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Thermodynamic Modeling of Asphaltene Aggregation E. Rogel 15315 SW 78 Court, Miami, Florida 33157 Received July 23, 2003. In Final Form: October 30, 2003
A new molecular thermodynamic model for the description of the aggregation behavior of asphaltenes in different solvents is presented. This new model is relatively simple and strictly predictive and does not use any experimental information from asphaltene solutions. In this model, asphaltene aggregates are described as composed of an aromatic core formed by stacked aromatic sheets surrounded by aliphatic chains. The proposed model qualitatively predicts the asphaltene aggregation behavior in a series of different solvents. In particular, the experimental trends observed for the variation of aggregate size with (1) asphaltene molecular characteristics (condensation index, aromaticity, and chain length), (2) asphaltene concentration, (3) solvent characteristics, and (4) temperature have been successfully reproduced by the proposed model. The model also provides a plausible explanation for the existence or absence of a critical micelle concentration (cmc) for asphaltene solutions. Specifically, the model predicted that the asphaltenes with low aromaticities and low aromatic condensations do not exhibit cmc behavior. Finally, the obtained results clearly support the classical model for asphaltene aggregates.
Introduction Asphaltene aggregation is a subject of remarkable importance for the oil industry. Reservoir damage, well bore plugging, pipeline clogging, production delays, and low conversion rates during refining are among many in a long list of problems where asphaltene aggregation plays a vital role. As the first step1-5 of the asphaltene precipitation process, asphaltene aggregation has attracted the intensive interest of chemists, physicists, and engineers. Numerous experimental studies have focused on the characterization of the asphaltene aggregation behavior in different solvents. Critical micelle concentrations (cmc’s) of asphaltenes have been reported in the literature using mainly surface tension,1,6-9 and also calorimetric measurements.4,10 The shape and size of the aggregates have been monitored as a function of asphaltene concentration,11-13 temperature,1,12,14 origin of the asphaltene samples,15,16 and also characteristics of the solvent.17,18 As a conse(1) Rogacheva, O. V.; Gimaev, R. N.; Gudaidullin, V. Z.; Danil’yan, T. D. Colloid J. USSR 1980, 42, 490. (2) Rao, B. M. L.; Serrano, J. E. Fuel Sci. Technol. Int. 1987, 4, 483. (3) Maruska, H. P.; Rao, B. M. L. Fuel Sci. Technol. Int. 1987, 5, 119. (4) Andersen, S. I.; Birdi, K. S. J. Colloid Interface Sci. 1991, 142, 497. (5) Andersen, S. I.; Speight, J. G. Fuel 1993, 72, 1343. (6) Sheu, E. Y.; De Tar, M. M.; Storm, D. A.; DeCanio, S. Fuel 1992, 71, 299. (7) Leo´n, O.; Rogel, E.; Espidel, Y.; Torres, G. Energy Fuels 2000, 14, 6. (8) Rogel, E.; Leo´n, O.; Torres, G.; Espidel, J. Fuel 2000, 79, 1389. (9) Mohamed, R. S.; Ramos, A. C. S.; Loh, W. Energy Fuels 1999, 13, 323. (10) Andersen, S. I.; Del Rı´o, J. M.; Khvostitchenko, D.; Shakir, S.; Lira-Galeana, C. Langmuir 2001, 17, 307. (11) Yarranton, H. W.; Alboudwarej, H.; Jakher, R. Ind. Eng. Chem. Res. 2000, 39, 2916. (12) Speight, J. G.; Wernick, D. L.; Gould, K. A.; Overfield, R. E.; Rao, B. M. L.; Savage, D. W. Rev. Inst. Fr. Pet. 1985, 40, 51. (13) Sirota, E. B. Pet. Sci. Technol. 1998, 16, 415. (14) Thiyagarajan, P.; Hunt, J. E.; Winans, R. E.; Anderson, K. B.; Miller, J. T. Energy Fuels 1995, 9, 829. (15) Szewczyk, V.; Be´har, F.; Be´har, E.; Scarsella, M. Rev. Inst. Fr. Pet. 1996, 51, 575. (16) Barre´, L.; Espinat, D.; Rosenberg, E.; Scarsella, M. Rev. Inst. Fr. Pet. 1997, 52, 161. (17) Sheu, E. Y.; Storm, D. A.; De Tar, M. M. J. Non-Cryst. Solids 1991, 131-133, 341-347.
quence of these experimental results, a complex picture of the behavior of the asphaltenes has emerged. In contrast with the experimental efforts, theoretical issues associated with asphaltene aggregation have not received the attention that they deserve. For instance, in overwhelming majority, current thermodynamic models have focused their attention on the prediction of asphaltene precipitation.19 Even though some of these models consider the colloidal nature of the asphaltenes, few of them address the aggregation behavior of the asphaltenes as the start of the asphaltene precipitation process.20-22 These thermodynamic treatments usually employ asphaltene aggregation models inspired by surfactant thermodynamics theories, but they still need intensive fit of experimental data and cannot be used to identify the essential physical factors involved in the process of asphaltene aggregation. Rather recently, an approach23 inspired by the thermodynamic theory for surfactants developed by Nagarajan and Ruckenstein24 has provided a qualitative description of the main experimental trends observed for asphaltene aggregation. This thermodynamic treatment is strictly predictive in the sense that it is free of information extracted from experiments on asphaltene aggregation and has provided results that support the classical aggregation model:25 the asphaltene aggregates are composed of an aromatic core surrounded by aliphatic chains. Besides, the model also supports that the attraction between asphaltene molecules is driven by the interaction between the polyaromatic sheets and is limited, among other factors, by the steric repulsion between the aliphatic chains surrounding the aromatic core. The main goal of the present paper is to develop an alternative thermodynamic approach to describe asphaltene aggregation and use it to verify if this new model also (18) Espinat, D., Ravey, J. C. Presented at the SPE International Symposium on Oilfield Chemistry, New Orleans, LA, Mar 2-5, 1993; Paper SPE 25187. (19) Andersen, S. I.; Speight, J. s. G. J. Pet. Sci. Eng. 1999, 22, 53. (20) Victorov, A. I.; Firoozabadi, A. AIChE J. 1996, 42, 1753. (21) Pan, H.; Firoozabadi, A. SPE Prod. Facil. 1998, May, 118. (22) Pan, H.; Firoozabadi, A. AIChE J. 2000, 46, 416. (23) Rogel, E. Langmuir 2002, 18, 1928. (24) Nagarajan, R.; Ruckenstein, E. Langmuir 1991, 7, 2934. (25) Yen, T.; Erdman, J.; Saraceno, S. Anal. Chem. 1962, 34, 694.
10.1021/la035339o CCC: $27.50 © 2004 American Chemical Society Published on Web 01/08/2004
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supports the classic model for asphaltene aggregates as well as to study the forces that drive the aggregation behavior. To this end, the thermodynamic theory proposed by Puvvada and Blankschtein26 for surfactants has been used as the starting point for the development of a molecular aggregation model for asphaltenes. This model as can be expected incorporates the classical view of the asphaltene aggregates and takes into account the effect of solvent properties, asphaltene molecular characteristics, and the interfacial effects due to the formation of an interface between the solvent and the asphaltene aggregate. This new approach is simpler than the previous one,23 and it is also strictly predictive. In this work, it has been used to qualitatively predict the critical micellar concentration and the asphaltene aggregate size distribution of different asphaltene solutions. The effect of (1) asphaltene characteristics (aromaticity (fa), length of the alkyl chains, and solubility of the polyaromatic ring), (2) asphaltene concentration, (3) solvent nature, and (4) temperature on aggregation has been explored using the developed model. In addition, this approach has also been employed to study the use of the vapor pressure osmometry technique as a tool to evaluate the molecular weight of asphaltenes. Aggregation Model
Rogel
Figure 1. Schematic representation of asphaltene aggregates: (a) cylinder, (b) sphere, and (c) disk.
General Considerations. The asphaltene aggregates are currently described as an aromatic core surrounded by aliphatic chains.27,28 According to this model, the aromatic core is composed of aromatic sheets stacked, one above the other, at repeat distances of some 3.5-3.7 Å. The attraction of asphaltene molecules is attributed to the π-π interactions between the aromatic structures that compose asphaltenes.29,30 On the other hand, the aliphatic chains induce steric repulsion between aromatic sheets and prevent the flocculation of the aggregates. The balance between attractive and repulsive interactions has been suggested as the origin of the complex colloidal behavior exhibited by the asphaltenes.31 It is also evident from numerous studies32-37 that hydrogen bonding between asphaltene molecules exists. However, its effect on asphaltene aggregation is still not very well understood.38 In the present work, the asphaltene aggregates are considered as generated by asphaltene molecules stacking as shown in Figure 1. Three different shapes are considered for asphaltene aggregates: rod, disk, and sphere. A schematic representation of the three possible shapes is also shown in Figure 1. In the model, each asphaltene molecule is composed of a polyaromatic ring (R) and a certain number of aliphatic fragments with chain lengths from 6 to 12. Then, a molecule of asphaltene Ri(Cj)n is composed of a polyaromatic nucleus Ri, with i ranging (26) Puvvada, S.; Blankschtein, D. J. Chem. Phys. 1990, 92, 3710. (27) Speight, J. G. The Chemistry and Technology of Petroleum; Marcel Dekker: New York, 1991. (28) Whitehead, E. V. In Asphaltenes and Asphalts 1. Developments in Petroleum Science; Yen, T. F., Chilingarian, G. V., Eds.; Elsevier: Amsterdam, 1994. (29) Wong, G. K.; Yen, T. F. J. Pet. Sci. Eng. 2000, 28, 55. (30) Syunyaev, R. Z.; Safieva, R. Z.; Safin, R. R. J. Pet. Sci. Eng. 2000, 26, 31. (31) Fenistein, D.; Barre´, L. Fuel 2001, 80, 283. (32) Moschopedis, S. E.; Speight, J. G. Fuel 1976, 55, 187. (33) Ignasiak, T.; Strausz, O. P.; Montgomery, D. S. Fuel 1977, 56, 359. (34) Taylor, S. R.; Li, N. C. Fuel 1978, 57, 117. (35) Speight, J. G.; Moschopedis, S. E. ACS Prepr. Div. Pet. Chem. 1981, 16, 907. (36) Monin, J. C.; Vignat, A. Rev. Inst. Fr. Pet. 1984, 39, 821. (37) Acevedo, S.; Leon, O.; Rivas, H.; Marquez, H.; Escobar, G.; Gutierrez, L. ACS Prepr. Div. Pet. Chem. 1987, 32, 426. (38) Rogel, E. Energy Fuels 2000, 14, 566.
Figure 2. Polyaromatic rings used to represent the aromatic moieties of asphaltenes.
from 1 to 7 according to Figure 2, and n aliphatic chains Cj where j represents the length of the aliphatic chains. As the molecules selected to represent asphaltenes do not have heteroatoms, the formation of hydrogen bonds among them has been ruled out.
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Free Energy Aggregation Contributions. The free energy change associated with the asphaltene aggregation represents the free energy difference between an asphaltene molecule present in an aggregate of number of aggregation N and shape Sh and one present in the singly dispersed state in the solvent:26
∆Gagg°(N,Sh) ) (µN° - Nµ1°)/N
(1)
Here, µN° represents the standard chemical potential of an asphaltene aggregate containing N asphaltene molecules and µ1° is the standard chemical potential of an asphaltene free in the solvent. The main goal of any molecular aggregation model is to evaluate this free energy difference ∆Gagg°(N,Sh). In the developed model, inspired in the earlier work by Puvvada and Blankschtein,26 the free energy difference associated with the asphaltene aggregation is composed of the following contributions: (1) Transfer of the Aromatic Moiety from Solvent to Aromatic Cores. During aggregation, the aromatic regions of the asphaltenes are transferred from their contact with the solvent to the aromatic core inside the asphaltene aggregate. The solubility of the aromatic molecules in different solvents is estimated using the following equation that has been successfully used to describe the solubility behavior of many solids including aromatic compounds39,40 and also of paraffins and asphaltenes:41
Xa ) exp[-(∆Hm/RT)(1 - T/Tm) - 1 + (Vl/Vs) ln(Vl/Vs) - (Vl/RT)(δs - δl)2] (2) where ∆Hm is the enthalpy of fusion at the melting temperature Tm, Vl is the molar volume of the solute in the liquid state, δl is the solubility parameter of the solute, and Vs and δs are the molar volume and solubility parameter of the solvent. In this paper, the physical properties needed to calculate the solubility in eq 2 are estimated based on the approach of molecular descriptors previously described.23 The free energy associated with the transfer of the aromatic moieties of asphaltenes from the solvent into the aromatic core is given by
∆Grams/RT ) -ln Xa
(3)
(2) Creation of an Aggregate Core-Solvent Interface. The free energy associated with the formation of this interface can be calculated via the macroscopic relation24,26
∆Gint/RT ) σagg(A - NchainAp)/N
(4)
where σagg is the macroscopic aggregate-solvent interfacial tension, A is the total area of the aggregate, Nchain is the number of external chains per aggregate, and Ap is the area occupied by each chain in the surface. Different approaches have been proposed to determine σagg.24,26 In the present work, the aggregate-solvent interfacial tension is calculated taking into account the curvature dependence of σagg,
σagg ) σ°[1 - (S - 1)δ/lc]
where σ° is the interfacial tension of a planar aromaticsolvent surface, δ is the Tolman distance, S is a factor of shape (3 for spheres, 2 for cylinders, and 1 for disks), and lc is the minor radius of the aggregate core. The Tolman distance, δT, is calculated using the following correlation previously developed for surfactants in aqueous solution:26
(5)
(39) Barton, A. F. M. Handbook of Solubility Parameters and Other Cohesion Parameters; CRC Press: Boca Raton, FL, 1985. (40) Reid, R. C.; Prausnitz, J. M.; Sherwood, J. K. The Properties of Gases and Liquids, 3rd ed.; McGraw-Hill: New York, 1977. (41) Chung, T. H. Presented at the 67th Annual Technical Conference and Exhibition of the Society of Petroleum Engineers, Washington, DC, Oct 4-7, 1992, Paper SPE 24851.
δT ) 0.1456lc
(6)
σ° ) σs + σarom - 2.0ψ(σsσarom)0.5
(7)
σ° is given by
In these equations, σs and σarom are the solvent and polyaromatic ring surface tension, respectively. The constant ψ depends on the nature of the interactions and, for compounds of similar polarity, is very close to unity. In the present case, this constant is considered as 1. In the present work, σarom is calculated using the relationship39
δ2 ) RV1/3σ-1
(8)
where R is a constant that varies only between certain limits according to the type of molecule. This relationship is reasonable as long as the area per molecule is proportional to V2/3.39 For the molecules shown in Figure 2, the molar volumes V and the molecular areas calculated are proportional. Using this approach, the surface tensions obtained for the seven molecules shown in Figure 2 vary from 64 to 110 mJ/m2. In comparison, experimental surface tensions for carbon,42 graphite,43 and asphaltenes44 are 95.67, 100-120, and 41 mJ/m2, respectively. (3) Steric Contribution. This contribution is due to the steric repulsions among the aliphatic chains at the interface between the aromatic core and the shell. The simplest way to evaluate the steric repulsion is given by24,26
∆Gste/RT ) -(Nchain/N) ln(1 - NchainACH2/A)
(9)
where ACH2 is the effective cross-sectional area of the methylene group L2, and A is the total area of the aromatic core. (4) Trapped Contribution. This contribution arises from the alkyl chains that are confined inside the polyaromatic core. It only applies to the discotic and spherical aggregates as can be seen in Figure 1. As the rod-shaped aggregates are formed by the piling of molecules in a single column, this contribution does not apply to them. As a first approximation, in the present work, this contribution per trapped chain is represented by the following empirical expression:24
∆Gtrapp/RT ) (Ntrapp/N)(-0.50 + 0.24nc)
(10)
where nc is the number of carbon atoms per aliphatic chain and Ntrapp is the number of chains trapped inside the aggregate. This expression was developed by the fitting of the critical micelle concentration of surfactants in aqueous solutions. The proposed model does not consider contributions from the interaction between the different species in solution. Therefore, this model cannot be applied to concentrated solutions of asphaltenes where interactions between the (42) Glass, A. S.; Wenger, E. K. Energy Fuels 1998, 12, 152. (43) Gonzalez-Martin, M. L.; Janczuk, B.; Labajos-Broncano, L.; Bruque, J. M. Langmuir 1987, 13, 5991. (44) Papirer, E.; Kuczinski, J.; Siffert, B. Fuel 1987, 66, 1691.
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species in solution are important and, of course, it cannot be used to predict a second phase transition like precipitation. Computational Approach. Based on the description of the contributions presented in the previous section, the free energy of aggregation ∆Gagg° is given by
∆Gagg°(N,Sh) ) ∆Gtrans + ∆Gint + ∆Gste + ∆Gtrapp (11) The aggregate size distribution is given by24,26
XN ) X1N exp[-N∆Gagg°/kT]
(12)
where X1 and XN are the molar fractions of monomer and aggregate of size N. Using the size distribution, the average sizes of the aggregates can be calculated:
Nn )
∑NXN/∑XN
∑N2XN/∑NXN Nn,app ) (X1 + ∑NXN)/(X1 + ∑XN) Nw,app ) (X1 + ∑N2XN)/(X1 + ∑NXN) Nw )
(13)
(14)
where Nn and Nw are the number-average aggregation number and the weight-average aggregation number. Nn,app and Nw,app represent the apparent number-average aggregation number and the apparent weight-average aggregation number. N ranges from 2 to infinity. In the present work, the cmc is estimated as that value of X1 for which the concentration of the singly dispersed asphaltene molecules is equal to that of the asphaltene molecules present in the form of aggregates:24
cmc ) X1 )
∑NXN
Figure 3. Contributions to the free energy of aggregation ∆Gagg of the R1(C7)3 molecule in pyridine at 25 °C as a function of the aggregation number N for (a) cylinders and (b) spheres.
(15)
Obviously, this is not a strictly thermodynamic method to obtain the cmc. The rigorous way is to construct a plot of one of the functions X1, ∑NXN, or ∑N2XN, which represent different properties of the solution, as a function of the total concentration X ) X1 + ∑NXN. The cmc is the value of the total concentration at which a sharp change in the function occurs. This is in accordance with the operational definition of cmc. However, in a preliminary study, it was found that eq 15 yields similar (within 5% error) results to the strictly thermodynamic method. For any asphaltene molecule, the ∆Gagg° depends on two independent variables, the aggregation number N, and the shape of the aggregate. The most favorable ∆Gagg° is obtained as a function of N minimizing with respect to the shape. Based on this result, the aggregate size distribution can be obtained as a function of X1 according to eq 12 and, therefore, average aggregation numbers and cmc values according to eqs 13-15, respectively. Results and Discussion Free Energy Aggregation Contributions. Typical free energy curves are shown in Figure 3 for the aggregation of asphaltene R1(C7)3 in pyridine considering the formation of (a) cylindrical aggregates and (b) spherical aggregates. These curves are similar for all the other molecules studied in this work using the following solvents: benzene, toluene, 1-methyl naphthalene, nitrobenzene, quinoline, and 1,2 dichlorobenzene. In Figure 3, the dominant contribution to the free energy of aggregation is the free energy of transfer of the polyaromatic ring from the bulk of the solvent to the aromatic core of the aggregate. This means that the low solubility of the polyaromatic
Figure 4. Comparison of the predicted free energy of aggregation for different asphaltene aggregate shapes: disks of different lengths (Å), spheres, and cylinders. The calculations correspond to pyridine solutions of R1(C7)3 at 25 °C.
ring is the main driving force for the aggregation behavior of asphaltenes. According to the model, all the other contributions are positive and, therefore, oppose the asphaltene aggregation. However, while the steric and trapped contributions increase as the size of the aggregate increases, the interfacial contribution decreases. This means that the steric and trapped contributions limit the growth of the aggregates while the interfacial contribution favors it. Comparison of Different Aggregate Shapes. Figure 4 shows the comparison of the calculated free energies of aggregation considering different aggregate shapes for asphaltene R1(C7)3 in pyridine. In this figure, cylindrical shape is preferred over spherical shape and disks of
Thermodynamic Modeling of Asphaltene Aggregation
different lengths. Cylinders are energetically favored over the other shapes, because is possible to build a cylinder without imposing restrictions on the movement of the alkyl chains, while in the case of spheres and disks, there are alkyl chains trapped inside the aggregates. This generates a positive free energy contribution that opposes the aggregation. Such contribution energetically disfavors spheres and disks in comparison to cylinders. In fact, the calculations made in this work using different asphaltene molecules and the solvents previously mentioned indicate that the cylindrical shape is always preferred over the spherical at relatively low aggregation numbers. At higher aggregation numbers, the spherical shape is preferred, which can be interpreted in terms of a shape transition at high concentrations. However, in all the studied cases at concentrations between 1 and 10 g/L, the cylindrical shape is preferred. These results are obtained considering the asphaltene as a monodisperse fraction represented by an average molecule composed of a polyaromatic ring and several alkyl chains. This strongly affects the shape of the aggregates. Therefore, some caution should be exercised in the comparison of these results with the experimental evidence about this point, which is, besides, very contradictory.14,18,45-47 Actually, the shape of the asphaltene aggregates is still an open question. Spheres,45 disks,46 and rodlike particles14 can fit the experimental data obtained using small-angle X-ray and neutron scattering data (SAXS and SANS, respectively).18,47 However, polyaromatic compounds such as alkyl hexabenzocoronene derivatives form columnar mesophases.48,49 In the columnar mesophases, the aromatic cores are stacked on top of each other in columns separated by fluid peripheral aliphatic chains. Critical Micelle Concentration and Asphaltene Aggregate Size Distribution. In this work, the term cmc is used because of its wide diffusion in the area. This does not mean that the asphaltene aggregates can be considered as micelles. In fact, in a strict way only surfactants in aqueous solution can form true micelles. Then, the term cmc should be interpreted as the concentration where asphaltene aggregates and not asphaltene micelles begin to form. On the other hand, even though values for cmc have been reported in the literature for asphaltenes using different techniques,1,4,7-9 there are some doubts about the existence of a cmc similar to the one shown by surfactants in aqueous solutions.10,11 In fact, the experimental evidence is contradictory and indicates that some asphaltenes exhibit cmc’s1,4,6-8 whereas others do not.10,11 The operational definition of cmc is the concentration at which a sharp transition in behavior for the solution is observed. For some asphaltenes, such as asphaltenes from Athabasca, Cold Lake, and Cerro Negro bitumens, it is impossible to identify a cmc in accordance with this operational definition. They do not exhibit a cmc, although aggregation apparently occurs.11 In Figures 5-7, the effect of (1) solubility of the polyaromatic ring, (2) aromaticity, and (3) solvent on the evolution of monomer concentration (X1) as a function of total concentration is shown. In the comparison of the (45) Storm, D. A.; Sheu, E. Y.; De Tar, M. M. Fuel 1993, 72, 977. (46) Ravey, J. C.; Ducouret, G.; Espinat, D. Fuel 1988, 67, 1560. (47) Storm, D. A.; Sheu, E. Y. In Asphaltenes and Asphalts 1. Developments in Petroleum Science; Yen, T. F., Chilingarian, G. V., Eds.; Elsevier: Amsterdam, 1994. (48) Yatabe, T.; Harbison, M. T.; Brandt, J. D.; Wagner, M.; Mullen, K.; Samori, P.; Rabe, J. P. J. Mater. Chem. 2000, 10, 1519. (49) Loi, S. P.h.D Thesis, Universitat Sieguen, Sieguen, 2001.
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Figure 5. Monomer concentration X1 as a function of the total concentration of asphaltene in toluene at 25 °C for molecules composed of polyaromatic rings (a) R1 or R4 and (b) R7 and C7 alkyl chains so that the aromaticity is 0.55.
Figure 6. Monomer concentration X1 as a function of the total concentration of asphaltene in toluene at 25 °C for molecules composed of a polyaromatic ring R4 and a diverse number of C7 alkyl chains.
figures, it can be seen that there are remarkable differences in terms of the increase of X1 as the total concentration of asphaltene increases. In systems that exhibit cmc in accordance with the operational definition, X1 increases as the total concentration increases until reaching a plateau and then it remains constant.50,51 Figure 5a,b shows the effect of the decrease of the solubility of the polyaromatic ring on the evolution of X1 as a function of the total concentration. According to this set of figures, the decrease of the solubility induces the (50) Ruckenstein, E.; Nagarajan, R. J. Phys. Chem. 1980, 84, 1349. (51) Nagarajan, R.; Wang, C. C. J. Colloid Interface Sci. 1996, 178, 471.
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Figure 8. Apparent aggregation number in different solvents as a function of the solubility of the polyaromatic ring for the series Rx(C7)3 at a total concentration of 5 g/L.
Figure 7. Monomer concentration X1 as a function of the total concentration of R4(C7)4 in (a) toluene and benzene at 25 °C and (b) nitrobenzene and pyridine at 25 °C.
existence of a cmc similar to the one shown by surfactants in aqueous solution: for the least soluble polyaromatic ring (R7), the curve X1 versus total concentration exhibits a break point and after that, X1 remains constant. In contrast, for the more soluble polyaromatic rings (R1 and R4), although a change in the slope of the curve can be identified, X1 increases in the studied range of total concentrations. In a previous work using another aggregation model,23 it was also found that for asphaltene molecules, a cmc might or might not be observed experimentally depending on the nature of the polyaromatic rings that composed the asphaltene molecules. In Figure 6, the evolution of X1 is compared for different molecules with the same polyaromatic ring but a different number of chains. As the aromaticity increases, the curves change slightly but consistently from a system in which X1 increases in all the range of concentrations studied to a system in which X1 remains constant after exhibiting a break point. Asphaltenes from heavy crude oils such as Cerro Negro, Athabasca, and Cold Lake are usually characterized by a low aromaticity and low aromatic condensation. For these asphaltenes, as mentioned before, the experimental identification of a cmc has been impossible.11 On the other hand, it has been reported that resins which also have lower aromaticity and lower aromatic condensation than asphaltenes do not exhibit cmc behavior.5 Figure 6 can also be interpreted in terms of the solubility of the asphaltene; a lower aromaticity implies a higher solubility of the asphaltene and vice versa. In other words, there is an increase in the solubility as the aromaticity decreases, and therefore the number of aliphatic chains in the asphaltene molecule. The higher the solubility of the asphaltene, the smoother the change in the curve X1 versus total concentration. At the limit of the higher solubility, X1 should be equal to the total
concentration, because there should not be aggregates. On the contrary, the lower the solubility, the sharper the change in the curve and the lower the concentration at which this change occurs. This means the lower the cmc. In the limit of the lowest solubility, the asphaltenes should precipitate at low concentration. Then, it should be impossible to evaluate aggregation. In fact, experimentally, it has been reported that some asphaltenes cannot be dissolved even in good solvents such as toluene. The effect of the solvent in X1 is shown in Figure 7. The same molecule in three different solvents exhibits contrasting behaviors. It is obvious that in pyridine and nitrobenzene, this molecule does not exhibit a cmc behavior even though aggregation occurs, as will be shown in the next sections. Good solvents such as pyridine and nitrobenzene seem to preclude the cmc behavior for molecules that exhibit this behavior in other solvents. However, even in pyridine and nitrobenzene, the molecules tested with the less soluble polyaromatic rings (R6 and R7) exhibit cmc behaviors. Then, the aromaticity and the nature of the polyaromatic ring also influence the aggregation behavior in the best solvents. Based on the preceding analysis, the proposed model offers a plausible explanation for the contradictory experimental evidence about the existence or absence of a cmc similar to the one exhibited by surfactants in aqueous solutions. Effect of Asphaltene Characteristics on Aggregation Behavior. Characteristics of the Polyaromatic Ring Solubility. In a previous section, it was found that the insolubility of the ring is the driving force for the aggregation. Figure 8 shows the effect of the solubility of the polyaromatic core in the aggregation numbers of some representative molecules (Rx(C7)3) in different solvents. This figure reveals the relation between the solubility of the polyaromatic ring and the apparent aggregation number at a total concentration of 5 g/L. The lower the solubility of the polyaromatic ring in the solvent, the larger the apparent aggregate number of the asphaltene. According to some authors,52,53 the characteristics of the aromatic zones of the asphaltenes are important factors in determining the flocculation behavior of the asphaltenes. In particular, the condensation index is a measure of the extension of the aromatic ring and is defined as the ratio between the number of bridging aromatic carbons and the number of peripheral nonbridging (52) Szewczyk, V.; Be´har, F.; Be´har, E.; Scarsella, M. Rev. Inst. Fr. Pet. 1996, 51, 575. (53) Ali, M. F.; Saleem, M. Fuel Sci. Technol. Int. 1988, 6, 541.
Thermodynamic Modeling of Asphaltene Aggregation
Figure 9. Apparent aggregation number of the Rx(C7)3 series in different solvents at a total concentration of 5 g/L as a function of the condensation index of the polyaromatic ring.
carbons. A high condensation index is found for asphaltenes extracted from problematic sources such as deposits or unstable crude oils (crude oils that exhibit asphaltene deposition). Figure 9 shows the apparent aggregation number of the Rx(C7)3 series at a total concentration of 5 g/L as a function of the condensation index of the polyaromatic ring. This figure again suggests that the condensation index of the polyaromatic ring plays a key role in the extension of the aggregation. As the condensation index of the polyaromatic ring increases, the apparent aggregation number increases in all the solvents studied. The missing aggregation numbers on this figure were very high, and for practical reasons, they are not shown. However, they follow the same tendency exhibited in Figure 9. This tendency is confirmed by the experimental evidence, which shows that asphaltenes with extended aromatic condensation form bigger aggregates at the same concentration.52,53 It has also been reported in a study using X-ray scattering that the aggregates that flocculate first are the largest in size.52 In a previous approach,23 it was found that the solubility of the polyaromatic ring and the condensation index are closely related. Number and Length of the Alkyl Chains. The number of alkyl chains per molecule of asphaltene should play an important role in determining the aggregation behavior. According to the proposed model, the alkyl chains affect the aggregation in two ways: (1) through the screening of the interaction between the solvent and the aromatic sheets and (2) through the steric interactions among chains. The effect of the number of alkyl chains on cmc values in different solvents is shown in Figure 10 for a molecule composed of a polyaromatic ring R4 and different numbers of alkyl chains C7. In this figure, the predicted cmc decreases as the number of alkyl chains in the molecule increases. The missing points in this figure correspond to systems where it is impossible to identify a break in the X1 versus total concentration curve. Figure 11 shows the apparent aggregation number in (a) toluene and (b) pyridine of a molecule composed of a polyaromatic ring R4 and different numbers of alkyl chains C7 (R4(C7)x). As can be seen, the increase of the number of alkyl chains decreases the aggregation number. This result indicates that the presence of alkyl chains disfavors the growth of the aggregates and, obviously, disfavors the aggregation. The alkylation of asphaltenes has been frequently used as a technique to determine the molecular weight of the asphaltenes.54 In this technique, the asphaltene molecules are modified by the addition of alkyl
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Figure 10. Effect of the number of alkyl chains on the predicted cmc of the R3(C7)x series in different solvents.
Figure 11. Apparent aggregation number of the R4(C7)x series as a function of the total concentration in (a) toluene and (b) 1,2 dichlorobenzene.
chains in order to decrease the aggregation of the asphaltenes and then, knowing the number of alkyl chains added, it is possible to calculate the molecular weight of the original asphaltene sample. The decrease in molecular weight of the alkylated asphaltene molecules54,55 has been used as a proof of the role of hydrogen bonding in the aggregation of asphaltenes. It is supposed that the reductive alkylation destroys the hydrogen bonding in asphaltenes and similar molecules.56 However, other (54) Acevedo, S.; Leon, O.; Rivas, H.; Marquez, H.; Escobar, G.; Gutierrez, L. ACS Prepr. Div. Pet. Chem. 1987, 32, 426. (55) Ignasiak, T.; Strausz, O. P.; Montgomery, D. S. Fuel 1977, 56, 359. (56) Taylor, S. R.; Li, N. C. Fuel 1978, 57, 117.
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Figure 13. Effect of changes in the molecular structure on the predicted cmc’s in toluene as a function of the aromaticity.
Figure 12. Effect of the length of the alkyl chains on the predicted (a) cmc and (b) apparent aggregation number at a total concentration of 5 g/L in toluene for the Rx(Cn)5 series.
authors57,58 have shown that the chemistry of reductive alkylation also destroys the aromatic stacking interactions in petroleum residue. In fact, this last effect can be explained by the proposed model. Figures 10 and 11 can also be interpreted in terms of aromaticity (ratio of aromatic carbon to total carbon atoms), since the increase of alkyl chains decreases the aromaticity as the number of aliphatic carbons also increases. Figure 12 shows the effect of the length of the alkyl chains on cmc and apparent aggregation number. According to the model, the increase of the length of the alkyl chains increases slightly the cmc. The model also predicts small changes in the aggregation number at 5 g/L total concentration of asphaltene. However, in this case, these small changes do not show a clear pattern. In the previous work,23 the model developed predicted bigger variations of the aggregation properties of the asphaltenes due to the change of the alkyl chains. However, in this new approach, the variations are smaller and, in fact, the difference between a C7 and a C12 chain as an appendage is not noticeable. As in the previous figures, Figure 12 can also be interpreted in terms of aromaticity. Aromaticity. Another structural aspect that has been claimed to influence notably the flocculation of asphaltenes is the aromaticity (fa), the ratio of aromatic carbon to total carbon atoms. In particular, it has been reported that an increase in aromaticity increases the tendency for flocculation of the asphaltenes. However, a change in aromaticity can be the result of different modifications in the asphaltene structure, for example, changes in the (57) Speight, J. G.; Moschopedis, S. E. ACS Prepr. Div. Pet. Chem. 1981, 26, 907. (58) Monin, J. C.; Vignat, A. Rev. Inst. Fr. Pet. 1984, 39, 821.
Figure 14. Effect of changes in the molecular structure on the predicted apparent aggregation numbers in toluene as a function of the aromaticity.
number or length of the aliphatic chains, as shown in the previous section, or changes in the polyaromatic ring. This makes it difficult to identify a pattern for the aggregation behavior as a function of aromaticity. In fact, in previous experimental works,7,8 there was no clear relationship between aromaticity and the cmc values of different asphaltenes in a set of various solvents. Figures 13 and 14 show the effect of different changes in the structure of the molecule R3(C7)5 on the calculated cmc’s and aggregation number at 5 g/L in toluene. In these figures, cmc values and aggregation numbers are plotted as a function of the aromaticity of the molecule. These are two examples of the complex pattern obtained for the aggregation behavior when the aromaticity changes for different structural modifications of the molecule. According to these results, it could be advisable not to use aromaticity as the unique parameter to estimate or guess the tendency of a particular asphaltene to aggregate or flocculate. Effect of the Solvent on Aggregation Behavior. Figures 8-10 reveal differences in the aggregation behavior depending on the solvent. In Figure 15, the aggregation number of various molecules of the series Rx(C7)3 at 5 g/L is plotted as a function of the solubility parameter of the solvent. As can be seen, there is a remarkable decrease in the aggregation number as the solubility parameter increases. This tendency agrees very well with the decrease of the amount of precipitated asphaltene as the solubility parameter increases.59 The missing points in this figure correspond to systems with (59) Mitchell, D. L.; Speight, J. G. Fuel 1973, 52, 149.
Thermodynamic Modeling of Asphaltene Aggregation
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Figure 15. Apparent aggregation number for the Rx(C7)3 series at a total concentration of 5 g/L as a function of the solubility parameter of the solvent.
Figure 17. Critical micelle concentrations for the Rx(C7)5 series in (a) toluene and (b) benzene as a function of the temperature.
Figure 16. Aggregation number for the Rx(C7)5 series in (a) toluene and (b) benzene at a total concentration of 5 g/L as a function of the temperature.
very high aggregation numbers, and for this reason, these points are not plotted. In the case of the cmc, the tendency predicted by the model is not so clear. Nevertheless, it was found that the studied molecule exhibit its highest cmc in pyridine (21.7 MPa1/2). Effect of the Temperature on Aggregation Behavior. Figures 16 and 17 show the effect of temperature on the aggregation of molecules of the series Rx(C7)5 in benzene and toluene as predicted by the proposed model. Figure 16 indicates that there is a decrease in the size of
the aggregates as the temperature rises in accordance with experimental evidence.11,12,14,16 However, the tendency for the cmc predicted by the model, the increase of the cmc as the temperature rises, does not agree with the experimental evidence available.1 According to measurements of the cmc of asphaltenes in toluene, the cmc decreases as the temperature increases. In the developed model, the free energy of aggregation is dominated by the term corresponding to the solubility of the polyaromatic ring. This term is less negative as the temperature rises because of the increase of the solubility of the polyaromatic ring with the increase of the temperature. In consequence, the changes in this term disfavor the aggregation as the temperature increases. Molecular Weight Determination using Vapor Pressure Osmometry. The proposed model can be used to evaluate the use of vapor pressure osmometry (VPO) to determine the molecular weight of asphaltenes. Usually, in this technique, the apparent molecular weight or aggregation degree of the asphaltenes can be measured as a function of their concentration in any solvent. It is supposed that at low concentration where the association among asphaltenes is negligible, the apparent molecular weight measured by VPO should be equal to the molecular weight of the asphaltenes in the monomeric state. Then, the molecular weight reported using VPO is usually a value obtained by extrapolation of the apparent molecular weight versus concentration data to zero concentration. This procedure to estimate molecular weights was evaluated for different solvents using the proposed model. In
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Conclusions
Figure 18. Comparison between actual molecular weights and estimated molecular weights for the molecules of the series Rx(C7)3 and Rx(C7)5 using VPO measurements as predicted by the proposed model.
other words, apparent molecular weight versus concentration curves were obtained for different molecules using the proposed model. Then, the molecular weight of the asphaltenes in the monomeric state was estimated by extrapolation to zero concentration. Figure 18 reflects the error in the estimation of the molecular weights of two series of compounds: Rx(C7)3 and Rx(C7)5. In this figure, estimated values are plotted against real ones. The missed points indicate that the estimated molecular weights are more than 2 times the real ones. The solid line indicates where the points would lie if estimated values and real values were the same. According to this figure, among the studied solvents, the best solvent to perform VPO measurements is pyridine. This result agrees with the experimental evidence that also suggests pyridine as the best choice to determine molecular weight using VPO measurements. Figure 18 also reveals that the estimated molecular weights can be higher or lower than the real ones. In fact, it is well-known that VPO measurements can yield molecular weights higher than the real ones. However, the possibility of obtaining lower molecular weights than the real ones is totally unexpected. According to the calculations made, it is possible to obtain lower values than the real ones if the slope of the curve of the molecular weight versus concentration is sharp enough and the apparent aggregation numbers are low. The results obtained also reveal that the lower the solubility of the polyaromatic ring, the larger the error in the estimation of the molecular weights. This is predictable since the lower the solubility of the polyaromatic ring in the solvent, the larger the aggregation number.
The aggregation behavior of average molecules representing asphaltenes in different solvents is described using a molecular thermodynamic approach based on a micellization model previously developed for surfactants in aqueous solution. The proposed model provides a qualitative description of many experimental tendencies reported for asphaltene aggregation. Additionally, the model is strictly predictive and does not use any experimental information from asphaltene solutions. The proposed approach is based on the classical model that describes asphaltene aggregates as polyaromatic cores, composed of stacked aromatic sheets, surrounded by aliphatic chains. Using this physical model, an expression for the free energy of aggregation that incorporates four contributions was developed: (1) transfer of the polyaromatic ring from the solvent to the aggregate core, (2) aggregate core-solvent interactions, (3) steric repulsion among the aliphatic chains in the aggregate crown, and (4) trapping of aliphatic chains inside the polyaromatic core. The results obtained indicate that the driving force for the aggregation is the insolubility of the polyaromatic ring in the solvent. According to the model, all the other contributions are positive and, therefore, oppose the asphaltene aggregation. The model predicts that the cylindrical shape is preferred over the spherical shape and disks of different lengths. According to the model, the existence or absence of an operational cmc for asphaltene solutions depends on the characteristics of the polyaromatic ring, the aromaticity, and also the nature of the solvent. In general, the model predicted that the asphaltenes with low aromaticities and low aromatic condensations do not exhibit cmc behavior. The proposed model qualitatively predicts the asphaltene aggregation behavior in a series of different solvents. In particular, the experimental trends observed for the variation of aggregate size with (1) asphaltene molecular characteristics (condensation index, aromaticity, and chain length), (2) asphaltene concentration, (3) solvent characteristics, and (4) temperature have been reproduced by the new model. The results obtained clearly support the classical model for asphaltene aggregates: a polyaromatic core surrounded by aliphatic chains. Acknowledgment. The author is grateful to Olga Leon and Lante Carbognani for the useful and enlightening discussions about asphaltene aggregation behavior and VPO measurements. LA035339O
