Reversible Description of Asphaltene Colloidal Association and

Multi-scale Simulation and Experimental Studies of Asphaltene Aggregation and ..... Investigation of structural parameters and self-aggregation of Alg...
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Langmuir 2003, 19, 40-47

Reversible Description of Asphaltene Colloidal Association and Precipitation Gre´goire Porte,*,† Honggang Zhou,‡ and Ve´ronique Lazzeri§ GDPC/CNRS Case 026, Universite´ Montpellier II, 34095 Montpellier cedex 05, France, Total Fina Elf, CSTJF avenue Larribau, 64018 Pau Cedex, France, and Atofina, Groupement de Recherche de Lacq, BP 34, 64170 Artix, France Received June 3, 2002. In Final Form: October 11, 2002 Asphaltene in crude oil and in other apolar solvents has intriguing solubility properties which indicate colloidal aggregation. However, none of the various models proposed so far is capable of accounting consistently for all properties. In the present article, we reconsider the current literature and list all robust experimental features redundantly reported on asphaltene solubilization. Then we build a new description, demanding that it should not be contradicted by any one of these listed facts. In our description, asphaltene aggregation and precipitation are distinct steps in a completely reversible process. Aggregation proceeds from specific strong interaction sites located at the periphery of the asphaltene molecules: they drive the reversible association in two-dimensional sheets, a morphology which is consistent with reported scattering and viscosity data. Precipitation eventually occurs, determined by van der Waals attractions between aggregates, when the solubility parameter of the solvent is shifted. One major interest of our description is that it accounts for the remarkable solubilizing properties of the “resins” within a completely reversible scheme.

Introduction Asphaltene is defined as the fraction of a crude oil which is insoluble in light saturated oils such as pentane and comprises the heaviest components of the oil.1 The soluble part is usually called the maltene part and also comprises many components ranging from light saturated, aromatic molecules to heavier “resins”. Indeed, the borderline between asphaltenes and resins is a matter of definition, and in this respect its position in the continuous distribution of heavy components remains somewhat arbitrary. Nevertheless, this denomination remains useful to classify the heavy components according to their solubility in apolar solvents. Many of the difficulties encountered in oil production are related to the precipitation of asphaltenes which sometimes causes plugging of the reservoir close to the well bore where the pressure decreases strongly. Motivated by such impact on production and transportation, the literature devoted to date to asphaltene solubility is huge, but a fully satisfying interpretation is still lacking. The problem is very difficult because little is known about the molecular structure of the asphaltene fraction: this is a complex mixture comprising many components which indeed may vary from one crude oil to the other.2,3 Most of them have a polyaromatic core bearing heteroatoms (O, N, S, a few metallic atoms, etc.), functional groups, and some presumably ramified aliphatic chains. But the compactness of the polyaromatic core, the positions of the heteroatoms and of the saturated chains relative to the * To whom correspondence should be addressed. E-mail: [email protected]. † Universite ´ Montpellier II. ‡ TotalFinaElf. § Atofina. (1) Sheu, E. Y.; Storm, D. A. In Asphaltenes: Fundamentals and Applications; Sheu, E. Y., Mullins, O. C., Eds.; Plenum Press: New York, 1995; Chapter I, p 1. (2) Altgelt, K. H.; Boduszynski, M. M. Composition and analysis of heavy petroleum fractions; Marcel Dekker: New York, 1994. (3) Altgelt, K. H.; Gouw, T. H. Chromatography in petroleum analysis; Marcel Dekker: New York, 1994.

core, and the nature and locations of the functional groups are essentially unknown. It is indeed hazardous to build a detailed precipitation scenario on the basis of such a vague molecular description. The many experiments reported to date indicate that the solubility of asphaltenes in the oil, as well as in conventional apolar solvents, presents intriguing features suggesting aggregation in a colloidal state. Various models were proposed for aggregation and precipitation with only limited success in accounting for the experimental facts. In the present article, we reconsider the solubility of asphaltenes in apolar solvents within a different approach. We propose a new description based on the idea that aggregation and precipitation are controlled by different intermolecular forces: strong specific forces drive the aggregation, whereas weaker nonspecific dispersion forces determine the precipitation. This point of view leads us to a structural picture where asphaltene in a good solvent self-assembles in the form of two-dimensional (2-D) sheetlike objects. We pay a lot of attention to checking the compatibility of our description with all characteristic features redundantly reported in the literature. Since the literature on asphaltene is so abundant and sometimes contradictory, we proceed in a systematic manner, and our article is organized as follows. In section 1, we give a brief recall of the various scenarios and interpretations proposed to date for asphaltene aggregation and precipitation. Section 2 also deals with the current literature but is rather focused on experimental results: we make a list of robust experimental features associated with asphaltene solubility. This list provides us with strong support for a critical evaluation of the various interpretations recalled in section 1: most of them show contradictions with one or several of the listed features. In section 3, we propose our alternative model based on the assumption that different forces drive aggregation and precipitation respectively, and we evaluate its compatibility with all the features listed in section 2. Section 4 is focused on the parameters driving the precipitation in our 2-D scheme. Section 5 is devoted to

10.1021/la0260279 CCC: $25.00 © 2003 American Chemical Society Published on Web 12/07/2002

Asphaltene Colloidal Association and Precipitation

Figure 1. Schematic picture for the plate-stack model.

the remarkable solubilizing power of the resins. And we end with a few concluding remarks. Background That asphaltenes are present in oil in an aggregated state4 is widely agreed to date. However, the form of these aggregates is by far less well agreed upon. Bulky spheroidal “micelles” are sometimes assumed with an insoluble asphaltene core decorated by a corona of “resins” having more affinity to the paraffinic components of the oil.4-7 Other models rather represent polyaromatic asphaltene molecules stacked into plate-pile-like clusters with peripheral alkyl chains waving around8-10 (see Figure 1 for a schematic picture). On the basis of scattering results, disklike shapes were proposed by some authors,11,12 whereas fractal morphologies with dimension 2 (q-2 dependence of the intensity of scattered neutrons or X-rays) were considered by others.13,14 Similar scattering data (ref 1, pp 15-20) were even analyzed in terms of spheroidal “micelles” with very broad size distributions followed by a fractal aggregation of the micelles (ref 1, pp 21-24). Regarding the mechanism leading from aggregation to true flocculation, two opposite hypotheses have been summarized by Cimino et al.15 In the lyophobic model,7,16,17 asphaltenes are considered as essentially insoluble in the oil and in common solvents. They remain however dispersed as colloidal particles “peptized” by the “resins” which are less aromatic: adsorbed at the surface of the aggregates, the resins provide steric stabilization against flocculation. Addition of light paraffinic compounds makes the solution a better solvent for the resins: they dissociate from the aggregates, which flocculate. The consequences of colloidal aggregation controlled by peptization in terms of a consistent thermodynamic model of self-assembly have (4) Pfeiffer, J. P.; Saal, R. N. J. J. Phys. Chem. 1940, 44, 139. (5) Mitchell, D. L.; Speight, J. G. Fuel 1973, 52, 149. (6) Koots, J. A.; Speight, J. G. Fuel 1975, 54, 179. (7) Leontaritis, K. J.; Mansoori, G. A. 1987 SPE International Symposium on Oilfield Chemistry; Society of Petroleum Engineers: Richardson, TX, 1987; paper SPE 16258. (8) Dickie, J. P.; Yen, T. F. Anal. Chem. 1972, 39, 1487. (9) Dickie, J. P.; Yen, T. F. Anal. Chem. 1967, 39, 1847. (10) Yen, T. F. Am. Chem. Soc., Div. Pet. Chem., Prepr. 1990, 35, 314. (11) Herzog, P.; Tchoubar, D.; Espinat, D. Fuel 1988, 67, 245. (12) Ravey, J. C.; Ducouret, G.; Espinat, D. Fuel 1988, 67, 1560. (13) Roux, J.-N.; Broseta, D.; Deme´, B. Langmuir 2001, 17, 5085. (14) Fenistein, D.; Barre´, L.; Brosseta, D.; Espinat, D.; Livet, A.; Roux, J.-N.; Scarsella, M. Langmuir 1998, 14, 1013. (15) Cimino, R.; Correra, S.; Del Bianco, A.; Lockhart, T. P. In Asphaltenes: Fundamentals and Applications; Sheu, E. Y., Mullins, O. C., Eds.; Plenum Press: New York, 1995; Chapter III, p 111 ff. (16) Leontaritis, K. J. 1989 SPE Production Operations Symposium; Society of Petroleum Engineers: Richardson, TX, 1989; paper SPE 18892. (17) Stephenson, W. K. Pet. Eng. Int. 1990, 6, 24.

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been reexamined theoretically in an interesting series of articles by Victorov et al.18-20 The opposite lyophilic model postulates that asphaltene aggregates are solvated by the surrounding media, with which they constitute a single phase in thermodynamic equilibrium.21,22 Resins play no special role, and flocculation is determined by changes in the interactions between the aggregate and the solvating medium. In both approaches, the solvating power of the oil is of major importance and is adequately represented by the Hildebrand solubility parameter δ which is the square root of the cohesive energy density.21 In many cases,15,21,22 the Flory-Huggins solubility formalism is utilized to put the lyophilic theory on a quantitative basis. Flory-Huggins theory was initially designed for polymer solutions. In the context of asphaltenes, it is thought to account properly for the large difference in molecular size between asphaltene and solvent: the Flory-Huggins χ parameter is then simply derived from the δ’s: χ ) (v/kBT)(δa - δs)2 (v is the molecular volume of the solvent). A review of the thermodynamic models based on solubility parameters (including or not colloidal association) is presented in ref 23 which underlines all points where models show a serious lack with respect to observations. So finally, both the aggregate morphology and the flocculation mechanism remain to date controversial. To find guidelines to discriminate between competing models and interpretations, we list in the following section the robust experimental facts reported redundantly in the literature on asphaltene solubility. Robust Experimental Features The following statements are well agreed when considering the current literature. (1) Asphaltenes are mixtures of many polyaromatic species of moderate molecular weight: typically 103 g/mol.30,31 The very broad range of molecular weight reported depending on the method of measurement is attributed to the state of aggregation of the asphaltenes. (2) Very moderate changes in the quality of solvent close to the precipitation threshold induce huge variations in the saturation concentration: the onset of flocculation is determined by the quality of the solvent only and is almost independent of the dilution (ref 26 and Figure 13 in ref 15). (3) For a given asphaltene, the precipitation threshold in apolar solvents corresponds to a given lower value of the index of refraction (RI) of the solvent below which precipitation occurs.22,27,28 This threshold depends only (18) Victorov, A. I.; Smirnova, N. A. Fluid Phase Equilib. 1999, 15860, 471. (19) Victorov, A. I.; Smirnova, N. A. Ind. Eng. Chem. Res. 1998, 37, 3242. (20) Victorov, A. I.; Firoozabadi, A. AIChE J. 1996, 42, 1753. (21) Hirschberg, A.; de Jong, L. N. J.; Schipper, B. A.; Meijer, J. G. SPE J. 1984, paper SPE11202, p 283. (22) Buckley, J. S.; Hirasaki, G. J.; Liu, Y.; Von Drasek, S.; Wang, J. X.; Gill, B. S. Pet. Sci. Technol. 1998, 16, 251. Buckley, J. S. Energy Fuels 1999, 13, 328. (23) Andersen, S. I.; Speight, J. G. J. Pet. Sci. Eng. 1999, 22, 53. (24) Cimino, R.; Correra, S.; Del Bianco, A.; Lockhart, T. P. In Asphaltenes: Fundamentals and Applications; Sheu, E. Y., Mullins, O. C., Eds.; Plenum Press: New York, 1995; p 111. (25) Acevedo, S.; Renaudo, M. A.; Escobar, G.; Gutie´rriez, L. B.; Gutie´rriez, X. In Asphaltenes: Fundamentals and Applications; Sheu, E. Y., Mullins, O. C., Eds.; Plenum Press: New York, 1995; Chapter IV, p 141. (26) Cimino, R.; Correra, S.; Sacomani, P.; Carniani, C. 1995 SPE International Symposium on Oilfield Chemistry; Society of Petroleum Engineers: Richardson, TX, 1995; paper SPE 28993. (27) Wang, J. Predicting Asphaltene Flocculation in Crude Oils. Ph.D. Thesis, New Mexico Institute of Mining and Technology, Soccoro, New Mexico, 2000.

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on the asphaltene and not on the solvent: different mixtures of apolar solvents having the same RI have the same solubilization properties for a given asphaltene. (4) Precipitation is most often reversible: Once precipitation has been caused by addition of pentane, redissolution is observed in many oils when pentane is evaporated from the oil-pentane mixture. Similarly, once precipitated in pentane and separated by filtration, asphaltene can be most often resolubilized in toluene even in the absence of resins. The question of reversibility is addressed in detail in ref 29 and on pages 116-117 in ref 1. Note however that redissolution may sometimes be very slow.13 But slow kinetics does not imply irreversibility. (5) Although their presence is not a prerequisite, resins efficiently cosolubilize asphaltenes: addition of extra maltenes often prevents precipitation or even permits resolubilization of precipitates (see pages 24, 25, and 112 in ref 1). (6) The neutron or X-ray scattering intensity from solutions is strong at low q’s and decays as q-2 at large angles.11-14 The Guinier regime, at low q’s, indicates that the molecular weight MW of the aggregates (proportional to the forward scattered intensity) varies like the squared radius of gyration Rg2 (related to the curvature at low q’s of the plot of I(q)). This scaling of the mass versus the size is very robust and does not depend on the specific model used to interpret the scattering data.13 Moreover, the data indicate aggregates of size 4-6.5 nm, quite robust against variations of the quality of the solvent (except close to the precipitation threshold13,29 where the strong upturn of the intensity at low q’s seems to indicate the formation of a population of larger macroaggregates, pretransitional to the true precipitation). (7) The intrinsic viscosity of the solutions is large (.2.5) at low concentration14,32 and diverges when approaching a mass fraction of the order of 15-20% typically.32 Actually, this list of facts is quite discriminative regarding candidate interpretations: any interpretation exhibiting a clear contradiction with even only one of these facts should be discarded. As we shall see below, the apparent incompatibility between points 1 and 2 can be released by the assumption of supramolecular colloidal aggregation: the entropy of mixing of the aggregates in the solvent is small on a per molecule basis, and therefore the dilution has only a marginal incidence on the flocculation threshold. The view of colloidal aggregates is indeed supported by the scattering results, point 6, and is to date widely agreed. The most convincing scattering data regarding aggregation are obtained by neutron scattering of solutions in a deuterated solvent such as d-toluene: deuteration puts the contrast precisely at the limit between the asphaltene and the solvent, making the data analysis clear and straightforward. Of course, it is not possible to deuterate selectively the deasphalted oil, and scattering data with crude oil provide less accurate structural information. Nevertheless, the X-ray scattering patterns from crude oils reported in ref 14, chapter 5, clearly indicate aggregation in the oil as well. The lyophobic description seems strongly supported by the solubilizing power of the resins (statement 5). However, it leads to a contradiction with the reversibility (require(28) Taylor, S. D.; Czarnecki, J.; Masliya, J. Fuel 2001, 80, 2013. (29) Fenistein, D. Structure Colloidale des Produits Pe´troliers Lourds. Thesis, Paris, 1998. (30) Swanson, J. M. J. Phys. Chem. 1942, 46, 141. (31) Koots, J. A.; Speight, J. G. Fuel 1975, 54, 179. (32) He´naut, I.; Barre´, L.; Argillier, J.-F.; Brucy, F.; Bouchard, R. SPE Oilfield Chemistry, Houston, TX, 13-16 Feb 2001; SPE No. 65020.

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ment 4): in colloidal science, the precipitation of sterically stabilized dispersions of insoluble particles is irreversible. This point is discussed in detail by Cimino et al. in ref 1, pages 116-117: flocculation after addition of paraffinic compounds which dissociates the resins from the aggregates would produce a precipitate impossible to redisperse (as aggregates) in toluene in the absence of resins (unless one assumes that toluene is a good solvent of the asphaltenes and that the peptizing scenario is not essential to stabilize the aggregates in toluene but only applies to solutions in the oil). Note furthermore that the lyophobic description cannot account for the low dependence of the onset of precipitation on the dilution (statement 2). Likewise, fractal morphologies are incompatible with reversibility. Fractal patterns resulting from aggregation remain stable only if all the sticking events are irreversibly frozen: rearrangements unavoidably lead to densification of the aggregates and ultimately end up in true precipitation. So the reversibility condition 4 rather imposes the lyophilic description. Yen’s plate-stack model which recently received renewed attention33,34 seems an appealing candidate in this respect: on the one side, π-bonds could provide the driving force for stacking the polyaromatic cores, whereas on the other side the fluctuation entropy of the corona of aliphatic chains prevents the aggregation to proceed up to precipitation (Figure 1). However, this model can produce small aggregates only: in ref 34, for instance, plate-stack-like aggregates built from most compact polyaromatic molecules have aggregation numbers below 30 whereas scattering data often indicate aggregation numbers as large as 100 typically. Moreover, such a structure would not lead to a q-2 decay for the X-ray or neutron scattered intensity. More important even, such a plate-stack structure should be characterized by a Bragg correlation peak in the scattering pattern related to the quasi-periodicity of the stacking: actually, no correlation maximum has ever been reported for asphaltene in solution (but only on the precipitate for which it reveals the multilayered structure discussed below). So we discard the plate-stack model, and we propose in a later section an alternative structure which hopefully accounts for all the above robust facts. An Alternative Scheme Intermolecular Forces. Statement 3 suggests that precipitation is mainly driven by weak aspecific dispersion forces. This is also well in line with the fact that the latent heat of precipitation is low and hardly measurable (ref 35). Following the current theory of solubility, the standard free energy (per unit volume of the solute) associated with precipitation is written (see ref 36, chapter 9, pp 139-151)

1 hprec ) (Wss + Waa - 2Was) 2

(1)

where the W’s stand for the interaction energies per unit volume of the solvent (subscript s) and of the asphaltene solute (subscript a). If the interactions are dispersion forces only, a good approximation is Wij = (WiiWjj)1/2 and by (33) Carbognani, L. A.; Rogel, E. Proceedings of the 3rd International Conference on Petroleum Phase Behavior and Fouling, AIChE 2002 Spring National Meeting; American Institute of Chemical Engineers: New York, 2002; p 303. (34) Rogel, E. Langmuir 2002, 18, 1928. (35) Achour-Boudjema, Z.; Be´harand, E.; Barreau, A. Private communication, 1998 (IFP internal report 44 752). (36) Israelachvili, J. N. Intermolecular and Surface Forces, 2nd ed.; Academic Press: San Diego, 1994.

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introduction of the solubility parameter, δi ) xWii, eq 1 becomes

hprec ) (δa - δs)2

(2)

If, on the other hand, other more specific interactions are also relevant (permanent dipole-permanent dipole and/ or hydrogen bonding, for instance), each of them brings an additive contribution to the free energy of precipitation: has,p for the dipoles and has,h for the hydrogen bonds. But apolar solvents are only sensitive to dispersion forces; therefore, the contributions of the specific forces remain invariant upon changing from one given apolar solvent to another one. So we can forget the index s in has,p and has,h and expression 2 simply becomes

hprec ) (δa,d - δs,d)2 + ha,p + ha,h + ...

(3)

where the indexes d, p, and h stand for dispersion, dipole, and hydrogen bonds, respectively. In all of what follows, the solubility parameters represent the work of the dispersion forces only. So from now and to the end of the article, we drop out the index d in all δ’s, but we keep in mind that they correspond to the dispersion contribution only. The solubility parameter for heptane for instance is taken from current tables:37 15.3 (J/cm3)1/2. In section 3 below, we present an experimental estimation of the typical solubility parameter of asphaltenes: 19.5 (J/cm3)1/2. (This value actually seems rather low compared to those found in other works, but note again that here δa only comprises the dispersion contribution, so the number seems reasonable if we consider the polyaromatic character of asphaltene molecules with a H/C ratio close to 1.) Putting these numbers in (2), we effectively obtain a quite low estimated value for the dispersion contribution to hprec (below 10 J/cm3 typically). Since the other more specific contributions remain identical when changing the apolar solvent, we follow Buckley et al. in refs 22 and 27 and conclude that the precipitation is mostly controlled by the dispersion forces, the free energy of which is low on a per unit volume basis. Moreover, the dispersion forces in dense media are determined by the polarizability at optical frequency and thus by the refraction index (RI) of the medium. Buckley et al. proposed a reliable convenient expression of the solubility parameter as function of the RI:22,27

n2 - 1 + 2.418 δs ) 53.827 2 n +2

Figure 2. Solubility limit of Lagrave crude oil as a function of the composition of the solvent in pentane and toluene. Axis units are volume/volume.

(4)

So, as long as we restrict the discussion to statement 3 and to the low latent heat of precipitation, all seems fine if we consider that dispersion forces dominate the precipitation. On the other hand, the extreme sensitivity of the solubility of asphaltenes to the solvent quality (statement 2) is more difficult to explain. The sensitivity is illustrated in Figure 2: the solubility limit of the asphaltene in Lagrave crude oil is represented as a function of the amount of added toluene (solvent) and pentane (nonsolvent). The solubility limit is a radial straight line corresponding to a pentane-to-toluene ratio close to 1 irrespective of the dilution. This means that at this ratio a tiny variation of pentane versus toluene (and thus of the quality of the solvent) results in a very large change in the solubility limit. Other plots of solubility limits showing (37) Hansen, C. M. Hansen Solubility Parameters: a User’s Handbook; CRC Press: Boca Raton, FL, 2000.

similar radial geometry have been presented in the literature (ref 26 and Figure 13 in ref 15). This redundant radial geometry is at the basis of the abundantly used technique of flocculation onset titration, an interesting detailed discussion of which is presented in ref 38. To illustrate further the sharp solubility contrast, we used optical density measurements to investigate the solubility behavior of an asphaltene fraction of a light crude oil (see experimental details in ref 39): the solubility limit is larger than 5 wt % in pure toluene, whereas it drops below 10 ppm by weight in a mixture of 80% pentane and 20% toluene. This corresponds to a lower boundary of 5 × 103 for the solubility contrast upon switching from pure toluene to the pentane-rich mixture. Actually, assuming the solubility limit at 5% (above 5% concentration, optical density measurements are not reliable) in pure toluene is most probably largely underestimated, so we expect the solubility contrast to be much larger than 5 × 103 (up to 106 in mole fraction if the asphaltene is soluble in all proportions in toluene). If, on the other hand, we consider that asphaltenes are dissolved at the molecular level, the regular solution theory should apply (at least approximately), and the saturation concentration Xasat (in mole fraction) of the asphaltene should be written

(

Xasat ) exp -

)

vahprec kBT

(5)

where va is the molecular volume of the asphaltene. So we expect the solubility contrast to be given by

Xa,s1sat Xa,s2sat

(

) exp -

va [(δ - δa)2 - (δs2 - δa)2] kBT s1

)

(6)

where Xa,sisat is the solubility of asphaltene in solvent i (i ) 1 or 2). Note again that the specific terms in (3) such as ha,p and ha,h do not appear in (6): since they are identical in the two apolar solvents, they have no effect on the solubility (38) Andersen, S. I. Energy Fuels 1999, 13, 315. (39) The experiment is performed as follows. Solid asphaltene was obtained by precipitation in a mixture of 40% toluene and 60% heptane. It was then dissolved in pure toluene at a concentration of 4.6% in weight. The complete dissolution was confirmed after centrifugation by measuring the optical density (wavelength of light, 632.8 nm) of the upper part of the sample. Then a large amount of heptane was added so that the relative volumic proportions were 80% heptane and 20% toluene: precipitation immediately took place. The precipitate was forced to sediment by centrifugation, and the asphaltene concentration in the supernatant was determined by measurement of its optical density in transmission photometry: 10 ppm. (This is actually the minimum concentration that can be measured reliably by optical density: the solution is totally transparent.)

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contrast. If we take va = 1000 cm3/mol in (6) according to statement 1, we get a value for the solubility contrast, Xa,tolsat/Xa,pentsat = 102, much smaller than effectively observed. Of course, the magnitude of the discrepancy depends strongly on the values taken for the solubility parameter and the molecular volume of the asphaltene on which there is a lot of uncertainty. Taking higher but still plausible values for δa and va would indeed make it smaller. However, the discrepancy is more easily released if we consider that according to scattering data (statement 6), asphaltenes in a good solvent self-assemble in supramolecular aggregates. So, the molecular volume to be used in (6) is not that of one single molecule: it should be of the order of the aggregate size. And arbitrarily large values of the solubility contrast can so be rationalized within (6) provided that the aggregation number is large enough (typically of the order of 102 according to scattering data; see below). However, an important feature is required in addition to ensure large solubility contrast: namely, that the intermolecular forces driving the aggregation are large compared to the dispersion forces. If the aggregation was driven by weak dispersion forces, the aggregates in solution would coexist with a noticeable concentration of free single molecules (the critical micelle concentration, cmc). Upon a decrease of the solvent quality down to the precipitation threshold, only the aggregate would precipitate: the free molecules would remain in solution and the solubility contrast would be moderate (of the order of 102 as calculated in (6) with individual molecular volume va). So, our discussion of statements 1-3 leads us to conclude that aggregation and precipitation are presumably controlled by different intermolecular forces: in good apolar solvents, aggregation is induced by strong specific interactions (hydrogen bonds, for instance), and in bad apolar solvents, weak nonspecific dispersion attractions between the aggregates determine precipitation. This statement of different forces driving aggregation and precipitation respectively is the most important ingredient of our description. Structure and Morphology of the Aggregates. Since strong forces drive the aggregation, the question arises about what mechanism prevents aggregation in a good solvent to proceed indefinitely rather than to stop at some measurable finite size (typically 4-6.5 nm according to scattering data). The answer certainly involves the actual morphology and structure of the aggregate. So we naturally turn to statements 6 and 7 dealing with scattering and viscosity data. According to the data reported in ref 29 for asphaltenes extracted from Safanyia crude oils, the radius of gyration of the aggregates is about 6.5 nm (q-dependence in the Guinier range) while the extrapolation of the intensity to zero q indicates a mass per aggregate of 1.2 × 105 g/mol (i.e., aggregation number of the order of 102). On the basis of the q-2 dependence of I(q) at intermediate q’s, the authors of ref 29 conclude in favor of a fractal structure of dimension 2, but as mentioned above, a fractal morphology is not consistent with the reversibility statement 4 and it leaves unanswered the question of infinite growth. Of course, bidimensional structures in the form of thin sheets would also be compatible with the q-2 dependence, and disklike morphologies were considered earlier:11,12 thin disks (0.34 nm thickness) were found to be actually consistent with similar sets of data from small-angle X-ray11 and neutron scattering.12 But the question of infinite growth remains. Reversible 2-D aggregation has been studied extensively in other contexts (surfactant systems; see ref 36, chapter 17, pp 366-394): provided that the linking energy exceeds

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a critical value of the order of a few times the thermal energy kBT (per molecule), aggregation starts and proceeds up to the formation of a single infinite sheet. However, infinite growth could well be simply prevented by the presumably high bending flexibility of such asphaltene monomolecular sheets: they would sphere up spontaneously and finite size vesicles would form at low bending elastic price where all specific interaction sites are linked. The vesicle morphology shows up several interesting properties. First of all, the characteristic features of the aggregates do not depend on the interaction energy of the specific sites: as soon as it exceeds the critical value, aggregation starts and proceeds up to the equilibrium size distribution of the vesicles which only depends on the bending rigidity of the asphaltene molecules and not on the quality of the solvent. This prediction is consistent with the scattering data in ref 29 which show essentially similar size distributions for the aggregates in different good solvents. (Close to the precipitation threshold, however,13 the scattered intensity shows a strong upturn at very low q which is the sign of an approaching phase separation: asphaltene-rich large domains grow and anticipate precipitation.) Of course, the vesicle assumption is consistent with the q-2 dependence of the scattering data (locally 2-D structure) as well as with the scaling relating the mass and the size of the aggregates (MW ∝ Rg2) in the Guinier range. Even the prefactor experimentally determined in ref 29 for the scaling happens to be in excellent agreement with the vesicle geometry: assuming a spherical vesicle of radius 6.5 nm made of a sheet of thickness δ ) 0.33 nm (effective van der Waals thickness of a polyaromatic sheet as derived from the Bragg scattering of graphite) and taking 1.1 g/cm3 for the density of asphaltene, we get the average mass: 1.16 × 105 g/mol in close agreement with the experimental value above. Viscosity data14,26 as well agree with the vesicle scheme. In the dilute range, the viscosity η of colloidal dispersions increases linearly with the volume fraction φ:

η ) η0(1 + [η]φ)

(7)

where η0 is the viscosity of the solvent and [η] is the socalled intrinsic viscosity of the particles which depends on their shape. For dense spheres, [η] ) 2.5 (Einstein relation). Intrinsic viscosities of the order of 20-30 are typically measured for asphaltene solutions.14,32 Assuming vesicles of average radius R and layer thickness δ, the effective volume fraction φves occupied by the vesicles is φves ) φ(4/3)πR3/4πR2δ where φ is the asphaltene concentration. Taking R ) 6.5 nm and d ) 0.33 nm as above, we get φves ≈ 7φ and using the Einstein relation we expect [η] ≈ 18, not far from the above-reported values. On the other hand, at high concentration, the viscosity of hardsphere suspensions is known to diverge when approaching the close-packing conditions. The viscosity of asphaltene solutions actually rises sharply at concentrations of the order of 15%32 as expected for close-packed vesicles with the above dimensions. (One could argue that at 15% concentration the effective volume fraction occupied by monodisperse vesicles is 7 × 15% ) 105%, larger than 1. But vesicles are certainly polydisperse and some of the smaller ones may well nest into bigger ones at high concentration; the question of nesting vesicles was addressed in detail in the context of surfactant solution in ref 40). So, up to this point, reversible aggregation in the form of vesicles is consistent with the structural data of (40) Herve´, P.; Roux, D.; Bellocq, A.-M.; Nallet, F.; Gulik-Krzywicki, T. J. Phys. II France 1993, 3, 1255.

Asphaltene Colloidal Association and Precipitation

Langmuir, Vol. 19, No. 1, 2003 45

statements 6 and 7 and makes no contradiction with any of the requirements 1-4. However, this picture implies that the strong specific interaction sites which drive the 2-D aggregation are located at the periphery of the polyaromatic core of the asphaltene molecules. This is indeed a strong assumption which is not yet supported by direct evidence. So, despite the many indirect agreements with the above-mentioned data, the vesicle model remains to date somewhat speculative. By chance, the precipitation scheme described below does not critically depend on a precise structural description but mainly relies on the basic assumption that different forces drive aggregation and precipitation respectively. Precipitation. As long as the quality of the solvent is good enough, the aggregates remain dispersed at equilibrium. Addition of a light aliphatic compound depresses the dielectric constant and therefore the solubility parameter37 of the solvent: the aggregates attract each other and precipitation occurs. Precipitation depends not only on the forces between the aggregates but also on the structure of the precipitate itself. Asphaltene precipitates have a multilayered structure where the platelike molecules stack up more or less parallel to each other.8 This structure is supported by X-ray diffraction patterns exhibiting the characteristic (002) quasi-Bragg peaks.41 (It is underlined in ref 41 however that the amount of X-rays scattered in the 002 peak is low and that the peak is broad indicating a lot of disorder.) In our view where the aggregates in solution have a locally 2-D sheetlike structure, we expect after precipitation that these sheets simply stack more or less regularly on the top of each other so to form the multilayered structure. So, the specific sites are in the same bound state in the precipitate as in the initially dispersed aggregates. Therefore, although providing the driving force for the aggregation, the specific sites in our scheme play no role in the precipitation. On the other hand, molecules in the aggregates are wetted by the apolar solvent while they are in contact with asphaltene neighbors in the precipitate, so the dispersion forces of a given molecule with its environment change upon precipitation. With these features in mind, let us write the chemical potentials of the asphaltene molecule in the aggregate (vesicle) and in the precipitate respectively (we take as standard state the isolated asphaltene molecule in the solvent):

µagg ) -gss0 +

kBT X ln n n

µprec ) -gss0 - va(δs - δa)2 + K0

(8) (9)

gss0 is the binding energy of the specific sites, identical in the aggregate and in the precipitate. n is the aggregation number of the vesicle (of the order of 102 according to the scattering data), and X is the concentration of asphaltene in solution (mole fraction). The second term in µagg stands for the entropy of mixing of the vesicles. The second term in µprec involves the solubility parameters δs and δa of the solvent and of the asphaltene, respectively (va is the volume per asphaltene molecule): it expresses the change in free energy (expression 2) when the asphaltene-solvent interactions at the inner and outer surfaces of the vesicles are replaced by the asphaltene-asphaltene interactions in the precipitate. The form of this term implicitly assumes (41) Andersen, S. I.; Speight, J. G.; Pedersen, C.; Oluf Jensen, J. Proceedings of the 3rd International Conference on Petroleum Phase Behavior and Fouling, AIChE 2002 Spring National Meeting; American Institute of Chemical Engineers: New York, 2002; p 13.

that all interactions involved in precipitation are dispersion forces only and that the asphaltene-asphaltene contacts in the precipitate are as tight as the asphaltenesolvent interaction in the dispersed vesicles. This latter assumption is strongly questionable: although flat on the average, asphaltene molecules are presumably rough and bumpy so that their stack in the aggregate presents voids and imperfections. As recalled above, the low degree of crystallinity exhibited by the diffraction patterns of solid asphaltene actually indicates a lot of disorder in the precipitate structure.41 In addition, although not dominant, residual specific interactions may well play a minor but noticeable role in the precipitation. Also, the aggregates in the dispersed state have presumably some internal degrees of freedom (in the form of the bending modes of the 2-D sheets) which are mostly frozen in the solid precipitate: the corresponding loss of entropy would indeed shift the onset of precipitation. To represent all these contributions which are very difficult to predict quantitatively, we introduce the additional empirical term K0 in µprec which we hereafter call the stacking misfit parameter (we believe the contribution of voids and imperfections to be dominant in K0). Solubility persists as long as µagg e µprec; precipitation occurs as soon as µagg > µprec. Due to the 1/n prefactor, the entropy of dilution of the vesicles is indeed very small as underlined above, and we neglect it hereafter. Then precipitation occurs whenever the quality of the solvent δs is shifted far enough above or below δa so that K0/va - (δs - δa)2 becomes negative. Of course, if δs is shifted back to a good solvent value the precipitate resolubilizes: the reversibility requirement 4 is satisfied. (Note that in the absence of a positive misfit parameter, asphaltene would be insoluble in all solvents just as is graphite which crystallizes into a perfect stacking.) Since dispersion forces dominate, there is a good correlation between solubility parameters and refractive index in agreement with requirement 3 (this feature is indeed not specific of the present model: any other interpretation relying on dispersion forces would as well fulfill requirement 3). To sum up briefly, in our description, aggregation in the form of 2-D structures is driven by specific interactions at the periphery of the asphaltene molecules, whereas precipitation is determined by the nonspecific van der Waals forces on the two faces of the 2-D sheets. Up to this point, the scheme meets most of the above listed requirements: 1-4, 6, and 7. One point remains to be checked (requirement 5): does our model account for the cosolubilizing power of the resins? But before addressing this aspect, we must consider further the leading parameters which determine the precipitation. Relevant Parameters for Precipitation: δa and K0. In the preceding section, asphaltene is implicitly considered as a single component characterized by two parameters, namely, δa the solubility parameter and K0 the stacking misfit parameter: forgetting the dilution entropy, precipitation is controlled by the sign of K0/va - (δs - δa)2. It must be stressed again that K0 is nothing more than an ad hoc fitting parameter taking care of various effects which are difficult to anticipate quantitatively. On the other hand, δa indeed has a more specific physical meaning but it remains difficult to measure directly because the vaporization temperature of the asphaltene is so high. The more indirect method involving measurement of the index of refraction is likewise not easy because asphaltene is a deep black material. A simple way however to evaluate δa and K0 together is to measure the upper and lower precipitation thresholds against solvents of respectively increasing and decreasing solubility parameters δs. A

46

Langmuir, Vol. 19, No. 1, 2003

Porte et al.

Table 1. Titration of the Onset of Precipitation Following Additions of Pentane and Methylene Iodide, Respectively, for a Series of Asphaltenes from Various Crude Oilsa crude oil

C5/o-xyl v/v

CH2I2/o-xyl v/v

δs,min (J/cm3)1/2

δs,max (J/cm3)1/2

δa (J/cm3)1/2

(K0/va)1/2 (J/cm3)1/2

Dalia-2 Vic Bil LAV6 M2 M3

4.08 1.43 1.62 1.75 2.41

6.08 7.12 7.58 5.75 6.21

15.0 15.8 15.7 15.6 15.4

23.4 23.5 23.6 23.3 23.4

19.2 19.6 19.6 19.5 19.4

4.2 3.85 3.95 3.85 4.0

a

Values for δa and (K0/va)1/2 are derived according to (10), (11), and (12).

continuously adjustable δs can be achieved, using mixtures of a good solvent A (δA) and a bad solvent B (δB) with the volume proportions cA and cB ) (1 - cA). The effective solubility parameter δs of the mixture is simply37

δs ) cAδA + (1 - cA)δB

(10)

One can use increasing proportions of pentane (δpent ) 14.3 (J/cm3)1/2) in o-xylene (δxyl ) 18.0 (J/cm3)1/2) in order to measure the lower precipitation threshold δs,min of the asphaltene. Likewise, methylene iodide (δCH2I2 ) 24.3 (J/ cm3)1/2) in o-xylene can be used to measure the upper threshold δs,max. With the above criterion for the precipitation thresholds, we immediately derive δa and (K0/va)1/2:

δa ) (δs,max + δs,min)/2

(11)

xK0/va ) (δs,max - δs,min)/2

(12)

and

To illustrate the feasibility of this titration method, we used this procedure to characterize the solubility properties of asphaltene extracted from different crude oils. After redissolution in excess o-xylene, titrations of the onset of flocculation upon addition of the two nonsolvents (pentane and methylene iodide, respectively) were performed using the classical spot test: the solvent/nonsolvent volume ratios (cA/(1 - cA)) at the thresholds are given for all samples in Table 1 from which δs,min and δs,max and finally δa and (K0/va)1/2 are derived according to expressions 10-12. So, δa is the value of the solubility parameter of the best possible apolar solvent of the asphaltene, whereas (K0/ va)1/2 is a measure of the width of the solubility window of the asphaltene. For all samples, (K0/va)1/2 is found to be close to 4 (J/cm3)1/2 in agreement with ref 38. Comparing δa and (K0/va)1/2 as evaluated above with the solubility parameter of the deasphalted oil as derived from RI measurement for instance can help to anticipate the risk of precipitation. Usually in oil production, the pressure drop results in lowering the solubility parameter of the oil as the solvent of its own asphaltene fractions. So the higher the δa and the lower the (K0/va)1/2, the higher the risk of flocculation. Cosolubilization of Resins and Asphaltenes. In the preceding section, we treated the asphaltene fractions as a single component characterized by a couple of parameters δa and (K0/va)1/2 only. This is by far an oversimplification. Asphaltene fractions are rather the most insoluble part of an almost continuous spectrum of different polyaromatic species, each of them having presumably its own couple of parameters δa and (K0/va)1/2. This broad spectrum is contiguous to the heaviest fractions of the maltenes usually referred to as resins. The intriguing cosolubilizing power of the resins (statement 5) has been known for a long time and is well documented in the literature:5-8,30,31 addition of resin in a solution of asphaltene shifts the onset of precipitation to a lower δs,min value. Actually, the lyophobic models, where the insoluble

asphaltenes are peptized by the resins, were motivated by the early observations of this solubilizing power. But, as mentioned earlier, this picture is incompatible with the reversibility requirement 4 which implies that asphaltene precipitates can be redissolved in a good solvent even in the absence of resin. Right in line with our scheme, we propose here a different interpretation. We assume that the resins only differ from the asphaltene in their solubility parameter δr which is lower. Otherwise, they just behave like the asphaltenes and in particular they bear the same specific interaction sites at the periphery. In ref 42, resins are assumed to have the same aggregation propensity as the asphaltenes. This assumption is quite plausible if one realizes that asphaltenes and resins are parts of a continuum and that therefore there must be a significant overlap between the properties. So we consider that resins participate identically to the formation of the 2-D aggregates. For the sake of simplicity, let us examine an ideal situation with two species only, denoted “resin” and “asphaltene”, with the same misfit parameter K0 and the same molecular volume var but different solubility parameters δr and δa, respectively. Their relative proportions (mole fractions) are denoted xr ) 1 - x and xa ) x. With these premises and neglecting again the entropy of dilution of the aggregates, the free energy densities (on a per molecule basis) in the aggregates and in the precipitate become respectively

µagg ) -gss0 + kBT[x ln x + (1 - x) ln(1 - x)]

(13)

and

µprec ) -gss0 + kBT[x ln x + (1 - x) ln(1 - x)] var[x(δa - δs) + (1 - x)(δr - δs)]2 + K0 (14) Again, gss0 appears symmetrically in both chemical potentials: specific interactions play no role in the precipitation. The second term in both expressions stands for the entropy of mixing the two components in the vesicles and in the precipitate. The van der Waals term in µprec comprises the contributions of both components weighted by their relative proportions: x and (1 - x). Since we assume the same misfit parameter K0 for both components, its contribution is unchanged in µprec. For the sake of an illustration, we have plotted in Figure 2 µagg and µprec as functions of the composition x assuming realistic values for K0 ()0.5 kBT) and var ()1.7 × 10-21 cm3; in postulating this value, we assume a molecular weight of 1000 g/mol and a density of 1 g/cm3) and considering a plausible situation for which the solubility parameter of the solvent (an appropriate mixture of pentane and toluene, for instance) is the same as that of the resin, δr - δs ) 0 (J/cm3)1/2, but is smaller than that of the asphaltene, δa - δs ) -2.04 (J/cm3)1/2. In absence of the resin (x ) 1 in both the aggregates and the (42) Murgich, J.; Abanero, J. A.; Strausz, O. P. Energy Fuels 1999, 13, 278.

Asphaltene Colloidal Association and Precipitation

Figure 3. Free energies (per molecule) for the asphaltene in the aggregates and in the precipitate according to (11) and (12), for the set of parameters given in the text. The common tangent construction gives the compositions of coexisting aggregates and precipitate.

precipitate), it is clear in Figure 3 that µprec < µagg and the asphaltene precipitates. If a moderate proportion of the resin is added (0.52 < x < 0.86), dispersed aggregates of composition x ) 0.52 coexist with a precipitate of composition x ) 0.86 (where indeed these compositions are given by the usual common tangent construction and the relative proportions of aggregates and precipitate are determined by the classical lever rule). If the resin proportion is even larger (x < 0.52), the bad asphaltene is totally resolubilized. So, the solubilizing power of the resins simply arises from their ability to cooperate with the asphaltenes to form mixed 2-D aggregates and our scheme appears consistent with requirement 5. Note that the cosolubilizing power is here fully reversible (requirement 4) in contrast with the conventional peptization scheme. Concluding Remarks In this article, we have reconsidered the intriguing solubility properties of asphaltenes in apolar solvents (such as the deasphalted oil). All models proposed to date show contradictions with at least one of the characteristic features redundantly reported in the current literature. So we here proposed an alternative description based on a simple idea: the forces involved in the colloidal aggregation on the one side and those driving the precipitation on the other side are different in nature and strength. The aggregation is driven by strong specific forces; therefore the size and shape of the aggregates are insensitive to the quality of the apolar solvent. The precipitation is determined by the weaker and nonspecific dispersion forces, and so it can be anticipated from suitable measurements of refractive indices or of solubility parameters.

Langmuir, Vol. 19, No. 1, 2003 47

These ingredients are sufficient to account for all intriguing solubility properties including the remarkable solubilizing power of the resins within a completely reversible frame. However, to build a consistent scheme where strong specific interactions drive finite size aggregation, we further assumed that aggregation proceeds in 2-D structures which finally sphere up in the form of hollow vesicles. This morphology is found to be quantitatively consistent with scattering and viscosity data. Precipitation then naturally leads to the multilayered structure revealed by the 002 X-ray diffraction of asphaltene precipitates. However, the 2-D aggregation implies that the specific interaction sites are mostly located at the periphery of the asphaltene molecules. Actually, this assumption is not unrealistic. As reported in ref 43, the free energy of transfer of water molecules from pure toluene to asphaltene solution is high: this indeed confirms that asphaltene molecules bear sites for hydrogen bonding. In the molecular description based on a dense polyaromatic core, there is not so much room where the approximately 10 wt % of N, S, and O heteroatoms can be located but at the periphery. The functional groups where the N, S, and O are located are most likely sites where hydrogen bonding can take place. Nevertheless, this view is to date nothing more than an assumption which remains to be proved experimentally. In our model, like in many others, the precipitation threshold indeed depends on the effective solubility parameter of the asphaltene δa. But the internal structure of the precipitate also plays an important role. In a somewhat naive first approximation, we introduced the phenomenological stacking misfit parameter K0 to account for this aspect. If the asphaltene fraction were a singlecomponent solute, both the solubility and the misfit parameters could be simply derived from a couple of titrations of precipitation onsets. In reality, asphaltene fractions are multicomponent mixtures: a reliable characterization would imply fractionation and evaluation of the precipitation thresholds of each fraction separately. As a last remark, 2-D self-assembling driven by strong forces produces aggregates that are very robust against large variations of temperature and pressure. Therefore, if our general scenario applies in usual laboratory conditions, it should survive to the production field conditions. However, both solubility parameters and misfit parameters are likely sensitive to temperature and pressure: extrapolating precipitation thresholds from lab to well conditions remains a difficult challenge. Acknowledgment. One of us (G.P.) was funded by TotalFinaElf (Grant No. 11910). The authors thank TotalFinaElf for the permission to publish this paper. LA0260279 (43) Andersen, S. I.; del Rio, J. M.; Khvostitchenko, D.; Shakir, S.; Lira-Galeana, C. Langmuir 2001, 17, 307.