Langmuir 2004, 20, 4559-4565
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Thermodynamic Characterization of Asphaltene-Resin Interaction by Microcalorimetry Daniel Merino-Garcia and Simon I. Andersen* IVC-SEPsDepartment of Chemical Engineering, Technical University of Denmark, DK-2800 Lyngby, Denmark Received January 8, 2004. In Final Form: March 15, 2004 This paper collects the work performed by isothermal titration calorimetry (ITC) to characterize the interaction between petroleum asphaltenes and resins. The interaction between these two fractions is of great interest in order to understand the mechanism of stabilization of asphaltenes in crude oil. To simplify the approach, this preliminary study focuses on toluene solutions of both fractions. This paper reports the experimental determination of the average number of sites in asphaltene molecules and the enthalpy of interaction between asphaltenes and resins. Two models have been used to fit the experimental data. The enthalpies calculated by ITC are in the order of -2 to -4 kJ/mol. These values are in the limit of hydrogen bonding and permanent dipole energies. Similar values have been obtained by using the enthalpy as a fitting parameter in the SAFT equation.
Introduction The decline of conventional oil production has forced the producers to exploit heavier oil reservoirs, increasing the content of complex fractions such as asphaltenes in the extracted oil. Asphaltenes are defined as the fraction of petroleum that is insoluble in an n-alkane (n-heptane) and soluble in toluene. This loose definition allows the presence in this fraction of molecules of a wide range of sizes, heteroatom content, and aromaticity. Field operations face continuous problems due to the tendency of this fraction to flocculate and precipitate alone or together with waxes. Resins are a petroleum fraction also found in vacuum residua. They are believed to be the transition between the polar asphaltenes and the nonpolar dispersing media formed by aromatic and saturates. According to the model developed in the early decades of the last century,1-3 asphaltenes form colloidal systems both in asphalts and in crude oils, which are stabilized by resins. Upon changes in pressure or composition in oil recovery operations, resins are no longer able to peptize asphaltenes and precipitation occurs. In laboratory experiments, it has been reported that the removal of resins causes the precipitation of asphaltenes.4 Resin molecules have similar structures to asphaltenes but longer alkyl nonpolar chains4 and smaller aromatic rings. This increases their solubility in aliphatic solvents. Resins contain oxygen mainly in steric and carbonyl functions, rather than hydroxyl.5 Nitrogen is found in amine, pyrrole, and indole functionalities. Chromatographic fractionation of resins shows that they are mainly basic in nature, with a predominance of pyridinic groups.6 The molecular weight of resins is in the range of 600-1000 units, according to VPO measurements.7 Resins * To whom correspondence may be addressed:
[email protected]. (1) Pfeiffer, J. P.; Saal, R. N. Phys. Chem. 1940, 44, 139. (2) Sachanen, A. N. The Chemical Constituents of Petroleum; Reinhold Publishing Corp.: New York, 1945. (3) Ray, B. R.; Witherspoon, P. A.; Grim, R. E. J. Phys. Chem. 1957, 61, 1296. (4) Koots, J. A.; Speight, J. Fuel 1975, 54, 179. (5) Moschopedis, S. E.; Speight, J. Fuel 1976, 55, 187. (6) Hammami, A.; Ferworn, K. A.; Nighswander, J. A. Pet. Sci. Technol. 1998, 16 (3&4), 227. (7) Speight, J. G. The Chemistry and Technology of Petroleum, 3rd ed.; Marcel Dekker, Inc.: New York, 1999.
are believed to aggregate less than asphaltenes, allowing the use of this technique to determine the monomeric molecular weight. Resins are usually separated from the deasphalted oil by adsorption on surface-active materials, but they can as well be obtained as the fraction of deasphalted oil that is insoluble in liquid propane.8 There is a group of compounds that can be considered either low-molecularweight asphaltenes or high-molecular-weight resins, in agreement with the concept of petroleum as a continuum. The separation procedure would determine to which fraction these compounds would go.9 In this work, silica gel has been used as the packing material of the chromatographic column. The amount of resins in petroleum varies in a wide range from 3 to 38 wt %,7 and it has been found to be greater for crudes with high asphaltene content.9 McLean and Kilpatrick10 reported a dependence of the stability of water-oil emulsions on the ratio between asphaltenes and resins (R/A). Nevertheless, a comprehensive study with more than 20 crudes has shown that instable oils may also have a ratio above 1.11 Due to the polar functional groups, resins can interact with asphaltenes by means of hydrogen bonds or chargetransfer complex formation, as shown by IR spectroscopy and proton magnetic resonance.5 Even if hydrogen bonding may be an important factor in the stabilization, resin interaction with asphaltenes is believed to be a combination of van der Waals, charge transfer, Coulombic, and exchange repulsion.12 According to this view, polarity is relevant in the process of approach of asphaltenes and resins. van der Waals (VdW) interaction would take over when the distance is close enough. At longer distances, the weak VdW forces may be screened by other molecules to a greater degree than the forces related to polarity. The review by Andersen and Speight13 shows that resin studies are scarce, in comparison with asphaltene re(8) Schwager, I.; Yen, T. F. Fuel 1978, 57, 100. (9) Goual, L.; Firoozabadi, A. AIChE J. 2002, 48 (11), 2646. (10) McLean, J. D.; Kilpatrick, P. K. J. Colloid Interfacial Sci. 1997, 196 (1), 23. (11) Carbognani, L.; Orea, M.; Fonseca, M. Energy Fuels 1999, 13, 351. (12) Murgich, J. Pet. Sci. Technol. 2002, 20 (9&10), 983. (13) Andersen, S. I.; Speight, J. G. Pet. Sci. Technol. 2001, 19 (1&2), 1.
10.1021/la0499315 CCC: $27.50 © 2004 American Chemical Society Published on Web 04/30/2004
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search. The stabilization of asphaltenes by resins has been studied by several techniques. Murzakov and co-workers14 reported a direct relationship between colloidal stability and resin concentration in gravimetric sedimentation analysis. Andersen and co-workers15 proved by microcalorimetric titration that the addition of resins eliminates the change previously assigned to the critical micellar concentration. Goual and Firoozabadi16 studied the effect of resins on the flocculation onset point of asphaltenes. Resins were observed to delay the onset point but also increased the amount precipitated. The more polar resins were more effective in the stabilization of asphaltenes, stressing the importance of the polar interactions in the system asphaltene-resin. The presence of resins also retarded the onset flocculation point of asphaltenes in Kuwaiti crudes.17 Carnahan et al.18 studied the influence of native and non-native resins on the flocculation point of Hamaca asphaltenes. The non-native resins (from Boscan) were more effective stabilizers. This indicates that resins from different sources may have different dispersive power. Resins are more effective as asphaltene stabilizers than organic solvents: Hotier and Robin19 reported that 1 cm3 of resins had the same dispersing power as 105 cm3 of benzene upon addition to asphaltene solutions. Despite these indications of the role of resins in the stability of asphaltene colloids, they have not been paid yet the attention they deserve. Isothermal titration calorimetry (ITC) has shown its capacity to investigate petroleum fractions in previous studies, such as the stepwise self-association of asphaltenes20 and the interaction of a model compound (nonylphenol) with asphaltenes.21 The main advantage of this technique is that it is able to determine simultaneously the number of asphaltene sites available for the interaction with resins, as well as the main thermodynamic parameters, such as the change in enthalpy (∆H) and free energy (∆G), by the application of a suitable model. Herein, the experimental protocol developed in the study with nonylphenol is further extended to the interaction with native resins. The aim is to provide experimental data to the models that describe asphaltene behavior. Models such as micellization22,23 and SAFT24,25 include resin-asphaltene (RES-ASP) interaction in their equations. The interaction term has several parameters that require either estimation or fitting without knowledge of actual ranges or magnitudes. The experimental values provided by a technique such as ITC would be useful in order to decrease the number of estimations. Asphaltenes and resins have been studied in toluene solutions. The understanding of asphaltene solutions in organic solvents is much easier than that in pure crude (14) Murzakov, R. M.; Sabanenkov, S. A.; Syunyaev, Z. I. Khim. Tekhnol. Topl. Masel 1980, 10, 40. (15) Andersen, S. I.; del Rio, J. M.; Khvostitchenko, D.; Shakir, S.; Lira-Galeana, C. Langmuir 2001, 17, 307. (16) Goual, L.; Firoozabadi, A. Proc. Int. Conf. Heavy Org. Deposition, 2002, Mexico, 2002. (17) Al-Sahhaf, T. A.; Fahim, M. A.; Elkilani, A. S. Fluid Phase Equilib. 1983, 194-197, 1045. (18) Carnahan, N. F.; Salager, J. L.; Anton, R.; Davila, A. Energy Fuels 1983, 13, 309. (19) Hotier, G.; Robin, M. Rev. Inst. Fr. Pet. 1983, 38 (1), 101. (20) Merino-Garcia, D.; Murgich, J.; Andersen, S. I. Accepted for publication in Pet. Sci. Technol. (21) Merino-Garcia, D.; Andersen, S. I. Langmuir 2004, 20 (4), 1473. (22) Victorov, A. I.; Smirnova, N. A. Fluid Phase Equilib. 1999, 158160, 471. (23) Fahim, M. A.; Al-Sahhaf, T. A.; Elkilani, A. S. Ind. Eng. Chem. Res. 2001, 40, 2748. (24) Buenrostro-Gonzalez, E.; Gil-Villegas, A.; Wu, J.; Lira-Galeana, C. Proc. Int. Conf. Heavy Org. Deposition, 2002, Mexico, 2002. (25) Ting, D.; Hirasaki, G. J.; Chapman, W. G. Pet. Sci. Technol. 2003, 21 (3&4), 647.
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oils because of their chemical simplicity. This adds a favorable feature in the calculation of several properties. In any case, it has to be taken into account that the behavior of asphaltenes in toluene solutions does not necessarily need to be the same as that in the live oil. The behavior observed may not be projected to the behavior in the oil. Besides, the asphaltenes obtained as a solubility class may differ from the ones separated in the oil recovery operations, which are precipitated by pressure drop. Due to these facts, the results presented in this article should be regarded as a preliminary work in the elucidation of the role played by resins in the stabilization of asphaltenes. Materials and Methods Asphaltenes from different sources have been used in this study: LM1 and LM2 (Venezuela), Alaska 95, Yagual (Mexico), and Ca30. Yagual and Ca30 have been reported to present deposition problems. They have been obtained following a modified IP143 procedure.26 Asphaltenes have been washed by vacuum filtration with n-heptane until the effluent was colorless, to remove the last traces of resins and waxes that could have been coprecipitated with the asphaltenes or just occluded by them. Resins have been obtained through chromatographic fractionation of the deasphalted oil. Silica was used as a packing material, and the different fractions were sequentially eluted with hexane (saturates), toluene (aromatics), and a 10% methanol/ toluene mixture (resins). Solvents were removed by distillation, and resins were further dried under vacuum. Toluene (spectroscopic grade) was obtained from Rathburn. It was dried with molecular sieves to minimize the influence of water, as it has been previously shown to play a significant role in the interaction between asphaltenes and resins.15 Isothermal Titration Calorimetry (ITC). The experimental setup of the calorimeter (VP-ITC 2000 Microcal) has been previously described.27 All tests are carried out at 30 °C. The calorimeter consists of two cells: a reference cell filled with pure solvent and a sample cell that is used as a titration cell. It initially contains a solution of asphaltenes in toluene, and the reagent (toluene solution of resins) is injected sequentially by means of a 290 µL syringe in small steps of usually 4.0-10.0 µL. Each experiment consists of 30-100 injections, depending on the volume per injection. The isothermal conditions are kept by means of a control system that supplies or retires heat, depending on the heat developed in the interaction among the several species. Syringe concentrations are in the range 5-100 g of resins/L, while asphaltenes are tested at 1.0 and 10 g/L. There are several processes ongoing in the cell: The injected toluene causes a decrease in asphaltene concentration that leads to a rearrangement of the equilibrium between free and associated asphaltenes. The solution of resin in the syringe is also in equilibrium between free and bonded molecules. The injection into a greater volume causes as well the dissociation of resinresin bonds. In this article, the term “bond” always refers to intermolecular physical bonds. The injection process also leads to some frictional heat. Finally, resins form bonds with asphaltenes. The objective is to determine the enthalpy of resinasphaltene association and the average number of sites available in asphaltenes for resins. Modeling. Reference experiments were performed in which the titration cell did not contain asphaltenes but only toluene. The heat developed is only due to the dilution of the resin solution. This heat was subtracted from the total heat developed when asphaltenes where present in the titration cell. The remaining heat was assumed to be due to the interaction between asphaltenes and resins. Two models have been tried in order to fit the experimental data and calculate the thermodynamic properties of the interaction. First, a polymerization approach was attempted. Asphaltenes are believed to associate stepwise,28 and in the past the self(26) IP 143/90. Standards for Petroleum and its Products; Institute of Petroleum: London, 1985. (27) Merino-Garcia, D.; Andersen, S. I. Pet. Sci. Technol. 2003, 21 (3&4), 507.
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association of asphaltenes has been successfully modeled with polymerization-type reactions.20
An + A1 T An+1 w [An+1] ) Kn+1[A1] [An]
(1)
The equilibrium constants and enthalpies were considered to be the same for all the reactions:
K ) K2 ) K3 ) ... ) Kn+1
(2)
∆Ha ) ∆Ha2 ) ∆Ha3 ) ... ) ∆Han+1
(3)
Resins are considered to act as terminators of the polymerization type reaction. The growth of the aggregate is stopped once a terminator is attached to it.
An + R T AnR w [AnR][AnR] ) KRn[R] [An]
(4)
To simplify the approach, it is considered that the equilibrium constants are the same as those of the propagation reactions, but the resin-asphaltene interaction is modeled with a different value of ∆H. The values of ∆Ha are calculated by applying eqs 1-3 to the titration of asphaltenes into dried toluene,20 and the ∆H of the interaction asphaltene-ligand is used as a fitting parameter, together with the equilibrium constant K.
K ) K2 ) K3 ) ... ) Kn+1 ) KT1 ) KT2 ) ... ) KTn
(5)
∆Ha ) ∆Ha2 ) ∆Ha3 ) ... ) ∆Han+1
(6)
∆H ) ∆H1 ) ∆H2 ) ... ) ∆Hn
(7)
The molecular weight of asphaltenes and resins has been set to 1000 and 600 g/mol, respectively. The same set of molecular weights was used independently of the origin of the samples. This terminator-propagator approach has been applied to model VPO measurements of asphaltenes in toluene solutions29 and the interaction of asphaltenes with a model compound, namely, nonylphenol.21 The calculated heat q is
q ) nA-N (mol) (∆H) + nA-A (mol) (-∆HA)
(8)
The second model, one set of independent sites (ONE), has been widely applied in biochemistry.30 It considers that the proteins (asphaltenes) contain a number of sites available for the interaction, and they all have the same affinity for the ligands (resins). Besides, the binding of one molecule is not affected by the neighbor sites. This means that two sites act as if they were very far from each other, even if they may be in the same molecule. This may be a good approximation to large hydrocarbon structures such as asphaltenes. It allows the calculation of the average number of interaction sites at the same time as the enthalpy of association. It starts again with the subtraction of the reference data. The resulting heat is assumed to be related only to the binding of resins to asphaltenes. Inherent in this, it is assumed that the injection of 290.0 µL in a cell of 1.46 mL does not lead to a substantial heat of dissociation of asphaltene aggregates, in accordance with Merino-Garcia et al.20 The heat developed in each injection is calculated with eq 9. The model has three fitting parameters that are obtained in the optimization routine: equilibrium constant K, enthalpy ∆H, and number of sites n.
q ) ∆HA-RV∆[RB]
(9)
The heat developed in each injection is calculated by multiplying the enthalpy by the variation in amount of resins bound to asphaltenes, ∆[RB]. The concentration of bound resins, RB, before and after each injection is calculated by means of eqs 10 and 11, where [A] is the total concentration of asphaltenes and (28) Murgich, J.; Lira-Galeana, C.; Merino-Garcia, D.; Andersen, S. I.; del Rio, J. M. Langmuir 2002, 18, 9080. (29) Agrawala, M.; Yarranton, H. W. Ind. Eng. Chem. Res. 2001, 40, 4664. (30) Freire, E.; Mayorga, O. L.; Straume, M. Anal. Chem. 1990, 62 (18), 950A.
Figure 1. ITC titrations in dried toluene, LM2: C(RES) ) 33.9 g/L, C(ASP) ) 30.0 g/L; (a) raw data, (b) integrated heats. Table 1. Percent Yield and Ratio of Asphaltenes and Resins Alaska 95 LM1 LM2 Yagual Ca30
resins
asphaltenes
R/A
16.0 16.6 30.0 4.3 4.7
5.3 8.6 9.8 2.0 4.6
3.0 1.9 3.1 2.2 1.0
[RT] and [R] are the total and free resin concentrations, respectively.
[RB] ) [A]
nK[R] K[R] + 1
[RT] ) [R] - [RB]
(10) (11)
Results and Discussion The yields of resins and asphaltenes of the four crudes are collected in Table 1. The amount of resins has been found to be greater for crudes with high asphaltene content, as reported by Goual and Firoozabadi.9 It is observed that the ratio R/A is not a good indication of the stability of asphaltenes. The unstable Yagual has a greater ratio than the stable LM1. On the other hand, the total amount of resins does correlate with the stability. Oils with large amounts of resins (LM1, LM2 and Alaska95) are stable, while the unstable oils (Yagual and Ca30) have a small concentration of resins. This fact may be related to the stability of the oil, in the sense that the absence of resins makes the surrounding media less attractive for asphaltenes and thus increases their tendency to precipitate as a separate phase. ITC experiments with resins were performed to study their tendency to self-associate. These experiments are used as a baseline for the asphaltene-resin experiments. Resin solutions with several concentrations were injected into dried toluene. The dilution of resins into toluene develops a significant endothermic heat, depicted in Figure 1a as positive peaks. The integration of the area below each peak gives the heat developed per injection. The trend of the heat
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Table 2. Fitted Parameters of EK in the Titration of Asphaltenes and Resins
Ca30 A95 YAGUAL LM2 LM1
RES ASP RES ASP RES ASP RES ASP RES ASP
Cs (g/L)
∆H (kJ/mol)
K (L/mol)
∆G (kJ/mol)
∆S (J/mol)
31.4 30 35.8 30 26.1 30 33.9 30 47.5 30
-4.4 -3.4 -3 -5.1 -4 -4.5 -3.4 -4.7 -8.2 -5.2
24 88 15 83 37 119 15 64 31 74
-8.0 -11.3 -6.8 -11.1 -9.1 -12.0 -6.8 -10.5 -8.7 -10.8
11.9 26.0 12.6 19.9 16.8 24.9 11.3 19.1 1.5 18.6
developed is similar to that of asphaltenes, so the same stepwise mechanism of self-association is assumed.20 Resins, as asphaltenes, are believed to form oligomers of low aggregation numbers (see eq 1). The heat developed is assigned to the dissociation of intermolecular bonds between resin molecules. It has been claimed that resins do not self-associate in crude oil.7 The behavior in a favorable solvent like toluene may be different, as suggested by Bardon et al.31 The heat developed in the dilution of resins is greater than that developed in the dilution of asphaltenes (Figure 1a). The average molecular weight of resins is lower than that of asphaltenes, so it is expected to see more heat developed in resin tests because there are more molecules per gram. Nevertheless, the heat developed per mole injected is lower for resins than for asphaltenes (Figure 1b). The curves have been fitted to the equal K model (eq 1-3). In this model, the formation of dimers, trimers, and so on is believed to have the same equilibrium constant (K) and enthalpy of formation (∆H).20 Thus, the curves are fitted with two parameters (Table 2). It has been observed that resins have lower equilibrium constants than asphaltenes. This indicates that asphaltenes have a higher tendency to associate, as expected. Resins are smaller molecules, and it may result easier for them to adapt to the surrounding media. With respect to ∆S, asphaltene self-association creates a greater change in entropy than resin self-association. This suggests that the conformation changes are greater in the self-association of asphaltenes. The enthalpies of self-association are in the same range for both fractions. The values are somewhat low, as hydrogen bonding ranges from -8 to -40 kJ/mol,32 while permanent dipole forces are usually between -4 and -20 kJ/mol. Several processes are involved in the self-association of asphaltenes, including tangling of alkyl branches, repulsion forces, and solvation effects. These contributions may provide an extra contribution to the total heat developed that is not explicitly taken into account in the simple model proposed and may be responsible for the underestimation of ∆H. The elemental analysis of four of the asphaltenes shows that there is a direct relationship between the oxygen and nitrogen contents and the enthalpy (Figure 2). On the contrary, the enthalpy increases when the aromaticity decreases, as expressed by the ratio H/C. This stresses the importance of the heteroatoms in the heat developed in ITC experiments. Resin solutions were then injected into 1 g/L asphaltene solutions. At such a low concentration, asphaltenes are in a low aggregated state, and there (31) Bardon, Ch.; Barre, L.; Espinat, D.; Guille, V.; Hui Li, M.; Lambard, J.; Ravey, J. C.; Rosemberg, E.; Zemb, T. Sci. Technol. Int. 1996, 14 (1&2), 203. (32) Prausnitz, J. M.; Lichtenthaler, R. N.; Azevedo, E. G. Molecular Thermodynamics of Fluid-Phase Equilibria; Prentice Hall: Englewood Cliffs, NJ, 1999.
Figure 2. Correlations of ∆HASP-ASP with the aromaticity and heteroatom content of asphaltenes: (a) ratio H/C; (b) nitrogen; (c) sulfur; (d) Oxygen.
Figure 3. Alaska 95, 60 g/L resins into 0, 1, and 10 g/L ASP: (a) raw data; (b) integrated heats after subtraction of reference data.
are many free interaction sites available for resins. Lower concentrations have not been used due to ITC sensitivity issues. The resin concentrations in the syringe were calculated from R/A. The intention was to study solutions that have R/A in the range of the actual ratio in the crude oil (Table 1). The idea was to get a concentration equal to 0.25, 1, and 4 times R/A in the cell at half of the number of injections in each experiment. By this, it was possible to have experiments with and without saturation of sites. In some cases, an extra concentration at around 90 g/L was used if saturation had not been reached with the previous concentrations. Experiments were as well performed with 10 g/L of asphaltenes in the cell. At that higher concentration, asphaltenes are more associated and there will be fewer sites available for the interaction with resins. Figure 3a shows the raw data from the experiments performed on the asphaltene from the Alaska95 crude.
Asphaltene-Resin Interactions
Langmuir, Vol. 20, No. 11, 2004 4563 Table 3. Fitted Parameters of the TERM Model in the ASP-RES Interaction crude A95
C(ASP) C(RES) ∆H K ∆S ∆G (g/L) (g/L) (kJ/mol) (L/mol) (J/mol) (kJ/mol) n 1 1 1 1 1
9.0 35.8 35.9 60.0 75.3
10 10 10
35.9 60.0 75.3
1 1
18.5 47.5
10 10
18.5 47.5
1 1 1 1
7.0 12.0 31.4 99.0
10 10
12.0 31.4
1 1 1 1
6.0 26.1 65.6 90.0
10 10
26.1 65.6
1 1 1
8.7 33.9 94.0
10 10
33.9 94.0
av
av LM1 av
Figure 4. Fit of TERM model, Ca30: C(RES) ) 31.4 g/L; C(ASP) ) 10 g/L.
av Ca30
av av Yagual
av av LM2
Figure 5. Fit of TERM model, Yagual: C(RES) ) 65.6 g/L; C(ASP) ) 10 g/L.
The peaks are the result of the combination of exothermic (negative) and endothermic (positive) processes. The injection of resins into pure toluene presents positive peaks because the main process ongoing in the cell is the dissociation of resin-resin bonds. However, the presence of asphaltenes makes the peaks become smaller or “less positive”. This means there is another exothermic contribution that was not present in the dilution of resins, namely, the interaction with asphaltenes counteracting the resin heat signal. The heat developed in the dilution of resins is used as a baseline and subtracted from the heat developed in the presence of asphaltenes. Following the same assumptions as in the study of the interaction with nonylphenol,21 the remaining heat (Figure 3b) is totally assigned to the interaction between asphaltenes and resins. It is observed that after a certain concentration is reached, the heat becomes zero. This means that all the interaction sites have been saturated and the newly injected resins do not bind to the asphaltenes. At higher asphaltene concentrations (10 g/L), the saturation is not reached, as there are more asphaltene sites in the cell. To obtain the main thermodynamic parameters of the interaction, the terminator-propagator (TERM) model was applied. It is able to fit successfully all experiments, both at 1 and 10 g/L of asphaltenes (Figures 4 and 5). The fitted ∆H and K are gathered in Table 3. It is observed that the enthalpies are consistently greater in experiments with higher asphaltene concentrations. It is possible that at 10 g/L, resins are to a certain extent able to dissociate asphaltene aggregates. This process develops an endothermic heat that is not taken into account in the model. This leads to an overestimation of the ∆H of the interac-
av av
-2.1 -2.7 -2.5 -2.6 -3.2 -2.6 -3.1 -4.3 -3.7 -3.7 -2.6 -2.7 -2.7 -3.9 -3.6 -3.8 -1.6 -1.9 -1.7 -1.7 -1.7 -2.1 -2.3 -2.2 -2.3 -2.4 -2.7 -2.1 -2.4 -2.9 -3.0 -3.0 -2.2 -1.9 -2.0 -2.0 -2.8 -2.9 -2.9
462.9 217.8 323.6 205.1 377.0 317.3 172.9 220.2 141.1 178.1 1046.1 1454.0 1250.1 2282.6 391.7 1337.2 996.6 1410.3 328.2 402.5 784.4 3173.0 518.1 1845.6 4522.3 1336.7 1086.7 723.6 1917.3 498.4 179.5 339.0 396.6 188.0 205.0 263.2 148.5 78.2 113.4
44.1 35.9 39.8 35.7 38.8 38.8 32.6 30.7 28.9 30.7 49.2 51.6 50.4 51.4 37.8 44.6 52.1 54.0 42.6 44.3 48.2 60.1 44.4 52.2 62.4 51.9 49.2 47.8 52.8 42.1 33.3 37.7 42.5 37.3 37.7 39.1 32.3 26.7 29.5
-15.5 -13.6 -14.6 -13.4 -14.9 -14.4 -13.0 -13.6 -12.5 -13.0 -17.5 -18.3 -17.9 -19.5 -15.0 -17.3 -17.4 -18.3 -14.6 -15.1 -16.3 -20.3 -15.7 -18.0 -21.2 -18.1 -17.6 -16.6 -18.4 -15.6 -13.1 -14.4 -15.1 -13.2 -13.4 -13.9 -12.6 -11.0 -11.8
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
tion, as it has to compensate for the dispersion of asphaltene aggregates. On the other hand, the variation of ∆H with resin concentration is very small. K presents a greater variation. The many assumptions of this simple model seem to have a greater influence on the equilibrium constant than in ∆H. The values are in the same range as the ones reported for asphaltene interaction with nonylphenol.21 They are 1 order of magnitude lower than the typical hydrogen bonding (-8, -40 kJ/mol)32 and in the lower limit of permanent dipole interactions (-4, -20 kJ/mol). Nevertheless, Buenrostro-Gonzalez et al.24 applied the SAFT-VR equation to model the precipitation of Maya asphaltenes, obtaining an enthalpy of interaction of -3.3 kJ/mol, as a fitted parameter. The agreement between this value and Table 3 is very satisfactory. This indicates that the ∆H obtained by means of ITC can be used in this type of equation to reduce the number of estimated or fitted parameters. ∆G is negative in all cases. This implies the process is spontaneous. The values obtained are inside the interval assigned to hydrogen bonding (between -10 and -40 kJ/mol).15 The contribution of ∆S to the free energy is greater than the one of ∆H; this may indicate that the process is entropically driven. The TERM model has an important drawback due to the fact that the number of sites per asphaltene molecule is fixed to 1 (see eq 4). This limits the predictive capacity of the model and creates a greater dependence of K and ∆H with the molecular weight assumed.
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Table 4. Fitted Parameters of the ONE Model in the ASP-RES Interaction crude A95 LM1 Ca30 Yagual LM2
C(ASP)
C(RES)
n
∆H
K
∆S
∆G
1 1 1 1 1 1 1 1
75.3 47.5 99.0 12.0 90.0 65.6 26.1 94.0
0.8 ( 0.8 1.1 ( 0.9 1.5 ( 0.9 1.6 ( 0.1 1.7 ( 0.6 1.8 ( 0.7 1.5 ( 0.2 1.6 ( 0.9
-3 ( 2 -0.5 ( 0.1 -0.8 ( 0.6 -0.7 ( 0.1 -0.8 ( 0.3 -1.1 ( 0.5 -0.6 ( 0.1 -1.1 ( 0.4
(26 ( 4) × 10 (8 ( 2) × 102 (35 ( 9) × 10 (16 ( 4) × 102 (38 ( 6) × 10 (36 ( 8) × 10 (24 ( 7) × 102 (36 ( 8) × 10
37.0 53.3 45.9 59.2 46.7 45.4 62.6 45.4
-14.2 -16.7 -14.7 -18.6 -15.0 -14.8 -19.6 -14.8
The ONE model (see eqs 16-18) was proposed, as it includes the number of sites as a third fitting parameter. It is as well able to fit successfully the experimental data when high concentrations of resins are injected into 1 g/L (Figures 6 and 7). If the resin concentration is not enough the reach zero heat developed (saturation of sites), the fitting does not converge. Thus, the model was not able to fit experiments with 10 g/L of asphaltenes, either. This is a drawback compared with the TERM model, which has been shown to converge in all cases. Table 4 gathers the thermodynamic parameters of resin-asphaltene interaction when the ONE model is applied. The average number of sites per asphaltene molecule is in the range of one to two. This is in agreement with the estimation of Buenrostro-Gonzalez et al.,24 who used three to four sites with a molecular weight of 3000 units to successfully fit onset precipitation data with the SAFT equation. The molecular weight used in this work is 1000, which means that both results are in the same range. Other researchers have used larger numbers: Murgich and co-workers33 assumed nine sites available for resins
molecular simulations in an asphaltene aggregate, based on the most probable interaction sites in a model molecular structure from Athabasca sand asphaltene. Wu et al.34 used six sites of interaction per asphaltene molecule in their SAFT calculations. The enthalpies are significantly lower than the ones obtained with the TERM model. This may be related to the increase in average number of sites, which was assumed to be one in the TERM model. The values of ∆H obtained with both models are 1 order of magnitude lower than the usual binding energies by hydrogen bonding or dipole interactions. It must be taken into account that the energies measured in this work account not only for association but also for the energies developed in the conformational changes of the molecules to accommodate for binding. Solvation effects have as well been disregarded. It is not clear either if all molecules in both fractions will be equally active in the interaction. It is practically impossible to develop a model that accounts for all these effects in a system of such a complexity as asphaltene and resin fractions. For the sake of simplicity, the heat developed is assigned to association, but it is necessary to keep in mind that the binding energies may be underestimated. Nevertheless, these experiments can provide data to state-of-the-art models, which do not consider the polydispersed nature of asphaltenes. In other to check the reliability of TERM and ONE models, it was attempted to fit the experimental data with one only set of parameters. Five combinations were tried. First, experiments at all concentrations were fitted with the set of parameters (∆H and K) obtained in the test with the highest resin concentration and 1 g/L of asphaltenes (TERM1). Second, the values (∆H, K) were taken from the experiment with same resin concentration but with 10 g/L of asphaltenes. It has previously been discussed that the ∆H depend on the asphaltene concentration, so it was expected that the values of TERM1 would not be able to fit experiments with 10 g/L. The third approach was based on the use of the average values for 1and 10 g/L gathered in Table 3. Forth, ONEa uses the parameters obtained with ONE model in the fit of the experiment with highest resin concentration and 1 g/L. ONEb only uses the number of sites n of that experiment, while ∆H and K are used as fitting parameters. Figure 8 shows an experiment in which all models manage to fit successfully the experimental data. Table 5 collects the parameters used in the calculations shown in Figure 8, together with the average absolute deviation. Figure 9 shows that the average ∆H and K are able to fit successfully all experiments with 1 g/L of Alaska95 asphaltenes. Despite all the assumptions made, it is possible to model all resin concentrations with one set of parameters. This indicates that the behavior of resins is the same throughout that concentration interval. On the other hand, asphaltenes present a concentration-depend-
(33) Murgich, J.; Abanero, J. A.; Struasz, O. P. Energy Fuels 1999, 13, 278.
(34) Wu, J.; Prausnitz, J. M.; Firoozabadi, A. AIChE J. 2001, 44 (5), 1188.
Figure 6. Fit of ONE model, A95: C(RES) ) 90 g/L; C(ASP) ) 1 g/L.
Figure 7. Fit of ONE model, LM2: C(RES) ) 94 g/L; C(ASP) ) 1 g/L.
Asphaltene-Resin Interactions
Langmuir, Vol. 20, No. 11, 2004 4565
Figure 10. Number of good fits of the different sets of parameters tried (total ) 29).
Figure 8. Predicting the titration of Alaska 95: C(RES) ) 35.8 g/L and C(ASP) ) 1 g/L.
good background for prediction. ONEa also fails to fit experiments with 10 g/L. It is observed that ONEb gives a good fit in 21 experiments out of 29. Nevertheless, ONEb had only the number of sites n fixed, while ∆H and K were allowed to vary. Thus, it cannot be considered a real prediction. However, the use of average parameters in the TERM model gives a good response as well in a considerable number of cases. The use of average values seems to be a good approach, as long as the concentration of asphaltenes is not changed. This set of parameters is able to fit resin behavior in a wide range of concentrations. This suggests that resins behave more ideally than asphaltenes, allowing this simple model to catch their behavior in these experiments. Conclusions
Figure 9. Predicted fits of Alaska 95 experiments with 1 g/L ASP, using the average ∆H and K: (-) fit of model; C(RES) ) 9 g/L (+), 35.8 g/L (/), 0.35.9 g/L (4), 60 g/L (0), 75.3 g/L ()). Table 5. Sets of Parameters Used in the Prediction Depicted in Figures 7-13 and Deviation of the Fits TERM1 TERM10 ONEa ONEb
n
∆H (kJ/mol)
K
% AAD
1.0 1.0 0.8 0.8
-3.2 -3.7 -3.0 -3.2
377 141 257 174
24 41 23 15
ent behavior that cannot be caught with one single set of ∆H and K. Resins are smaller molecules with less tendency to associate and, thus, behave more ideally than asphaltenes. The surrounding media seems to be more favorable to resins, while asphaltenes are not so easily accommodated in the solvent and prefer to associate with each other. Figure 10 shows the results of the five combinations of parameters in the 29 experiments performed. TERM1 and TERM10 give poor performances. They are only able to fit some of the experiments performed with the same concentration. Parameters obtained with 1 g/L of asphaltenes are not a good estimation for the behavior at 10 g/L. The state of asphaltenes is different, and the parameters from other concentrations do not provide a
ITC experiments were performed with asphaltenes and resins in toluene solutions. It has been observed that the heat developed reaches a value of zero, indicating that saturation of sites is accomplished. Two models were applied to fit the experimental data. In light of the very complex mixtures analyzed, both approaches are very simplistic, as each process is characterized with one set of values of ∆H and K. A more detailed model would be necessary, but that would increase the number of parameters greatly. Still, some interesting results have been obtained: experimental values of ∆H have been obtained, together with the specific number of sites. There is good agreement with the usual estimations in asphaltene modeling. The predictive capacity seems to be greater for the TERM model. Since the TERM model is a slightly more complex approach than ONE, it is able to catch better the behavior of asphaltene-resin mixtures. The ∆H values are as well more reliable, in the sense that similar values have been used in the past in modeling asphaltene behavior. The main drawback of that model is that the number of sites was fixed to 1. It is observed that a model that allows the variation of this parameter gives optimal values that are very close to 1. This may indicate that the assumption of n ) 1 may not be too far from reality. Acknowledgment. The authors thank the Danish Technical Research Council (STVF under the Talent Program) for financial support and Mr. Z. Tecle and Mr. T. Dang for their help in the laboratory. LA0499315
