Energy Fuels 2011, 25, 503–508 Published on Web 12/07/2010
: DOI:10.1021/ef1010397
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Molecular Dynamics Simulations of Asphaltene Aggregation in Supercritical Carbon Dioxide with and without Limonene† Thomas F. Headen‡,§ and Edo S. Boek*,§, ‡
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Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom, § Schlumberger Cambridge Research, High Cross, Madingley Road, Cambridge CB3 0EL, United Kingdom, and Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, United Kingdom Received August 7, 2010. Revised Manuscript Received November 6, 2010
We study the aggregation of asphaltene in supercritical carbon dioxide (sc-CO2) using molecular dynamics (MD) computer simulations. We use a well-defined asphaltene molecular structure (asphaltene “C” from Headen, T. F.; Boek, E. S.; Skipper, N. T. Energy Fuels 2009, 23, 1220-1229) obtained using a preliminary version of the quantitative molecular representation algorithm (Boek, E. S.; Yakovlev, D. S.; Headen, T. F. Energy Fuels 2009, 23, 1209-1219). We compare the aggregation of asphaltene in sc-CO2 with our previous MD aggregation studies in toluene and heptane. Also, we study asphaltene aggregation in the presence of limonene, a well-known aggregation inhibitor. First, we present simulations of sc-CO2 at a range of temperatures and pressures to test the ability of the force field used to correctly predict the system density. Simulations of asphaltenes were conducted in a similar fashion to those presented by Headen, T. F.; Boek, E. S.; Skipper, N. T. Energy Fuels 2009, 23, 1220-1229 for simulations in toluene and heptane, six asphaltene molecules in a bath of solvent at 7 wt %. Simulations were conducted at a range of different temperatures and pressures in both sc-CO2 and a 50 wt % mixture of sc-CO2 with limonene. Asphaltenes in sc-CO2 showed a strong propensity for aggregation, with all six molecules forming a strongly bound aggregate at all temperatures and pressures tested. Simulations in 50 wt % limonene/sc-CO2 show a considerable decrease in the aggregation compared to pure CO2. The temperature and pressure dependence of asphaltene aggregation in the mixture was complex, showing minimum aggregation (for the limited range of conditions studied) at 150 bar and 350 K.
that limonene (Figure 1) can be used as a dispersant to remove and/or prevent precipitation of the asphaltenes. In the past decade, the use of limonene has expanded tremendously to remove asphaltene from well tubulars.5 In this study, we aim to compare asphaltene aggregation in CO2 with and without limonene to aggregation in toluene and heptane, at the molecular level.
Introduction Molecular dynamics (MD) simulations are able to predict the behavior of asphaltenes on the molecular level.1,2 For these simulations, it is very important to use asphaltene molecular structures that are truly representative of experimental observations. The development of a modified quantitative molecular representation (QMR) technique has allowed simulations of asphaltene molecular structures consistent with available experimental data [mass spectrometry, nuclear magnetic resonance (NMR), and elemental analysis].2 Previous simulations using these molecules have considered aggregation in toluene and heptane1 and adsorption on a calcite surface.3 In this report, we study asphaltene aggregation in supercritical carbon dioxide (sc-CO2), with and without the presence of a dispersant limonene. sc-CO2 is used as one method of enhanced oil recovery (EOR); however, a challenge to its use is the precipitation of asphaltenes.4 Experimental studies have shown
MD Simulation Methods Classical MD uses well-defined classical intra- and intermolecular potentials to calculate interatomic forces. The system is allowed to evolve over time by stepwise integration of the equations of motion. Using this method, it is possible to simulate systems containing a total of ∼10 000 atoms over a few nanoseconds on ∼8 processor nodes in reasonable time (a few days). For this study, the GROMACS MD code6 with the optimized potentials for liquid simulations-all atoms (OPLS-AA) forcefield parameters7,8 for asphaltenes and limonene and the EMP2 rigid CO2 force field9 were used. The use of these force fields has been proven to work for asphaltenes in previous papers
† Presented at the 11th International Conference on Petroleum Phase Behavior and Fouling. *To whom correspondence should be addressed. E-mail: e.boek@ imperial.ac.uk. (1) Headen, T. F.; Boek, E. S.; Skipper, N. T. Energy Fuels 2009, 23, 1220–1229. (2) Boek, E. S.; Yakovlev, D. S.; Headen, T. F. Energy Fuels 2009, 23, 1209–1219. (3) Headen, T. F.; Boek, E. S. Energy Fuels 2010, manuscript submitted for publication. (4) Okwen, R. T. Formation damage by CO2 induced asphaltene precipitation. Proceedings of the International Symposium and Exhibition on Formation Damage Control; Lafayette, LA, Feb 15-17, 2006; SPE 98180.
r 2010 American Chemical Society
(5) Rae, P.; Di Lullo, G.; Ahmad, A. Towards environmentally friendly additives for well completion and stimulation operations. Proceedings of the Society of Petroleum Engineers (SPE) Asia Pacific Oil and Gas Conference and Exhibition; Jakarta, Indonesia, April 17-19, 2001; SPE 68651. (6) van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. J. Comput. Chem. 2005, 26, 1701–1718. (7) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. J. Am. Chem. Soc. 1996, 118, 11225–11236. (8) Jorgensen, W. L.; Laird, E. R.; Nguyen, T. B.; Tirado-Rive, J. J. Comput. Chem. 1993, 14, 206–215. (9) Harris, J. G.; Yung, K. H. J. Phys. Chem. 1995, 99, 12021–12024.
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Figure 2. Chemical structure of asphaltene C, an “island”-type asphaltene structure with one large pericondensed aromatic core. This image was reproduced with permission from ref 1.
Figure 1. Chemical structure of limonene.
(e.g., see ref 10). The GROMACS suite of programs contains libraries of many force fields. All angle, dihedral, improper dihedral, Lennard-Jones (LJ), and coulomb potentials for the OPLS-AA force field were available in GROMACS. The OPLS force field has been shown to work well for aromatic liquids in reproducing experimental data.5,11 The EMP2 force field has been shown to accurately predict the critical properties of CO2.9 For asphaltenes and limonene, rigid bond lengths were used to remove the fastest moving molecular motions; this was achieved using the SHAKE algorithm.12 Bond angles and dihedral angles remained flexible (within appropriate force fields) to allow for molecular flexibility. Carbon dioxide was simulated as a completely rigid molecule. The SHAKE algorithm is unstable in keeping linear triatomics rigid; therefore, the molecule was setup as follows. The mass and moment of inertia of the molecule are represented as diatomic with a rigid bond. The interaction sites for carbon and oxygen are then built on the “scaffolding” using the GROMACS virtual site construction. A time step of 1 fs was used for all simulations. Periodic boundary conditions with the minimum image convention are used, so that a small box of ∼10 000 atoms can represent the bulk. Long-range coulomb intermolecular forces are treated using the particle mesh Ewald (PME) technique,13 which allows for the use of fast Fourier transforms (FFTs). The short-range coulomb cutoff was set to 0.9 nm (beyond 0.9 nm, coulomb interactions are calculated in reciprocal space using the PME method), and the LJ forces were cut off at 1.24 nm. Long-range dispersion forces were corrected for both energy and pressure. Constant temperature simulations were achieved using the Nose-Hoover thermostat, and constant pressure simulations used Parinello-Rahman pressure coupling. The asphaltene structure chosen for use in this simulation study was “asphaltene C” from ref 1. This is a structure generated from a preliminary version of QMR, which of the three molecules studied in ref 1 is believed to have the closest match to the “archetypical” asphaltene molecule (i.e., 4-8 fused aromatic rings in a single aromatic core).14 Its molecular structure is given in Figure 2. Please note that this is an island model.15
In recent years, there has been an increasing effort to understand the structure of asphaltene aggregation on a molecular level using molecular simulation.16-21,26 Some of the first simulations to be conducted on “island”-type22 asphaltene models were by Pacheco-S anchez et al.16 They used MD to show that asphaltene aggregation does occur spontaneously for smaller asphaltene molecules forming di-, tri-, and tetramers during a short 100 ps simulation. The structure of the aggregates formed showed no overriding structure type: face-to-face, offset stacked, and T-shaped aggregates were observed. Simulations of asphaltene dimers with explicit solvent molecules conducted over 100 ps by Carauta et al.18 have shown that the asphaltene dimers bind faceto-face at a distance of ∼3.6 A˚ in heptane and ∼5 A˚ in toluene. Furthermore, they show that the effect of an increasing temperature (from 323 to 573 K) is to decrease the distance between the asphaltene dimer. A similar temperature dependence has been observed by Zhang et al.20 from MD simulations of asphaltene molecules in model asphalts over 3 ns. For any of these simulation studies to yield meaningful results, the model asphaltene structures used must be representative of asphaltenes as a whole. Indeed, a range of different types of asphaltene molecular models have been used in asphaltene simulation, from archipelago-type structures, with multiple small aromatic islands connected by aliphatic chains,23 to large island asphaltenes, with a single large aromatic core.24 Experimental studies using fluorescence depolarization measurements,22 high-resolution mass spectroscopy,25 and ultraviolet (UV) absorption and fluorescence emission26,27 have all shown an asphaltene structure with a single aromatic core (possibly two) containing 4-10 aromatic rings. Previous studies have used “average” model structures that are consistent with experimental data.18,28,29 Sheremata et al.30 have developed QMR as a method for generating a group of structures that best represent experimental data (mass spectrometry, NMR, and (19) Carauta, A. N. M.; Correia, J. C.G.; Seidl, P. R.; Silva, D. M. THEOCHEM 2005, 755, 1–8. (20) Zhang, L.; Greenfield, M. L. Energy Fuels 2007, 21, 1102–1111. (21) Zhang, L.; Greenfield, M. L. J. Chem. Phys. 2007, 127, No. 194502. (22) Groenzin, H.; Mullins, O. C. Energy Fuels 2000, 14, 677–684. (23) Ortega-Rodrı´ guez, A.; Cruz, S. A.; Gil-Villegas, A.; GuevaraRodrı´ guez, F.; Lira-Galeana, C. Energy Fuels 2003, 17, 1100–1108. (24) Murgich, J.; Rodrı´ guez, M. J.; Aray, Y. Energy Fuels 1996, 10, 68–76. (25) Rodgers, R. P.; Marshall, A. G. Petroleomics: Advanced characterization of petroleum-derived materials by Fourier transform ion cyclotron resonance mass spectrometry (FT-ICR MS). In Asphaltenes, Heavy Oils and Petroleomics; Mullins, O. C., Sheu, E. Y., Hammami, A., Marshal, A. G., Eds.; Springer: New York, 2007; Chapter 3. (26) Ruiz-Morales, Y.; Wu, X.; Mullins, O. C. Energy Fuels 2007, 21, 944–952. (27) Ruiz-Morales, Y.; Mullins, O. C. Energy Fuels 2007, 21, 256–265. (28) Groenzin, H.; Mullins, O. C. Energy Fuels 2000, 14, 677–684. (29) Murgich, J.; Rodrı´ guez, J. M.; Aray, Y. Energy Fuels 1996, 10, 68–76. (30) Sheremata, J. M.; Gray, M. R.; Dettman, H. D.; McCaffrey, W. C. Energy Fuels 2004, 18, 1377–1384.
(10) Boek, E. S.; Padding, J. T.; Headen, T. Multi-scale simulation of asphaltene aggregation and deposition in capillary flow. Faraday Discuss. 2010, 144, 271–284. (11) van der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. J. Comput. Chem. 2005, 26, 1701–1718. (12) van Gunsteren, W. F.; Berendsen, H. J. C. Mol. Phys. 1977, 34, 1311–1327. (13) Darden, T.; York, D.; Pedersen, L. J. Chem. Phys. 1993, 98, 10089–10092. (14) Asphaltenes, Heavy Oils and Petroleomics; Mullins, O. C., Sheu, E. Y., Hammami, A., Marshal, A. G., Eds.; Springer: New York, 2007. (15) Groenzin, H; Mullins, O. C. Energy Fuels 2000, 14, 677–684. (16) Pacheco-S anchez, J. H.; Zaragoza, I. P.; Martı´ nez-Magadan, J. M. Energy Fuels 2003, 17, 1346–1355. (17) Pacheco-S anchez, J. H.; Alvarez-Ramı´ rez, F.; Martı´ nezMagad an, J. M. Energy Fuels 2004, 18, 1676–1686. (18) Carauta, A. N. M.; Seidl, P. R.; Chrisman, E. C. A. N.; Correia, J. C. G.; Menechini, P. O.; Silva, D. M.; Leal, K. Z.; de Menezes, S. M. C.; de Souza, W. F.; Teixeira, M. A. G. Energy Fuels 2005, 19, 1245–1251.
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Table 1. Densities for Supercritical (350 and 400 K) and Liquid (300 K) Carbon Dioxide at Different Pressures from MD Simulation and Experiment (in Parentheses) density (g cm-3)
100 bar
150 bar
200 bar
300 K 350 K 400 K
0.7703 (0.8026) 0.2119 (0.2292) 0.1551 (0.20)
0.8464 (0.8668) 0.4021 (0.4503) 0.2550 (0.30)
0.8864 (0.9060) 0.5831 (0.6154) 0.3618 (0.45)
Table 2. Comparison of Experimental and Simulated Densities and Enthalpies of Vaporization for Liquid Limonene
experiment32 (at 298 K) simulation (at 298 K)
density (g cm-3)
enthalpy vaporization (kJ mol-1)
0.8411 0.8413
49.6 53.9
elemental analysis) rather than just being consistent with the data. It was shown that 5-6 molecules were needed to represent the experimental data well. The method is based on an algorithm that builds a very large number of asphaltene molecules from building blocks. From this set, the best mixture of 5-6 molecules is chosen to fit the experimental data. This method has recently been updated2 to allow for the formation of smaller (one aromatic core) and three-dimensional structures. This gives the best fit to experimental data with low-molecularweight asphaltenes (500-2000 amu). This is quite different from the asphaltene molecular weight used by Sheremata et al.,30 where a molecular weight of ∼4000 Da, determined from vapor pressure osmometry (VPO), was used. This tends to the conclusion that asphaltenes have just one or perhaps two aromatic cores, because larger archipelago-type models would have too high a molecular weight. Recently, Headen et al. have studied the aggregation of asphaltenes in toluene and heptane using MD simulations.1 Here, we extend this approach to aggregation in sc-CO2 using one of the asphaltene structures considered in that paper.
Figure 3. Snapshot of asphaltene simulation in carbon dioxide at 350 K and 150 bar. Carbon dioxide molecules have been removed for clarity.
The match between the experimental and simulated densities and enthalpies of vaporization is close. We can therefore conclude that the EMP2 and OPLS-AA force fields are suitable for simulating carbon dioxide and limonene, respectively. Simulations of Asphaltene Aggregation in CO2
Simulations of Bulk CO2 and Liquid Limonene
Simulations were conducted with six asphaltene molecules in a bath of CO2 at 7 wt % (1317 CO2 molecules). Six molecules was enough to observe nano-aggregation on a reasonable time scale. Similar size simulations were run in toluene and heptane (at the same weight percentage of asphaltene),1 so that we can compare directly for the same system sizes. The simulation box was created by solvating a periodic array of six asphaltene molecules with randomly oriented CO2 molecules. The box was equilibrated by a short 50 ps NVT run. Molecular positions and energies were monitored over a 20 ns NPT simulation. Statistics for the cumulative coordination number were only analyzed after equilibrium density was reached. Simulations were conducted at the same temperatures and pressures as for bulk CO2 above. In all conditions, there was quick and lasting aggregation of the asphaltene molecules, forming an aggregate of six molecules, mainly by stacking of the aromatic cores. Figure 3 shows a snapshot from the simulation at 150 bar and 350 K. As with simulations in toluene and heptane, the aggregate structure was not rigid, there was no single minimum energy structure, and the asphaltene molecules move around each other, with parallel stacking being the preferred orientation. The aggregation appears much stronger than in toluene and heptane were simulations showed a maximum aggregate size of three molecules. The calculation of the asphaltene-asphaltene radial distribution function, g(r), is not appropriate where all asphaltene molecules aggregate (average density is not reached at long distances). Therefore, the cumulative coordination number has
The ability of the EMP2 force field to correctly simulate the supercritical and liquid properties was tested by running isothermal-isobaric (NPT) simulations at a range of different temperatures (300, 350, and 400 K) and pressures (100, 150, and 200 bar) and comparing the predicted density to the experimental density. Note that, at 300 K, carbon dioxide is a liquid rather than supercritical. Each simulation box contained 500 CO2 molecules in a cubic box. Each simulation was run for 1 ns, and the average density was taken after a 50 ps equilibration period. Table 1 shows the simulation and experimental (in parentheses) densities at each temperature and pressure. Accurate densities for liquid and sc-CO2 were available for temperatures at 300 and 350 K.31 For 400 K, less accurate data were available. The simulation appears to consistently underpredict the experimental density, with simulations at conditions close to the critical point (304 K and 73.8 bar) being a reasonable match with the experiment. The applicability of the OPLS-AA force field to limonene was tested by a NPT simulation of 343 molecules in a cubic box over 2 ns. The density was calculated as for CO2, and the enthalpy of vaporization was calculated by a comparison of the system potential energy to that of a single molecule in vacuum. Table 2 presents the experimental and simulated properties. (31) Jarrell, P. M.; Fox,C. E.; Stein, M. H.; Webb, S. L. Practical Aspects of CO2 Flooding; Society of Petroleum Engineers (SPE): Richardson, TX, 2002; SPE Monograph Series, Vol. 23.
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Figure 6. Distance-time plot between the center of mass of asphaltenes in carbon dioxide at 150 bar and 400 K.
Figure 4. Asphaltene-asphaltene cumulative number distribution function for simulations of six asphaltene molecules in CO2 (solid line) and a 50 wt % mixture of CO2 and limonene (dashed line) at 7 wt % at 350 K.
Figure 7. Distance-time plot between the center of mass of asphaltenes in toluene under standard conditions, showing considerably less aggregation than in CO2, with only the formation of di- and trimers. (Figure 7 is taken from reference 1).
Figure 5. Asphaltene-asphaltene cumulative number distribution function for simulations of six asphaltene molecules in CO2 (solid line) and a 50 wt % mixture of CO2 and limonene (dashed line) at 7 wt % at 150 bar.
been calculated instead. This is defined as the number of molecules at a distance lower than a distance r and can be calculated from the simulation g(r) using Z r FgðrÞ4πr2 dr NðrÞ ¼ 0
where r is the number density of asphaltenes per unit volume. Figure 4 shows the N(r) for different temperatures at 150 bar. Figure 5 shows the N(r) for different pressures at 350 K. There is some variation between the plots but no systematic change with either temperature or pressure, suggesting that these changes are due to random variation between the simulations (this is confirmed by looking at similar plots at other temperatures and pressures).
Figure 8. Distance-time plot between the center of mass of asphaltenes in heptane under standard conditions, showing considerably less aggregation than in CO2, with only the formation of di- and trimers. (Figure 8 is taken from reference 1).
The dynamical behavior of the asphaltenes in the aggregate can be studied by following the distance between the asphaltene pairs as a function of time. Figure 6 shows the distances between one of the asphaltenes and the five other asphaltenes in the simulation at 150 bar and 400 K. Similar aggregation behavior is seen at other temperatures and pressures.
(32) Chickos, J. S.; Acree, W. E. J. Phys. Chem. Ref. Data 2003, 32, 519.
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Table 3. Equilibrium Density of Each System after NPT Simulation for 7 wt % Asphaltene in a 50 wt % Mixture of Limonene and Carbon Dioxide pressure (bar)
temperature (K)
system density (g cm-3)
150 150 150 100 200
300 350 400 350 350
0.9126 0.8357 0.7070 0.7914 0.8332
Figure 11. Snapshot of simulation of 7 wt % asphaltene in a 50 wt % mixture of limonene and carbon dioxide (350 K and 150 bar) at ∼11 ns (see Figure 9), showing that the six-molecule aggregate has split up to a trimer, a dimer, and a single molecule.
Figure 9. Distance-time plot for asphaltene-asphaltene interactions for simulation of 7 wt % asphaltene in a 50 wt % mixture of limonene and carbon dioxide at 150 bar and 350 K.
toluene and heptanes (Figures 7 and 8), respectively, taken from ref 1. There is considerably closer aggregation in CO2 than in toluene and heptane, where we observe no aggregates larger than trimers. The simulations show that sc-CO2 is a strong precipitant for asphaltenes. Simulations of Asphaltene Aggregation in CO2 with Limonene Simulations were conducted as above over 20 ns, with six molecules of the asphaltene in solvent at 7 wt %. In this case, the bulk carbon dioxide was replaced by a 50 wt % mixture of limonene and CO2, 212 molecules of limonene and 659 molecules of CO2. Simulations were conducted in the NVT ensemble, with a 0.5 ns NPT run prior to this to ensure that the system had reached equilibrium density. Table 3 gives the density for each system. The trends observed are complex. Figures 4 and 5 compare the asphaltene-asphaltene N(r) in carbon dioxide and the limonene/CO2 mixture. It is clear that limonene does reduce aggregation. The aggregation behavior with temperature and pressure appears to be complex. Figure 4 shows that the minimum aggregation occurs at 150 bar, with more aggregation at 200 bar and the most at 100 bar. This implies that there is an optimum pressure to maximize the solubility of asphaltenes in the CO2/limonene mixture. A similar aggregation behavior has been reported by Gonzalez et al. from application of the perturbed-chain statistical associating fluid theory (PC-SAFT) equation of state to model live oils with CO233 but at higher temperatures. Figure 9 shows the distance-time plots for all asphaltene pairs for the simulation at 150 bar and 350 K. Again, this shows that there is no one minimum energy aggregate structure.
Figure 10. Snapshot of simulation of 7 wt % asphaltene in a 50 wt % mixture of limonene and carbon dioxide (350 K and 150 bar) at ∼4.5 ns (see Figure 9), showing aggregation of all six molecules.
The plot shows very close distances between asphaltene pairs, indicating close aggregation by stacking. The most important point to note is that distances between pairs do change the course of the simulation, showing that the aggregate structure is not constant but changes over time. There is not one minimum energy structure. This plot can be compared to identical simulations (six asphaltene molecules at 7 wt %) in
(33) Gonzalez, D. L.; Vargas, F. M.; Hirasaki, G. J.; Chapman, W. G. Energy Fuels 2008, 22, 757–762.
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Conclusions This study represents an expansion of the simulation techniques of QMR-generated asphaltenes outlined in refs 1 and 2 to new solvent systems. The GROMACS MD simulation package and the EMP2 carbon dioxide force field has been shown to predict the properties of bulk sc-CO2 with reasonable accuracy. Simulations of six asphaltene molecules in bulk carbon dioxide at supercritical and liquid conditions show very strong aggregation, with all six molecules forming a dense aggregate within a few nanoseconds. However, the asphaltene dynamics show that there is not one preferred structure, with asphaltenes moving around each other in the aggregate through the course of the simulations. Parallel stacking of the aromatic cores is the preferred method of aggregation. Simulations of asphaltenes in a 50 wt % mixture of carbon dioxide and the dispersant solvent limonene show considerably decreased aggregation. The temperature and pressure dependence of asphaltene aggregation in the mixture was complex, showing minimum aggregation (for the limited range of conditions studied) at 150 bar and 350 K. It should be noted that results presented in this study are only for a single asphaltene srtucture and for a small simulation system. However, it does show the usefulness and generality of the approach, with the ultimate aim to be able to predict asphaltene phase behavior in a range of different chemical and physical environments. We find nano-aggregate structures consistent with the experiment, so that we can claim that our work is consistent with the island model adopted. Future work will include the simulation of much larger systems of a larger number of asphaltene molecules in a range of solvents. This will show if finite-size effects are limiting the aggregation for the smaller systems. The effect of resin molecules in a system that is more representative of the maltenes must also be considered, along with a mixture of representative asphaltene structures. Specifically, for investigating the effects of CO2 EOR, a more complex system with all saturates, aromatics, resins, and asphaltenes (SARA) fractions must be used to obtain more realistic results. In future studies, we will also address the dispersant influence on the molecular structure of asphaltene agglomerations.
Figure 12. Histogram of the asphaltene aggregate size in the range of solvents.
The plot clearly shows at ∼4.5 ns the formation of an aggregate of all six asphaltene molecules; all distances between the asphaltene centers of mass are below 2 nm. This aggregate is shown in Figure 10. However, this does not last for long, and at ∼11 ns, this has broken down to a trimer, a dimer, and a single molecule, shown in Figure 11. We can also compare the effect of different solvents on asphaltene aggregation by calculating a histogram of the number of molecules in each aggregate (see Figure 12). Molecules are defined to be aggregated when the minimum distance between two molecules in the cluster is less than 0.3 nm. It is clear that, in carbon dioxide, all six molecules form a single aggregate. Toluene and heptane show reasonably similar behavior, with most populated aggregation numbers of 3 and 2, respectively. For the limonene/CO2 mixture, there is a gradual increase in the population of each aggregation number, with the most popular being six molecules. Importantly, aggregation numbers up to six are seen in these solvents; this indicates that there are some finite size effects occurring. A larger simulation box is required to obtain more robust results for the aggregation number.
Acknowledgment. The authors thank the Natural Environment Research Council, U.K., for funding and Schlumberger Cambridge Research for use of computer resources.
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