Energy Fuels 2010, 24, 2266–2274 Published on Web 01/07/2010
: DOI:10.1021/ef900901w
Composition of Asphaltene Solvate Shell at Precipitation Onset Conditions and Estimation of Average Aggregate Sizes in Model Oils† Jamilia O. Safieva,‡ Victor V. Likhatsky,§ Vladimir M. Filatov,§ and Rustem Z. Syunyaev*,§ ‡
N. M. Emanuel Institute of Biochemical Physics, Russian Academy of Sciences (RAS), Moscow 119334, Russia and § Department of Physics, Gubkin Russian State University of Oil and Gas, Moscow 119991, Russia Received August 19, 2009. Revised Manuscript Received December 15, 2009
Macroscopic properties of petroleum disperse systems are functions of its particle size. Asphaltene particles in model oils are in fact building agents. Compositional changes of disperse medium have an effect on the internal structure of the dispersed system. Optical methods are informative enough for analysis of structural evolutionary processes. Near-infrared (NIR) spectroscopy was used to determine asphaltene precipitation onset conditions in model oils (asphaltenes were dissolved in binary solvent: toluene and n-alkane precipitant n-hexane/n-heptane). Asphaltene precipitation onset was determined as a point where the deviation from Beer’s law takes place. Solvate shells of asphaltenes in binary solvents are formed according to differences between intermolecular interaction potentials of components of the model oil. The model of non-uniform distribution of components in solvate shells of asphaltene aggregates at the moment of aggregation stability loss (first stage of precipitation onset) is proposed. On the basis of experimentally determined asphaltene precipitation onset conditions, average aggregate sizes in toluene solutions, set of assumptions concerning geometry of solvent and precipitant molecules, and interaction energy of molecule pairs, the proposed model allows for estimation of the precipitant fraction threshold value in solvate shells of asphaltene aggregates at the moment of stability loss. Polarization of fluorescence was used for the determination of the concentration dependence of average sizes of aspahltene aggregates in toluene solution. The linear aggregation model was used for characterization of asphaltene solutions in toluene; the fraction of n-mers was determined. The concentration dependence of the asphaltene aggregation rate constant was calculated within this model.
substance, well-known in the literature as the Yen model or stacking.3,4 It is monomer-monomer association with the formation of quasi-spherical nanoaggregates, which contain 8-10 monomers.5 Partial mutual compensation of the IIP occurs at this step, limiting the growth of nanoaggregates. At further evolution, nanoaggregates act as kinetic units. The self-association process ends when all asphaltenes are in nanoaggregate form. Further development and formation of new structural units is determined by characteristics of the petroleum-dispersed system. Multi-component composition of petroleum gives a set of opportunities for its structural units construction by different possible variants of asphaltene solvate shell formation from compounds with low IIP: resines and aromatics. Their relative IIP is less than the IIP of asphaltenes. Construction of the kinetic unit of the second level comes to an end at this step. These units are distributed in medium. They contain small molecules with conjugated bonds and small molecules with saturated bonds in solvate shells. Differences in electronic density become insignificant in this step; therefore, mixtures can be considered as ideal. Thus, the hierarchy of the structural organization actually corresponds to the IIP hierarchy in the system. Solvate shells are extremely
1. Introduction Asphaltene aggregation and deposition cause problem situations during production, transportation, and refining.1,2 Asphaltenes are the most mysterious and intriguing components of petroleum systems. The irregularity of their chemical structure, presence of heteroatoms in the structure, and significant electron density (because of the significant amount of unsaturated bonds in aromatic fragments) lead to high values of intermolecular interaction potentials (IIPs) of asphaltenes in comparison to IIPs of other components in oil systems. High electron density means contribution of dispersion interactions. Asphaltenes are the most polar petroleum macromolecules, and there is also contribution of dipole interactions. High polarity defines surface activity. In fact, the structure of asphaltenes determines the relative excess of their contribution to the total IIP in comparison to the contribution from other components. Asphaltenes become centers of system structuring. Nearest coordination spheres are formed around asphaltene molecules according to these contributions. First of all, asphaltenes show a tendency to associate with each other. This is a first step to the organization of the † Presented at the 10th International Conference on Petroleum Phase Behavior and Fouling. *To whom correspondence should be addressed. E-mail: syunyaev@ gubkin.ru. (1) Asphaltenes, Heavy Oils, and Petroleomics; Mullins, O. C., Sheu, E. Y., Hammami, A., Marshall, A. G., Eds.; Springer: New York, 2007; p 669. (2) Syunyaev, Z. I.; Safieva, R. Z.; Syunyaev, R. Z. Petroleum Dispersed Systems; Khimiya: Moscow, Russia, 1991; p 224.
r 2010 American Chemical Society
(3) Yen, T. F.; Erdman, J. G.; Saraceno, A. J. Anal. Chem. 1962, 34, 694–700. (4) Yen, T. F. In Structures and Dynamics of Asphaltenes; Mullins, O. C., Sheu, E. Y., Eds.; Plenum Press: New York, 1998; p 438. (5) Akbarzadeh, K.; Hammami, A.; Kharrat, A.; Zhang, D.; Allenson, S.; Creek, J. L.; Kabir, S.; Jamaluddin, A.; Marshall, A. G.; Rodgers, R. P.; Mullins, O. C.; Solbakken, T. Oilfield Rev. 2007, 19, 22–43.
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labile and can vary because of changes in disperse media, injection of additives, etc.2 Further evolution and moving to the next level at concentrations above 5-10 g/L is accompanied by nanocluster formation. Sizes of nanoclusters allow them to participate in Brownian motion. Further ways are various. At the presence of enough nanoclusters, the interaction of their solvate shells and partial linkage can occur, which actually means gel formation. Kinetic gel formation occurs in a sample, and this means switching of the system to a mode of viscoelastic behavior of a grid of connected nanoclusters. If there are no such components as resins and polynuclear aromatics to form solvate shells of asphaltenes, evolution of the system structure is different.6 In model oils, nanoaggregates and nanoclusters form shells from suitable molecules (aromatics). Such kinetic units form sols. Asphaltene precipitation and deposition is a consequence of forming floccules and loss of their kinetic stability. A flocculation phenomenon, as an initial event of the whole process that leads to asphaltene deposition, attracts attention.7 The definition of asphaltenes is based on the solubility.1,8,9 The solubility parameter concept10 is used for the definition of onset parameters.1,11 A change of pressurevolume-temperature (PVT) conditions may lead to destabilization of asphaltenes in crude petroleum that results in flocculation.12 The development of a thermodynamic model with good predictive ability that uses a minimal set of experimental data is an actual problem.13,14 Petroleum systems are well-balanced systems. “More realistic” models11 (Figure 1) admit the presence of saturated hydrocarbons in nearest coordination spheres of asphaltene aggregates, and this is more fair. Sometimes the loss of aggregative stability, caused by differences in IIPs of components, is explained in terms of surface tension coefficients.15 At present work, the possible approach is submitted, which can be helpful in the prediction of the asphaltene phase behavior. Non-uniform distribution of solvent components in the asphaltene aggregate solvent shell at the moment of stability loss (at onset conditions when flocculation occurs) can be estimated by the proposed model. From experimental estimation of average sizes of asphaltene nanoaggregates in toluene solution by the polarization of fluorescence, set of assumptions concerning molecule geometry and interaction energies between them, and measured asphaltene precipitation onset data, one can calculate critical values of the precipitant fraction in asphaltene aggregate solvate shells in the moment of stability loss. Asphaltene precipitation onset data were received by near-infrared (NIR) spectroscopy. Onset data were used in the theoretical model for estimation
Figure 1. More realistic model of structural units in petroleum systems from Wiehe.11 Table 1. Geometrical Parameters and Physicochemical Characteristics of Toluene, n-Hexane, and n-Heptane molecular weight (g/mol) density (g/cm3) molar volume, Vm (m3/mol) solubility parameter, δ (Pa0.5) radius of monomer, Rm (nm)
n-hexane
n-heptane
toluene
86.18 0.66 0.00013 14900 0.37
100.21 0.684 0.00015 15200 0.39
92.14 0.867 0.00011 18200 0.35
of the precipitant fraction in the solvate shell of a no longer stable asphaltene aggregate. Asphaltenes were extracted from western Siberian crude oil, and model oil systems were made. n-Heptane and n-hexane were used as precipitants. The theoretical part of the proposed model employs the following set of parameters for each model oil component: radius, solubility parameter, and IIP. 2. Materials and Methods 2.1. Samples. Asphaltenes from western Siberian crude oil were used. The asphaltenes were extracted from the crude oil using the following method. The oil cut above 200 °C was mixed with petroleum ether (50-60 °C) in a 1:40 ratio (v/v). The system was left for sedimentation (30 h) after stirring at ambient conditions. Then, the precipitate was filtered through filter paper (0.45 μm) at vacuum (100 mmHg). The precipitate was washed with petroleum ether. The asphaltenes were stored at the temperature of -20 °C in vacuum-sealed ampules under an argon (Ar) atmosphere to avoid oxidation.16 Onset data were taken at the concentrations of asphaltenes in toluene in the range of 2-15 g/L. n-Hexane and n-heptane were used as precipitants (Table 1). A fixed amount of extracted asphaltenes, with an accuracy of (0.001 g, was dissolved in toluene when making model oils. 2.2. NIR Spectroscopy. The minimum amount of the precipitant that is necessary to induce asphaltene precipitation is defined as the onset point. Different techniques are used to measure onset points (UV-vis,17 small-angle X-ray scattering,18 microscopy,19 turbidity,20 and Fourier transform infrared spectroscopy21). Most techniques employ a fixed wavelength for measuring changes of the optical response as the precipitant is added. More accurate techniques may be necessary for some experiments, such as the investigation of the effect of different chemical additives on asphaltene aggregation and settling and evaluation of their effectiveness in keeping asphaltene particles dispersed.20,22 Asphaltene chemicals can be classified into categories according to their performance, and to choose the most
(6) Andreatta, G.; Goncalves, C. C.; Buffin, G.; Bostrom, N.; Quintella, C. M.; Arteaga-Larios, F.; Perez, E.; Mullins, O. C. Energy Fuels 2005, 19, 1282–1289. (7) Lian, H. J.; Lin, J. R.; Yen, T. F. Fuel 1994, 73, 423–428. (8) Wang, J.; Buckley, J. S. Energy Fuels 2001, 15, 1004–1012. (9) Buckley, J. S.; Hirasaki, G. J.; Liu, Y.; Von Drasek, S.; Wang, J.; Gill, B. S. Pet. Sci. Technol. 1998, 16, 251–285. (10) Hildebrand, J. H. The Solubility of Non-electrolytes; Reinhold: New York, 1936. (11) Wiehe, I. A. Process Chemistry of Petroleum Macromolecules, 1st ed.; CRC Press: Boca Raton, FL, 2008; p 427. (12) Correra, S.; Merino-Garcia, D. Energy Fuels 2007, 21, 1243– 1247. (13) Andersen, S. I.; Speight, J. G. J. Pet. Sci. Eng. 1999, 22, 53–66. (14) Vargas, F. M.; Gonzalez, D. L.; Creek, J. L.; Wang, J.; Buckley, J. S.; Hirasaki, G. J.; Chapman, W. G. Energy Fuels 2009, 23, 1147–1154. (15) Anisimov, M. A.; Dmitrieva, I. A.; Krupina, A. A.; Kurlyandskii, A. S.; Yudin, I. K. Chem. Technol. Fuels Oils 1988, 24, 363–366.
(16) Balabin, R. M.; Syunyaev, R. Z. J. Colloid Interface Sci. 2008, 318, 167–174. € (17) Ostlund, J. A.; L€ ofroth, J. E.; Holmberg, K.; Nyden, M. J. Colloid Interface Sci. 2002, 253, 150–158. (18) Simon, S.; Jestin, J.; Palermo, T.; Barre, L. Energy Fuels 2009, 23, 306–313. (19) Abdel-Moghny, T.; Desouky, S. M.; Ramzi, M. J. Dispersion Sci. Technol. 2008, 29, 397–405. (20) Kraiwattanawong, K.; Fogler, H. S.; Gharfeh, S. G.; Singh, P.; Thomason, W. H.; Chavadej, S. Energy Fuels 2009, 23, 1575–1582. (21) Sousa, M. A.; Oliveira, G. E.; Lucas, E. F.; Gonzalez, G. Prog. Colloid Polym. Sci. 2004, 128, 283–287. (22) Kraiwattanawong, K.; Fogler, H. S.; Gharfeh, S. G.; Singh, P.; Thomason, W. H.; Chavadej, S. Energy Fuels 2007, 21, 1248–1255.
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Table 2. NIR Spectrometer InfraLum FT-10 Characteristics spectral range (cm-1) resolution (cm-1) wave number accuracy (cm-1) photometric accuracy (%) radiation source detector
7500-14500 1-16 0.01 0.1 halogen incandescent lamp silicon photodiode
effective additive, additional accuracy may be necessary. The NIR spectroscopy provides quick, accurate, direct, and reproducible measurements of the onset points. NIR spectroscopy is a common method for studying oil systems and is often involved in onset measurements.23,24 Technical specifications and experimental parameters of the NIR spectrometer InfraLum FT-10 are listed in Table 2. Four pure hydrocarbons (toluene, n-hexane, benzene, and isooctane) were used for instrument calibration. Every measurement was carried out comparatively to pure precipitant solution. A comparison solution was measured before and after each measurement of the sample. The NIR procedure ensures the satisfactory accuracy and precision of the measured analytical signal. Unless explicitly defined, a 95% confidence interval for data values is reported in all cases. 2.3. Precipitation Onset Using NIR. Series of aspahltene solutions with different concentrations in toluene were prepared. Solutions were kept for 12h until asphaltenes were fully dissolved before titration. The amount of precipitant that was needed to initiate asphaltene precipitation was measured. n-Heptane and n-hexane were chosen as precipitants to reduce errors because of vaporization (use of pentane gives errors). Titrations were carried out with 10 mL of asphaltene-toluene mixtures. This amount was placed in a bulb, and the titrants (n-alkanes) were added at a controlled flow rate of 0.2 mL/min at a constant mixing. The titrated sample was circulated through the flow cell by a high-flow (5 mL/min) circulating pump. Flow rates were chosen according to recommendations of the American Society for Testing and Materials (ASTM) standard D 6703-01.25 To measure onset precipitation, research groups employ different fixed wavelengths in the range of 340-1600 nm. In this study, two ways of obtaining onset data were tested. Changes of the integral transmittance signal in the NIR range (9800-12 600 cm-1) were monitored as the quantity of precipitant in the system was increasing. Typical NIR transmittance spectra of asphaltene solution in a binary solvent (toluene/ n-alkane) before precipitation onset are shown in Figure 2. The second approach is measuring changes of an optical density at a fixed wavelength. Five fixed wavelengths were tested for applicability to show asphaltene precipitation onsets. In Figure 3, the toluene molar fraction dependence of optical density is plotted at 450, 540, 700, 740, and 750 nm. The minimum absorbance is clearly seen on 750 nm, and this wavelength was chosen for further experiments. The onset was determined as the precipitant amount corresponding to the point where the deviation from Beer’s law takes place.22 Onset was expressed as the toluene mole fraction in this mixture XT γ ¼ ð1Þ XT þ XP
Figure 2. NIR transmittance spectra at the wavenumber range of 9800-12 600 cm-1 for asphaltene solution in toluene (2 g/L) at n-hexane titration (toluene mole fraction γ decreases from 0.92 to 0.6).
Figure 3. Choice of operating wavelength for onset measurements. Optical density curves at wavelengths of 450, 540, 700, 740, and 750 nm for asphaltenes (2 g/L) as a function of the toluene mole fraction. n-Hexane titration. Onset is at γ = 0.413.
3. Results and Discussion 3.1. Experimental Section. 3.1.1. Estimation of Average Asphaltene Nanoaggregate Sizes in Toluene Solution. Evaluation of average asphaltene nanoaggregate sizes in toluene solutions of different concentrations was made by the polarization of fluorescence according to the classical LevshinPerrine equation. Asphaltene nanoaggregates were modeled as quasi-spherical particles. The experimental procedure was based on polarization of luminescence, and this method was reported in detail earlier in our previous work.26 The concentration dependence of average aggregate sizes in asphaltene/toluene solution was received and is presented in Figure 4. The average volume of asphaltenes at minimal concentration (0.001 g/L) can be taken as the volume of an individual asphaltene molecule (asphaltene monomer); the mentioned
where XT and XP are the mole amounts of toluene and precipitant (n-hexane or n-heptane) in the bulk phase. The onset measurement was carried out 3 times to verify the onset values. The path length was 1.0 mm. All experiments were performed at room temperature (23 °C). (23) Oh, K.; Deo, M. D. Energy Fuels 2002, 16, 694–699. (24) Oh, K.; Ring, T. A.; Deo, M. D. J. Colloid Interface Sci. 2004, 271, 212–219. (25) American Society for Testing and Materials (ASTM). ASTM D 6703-01: Standard Test Method for Automated Heithaus Titrimetry; ASTM: West Conshohocken, PA, 2001.
(26) Syunyaev, R. Z.; Balabin, R. M. J. Dispersion Sci. Technol. 2008, 29, 1505–1514.
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Further, using equation Xn ¼ nY n - 1 ð1 - YÞ2
ð4Þ
where Xn is the fraction of aggregates that contain n individual molecules and X is the monomer fraction. One can obtain fractions of asphaltene monomers, dimers, trimers, etc. for a given concentration in the system. Figure 4 shows the concentration dependence of n-mer asphaltene fractions in toluene solution, which was calculated on the basis of the linear aggregation model while taking into account that the aggregation constant Y is concentrationdependent. The inset of Figure 4 shows the concentration dependence of average asphaltene aggregate volumes and was received from polarization of fluorescence, and the concentration dependence of NAV was calculated on its basis. The chosen concentration range corresponds to monomernanoaggregate-cluster conversion.5 The linear regime of aggregate formation lasts from 10-3 to 10 g/L; asphaltene n-mer fractions are increasing in this concentration range. Starting from 10 g/L, the monomer fraction curve changes its slope, monomers in the system are decreasing faster, fractions of n e 4-mers are also decreasing now, and explicit increasing of fractions of n-mers of higher order is observed. The measured critical concentration can be called the critical aggregation concentration (CAC) analogous to the critical micelle concentration.27 n-mer fractions in toluene systems of different concentrations are presented also in Table 3. The point of cluster formation (10 g/L) is characterized by increasing the fractions of n g 4-mers in the system and by the appearance of asphaltene aggregates that consist of more than eight monomers (clusters). In this work, asphaltene solutions in toluene were titrated by n-alkanes. Increasing the fraction of precipitant in a bulk phase leaded to changes in solvate shells of asphaltene aggregates. This was followed by consistent growth of aggregates, which moved the system to the formation of nanoclusters with low stability. Composition changes of solvate shells determine the formation of nanoclusters and, finally, asphaltene precipitation onsets. 3.1.2. Determination of the Onset of Asphaltene Precipitation: n-Alkane Titrations of Toluene Solutions. A change of optical density at 750 nm of asphaltene solutions in toluene at a concentration range of 2-15 g/L as the precipitant (n-hexane/n-heptane) fraction in the system increases is shown in Figure 5. As the asphaltene concentration increases, the precipitant needed for onset decreases. At lower concentrations, asphaltenes are effectively dissolved in toluene and a larger amount of precipitant is required to start the aggregation process. Investigation of the precipitant carbon number influence on the onset of asphaltene precipitation was conducted. Results on the concentration dependence of onset points in the case of titration by n-hexane and n-heptane are presented in Figure 6. As seen from Figure 6, toluene mole fractions in solution at the asphaltene precipitation onsets are γ = 0.417-0.477 for n-hexane titration and 0.413-0.465 for n-heptane titration (concentration range is 2-15 g/L). One can see that, for employed asphaltenes, n-heptane titration leads to onset delay in comparison to the use of n-hexane. Received data correspond well with the
Figure 4. Linear aggregation model of asphaltenes. Concentration dependence of n-mers in asphaltene/toluene solution. (Inset) Measured average volume of aggregates.
concentration is knowingly below the dimerization threshold, which was reported in the literature earlier.27,28 Normalization of the concentration dependence of average aggregate volumes (V) to the value of asphaltene monomer gives a concentration dependence of average aggregate size NAV (number of monomers in average aggregate). Obtained results were used for evaluation of asphaltene n-mer fractions (X2, dimers; X3, trimers; X4, tetramers; etc.) in toluene solution, which are independent kinetic units. For estimation of asphaltene kinetic unit fractions in the system, a linear asphaltene aggregation model was used, because its description of a nanocolloidal structure seems most adequate. This model was described for asphaltenes by AguileraMercado et al.29 A linear aggregation model implies the addition of the monomer to already existing aggregates, within the quasichemical approach ð2Þ ½A1 þ ½An - 1 ¼ ½An where [An] is the concentration of aggregates that contain n monomer asphaltenes. Aguilera-Mercado et al.29 indicate that it is necessary to take into account the concentration dependence of the aggregation rate constant Y. This constant is not the same at each step of the aggregation process and depends upon the concentration of asphaltenes in the system. In this study, it becomes possible to take this fact into account, because of the obtained concentration dependence of average volumes of asphaltene aggregates in solution. Using an equation that links the average monomer quantity in asphaltene aggregate NAV and the aggregation constant Y, 1þY 2 ¼ pffiffiffiffi - 1 ð3Þ NAV ¼ 1 -Y X it is possible to receive the dependence of Y on the concentration parameter. (27) Structures and Dynamics of Asphaltenes; Mullins, O. C., Sheu, E. Y., Eds.; Plenum Press: New York, 1998; p 438. (28) Evdokimov, I. N.; Losev, A. P. Fuel 2007, 86, 2439–2445. (29) Aguilera-Mercado, B.; Herdes, C.; Murgich, J.; M€ uller, E. A. Energy Fuels 2006, 20, 327–338.
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Table 3. Linear Aggregation Model with the Average Volume of Aggreagtes V, Amount of Monomers in Average Aggregate NAV, Reaction Constant Y, Asphaltene Monomer Fraction X1, and n-mer Fractions X2, X3, X4, X5, X8, X12, and X20 concentration (g/L) log C
C
V (nm3)
NAV
Y
X1
X2
X3
X4
X5
X8
X12
X20
-3 -2 -1.25 -1 0 0.4 1 1.2 1.5 1.75
0.001 0.010 0.056 0.100 1.000 2.512 10.000 15.849 31.623 56.234
15 21 24 25 33 32 42 66 210 310
1 1.4 1.6 1.6 2.2 2.1 2.8 4.4 14 20.6
0.00 0.16 0.23 0.25 0.38 0.36 0.48 0.63 0.86 0.90
1 0.69 0.59 0.56 0.39 0.41 0.27 0.14 0.02 0.008
0.00 0.23 0.27 0.28 0.29 0.29 0.26 0.17 0.03 0.02
0.00 0.06 0.09 0.11 0.16 0.16 0.19 0.16 0.04 0.02
0.00 0.01 0.03 0.04 0.08 0.08 0.12 0.14 0.05 0.03
0.00 0.01 0.01 0.04 0.03 0.07 0.11 0.05 0.03
0.001 0.01 0.04 0.05 0.03
0.001 0.01 0.05 0.04
0.001 0.02 0.03
Figure 6. Onset data versus the asphaltene concentration in toluene. Onset for 2 g/L comes at γ = 0.413 in the case of n-heptane and 0.417 in the case of n-hexane. Onset for 3 g/L comes at γ = 0.422 in the case of n-heptane and 0.425 in the case of n-hexane. Onset for 6 g/L comes at γ = 0.443 in the case of n-heptane and 0.446 in the case of n-hexane. Onset for 15 g/L comes at γ = 0.465 in the case of n-heptane and 0.477 in the case of n-hexane.
volumes of asphaltene aggregates, geometrical assumptions concerning molecules sizes, and interaction energies between components of the investigated oil system. 3.2.1. Statistical Distribution of Molecules in Solvate Shells. This study examines changes in the solubility of asphaltene compounds in model solutions as a result of induced compositional variations of disperse media. The model oil system is composed of asphaltenes (A) dissolved in toluene (T)-precipitant (P) binary solvent. Precipitant means n-hexane or n-heptane. To study how bulk-phase composition changes the immediate surrounding of the asphaltene molecule, it is necessary to calculate a probability of realization of different compositions of solvate shells at fixed molar content of the mixture in a bulk phase. In an A-T-P mixture, the composition of an A solvate shell is surely not like the macroscopic component ratio, because asphaltene molecules prefer to associate with toluene. The model solution composes A, P, and T molecules. Solvate shells arrange around asphaltene molecules. They can involve different amounts of P and T molecules. The probability distribution of filling solvate shell vacancies by
Figure 5. Precipitation onsets. Titration with n-heptane and n-hexane. Optical density at 750 nm for asphaltenes at a concentration range of 2-15 g/L.
results presented in the literature; onsets by an optical analytical signal show that precipitants with a smaller carbon number lead to relatively quick onsets.13,23,30 An increased amount of precipitated asphaltenes with a decreasing n-alkane carbon number is reported earlier.23 The yield of asphaltenes is a function of the alkane precipitant with the same trend.13 3.2. Model of Non-uniform Distribution of Molecules in Solvate Shells. The presented approach allows for estimation of changes of binary solvent (toluene and alkane) components distribution in asphaltene solvate shells at the moment of aggregative stability loss (initial stage of asphaltene precipitation onset). The model is based on experimentally determined onset conditions and estimation of average (30) Ma, C. F.; Yang, Z.; Lin, X. S.; Yang, J. T.; Guo, T. M. Fluid Phase Equilib. 1999, 157, 143–158.
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By analogy, for the quantity of P molecules UAP dZP ¼ XP exp dV kB T Effective molar fractions of P and T molecules around A are dZT dZP XT 0 ¼ and XP 0 ¼ dV dV The probability of the presence j and (1 - j) for T and P molecules in A solvate shell is 3 2 UAT X exp T 7 6 7 6 kB T 7 and ð1 - jÞ j ¼6 4 UAT UAP 5 þ XP exp XT exp kB T kB T 2 3 UAP X exp P 6 7 6 7 kB T 7 ¼6 4 UAT UAP 5 þ XP exp XT exp kB T kB T Then, the probability distribution of A solvate shell vacancies filling by P and T can be estimated using equation 2 3ZT UAT XT exp 6 7 6 7 kB T 7 ΦðZT , ZÞ ¼ CZZT 6 4 UAT UAP 5 þ XP exp XT exp kB T kB T 3 ZP 2 UAP XP exp 7 6 7 6 kB T 7 6 ð6Þ 4 UAT UAP 5 þ XP exp XT exp kB T kB T
Figure 7. Non-interacting molecules. Probability density distribution of the toluene fraction (U = 0) in the solvate shell at different toluene mole fractions in a bulk phase γ.
the precipitant/toluene molecules can be described by the following equation. Neglecting both differences of interaction energies A-T and A-P and sizes of all molecules leads to zero approximation for the probability distribution function31 Z! γZT ð1 - γÞZ - ZT ΦðZT , ZÞ ¼ ð5Þ ZT !ðZ - ZT Þ! where γ is the toluene mole fraction, (1 - γ) is the precipitant mole fraction, Z is the total number of molecules in the solvate shell of the asphaltene, and ZT is the number of toluene molecules in the solvate shell of the asphaltene. The equation is defined for whole numbers of Z and ZT. At zero approximation, A, T, and P molecules are hard non-interacting spheres of the same size. The total number of molecules in the solvate shell is 12 at close packing. According to this assumption, interactions between A-T, A-P, and T-P are neglected. Figure 7 shows how the probability distribution of filling asphaltene solvate shell vacancies by T and P molecules at Z = 12 depends upon γ. When using a hard non-interacting sphere model, the probability distribution of solvate shell composition has extreme width at the equal ratio of the component. Varying γ gives a symmetrical picture. The next approximation takes into account the interaction energy of asphaltenes with T and P molecules. The IIP leads to the difference between the equilibrium concentration of P and T around A molecule and the bulk concentration of P and T. If the A-T interaction energy is UAT and the A-P interaction energy is UAP, according to statistics of BoltzmannGibbs, quantities of T and P molecules in dV volume around A are UAT dV dZT ¼ XT exp kB T
T where CZ Z = (Z!)/(ZT!(Z - ZT)!). In this model, the probability of solvate shell formation depends upon dimensionless energy U, which characterizes the difference between A-T and A-P interaction energies, divided into heat energy kBT (eq 7). At a fixed value U for toluene-precipitant mixtures of different bulk molar composition, the quantity of T molecules in the solvate shell varies. UAT - UAP ð7Þ U ¼ kB T
(31) Hirschfelder, J. O.; Bird, R. B.; Curtiss, C. F. The Molecular Theory of Gases and Liquids; John Wiley and Sons, Inc.: New York, 1964; p 1280.
(32) Bakhshiev, N. G. Photophysics of Dipole-Dipole Interactions. Processes of Solvation and Complexation; St. Petersburg State University Publishers: St. Petersburg, Russia, 2005; p 500.
At fixed U for solutions of different mole toluene/n-alkane ratios, the number of precipitant molecules in asphaltene solvate shells (Z - ZT) runs a range of values. The set of probability distribution curves shift to the region of lower (Z - ZT) values. In comparison to zero approximation performance, the picture becomes asymmetrical (Figure 8). The picture demonstrates the tendency of asphaltenes to envelope themselves by the solvate shell that is composed mainly from toluene molecules. Such an approach is successfully used in the photophysics of dyes.32 3.2.2. Criteria of Onset. Asphaltene precipitation onset data, which was demonstrated in the experimental part, were carried out for two types of precipitants. The control parameter that defines the composition of solvate shells is U (eq 7). Physical interpretation of this non-dimensional parameter shows the difference of the pair interactions for
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Figure 9. Energy map defines the fraction of precipitant molecules in the solvate shell of the asphaltene aggregate.
Figure 8. Interacting particles. Probability density distribution (U = 3) of precipitant in the solvate shell of the asphaltene aggregate.
asphaltene/toluene/n-heptane is equal to 0.16; U for asphaltene/toluene/n-hexane is 0.78. The distribution probability of T and P molecules in A solvate shell depends upon the U value. On the basis of calculated U values for systems with n-hexane and n-heptane, energy maps were made. The energy maps show maximum probability of A solvate shell composition in investigated solution with given γ. On Figure 9, one can see how the fraction of precipitant molecules ZP included in the solvate shell of the asphaltene aggregate depends upon γ (eq 1) for two types of precipitants: n-heptane and n-hexane (curves are presented for calculated U values). These graphs allow for estimation of the fraction of precipitant molecules in asphaltene aggregate solvate shells at the moment of aggregative stability loss (experimentally determined onset composition of the bulk phase γ). It is assumed that aggregative stability loss means the initial stage of asphaltene flocculation in the system. When asphaltene solvate shells reach estimated critical compositions, colloid asphaltene solution looses its stability and the association of two no longer stable aggregates becomes energetically favorable (Figure 10). The tendency of asphaltenes to interact with T molecules works here. To make “savings” of the decreasing toluene fraction in the system, it now becomes favorable for aggregates to be in associated forms and to continue enveloping themselves mainly by T molecules. Coordination number Z1, defining a solvate shell of asphaltene aggregate, depends upon geometrical parameters of A, T, and P molecules. The geometrical parameters can be estimated from physicochemical characteristics of toluene, precipitants, and asphaltene (Table 1). Also, the average asphaltene aggregate size, which exists at a given concentration, is important. For the hard spheres approximation, the coordination number Z1 is determined by the number of “sites” on a surface of asphaltene aggregate. A relation determines the radius of the solvent molecule 1=3 3M ð11Þ R ¼ 4πNA F
asphaltene-toluene and asphaltene-precipitant divided by the thermal motion energy (kBT). The next procedure was used to determine U for each investigated model oil system. At the mixture of two moderately polar substances,33 an energy of mixing ΔU12 will be determined by the expression pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð8Þ ΔU12 ¼ U11 U22 where U11 and U22 are a pair interaction energies of individual components. n-Heptane and n-hexane are precipitants for asphaltenes, and pair interactions of these molecules with asphaltene are considered in some works.34-36 Consequently, the parameter U in the case of the three-component system (solventasphaltene-precipitant) can be expressed through energies of pair interactions pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi UAA UTT - UAA UPP UAT - UAP ¼ ð9Þ U ¼ kB T kB T where UAA is the interaction energy for asphalteneasphaltene, UTT is the interaction energy for toluenetoluene, and UPP is the interaction energy for n-heptanen-heptane (or n-hexane-n-hexane). For the calculation of energies UTT and UPP, the solubility parameter definition is used.10 The designed formula for U looks like U ¼
UAA 1=2 ðδT VT, m 1=2 -δP VP, m 1=2 Þ kB T
ð10Þ
where δT and δP are solubility parameters of toluene and precipitant (MPa0.5) and VT,m and VP,m are molar volumes of toluene and precipitant (cm3/mol). The interaction energy for two model asphaltenes UAA was received in a previous work.34 Data for the calculation are introduced in Table 1. The calculated U value for (33) Prigogine, I. The Molecular Theory of Solutions; North Holland Publishing Company: Amsterdam, The Netherlands, 1957; p 448. (34) Headen, T. F.; Boek, E. S.; Skipper, N. T. Energy Fuels 2009, 23, 1220–1229. (35) Rogel, E. Colloids Surf., A 1995, 104, 85–93. (36) Ortega-Rodrı´ guez, A.; Cruz, S. A.; Gil-Villegas, A.; GuevaraRodrı´ guez, F.; Lira-Galeana, C. Energy Fuels 2003, 17, 1100–1108.
where M is the molecular weight, NA is Avogadro’s number, and F is the density. 2272
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aggregate consists of P molecules on 55%, while other vacant cites are occupied by T. In the case of n-hexane titration for stability loss, 39% of the solvate shell is enough. These estimations are based on energy maps. The solvent composition at the onset point is known from experiment; this value is chosen on the x axis. The corresponding value on the y axis is a composition of the solvate shell of the no longer stable aggregate. Coordination number Z2 of the associated aggregate was calculated and made 159 vacant cites. This value is less than the total sum of vacant cites of two single no longer stable aggregates: 159 < (107 2). It is assumed that decreasing the T molecules fraction, because of titration, leads the system to reorganization according to the IIP of components. In the case when 2 g/L solution is titrated by n-heptane, 59 n-heptane molecules and 48 toluene molecules at the onset point surround an average aggregate. Association of two unstable aggregates gives a larger aggregate with Z2 = 159; 96 vacant sites are occupied by T molecules, and the other 63 are given to P (40% of the solvate shell). As the fraction of n-heptane in the system increases, this percentage grows until it reaches a value of 55%, when this associated aggregate also loses stability and becomes ready to associate by an analogous scheme. Cluster formation in the system is proposed according to the presented scheme. It leads to the formation of floccules and further asphaltene precipitation. From this moment, optical density starts to grow mainly because of light scattering of the asphaltene particles.1
Figure 10. Criteria of onset. (Left) Asphaltene aggregate in toluene solution. (Right) Asphaltene aggregate in toluene/precipitant solution at the onset ratio with the critical amount of precipitant fraction in the solvate shell, which is no longer stable. Associated asphaltene aggregate composed of two no longer stable aggregates with the solvate shell made mainly from toluene molecules. ZT* is the fraction of toluene in the solvate shell of the unstable aggregate.
At further calculations, the mean radius of a solvent/ precipitant molecule was equal to Rm = 0.37 nm; this rough estimate does not have a significant influence on the solvent molecules distribution in A solvate shells. The aggregate radius was taken from the concentration dependence of asphaltene aggregate volumes (Figure 4). The asphaltene aggregate was taken as a hard spherical particle. For the investigated concentration of 2 g/L, the calculated radius is RA = 2 nm. For calculation of the Z1 coordination number of the asphaltene nanoaggregate, the equation used was Z1 ¼
4πðRA þ Rm Þ2 k πRm 2
ð12Þ
Conclusions In multi-component petroleum systems, asphaltenes are centers of attraction for molecules with similar energies (resins and aromatics). Asphaltenes play a critical role in system organization: they repulse saturated hydrocarbons and have a tendency to form solvate shells out of resins and aromatics. Saturated hydrocarbons can still be present in asphaltene solvate shells in small amounts. Within the framework of the model oil system that consists of asphaltene A, toluene T, and precipitant P (n-heptane/ n-hexane), the molecular distribution of components in nearest coordination spheres of asphaltenes was investigated. Toluene/precipitant ratios in asphaltene solvate shells are determined by differences in interaction energies for A-T and A-P pairs. These ratios are calculated from molecular distribution functions and experimentally determined onsets. The model of non-uniform distribution of solvent components in solvate shells of asphaltene aggregates at the first stage of precipitation onset is proposed. The linear aggregation model was used for characterization of asphaltene solutions in toluene; n-mers fractions were calculated for concentrations in the range of 0.00156 g/L. The concentration dependence of average asphaltene aggregate sizes in toluene solution was measured by the polarization of fluorescence. The concentration dependence of the aggregation rate constant is calculated on the basis of experimental data, and it becomes possible to take it into account in calculations within the linear aggregation model.
where RA is the radius of the asphaltene nanoaggregate (nm), Rm is the radius of the molecule included into the solvate shell of the asphaltene nanoaggregate (nm), and k is the packing coefficient for hard spheres.37 The coefficient k is equal to 0.65, which corresponds to an extreme case. The result of association of two nanoaggregates with radius RA and coordination number Z1 is the associated aggregate with coordination number Z2 and radius RDA. The new associated aggregate is approximated by a spherical particle with a volume that is, in fact, the sum of the volumes of two nanoaggregates. From the volume of the associated aggregate (which is assumed to be spherical), its radius can be calculated. Further, the coordination number Z2 can be calculated knowing Rm and RDA. To obtain values Z1 and Z2 (where Z1 is the coordination number of the asphaltene nanoaggregate and Z2 is the coordination number of two associated asphaltene nanoaggregates), the following equation was used: !2 4πðRDA þ Rm Þ2 21=3 RA k ¼ 4k 1 þ ð13Þ Z2 ¼ Rm πRm 2 where RDA is the radius of two associated asphaltene nanoaggregates (nm). Coordination number Z1 for the average asphaltene aggregate at a concentration of 2 g/L is 107. This means that the aggregate has 107 places for solvent/precipitant molecules. As the precipitant fraction in the bulk phase of the system increases, the fraction of T molecules in the solvate shell of the aggregate decreases. At the moment of stability loss because of n-heptane titration, the solvate shell of the
Nomenclature γ = toluene mole fraction XT = mole amount of toluene in the bulk phase XP = mole amount of precipitant in the bulk phase
(37) Anikeenko, A. V.; Medvedev, N. N. J. Struct. Chem. 2007, 48, 774–781.
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[An] = concentration of aggregates made of n individual asphaltene molecules X = asphaltene monomer fraction Y = reaction constant NAV = average aggregate size (number of monomers in average aggregate) Z = total number of molecules in the solvate shell of the asphaltene ZT = number of toluene molecules in the solvate shell of the asphaltene ZP = number of precipitant molecules in the solvate shell of the asphaltene Z1 = coordination number of the asphaltene nanoaggregate Z2 = coordination number of two associated asphaltene nanoaggregates XT0 = effective mole fraction of toluene XP0 = effective mole fraction of precipitant j = probability of finding toluene molecules in the solvate shell of the asphaltene RA = radius of the asphaltene nanoaggregate (nm)
RDA = radius of two associated asphaltene nanoaggregates (nm) Rm = radius of the molecule included in the solvate shell of the asphaltene nanoaggregate (nm) k = packing coefficient for hard spheres UAT = interaction energy between an asphaltene molecule and a toluene molecule UAP = interaction energy between an asphaltene molecule and a precipitant molecule NA = Avogadro’s number (6.022 1023 mol-1) kB = Boltzmann constant (1.38 10-23 J/K) T = temperature (K) M = molecular weight (g/mol) F = density (g/cm3) δ = solubility parameter (MPa0.5) Vm = molar volume (cm3/mol) Subscripts A = relating to asphaltenes T = relating to toluene P = relating to precipitant (n-hexane or n-heptane)
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