. In this case, all differences of the precipitate properties would be due to asphaltene-n-heptane interactions. Inverse Gas Chromatography. Inverse chromatography experiments were carried out using a Shimadzu GC 14 gas chromatograph equipped with a heated on-column injector and a flame ionization detector. The injector and detector temperatures were kept at 523 K during all experiments. Helium flow rate was adjusted to obtain adequate retention times. Exit gas flow rates were measured with a soap bubble meter. The temperature of the oven was measured with a Pt 100 probe and controlled to within 0.1 K. A PC directly recorded detector signals, and corresponding chromatograms were obtained using Borwin 2.1 software. Stationary phases used with packed columns were prepared by soaking in 10% crude oil/
Determination of Hildebrand’s Solubility Parameters Using Flocculation Threshold Data. Solubility parameters obtained using flocculation threshold data were calculated with the method proposed by Donaggio et al.16 Donaggio applied to asphaltenic crude oils the Θ condition concept elaborated by Flory17 for polymer solutions and identified Θ conditions with the flocculation threshold. When interactions between nonneighboring monomer units in polymeric asphaltenes are repulsive, asphaltenes swell the “good” solvent with respect to the noninteraction situation. Θ conditions occur when interactions between monomer units and solvent molecules become comparable. In the presence of the “bad solvent”, monomer units attract each other and the resulting contraction leads to a compact conformation of aggregates which could flocculate. The flocculation occurs when the value of the χ parameter is 0.5, and that allows calculation of solubility parameters of the oil and of asphaltenes according to eq 4:
(δasph. - δoil) + (Φtoluene + Φn-heptane) × δoil )
x
0.5RT + (Φtolueneδtoluene + Φn-heptaneδn-heptane) (4) v1
where δasph. and δoil are, respectively, the solubility parameters of the asphaltenes and of the oil after flocculation of asphaltenes; φtoluene and Φn-heptane are molar fractions of toluene and n-heptane, and v1 is the molar volume of the overall solvent mixture. Solubility parameters δasph. and δoil were used to calculate the solubility parameter of the crude oil. Indeed, according to Hildebrand’s theory, the solubility parameter of the mixture of two mutually soluble liquids is proportional to the volume fraction of each liquid that can be written as follows:
δcrude oil )
(
)
Φoilδoil + Φasph.δasph. Φoil + Φasph.
(5)
where Φasph. and Φoil are, respectively, the molar fraction of asphaltenes and of the crude oil after flocculation of asphaltenes. Estimated solubility parameters are reported in Table 1. Determination of Hildebrand’s Solubility Parameters δIC Using Inverse Gas Chromatography. Determination of the Crude Oil Solubility Parameter δIC crude oil. The retention data determined with inverse chromatography experiments were used to calculating Hildebrand’s solubility and LSER parameters. We have (17) Flory, P. J. Principles of Polymer Chemistry; Cornell University Press: Ithaca, 1953.
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Table 1. Crude Oil Solubility Parameter δ (cal/cm3)1/2 a crude oils
IC δcrude oil
F1 F2 F3 F4 F5 F6
7.03 7.65 7.95 8.085 10.03 9.845
D δcrude oil
δD oil
δD asph.
7.00 7.72 8.69
6.42 6.99 8.82
15.6 15.4 15.7
10.07 10.33
9.6 8.9
16.0 16.1
a δIC crude oil: determined with eq 8 using retention data obtained D with inverse gas chromatography (IC) at 323 K. δD oil, δasph.: estimated value of solubility parameter of oil and of asphaltenes D using Donaggio’s Method at 298 K. δcrude oil: solubility parameter of crude oil calculated using eq 4.
Table 2. LSER Descriptors and Solubility Parameter δasph.(cal/cm3)1/2 of Asphaltenes at 323 K Obtained from the Crude Oil F1 Determined Crude Oil F1 + 6 volumes of toluene
c
r
s
a
b
l
δasph.
10 volumes C7 11 volumes C7 12 volumes C7 13 volumes C7
-3.63 -3.02 -3.04 -2.94
0 0 0 0
0.60 0.590 0.623 0.580
1.060 0.998 1.160 0.980
0.100 0.102 0.109 0.090
0.920 0.830 0.804 0.820
12.60 12.32 12.00 11.59
used retention data of fluids F1 and F2 determined in this work and of fluids F3, F4, F5, and F6 determined previously.18 According to the Flory-Huggins theory, the parameter χ ∞12 characterizing interactions between the solute and the stationary phase obtains using the following expression:
(
χ ∞12 ) ln
)
273.15Rv2 V 0g P 01 V1
- P1
(B11 - V1) RT
(6)
> In eq 6, R is the gas constant, v2 is the specific volume of the stationary phase, and V 0g is the probe-specific retention volume. B11 is the second virial coefficient of the solute in the gaseous state, and P 01 is the probe vapor pressure at temperature T (K). The values of P 01 and B11 have been taken from literature.19 The molar volume of the solute, V1, was calculated using the liquid density taken from TRC Tables.19 If it is assumed that the interaction parameter can be expressed as a function of the solubility parameters of the probe and of the stationary phase:
χ)
v10 × (δ1 - δ2)2 RT
(7)
where v10 is the molar volume of the solute, and δ1 and δ2 are solubility parameters of the solute and of the stationary phase, respectively. Then, the solubility parameter of the stationary phase δ2 can be calculated by fitting χ ∞12 and δ1 to the following equation:
(
) ( )
χ ∞12 δ22 δ21 2δ2 ) δ1 RT V1 RT RT
(8)
If the left-hand side of eq 8 is plotted against δ1, a straight line having a slope of 2δ2/RT and an intercept of - δ22/RT is obtained. The solubility parameter of the stationary phase δ2 can be calculated from the slope or the intercept of the straight line. The agreement of both δ2 values confirms the applicability of the method to the considered system. The inverse chromatography is currently used to characterize molecular interactions in macromolecular systems.20-22 (18) Mutelet, F.; Ekulu, G.; Rogalski, M. J. Chromatogr. A 2002, 969, 207-213. (19) Thermodynamics Research Center, Texas Engineering Experiment Station, The Texas A.& M. University System: College Station, April 1987. (20) Voelkel, A.; Fall J. J. Chromatogr. A 2002, 982, 245-254. (21) Voelkel, A.; Grzeskowiak, T. Colloids Surf., A: Physicochemical and Engineering Aspects 2002, 208, 177-185.
Figure 3. Solubility parameter of asphaltenes δasph. as a function of the ratio of the amount of n-heptane (mn-heptane/ mcrude oil) used to induce the flocculation.
Calculated values of solubility parameters are given in Table 1. Values of solubility parameters obtained from inverse chromatography measurements are in good agreement with values calculated using Donaggio’s method and flocculation threshold data. Determination of the Asphaltene Solubility Parameter δIC asph.. The same method was applied to determining solubility parameters of asphaltenes deposited from the crude oil F1, using different amounts of n-heptane but always much higher than the amount corresponding to the flocculation threshold. Results are presented in IC Table 2. It may be observed that values of δasph. decrease with an increasing amount of n-heptane. This relationship is linear as shown in Figure 3. When the straight line in Figure 3 is extrapolated to the amount of n-heptane corresponding to the flocculation threshold of the crude oil F1, we find that the value of the solubility parameter at this concentration is 14.6 (cal/ D cm3)1/2. This value may be compared with δasph. ) 15.6 3 1/2 (cal/cm ) obtained with this oil using flocculation threshold data and Donaggio’s model. When one takes into account a significant difference of temperature between the two experiments, results obtained with both methods may be considered as very similar. This conclusion is important for the comprehension of the flocculation process. Indeed, the similar value of solubility parameter of asphaltenes in solution and in the deposited state means that the flocculation implies no significant change of the asphaltene aggregate state. A decrease of the solubility parameter value with an increasing amount of n-heptane may be interpreted as a confirmation of the hypothesis that n-heptane molecules participate in the formation of asphaltene aggregates. (22) de Schaefer, C. R.; de Ruiz Holgado, M. E. F.; Arancibia, E. L. J. Colloid Interface Sci. 2001, 239, 222-225.
Solubility Parameters of Crude Oils and Asphaltenes
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Table 3. LSER Descriptors of Probes Used To Characterize Crude Oils and Asphaltenes solutes
R2
π2H
ΣR2H
Σβ2H
log L16
n-hexane n-heptane n-octane n-nonane cyclohexane 1-hexene benzene toluene ethylbenzene ch2cl2 chcl3 ccl4 1-butanol 2 methyl-1-propanol 2-propanol 2 pentanone methyl ethyl ketone triethylamine pyridine thiophene nitropropane trifluoroethanol diethyl ether hexafluoro-2-propanol 1,4-dioxane
0 0 0 0 0.305 0.078 0.61 0.601 0.613 0.387 0.425 0.458 0.224 0.217 0.212 0.143 0.166 0.101 0.631 0.687 0.242 0.015 0.041 -0.24 0.329
0 0 0 0 0.1 0.08 0.52 0.52 0.51 0.57 0.49 0.38 0.42 0.39 0.36 0.68 0.7 0.15 0.84 0.57 0.95 0.6 0.25 0.55 0.75
0 0 0 0 0 0 0 0 0 0.1 0.15 0 0.37 0.37 0.33 0 0 0 0 0 0 0.57 0 0.77 0
0 0 0 0 0 0.07 0.14 0.14 0.15 0.05 0.02 0 0.48 0.48 0.56 0.51 0.51 0.79 0.52 0.15 0.31 0.25 0.45 0.1 0.64
2.668 3.173 3.677 4.182 2.964 2.572 2.768 3.325 3.778 2.019 2.48 2.833 2.601 2.413 1.764 2.755 2.287 3.04 3.022 2.819 2.894 1.224 2.015 1.392 2.892
Table 4. LSER Descriptors of Crude Oils Determined at 323 K crude oils F1 F2
c
r
s
a
b
l
r
n
F
-2.64 0 0.320 0.700 0.172 0.842 0.993 22 607 -2.33 0 0.594 0.943 0.087 0.826 0.994 22 598
LSER Characterization of Crude Oils and Asphaltenes. Crude Oils F1 and F2. The retention data of 26 solutes determined with inverse chromatography experiments were used to calculate LSER coefficients of crude oils. LSER parameters of these solutes are given in Table 3. Retention data were obtained with fluids F1 and F2; F3 and F4 were used as stationary phases in chromatographic columns. For each crude oil, coefficients c, r, s, a, b, and l of eq 3 oils were obtained by multiple linear regression of retention data. Values of crude oil LSER coefficients are reported in Table 4. They afford information about the chemical properties of a given crude oil. Thus, it can be observed that the crude oil F1 is more acid than crude oil F2. The polar character of F2 is evidenced by the value of the polarizability parameter twice larger than the value found with fluid F1. Dispersive interactions are considered with parameters “r” and “l”. The “l” term expressing general dispersion interactions is large with both fluids studied, and that reflects the high ratio of heavy molecules. The “r” term expressing partly the oil polarity vanishes, as was reported previously by Selves et al. and Mutelet et al.18,23-24 This result is surprising in the case of highly aromatic oils. Indeed, dispersion forces and n-π interactions present in aromatic systems result usually in high values of the excess molar refractivity, R2. The fact that the “r” parameter is equal to zero in the case of crude oils may be due to formation of aggregates through n-π and π-π interactions. Significant values of “s” and “a” indicate the presence of polarizable hydrogen bond acceptor (basic) sites. The low values of coefficients “b” and “r” indicate a small number
of hydrogen bond donor sites. This discussion shows that LSER analysis affords detailed analysis of interactions characteristic for a given system. Asphaltenes of the Crude Oil F1. As was stated above, samples of asphaltenes of the crude oil F1 were obtained using different amounts of n-heptane but always much higher than the amount corresponding to the flocculation threshold. LSER parameters of these fractions were determined by the method described above and are presented in Table 1. The polarity “s” and the hydrogen bond basicity “a” of asphaltene are much higher than corresponding parameters of the oil. While asphaltenes are a more polar fraction of the oil, this result is not surprising. Nevertheless, the hydrogen bond acidity “b” of asphaltenes is lower; that indicates that acid species present in the oil do not precipitate with asphaltenes. Moreover, it was found that the more acid oil F1, Table 1, is also more stable with respect to flocculation, Figure 1. Therefore, the stability of asphaltenes in solution can be enhanced by petroleum acids and resins. This confirms the old theory attributing to resins a crucial role in stabilizing the asphaltene micelles.24-28 In the case of a high excess of n-heptane, chemical properties of asphaltenes precipitated with different ratios of n-heptane are very similar. Decreasing values of thecoefficient l, characterizing dispersion forces, with an increasing amount of n-heptane, indicate that aggregates contain not only asphaltenes but also some amount of n-heptane that increases with n-heptane total concentration. Relation between Hildebrand’s Solubility Parameter and LSER Descriptors. Global solubility parameter of the crude oils was factorized in terms of LSER coefficients (a, b, r, s, l) corresponding to a given fluid.The resulting relationship is as follows:
δcrude oil ) -2.51s - 2.60a - 3.91b + 16.00l (9) s.d ) 0.354; r2 ) 0.979; n ) 6 Equation 9 shows that the solubility parameter is determined mainly with dispersion interactions. This finding is important because it confirms the validity of Hildebrand and Flory theories to deal with the problem of asphaltene flocculation. The acidity-basicity balance in the fluid cannot be neglected, but it plays a secondary role only. A large basicity lowers the oil solubility parameter and increases its stability with respect to the flocculation. This analysis confirms the fact that the three-dimensional factorization of the solubility parameter proposed by Hansen6,7 is adequate to describe molecular interactions occurring in the petroleum fluids. Nevertheless, LSER offers a better insight into the spectrum of molecular forces. In the case of the crude oil F1, LSER analysis makes it possible to separate the hydrogen bonding contribution into the acidity and the basicity terms. Moreover, this analysis allows estimat(23) Selves, J. L.; Abraham, M. H.; Burg, P. Fluid Phase Equilib. 1998, 148, 69-82. (24) Burg, P.; Selves, J. L.; Colin, J. P. Anal. Chim. Acta 1995, 317, 107-125. (25) Gonzalez, G.; Middea, A. Colloids Surf. 1991, 42, 207-217. (26) Chang, C.-L.; Fogler, H. S. Langmuir 1994, 10, 1749-1757. (27) Chang, C.-L.; Fogler, H. S. Langmuir 1994, 10, 1758-1766. (28) De Boer, R. B.; Leerlooyer, K.; Eigner, M. R. B.; Van Bergen, R. D. SPE Prod. Fac. 1995, 2, 55-61.
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obtained with different fluids might be represented as a series of parallel straight lines. This model allows us to estimate flocculation threshold concentration with an average deviation of 16%. This result is far from the experimental accuracy, but it cannot be improved using correlation based on the solubility parameter only. Equation 11 may be presented in the following equivalent form:
δfloc ) δC7ΦC7 + δtolueneΦtoluene + δcrude oilΦcrude oil ) 7.96 - 0.09δcrude oilΦcrude oil (12) Figure 4. General linear relationship determining the ratio of the solvent (mtoluene/mcrude oil) and of the antisolvent (mn-heptane/ mcrude oil) at the flocculation threshold. Results were obtained with flocculation onset data of five crude oils.
ing a quantitative contribution of every molecular interaction influencing physical properties of the system studied. Prediction of the Flocculation Onset of Crude Oils Using Hildebrand’s Solubility Parameter. According to Figure 1, concentrations of the solvent (mtoluene/mcrude oil) and of the antisolvent (mn-heptane/ mcrude oil) are linearly related for a given fluid. On the basis of this result, we looked for an empirical correlation, making it possible to establish a general linear form to estimating flocculation threshold condition. As can be seen in Figure 4, all experiment points obtained with five crude oils may be represented with the unique straight line crossing the origin of the graph. The corresponding equation is
mtoluene mn-heptane ) 1.3683 mcrude oil mcrude oil
(10)
s.d. ) 1.14; r2 ) 0.920; n ) 28 While the regression coefficient is 0.92, we conclude that eq 10 is significant and expresses qualitatively a relationship between amounts of the solvent and antisolvent at the flocculation threshold. According to this result, the flocculation onset occurs at a constant ratio of the solvent and antisolvent with all the crude oils studied. In the next correlation, we proposed to differentiate the crude oils with their solubility parameters. The best relationship giving the flocculation threshold composition as a function of the solubility parameter of the oil was found to be
[
] ]
mtoluene Fn-heptane δtoluene - 7.96 mn-heptane ) + mcrude oil mcrude oil Ftoluene 7.96 - δn-heptane Fn-heptane 7.96 - 1.09δcrude oil (11) Fcrude oil δn-heptane - 7.96
[
s.d. ) 0.610; r2 ) 0.965; n ) 28 Equation 11 was established with flocculation threshold data of 5 fluids diluted with toluene. The training set used in calculations contained 28 data points. Equation 11 states that in the general straight line, eq 11, the slope is independent of the crude oil properties and the intercept is a weak function of the crude oil solubility parameter. According to eq 11, flocculation results
Equation 12 shows that highly diluted crude oils flocculate at the constant value of the solubility parameter of the mixture. Rough correlation of the flocculation onset given with eqs 10 and 11 should be considered as a qualitative estimation of the oil propensity to flocculate. In any case, they afford quantitative estimates of the flocculation onset. Conclusions It was demonstrated that Hildebrand’s solubility parameter of crude oils might be factorized in terms of LSER coefficients determined by inverse chromatography experiments. Results obtained showed that the solubility parameter is determined mainly with dispersion interactions. Therefore, Hildebrand and Flory theories are an adequate model for dealing with the problem of asphaltene flocculation. The acidity and the basicity of the oil play a secondary role but cannot be neglected. Indeed, a large basicity lowers the oil solubility parameter and increases its stability with respect to the flocculation. The LSER model offers an insight into the intensity and the nature of molecular forces involved in flocculation processes. Moreover, inverse gas chromatography data might be used to calculate directly the solubility parameter of the crude oil or of asphaltenes. Indeed, we found that solubility parameters of crude oils that were determined with the inverse gas chromatography agree well with these obtained using flocculation threshold data. Moreover, similar values of the asphaltene solubility parameter were found with both methods despite differences of the asphaltene state. While during flocculation experiments, asphaltenes are dissolved in the oil, they are present as a solid precipitate in the chromatographic column. Similar values of solubility parameters suggest that the physical state of asphaltenes does not change during the solutionprecipitate transition. On the other hand, an agreement of solubility parameters obtained using two different experiments confirms the validity of the theory used to interpret experimental data. Therefore, we consider that the Hildebrand and Flory theory is an adequate model to represent the flocculation of asphaltenes. At last, the inverse gas chromatography made it possible to determine the influence of the n-heptane excess on the properties of flocculated asphaltenes. Results obtained suggest the inclusion of n-heptane into asphaltene aggregates. This phenomenon is enhanced by increasing amounts of n-heptane. Results obtained justify using inverse gas chromatography characterization and as a complementary
Solubility Parameters of Crude Oils and Asphaltenes
method to study properties of crude oils. We prepare a project of chromatographic characterization of a series of crude oils from various origins that were well characterized with the usual chemical methods. It will be interesting to compare the H/C ratio and aromaticity of oils as well as the number of aromatic rings and the
Energy & Fuels, Vol. 18, No. 3, 2004 673
type of alkyl chains attached to the aromatic ring with solubility and LSER parameters. Acknowledgment. The authors acknowledge the financial support of CNRS, TotalFinaElf, and IFP. EF0340561
