simulation of asphaltene aggregation through molecular ... · an issue of continuous importance...

Simulation of Asphaltene Aggregation through Molecular Dynamics:Insights and LimitationsT. F. Headen,†,‡ E. S. Boek,†,§ G. Jackson,† T. S. Totton,∥ and E. A. Muller*,†

†Department of Chemical Engineering, Imperial College London, London SW7 2AZ, U.K.‡ISIS Neutron and Muon Source, Science and Technology Facilities Council, Rutherford Appleton Laboratory, Harwell Campus,Didcot OX11 0QX, U.K.§Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, U.K.∥BP Exploration Operating Co. Ltd., Sunbury-on-Thames TW16 7LN, U.K.

*S Supporting Information

ABSTRACT: We report classical atomistic molecular dynamics simulations of four structurally diverse model asphaltenes, amodel resin, and their respective mixtures in toluene or heptane under ambient conditions. Relatively large systems (∼50 000atoms) and long time scales (>80 ns) are explored. Wherever possible, comparisons are made to available experimentalobservations asserting the validity of the models. When the asphaltenes are dissolved in toluene, a continuous distribution ofcluster sizes is observed with average aggregation number ranging between 3.6 and 5.6, monomers and dimers being thepredominant species. As expected for mixtures in heptane, the asphaltene molecules tend to aggregate to form a segregatedphase. There is no evidence of the distinct formation of nanoaggregates, and the distribution of clusters is found to be continuousin character. Analysis of the shape of the clusters of asphaltenes suggests that they are generally spherical in character, with thearchipelago models favoring longer prolate structures and the continental model tending toward oblate structures. The aggregatesare seen to be diffuse in nature, containing at least 50% solvent on average, being denser in heptane than in toluene. Mixtures ofasphaltenes with different architecture are found to have cluster properties that are intermediate between those of the individualcomponents. The presence of resins in the mixture does not appear to alter the shape of the asphaltene aggregates or their size ordensity when toluene is the solvent; on the other hand, the resins lead to an increase in the density of the resulting aggregates inheptane. Quantification of these observations is made from histograms of the cluster distributions, potential of mean forcecalculations, and an analysis of the shape factors. We illustrate how the time scales for complete aggregation of molecules inheptane are longer than the longest of the simulations reported in the open literature and as an example report a long simulation(0.5 μs) that fails to reach an equilibrium state, suggesting that acceleration techniques (e.g., using coarse-grained models) areneeded to appropriately explore these phenomena.

1. INTRODUCTION

Asphaltenes are a solubility fraction of crude oils, defined asbeing the part of the crude insoluble in n-alkanes (usuallyheptane) and soluble in aromatic solvents (usually toluene).Asphaltenes are among the most polar and heaviest (in terms oftheir molecular size) components of mixtures of carbonaceousfluids and hence are prone to aggregation, flocculation, anddeposition. Aggregation is an extremely complex process andmay be triggered by reductions in pressure and temperatureand/or by blending with other incompatible oils and/or by theincorporation of gases such as CO2. The study of the phasebehavior and aggregate structures of carbonaceous deposits isan issue of continuous importance throughout the oil industry,particularly in the area of flow assurance.1

The complexity of the crude oil mixture in terms of thenumber of possible individual components makes theexperimental analysis an ongoing tour de force that, althoughenlightening, has not yet provided the community withunequivocal answers as to the aggregation mechanisms andphysical behavior of asphaltenes in solution. Models forasphaltene aggregation are plentiful and conflicting and spandecades of research. For example, the “Yen−Mullins” model2 is

a well-cited interpretation of asphaltene aggregation predictingthat asphaltenes form small and dense nanoaggregates, which inturn aggregate loosely into clusters. While the hierarchicalstructure of two aggregate sizes seems to explain, for example,the discrepancy between some experimental results3,4 thatindicate an aggregation number of ∼4 to 8 and X-ray andneutron scattering results5−7 that show larger, more diffuseclusters, the model has not been universally accepted orconfirmed. The effect of concentration on the phase behavior isalso nontrivial. Asphaltenes may be present at parts per millionlevels in the live unstable crudes, generating troublesomeorganic deposits; however, Boscan crudes are known to contain17% asphaltenes and are stable with no deposits formed at anystage of production, while highly paraffinic crudes withasphaltene contents of 0.1% or less present serious productionissues. It is surprising that in spite of more than half a decade ofexperimental and theoretical modeling, questions still remain interms of the description and interpretation of the most

Received: August 26, 2016Revised: December 20, 2016Published: January 3, 2017

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© 2017 American Chemical Society 1108 DOI: 10.1021/acs.energyfuels.6b02161Energy Fuels 2017, 31, 1108−1125

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fundamental details of asphaltene precipitation. Molecularsimulation provides a potential capability to expand ourknowledge of the aggregation and deposition mechanisms ofasphaltenes through an increased understanding of aggregatestructure and energetics and is the topic of our currentcontribution.To be able to successfully simulate systems containing

asphaltenes, it is vital to have an accurate description of themolecular structure of asphaltenes. This is a challenging step, asasphaltenes represent a whole class of molecules rather than anindividual species. In general, an assumption is made that amolecule, or a small group of molecules, that have chemicalcharacteristics similar to those of asphaltenes, can represent thecontinuum of asphaltene molecular structures. The crux is toobtain molecular structures that faithfully represent the entirechemical family. There are very few systematic methodologiesto propose sensible asphaltene structures, and the folklore isbased on experimental information that is only marginal and inmany instances inconclusive and contradictory. Special mentionis made of the quantitative molecular representation (QMR)methods that have been used to propose representativestructures of asphaltenes8 in order to remove some of theempiricism surrounding this aspect of the problem.We first review the state of the art of asphaltene simulation

and the types of molecular structures that have been used todate. Atomistic simulation of asphaltene aggregation is thenpresented at a size and time scale that is at the limit of what canbe reasonably achieved using modern multicore processors withGPU acceleration of a parallel molecular dynamics (MD) code.Finally, we discuss the insight that simulation can give regardingthe aggregation mechanisms for asphaltene in good and badsolvents, the limitations of this atomistic approach, andpotential methods for increasing the size and length scalesaccessible through simulation.

2. BACKGROUND2.1. Atomistically Detailed Simulation Studies. In

recent years, as high-performance computing has becomemore prevalent, there has been an increasing effort tounderstand the structure of asphaltene aggregation at themolecular level using molecular simulation. The earliestsimulation papers9−11 were constrained by the computationalresources available and as a consequence were limited toconsidering single model asphaltene molecules or asphalteneswithout explicit solvent molecules in what today would beconsidered rudimentary systems, not because of the scientificcontent but rather as result of the inexorable advance ofMoore’s law. In addition, only relatively short simulation times(up to ∼500 ps) were achievable, and therefore, dynamicproperties such as diffusion or the observation of spontaneousaggregation were not possible. Instead, the early studies tendedto use a combination of energy minimization and “manualdocking” to explore different conformations for asphalteneaggregation and examined data during a short MD run in thisconformation.One of the earliest studies, by Rogel,11 investigated

asphaltene aggregation through molecular dynamics simula-tions of two model asphaltene structures. Asphaltene aggregateswere formed through a combination of molecular mechanicsand dynamics to produce reasonable low-energy structures.Solubility parameters where calculated from monomers andaggregates of the model asphaltenes, showing a reduction in thesolubility parameter with increasing aggregate size. Some

simulations were also carried out with a small number (45)of toluene or heptane solvating molecules. The interactionenergies between asphaltene molecules were calculated as −160and −40 kJ/mol in heptane and toluene, respectively, showingqualitative agreement with the solubility definition butsuggesting a rather large difference (>100 kJ/mol) in thesolvation energies of the respective solvents. A later studyconsidered a larger diversity of asphaltene model molecules inorder to estimate asphaltene densities. The simulations tendedto overestimate the densities compared with experiment.12 Itshould be noted that all of the asphaltene structures used had arelatively large number (8−22) of condensed aromatic rings.In another pioneering study, Murgich et al.9 conducted

molecular mechanics calculations using relatively large “con-tinental” asphaltene structures (with 24 aromatic rings) inconjunction with resins and showed that aggregation mainlyoccurred as a result of the stacking of the polyaromatic cores ofthe asphaltene. A later study using a smaller model asphaltenemolecule with seven fused rings in its polyaromatic core13 ledto similar findings. The structures used in both of these studieswere built to be consistent with measured spectroscopic datafor asphaltenes from Venezuelan crude and Athabasca bitumen.Pacheco-Sanchez et al.14 used MD to show that asphaltene

aggregation occurs spontaneously even for smaller asphaltenemolecules forming dimers, trimers, and tetramers during a short100 ps simulation. The structures of the aggregates formeddisplayed no overriding structure type: face-to-face, offset-stacked, and T-shaped aggregates were observed. An asphaltenestructure in the solid phase was also examined, comparing thesimulated structures to experimental scattering data.15 Fourdifferent asphaltene structures were chosen from the literature:models were extracted from the work of Groenzin andMullins,16 Murgich et al.,9 Zajac et al.,17 and Speight,18 eachformulated from analytical study of asphaltenes. All foursimulation studies replicated the experimentally determinedstructure factor to reasonable accuracy. In a further study, theGroenzin−Mullins asphaltene model was simulated in a box ofexplicit solvent, and the effect of pressure on aggregation wasinvestigated.19 Finally, Vicente et al.20 adopted the samesimulation approach to provide the enthalpy of mixing andcohesive energies for the Groenzin−Mullins model molecule inorder to determine the Hildebrand solubility parameter, closelymatching experimentally determined results.Simulations of asphaltene dimers with explicit solvent

molecules conducted over 100 ps by Carauta et al.21 haveshown that the asphaltene dimers bind face-to-face at distancesof 3.6 Å in heptane and 5 Å in toluene, matching the solubilitytrend. Furthermore, they show that the effect of increasing thetemperature (from 323 to 573 K) is to decrease the distance inthe asphaltene dimer. A further study used molecularmechanics followed by quantum-mechanical calculations tostudy the structure of asphaltene dimers in solution usingsmaller model compounds (with approximately six aromaticrings) containing oxygen heteroatoms.22

In general, these early studies are limited by either the lack ofexplicit solvent or the short time scales over which structuraland thermodynamic data were collected. However, the resultsare qualitatively consistent with the solubility behavior ofasphaltenes and indicate that face-to-face stacking of thearomatic cores is a primary structural characteristic, as shownthrough X-ray diffraction from solid asphaltene samples.23 Inmore recent years, increased computing power has led to thestudy of larger model systems being simulated for longer

Energy & Fuels Article

DOI: 10.1021/acs.energyfuels.6b02161Energy Fuels 2017, 31, 1108−1125

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periods of time, bringing the simulations a step closer to theexperimental systems.Greenfield and co-workers have written a series of papers on

the simulation of model asphalt described as a ternary mixturecontaining model asphaltenes, resins, and maltenes.24−32 Theinitial studies24−26 used model asphaltenes from Groenzin andMullins16 and from a study by Artok et al.33 employingpyrolysis−GC−MS, NMR spectroscopy, gel-permeation chro-matography, and MALDI-TOF-MS to study asphaltenestructure and derive model asphaltenes. The other componentsof the asphalt were modeled as dimethylnaphthalene and thealkane n-C20 for the aromatic and saturate fractions of the crudeoil, respectively. The simulations were used to estimate thedynamical properties of the model asphalt such as bulk viscosityand diffusion of the molecular components.25 This relativelysimplistic simulation was able to predict experimentallydetermined viscosities to within an order of magnitude. Adetailed analysis of the orientational structure within themixture was obtained by considering the angle between theasphaltene aromatic planes as a function of the radialdistribution function.26 The addition of a polymer modifier(polystyrene) was also examined.27 More recent studies haveused a modified model system. Adapted versions of asphaltenemolecules from Mullins2 were used as the asphaltenecomponentthe positions of the alkyl chains on the asphaltenecore were changed to reduce the high internal energies causedby steric repulsion.30 Polar molecules were also used to morerealistically model the aromatic component of the asphalt.31 Asimilar analysis of the dynamical properties of the asphalt wasconducted with this improved model system.32

Given that there is a continuing level of uncertainty in thegeneral molecular structural characteristics of asphaltenes, i.e.,the recognition that asphaltenes have a wide variety of differentstructures, it makes sense to try and understand the effects thatdifferent structural characteristics have on the physicalproperties. Along this vein, the separate studies by Kuznickiet al.34 and Ungerer et al.35 focused on investigating thedifferences among these geometries. Kuznicki et al. used threedifferent molecular structures of asphaltenes, one archipelagostructure with two aromatic cores and two similar islandmolecules, one of them with a carboxylate group (COO−)terminating a side chain.34 Simulations of 12 continentalasphaltenes with 12 archipelago asphaltenes were thenconducted in three different solvents (toluene, heptane, andwater). The study also considered a two-phase system of waterand toluene and compared the differing aggregation at theinterface with and without the anionic carboxyl group. In thesingle-solvent simulations, similar structural features foraggregation were seen in all of the solvents. However, thestrength of the aggregation varied, as indicated by identical peakpositions in the radial distribution function with varying peakheights in the order toluene < heptane ≪ water. Thesimulations in the mixed toluene/water system suggested thatthe presence of ionic terminal groups on the aliphatic chains ofspecific asphaltene fractions can dramatically enhance theinterfacial activity of the entire asphaltene population. Ungereret al.35 used three different asphaltene structures that wereconsistent with elemental analysis data for asphaltenes from anArabian crude: an “island” structure with eight aromatic rings, alarger “continental” structure with 15 aromatic rings, and an“archipelago” structure with three conjoined polyaromaticcores. Simulations of nine asphaltene molecules and 600solvent (toluene or heptane) molecules were conducted. The

results showed that limited aggregation occurred for thearchipelago model, whereas strong and irreversible aggregationoccurred for the continental model in both toluene andheptane. The island model formed some small aggregates oftwo or three molecules in both toluene and heptane, with largerand more stable aggregates occurring in heptane, qualitativelymatching experimental observations.For the simulations discussed thus far, the asphaltene

structures were essentially constructed “by hand” to beconsistent with a particular set of experimental data. There isno guarantee that the model molecules are the mostrepresentative structure for any particular data set. Methodsfor automatically generating structures and then selecting asubset that best matches experimental data are termedquantitative molecular representation (QMR) methods.8,36−39

One starts the procedure with a database of smaller structuralunits, which are then connectedfollowing defined chemicalrulesto form a large number of potential asphaltenestructures. This large set is then refined to a smaller subsetby minimizing the difference between experimentally deter-mined analytical data and simulated data from the asphaltenestructures, as defined through an empirical objective function. Ithas been found that a group of three to five molecularstructures is sufficient to accurately reflect the analytical data.8

The initial studies of Sheremata et al.38 allowed connection ofthe molecular building blocks only through alkyl chains,generating large archipelago-type structures. This approachwas extended by Boek et al.8 to include other potential linkagesas long as they were chemically consistent, in so doinggenerating island structures with larger aromatic corescomprising four to seven aromatic moieties. Following thisapproach, a set of three structures generated from elementalanalysis and 1H/13C NMR data of Athabasca bitumen with aQMR method were simulated by Headen et al.40 The molecularweight used is a variable factor in the QMR method and waschosen, for that study, as the rather small value of 750 Da.Simulations of six asphaltene molecules were conducted intoluene and heptane for each of the structures. Although boththe island and archipelago asphaltenes exhibited aggregation intoluene and heptane, the aggregation “events” were seen to beshort-lived, with asphaltene−asphaltene contacts being brokenand reformed several times over the course of a 20 nssimulation. Simulation of the resin molecules showedconsiderably less aggregation. Additionally a constraint-forcemethod was used to obtain an estimate of the potential of meanforce (PMF) between two asphaltene molecules, yielding a freeenergy of dimer formation of ∼10 kJ/mol. Studies based on theQMR-generated molecules have been extended to studies ofasphaltene aggregation in supercritical carbon dioxide41 andpreliminary studies of asphaltene aggregation on a calcitesurface42 and of asphaltene molecules at the oil−waterinterface.43

The asphaltene molecules used by Headen et al. have beenemployed by other groups as reference asphaltene compoundsin their own simulation studies. Sedghi et al.44 used eightdifferent variations of the “asphaltene C” structure of Headen etal.40 in order to study the effects of structural changes. Thework also represented an increase in scale: the authors kept thesame asphaltene concentration of 7 wt % but simulated 36molecules for 90 ns, claiming that the formation of asphaltenenanoaggregates followed later by the formation of clusters/flocsin accordance with the modified Yen model of asphalteneaggregation. An umbrella sampling method was used to



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calculate the free energy of dimer formation for each of thedifferent asphaltene structures. It was shown that the size of thearomatic core has the largest effect on the aggregation energy:for example, increasing the number of aromatic rings from eightto 11 led to an increase in the free energy of aggregation from−14 to −19.4 kJ/mol. The length of the peripheral alkyl chainshad little effect on the aggregation energy. The influence of theinclusion of heteroatoms was less conclusive. No clear linkbetween the aggregation energy and the polarity of themolecule was found, but the addition of heteroatoms into thearomatic core did increase the energy of aggregation.QMR is not without issues. It requires as an input library of

fragments to generate the larger structures, so unless there iscertainty in the choice of the fragments, the validity of theresulting structures is open to question. Moreover, the sets ofmolecules that match the experimental data are generally notunique, so a large number structures are obtained and a level orarbitrariness is introduced when deciding which one of these isthe most representative of the asphaltene fraction. A similarapproach to QMR for generating asphaltenes was employed byFrigerio and Molinari.45 They used the Scienomics MaterialsProcesses and Simulation (MAPS) platform46 to constructasphaltene molecules from molecular building blocks identifiedby chemolysis and pyrolysis of asphaltene samples. The largenumber of resulting structures were then refined by comparisonto analytical data (elemental analysis, GPC, and 1H/13C NMR).A total of nine structures were chosen for the study, withmolecular weights ranging from 324 to 1625 Da. Simulations ofaggregation in a number of different solvents (tetrahydrofuran,toluene, heptane, and pentane) were conducted for two of thelarger asphaltene models (MW = 1519 and 1467 Da). Face-to-face aggregation of the aromatic planes was seen in each of themodel solvents. The study also simulated four asphaltenes aspure components to obtain values of the Hildebrand solubilityparameter between 17.7 and 23.4 MPa1/2, which are close tothe values for aromatic solvents such as toluene (18.9 MPa1/2).However, as in QMR, the result of the Frigerio and Molinarimodel is biased by the number and morphology of the buildingblocks employed: a large proportion of their building blockshad an unexpectedly large proportion of aromatic moieties andno saturated rings. The resulting molecules thus exhibited largepericondensed domains, which explains the observation thataromatic stacking would be the predominant mode ofaggregation of their models.We also highlight the archipelago molecules generated by

Strausz et al.47 These models were constructed from a detailedwork to identify the most abundant fragments using mildpyrolysis and several very selective chemical decompositionschemes of asphaltenes from Athabasca. This work containsvaluable quantitative information about (a) the distribution ofthe sizes of the side chains and the type of bridges (pure−CH2− groups and those with −S−, −O−, and ester links)existing between the ring systems, (b) the size of the aromaticring systems, and (c) biomarkers and porphyrins covalentlyattached to some asphaltene molecules.An alternative approach to the ad hoc proposal of asphaltene

structures for simulation is to model existing compounds orasphaltene surrogates (e.g., dyes and chromophores) that arepresumably similar in structure to asphaltenes.48 As a proof ofconcept, Jian et al.49 simulated derivatives of violanthrone-78 asa model for asphaltene. Another recent example is the study ofalkyl-substituted hexabenzocoronene molecules.50 The poten-tial advantage of these studies is that it may be possible to

obtain experimental data for the pure compound that can bereadily compared to simulation results, and therefore, theyserve as an important validation of the classical force fields inwidespread use in the community.

2.2. Comparison of Results from Simulation Studies.An important aim of simulations of asphaltenes is to be able topredict properties inaccessible through experiments and by thisto gain physical insight into the molecular-level processes thatdrive macroscopically observed behavior. A key issue, however,is to assess the reliability of the asphaltene models, as the resultsare clearly contingent on this choice. This apparently simplepoint is a very contentious one, as there is an inherent difficultyin mapping out a “characteristic asphaltene”. The ultimatebehavior of a molecular model of an asphaltene is dictated bythe details of the molecular geometry and chemicalconstituents, i.e., the morphology of the molecule. Even thecalculation of the most basic of properties, such as the averageor representative molecular weight, is the subject of a long-standing debate with values that vary by orders of magnitudeeven for laboratories separated by two floors within the samebuilding.51−53 The futility of attempting to compare directlywith small-scale experiments then becomes apparent. Hence,the simulation studies generally involve comparisons withprevious results. A particularly interesting breakthrough on theelucidation of what an asphaltene molecule “looks like” hasrecently been provided by Schuler et al.54 In that paper, acombination of atomic-resolution imaging of over 100asphaltene molecules using atomic force microscopy andmolecular orbital imaging by scanning tunneling microscopyis presented. The work confirms that some real asphaltenemolecules consist of a central aromatic core with peripheralalkane chains. In some cases, this central core is divided intoseveral distinct interconnected polycyclic aromatic cores (i.e.,“archipelago”-type molecules), while in others a single aromaticcore with peripheral alkanes is the dominant asphaltenemolecular architecture. A clear conclusion is that real cutswill exhibit a complex mixture of these two general motifs. Thisis a particularly reassuring result as it suggests that most of therecent literature has focused on suitable types of molecules.The other key issue in simulations is the use of appropriateforce fields. In the case of the atomistic models described in thisarticle, the simulations are based on intermolecular potentialshistorically validated for liquid-phase simulation of well-knownand well-characterized small molecules. These potentials are theworkhorse of computational biochemistry, are assumed to betransferable to other molecules, and in general seem to be inquantitative agreement in all but very extreme scenarios.55

The computer modeling studies to date have focused on theenergetics of aggregation and the diffusion of asphaltenemolecules. The asphaltene−asphaltene interaction energy is thesum of the nonbonded interactions between a pair ofasphaltene molecules. In general, the overall magnitudes ofthe asphaltene−asphaltene interaction energies are similaramong the various models, especially when molecular weightis taken into accountthe largest molecules have the largestinteraction energies. The results reported in the literature spanvalues from −89 kJ/mol (ref 56) to as high as −372 kJ/mol (ref9). This calculation does not include the change in energy dueto the asphaltene−solvent interactions or the entropy change inthe process of aggregation. For this one would have to considerthe free energy of aggregation ΔGagg in the given solvent (asopposed to a calculation of the docking energy of molecules invacuum). Only two sets of authors have reported this type of



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calculation: Headen et al.40 calculated the PMF by conducting aseries of simulations in which two asphaltene molecules wereconstrained by the SHAKE algorithm to be a fixed distanceapart. The PMF (or equivalently the free energy ofaggregation) can be calculated from the force required tokeep the asphaltene molecules at the set constrained distance.Sedghi et al.44 used a similar umbrella sampling method57 toassess the force−distance curve for asphaltene−asphalteneinteractions: a series of simulations were conducted in whichharmonic-spring bias potentials were used to keep theasphaltene molecules within a range of distances from eachother. From this a more complete force−distance curve couldbe built. The results from the two calculations gave very similarresults. Sedghi et al.44 observed a slightly higher aggregationenergy in heptane than in toluene, a result that meets theexperimental definition of asphaltenes.Diffusion coefficients can be calculated directly in MD

simulations by tracking the mean-square displacement of thecenter of mass of asphaltene molecules as a function of time.58

The literature reports a relatively wide variation in thesimulation results from 0.01 × 10−10 to 8 × 10−10 m2/s.25,32,59 These values are consistent with diffusion constantsfrom NMR measurements, which suggest values between 1 ×10−10 and 3 × 10−10 m2/s depending on concentration60 andstructure.61

To date, the longest and largest atomistic simulationsreported have been conducted for 80 ns on systems containing36 asphaltene molecules in explicit heptane at 7 wt %.44

Complete aggregation of the system is seen to occur on thistime scale, specifically as a precipitous event at approximately60 ns. Even in this poor solvent, the aggregation into clusters offive to 10 molecules takes over 20 ns. These time scales suggest

some minimum simulation times that should be used tounderstand asphaltene aggregation. Hence, we examine largesystem sizes (27 asphaltene molecules) and, most particularly,long simulation times (80−500 ns) in an attempt to reachequilibrium conditions.

3. METHODS3.1. Asphaltene Structures. A common underlying assumption

in atomistic simulations is that a unique asphaltene molecule may berepresentative of the full solubility class. It is known that asphalteneshave a wide multimodal distribution of sizes, so it is unlikely that onlyone average molecule can be a valid descriptor for such a complexsystem. For practical reasons, however, any study is bound to belimited to a small number of prototypical molecules, mostly as aconsequence of the rather limited computational power availablecoupled with the uncertainty and experimental challenge of thedescription of asphaltenes. We chose five structures from the literaturethat are consistent with available analytical data for asphaltenes andthat among them represent different aspects of the asphaltenestructure (e.g., island vs archipelago). These hypothetical structuresare presented in Figure 1.

The first three structures, asphaltenes A and C and resin B, are thesame as those employed in a previous study of MD simulation ofasphaltenes40 and can be traced to the output of a QMR analysis.8 Wedenote structure “B” as a resin because it has a low molecular weight, asmall aromatic core, and a reduced number of polar functional groups,consistent with the structural characteristics of a resin. We note thatthe structures depicted in Figure 1 slightly differ from those shown inthe original publication, with additional CH2/3 groups on asphaltenesA and C. This corrects a mistake in the drawing of the structures usedin the original paper. Asphaltenes D and E are structures empiricallysuggested by Ungerer et al.35 These are larger structures than A−Cand help inform which structural characteristics of asphaltenes affectaggregation. Asphaltene D is a large continental asphaltene with asingle aromatic core, while asphaltene E is an archipelago structure

Figure 1. Asphaltene molecular structures used in this study. A−C are from Headen et al.40 and D and E from Ungerer et al.35



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with three aromatic cores. They have similar molecular weights(∼1300 Da) and H/C ratios of 1.2. Taking note of the findings in arecent paper of Li and Greenfield,30 we have slightly adapted thestructures for asphaltenes A and D to remove the high-energystructures caused by the “pentane effect”. This was achieved by therepositioning of an aliphatic side chain to a less sterically hinderedposition. While this does not significantly change the overall chemistryof the molecule, it removes high-internal-energy structures that areunlikely to occur in natural asphaltenes that have developed overgeological time scales. Since all of the asphaltene models proposed inthe literature are “conceptual’ models, it is important to make sure thatthey are stable, low-energy structures. An excellent discussion of thistopic is given in the recent paper by Martin-Martinez et al.62 proposing“improved” models of published structures. On this topic, it should benoted that for asphaltene D the aromatic plane as presented byUngerer et al. cannot be represented by an alternating double−singlebond format (and is therefore electron-deficient). To resolve this, oneof the peripheral aromatic carbon atoms has been switched to an sp3

CH2 carbon.Clearly, the choice of the model molecules in Figure 1 is arbitrary

and incomplete, but it allows one to compare some of the limitingcases (e.g., single molecules in toluene) with recently published results.A limitation of these models is the absence of carboxylic acid groups orbasic nitrogen sites. Selective methylation of asphaltenes has beenshown to drastically reduce the resulting MW, indicating thathydrogen bonding may be relevant to the aggregation process.3.2. Simulation Details. We used well-defined classical intra- and

intermolecular potentials of the OPLS-AA force-field family63,64 todescribe interatomic forces. In view of the uncertainties surroundinglarger issues, such as the particular morphology, concentration, andcomposition of asphaltenic systems, the choice of this particular forcefield over any other modern and well-validated one is not of primeimportance. Notwithstanding, the OPLS force field has been shown towork well for aromatic liquids in reproducing experimental data.65 It isimportant to note that improper dihedrals must be used with aromaticstructures in order to keep the aromatic ring flat.Simulation cells were constructed by random placement and

rotation of asphaltene molecules followed by random placement androtation of sufficient solvent molecules to give the requiredconcentration. This procedure was carried out at low density toreduce the probability of molecular overlap. After an initial energyminimization step to remove any high-energy structures, the systemwas allowed to reach equilibrium density by running an MDsimulation in the isobaric−isothermal (NPT) ensemble. The temper-ature and pressure were maintained using the Nose−Hoover66,67 andParinello−Rahman68,69 algorithms, respectively. A pressure of 1 barand temperature of 300 K were used throughout our study.The GROMACS MD simulation code (version 4.6) was employed

for all of the simulations70 using the leapfrog MD algorithm71 and theVerlet pair list scheme for neighbor searching.72 This allowed the useof GPU acceleration of the MD code, increasing the speed ofexecution on a workstation by a factor of approximately 4. A time stepof 1 fs was used for all of the simulations, and bond lengths were keptrigid using the LINCS algorithm.73 Cubic periodic boundaryconditions were employed to approximate infinite bulk behavior.The cutoff of the nonbonded interactions was set at 1 nm, with astandard correction for the energy and pressure employed to accountfor long-range dispersion interactions. Long-range electrostaticinteractions were handled using the particle mesh Ewald procedure.74

The atom positions for the asphaltene molecules were recorded every1000 time steps (1 ps) to allow for comprehensive analysis of theasphaltene clusters.Bulk fluid simulations, in which asphaltene molecules of interest

were simulated in solvent at 7 wt %, form the core of the results. Theconcentration is representative of the upper limit of concentrationsexpected, typical of heavier crudes such as those of Venezuelan orMexican origin. This rather high concentration allows for simulationscontaining a minimum number of solvent molecules and representsthe cases where precipitation is enhanced. The simulations were runfor at least 80 million time steps (80 ns), and the minimum number of

asphaltene molecules considered was 27. In the case of the systemswith resin molecules, they replaced solvent molecules to give anapproximate composition of 7 wt % asphaltene, 7 wt % resin, and 86wt % solvent. The total weight percent of the asphaltene fraction wasagain capped at 7% in the case of the mixtures considered. Table S1 inthe Supporting Information gives details of the individual simulations.

To complement the results, a second type of simulation wasemployed to calculate the asphaltene−asphaltene PMF curves usingumbrella sampling. A detailed description of the method can be foundelsewhere;75,76 in particular, an application to asphaltene simulations isdescribed by Sedghi et al.44 The method relies on performing a seriesof simulations in which a biasing potential is used to keep theasphaltene centers of mass at an average fixed distance that is varieddiscretely between a large separation and a close distance. The resultsfrom these simulations are then recombined and the effect of thebiasing potential is removed using a weighted histogram analysismethod. This is implemented in GROMACS using the g_whamutility.77 The spring constant (bias) was chosen to ensure sufficientoverlap between each umbrella window simulation and completesampling of the reaction coordinate. For all of the simulationspresented below, a spring constant of 1000 kJ/mol−1 nm−2 wasdeemed satisfactory. Each umbrella window simulation was run withsufficient solvent to give an asphaltene concentration of 1 wt % for 10million time steps in the NVT ensemble after initial equilibration of500 ps in the NPT ensemble to obtain the initial equilibrium density.Table S2 gives the details of the PMF simulations. For PMFcalculations of this type, where the molecules are free to move in threedimensions, a correction is applied to remove the increase in entropyas the distance between the molecules, r, is increased: this correctionwas performed by adding kBT ln(4πr2).77

3.3. Cluster Analysis Methods. The aggregation number, i.e., thenumber of molecules that constitute a cluster over the course of thesimulations, was used as a guide to monitor both the approach toequilibrium and the expected average asphaltene cluster size. TheGROMACS utility g_clustsize was employed to calculate the averagecluster size and a histogram of cluster sizes from the simulationtrajectory file. Molecules were arbitrarily considered to be clustered ifthe minimum distance between molecules (the distance of closestapproach) was less than 3.5 Å. The tracking of the minimum distancebetween two randomly chosen molecules of asphaltene C in heptane isdisplayed in Figure 2. The events where the molecules were clusteredare clearly visible from the collection of state points where theminimum approach distance was below 3.5 Å. The average cluster size,

Figure 2. Plot of the minimum distance between two individualasphaltene molecules during a 5 ns time window of an 80 nssimulation of 27 molecules of asphaltene C in heptane. The redhorizontal dashed line marks the cutoff employed to discriminatewhether molecules form part of a cluster.



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http://pubs.acs.org/doi/suppl/10.1021/acs.energyfuels.6b02161/suppl_file/ef6b02161_si_001.pdf



number of clusters, and cluster size distribution were recorded fromeach frame of the simulation trajectory. The average cluster size, Nn,was calculated from

=∑ ·∑

Ni N

Nni i

i i (1)

where Ni is the number of clusters comprising i molecules. The sum ineq 1 runs from i = 2, i.e., it does not account for monomers. In section5 we discuss the effect of including the monomers in the calculations.The histogram of cluster sizes was calculated by averaging the numberof clusters of n molecules over the full length of the simulation.

A standard metric for the size of polymers or other macromoleculesin solution is the radius of gyration (Rg), defined as

∑= −=

RN

r r1

( )k

N

kg2

1cm

2

(2)

where rk is the position vector of atom k and rcm is the position vectorof the center of mass of the cluster. Although the radius of gyrationprovides a useful, shape-independent measure of cluster size, it doesnot give information about the shape of the cluster. A moreappropriate related property is the gyration tensor (S), given by78

∑ ∑ ∑

∑ ∑ ∑

∑ ∑ ∑

=

− − − − −

− − − − −

− − − − −

⎛

⎝

⎜⎜⎜⎜⎜⎜⎜

⎞

⎠

⎟⎟⎟⎟⎟⎟⎟N

x x x x y y x x z z

y y x x y y y y z z

z z x x z z y y z z

S1

( ) ( )( ) ( )( )

( )( ) ( ) ( )( )

( )( ) ( )( ) ( )

ii

ii i

ii i

ii i

ii

ii i

ii

ii

ii

cm2

cm cm cm cm

cm cm cm2

cm cm

cm cm cm cm cm2

(3)

where the subscript i represents atom i of the cluster and the subscript“cm” represents the center of mass of the cluster. Transformation ofthe gyration tensor to the principal axis involves the diagonalization ofS:

λ λ λ=S diag( , , )1 2 3 (4)

The eigenvalues of S (the principal moments) are commonly sorted inthe order λ1 ≥ λ2 ≥ λ3, and the square of the radius of gyration isrecovered from the sum of the eigenvalues: Rg

2 = λ1 + λ2 + λ3. Ameasure of the dimensionality and symmetry of a cluster is given bythe relative shape anisotropy, κ2, defined as

κλ λ λ λ λ λ

λ λ λ= −

+ ++ +

1 3( )

( )2 1 2 2 3 3 1

1 2 32

(5)

κ2 can take values between 0 and 1, where a value of 0 corresponds toa perfectly spherical cluster and a value of 1 corresponds to a linearchain.Another key factor in understanding the structure of asphaltene

aggregates is the level of solvent penetration into the aggregate. Whatis needed is an estimate of the density of the asphaltene aggregate inthe simulations. To obtain this estimate, we assume that the volume ofeach cluster can be approximated by calculating the volume of an“effective” ellipsoid that would give the same principal moments of thegyration tensor (λ1, λ2, and λ3). This equivalent ellipsoid would haveaxes a, b, and c equal to λ5 n (n = 1−3), and therefore, we canapproximate the “encompassing” volume of the cluster as

π λ λ λ=V43

5cluster3

1 2 3 (6)

Further discussion of the analysis is given in the SupportingInformation. The mass of the cluster can then be readily calculatedfrom the mass of each molecule and the number of molecules in thecluster. The estimate of the density of the cluster is therefore obtainedfrom

ρ =∑ m

Vi i

clustercluster (7)

where mi is the mass of the ith molecule in the cluster. We note thatthe cluster calculations were performed by considering only asphaltenemolecules. This means that the solvent molecules, even if they werewithin a cluster, were not part of the shape analysis.The radius of gyration, relative shape anisotropy, and density

estimate were calculated for each cluster in trajectory frames every10 000 time steps (10 ps). The average of each of these quantities wascalculated in each trajectory frame, and the distributions of the

properties were calculated over the length of the whole simulation. Onrare occasions a cluster was larger than the size of the simulationperiodic cell. In order to avoid spurious results, such clusters wereignored in the calculation of averages and distributions of clusterproperties.

4. SIMULATION RESULTS AND ANALYSIS4.1. Simulations of 27 Identical Asphaltenes in

Toluene or Heptane. In Figure 3 we show equilibrium

snapshots of simulations of 27 molecules of asphaltene C intoluene and in heptane. The higher degree of aggregation ofasphaltenes in heptane is visually evident, while a significantnumber of free asphaltene monomers, dimers, and trimers areseen in toluene. Stacking of the aromatic planes is clearly visibleas a means of aggregation, although for larger clusters thiscolumnar character is quickly lost.The average cluster sizes in toluene and heptane over the 80

ns simulation were calculated as 3.97 and 7.74, respectively.The average cluster sizes in toluene and heptane as functions oftime are given in Figure 4. Both simulations appear to reach aplateau in terms of the average cluster size, suggesting that no

Figure 3. Representative snapshots from simulations of 27 moleculesof asphaltene C in toluene and heptane at an asphaltene concentrationof 7 wt %. Solvent molecules have been removed for clarity. The cyan,white, and yellow spheres represent the carbon, hydrogen, and sulfuratomic centers, respectively. The blue boxes outline the simulationcells. Periodic boundary conditions were applied in all Cartesiandirections.



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further aggregation is expected (see the discussion in section6.2, where we expand on this comment). The average clustersize in heptane approaches an upper limit that is commensuratewith the total number of molecules, and therefore, it ispresumed that the cluster size reported is limited by finite-sizeeffects, as the trend suggests complete phase segregation. Thecapped cluster size seen in toluene, however, implies that thereis a degree of clustering and aggregation that is limited not bymass but rather by the balance between the energeticallyfavorable cohesion and the entropically unfavorable clustering.For the case of the archipelago-type asphaltene A, the

difference between the clustering behaviors in toluene andheptane is less distinct. A plot of aggregate sizes over 80 nssimulations is shown in Figure 5. There is an indication thatasphaltene A is less soluble in toluene at these concentrations,tending to form larger clusters and separating out. Lightercrude oils (e.g., Arabian crudes) presumably have asphalteneswith a smaller proportion of pericondensed rings and are

particularly sensitive to asphaltene precipitation at very lowconcentrations, much below the concentration studied here.While not conclusive, there is a suggestion that the more openasphaltene structures may have a lower solubility in toluene.The key differences between the island-type asphaltene C andthe archipelago-type asphaltene A are morphological, involvingboth the aggregate shape and density. A comparison of thedistributions of cluster radius of gyration, relative shapeanisotropy, and density is given in Figure 6. As asphaltene Ais a larger molecule, it is unsurprising that its cluster radius ofgyration is generally larger than that for asphaltene C (Figure6a). It is worth noting that for asphaltene C in heptane (bluedashed curve) there is a bimodal distribution in the cluster size,indicating larger clusters (Rg ∼ 15 Å) in coexistence withsmaller clusters (Rg ∼ 8 Å); however, this might be an artifactof the finite size of the cell. For this particular system/solvent,the final equilibrium state is most likely complete phaseseparation, with a (relatively pure) asphaltene phase in

Figure 4. Average asphaltene cluster sizes from simulations of 27 molecules of asphaltene C in toluene and heptane.

Figure 5. Average asphaltene cluster sizes from simulations of 27 molecules of asphaltene A in toluene and heptane.



1115


coexistence with a supernatant solvent with some (very limited)asphaltene solubility. Attaining this equilibrium state willrequire simulations with orders of magnitude larger length-and time-scales, and the results shown here correspond to theinitial stages of this process.The distributions of relative shape anisotropy (eq 5) are

given in Figure 6b. The clusters of asphaltene A are lessspherical than those of asphaltene C. The extended archipelagostructure is likely to produce more extended asymmetricclusters, analogous to what is commonly seen for elongatedpolymers in solution. The estimated densities of the clustersalso show differences (Figure 6c). Clusters of asphaltene C areconsistently denser than those formed by asphaltene A, andasphaltenes in heptane show denser aggregates than those intoluene. In general, the results are in agreement with themeasurements of Gawrys et al.,79 who suggested a range ofsolvent entrainment from 30 to 50% (v/v). For asphaltene C intoluene, the average density suggests that half of the volumeassigned to the cluster is filled with entrained solvent. It isreassuring to note that this observation is consistent withobservations from small-angle X-ray scattering (SAXS) andsmall-angle neutron scattering (SANS) experiments79 andprevious simulations.80

The large continental asphaltene D, with its large aromaticcore, is expected to show high levels of clustering andaggregation. However, the corresponding analysis in terms ofcluster aggregation numbers suggests that the cluster sizes in

heptane are lower than for the other asphaltenes and that thedifference in aggregation number for simulations in toluene andheptane is small. (The average cluster size over the simulationand the average cluster size distribution are reproduced in theSupporting Information.) At first glance, the observation oflower aggregate size is anomalous, but the distribution ofcluster sizes indicates that aggregation is indeed strong, as thereare very few monomers in solution. A likely explanation is thatin the early stages of the simulation the molecules quickly formdimers, trimers, or other small clusters. There is littledisaggregation and reformation of asphaltene contacts forasphaltene D compared with the smaller asphaltenesthe onlyway for clusters to grow is therefore for these small clusters tocoalesce. Diffusion of the larger clusters is particularly slow, andtherefore, coalescence is likely to take considerably longer,beyond the time scales reasonably available to atomisticmolecular dynamics simulations.The archipelago-type asphaltene E shows cluster properties

similar to those of archipelago-type asphaltene A, and forsuccinctness, the average cluster properties and plots of averagecluster size and distributions of cluster properties for thisasphaltene are given in the Supporting Information.

4.2. Simulation of Mixtures of Asphaltene Structures.4.2.1. Effect of Resins. To evaluate the effect of the presence ofresin molecules, 7 wt % of the solvent (toluene or heptane) wasreplaced with an equivalent mass of resin B (Figure 1). Forsimulations of 27 molecules of the island-type asphaltene C,

Figure 6. Comparison of the distributions of (a) cluster radius of gyration, (b) relative shape anisotropy, and (c) density from simulations of 27molecules of asphaltene A (red) or C (blue) in toluene (solid lines) or heptane (dashed lines).



1116




there is little to no difference in the cluster size or propertieswhen 7 wt % of toluene is replaced by resin. In the case thatthis fraction of heptane is replaced by resins, there areindications of an improvement in the solubility of theasphaltene: there is a clear reduction in the density of theasphaltene clusters, and the radius of gyration of the clustersbecomes smaller (Figure 7). It should be noted that onlymolecules of asphaltene C were included in the calculation ofthe cluster propertiesfor these calculations the resin wasconsidered part of the solvent.The changes observed in the heptane-based systems upon

addition of resin can be rationalized by exploring the behaviorsof the pure resin (27 molecules; 7 wt %) in toluene andheptane (without any asphaltenes). As expected, the resin is

soluble in both cases, but inspection of the resin−resin radialdistribution function (RDF) g(r) (Figure 8) shows no peak inthe RDF in toluene, whereas a peak is present in heptane,indicating some level of incompatibility with the solvent. Whenasphaltenes are also present, the formation of resin−asphalteneaggregates is likely to be favorable in heptane, thus reducing thedensity of the asphaltene aggregate as a result of entrainment ofthe resin. Our simulations show no evidence of resin moleculessolvating or solubilizing the asphaltene clusters (as in a micellarpicture of asphaltene solubility81); the distribution of resinmolecules within a cluster is therefore homogeneous and notlimited to the periphery (Figure 9). These observations areconsistent with the absence of peaks in g(r) for the aromatic−

Figure 7. Asphaltene cluster properties obtained from 80 ns simulations of 27 molecules of asphaltene C with 45 molecules of resin B in eithertoluene or heptane: (top) distributions of the cluster radius of gyration; (middle) distributions of the estimated cluster density; (bottom)distributions of cluster relative shape anisotropy. Solid lines are for the pure solvent (without resin), and dashed lines are for the solvent with 7 wt %resin.



1117


asphaltene and resin−asphaltene pairs in bitumen reported byZhang and Greenfield.27

4.2.2. Mixtures of Asphaltenes. We performed simulationsof a mixture of two morphologically different asphaltenestructures. There is an expectation that the presence ofpolydispersity in asphaltenes may hinder aggregation by virtueof steric hindrance due to the increased incompatibility in theshapes of the different molecules. A mixture (50:50 on a weightbasis) of island-type asphaltene C with archipelago-typeasphaltene A was studied, with the total combined weightfraction of the asphaltene fraction kept at 7 wt %, as in thepure-component cases. The results (see the SupportingInformation) indicate that for all the cluster propertiesaggregation number, radius of gyration, shape anisotropy, and

densitythe values of the properties obtained for thesimulation of mixed species lie between the values obtainedfor the pure components, i.e., the mixture behaves in an idealfashion in terms of the asphaltene composition dependence.There is no obvious reduction in cluster size upon mixing of thedifferent asphaltene structures, nor is there a significant changein the distribution of the cluster properties. As displayed inFigure 10, the distributions of the cluster radius of gyration anddensity lie between the distributions for the single (pure)asphaltene simulations. A similar result is also seen forsimulations of a mixture of the two archipelago-typeasphaltenes A and E (see the Supporting Information). Theseobservations are consistent with recent report on simulations ofmixtures of asphaltenes by Santos Silva et al.,82 where thebehavior of a mixture of models was found to be consistentwith the behaviors of the individual asphaltenes.In a similar fashion, we probed the effect of the addition of

the resin to the solvent on a mixed asphaltene system. Here weran the latter asphaltene mixture (A + C) with a proportion ofthe solvent (∼7 wt %) replaced by resin B. The calculateddistributions of cluster sizes and cluster densities are given inFigure 11. The effect on the cluster radius of gyration is limited,although in both toluene and heptane the introduction of resindoes appear to produce a bimodal distribution, increasing thenumber of smaller clusters and favoring the solubility of theasphaltenes. The differences in cluster density in thesimulations are more marked. Unlike the simulation whereonly asphaltene C is present, where the addition of resin has anegligible effect on the cluster properties, there is a cleardecrease in cluster density for the mixture of asphaltenes A andC and an increase in the overall solubility with the introductionof resin. Clearly, more cases with larger degrees ofpolydispersity in the asphaltene, resin and solvent fractionsneed to be considered in order to reach more general andmeaningful conclusions.

4.3. Potential of Mean Force between Pairs ofAsphaltene Molecules. The potential of mean force(PMF) between the centers of mass of two asphaltenemolecules provides a quantitative description of the strengthof aggregation between asphaltene molecules.81 The differencein energy between the minimum of the PMF and the value ofthe PMF at long distances can be interpreted as the free energyof dimer formation, ΔGdimer. Values of the free energy of dimerformation for asphaltene models are given in Table S2 and areseen to exhibit a large spread of over an order of magnitude,from 8.4 kJ/mol for asphaltene C in toluene to 66.4 kJ/mol forasphaltene D in heptane.83 This is partially due to the inherentdifferences in the close packing of the molecules, where themore continental morphologies can form highly energetic face-to-face interactions, and also partially due to the difference inflexibility of the molecules, as the springs fix the center of massbut the different molecules will bend and flip in significantlydifferent fashions depending on their general morphology. Asan example, the PMF curves for the island-type asphaltene Cand continental-type asphaltene D are given in Figure 12. Theequilibrium separation between the centers of mass of themolecules forming a dimer is ∼6 Å. The free energies of dimerformation for the large continental asphaltene D in bothtoluene and heptane (Figure 12) are considerably higher thanthose for asphaltene C, as the large aromatic core of asphalteneD makes aromatic stacking highly favorable. Similarly, the freeenergy of dimer formation is considerably higher in heptanethan in toluene, indicating the propensity for clustering in

Figure 8. Radial distribution functions for resin−resin contacts from40 ns simulations in toluene and heptane.

Figure 9. Snapshot from a simulation of 27 asphaltene C and 45 resinB molecules in toluene. The resin carbon atoms are represented asorange, the asphaltene carbons as cyan, and hydrogens as white; thesolvent molecules have been omitted for clarity. There is no indicationthat resin molecules “solvate” asphaltene molecules.



1118






heptane. What is notable is the small difference in the solvationenergies between solvents, suggesting that the precipitation ofasphaltenes is crucially driven by extremely small changes in thephysicochemical characteristics of the mixture (solvent).We conducted umbrella sampling simulations involving a

single asphaltene molecule and an asphaltene dimer to explorethe energy cost of “growing” clusters from dimers. In these

simulations, two umbrella sampling “springs” were used. One“spring” was used to maintain a preformed dimer at a fixedseparationin this case the equilibrium separation was thesame for all of the umbrella windows and was set at 6 Å. Thesecond spring was fixed between the center of mass of a thirdmolecule and the center of mass of one of the molecules in thepreformed dimer. The equilibrium distance for the second“spring” of the reference molecule to the third molecule wasthen varied between 3 and 20 Å. The resulting PMF curve forasphaltene C trimer formation in toluene is shown in Figure 13as a function of the distance between the centers of mass of thethird molecule and the reference molecule. There is a smallreduction in the free energy of aggregation compared with thatof dimer formation, which indicates that as the aggregateincreases in size further aggregation becomes less favored.

4.4. Dimensional Map of Asphaltene Aggregates. It isinstructive to represent the shape of a cluster in terms of ratiosof the principal moments of the gyration tensor (λ1, λ2, and λ3).We can define the following ratios, remembering that bydefinition λ1 > λ2 > λ3:

λλ

λλ

= =r r11

22

2

3 (8)

Figure 10. Distributions of asphaltene cluster radius of gyration and (inset) estimate of cluster density from simulations of asphaltene C, asphalteneA, and a 50:50 (by weight) mixture in toluene (left) and heptane (right).

Figure 11. Distributions of cluster radius of gyration (left) and estimate of cluster density (right) for simulations of mixtures of asphaltenes A and Cin toluene and heptane with and without resin B.

Figure 12. Potential of mean force between two molecules ofasphaltene C in toluene (purple) and heptane (green) and betweentwo molecules of asphaltene D in toluene (cyan) and heptane (gold).



1119


where r1 = 1 for an oblate shape (λ1 = λ2 > λ3) and r2 = 1 for aprolate shape (λ1 > λ2 = λ3). A plot of r1 against r2 cangraphically represent the shape of the cluster; the closer thepoint for the cluster is to the x or y axis, the more it can bethought of as prolate or oblate, respectively. It should be notedthat when r1 = r2 we obtain λ λ λ=2 3 1 , so that the cluster isneither prolate or oblate, while a sphere would be the specialcase where r1 = r2 = 1 (corresponding to the origin of the plot).For each of the simulations of 27 identical asphaltenes, a two-

dimensional histogram was constructed by calculating thenumber of clusters formed during the simulation that fell withinbounds Δr1Δr2. The corresponding plots are shown in Figure

14 for the island-type asphaltene C and the large continental-type asphaltene D (dimensional maps for other simulations areavailable in the Supporting Information). There are cleardifferences in the shapes of the clusters for the differentasphaltenes. The smaller asphaltene C forms predominantlyslightly prolate-shaped clusters. For the large continental-typeasphaltene D, on the other hand, there is a clear preference foroblate shapes. This is likely to be due to the underlying shape ofthe continental asphaltene: aromatic stacking will biascolumnar-like stacking when few molecules make up theclusters.In order to directly compare the cluster shapes for clusters of

different asphaltenes, in Figure 15 we have plotted the average

Figure 13. Potential of mean force curves for asphaltene C in toluenebetween two monomers (red) and between a monomer and a dimer(green).

Figure 14. Dimensional histograms of clusters formed during simulations of 27 molecules of asphaltene C (top) and asphaltene D (bottom) intoluene and heptane.

Figure 15. Dimensional map with average cluster properties from MDsimulations of 27 identical asphaltenes.



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values of r1 and r2 for each simulation. Clusters in heptane areon average more spherical, mostly by a reduction in r1 (areduction in the longest dimension of the cluster). This analysisagrees with the fact that heptane is a poor solvent and theasphaltene molecules will attempt to form the densest clusterswith the least available exposed area. The archipelago-typeasphaltenes A and E are on average more prolate than oblate,which is perhaps no surprise given their molecular shapes and isconsistent with the general behavior of oligomers in goodsolvents.

5. MODELS OF ASPHALTENE AGGREGATION INTOLUENE

The aggregation structure of asphaltenes in good solvents andstable crudes has received considerable attention in recentyears.2,84 Here we do not attempt to review all of the literatureon the subject; a brief overview is that there are currently twomodels considered for asphaltene association at the nanoscale.The first is the Yen−Mullins model,2 which postulates twolevels of aggregation: the formation of nanoaggregatesaggregates containing <10 asphaltene moleculespredomi-nantly held together by stacking of aromatic cores and theposterior appearance of nanoaggregates that consist of moreloosely bound clusters with a size of approximately 10 nm. Thesecond model, proposed by Gray et al.,84 is a “supramolecularassembly model”, whereby a broad range of intermolecularinteractions (π−π stacking) lead to diffuse asphalteneaggregation.What insights can the simulations described above give as to

the nature of asphaltene aggregation at the nanoscale? The firstthing to note is that the distributions of aggregate sizesthroughout the simulations exhibit a large number ofmonomers and dimers: for all but the simulations of the largecontinental-type asphaltene D (which tends to be ananomalous molecule), the monomer is the most common“aggregate”. We believe that this is not just an effect on theshort time scales involved in the simulation (see the nextsection).The fact that we have a highly skewed distribution of

aggregate sizes means that we need to be careful about how the“average” aggregation number is defined. In fact, depending onthe experimental technique employed, the measure ofaggregation may change: if the method is sensitive only toaggregation “events”, it will not include monomers in thecalculation, but if the method essentially calculates themolecular weight of the aggregate, then monomers will beincluded. For example, small-angle scattering provides a weight-averaged molecular weight,6 which is best compared to aweight-averaged cluster size, Nw, where the index i runs from i =1:

=∑ ·∑ ·

Ni N

i Ni i

i iw

2

(9)

The average cluster sizes given in Table S1 are an average(defined by eq 1) for clusters containing at least two molecules. Ifone considers evaluating eq 1 including the monomers (theindex i = 1, 2, 3, ···), for simulations of asphaltene C in toluenethe number- and weight-averaged cluster sizes are 2.4 and 4.4respectively. The weight-averaged aggregation number ap-proaches the values stated from NMR and DC conductivitymeasurements,2 approximately 8 and 6, respectively. A recentanalysis of small-angle X-ray scattering from low concentrations

of asphaltenes in toluene using a two-state aggregation modelgave an aggregation number of 3.3 ± 1.3,6 in good agreementwith our current findings. It is important to note that with aweight-averaged aggregation number of 4.4, the most common“aggregate” is still an asphaltene monomer. These resultstherefore suggest that the nanoaggregate model should beinterpreted in terms of a preferential distribution of asphaltenecluster sizes where monomers, dimers, and trimers are presentin significant numbers, or better yet should be discarded infavor of the recognition of a continuous distribution of n-mers.The second clear result from the analysis of the asphaltene

clusters is that they can be diffuse, containing a significant levelof solvent50% or more. This compares well with results fromabsolute intensities of small-angle scattering experiments.79 Thenanoaggregate model implies that the nanoaggregates them-selves are denseformed predominantly through π−πstackingand the diffuse nature of the clusters measuredthrough SAXS/SANS is due to fractal aggregation of thesedense nanoaggregates. The simulations described above runcounter to the hypothesis that dense nanoaggregates areformedthey tend to show that the density of the aggregatesformed is similar regardless of their size. There is no evidenceof a model where two steps are involved. However, it is quiteclear that much larger simulations will be needed to show thiswith confidence.Analysis of the principal dimensions of all of the asphaltene

aggregates present during the simulation suggests that prolate-type structures are more common than oblate ones. Theexception is the continental-type asphaltene D, which has a verylarge aromatic core and a strong steric propensity for π−πstacking, leading to oblate cylindrical structures. The size andshape of asphaltene aggregates have been extensively studied bysmall-angle X-ray and neutron scattering. The interpretation ofthe scattering data to specific form factors is difficult because ofthe polydispersity of the system. A particular distribution (e.g.,Schultz, log-normal, etc.) has to be assumed from the outset,and often many parameters have to be estimated from the data.One of the most thorough small-angle scattering studies ofasphaltenes in solution was conducted by Eyssautier et al.,85

who used both SAXS and SANS with solvent contrast variationto obtain a comprehensive data set. The results wereinterpreted as fractal clusters of disk-shaped nanoaggregateswith a height of 6.7 Å and a diameter of 32 Å. On thedimensional maps plotted in Figure 15, this would berepresented at (r1 = 1, r2 = 2.2), which is considerably differentfrom the values seen for clusters in the simulations above.Notwithstanding, the present simulations are too small and tooshort to observe clusters at the length scale seen by small-anglescattering (Rg ∼ 50 Å). Larger and longer simulations arerequired to determine if there are indeed two aggregationlength scales (i.e., nanoaggregates forming clusters) or if theseloose aggregates continue to increase in size as larger systemsizes are used.Are the time and length scales too short/small for all of the

simulations presented in the current work? We believe that forthe simulations in toluene the simulation time was long enough(but possibly a larger system would improve the statistics). Tosupport this assertion, we ran a “cluster breaking” simulationessentially taking the asphaltene cluster structure from the longsimulation of asphaltene C in heptane, where all of themolecules are in a cluster, removing the heptane, and replacingthe solvent with toluene (keeping the asphaltene atoms“frozen” during the process). We observed (see Figure S12)



1121




that in less than 20 ns the system evolved to a similar averagecluster size as for the simulation with toluene (simulation 1),suggesting that (a) we sampled for a long enough time intoluene and (b) the aggregation observed in our simulations isreversible in nature.

6. CONCLUSIONS6.1. General Observations. We have employed atomistic

molecular dynamics simulations of large systems (∼50 000atoms) and long time scales (80 ns) focused on four differentasphaltene structures, a model resin molecule, and theirmixtures. Asphaltenes were simulated in an explicit solvent,either toluene or heptane, under ambient conditions. Theseconditions are not the same as experienced in either anupstream or downstream oil production environment, whereasphaltene aggregation and deposition are likely to be aproblem. By definition, however, they do represent thesolubility extremes for asphaltenes and as such are vitalmodel systems for comparison to experiment. A case is also tobe made toward the degree to which the models represent realsystems with respect to morphology, number and location ofheteroatoms, average molecular weight, etc. While all of theseaspects could be contentious, some observations of asphalteneaggregation behavior are common to all asphaltene structuraltypes and are presumed to be universal. These include thefollowing:

• In a good solvent there is a distribution of cluster sizeswhere monomers and dimers constitute the mostcommon “cluster” size.

• The average aggregation number of clusters rangesbetween 3.6 and 5.6 molecules (as defined by eq 1). Thisis lower than seen by some indirect experimentalmethods (six to eight molecules), but the number isdependent on the type of average that is measured. Theresults closely match the estimate of aggregationnumbers obtained from small-angle X-ray scattering data.

• Analysis of the principal axes of the gyration tensorindicates that on average the clusters are relatively

spherical with λ λ/1 2 < 1.9 and λ λ/2 3 < 1.6. There is

no evidence of thin disk-shaped nanoaggregates assuggested by small-angle scattering results.7 Differencesin the average shape of the clusters are due to theunderlying structure of the molecule, with archipelago-type asphaltene favoring longer prolate structures andlarge continental-type asphaltene favoring oblate shapes.This is in agreement with previous observations fromboth experiment and simulation.80

• Estimates of the density of the aggregates fromsimulation show that they are diffuse in nature,containing on average at least 50% solvent, in excellentagreement with experimental observations.79

• Simulations of mixtures of different types of asphaltenestructure show cluster properties that are intermediatebetween those of the individual components. There doesnot appear to be an overall reduction in the asphaltenecluster size when two asphaltene structures are used.

• The replacement of a portion of the solvent molecules (7wt %) with a model resin does not alter the asphalteneaggregate shape, size, or density when toluene is thesolvent. However, in heptane the effect of resin is todecrease the density of the asphaltene aggregates, mostpossibly by intrusion. These results indicate that theresins do not play a solvation (or surfactant-like) role inthe formation of asphaltene clusters. The results inheptane match the experimental findings of thecoprecipitation of more soluble molecules with asphalte-nes.86

• Potential of mean force calculations using umbrellasampling and weighted histogram analysis show that thefree energy of dimerization of asphaltenes is lower intoluene than in heptane. For asphaltene C, the freeenergy of forming a trimer from a dimer and a monomerin toluene is lower than the free energy of dimerization.If this trend repeats itself for larger clusters, it wouldexplain the fact that in toluene the aggregation ofasphaltenes is limited to a small number of moleculesi.e., reductions in free energy of aggregation as moremolecules are added to the cluster eventually limit thecluster growth. In heptane, complete aggregation should

Figure 16. Average cluster sizes for simulations of 27 molecules of asphaltene C in toluene and heptane over 0.5 μs. Bold lines are running averagestaken every nanosecond (cf. Figure 4).



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occur by definition,44 and this would be in line with anincrease in free energy as the cluster size increases.

• We find no evidence to support the claim that there is afundamental difference between the aggregates of a fewasphaltene molecules (so-called nanoaggregates) andthose of larger clusters. In fact, the asphaltene clusterdistributions are seen to be continuous, suggesting adistributed model is more accurate than the Yen−Mullins model, though the latter is conceptuallyappealing and widely accepted.

6.2. Outlook. As computational power has increased, thetime scales achieved for molecular dynamic simulation ofasphaltenes have also increased, from O(10−100 ps) up toO(10 ns). However, even these time scales are most likely small(cf. Figure 5), where the relaxation times for asphaltene A areclearly large, as only after ∼40 ns one can observe differences inbehavior between toluene and heptane. We have run uniquelylong 500 ns (0.5 μs) simulations of the island-type asphaltene Cin toluene and heptane, continuing from the end of the 80 nssimulations (simulations 1 and 2). The average cluster sizesover the course of these simulations are depicted in Figure 16.There is no obvious drift in the average aggregation number forthe simulation in toluene, with the cluster size oscillatingbetween 3 and 5. However, in heptane there is a discernibleupward trend in the aggregation number, although this is onlyclear over such a long time scale (by the standards of atomisticMD).The differences in aggregation at the beginning and end of

the 500 ns simulations are clearer if we look at the distributionsof aggregation numbers for the first and last 100 ns (Figure 17).In Figure 17 we have plotted the number of clusters of eachsize, N(cluster size), multiplied by the cluster size for eachparticular instance. The ordinate is therefore proportional tothe probability of finding a molecule in a cluster of a given size.Such a plot gives an average snapshot of the distribution ofmolecules in clustered states. Here there is clear differencebetween the behavior in toluene and that in heptane. Inheptane, there are few monomers and dimers, and the majorityof asphaltenes form part of large clusters (or a single clusterincluding all of the molecules); in toluene, the most likely“cluster” is in fact an asphaltene monomerthere areobservable numbers of dimers and trimers, but as the clustersize increases, the likelihood of the formation of a multi-

molecular cluster decays rapidly. However, in toluene there islittle difference in the distribution from the beginning to theend of the 500 ns simulation, with monomers or smallaggregates being most common, whereas in heptane by the last100 ns of the simulation there is a clear preference for largerclusters of 18 to 25 molecules, in sharp contrast to the resultsinferred from looking only at the first 100 ns of the simulation.Here we are clearly encountering finite size effects, as thenumber of molecules in the box is 27. If a larger system weresimulated, one may assume that the cluster size would continueto grow.These simulations are the largest and longest atomistic

molecular dynamics simulations conducted on asphaltenes insolution at the present time. In spite of this, it is clear that thesesimulations fall short of being able to fully replicate theaggregation behavior even for these modest-sized systems ingood solvents. The radius of gyration of asphaltenes in tolueneas seen by small-angle scattering is on the order of ∼50 Å. Toaccurately represent this, a simulation box would need to belarger, say at least 200 Å in each dimension, compared to ∼80 Åfor the simulations reported here. To put this into context,simulations would take on the order of 15 times longer to run.In addition to the simulation box size, our 500 ns simulationsindicate that in poor solvents (e.g., heptane), changes can occurover time scales that are very long compared with thoseassociated with atomistic MD.A way to access these longer time and length scales is to use

coarse-graining (CG) of the force field, representing groups ofatoms by a single “bead”. The simplest form of CG for organicsystems is to lump together the hydrogen with the carbon in“united atom” models, as used in some simulations ofasphaltenes.34,49 This is usually implemented solely for thealiphatic carbons. It reduces the total number of atoms (quiteconsiderably for highly saturated organics) and also removesthe highest-frequency molecular vibrations, the C−H bonds,therefore increasing the time step that can be used. However,more aggressive CG is needed to explore the problem in anappropriate fashion.To date there have been relatively few attempts to study

asphaltenes over larger length and time scales using coarse-grained models with molecular mechanics,81 standard molec-ular dynamics,87−89 or dissipative particle dynamics.90−93

However, most of the aforementioned models lack a traceable

Figure 17. Distributions of cluster sizes for the first (red) and last (green) 100 ns of 500 ns simulations of 27 molecules of asphaltene C in tolueneand heptane at 7 wt %.



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link to the atomistic model they attempt to represent. Thebeads (or superatoms) have a distant relation to the underlyingatomistic force fields. A further consideration is that the loss ofstructural detail in the CG approach does require carefulbenchmarking against experimental and/or more detailedsimulation results. In need of particular care is the modelingof the polynuclear aromatic hydrocarbon core of the models,for which the current models, based on the properties ofbenzene, provide a poor representation and an unphysicaloverprediction of the face-to-face aggregation.94 Provided thatone has faith in both the representability of the proposedasphaltene morphologies and the transferability of the atomisticintermolecular potentials, the results from the detailed atomisticsimulations presented here provide a benchmark for propertiessuch as the dimerization free energy, clustering tendencies, etc.with which to test future coarse-grained simulation studies.Notwithstanding the hurdles, CG methods have the potentialto increase the size or time scale available by a factor of 10−100compared with fully atomistic MD and are the way forward forlarge-scale modeling of petroleum fluids.95,96

■ ASSOCIATED CONTENT*S Supporting InformationThe Supporting Information is available free of charge on theACS Publications website at DOI: 10.1021/acs.energy-fuels.6b02161.

Tables with simulation details of all runs conducted andnumerical results presented (S1); additional results forasphaltene E, asphaltene D, and a mixture of asphalteneA and asphaltene E in toluene and heptane (S2−S4);cluster dimensional maps for asphaltenes A and E (S5);plot of the numbers of monomers during 500 nssimulations of asphaltene C in toluene and heptane(S6); discussion of the reversibility of the clusteringprocess (S7); and further discussion of eq 6 (S8) (PDF)

■ AUTHOR INFORMATIONCorresponding Author*E-mail: [email protected]. A. Muller: 0000-0002-1513-6686NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSThe authors acknowledge the funding and technical supportfrom BP through the BP International Centre for AdvancedMaterials (BP-ICAM), which made this research possible.Enlightening discussions with Prof. Juan Murgich are gratefullyacknowledged. The simulations described herein wereperformed using the facilities of the Imperial College HighPerformance Computing Service and the BP High PerformanceComputer Centre. Additional support of the MolecularSystems Engineering Group from the Engineering and PhysicalSciences Research Council (EPSRC) of the United Kingdom(Grants EP/E016340 and EP/J014958) is also gratefullyacknowledged.

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