pubs.acs.org/Langmuir © 2010 American Chemical Society
Probing Asphaltene Aggregation in Native Crude Oils with Low-Field NMR Lukasz Zielinski,* Indrajit Saha,‡ Denise E. Freed, and Martin D. H€urlimann Schlumberger-Doll Research, One Hampshire Street, Cambridge, Massachusetts 02139
Yongsheng Liu ‡
Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215. Current address: Vanderbilt University Institute of Imaging Science, Vanderbilt University, Nashville, TN 37232 Received February 17, 2009. Revised Manuscript Received January 5, 2010
We show that low-field proton nuclear magnetic resonance (NMR) relaxation and diffusion experiments can be used to study asphaltene aggregation directly in crude oils. Relaxation was found to be multiexponential, reflecting the composition of a complex fluid. Remarkably, the relaxation data for samples with different asphaltene concentrations can be collapsed onto each other by a simple rescaling of the time dimension with a concentration-dependent factor ξ, whereas the observed diffusion behavior is unaffected by asphaltene concentration. We interpret this finding in terms of a theoretical model that explains the enhanced relaxation by the transitory entanglement of solvent hydrocarbons within asphaltene clusters and their subsequent slowed motion and diffusion within the cluster. We relate the measured scaling parameters ξ to cluster sizes, which we find to be on the order of 2.2-4.4 nm for an effective sphere diameter. These sizes are in agreement with the typical values reported in the literature as well as with the small-angle X-ray scattering (SAXS) experiments performed on our samples.
1. Introduction Aggregation processes are a central issue in the study of complex fluids. They affect the stability of emulsions and colloids, control phase separation and gelation phenomena, and determine phase boundaries.1,2 An important example of a natural complex fluid is crude oil. Crude oils are mixtures of hydrocarbons of different sizes and chemical properties. A simple chemical classification divides the components into saturates, aromatics, resins, and asphaltenes. In conventional crude oils, the composition is dominated by saturates and aromatic molecules. However, even in small concentrations, asphaltenes are an important ingredient of crude oil because they can easily aggregate and affect the rheological properties of the fluid. They are defined as the fraction of the crude oil that is insoluble in n-alkanes and soluble in toluene. The asphaltene fraction is the most polar fraction of the crude oil and is a mixture of many different molecules, all of which contain polyaromatic rings, alkyl chains, and heteroatoms. Asphaltenes are well dissolved in their native oils under reservoir conditions but may become unstable and precipitate when the temperature or pressure is varied, as well as under dilution by nonnative solvents.3 They contribute significantly to the rich phase behavior exhibited by crude oils. Their aggregation not only poses interesting scientific questions but also has great economic significance because asphaltene precipitation can clog reservoir formation and production pipelines, causing huge losses in the production process. The study of asphaltene aggregation is an active area of research, yet important details of the aggregation mechanism (1) Sciortino, F.; Mossa, S.; Zaccarelli, E.; Tartaglia, P. Equilibrium cluster phases and low-density arrested disordered states: The role of short- range attraction and long-range repulsion. Phys. Rev. Lett. 2004, 93, 055701. (2) Manley, S.; Davidovitch, B.; Davies, N. R.; Cipelletti, L.; Bailey, A. E.; Christianson, R. J.; Gasser, U.; Prasad, V.; Segre, P. N.; Doherty, M. P.; Sankaran, S.; Jankovsky, A. L.; Shiley, B.; Bowen, J.; Eggers, J.; Kurta, C.; Lorik, T.; Weitz, D. A. Time-dependent strength of colloidal gels. Phys. Rev. Lett. 2005, 95, 048302. (3) Mullins, O. C., Sheu, E. Y., Hammami, A., Marshall, A. G., Eds. Asphaltenes, Heavy Oils, and Petroleomics; Springer: New York, 2007.
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are still not well understood. It has been described in terms of colloidal models of diffusion- and reaction-limited aggregation;4,5 in terms of the free energy of various stacking arrangements;6 and also in terms of the phase separation of miscible fluids, with asphaltene “clusters” being the denser glass phase.7 Proposed aggregation states range from monomers and dimers to nanoaggregates and clusters of nanoaggregates with fractal dimensionality and finally to microscopic flocs.3,8-10 Because studying asphaltene aggregation properties in the actual crude oil is difficult, the vast majority of relevant experimental work has been conducted on model systems, where asphaltene obtained from some crude oil was then dissolved in a simple solvent such as toluene. It is well established, however, that asphaltene aggregation is strongly affected by the properties of the solvent and by the presence of polar molecules such as resins. Robust methods are needed, therefore, to allow the observation of asphaltenes in their native oil because that is their environment of greatest interest. It is challenging to adapt the standard experimental techniques of small-angle neutron (SANS) and X-ray (SAXS) scattering and dynamic light scattering (DLS) to the study of asphaltene in native oils. In SANS, the hydrogen density contrast between the (4) Yudin, I. K.; Nikolaenko, G. L.; Gorodetskii, E. E.; Kosov, V. I.; Melikyan, V. R.; Markhashov, E. L.; Frot, D.; Briolant, Y. Mechanisms of asphaltene aggregation in toluene-heptane mixtures. J. Pet. Sci. Eng. 1998, 20, 297-301. (5) Fenistein, D.; Barre, L.; Broseta, D.; Espinat, D.; Livet, A.; Roux, J.-N.; Scarsella, M. Viscosimetric and neutron scattering study of asphaltene aggregates in mixed toluene/heptene solvents. Langmuir 1998, 14, 1013-1020. (6) Rogel, E. Thermodynamic modeling of asphaltene aggregation. Langmuir 2004, 20, 1003-1012. (7) Sirota, E. B.; Lin, M. Y. Physical behavior of asphaltenes. Energy Fuels 2007, 21, 2809-2815. (8) Roux, J.-N.; Broseta, D.; Deme, B. SANS study of aphaltene aggregation: concentration and solvent quality effect. Langmuir 2001, 17, 5084-5092. (9) Porte, G.; Zhou, H.; Lazzeri, V. Reversible description of asphaltene colloidal association and precipitation. Langmuir 2003, 19, 40-47. (10) Gawrys, K. L.; Blankenship, G. A.; Kilpatrick, P. K. Solvent entrainment in and flocculation of asphaltenic aggregates probed by small-angle neutron scattering. Langmuir 2006, 22, 4487-4497.
Published on Web 02/04/2010
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asphaltenes and the maltene is small because it is not possible to deuterate the maltene. In SAXS, the background maltene scattering must be separately measured and accounted for, and DLS is limited by the opacity of most crude oil samples. Despite these difficulties, both SANS11,12 and SAXS13 as well as DLS4 have been successfully performed on some crude oil samples. Another technique applied to the study of crude oils is low-field NMR, which has been used to classify them qualitatively as asphaltenerich or -poor.14 Here we demonstrate that low-field proton NMR can be used as a quantitative technique to monitor asphaltene aggregation in crude oil. The analysis of our experiments, using a new theoretical model discussed below, results in asphaltene cluster sizes that are in good agreement with sizes found in different crude oils in a small-angle neutron scattering study recently reported in ref 12.
2. NMR Measurements Direct detection and identification of NMR signal from asphaltene molecules is difficult. The signal is intrinsically weak and characterized by short relaxation times. In fact, as will be discussed below, to first order asphaltenes do not contribute directly to the NMR signal measured in our low-field experiments. Their presence, however, strongly affects the relaxation properties of the other molecules in crude oil and in this way can be detected indirectly. NMR relaxation in fluids is sensitive to molecular motion, which in turn depends on the sizes of the molecules and their mutual interactions.15 The sensitivity to different time scales of motion is controlled by the Larmor frequency, or magnetic field strength, used in the experiment. Low-field NMR, with proton Larmor frequencies of a few megahertz, is suitable for the study of correlation times on the order of hundreds of nanoseconds, which is precisely the range that one expects from aggregating asphaltene clusters. As a rough estimate of the asphaltene cluster rotation correlation times τA, one may use the Einstein-Stokes equation for a sphere of diameter d suspended in a fluid of viscosity η, τA ¼
πd 3 η 6kT
ð1Þ
where T is the temperature and k is the Boltzmann constant. For example, at room temperature (kT ≈ 0.025 eV), for η = 10 cP, which is a typical viscosity of a conventional oil, and for d=10 nm, eq 1 gives τA =1.3 μs corresponding to a frequency of 0.8 MHz whereas for d=5 nm eq 1 gives τA = 160 ns corresponding to a frequency of 6.3 MHz. In our experiments, we used two Larmor frequencies, ω0/2π = 2 and 5.06 MHz, which span the range of interest. All of the diffusion and relaxation measurements were performed with an Apollo Tecmag spectrometer in the fringe field of a Nalorac 2T superconducting magnet at a proton Larmor frequency of 5.06 MHz and with a permanent gradient of 55 G/ cm. The total equilibrium magnetization measurements were (11) Mason, T. G.; Lin, M. Y. Time-resolved small angle neutron scattering measurements of asphaltene nanoparticle aggregation kinetics in incompatible crude oil mixtures. J. Chem. Phys. 2003, 119, 565. (12) Headen, T. F.; Boek, E. S.; Stellbrink, J.; Scheven, U. M. Small angle neutron scattering (sans and v-sans) study of asphaltene aggregates in crude oil. Langmuir 2001, 25, 422-428. (13) Henaut, I.; Barre, L.; Argillier, J.-F.; Brucy, F.; Bouchard, R. Rheological and structural properties of heavy crude oils in relation with their asphaltenes content. SPE 65020, 2001. (14) Mutina, A. R.; H€urlimann, M. D. Correlation of transverse and rotational diffusion coefficient: A probe of chemical composition in hydrocarbon oils. J. Phys. Chem. A 2008, 112, 3291. (15) Kowalewski, J.; M€aler, L. Nuclear Spin Relaxation in Liquids: Theory, Experiments, and Applications; CRC Press: Boca Raton, FL, 2006.
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Table 1. Asphaltene Percent Weight Concentrations in the Two Sets of Samples Measured sample
oil 1
oil 2
1 0.00 0.00 2 0.42 2.32 3 0.80 3.89 4 1.20 5.68 5 1.60 6.98 9.84a 6 1.68a 7 2.06b 10.97b a Original crude oil from which the asphaltenes in the given set were extracted. b A supersaturated sample, with asphaltene concentration higher than in the original oil.
made at 2 MHz using Oxford Instruments’ Maran Ultra. For each sample, we measured the longitudinal (T1) relaxation, the transverse (T2) relaxation, and the diffusion coefficient. For T1 experiments, we used the inversion recovery sequence with 30 different recovery times logarithmically spaced between 1 ms and 10 s. For T2 experiments, we used the CPMG train of refocusing 180 pulses, typically acquiring 8000 echoes with an echo spacing of 298 μs, and for diffusion measurements, we used the second direct echo with variable echo spacing ranging from 298 μs to 17.8 ms. The durations of the rf pulses were t180 = 22 μs and t90 = 12 μs. Complete details of the experimental protocols for both the relaxation and diffusion measurements can be found in ref 14.
3. Samples In an attempt to isolate the effects of asphaltenes from other factors affecting relaxation and to study asphaltene aggregation properties in their natural environment, we systematically varied the asphaltene concentration in the native crude oil (i.e., in the oil from which they originated). We did this by first extracting the asphaltene from the crude oil with heptane and then mixing it back in with the resultant maltene (the deasphalted crude oil) in varying proportions. In this way, we prepared two sets of samples referred to as oil 1 and oil 2, with asphaltene concentrations ranging from 0 to 2.06% for oil 1 and from 0 to 11% for oil 2 (Table 1). Gas chromatography showed that both maltenes (sample 1 in each set) consisted of molecules with the number of carbons being greater than 10. Sample 6 in each set is the original source oil for this set, and sample 7 is “supersaturated” in the sense that its asphaltene concentration is higher than in the source crude oil. To emphasize, the asphaltenes were mixed into their own native oil rather than into some other solvent such as toluene, as typically done in similar studies. All the solutions were stable during and between experiments and showed no hysteresis due to heating, shaking, or sonicating.
4. Experimental Results Figure 1 summarizes the experimental results of the transverse and longitudinal relaxation measurements for the seven samples derived from oil 2. Here, Meq is the total measured equilibrium (longitudinal) magnetization of each sample at the given temperature and Larmor frequency, M^(t) denotes the transverse magnetization at CPMG echoes, and Mz(t) denotes the longitudinal magnetization parallel to the direction of the external magnetic field. As expected for these multicomponent fluids, the decays clearly deviate from single-exponential behavior. Also, the relaxation is faster for samples with a higher asphaltene concentration. An important observation is that the direct NMR signal of asphaltene molecules decays very quickly and is not detected in the present experiments. This is shown in Figure 2, where the equilibrium magnetization Meq, normalized per gram of sample, DOI: 10.1021/la904309k
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Figure 1. Normalized (a) transverse and (b) longitudinal magnetization vs time at 45 C and 5 MHz for the seven oil 2 samples. For clarity of presentation, in graph a only every fifth echo is plotted. Both transverse and longitudinal relaxation decays are multiexponential, and the decay rates are faster for samples with higher asphaltene content. Oil 1 showed similar behavior.
Figure 2. Total equilibrium magnetization per gram for oil 1 (4) and oil 2 (0) at 45 C. The dashed line has a slope of -1. Similar behavior was observed at 92 C. Within experimental accuracy, no signal from asphaltenes is detected. is plotted as a function of asphaltene concentration. The fact that the signal amplitude decreases with a slope of -1 suggests that asphaltene protons are not seen on the measurement timescale. Only the signal from maltene molecules is observed directly.
5. Preliminary Discussion The enhanced relaxation in samples with asphaltene in Figure 1 results from the interactions of maltene molecules with the asphaltenes. Possible mechanisms include the effects due to the presence of free radicals and paramagnetic atoms on the aromatic 5016 DOI: 10.1021/la904309k
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asphaltenic cores as well as the effects due to the slowed mobility of the hydrocarbon chains upon contact and entanglement with the heavy asphaltene macromolecules. The latter effects must be significant in our samples because the transverse relaxation rate, R2 = 1/T2, increases faster with the addition of asphaltene than does the longitudinal relaxation rate, R1 = 1/T1, signaling the presence of motions with characteristic correlation rates comparable to or slower than the Larmor frequency.15 Because the direct asphaltene signal is not detected and because asphaltene clusters are the only objects that may possibly exhibit such long correlation times in our oil samples, the maltene molecules must become temporarily entangled within the asphaltene clusters and rotate at their much slower rates. In effect, asphaltenes in a crude oil act as a contrast agent: they enhance relaxation rates without themselves contributing to the signal. A simple order-of-magnitude calculation shows that, under typical conditions, all of the maltene molecules come into the vicinity of the asphaltenes on the timescale of the measurement. For the echo spacing tE=0.3 ms used in our experiments and the mean diffusion coefficient of maltene that we measured at 45 C, Dm = 0.1 μm2/ms, the diffusion length is (6DmtE)1/2 = 0.4 μm, which is orders of magnitude larger than the typical spacing between asphaltene clusters, even at low concentrations. The interaction times between the maltene molecules and the asphaltene clusters are hard to estimate, but there is no expected chemical bond formation between maltenes and asphaltenes or interactions other than diffusion, perhaps constrained by entanglement. A priori, the expected timescale of interaction should be set by the diffusion time of maltene across the size of the asphaltene cluster. If we take the cluster size to be 10 nm, then that diffusion time is ∼(10 nm)2/6Dm ≈ 167 ns, which is much shorter than the measured relaxation times in our experiments. Accordingly, fast exchange is expected with complete mixing of maltene populations. In this case, the relaxation rate of each maltene molecule is an average over the bulk relaxation rate and the relaxation rate when the maltene molecules are associated with the asphaltene. This prediction of fast exchange is borne out in Figure 1, which does not show any clear two-scale relaxation that would be characteristic of separate maltene populations. Similar conclusions were reached in other low-field NMR studies.16 When the molecules are not in the immediate vicinity of an asphaltene aggregate, they relax at their characteristic “bulk” rate Rm (i.e., at the rate they have in the corresponding maltene) without any asphaltenes present. It was shown in ref 17 that for maltenes consisting of mixtures of alkanes the relaxation is dominated by the intramolecular dipole-dipole interaction. The relaxation rate for a particular maltene molecule is proportional to (τR)1/2, where τR is the characteristic rotational correlation time of this maltene molecule. It was found that this correlation time has a power law dependence on the size of the maltene molecule.17 Given a wide distribution of maltene molecules and the corresponding range of values of (τR)1/2, this leads to a distinctly multiexponential bulk decay that can be described by a distribution of maltene relaxation rates F(Rm). The simplest way to model the asphaltene-induced relaxation is to apply the inner-sphere model18 in which the maltene molecules attach to the asphaltene cluster and rotate with it. This (16) Jestin, J.; Barre, L. Application of NMR solvent relaxation and SAXS to asphaltenes solutions characterization. J. Dispersion Sci. Technol. 2004, 25, 341. (17) Freed, D. E. Dependence on chain length of NMR relaxation times in mixtures of alkanes. J. Chem. Phys. 2007, 126, 174502. (18) Bloembergen, N.; Morgan, L. O. Proton relaxation times in paramagnetic solutions. Effects of electron spin relaxation. J. Chem. Phys. 1961, 34, 842.
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6. Scaling of Asphaltene-Induced Relaxation Instead of a simple additive relaxation rate, we find that within the experimental uncertainty the relaxation data for each of the two crude oil sample sets can be collapsed onto the maltene curve by rescaling the time dimension by a factor ξc that depends on asphaltene concentration, Z Mc ðtÞ ¼ M0 ðξc tÞ ¼
Figure 3. Same data as shown in Figure 1: (a) transverse and (b) longitudinal relaxation, with the time axes rescaled by ξ2c or ξ1c, respectively, corresponding to each sample. The insets show enlarged images of early decay on the same scale as in Figure 1. For clarity, only every 10th echo is plotted in graph a.
results in dipolar relaxation governed by the correlation function G(t) ≈ exp(-t/τA), with the corresponding spectral density function J(ω) ≈ τA/(1 þ ω2τA2). Here, τA is the rotational correlation time of asphaltene clusters. The asphaltene-induced relaxation rate Rc of solvent molecules in such a system, both longitudinal and transverse, is predicted to be proportional to the asphaltene concentration c and is identical for all solvent molecules, independent of their size. If F(Rm) is the distribution of R2m (transverse) or R1m (longitudinal) relaxation rates in maltene in the absence of any asphaltene, then the simple model predicts an additional overall exponential decay of the magnetization due to the presence of asphaltene, Z Mc ðtÞ ¼
FðRm Þe -ðRm þRc Þt dRm
¼ e -Rc t M0 ðtÞ
ð2Þ
ð3Þ
Here, Mc(t) stands for the concentration-dependent magnetization decay M^(t) for the case of transverse relaxation and for Meq - Mz(t) for the case of longitudinal relaxation, as plotted in Figures 1 and 3. M0(t) is the relaxation of pure maltene (i.e., the deasphalted oil; samples 1 in our oil 1 and oil 2 data sets). However, a close inspection of the experimental data in Figure 1 shows that the relaxation induced by asphaltene does not follow the prediction of eq 3. This indicates that the simple inner-sphere model and the assumption of a fixed asphaltene-induced relaxation rate Rc are not appropriate for the maltene - asphaltene system. Langmuir 2010, 26(7), 5014–5021
FðRm Þe -ξc Rm t dRm
ð4Þ
where ξc = ξ1c for longitudinal relaxation and ξc = ξ2c for transverse relaxation. In Figure 3 we show how remarkably well this rescaling works for both the transverse and longitudinal relaxation. This Figure is to be compared against Figure 1, where the same data is presented unscaled. At first sight, this scaling behavior is surprising because the relaxation behavior of crude oils is so complex. The observed decays are all multiexponential, reflecting the wide spectrum of relaxation timescales that are derived from the range of molecular sizes of the solvent molecules and their interactions with asphaltene.17 In fact, even for the maltene, each molecule has a different relaxation rate Rm that depends on its size. A comparison of eqs 2 and 4 demonstrates that the asphaltene-induced relaxation rate Rc cannot be a constant for a given concentration of asphaltene, as assumed in the inner-sphere model, but that it also depends on the maltene molecule. The observed scaling behavior in Figure 3 implies that the asphaltene-induced relaxation rate Rc in eq 2 is proportional to the intrinsic relaxation rate Rm of the maltene molecule in the asphaltene-free solution: Rc = (ξc - 1)Rm. In this case, eq 2 leads to eq 4. Thus, different maltene components are affected differently by the presence of asphaltenes. The increase in the relaxation rate is larger for the longer and less mobile hydrocarbon chains, which relax faster than the short chains even in the absence of asphaltene.
7. Sensitivity to Asphaltene Configuration Even though it is not easy to discern in Figure 3, the data for the original oils, sample 6 for oil 1 and oil 2, do not collapse as well onto the curves of the corresponding maltene (sample 1) as do the other samples. In fact, they have considerably dissimilar NMR relaxation properties, even on a qualitative level. For example, as is apparent in Figure 1 for oil 2, sample 6 relaxes much faster than sample 7, which has a higher asphaltene concentration. For oil 1, however, the relaxation of sample 6 is more complex. Compared to the other samples in this set, the relaxation of the original oil is anomalously fast for short times but slow at later times so that the remaining transverse magnetization at longer times exceeds those of samples with lower asphaltene concentration. In either case, the original oil samples clearly do not follow the trends exhibited by the reconstituted samples with changing asphaltene concentration. Such behavior is not entirely surprising, given that maltene relaxation is a simple function of not only asphaltene concentration but also the size and aggregation state of the asphaltene molecules, as will be discussed further below. Our results indicate that the configuration of the asphaltene molecules after extraction and redissolution (samples 1-5, and 7) is likely somewhat different than the configuration in the original oil (sample 6). For example, above a certain concentration, the asphaltenes may not have properly redissolved in the maltene or the sizes of the asphaltene aggregates may be quite different in the native oil and the other samples. This further demonstrates the difficulty to prepare adequate model systems to study the effects of asphaltene accurately. To DOI: 10.1021/la904309k
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by our sample preparation, in particular, by the redissolution of the asphaltenes.
9. Porous Asphaltene Model: New Model for Asphaltene-Induced Relaxation
Figure 4. ξ2c and ξ1c scaling parameters for oil 1 (small black symbols) and oil 2 (large red symbols) at 5 MHz. By construction, ξ2c = ξ1c = 1 for both oils at zero asphaltene concentration. For higher % concentrations, the initial linear increase in ξ reaches a plateau, indicating different aggregation behavior of additional asphaltene.
better preserve the asphaltene aggregation properties present in the native oil, it may be preferable to dilute it with its own maltene rather than attempt to redissolve the extracted asphaltene powder back into the maltene, which is the approach that we took in preparing our samples.
8. Scaling Parameter In Figure 4, we present a compilation of all the extracted values for the scaling parameter for longitudinal relaxation (ξ1c) and transverse relaxation (ξ2c). Note that the values of ξ1c are smaller than those of ξ2c. This indicates that longitudinal relaxation is affected less than transverse, which is expected if the asphalteneinduced relaxation is due to the slowing of the maltene motions. The scaling parameters increase in an approximately linear fashion for asphaltene concentrations of up to ∼4%. This is precisely the behavior expected in the dilute concentration regime, where the aggregates are noninteracting and separated from each other. The transition between the dilute and interacting regimes has been studied by viscometric and scattering experiments in both crude oils and toluene-dissolved asphaltenes and was found to occur at asphaltene concentrations on the order of a few percent,8,13 which agrees well with our observed transition in the behavior of ξ. In the dilute concentration regime, the addition of extra asphaltene does not change the aggregate size or structure but rather adds more clusters of the same size, as confirmed by small-angle scattering experiments.8,13 Consequently, relaxation rates should increase linearly with asphaltene concentration. Such a linear increase in the relaxation rate of a simple solvent (toluene) has been reported in ref 16. Figure 4 shows that the same trend holds for all of the components of the much more complex maltene. At higher concentrations, intercluster interactions develop and the picture of freely tumbling large aggregates is no longer applicable. All of the ξ’s reach a plateau. This could also be due to the imperfect dissolution of additional asphaltene, even though no clear precipitation and settling were observed, or to the changing cluster size, even prior to the onset of strong entanglement between clusters. The experimental results for the scaling parameters in Figure 4 show considerable scatter between samples with different concentrations, which is much larger than the estimated measurement uncertainties for individual samples. This scatter is likely caused 5018 DOI: 10.1021/la904309k
As discussed above, the simple stochastic model underlying the inner-sphere model cannot account for the behavior shown in Figure 3. In principle, the scaling behavior of longitudinal (T1) and transverse (T2) processes could be explained by an increase in viscosity upon addition of asphaltenes that results in an overall slowing of all motions of the maltene molecules. However, in this case, if both types of relaxation follow the scaling in eq 4, then T1 and T2 would have to be equal to each other for all concentrations of asphaltene. This is contrary to the experimental observations. In addition, a significant increase in viscosity is inconsistent with the diffusion results obtained for these samples. As mentioned in the NMR Measurements section, we measured the distributions of translational diffusion coefficients for all of our samples. Experimental details are given in ref 14. The distributions showed little change with asphaltene concentration, with an average diffusion coefficient of 1 10-10 m2/s at 45 C. This implies that the local mobility of the maltene molecules and thus their internal viscosity are little affected by short, temporary entanglements with asphaltenes. However, such interactions have a much more pronounced effect on the relaxational properties of the maltene because any reduction of the maltenes’ rotational motions can drastically increase the instantaneous relaxation rates. The scaling behavior could also be explained by modifying the inner-sphere model so that the number of maltene molecules stuck to the aggregate at any time depends on the particular type of maltene molecule. If small molecules spend less time attached to the asphaltene aggregate than larger maltene molecules in just the right proportion, then asphaltene-induced relaxation could result in the scaling displayed in Figure 3. Here, instead, we present an outline of an alternative model, the porous asphaltene model, that can naturally account for the scaling. A more detailed treatment will be published elsewhere.19 We start with two general observations. First, the observed scaling behavior shows that asphaltenes in a given oil relax large solvent molecules more effectively than small molecules. For a particular solvent molecule, the asphaltene-induced relaxation rate Rc is proportional to its relaxation rate in the oil without asphaltene; therefore, Rc depends on the size of the solvent molecule. Second, the addition of asphaltene to the oil increases the transverse relaxation rates faster than the longitudinal relaxation rates. This indicates that there is some slow motion associated with the asphaltene as a result of the rotation of the large aggregate. Therefore, any model that accurately describes relaxation in our system has to incorporate at least two different types of correlation timescales: one related to the motions of the maltene molecules and the other related to the overall rotation of the asphaltene aggregate. The relaxation behavior induced by conventional relaxation contrast agents and other macromolecules is typically described with models based on the inner-sphere 18 and outer-sphere models.20,21 In the inner-sphere models, as described above, the solvent molecules attach to the macromolecule and acquire a slow correlation timescale τA that corresponds to the rotation of the (19) Qi, Y.; Freed, D. E.; Sen, P. To be submitted for publication. (20) Torrey, H. C. Nuclear spin relaxation by translational diffusion. Phys. Rev. 1953, 92, 962-969. (21) Hwang, L.-P.; Freed, J. H. Dynamic effects of pair correlation functions on spin relaxation by translational diffusion in liquids. J. Chem. Phys. 1975, 63, 4017-4025.
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macromolecule. In the outer-sphere models, the correlation timescale reflects the external diffusion of solution molecules past the macromolecules. Two different timescales can be obtained by combining these two models, as was done by Poindexter,22 but the resulting relaxation times do not follow the scaling of the data shown in Figure 3. A fast timescale can also be included in the inner-sphere model by considering the bounded motion of the solvent molecules,23 but again, this approach cannot reproduce the scaling of Figure 3. Instead, in the porous asphaltene model, we assume that the asphaltene aggregates form loose porous structures such that the solvent molecules can diffuse through them. This is supported by neutron and X-ray scattering experiments that found that the asphaltene aggregates can be characterized with a fractal dimension of df < 3.12,24 As argued above, we further assume that the maltene molecules are in fast exchange between these porous asphaltene aggregates and regions free of asphaltene. When the maltene molecules come into contact with a porous asphaltene aggregate, they get entangled but not completely immobilized. In this case, we expect the diffusional motion of the entrained maltene molecule to be highly correlated, so we model the maltene motion within the aggregate as diffusion in restricted dimensions, characterized by a timescale of τM. In addition, because the neutron-scattering experiments find a fractal dimension to be between 2 and 3 for asphaltene aggregates, it is reasonable to assume that the motion is considerably less than 3D. The timescale τM characterizing the restricted translational motion of a maltene molecule again depends on the molecular size of the particular maltene molecule. We expect τM for entangled chains to be approximately proportional to the rotational timescale in bulk τR, which we introduced earlier. Concurrently with the maltene motion within the asphaltene aggregate, the whole aggregate including the entangled maltene molecules undergoes rotational Brownian motion on a timescale of τA. Here, τA is related to the size of the asphaltene aggregate through the Einstein-Stokes equation given in eq 1. We further assume that the relaxation of the proton spins of the entangled maltene molecules is dominated by their dipole-dipole interaction with the electronic spins on paramagnetic impurities or free radicals imbedded in the asphaltene molecules. This interaction is modulated by the composite motion of the restricted diffusion by the maltene molecules in the aggregate and the overall tumbling of the aggregate. Assuming that these two motions are uncorrelated, the relevant correlation function becomes at long times
becomes in fact directly proportional to the bulk rate, which explains the observed scaling in our data. For d > 2, the spectral density shows weak frequency dependence in the regime of interest, which is inconsistent with the observed difference between longitudinal and transverse relaxation times.
10. Extraction of Asphaltene Aggregate Size To extract the asphaltene rotational time τA and thus the aggregate size from the relaxation measurements, we have to probe the frequency dependence of the spectral density J(ω). Conceptually, the simplest approach is to measure the longitudinal relaxation time as a function of frequency by field cycling NMR. Alternatively, we can obtain this timescale by comparing the longitudinal with the transverse relaxation rates. Within our model, the asphaltene-induced relaxation rates are related to the spectral density in eq 6 by R1c 6cJðω0 Þ R2c c½4Jð0Þ þ 3Jðω0 Þ
ð7Þ
where ω0 is the operating Larmor frequency. The total relaxation rates for each maltene component are given by R1total ¼ R1m þ R1c ¼ ξ1c R1m R2total ¼ R2m þ R2c ¼ ξ2c R2m
ð8Þ
where the second equality for each R1 and R2 follows from eq 4. Here as before, R1m and R2m are the bulk maltene relaxation rates (i.e., the relaxation rates for each maltene component that would be observed in the absence of any asphaltene). With the assumption that at any given time only a small fraction of the maltene molecules are associated with the asphaltene aggregates, it then follows from eqs 6, 8, and 10 that the ratio (ξ2c - 1)/(ξ1c - 1) is a function only of ω0τA: ξ2c -1 1 2 ¼ þ ξ1c -1 2 3R fð1þiω0 τA Þ -1=2 g
ð9Þ
Equation 6 yields the correct dependence on the size of the maltene molecules: the asphaltene-induced relaxation for small maltene molecules (short τM) is less than that for large molecules (longer τM). With τM τR, the asphaltene-induced relaxation rate
Using this relation, we extracted from our measurements the values of τA ≈ 60 ns for oil 1 and τA ≈ 1 μs for oil 2. Once the asphaltene correlation time is known, one can use eq 1 to estimate the hydrodynamic radius of the aggregates assuming their spherical shape. The measured values of viscosity η were 45 and 40 cP for oil 1 at 45 and 54 C, respectively, and 100 and 85 cP for oil 2 at the same temperatures. This gives a diameter of a typical asphaltene aggregate of 2.2 ( 0.4 nm for oil 1 and 4.4 ( 0.4 nm for oil 2. We did not observe any clear variation with temperature. These sizes are consistent with the typical values reported for asphaltenes in the literature,3,25,12,26,27 though these are known to vary anywhere from 3 to 12 nm depending on the measurement technique used and on the origin of the asphaltene studied. Given that native oil 1 and oil 2 came from different reservoirs and have different properties, it is not surprising that their asphaltene
(22) Poindexter, E. H. Dynamic nuclear polarization and molecular aggregation in asphaltene suspensions. J. Colloid Interface Sci. 1972, 38, 412. (23) Lipari, G.; Szabo, A. Model-free approach to the interpretation of nuclear magnetic resonance relaxation in macromolecules. 1. Theory and range of validity. J. Am. Chem. Soc. 1982, 104, 4546 (24) Barre, L.; Simon, S.; Palermo, T. Solution properties of asphaltenes. Langmuir 2008, 24, 3709-3717.
(25) Tanaka, R.; Winans, R. E.; Hunt, J. E.; Thiyagarajan, P.; Sato, S.; Takanohashi, T. Aggregates structure analysis of petroleum asphaltenes with small-angle neutron scattering. Energy Fuels 2003 17, 127-134. (26) Kawashima, H.; Takanohashi, T.; Iinoand, M.; Matsukawa, S. Determining asphaltene aggregation in solution from diffusion coefficients as determined by pulsed-field gradient spin-echo 1h nmr. Energy Fuels 2008, 22, 3989. (27) Barre, L.; Espinat, D.; Rosenberg, E.; Scarsella, M. Colloidal structure of heavy crudes and asphaltene solutions. Rev. Inst. Fr. Pet. 1997, 52, 161-175.
GðtÞ ¼ ðt=τM Þ -d=2 expð -t=τA Þ
ð5Þ
where d is the dimensionality of the diffusive motion of the maltene molecules within the asphaltene aggregate. For d = 1, the corresponding spectral density can be computed exactly, JðωÞ R ½τM τA =ð1=iωτA Þ1=2
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ð6Þ
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Figure 5. SAXS data for oil 2 sample 1 (blue dots) and sample 3 (red dots). The continuous lines for each data set are fits with Beaucage functions. The dotted lines are power law fits to the low-q regime, and dashed lines are the Zimm model fits in the intermediate-q pseudoplateau regime.
aggregate sizes may be quite different as well. As described below, the hydrodynamic radius extracted from NMR experiments is expected to be smaller than the radius of gyration obtained from scattering.
11. Comparison with SAXS Measurements To assess the results obtained from the NMR measurements, we performed small-angle X-ray scattering (SAXS) measurements on samples 1 and 3 of oil 2. In the limit of small wave vectors q, the q dependence of the SAXS scattering intensity is controlled by the radius of gyration of the aggregate, Rg: I(q) exp{-q2Rg2/3}. This is referred to as the Guinier regime and typically applies for qRg < 1. For aggregates that are fractal composites of smaller aggregates, the dependence for larger wave vectors turns into a power law behavior (i.e., I(q) q-df, where df is the fractal dimension). The Beaucage function28 can be used to interpolate between these two regimes: 2
3 ) 3 2 2 q R ½erfð0:433qR Þ d g g f 5 þ df Γ IðqÞ ¼ I0 ðΔFÞ φV 4exp 3 2 ðqRg Þdf (
2
ð10Þ Here, I0(ΔF)2 is the contrast term, φ is the volume fraction of the aggregates, which is proportional to the concentration c used above, V is the volume of the aggregates, and df is the fractal dimension. Results for the two samples are presented in Figure 5. The experiments were conducted on beamline 8-1D-I at the Argonne National Laboratory Advanced Photon Source. The beam energy was 7.35 keV with a resolution of 3 10-4 and a wavelength of λ = 0.16887 nm. With a scattering distance of 3.5 m, the range of scattering wave vectors q extended from 1.6 10-2 to 1.18 nm-1 for sample 1 and from 1.6 10-2 to 1.46 nm-1 for sample 3. A qualitative inspection of the data in Figure 5 is sufficient to conclude that both samples are colloidal systems with aggregates having polydisperse sizes. For the lowest wave vectors, both samples show a dependence of I(q) q-d with an exponent of d = 3.07 ( 0.05. This power law behavior at low q indicates the presence of structures that are much larger than the inverse of the smallest wave vector (i.e., Rg . 62 nm). At intermediate values of q, the data in Figure 5 show in both cases a pseudoplateau, followed again by power law behavior at the largest wave vector. (28) Beaucage, G. Small-angle scattering from polymeric mass fractals of arbitrary mass-fractal dimension. J. Appl. Crystallogr. 1996, 29, 134-146.
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These features are due to the presence of aggregates with a size in the range of a few nanometers, and as shown below, they can be well described by Beaucage functions. The scattering amplitude at intermediate wave vectors is much higher in sample 3 than in sample 1. This confirms that the corresponding concentration of small aggregates is much higher in sample 3 than in the maltene sample, as expected. We did not anticipate the presence of the large aggregates, especially in the maltene sample. However, even though the scattering intensity at the small wave vectors is dominated by the scattering from the largest aggregates, the relative volume fraction of these large aggregates is more than 2 orders of magnitude smaller than that of the smaller aggregates. Note that for a given volume concentration of aggregates the prefactor in eq 10 is proportional to the volume of the aggregate. The low-q scattering intensity will therefore be completely dominated by scattering from large aggregates, even if they are present in only small volume concentrations. To estimate the size of the smaller aggregates, we first performed Zimm analysis on the data at intermediate wave vectors. As the value of q is increased, the contribution to I(q) from the large aggregates decreases until it is sufficiently attenuated so that the scattering by the smaller aggregates becomes dominant. As long as the wave vector at the crossover is not much larger than the inverse of the corresponding radius of gyration, the Guinier regime applies in this intermediate range and Zimm analysis can be applied. In Zimm analysis,29 an average radius of gyration ÆRg2æ1/2 is extracted from the lowest-order expansion of the q dependence in the Guinier regime: ! q2 ÆRg 2 æ 1 1 ¼ 1þ þ ::: IðqÞ Ið0Þ 3
ð11Þ
For polymers, this equation has been shown to be valid for Rgq < 2.30 For sample 1, the Zimm fit over the range of q between 0.38 and 0.56 nm-1 results in an average radius of gyration for the smaller aggregates of ÆRg2æ1/2 = 2.7 nm. For sample 3, the extracted value from the Zimm fit over the range between 0.29 and 0.56 nm-1 is ÆRg2æ1/2 = 5.0 nm. This size for sample 3 is noticeably affected by the exact range of data points included in the fit. This indicates that these aggregates span a range of sizes around this value. The postulate of polydispersity is further supported by the inspection of Figure 5, where the Zimm fits and the initial power law behavior are shown as dashed and dotted lines, respectively. Compared to sample 1, the data for sample 3 shows significantly larger deviations from these asymptotic behaviors at intermediate wave vectors, which again suggests the presence of scatterers of different sizes. The average radius of gyration ÆRg2æ1/2 obtained from the Zimm analysis is given by 0P
ÆRg 2 æ1=2
11=2 ji Vi Rg, i 2 B C ¼@ i P A j i Vi
ð12Þ
i
This average is heavily weighted toward larger sizes. Because the distribution of sizes for sample 3 includes sizes corresponding to wave vectors close to the crossover region, the interpretation of (29) Zimm, B. H. The scattering of light and the radial distribution function of high polymer solutions. J. Chem. Phys. 1948, 16, 1093-1099. (30) Burchard, W. Solution properties of branched macromolecules In Branched Polymers II. Adv. Polym. Sci. 1999, 143, 113-194.
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the average radius of gyration obtained from the Zimm analysis becomes problematic. For a more quantitative analysis, we analyzed the q dependence over the whole range by fitting the data to a superposition of Beaucage functions that correspond to aggregates of different sizes. In the case of sample 1, we were able to obtain a good fit to the entire data with just two functions: over 99% of the mass fraction is described by a Beaucage function with a radius of gyration of 1.95 ( 0.05 nm and a fractional dimension of df = 2.07 ( 0.07. Less than 1% of the mass fraction is associated with large aggregates that are at least 100 nm in size and dominate the small-q behavior. The resulting fit is shown as a solid black line in Figure 5. In this analysis, we have made the assumption that the volume of the smaller aggregates in eq 10 scales with the radius of gyration like V Rgdf and the volume of the large aggregate scales as its radius of gyration cubed. Furthermore, we have assumed in the fit that the large aggregates are composed of smaller aggregates. As discussed in ref 28, this can be taken into account by multiplying the last term in eq 10 for the large aggregates by a Guinier term, exp{ -q2Rg small2/3}, corresponding to the smaller aggregates. For sample 3, we were not able to get a good fit with only two Beaucage functions. Instead, we found that the data requires at least three sizes to obtain an adequate fit. This is consistent with our conclusions based on the Zimm analysis that the smaller aggregates exhibit noticeable polydispersity. The results of this fitting procedure are 85 ( 1% per volume of the aggregates have a size of Rg = 2.65 ( 0.05 nm and 14 ( 1% have a size of Rg = 10.5 ( 1.0 nm, both with a fractal dimension of df = 2.29 ( 0.03. In addition, significantly less than 1% of the total volume of asphaltenes is in large aggregates of at least 100 nm. It is important to keep in mind, however, that the reported SAXS sizes in the case of polydispersed media, where the Guinier plateau is not clearly defined, can be model-dependent. They will depend on the assumed shapes of the particles and their distribution, the details of their fractal structure, and so on. We used Beaucage functions because they interpolate between the two known regimes, but using just two Beaucage functions versus several or changing the fitting range for the Zimm model will affect the extracted sizes.
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Recall that the aggregate size obtained from NMR for oil 2 was 4.4 ( 0.4 nm corresponding to a radius of RNMR = 2.2 ( 0.2 nm. The NMR size was obtained from eq 1 using the measured rotational correlation time and maltene viscosity. Thus, RNMR is a hydrodynamic radius that for fractal structures is typically smaller than the radius of gyration measured with scattering experiments. The hydrodynamic radius from a dilute-concentration viscosity expansion was estimated in ref 24 to be 0.6 of the radius of gyration. The hydrodynamic radius corresponding to rotational diffusion, which is the quantity measured with NMR, should also be smaller than the radius of gyration though not necessarily by the same factor. Thus, RNMR = 2.2 ( 0.2 nm obtained from the relaxation measurements is consistent with the range of aggregate sizes extracted from SAXS as quoted above, though the precise relation between RNMR and Rg for polydisperse systems is not known.
12. Conclusions We developed a method to study and quantify asphaltene aggregation within crude oils with low-field NMR measurements. Our method is based on the observation that the relaxation enhancement of the ambient oil due to asphaltene is directly proportional to the relaxation rate of the given crude oil component (i.e., the larger the hydrocarbon chain, the more strongly it is relaxed by the dissolved asphaltenes). We were able to explain this behavior with a new theoretical model, the porous asphaltene model, that shows that the effectiveness of the asphaltene cluster as a relaxing agent is related to its size. By comparing the longitudinal and transverse relaxation rates, we were able to extract the aggregate sizes in our oils quantitatively, which we verified with small-angle X-ray scattering. Acknowledgment. We thank Abdel Kharrat for the preparation of the samples and Rama Bansil for assistance with the SAXS measurements. D.E.F. thanks Yang Qi and Pabitra Sen for their contributions to the development of the theoretical model. Y.L. was supported by NSF DMR 0804784. The SAXS measurements were made at the Advanced Photon Source at Argonne National Laboratory, supported by the Basic Energy Sciences Division of the U.S. Department of Energy.
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