Thermodynamic Modelling of Asphaltene Precipitation and Related Phenomena 2015 Advances in Colloid...

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Historical perspective

Thermodynamic modelling of asphaltene precipitation andrelated phenomena

Esther Forte, Spencer E. Taylor BP Centre for Petroleum and Surface Chemistry (BP-CPSC), Department of Chemistry, University of Surrey, Guildford, Surrey GU2 7XH, United Kingdom

a b s t r a c ta r t i c l e i n f o

Available online 15 December 2014

Keywords:AsphaltenePhase behaviourModellingEquations of stateSAFT

Asphaltenesare considered to be the heaviest and most polar fractions of crude oilsand are frequently implicatedin problems encountered during production and rening as a result of phase separation. In recent years,

considerable effort has been given to understanding the phase behaviour of these structurally heterogeneousmaterials fromboth experimental andcomputational perspectives. Variousexperimental studieshave conrmedthe long-advanced colloidal behaviour of asphaltenes in organic media, and this has inspired a number ofmodelling strategies. The present review is specically concerned with advances in modelling asphaltenephase behaviour with emphasis on the use of the statistical associatinguid theory (SAFT), which it attemptsto place into the wider context of thermodynamic treatments.

2014 Elsevier B.V. All rights reserved.

Contents

1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12. Lattice uid theories . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33. Equations of state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3.1. Cubic equations of state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.2. Cubic plus association . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53.3. Statistical associatinguid theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

4. Other approaches. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85. Conclusions and future trends . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1. Introduction

Asphaltenes have attracted much research curiosity for many years.Interest has ranged from their chemical characterisation in order todene their molecular structure, to understanding their solution andinterfacial behaviour, including their aggregation and precipitationtendencies. However, even today, many of these aspects are still openquestions where further research is needed. The main reasons for thisstem from the limited or ambiguous knowledge concerning theircharacterisation.

Crude oils are complex mixtures of thousands of components[1],which are difcult to analyse and therefore characterise[2].The vastamount of components existing in crude oil has led to comparison

with the amount of genes in the genome, giving rise to the use ofthe words petroleome and petroleomics . The difculties incharacterising the crude oil are also evident in the case ofasphaltenes, the heaviest nondistillable fraction in crude oil, wherethe characteristics of this fraction will also depend on the sourceof the crude oil[3] . Generically, they are classied solely on theirsolubility properties, typically as the fraction of oil that is solublein toluene and insoluble in n-heptane.

In the oil industry upstream and downstream operations could eachbenet from a comprehensive understanding of asphaltene-relatedphenomena. Over the years, many studies have shown asphaltenes tobe active at water-oil interfaces, resulting in the stabilization of oil/water emulsions, and solid-oil interfaces, causing modications torock wettability (refs.[4,5]and references therein). On the other hand,a numberof problems also resultfrom theirocculationand sedimenta-tion caused by changes in solvency[6,7].

Advances in Colloid and Interface Science 217 (2015) 1 12

Corresponding author.E-mail address:[email protected](S.E. Taylor).

http://dx.doi.org/10.1016/j.cis.2014.12.002

0001-8686/ 2014 Elsevier B.V. All rights reserved.

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The phase behaviour of reservoir uids is intricate. Regions of up tofour phases in equilibrium (solid-liquid-liquid-vapour) have beenidentied in asymmetric oil mixtures containing asphaltenes, resinsand light hydrocarbons as constituents[8]. Asphaltenes and otherpetroleum fractions also exhibit complex path-dependent phasebehav-iour, which implies an added difculty in the prediction of asphalteneprecipitation. In particular precipitated asphalteneshave beenobservedto undergo a complex transition from solid to liquid in a temperature

range of ~(300

500) K[9

12]and additionally to present amphotropic[13]liquid-crystal domains[14].From a physicochemical viewpoint, asphaltenes have presented a

very interesting research topic, not least because of their colloidal na-ture in crude oils[1518]with the earliest theories based on interac-tions with structurally-similar resins. Asphaltenes are known tocontain a high proportion of polycyclic aromatic groups and aliphaticchains. Two different molecular architectures have been proposedwhich are consistent with established atomic compositions and sup-ported by a range of analytical techniques. The rst is an archipelagostructure wherein differentiated aromatic groups are linked togetherthrough alkyl bridges; the second is an islandor continentalstruc-ture wherein the core of the molecule is based on a single polycyclic ar-omatic hydrocarbon ring that contains peripheral alkane substituents.Different authors have suggested models with one or the other beingpredominant for different asphaltene samples (e.g., refs.[1925]favourthe archipelago architecture and[2631]favour the continental) orasphaltene fractions[32], notwithstanding that the reliability of somecommon experimental methods may be a matter of concern[3335]. Apredominant molecular structure for asphaltenes supporting the conti-nental archetype has been identied in the Yen-Mullins model[3638](cf. Fig. 1); these structures can further assemble in the form ofnanoaggregatesat low concentrations (~100 mg L1) and clustersathigher concentration (~3 g L1). In the past, self-aggregation leadingto the formation of aggregates has led to much disagreement regardingasphaltene molecular weights; over the years values have ranged froma few hundred to several million (see refs.[26,3941]and referencestherein). In turn, from a modelling perspective this has led to differentrepresentations of the basic structural unit in the model (i.e., ranging

from molecular to aggregated).However, the lack of a comprehensive understanding of the nature

of asphaltenes as well as their interactions with other components ofcrude oil has motivated the development of a variety of differentapproaches to model their behaviour in solution and mechanisms

involved in their aggregation and subsequent precipitation. Central tothe modelling discussions is the question of the intermolecular forcesinvolving the asphaltenic constituents and other components in crudeoil, which affect their solubility and aggregation properties. Perhapsone of the most systematic studies is that of Wiehe[42], who studiedthe dominant interactions in asphaltenic fractions through a solubilityanalysis in a wide range of solvents arranged on the basis of theircomplexingandeld forcesolubility parameters. These parameters

provide indications of whether directional (hydrogen-bonding or elec-trostatic)or nondirectional(vander Waals and otherpolar)interactionsdominate their solubility. Those with high eld force but lowcomplexing solubility parameters were found to be the best solvents,supporting the idea that non-polar van der Waals interactions play amajor role. The importance of van der Waals dispersion interactions inaggregates of asphaltenes and resinshasalso been supported by severalotherauthors [4345], although electrostatic interactionshave been ad-ditionally suggested [44,46]. However, thecontributionfrom hydrogen-bonding interactions should not be disregarded in the case ofasphaltenes with a high proportion of polar functionality or heteroatomcontent, as these are likely to promote their propensity to stabilisewater-oil emulsions[47].

Of particular interest from a modelling perspective is the nature ofthe instability responsible for the precipitation of asphaltene-richphases for which bothsolid-liquid [48,49] and liquid-liquid [50] immis-cibilities have been suggested, which has given rise to some disagree-ment in the approach to model these systems.

Furthermore, two different conceptual descriptions of the mecha-nism by which asphaltenes are considered as being stable in crudeand residual oils have provided the basis for modelling asphaltene sta-bility over the years. As alluded to earlier, the rst supports the notionthat the phase behaviour of these systemsis governed by their colloidalnature, in which it was originally considered that asphaltenes aredispersed in the oil matrix in the form of aggregates that are stabilisedby structurally similar resins which possess a slightly greater afnityfor the bulk oil. In this case, asphaltene precipitation is assumed to bethe result of a loss in the stabilising effects of the resin molecules. Theresulting colloidal picture led Nellensteyn [51] to introduce the concept

of a micellefor the rst time by in petroleum science. Later, Pfeifferand Saal[52]further developed the resin-stabilised asphaltene micellemodel. Within this rst perspective, most attention is paid toasphaltene-asphaltene and asphaltene-resin association based on pi-pistacking of the aromatic units At that time, no specic details were

Molecule(~1.5 nm)

Nanoaggregate(~2 nm)

Cluster(~5 nm)

Fig. 1. Conceptualview ofthe modied Yen-Mullinsmodel. Theproposed molecularstructureis seenin theleftimage.The polycyclic aromatichydrocarbon of themoleculesis representedby a at oval in the middle image; these can form nanoaggregates with aggregation numbers of about six which contain a single aromatic disordered stack in the interior (cf. middleimage). The latter can form clusters with aggregation number of about eight; this is represented in the right image, where the spheres depict the aromatic disordered stack in a

nanoaggregate. The lines are the (mainly) alkane substituents. Adapted from ref.[36].

2 E. Forte, S.E. Taylor / Advances in Colloid and Interface Science 217 (2015) 112


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given regarding the formation of micellar aggregates, although now,based on the known solvophobic character of nonpolar solvents, inter-molecular interactions areknown to be much weakerthan the more fa-miliar hydrogen bonds in water, for example. These differences arereected in measurable physical properties such as cohesive densityand surface tension; comparing water and nonpolar solvents, for exam-ple, indicatesthat thefree energybenets of micellisation would be lessin a nonpolar solvent than in water. Therefore, for the formation of

inverse

micelles in hydrocarbons, the solvophobic effect suggeststhat the critical micelle (or aggregation) concentration will be less pro-nounced and aggregation numbers will be much smaller, as previouslyelucidated by Ruckenstein and Nagarajan[53]thirty-ve years ago,and supported by very recent experimental results[54].

The second description is based on a more general (molecular)picture in which asphaltenes are considered to be dissolvedin theoil, rather than beingsuspendedas colloids. Here, asphaltene precip-itation is assumed to be the result of a phase-separation process, andtherefore no attention is paid to the structural characteristics of thesystem. Within this second conceptual description, focus is placedon mimicking the essential molecular characteristics of a set of repre-sentative components in the oilmixture. The role of resins is not clearlydistinguished from that of any other oil components and as a resultthese are not always modelled as a separate molecular entity. One ofthe rst thermodynamic solubility models (also called the liquidmodel by the authors) is that of Hirschberg et al. [55].In their work,two pseudocomponent [asphalt (i.e., asphaltenes + resins) andsolvent]and three pseudocomponent (asphaltenes, resins and solvent) modelsareconsidered,depending upon theconditions at whichresinsare asso-ciated with asphaltenes or are separate.

These models have been used by different authors with slight varia-tions. Leontaritisand Mansoori [56] consideredasphaltenes as solid-likeparticlesthat areconsidered to be suspendedin thecrudeoilin theformof colloids stabilised by repulsive interactions brought about by resinmolecules adsorbed on the surface. The oil phase is assumed to beasphaltene-free and it is only the chemical potential of the resins inthesolid and liquid phases that areused to determine thephase separa-tion[56].1 Firoozabadi and coworkers[57,58]use a thermodynamic

model of micellisation based on the earlier works of Nagarajan andRuckenstein [59], Blankschteinet al. [60] and Puvvada and Blankschtein[61], in which asphaltenes are assumed to aggregate in the core of mi-cellar structures peptized by bipolar resins present on the surface. Equi-librium between the asphaltenic monomers in solution and thoseforming micelles of a given number of aggregates is considered.2 Acolloidal-based description has also been suggested within a liquid-liquid equilibrium interpretation [6264], wherein equilibrium isbased on both, asphaltene and resin, types of molecules.

Theuse of colloidal models is notwithoutsome controversy,howev-er. Recent studies refuting the colloidal model are discussed byPunnapala and Vargas[65], while micellar models of asphaltene aggre-gationhave been suggestedas being inadequate from a lack of evidencefor a critical micelle concentration, or concentration at which the

asphaltenes start to associate, using isothermal titration calorimetry[66]. However, whilst this approach failed to detect nanoaggregate for-mation at low asphaltene concentrations, the nding is consistent withthedominant entropic contributionto theprocess [67],andanumberoftechniques have indeed provided evidence for nanoaggregate

formation in asphaltene systems, including high-Q ultrasonics[68],NMR spectroscopy[69], electrical conductivity[67], small-angle neu-tron and x-ray scattering[70], mass spectrometry[70], centrifugation[67], and the analysis of gravity gradients in oilelds[7173].

The reversibility of the process of asphaltene precipitation is also acontroversial topic. The effect of pressure on asphaltene precipitationis generally thought to be reversible [40,74,75], whereas most disagree-ment is found regarding the inuence of temperature and composition.

The re-dissolution of precipitated asphaltene at low temperatures iskinetically slow and long periods of time may be required to verify thereversibility of the process. Some authors have regarded asphaltene pre-cipitation only as partially reversible[76], especially when asphaltenesare destabilised well beyond the onset conditions [77,78]. Apparent irre-versibilities have also been associated with inappropriate reversibilitycriteria [79] andto theexistenceof an energy barrier to asphaltene disso-ciation[80]. In spite of the difculties, the number of studies supportingreversibility is remarkable[74,75,7983].

An interesting question is relevant to the energeticversusentropicbalance, specically in relation to the level of detail needed to modelthese systems. In the models used to describe asphaltene precipitation,there has been support coming from two different directions. One is aneffort to describe in detail the type of interactions playing a role, whichis considered as the dominant mechanism. The second perspectiveconsiders asymmetry in sizes between the different components inthe mixture to be the dominant cause producing the instabilities andsegregation into two liquid phases. The latter has been shown to be animportant mechanism leading to uid-uid phase separation inpolymer solutions, or colloid-polymer systems, even in the case ofathermalor purely repulsive systems, examples of which are givenin refs.[8489].

In the next sections we will review themainapproaches used to de-scribethe phase behaviourof asphaltenes.This present reviewattemptsto complement earlier reviews on thesubject [6,45,78,9092].Themostrecentarefrom Greeneld [92], where emphasis is on the application ofmolecular simulation techniques, and Wiehe[45], which focuses onasphaltene solubility and the use of solubility parameters and theFlory-Huggins theory. In the present review we offer a detailed discus-

sion on the main uid theories applied in this eld.

2. Lattice uid theories

A traditional approach to study asphaltene precipitation has beenthe use of polymer models, in particular lattice theory [93]. The combi-nation of the Flory-Huggins[94,95]polymer-solution theory with theregular-solution theory of Scatchard-Hildebrand[96,97]has been themost common methodology to study the precipitation of asphaltenesin the literature. The conventional application of the theory is basedon a pseudo-binary approximation that assumes the mixture consistsof two pseudocomponents; these are the solvent (i.e., the oil) and thepolymer (i.e., the asphaltenes). According to this model, the system ischaracterised based on the solubility parameter and the molar volume

of its components, where an expression to determine the solubility ofasphaltene in oil is obtained from evaluation of the Gibbs free energyof mixing as3

Gmix RT nslnsnalnansavsRT

as 2

h i 1

where R is the universal gas constant, Tis the absolute temperature, n isthe numberof moles, is the volume fraction, is the solubility param-eter and the subscripts a and s refer to asphaltenes and oil, respectively.Because the effect of pressure is not taken into account within lattice

1 This approach considers the process as being irreversible and not based on solvingequilibria for the asphaltenic monomers in solution and in the colloids. No distinction ismade regarding the number of asphaltenic units in the colloids and the equilibrium issolved only based on the resins. In the absence of resins, asphaltene moleculesocculateand precipitate in this model.2 Micelles of different size,i.e., different aggregation numbers, are regarded as different

species. The average state of an asphaltene molecule in a micellar coreis to be assumed tobe similarto itsstate in a puresolidasphaltene phase. In theabsenceof resins,asphaltenicmolecules are assumed to precipitate immediately due to the low solubility of the

asphaltene monomeric molecules in the bulk.

3 The rst terms are due to the entropyof mixing;the last one is due to the enthalpy of

mixing given by the regular solution model.

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theories, combinations with cubic equations of state have been used tosolve for vapour-liquid equilibrium.

One oftherst applicationsof this Flory-Huggins-Hildebrand theorywas used by Hirschberg et al. [55]to calculate the amount of asphaltprecipitated from a liquidphase whose composition hadbeen previous-ly calculated using the Soave-Redlich-Kwong equation of state [98]. Themodel of Hirschberg and coworkers was later used by other authors[99101], but it is limited to a monodisperse asphaltenic fraction that

precipitates as a pure component. Modi

cations have been suggestedto deal with the assumption that the precipitated phase contains notonly pure asphaltene but consists of a phase concentrated inasphaltenes containing also a fraction of solvent. This is the work ofCimino et al.[102], which, however, assumes a pure solvent phase andcannot therefore be applied to estimate the amount of asphaltene pre-cipitated. Other authors have avoided this type of simplifying assump-tion. This is the case of Wang and Buckley [103], where a correlationwith the refractive index of non-polar species is used to estimate thesolubility parameter of the oil[103], reducing the uncertainty of themodel. In the work of Yarranton et al. [104106], the bitumen orheavy oil is considered to consist of the SARA (saturates, aromatics,resins and asphaltenes) pseudocomponents, the solubility parametersof which are obtained from a correlation with enthalpy of vaporisationand molar volume data. Oil phases consisting of both asphaltene andnon-asphaltene components are also assumed in the work ofMohammadi and Richon[107]. Further modications of the Flory-Huggins theory have been presented and successfully applied to de-scribe asphaltene precipitation. One example of such modications isbased on including a binary interaction parameter [108] thatcharacterises the interaction between unlike molecules, as applied byPazuki and Nikookar [109] and Modi and Edalat [110]; this interactionparameter is determined as a function of molecular weight[109,110].Mohammadi et al.[111]have combined the approach with chemicaltheory to account for asphaltene self-association resulting in n-mer ag-gregates. The theory has been also extended to predict asphaltene con-centration gradients in oil reservoirs by incorporation of a gravitationalterm[112]. Recently, an application of the Flory-Huggins theory com-bined with the Non Random Two Liquid (NRTL) model[113]has been

presentedto describeasphalteneprecipitation in differentsolvent ratios[114].

Other polymer theories have been used to model asphaltene phasebehaviour. In particular, a number of authors[104106,115119]havedeveloped thermodynamic models based on the Scott-Magat polymertheory[120,121], where the heterogeneous structure and polydispersi-ty in the asphaltene molecular weight is taken into account in themodel. Although there is recent practical evidence from sulphur analy-sis and speciation of reservoir crude oils that there are circumstanceswhere polydispersity can be ignored at the molecular [73] andnanoaggregate/cluster [72] levels, polydisperse models have beendeveloped to account for size and molecular weight distributions of ag-gregates due to asphalteneself-aggregation[115,119,122,123]. In these,the polydispersity is specied through a continuous molecular-weight

distributionfunction,which maybe usefulto account fora size distribu-tion of aggregates due to asphaltene self-association. The rst applica-tion of this type of model to study precipitation of an asphaltenefraction characterised by a molecular-weight distribution is that ofKawanaka et al. [122]in which a gamma distribution is arbitrarilychosen [122]; the variance of the distribution is treated as an adjustableparameter. Although gamma distribution functions have been a com-mon choice[105,106,115,124], Schultz-Zimm distribution functions[104]and fractal distribution functions[119,123]have also been sug-gested. A comparison between these different distribution functions ismade in the study of Manshad andEdalat [117], where the use ofa frac-tal distribution function leads to best agreement with experimentaldata. A typical element in these studies is to model asphaltenes as theonly self-associating fraction. In the work of Yarranton et al.[124]a

single molecular weight distribution for a mixture of asphaltenes and

resins (or a combined pseudocomponent) is seen to best characterisethe self-association and precipitation of asphaltenes and resins that isobserved when low carbon number alkanes are used as precipitant.

The simplicity of lattice uid theories has motivated its extensiveapplication in the eld, but these approaches present important limita-tions. Until recently theeffectof density or compressibility on the phasebehaviour was not taken into account to allow for the dependence onpressure. However, this has been accomplished in a very practical way

by calculating pressure variations associated with asphaltene gradientsin oil columns, throughthe introduction of a gravity term into theequa-tion of state[112,125].

Accounting for the effect of temperature is also not straightforward,and so is usually described empirically. Thetemperature dependence ofthe solubility parameters, densities and mass distribution is obtainedthrough tting to empirical correlations; however, some authors haveattempted the extension to different conditions[105,106,126]. An ex-ample is seen inFig. 2, where predictions are calculated after tting toasphaltene yields fromn-heptane and then adjusting the temperaturedependence with another oil. A different drawback of regular solutiontheory is the fact that the values for the solubility parameters ofasphaltenes and other crude oil components are not well known.Although these are typically determined through correlation ofexperimental data, solubility parameters are also obtained usingequations of state [93,109,123,127133]. Other authors have alsohighlighted the need for a more detailed description of physico-chemical phenomena than that underlying regular solution theory,commenting on some of the limitations and misapplication of thetheory to these mixtures[134].

3. Equations of state

One of theadvantages in theuse of equationsof state is the versatil-ity in their application, which is not restricted to a range of conditions.Equationsof state arealso notlimited to modellingprecipitation bound-aries, but can be used to describe the entire phase equilibrium diagramof the mixture. In this section we will review the application of cubic

equations of state, cubic plus association and the statistical associatinguid theory in theeld of asphaltene precipitation.

0.00

0.05

0.10

0.15

0.20

0.25

0.4 0.5 0.6 0.7 0.8 0.9

T=273 K

T=296 KT=273 K

T=296 K

T=323 K

Fig. 2.Fractional yield (mass ratio of precipitate after washing and drying per mass ofheavy oil)versussolvent mass fraction sfor a Lloydminster heavy oil dilutedwith eithern-pentane or n-heptane at various temperatures. Solid curves are results using theregular- solution model of[106]for polydisperse asphaltenes; the continuous curvescorrespond to dilution with n-pentane and the discontinuous curves to dilutionwithn-heptane. Symbols are experimental data at temperatures of: red squares,273 K; green circles, 296 K; blue triangles, 273 K; purple diamonds, 296 K and orangeinverted triangles, 323 K. Curves have the same colour code at each temperature.

Adapted from ref.[106].



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3.1. Cubic equations of state

Cubic equations of state have a long history and tradition as widelyapplied tools in industry. Since the rst cubic equation of van derWaals in 1894[135], a large number of cubic equations of state havebeen proposed (excellent reviews can be found in refs. [136140]).The most popular are perhaps those of Peng-Robinson (PR)[141]andSoave-Redlich-Kwong (SRK)[98]. A number of authors have used

cubic equations to model asphaltene phase behaviour[58,142

150]. Inthe model of Kohse et al.[144], the Peng-Robinson equation of state isused. In this work[144]a crude oil containing asphaltene is lumpedinto twelve pseudocomponents; the heaviest pseudocomponent issplitintoa non-precipitatingcomponentand a precipitating component(essentially asphaltene, which is modelled as a pure solid). The param-eters of the solid model are adjusted to match precipitation data for theasphaltene of study. In the application of Sabbagh et al.[147], the Peng-Robinson equation of state is used to model asphaltene precipitationfromn-alkane-diluted bitumens. In their study, asphaltenes are consid-ered to be macromolecular aggregates with a broad mass distributionand represented by a large number of pseudocomponents (N30); theparameters for these fractions are obtained from those for asphaltenemonomers[147]. Peng-Robinson is also the equation of state of choiceintheworkofBeharetal. [146], in which a large numberof components(29) and pseudocomponents (6) is again used to characterisethecrude.In their work, the thermodynamic model is integrated intoan industrialreservoir simulator with the aim of determining the asphaltene depos-ited at different stages of a reservoir[136]. A thermodynamic approachusing a cubic equation of state is also implemented into a reservoir sim-ulator in the work of Fazelipour et al. [148]. Following the model ofNghiem et al. [142], the heaviest fraction in the oil is assumed to consistof a non-precipitating and a precipitating component. The latter is con-sidered to be asphaltene, which is treated as a component that precipi-tates in a pure solid phase. Oil and gas phases are modelled with the PRequation of state[148]. This solid model for asphaltene is also used inthe work of Tavakkoli et al.[151]and in the work of Jamaluddin et al.[145]who use a seventeen component (and pseudocomponent) repre-sentation of the live oil of study. Another example using thisequation

of state is that of Castellanos Daz et al. [150], in which this is appliedto bitumen, propane and carbon dioxide mixtures. At least sixteenpseudocomponents are used to represent accurately the normal boilingpoint curve of the bitumen of study. After optimising the interactionparameters to t experimental saturation pressures of mixtures ofeach solvent with the bitumen, the model is used to predict asphalteneprecipitation fromn-heptane dilutions of the bitumen. However, theprediction of asphaltene yields is seen to fail at high dilution ratios[150].

A number of authors [57,58,143,149,152154] use the Peng-Robinson equation of state to calculate the fugacity coefcients of themonomeric species within a thermodynamic micellisation model. Inthis model, asphaltenes are assumed to associate to form micelleswith resinson their surface; monomeric asphaltenes,monomeric resins

and micelles are considered solutes in the solvent. The precipitate is inmost studies considered a mixture of asphaltenes and resins which issolid at ambient conditions [58,149,154] and liquid at high temperature[143,153].

The predictive capabilities of cubic equations of state have beenquestioned, as for example in ref.[155], where results using the SRKequation of state are compared to calculations with a more sophisticat-ed approach based on the Statistical Associating Fluid Theory discussedinSection 3.3. Parameters regressed with experimental onset pressuredata for a given percentage of injected gas are obtained and then usedto predict the temperature dependence of the onset pressure fordifferentamounts of injected gas. Considerable loss in predictive perfor-mance is observed for the cubic equation of state.

The success of cubic equations of state within the petroleum indus-

try hasbeen motivated by their simplicity and current state of maturity.

However, it should be recalled that cubic equations were establishedfollowing a simple description of molecules based on a molecularmodel of a single sphere with a hard core and attractions mediatedthrough long-range dispersion forces. Unfortunately, such models maynot be appropriate for systems which exhibit hydrogen bonding or forhighly asymmetric molecules.

3.2. Cubic plus association

Theeffort in extendingthe range of application of cubic equations ofstate to systems that associate as a result of directional interactions, e.g.,hydrogen bonding as in water, motivated the development of hybridequations combining cubic equations of state with association theories.This gave birth to the Cubic Plus Association (CPA) equation of state[156],which in its initial formulation combined the SRK equation ofstate with the thermodynamic perturbation theory of Wertheim[157160]. The latter constitutes the association term in StatisticalAssociating Fluid Theory introduced in the next section.

A number of authors have used the CPA equation of state to modelasphaltene phase behaviour [161165]. In the work of Li andFiroozabadi[161,162], the PR equation of state is used within the CPAframework. The rst study focuses on asphaltene precipitation in

model solutions as well as in heavy oil and bitumen, whereas the lattertwo are considered to be a mixture of three pseudocomponents: satu-rates, aromatics/resins and asphaltenes[161]. A representative resultof their study can be seen inFig. 3, in which the effect of temperatureis analysed in comparison with experimental data. In the secondstudy, asphaltene precipitation from a liveoil is modelled, where thelive oil is considered to be a mixture of a considerable number ofcomponents and pseudocomponents, together with a hydrocarbonresidue[162]. The latter is divided into a heavy pseudocomponentand asphaltene. Self-association between asphaltene molecules aswell as between these and heavy pseudocomponent molecules is con-sidered. Although requiring the use of a temperature-dependentcross-association energy between asphaltene and heavy componentmolecules, the approach successfully reproduces the bubble curve,asphalteneprecipitation boundary and gas-oil-asphaltene phasebehav-iour. The live oil is split in a similar manner in a mixture of pure compo-nents and pseudocomponents, resins and asphaltenes in the work ofShirani et al.[164]. Different from the previous study, association ofasphaltenes with other components is neglected in favour of consider-ing asphaltene self-association to be predominant. In the work ofZhang et al. [163] a black-oil reservoiruid is characterised by eighteencomponents and pseudocomponents and both asphaltene self-association and asphaltene-resin association are considered.

0.0

0.2

0.4

0.6

0.8

1.0

0.4 0.5 0.6 0.7 0.8 0.9 1.0

273K

296K

323K

Fig. 3. Fractional precipitation a (mass ratio of precipitate per mass dissolved) ofAthabasca asphaltenes in solutions ofn-heptane and toluene versus the volume fractionof n-heptaneC7at the temperatures shown. Continuous curves are results using theCPA equation of state, whereas symbols are experimental data[147]. Adapted from ref.

[161].



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Other association models, such as chemical theories incorporated incubic equations of state, have also been applied to the study ofasphaltene phase behaviour[166168]. In the work of Vafaie-Seftiet al. [166]a model consisting of at least fteen components (andpseudocomponents) is used with the PR equation of state combinedwith a chemical contribution[169,170]to describe different oils; bothasphaltenes and resins are considered to associate. The PR equation ofstate is also combined with a chemical approach in the study of Du

and Zhang[167]. While lighter components (~10 in number) are treat-ed explicitly, components heavier than hexane are lumped into twelvepseudofractions; the latter are also split into parafnic, naphthenicand aromatic subfractions, where asphaltenes are considered to be theheaviest aromatic fraction. Resinsare notspecied as a differentfractionand only asphaltene self-association is considered[167]. Shirani et al.[168]compare the use of both PR and SRK coupled with a chemicalterm to study asphaltene precipitation. In their work a model basedon aboutfteen components and pseudocomponents is used and bothasphaltene self-association and asphaltene-resin associationare consid-ered. Their results show a betterperformance of thePR equation of statein comparisonwith experimental data [168]. In these chemical theories,association is considered to be theresult of a chemicalreactionbetweenthe monomers, giving rise to new distinct species. A limitation of theseapproaches is that the corresponding temperature-dependent chemicalequilibrium constants appear in the thermodynamic relations and needto be evaluated.4

3.3. Statistical associatinguid theory

An alternative to previous approaches is the useof perturbation the-ories that are rooted in statistical mechanics. The Statistical AssociatingFluid Theory (SAFT)[173,174]is one such approach. The SAFT formal-ism stems from the thermodynamic perturbation theory of Wertheim[157160,175,176]explicitly to take into account the possible non-spherical nature of molecules as well as association through directionalinteractions characteristic of hydrogen bonding. The main assumptionis that of considering the thermodynamic properties of chain-like andassociating uids can be obtained from knowledge of the properties of

a monomeric uid of reference (consisting of single spherical seg-ments). The equation is typically written in terms of the Helmholtzfree energy as a sum of contributions

A Aideal

Amono

Achain

Aassoc

2

whereAideal is the ideal free energy,Amono is the contribution to the freeenergy due to interactions between monomers or individual segments,Achain accounts for the possibility of chain formation, and Aassoc is thehydrogen-bondingintermolecular association. The equation is very ver-satileand a testamentto this is thenumber of many differentversions ofthe theory that have been developed over the years. Although differ-ences may be subtle, the main attribute leading to the various versionsis the choice ofuid of reference.

In the original SAFT formulation[173,174], molecules are modelledas associating chains of Lennard-Jones (LJ) segments, while in a simpli-ed treatment[177,178], associating chain molecules of hard-sphere(HS) segments are considered, SAFT-HS, and the dispersion forces aretreated at the van der Waals mean-eldlevel (i.e., in the absence ofcorrelations between particles). The SAFT-HS approach has proved tobe successful for modelling strongly hydrogen-bonded associating sys-tems (such as water + alkanes[179]), although is not adequate for sys-temswhere dispersion interactionsare dominant. Thus, the introductionof mixing rules forthe dispersion terms [180,181] led to theSAFT-VR ap-proach[182,183], in which the uid is described in terms of associating

chains of segments interactingthrough an attractive potentialof variablerange (VR), typicallya square-well,althoughthe extension to Sutherlandand Yukawa potentials was also presented in the original manuscript. Inthis version of thetheory, theproperties of themonomeric segmentsareobtained through a Barker and Henderson high-temperature perturba-tion expansion[184186], truncated at second-order, from a referencehard-sphere uid. Recently, a new formulation of the SAFT-VR theoryhas been developed for Mie potentials (SAFT-VR Mie)[187], which im-

proves the predictive capability of the equation in the description ofsecond-derivative properties. A third-order perturbation expansion isfurther shown to improve the description of the vapour-liquid equilibri-um ofuids in the critical region[187]. The so-called soft-SAFT[188]uses a Lennard-Jones reference uid as in the rst SAFT equation, butwith different expressions for the referenceuid based on the equationof Johnson et al.[189],a very accurate equation of state for mixtures ofassociating Lennard-Jones chains. A version that has become very popu-lar for chain uids is the perturbed-chain SAFT (PC-SAFT)[190,191]inwhich the usual monomer reference system is replaced by a hard-sphere-chain reference uid. A high-temperature expansion truncatedat second-order is used to obtain the attractive-chain perturbation con-tribution, but the formal expressions that would be obtained based ona Barker and Henderson expansion were simplied using power seriesin density with coefcients adjusted to t pure-component propertiesofn-alkanes. More recently, other heteronuclear versions of the SAFTequation have been developed such as the SAFT-approach[192194],where the equation is coupled with a group contribution formalism.

The SAFT equation of state has been very successfully applied tostudy the thermodynamic properties and phase behaviour of complexuids and mixtures, and the interested reader is referred to the existingreviews specically dedicated to this theory[171,172,195197].

In the area of present interest, a number of SAFT equations of statehave been applied to model the phase equilibria of asphaltene-containing systems. In general, these applications consider thatasphaltene precipitationis based on a liquid-liquid equilibrium process,although both colloidal and molecular models(cf., Section1) have beenassumed. Following a molecular description, asphaltene clustering andaggregation is considered a result of the molecular environment, and

not necessarily an initial assumptionof themodel;models thatconsiderasphaltene clusters (orsmall aggregates) have, however, also been usedin a number of works [64,65,155,198208] away from an explicit colloi-daldepiction.Similarities with thephase behaviourof oligo-or polymersystems, have directed the focus of attention to molecular asymmetryand van der Waals interactions, which are assumed to be the featuresthat dominate their phase behaviour. An advantage of the physically-sound pure-component parameters used in SAFT is that they correlatewell with molecular weight for families of compounds within a ho-mologous series. This allows the estimation of intermolecularmodel parameters for asphaltenes based on molecular weight. Aswill be mentioned, this approach has been used in numerous studies[65,198201,203,204,209].

Inthe work ofWu etal. [63,210], a formulation of the SAFTequation

of state at the level of SAFT-HS combined with colloid theory was usedto describe the precipitation of asphaltene from crude oil. The system isassumed to consist of asphaltenes and resins(the solutes) interacting ina structurelessmedium which hasa screeningeffectover thedispersionforces between asphaltenes and resins. The medium (oil) is treated atthe level of the McMillan-Mayer theory of solutions[48]5 and its effecton the dispersion interaction between the components (asphaltenesand resins) is determined through the use of a potential of mean-force[212]expressed through the corresponding Hamaker constant [211]in the oil. The Hamaker constant of the relevant interactions depends

4 Refs. [171,172] offer a detaileddiscussionabout these types of theoriesin comparisonto physical association schemes such as those that constitute the SAFT (and CPA)

formalisms.

5 Characterised by theuse ofa potential ofmean-force in place ofthe intermolecularpo-tential between solute molecules, as it is common treatment for colloidal systems[211],and the pressure is considered to be the osmotic pressure due to the explicit treatment

of the effect of the solutes only.



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on that of the oil, which is obtained as a function of the density and com-position. A simple model is used for the asphaltenes, considered as at-tractive hard-core spheres; the resins are modelled as attractive hard-core chains. Association sites are added (two in asphaltene and one inresin molecules) to mimic aggregation through directional short-rangeassociation. Only asphaltene-asphaltene and asphaltene-resin associa-tions are allowed. The molecular parameters for the asphaltene andresin components6 are estimated from average properties7 to describe,

mainly qualitatively, experimental observations regarding the effect oftemperature and composition[210]. Because the medium is treated asa continuum, it is not possible to calculate bubble pressures. In a latterstudy, a volume-shifted PR equation of state is used to evaluatevapour-liquid equilibria and obtain the composition of oil in equilibriumwith a gas phase[63]. Such a treatment is applied to several reservoiruids based on experimental compositional data, where heavy fractionsare divided into a set of pseudocomponents represented by a molecularweight and liquid density. Once the composition and density of the me-dium (liquid phase) are determined, asphaltene precipitation (under-stood as liquid-liquid equilibrium) is then calculated using the SAFTmolecular model presented earlier[210]. In this study, the estimatedvalues for the molecular parameters are kept constant with the excep-tion of those relating to the association interactions (i.e. the number ofassociation sites in the asphaltene molecules and the asphaltene-asphaltene and asphaltene-resin association energies), which areadjust-ed tot experimental onset pressure data for each particular crude oilconsidered.

The SAFT-VR equation of state has also been applied to the study ofthese systems. One of these applications is the work of Buenrostro-Gonzalez et al. [64]. In this study, theequationis used in the frameworkof the McMillan-Mayer theory following the work of Wu et al.[63,210].Analogous molecular models for the solutes are used (i.e., asphaltenesand resins are respectively considered as attractive hard spheres8 andhard chains). Thedispersion interactions considered are based on Suth-erland potentials, where the screening effects of the medium over theenergetic interaction of the solutes are, as before, estimated based onthe corresponding Hamaker constant. As in the studies of Wu et al.[63,210]asphaltene and resins are also considered to associate through

short-ranged anisotropic interactions, which are thought to be domi-nant over dispersion interactions. The parameters of the model arebased on similar estimations, whereby a good prediction of asphalteneprecipitation with different n-alkanes is obtained through parameteradjustment to a single titration curve. The same set of parameters isthen able to predict asphaltene precipitation at high pressure, withonly littleadjustmentof theassociation parameters to a fewdata points.A representative result of these predictions is shown in Fig. 4. The orderof magnitude of the estimated energetic parameters is seen to agreewell with expected values for this type of interactions reported in theliterature[44,93,211,213]. As before, a volume-shifted Peng-Robinsonequation of state is also used here to explicitly model the nature of theoil based on a considerable number of components and pseudo-components, and determine the properties of the medium and

bubble-point pressures at conditions of vapour-liquid equilibria.Another application of theSAFT-VR equation to modelthese systems

have been presented more recently by Artola et al. [209]. The SAFTmodels described up to this point have focused on describing in detail

the nature of the interactions between the major components inheavy oil. In this work the asymmetry in size between the differentcomponents in the oil is considered to be the dominant mechanism inthe liquid-liquid phase separation. Vargas et al. [204]had alreadypointed out existing similarities in the phase behaviour of polymer oroligomer solutions with that of petroleum systems. Based on these ob-servations, therefore, Artola et al. [209] built a representation ofasphaltenic molecules using polystyrene as a prototype moleculecombining both aromatic rings and alkyl chains. Asphaltene moleculesare then modelled as styrene oligomers or polymers using what theauthors call a polystyrene-asphaltene mapping approach. A simplerdescription of the interactions between the components of the mixtureis used, where association interactions are not considered. Crude oilsystems are considered to be described by mixtures of asphaltene (or

polystyreneof a certain molecular weight) and alkane-like components.The molecular model for the latter is based on what could be under-stood as a simplied homonuclear group-contribution approachwhere alkane molecules (excepting methane) are built using the sameSW-potential parameters. The general features of the phase behaviourof the asphaltene-containing oil of previous work[64]are describedwith a basic lumping scheme where only four alkane-like pseudo-components plus asphaltene are assumed to represent the crude.These results arereproduced in Fig. 5. Theasphaltene here is considered

6 These are the standard parameters used in SAFT frameworks, where the dispersion-interaction parameters are dened based on the Hamaker constants of the purecomponents.7 For example, average molecular weights and densities for pure asphaltene and resins

areused, from which, by considering a packing fraction in the solidrange,the diameter ofasphaltene molecules can be derived.This is similar for resins, butwith a packing fractionin the liquid range.8 As in previous work [63,210], theasphaltenemodel is considered to be based on a sin-

gle hard-core sphere of large diameter (17 ), which may more appropriately mimic thesize of a small aggregate formed by three or four asphaltene monomeric units, instead of

a single one.

0

5

10

15

20

25

30

35

40

45

340 360 380 400 420

p/

MPa

T/ K

Bubble curve

Precipitation on set

Fig. 4.Precipitation onset and bubble point data of a crude oil. The symbolscorrespondtoexperimental data[64], where the blue diamonds are asphaltene precipitation onsetpoints and the redcircles are bubble points. The continuous curve corresponds to calcula-tions of the bubble curve using a volume-shifted Peng-Robinson, whereas the discontinu-ous curve corresponds to calculations of the precipitation boundary using SAFT-VR in thecontext of the McMillan-Mayer theory, following the work of Wu et al.[63,210]. Adaptedfrom ref.[64].

0

10

20

30

40

50

60

70

80

90

100

0 200 400 600 800

p/

MPa

T/ K

LLE

VLE

VLLE

Single-phase

Precipitation

boundary

Bubble

curve

Fig. 5. Constantcompositionp Tuidphase diagramof a crude oil (symbols correspondto experimental data[64]) modelled with a simple lumping scheme using SAFT-VR

(continuous curves). Adapted from ref.[219].



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to be represented by a lower molecular weight than in the previousstudy[64], assumed to be that of an individual molecule rather thanan aggregate. Comparisonswith both bubblepointsand asphaltene pre-cipitation data are depicted in the phase diagram. Instead of accuratelycorrelating experimental data, a keydifference with other studies is thatof presenting an approach using minimal tting that is able to explainthe position of the bubble curve and the asphaltene-precipitationboundary within the phase diagram. The bubble curve data is seen to

fall on the boundary of a three-phase vapour-liquid-liquid equilibrium(VLLE) region, whereas the asphaltene-precipitation data is shown tobe related to the liquid-liquid (LLE) boundary of the diagram. ThePC-SAFT equation of state has also shown to be successful to modelthe phase behaviour of asphaltene mixtures, as demonstrated bythe numerous works of Chapman and coworkers [155,198208]and others[65,163,214216]. In most of these studies, the effects ofsizeasymmetry andvanderWaals interactionsare assumedto dominatethe phase behaviour, and association interactions are therefore not con-sidered. Among the various applications, the equation of state has beenused to describe a recombined oil (stock-tank oil with its separatorgas) represented by six[198,200]or seven[199]pseudo-components.9

Molecular parameters are, where possible, derived from correlationsfor n-alkanes and polynuclear aromatics with molecular weight.Parameters for asphaltene, represented by pre-aggregate models of~1700 g mol1, are obtained from ts to titration data for the refractiveindex at the onset of asphaltene precipitation. Binary interaction pa-rameters are adjusted based on vapour-liquid equilibrium propertiesof mixtures of representative compounds of each pseudo-componentconsidered[198,200]. In the works of Gonzalez et al.[199]and Vargaset al.[204], experimental data for the effect of gas injection over theonset of asphaltene precipitation and bubble point pressure wasreproduced for a similar recombined oil sample. Another interestinganalysis presented with the PC-SAFT equation of state has been to ex-amine the effect of the addition of carbon dioxide; when CO2is usedas precipitant, different from other gases, a crossover temperature ispredicted with the equation, below which the additionof CO2stabilisesthecrude oil mixture [203] (see Fig. 6). Such predictions provide insightto experimental observations[99]. An analysis of the effects of oil-based

drilling mud contamination on the onsets of asphaltene precipitationand bubblepoint pressureshasalsobeen carried out [201,204], demon-strating that the equation is able to reproduce the experimental trendsthat feature a pressure drop with increasing percentages of contam-ination. Although oil-based mud is known to be a precipitant forasphaltenes, it dilutes the gaseous components of the oil, reducingthe gas-to-oil ratio and, consequently, the asphaltene instabilityonset pressure[204]. The effect of asphaltene polydispersity on itsstability has also been examined[200,201,204,216]. In these studiesthe polydisperse asphaltenes are subdivided into a number of pseudo-components, which are characterised based on their solubilities indened fractions ofn-alkanes, and where the lighter sub-fraction isequivalentto what are generically known as resins. Even though mainlyqualitative results are shown, theapproachdemonstratesthat the addi-

tion of resins stabilizes the asphaltenesvianon-polar interactions only,increasing the stable region of the phase diagram upon the addition ofprecipitant [200]. Parameters for each asphaltene subfraction arecharacterised by correlations of benzene derivatives in the study ofGonzalez et al. [201]. Recently, Punnapala and Vargas [65] haverevisitedthecharacterizationprocedureused in PC-SAFT so as to reducethe number of adjustable parameters in the asphaltene model. Intheir work, the model parameters for the asphaltene pseudo-fractionare obtained from correlations for n-alkanes and polyaromatic com-pounds using the average molecular weight and the aromaticity as ad-

justable parameters regressed against onset pressures. Generally tenpseudocomponents are used within this uid characterisation. Studies

combining thermodynamic with reservoir and/or pipeline multiphaseow modelling have also been carried out. One such study is the workof Gonzalez et al. [202], in whicha commercialsoftwarepackage includ-ing transport phenomena is combined with asphaltene and wax ther-modynamic modelling using PC-SAFT and a solid-solution model[217], respectively. In this way, estimations of solid precipitation forthe different conditions of pressure, temperature and compositionalong the production lines and during the lifetime of the process canbe achieved. Further integration of molecular thermodynamics withinmodels to represent the mechanism of asphaltene transport in macro-scopic systems has been shown by Vargas et al. [206], in which an ap-proach to model a multi-step process of precipitation, aggregation,advection and deposition of micro-aggregated asphaltenes in awellbore is proposed. This is based on reaction kinetic models to de-scribe the rate of aggregation, precipitation and deposition. The trans-

port of the micro-aggregates through the wellbore is then describedbased on a material balance incorporating these phenomena[206].

Very recently, however, Sedghi and Goual[221]combined PC-SAFTwith Gibbs energies of asphaltene association parameters derivedfrom Molecular Dynamics (MD) simulations of asphaltene moleculeswhich were based on the average aggregation number of asphaltenenanoaggregates (as appear inFig. 1). This combination enabled theseauthors to predict theonset of asphaltene precipitation in terms of pres-sure, temperature and system composition. In the same study, PC-SAFTwas shown to model reasonably well the inhibition ofn-heptane-induced asphaltene precipitation by n-octylphenol using cross-association parameters calculated using mixing rules developed bySandler and coworkers[137,222].

In general, however, molecularparameters are in most casesxedor

estimated based on assumed approximations, the strong foundations ofthe theoryand theassociated physical meaning of theparameters makeassigningvaluesmore reliable. At the moment, however, robust modelsfor the typical components found in crude oils have not been identiedto allow for prediction of thermophysical properties in different reser-voir uids. With the limited amount of experimental data currentlyavailable, increasing the complexity of the model may not be always

justied.

4. Other approaches

Although outside the scope of this review, efforts in thiseld havealso been presented that use integral equation theories to study

structural properties of asphaltene-containing systems[218,219].9

Aromatics and resins are grouped into one pseudo-component.

15

25

35

45

55

65

320 370 420 470 520

p/

MPa

T/ K

Original

reservoir fluid

+ 10% CO2

+ 20 % CO2

Fig. 6.Constant compositionp Tuid phase diagram of a reservoir uid (symbols cor-respond to experimental data[220]) modelled using PC-SAFT (blue curves). The redcurves represent the PC-SAFT calculations upon the addition of a 10% mole fraction ofCO2and the orange curves the corresponding to the addition of a 20% mole fraction ofthe same component. In allcases thecontinuouscurvescorrespond to bubblecurve calcu-lations and the discontinuous to the precipitation boundary. Adapted from ref.[203].



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5. Conclusions and future trends

As a consequence of asphaltenes being linkedwith various problemsin the petroleum industry, both upstream and downstream, a substan-tial amount of work in the literature has been concerned with theprediction of asphaltene precipitation and related phenomena. One ofthe main objectives of this article was therefore to delineate the stateof the art with respect to asphaltene stability modelling.

Since thenatureof asphaltene self-interactionsand those with otheroil components is not well understood, both experimental and theoreti-cal research to gain an insight in this directionwill continue to be invalu-able. Results from experimental asphaltene science have advancedknowledge considerably within the past decade, and it is now acceptedthat asphaltenes leadan enigmatic colloidal existence based on differentlevels of association,as encompassed in the Yen-Mullinsmodel. Interest-ingly, recent evidence seems to indicatethat this model is also consistentwith asphaltene adsorption at water-oil interfaces, in which adsorptionof the monomer units dominates; nanoaggregates and clusters appearnot to adsorb (at least not as strongly, or within the same timescale),and the overall adsorption behaviour can be treated using a simpleLangmuir equation of state[223]. The signicance of this lies in the roleof asphaltenes in stabilising water-in-crude oil emulsions, for example,where the build-up of viscous interfacial layers (skins) occurs[224],which, additionally, may be amenable to theoretical treatments basedon ideas discussed herein relating to solution behaviour. It wouldtherefore appear that the development of ever-more reliable theoreticalapproaches to asphaltene stability should follow from the improved un-derstanding being achieved using an increasingly sophisticated range ofexperimental methodologies to study asphaltenes in solution and atinterfaces.

In this respect, uid theories incorporating different levels of de-tail have shown to be sufcient for reproducing experimental ob-servables found in crude oil systems. The use of lattice uidtheories combined with regular solution theory has been one of themost frequently applied tools, perhaps motivated by its simplicity,in that it may be linked to a higher level of empiricism and restrictedversatility. The application of cubic equations to describe asphaltene

precipitation has in general involved the use of a large number of com-ponents and pseudocomponents. It would be worth assessing the needfor such detailed lumping schemes in future advances.

Thermodynamic toolscan helpto ll thegapsin ourunderstandingofasphaltene precipitation phenomena. In general, molecular-basedequations of state can help in this respect, as their rm foundationsgive condence in capturing the correct physical requirements.However, additional experimental efforts are still essential to exploitfully the potential of these approaches.Further workin the experimentalcharacterisationof asphaltenes and their interactionswith other oil con-stituents mayjustify the computational effort needed to add more detailinto the molecular models. Increasing the currently sparse phase behav-iour data available for these systems, covering wider ranges of experi-mental conditions, will be important to provide a more consistent and

robust development of lumping schemes and adjustment of intermolec-ular model parameters. Such efforts can certainly contribute to ensuringthat these tools are not used as mere correlations of experimental databut ultimately to maximize the predictive power of these approaches.

Finally, molecular-based equations with well-dened potential en-ergy functions open up an interestingeld of application through cou-pling with computer simulations such as molecular dynamics andMonte Carlo[225]. This would allow the estimated intermolecularmodel parameters from an equation of state to be used in molecularsimulations to study structural, interfacial and dynamic properties; therecent SAFT Mie[187,194]is one such equation and it has been shownto provide an accurate and reliable direct link with molecular simula-tions[225228]. Thus, the use of coupled approaches in the eld ofasphaltene stability could be a very promising approach to aid our

understanding of these complex systems.

Acknowledgements

Theauthors aregrateful fornancial support andpermission to pub-lish from BP America. EF thanks A. J. Haslam and E. A. Mller for theiruseful comments on this work. We also acknowledge the editor andthe anonymous referees for their valuable suggested improvements.

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