Effects of Resins on Aggregation and Stability of Asphaltenes - Energy

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Effects of resins on aggregation and stability of asphaltenes Mikhail A. Anisimov, Yu. M. Ganeeva, Evgenii Gorodetskii, V. A. Deshabo, V. I. Kosov, V. N. Kuryakov, D. I. Yudin, and I. K. Yudin Energy Fuels, Just Accepted Manuscript • Publication Date (Web): 09 Sep 2014 Downloaded from http://pubs.acs.org on September 10, 2014

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EFFECTS OF RESINS ON AGGREGATION AND STABILITY OF ASPHALTENES M.A. Anisimov1*, Yu.M. Ganeeva2, E.E. Gorodetskii3, V.A. Deshabo3, V.I. Kosov3, V.N Kuryakov3, D.I.Yudin3, and I.K.Yudin3 1

Institute for Physical Science and Technology, University of Maryland, College Park, MD 20742, U.S.A. 2 A.E. Arbuzov Institute of Organic and Physical Chemistry of Kazan Scientific Center of the Russian Academy of Sciences, Akad. Arbuzova 8, Kazan, Russia 3 Oil and Gas Research Institute of the Russian Academy of Sciences, Gubkina 3, Moscow, Russia

ABSTRACT

Effects of the addition of resins on aggregation and stability of petroleum asphaltenes in hydrocarbon solutions are studied by dynamic light scattering. The average aggregate size was monitored in real time as a function of the concentration of the precipitant (heptane) and resins. It is shown that resins serve as inhibitors for asphaltene aggregation, shifting the onset of aggregation. However, the dependence of the onset on the concentration of resins has a tendency to saturate. The characteristic time of aggregation decreases exponentially upon increase of the precipitant concentration, while it grows linearly upon increase of the concentration of resins. A definition of the onset of asphaltene aggregation based on the time dependence of the aggregate-size growth is suggested. It is also shown for all the samples studied (with and without resins) that the aggregation is controlled by diffusion-limited kinetics. The size of the aggregates as a function of time follows a diffusion-limited-kinetics power law with an exponent α = 0.36±0.04, which is related to the fractal dimension d f of asphaltene clusters as α = 1 (1 + d f ) .

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INTRODUCTION

Modeling of crude oils and petroleum fractions is a challenging task, not only because of their complexity, but also because of sharp changes in their properties upon relatively small variations of the composition or external conditions. Such abrupt changes in the system are usually caused by phase transitions. An important example is loss of stability of crude oil, which is accompanied by precipitation of heavy fractions containing asphaltenes, resins, and waxes [1]. Asphaltene fraction is the heaviest and most polar fraction of crude oils, with pronounced surfaceactive properties [1-3]. The molecular weight of asphaltenes, depending on their origin, usually varies from 400 to 1000 Da [4] but could be much higher [5]. Although the average molecular weight of resins is lower than that of asphaltenes [6], this is not a significant factor in determining the difference in the behavior of asphaltenes and resins. The main difference is associated with a lower polarity of resin’s molecules. The dipole moment of asphaltenes molecules lies in the range from 3.3 to 6.9 D, while the dipole moment for resins ranges from 2.4 to 3.2 D [7,8]. As a result, asphaltenes are commonly defined as being soluble in aromatics and insoluble in saturated hydrocarbons, while resins are not soluble in liquid propane but soluble in pentane and highermolecular-weight n-alkanes [9,10]. The number of condensed-ring units in resins is usually lower than that in asphaltenes, while the length of alkyl chains is higher [11]. One of the most important properties of resins is the amphiphilic nature of the molecules and, hence, their surface activity [12]. Measurements of the adsorption isotherms of resins [13] show that the shape of these isotherms depends not only on a higher sorption capacity of resins, but also on their ability to penetrate through the fractal microporous structure of asphaltene aggregates. Addition of resins to the solution increases the solubility of asphaltenes in a low-molecular-weight solvent [14,15]. Furthermore, addition of resins increases the mass of the precipitate [8,16]. This apparently ambivalent behavior of resins can be explained by their ability to form a multilayer adsorption structure on the surface of ACS Paragon Plus Environment

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asphaltene aggregates [17], leading to additional attractions of asphaltene clusters and increase the efficiency of their collisions [18]. Crude oils can be viewed as a colloid solution of asphaltene nano-size clusters in a lowermolecular-weight hydrocarbon medium [1-3,19]. A common point of view is that steric repulsions between asphaltene clusters in aromatic solvents dominate. However, the interactions become attractive when more saturated hydrocarbons are added to the system [20]. This picture was confirmed by Wang et al. [21,22], who measured the interaction forces between asphaltene aggregates adsorbed on silica wafers and silica spheres in toluene-heptane solutions. It was concluded that there are steric long-range repulsions in pure toluene, which can be well described by scaling theory of polymer brushes in good solvent [23]. In saturated hydrocarbons the effective repulsion between the asphaltene clusters is replaced by the effective attraction that can be described by van der Waals forces. Despite a considerable variation of asphaltenes of different origin, the evolution of the interaction forces between the asphaltene clusters with a change in the solvent quality seems to be universal [24]. The dominance of attractive forces may lead to the loss of stability of the system and formation of a new phase [25]. In this case, one of the challenges that arise in the study of petroleum systems is the determination of the onset of the formation of the new phase [26]. Kinetics near the solubility boundary is usually very slow [27]. The onset of the new phase formation, depending on the detection technique, may not be noticeable after hours or even days after sample preparation, when the homogeneous state remains metastable. Therefore, reports on the solubility and stability boundaries are meaningful only if the detection methods and measurements’ protocol are specified. For example, optical-microscope observations show that asphaltene aggregates in toluene-heptane mixture may occur at relatively low heptane concentrations after a thousand hours after sample preparation [28].


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In this respect, it is important to distinguish between the solubility boundary (the first-order phase transition between equilibrium phases) and the stability boundary (the absolute stability limit of a homogeneous phase, known as the spinodal [29]). Exactly at the solubility boundary, the induction time is infinite because the thermodynamic driving force (the difference between the chemical potentials) is zero. One needs to impose certain oversaturation to observe the new phase formation in real experiment. This is why accurate determination of the solubility boundary, especially in a multicomponent fluid, is so difficult. On the other hand, the thermodynamic stability limit is practically inaccessible because it is preceded by a so-called “kinetic spinodal” [30], the homogeneous nucleation limit, where the induction time is zero. However in practice, the appearance of the new phase occurs through the heterogeneous nucleation in the metastable region, somewhere between the solubility boundary and the kinetic spinodal, depending on experimental conditions [28]. Determination of the solubility (precipitation) boundary in asphaltene solutions is additionally complicated by the fact that asphaltenes is a petroleum fraction with a continuous distribution of different groups of molecules; each group follows its own specific precipitation kinetics. In other words, the onset of asphaltene precipitation is not unique and should be regarded as an idealized quantity, however reproducible under well-defined experimental conditions. Experimental methods to study onsets and processes of asphaltene aggregation include: centrifugation and microscopic observation [24,28,31-33], static and dynamic light scattering [3440], small-angle neutron- and X-ray scattering [41,42]. A conventional definition of the onset of asphaltene aggregation becomes particularly important when one needs to compare the results obtained by different methods or to consider the influence of various factors. In the present paper we report experimental studies of the stability of petroleum systems containing asphaltenes and aggregation kinetics of asphaltene clusters with and without resins. In particular, we show that asphaltene aggregation in all the samples studied (with and without resins)


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is universality controlled by diffusion-limited kinetics with a power law associated with the fractal dimension of asphaltene clusters. EXPERIMENTAL SECTION Sample Preparation

Asphaltenes were extracted from Romashkinskaya oil (Tatarstan, Russia) by a 40-fold dilution of the oil with petroleum ether [43]. Resins were isolated from Akanskii oil (Tatarstan, Russia). After de-asphalting, oils and resins were separated by liquid chromatography with petroleum ether (bp 40-70 °C) + carbon tetrachloride (3:1) to yield resin-free oils and isopropyl alcohol + benzene (1:1) to yield alcohol-benzene resins [43]. The latter products were used in this work. It is commonly understood that asphaltene properties strongly depends not only on their origin but also on extraction procedures. In our previous studies [34,37,47] we used C7 asphaltenes (extracted with heptane). It was interesting to compare our previous studies with asphaltenes separated by petroleum ether. Extraction of asphaltenes by petroleum ether is a standard procedure at the Institute of Organic and Physical Chemistry of the Russian Academy of Sciences in Kazan (Tatarstan). We used the following procedure for sample preparation. A solution of 0.1 g/l asphaltenes in toluene (total volume of 40 ml) was preserved within a day after the preparation in a sealed vial at room temperature. The solution was then divided into four parts. Resins (0.2, 0.6, and 1 g/l) were added in three samples, such that the resin/asphaltene ratio, k, was 2, 6, and 10, respectively. In all cases, the solution was a slightly colored clear liquid. Precipitation of asphaltenes was achieved by adding a predetermined amount of heptane. After the addition of heptane to the sample, the optical


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cell was sealed and the solution was stirred vigorously for 10-20 seconds. Light-scattering monitoring started 1 minute after the addition of heptane.

Dynamic Light Scattering

To monitor the size of asphaltene particles in the process of aggregation, we used dynamic light scattering (DLS), also known as photon-correlation spectroscopy [44,45]. This method has been proven to be an effective tool for monitoring asphaltene aggregation (including in opaque media) in real time [37,46,47]. The primary property obtained by this method is the time-dependent correlation function of the light-scattering-intensity fluctuations. If the correlation function decays exponentially, the decay time is the diffusive relaxation time of the inhomogeneities that cause light scattering. In our case, the growing asphaltene aggregates exhibit a Brownian motion with a certain diffusion rate. The time-dependent autocorrelation function G(τ ) of the scattered light is a function of the “delay” time τ and for a single-exponential decay it can be represented as [43]

G (τ ) = b 1 + ε exp ( −τ τ D )  , where

(1)

b is the baseline correlation level proportional to the total light-scattering intensity, τ is the

“delay” time that defines the time-scale of the measured correlation function, and

τ D is the decay

time (the characteristic time of diffusion at a given length scale). The coefficient ε depends on the amount of stray light and on the aperture; this coefficient is always smaller than unity. The diffusion coefficient D of the particles is directly related to the decay rate τ D of the time-dependent correlation function. For the homodyning regime of photon counting, D and τ D are related by [44]


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1

τD

= 2Dq2 ,

where q is the wave number of the scattered light q =

(2) 4πn

θ  sin   , n is the refractive index of the λ 2

solvent, λ is the wavelength of the incident light in vacuum, and θ is the scattering angle. Equation (2) follows from a Fourier transform of the common diffusion equation that describes diffusion of a particle at a length scale of 2π/q. The mean hydrodynamic radius of the particles, R, then can be calculated by using the Stokes–Einstein equation [44]:

D=

k BT , 6πη R

(3)

where kB is Boltzmann’s constant, T is the temperature, and η is the shear viscosity of the solvent. The size R calculated from Eq. (3) is called the hydrodynamic radius. It may be larger than the radius of the bare particles because of a possible layer of solvent molecules, surfactant molecules, or (for charged particles) adsorbed ions. In most cases these layers add a negligible correction to the size except for the smallest sizes measurable. Equations (1-3) are valid for non-interacting spherical particles. If the particles are involved in an aggregation process, they certainly interact. However, these equations are still applicable to monitor the change of the apparent (“effective”) particle size if the size does not significantly change during the measurement time. For the DLS measurements we used a commercial multifunctional device Photocor Complex equipped with a multi-channel digital correlator Photocor-FC [48]. The light source is a heliumneon laser (wavelength 633 nm, output power 15 mW). A cross-correlation photon-counting system was used for receiving the scattered light. Light scattering was observed at a scattering angle of 90°. The optimal measurement time (accumulation time) was chosen as a compromise between the desire of achieving sufficient statistical accuracy and the requirement of an insignificant variation of the


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aggregation size within the data accumulation. The accumulation time of the correlation function, depending on the light-scattering intensity, may vary from seconds to hours, typically 1-10 min. Since the total time of aggregation in our samples was in the range from 1 to 15 hours, the accumulation time was chosen for 1 minute. The next measurement is started immediately after the previous one. With dynamic light scattering, one can measure a particle size in the range from nanometers to microns. However, the signal/noise ratio in DLS depends on several factors, in particular, on the size of the particles, the number density of the particles, and on the optical contrast (the refractive index difference between the particles and the solvent). Since the concentration of asphaltenes was very low (0.1 %), at the initial stage of aggregation the DLS signal/nose ratio was not sufficient to detect asphaltene clusters smaller than 50 nm. Correlation functions obtained during the asphaltene aggregation within 1 hour of monitoring are shown in Figure 1. As seen from this figure, the amplitudes of the correlation functions (mainly associated with the number of the scatters) and the inflection points (indicating the relaxation time, inversely proportional to the Brownian diffusion rate) increase with the time of monitoring. The main assumption in the application of DLS for monitoring asphaltene aggregation is scattering from independent particles exhibiting a Brownian motion. In reality, the Brownian motion is complicated by a directional motion caused by laser-beam local heating and by sedimentation due gravity. Directional motions of the scatters make non-exponential contribution to the measured correlation function. These effects become especially pronounced at later stages of aggregation and they significantly complicate the interpretation of the correlation functions. Figure 2 shows a correlation function in which there occurs some slow sedimentation of larger particles during the aggregation of asphaltenes. Over time the concentration of sedimenting particles increases, which leads to slow growth of a non-exponential tail of the correlation function. After about two hours of continuous monitoring the correlation functions had been significantly ACS Paragon Plus Environment

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distorted and had become difficult to interpret. This is why we limited the time of the analysis to 100-120 minutes.

RESULTS AND DISCUSSION

We monitored asphaltene aggregation in mixtures of toluene–heptane for four different resin/asphaltene mass ratios, k = 0, 2, 6, and 10 . In all the samples studied, the concentration of asphaltenes in toluene was 0.1 g/l.

Aggregation in Resin-Free Samples

Kinetics of aggregation in this sample was studied at heptane concentration of 0.57, 0.60, 0.63, 0.66, 0.73, 0.78 and 0.85 mass fractions. The results are shown in Figures 3a and 3b. From these figures one can see that the rate of aggregation at relatively low concentrations of heptane increases with the increase of heptane concentration. However, at higher concentrations of heptane (73, 78, and 85 %), as one sees from Figure 3b, the rate of aggregation becomes almost independent of the concentration of heptane. Figures 4a and 4b present the results on a double-logarithmic scale. Linear dependence on this scale means that the size of the aggregates follows a power law as a function of time. It is seen that after an initial transient process (approximately the first 10 minutes) the size of the aggregates is a power law with approximately the same value of the exponent (given by the slope). For different experimental runs all the exponents lie in the range of α = 0.36 ± 0.04 . Therefore, we approximate the time dependence of the aggregate size as


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α

 t  R ( t ) = R0  1 +  .  τc 

(4)

A power-law dependence of the aggregate growth typically corresponds to diffusion-limited aggregation kinetics (DLA) [49-51]. The length-scale factor R0 and time-scale factor τ c can be viewed as the size of the aggregation “seed” and the characteristic time of nucleation of asphaltene

( )

complexes, respectively. At the condition t /τc

α

>>1, which is always satisfied in our experiments,

α the dependence of the aggregate size R ( t ) on the time can be represented in the form R ( t ) = At

with A = R0 τ cα . Our result, α = 0.36 ± 0.04 , agrees with the corresponding exponent value of

α = 0.351 reported by Almusallam et al. [52], who studied effects of alcohols on the aggregation of asphaltene in toluene/precipitant solutions. The dependence of the amplitude A on the concentration of precipitant is shown in Figure 5. The amplitude first grows upon the addition of heptane and eventually saturates at about 73% of heptane. We emphasize that the experimentally detectable parameter is the amplitude of the aggregate-size growth,

A = R0 τ cα , but not separately the scale

factors R0 and τ c . Hence, to determine the absolute value of the characteristic time of aggregation,

τ c , the size of the seed value R 0 should be set by additional physical considerations. It was reported [53-55] that asphaltene nano-aggregates with a characteristic size of a few nm can exist at a concentration higher than 15 mg / L of asphaltenes in toluene. We assume that such a size can be interpreted as an initial seed size for the asphaltene aggregation. We have adopted the same initial seed size for all investigated samples, namely R0 = 3 nm. Any variation of R0 within physically reasonable ranges leads to an insignificant change in the values of the characteristic time

τ c . A linear extrapolation of the amplitude A to zero shown in Fig. 5 gives the concentration of the precipitant at about 48%, as a rough practical estimate of the asphaltene aggregation threshold.


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Characteristic Nucleation Time and Definition of Aggregation Threshold

The determination of the onset of asphaltene aggregation by linear extrapolation of the aggregation size amplitude at the initial stage of monitoring is ambiguous. First of all, the time dependence of the amplitude is not linear, exhibiting a sharp saturation at higher concentration of heptane. Secondly, and more importantly, the absence of experimental data at concentrations of heptane below 57% simply means that either the induction period was longer than the observation time or the number of scatters was too small, and thus undetectable by DLS. Furthermore, asphaltenes are characterized by a continuous distribution of different groups of molecules; each group follows its own specific kinetics of precipitation. This feature suggests that close to the aggregation threshold the amplitude of the asphaltene-size growth A ( x ) should deviate from the linear extrapolation and exhibit a “tail” elongated toward lower concentrations of precipitant. This is why we were curious whether the experimentally observed behavior of A ( x ) would be consistent with a scenario in which the asphaltene aggregation could be possible below the threshold concentration (obtained by linear extrapolation of the amplitude to zero). An explicit analytic form of the function A ( x ) can be obtained from a closer look at the DLA characteristic time. Generally, the characteristic time τ c is a function of two variables, namely the concentration of heptane, x , and the resin/asphaltene mass ratio, k . The dependence of the characteristic time of aggregation, on the heptane concentration at k = 0 is shown in Figure 6. In the regime where A ( x ) can be approximated by a linear function, as shown in Figure 5, τ c =

1/α

( R0 A)

∝ ( x − xonset )

−1/α

.

However, in the full range of the precipitant concentration this dependence is better approximated by the following exponential function:


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

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 ( x0 − x )    ,  δ  

τ c ( x, k = 0 ) = τ csat 1 + exp  

(5)

with τ csat = 3.4 ⋅ 10 -4 s, x0 = 0.678, δ = 0.036 . The concentration x 0 defines crossover from the sharp change in the rate of growth of asphaltene aggregates to the saturation regime, while δ is a fitting parameter proportional to the width of the crossover behavior. The smaller δ, the sharper the crossover. The superscript “sat” in τ csat indicates the characteristic time in the saturation region at high concentrations of heptane. When x > x0 and ( x − x 0 ) δ >> 1 the exponential in Eq. (5) can be neglected and both τc and А saturate. When x < x0 and ( x 0 − x ) δ > > 1 , the unity in Eq. (5) can be neglected. This is the region of low concentration of the precipitant and longer times of nucleation. In this region, the characteristic time τ c exponentially decreases and tends to saturate at a low level; while the amplitude A = R0 τ cα increases with increase of the heptane concentration. The decay of the characteristic time corresponds to an explicit concentration dependence of the amplitude A, indicated in Figure 7 by the solid curve. The dependence is obtained by substitution of τc given by Eq. (5) into

A = R0 τ cα . This dependence enables us to introduce an idealized,

mathematically formal (thus less ambiguous) definition of the aggregation threshold as the precipitant concentration corresponding to the intercept of the tangent at the inflection point with a line of zero amplitude, as shown in Figure 7. At the inflection point of A ( x ) , which corresponds to the maximum growth rate, we obtain 2

sat  x0 − x ∗    x0 − x ∗   d2A ∗ −α − 2  τ c  = R − x exp 1 − exp α τ α ) ( )   0(  δ   δ   = 0 , (6) dx 2  δ     

( )

∗ −1 with the concentration at the inflection point x = x0 − δ ln α = 0.641 . Equation of the tangent at

the inflection point has the form


12

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y ( x ) = A ( x∗ ) + ( x − x∗ )

 1  dA( x ) R0 ∗ d R x x = + −   . ( ) 0 dx x= x∗ τ c ( x∗ )α dx  τ c ( x )α  ∗ x=x

(7)

Introducing a “formal” definition of the aggregation “onset” as y ( x = xonset ) = 0 , we obtain

xonset = x∗ − (1 + α −1 ) δ = 0.504 . The deviation of the solid curve A ( x ) from linearity at x ≤ xonset and the tail of this curve toward lower concentrations of heptane are consistent with the fact that asphaltenes are not represented by a single species and, consequently, the actual onset of aggregation is smeared over a range of the precipitant concentration. The only reason of introducing of xonset by linearization of

A ( x ) at the inflection point is that its position is unambiguously defined. This also enables us to apply this definition to the samples containing resins and to analyze all the experimental data in a consistent way. However, we do not overemphasize advantages of this formal definition that gives the onset concentration at about 50 % of heptane with respect to “naïve” linear extrapolation of the amplitude A ( x ) (shown in Figure 5) that gives the onset of aggregation just below 50 % of heptane. Undoubtedly, the actual thermodynamic precipitation boundary is located at a lower concentration of heptane; however, it is hardly detectable.

Effects of Resins

Three different resin/asphaltene mass ratios, k = 2, 6, and 10 were studied. The concentration of heptane was chosen to be 0.65, 0.70, 0.75 and 0.80 (mass fraction). The particle size growth is demonstrated in Figure 8. Similar to the behavior of the resin-free sample, the aggregation of asphaltenes in the presence of resins is well described by a power law R ( t ) = Atα with the same exponent α = 0.36 . ACS Paragon Plus Environment

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Assuming, as above, R0 = 3 nm in the amplitude A ( x, k ) = R0 τ c , we find that for fixed α

values of the heptane concentration the dependence of the characteristic time of aggregation τ c ( x , k ) on the resin concentration has the form shown in Figure 9. As seen from this figure, the

characteristic times of aggregation are linear functions of the resin/asphaltene ratio. Resins are inhibitors of the asphaltene aggregation. They make the asphaltene aggregation slower. However, the larger the concentration of the precipitant or, in other words, the further away the system from the aggregation threshold, the weaker the inhibitor effect of resins. The DLA characteristic time in the presence of resins can be represented as

τ c ( x, k ) = τ c ( x, k = 0 ) + ξ ( x ) k ,

(8)

where τ c ( x , k = 0 ) is the DLA characteristic time for resin-free samples, shown in Fig. 6 and approximated by Eq. (5). Dependence of the slope ξ ( x ) = ∂ τ c ( x , k )  / ∂ k (the response of the characteristic time to the addition of resins) on the heptane concentration is shown in Figure 10 and can be described by an exponential function, similar to Eq. (5):



 ( x 0 k − x )    , δ k   

ξ ( x ) = ξ sat 1 + exp  

(9)

sat -4 with ξ = 1.2 ⋅10 s, x0 k = 0.735, δ k = 0.039 .

Comparison between the experimental data and approximations given by Eq. (7) is presented in Figures 11 and 12. Threshold concentrations of heptane in solutions with different contents of resins are obtained by the same method as for resin-free samples. They are shown in Fig. 12 as intercepts of the tangent at the inflection point of the amplitude A ( x ) with a line of zero amplitude.

Discussion


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The first experimental result to be explained is the saturation of the aggregate-size amplitude growth at high heptane concentrations; the fact is observed for all the samples studied, with and without resins. This saturation in the aggregate-size growth is associated with the decay and final saturation (at a very low level) of the characteristic nucleation time τ c . The formation of the new phase occurs in the metastable region, between the thermodynamic solubility boundary and the absolute stability limit of the homogeneous state (spinodal). The thermodynamic driving force of this process is the degree of oversaturation. The higher the degree of oversaturation, the smaller the characteristic nucleation time. The saturation of the amplitude of cluster-size growth at high degrees of oversaturation can be explained as follows. At the spinodal, the driving force reaches its maximum and does not change with further increase of the precipitant concentration. Correspondingly, far away from the aggregation threshold, when the heptane concentration approaches the region of absolute stability limit of the homogeneous phase, the characteristic time

τ c and the amplitude A should also saturate. Regarding the determination of the aggregation threshold our results confirm the ambiguity in its definition. One way to make this definition less ambiguous, although formal, is to analyze an explicit analytical dependence of the asphaltene-size growth as a function of the precipitant concentration. However, the actual thermodynamic solubility boundary (unfortunately, hardly detectable and thus poorly reproducible) is located at a lower concentration of precipitant than obtained by extrapolation of any kind. The induction (latent) time and realization of asphaltene aggregation in metastable region depend on the conditions for heterogeneous nucleation. In additional experiments, we examined solutions with the concentrations 0.47 and 0.52 mass fraction of heptane. For these samples aggregation of asphaltenes was not observed during continuous monitoring for 24 hours. Thereafter, the samples were removed from the DLS setup, vigorously shaken for 10 seconds, and then placed back in the setup. Dispersed particles were observed with a


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size around 800 nm. This size was not changed for the next 8 hours. A possible interpretation of this result is that a small number of particles were initially formed on the surface of the optical cell via heterogeneous nucleation. These particles were undetectable in bulk. After shaking they disperse, however without further aggregation. The importance of the surface in promoting asphaltene aggregation of asphaltenes was demonstrated by Maqbool et al. [28]. The other result that can be explained relatively easily is the observed saturation of the inhibition effect of resins on asphaltene aggregation at high resins/asphaltene ratios. Phenomenologically, the aggregation of asphaltenes depends on two factors: the first one comes from thermodynamics - the change of the solvent quality - and the second one is the efficiency of collisions between the aggregating clusters. The quality of the solvent is manifested mainly by the shift of the onset of aggregation. The efficiency of collisions determines the rate of aggregation. Our results show that the addition of resins has a relatively small influence on the quality of the solvent (defined as a minimum heptane/toluene ratio needed to detect the onset of aggregation). The onset of asphaltene aggregation is shifted upon changing the resin/asphaltene ratio from 0 to 10 from about 50 % to about 55 % of heptane. Moreover, the dependence of the onset on the concentration of resins has a tendency to saturate. The tendency of the aggregation threshold to saturate is demonstrated in Figure 13: for asphaltene/resin ratio of 6 and 10 the difference is almost within the experimental uncertainty. At the same time, a significant slowdown in the aggregation rate by increasing the resin/asphaltene ratio indicates a decrease in the effectiveness of collisions between asphaltene clusters coated by brushes of resin molecules. This effect correlates with the study of Pereira et al. [18] in which stabilization of asphaltenes against flocculation is explained by a low adsorption tendency of resins with weak self-interaction. Similar effects were observed by other investigators [8,13,14]. The mechanism of the saturation in the change of the aggregation onset can be explained by the limited capacity of interaction of asphaltene aggregates with resins: only a certain number of resin molecules can be incorporated into the asphaltene aggregate. Effects of ACS Paragon Plus Environment

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resins in the asphaltene aggregation are mainly associated with their adsorption on the surface of asphaltene aggregates [55,56]. This mechanism is well illustrated by a so-called “archipelago” model [19,56]. A nontrivial fact is that the saturation in resins’ inhibition of the asphaltene aggregation occurs at a relatively large resin/asphaltene mass ratio (about 10). Asphaltene aggregation in our samples is universality controlled by a diffusion-limited kinetics power law R ( t ) = Atα with α = 0.36 ± 0.04 . This value of α is the same for all the samples studied with and without resins. A fundamental question arises: what is the connection between the value of the exponent α in this law and the fractal dimension of the asphaltene aggregates? It is known that asphaltene aggregates are fractals [2,57,59,60]. However, asphaltenes of different origin may manifest different fractal dimensions df [57,59]. Furthermore, the relation between the exponent α and df is not universal. In particular, we argue that in our study the value of α is not equal to the inverse of the fractal dimension df in disagreement with the assumption of our earlier work [34,37] and with the studies of the diffusion-limited aggregation in classical colloids [49-51]. We explain this difference by the complexity and low surface tension of asphaltene clusters in comparison with classical colloidal particles. Weitz et al. [49] considered an approximation for the DLA growth rate of a mean cluster mass, M, in which dM / dt = constant, independent of the fractal nature of the clusters. Together with the fractal scaling of the mass with radius, M ∝ R f , this approximation gives R ( t ) ∝ t1/ df . d

Weitz et al. [50] obtained d f = 1.77 ± 0.05 for an aqueous gold colloid. This value corresponds to the exponent α = 1 / d f ≅ 0.5 6 . However, this approximation is not universally valid. For example, Grillo et al. [61] have shown that the growth rate in diffusion-limited aggregation of vesicles can be approximated as dM / dt ∝ M −2 , which corresponds to α = 1/ 3d f . Since the fractal dimension of vesicles d f = 2 , the DLA exponent for the vesicle aggregate size is α = 1/ 6 , in agreement with ACS Paragon Plus Environment

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experiment. Similarly, the value of α = 0.36 ± 0.04 obtained in our study can be explained as associated with the growth rate of a mean asphaltene cluster mass approximated as

dM / dt ∝ M −1/df ∝ R . Hence, we obtain α = 1 (1 + d f ) corresponding to the fractal dimension of asphaltene aggregates d f = 1.75 ± 0.18 ; this value agrees the fractal dimension d f = 1.77 ± 0.05 of classical colloidal fractals [49]. The value of α = 0.351 reported by Almusallam et al. [52] also agrees with this fractal dimension. The result α = 1 (1 + d f ) , derived as a certain approximation of the Lifshitz-Slezov-Wagner theory [27], will be published elsewhere. At higher concentrations of asphaltene, crossover from diffusion-limited aggregation to reaction-limited aggregation could be possible, as it was observed for a gold colloid [50] and was discovered in our earlier study of C7 asphaltenes [34].

CONCLUSION

Monitoring of asphaltene aggregation by DLS in 0.1 g/L toluene solutions with and without resins upon addition of heptane shows that the aggregation kinetics is diffusion-limited, i.e., the aggregate size follows a power law as a function of time with an exponent α = 0.36±0.04 which is related to the fractal dimension d f of asphaltene aggregates as α = 1 (1 + d f ) . We have found that in terms of aggregation kinetics the petroleum-ether asphaltenes at a low concentration of precipitant are similar to C7 asphaltenes (extracted with heptane) studied in our previous work, thus confirming, in agreement with Haji-Akbari et al. [24], that despite a considerable variation of asphaltenes of different origin, the evolution of the interaction forces between the asphaltene clusters with a change in the solvent quality seems to be universal. The characteristic time оf aggregation decreases exponentially upon increase of precipitant’s concentration but grows linearly upon increase of the resin/asphaltene ratio. The amplitude of ACS Paragon Plus Environment

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cluster-size growth is saturated at high concentrations of precipitant (heptane), far away from the precipitation threshold. We explain this effect by transition from metastable-state aggregation conditions to conditions beyond the absolute thermodynamic-stability limit of the homogeneous state. We have suggested an idealized (mathematically formal) definition of the onset of asphaltene aggregation (with or without resins) based on the concentration dependence of the amplitude of cluster-radius growth, as shown in Figure 7. This definition enables us to uniformly compare the asphaltene aggregation with and without resins. The onset of aggregation increases upon the addition of resins, but only for limited resins’ content, below 6 resins/asphaltene mass ratio. We have also discussed ambiguity in the experimental determination of the aggregation threshold. In agreement with other investigators, we show that the induction (latent) time and realization of asphaltene aggregation in metastable region depend on the conditions for heterogeneous nucleation. Finally, we note that the observed character of aggregation of real asphaltenes in solution is remarkably similar to that recently found in toluene/heptane mixtures with a single compound hexatert-butylhexa-perihexabenzocoronene [62], thus confirming the possibility of modeling the asphaltene aggregation by well-defined compounds.


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AUTHOR INFORMATION

Corresponding Author *Telephone: +1-301-405-8049. Fax: +1-301-314-9404. E-mail: [email protected].

NOTES

The authors declare no competing financial interest.

ACKNOLEDGMENTS Authors acknowledge fruitful discussions and collaboration with Dr. A.R. Muratov, Dr. V.E. Podnek, and Dr. D. Subramanian. In Russia, the research was supported by the Russian Foundation for Basic Research, Grant No. 10-08-01051-a.


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(30) Kiselev, S.B. Kinetic boundary of metastable states in superheated and stretched liquids. Physica A 1999, 269, 252-268. (31) Hoepfner, M.P.; Limsakoune, V.; Chuenmeechao, V.; Maqbool, T.; Fogler H.S. A Fundamental Study of Asphaltene Deposition. Energy Fuels 2013, 27, 725−735. (32) Kraiwattanawong, K.; Fogler, H.S.; Gharfeh, S.G.; Singh, P.; Thomason, W.H.; Chavadej S. Effect of Asphaltene Dispersants on Aggregate Size Distribution and Growth. Energy Fuels 2009, 23, 1575–1582. (33) Seifried, C.M.; Crawshaw, J.; Boek E.S. Kinetics of Asphaltene Aggregation in Crude Oil Studied by Confocal Laser-Scanning Microscopy. Energy Fuels 2013, 27, 1865−1872. (34) Anisimov, M.A.; Yudin, I.K.; Nikitin, V.; Nikolaenko, G.; Chernoutsan, A.; Toulhoat, H.; Frot, D.; Briolant, Y. Asphaltene Aggregation in Hydrocarbon Solutions Studied by Photon Correlation Spectroscopy. J. Phys. Chem. 1995, 99, 9576-9580. (35) Evdokimov, I.N.; Eliseev, N.Y.; Akhmetov, B.R. Asphaltene dispersions in dilute oil solutions. Fuel 2006, 85, 1465−1472. (36) Rajagopal, K.; Silva, S.M C. An Experimental Study of Asphaltene Particle Sizes in nHeptane-Toluene Mixtures by Light Scattering. Brazilian J. Chem. Eng. 2004, 21, 601 – 609. (37) Yudin I.K.; Anisimov, M.A. Dynamic Light Scattering Monitoring of Asphaltene Aggregation in Crude Oils and Hydrocarbon Solutions. In Asphaltenes, Heavy Oils and Petroleomics; Mullins, O. C., Sheu, E. Y., Hammami, A., Marshall, A. G., Eds. Springer: New York, 2007; Chapter 17. (38) Eyssautier, J.; Frot, D.; Barré, L. Structure and Dynamic Properties of Colloidal Asphaltene Aggregates. Langmuir 2012, 28 (33), 11997−12004. (39) Mansur, C.R.E.; de Melo, A.R.; Lucas, E.F. Determination of Asphaltene Particle Size: Influence of Flocculant, Additive, and Temperature. Energy Fuels 2012, 26, 4988−4994. ACS Paragon Plus Environment

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(50) Weitz, D.A.; Huang, J.S.; Lin, M.Y.; Sung, J. Limits of the Fractal Dimension for Irreversible Kinetic Aggregation of Gold Colloids. Phys. Rev. Lett. 1985, 54 (13), 141611419. (51) Lin, M.Y.; Lindsay, H.M.; Weitz, D.A.; Ball, R.C.; Klein, R.; Meakin, P. Universality in colloid aggregation, Nature 1989, 339, 360-362. (52) Almusallam, A.S.; Shaaban, M.; Nettem, K.; Fahim, M.A. Delayed Aggregation of Asphaltenes in the Presence of Alcohols by Dynamic Light Scattering, J. Dispersion Science and Technology, 2013, 34, 809–817. (53) Mullins, O.C.; Seifert, D.J.; Zuo, J.Y.; Zeybek, M. Clusters of Asphaltene Nanoaggregates Observed in Oilfield Reservoirs. Energy Fuels 2013, 27, 1752−1761. (54) Yarranton, H.W.; Ortiz, D.P.; Barrera, D.M.; Baydak, E.N.; Barré, L.; Frot, D.; Eyssautier J.; Zeng, H.; Xu, Z.; Dechaine, G.; Becerra, M.; Shaw, J.M.; McKenna, A.M.; Mapolelo, M.M.; Bohne, C.; Yang, Z.; Oake, J. On the Size Distribution of Self-Associated Asphaltenes. Energy Fuels 2013, 27, 5083−5106. (55) Adams, J.J. Asphaltene Adsorption, a Literature Review. Energy Fuels 2014, DOI: 10.1021/ef500282p. (56) Spiecker, P.M.; Gawrys, K.L.; Trail, C.B.; Kilpatrick, P.K. Effects of petroleum resins on asphaltene aggregation and water-in-oil emulsion formation. Colloids and Surfaces A: Physicochem. Eng. Aspects 2003, 220, 9-27. (57) Hoepfner, M.P.; Fávero, C.V.B.; Haji-Akbari, N; Fogler H.S. The Fractal Aggregation of Asphaltenes. Langmuir 2013, 29, 8799−8808. (58) Maqbool, T.; Balgoa, A.T.; Fogler, H.S. Revisiting Asphaltene Precipitation from Crude Oils: A Case of Neglected Kinetic Effects. Energy Fuels 2009, 23 (7), 3681–3686. (59) Rahmania, N.H.G.; Dabrosb T.; Masliyah J.H. Fractal structure of asphaltene aggregates. J. Coll. Interface Science 2005, 285, 599–608. ACS Paragon Plus Environment

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(60) Gmachowski L.; Paczuski M. Fractal dimension of asphaltene aggregates determined by turbidity. Colloids and Surfaces A: Physicochem. Eng. Aspects 2011, 384, 461– 465. (61) Grillo, I.; Kats, E.I.; Muratov, A.R. Formation and growth of anionic vesicles followed by small-angle neutron scattering. Langmuir, 2003 19 (11), 4573–4581. (62) Breure, B.; Subramanian, D.; Leys, J.; Peters, C.J.; Anisimov, M.A. Modeling Asphaltene Aggregation with a Single Compound. Energy Fuels 2013, 27, 172–176.


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FIGURES

Figure 1. DLS correlation functions (in term of the “delay” time) for the sample with initially 0.1 g/l asphaltenes in toluene, measured during the first hour after adding 0.63 mass fraction of heptane. From the bottom to the top: 2 min – 58 min with increment 8 min.


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Figure 2. DLS correlation function obtained for the sample with initially 0.1 g/l asphaltenes in toluene after 100 minutes since addition of 0.63 mass fraction of heptane.


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Heptane 0.66 Heptane 0.63 Heptane 0.60 Heptane 0.57

700

Heptane 0.85 Heptane 0.78 Heptane 0.73

1200 1000

Radius, nm

600

Radius, nm

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500 400 300

800 600 400

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200

100

a 0

1000

2000

3000

4000

5000

b

0 6000

0

1000

2000

3000

4000

5000

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Time, s

Time, s

Figure 3a. Time dependence оf the size оf Figure 3b. Time dependence оf the size оf asphaltene aggregates in resin-free samples at asphaltene aggregates in resin-free samples at concentrations

оf

heptane

aggregation threshold.

close

to

the larger concentrations оf heptane, far away from the aggregation threshold.


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1000 800

1200


600

Heptane 0.85 Heptane 0.78 Heptane 0.73

1000

Radius, nm

400

Radius, nm

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200

800 600

400

100 80

b

a

60 60

600

6000

60

600

6000

Time, s

Time, s

Figure 4a. The same data as in Figure 3a but Figure 4b. The same data as in Figure 3b, but plotted in log-log scale. All the lines have the plotted in log-log scale. The slope is 0.36. same slope, 0.36.


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-1/α

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Amplitude A, nm·s

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50 40 30 20 10 0 0.5

0.6

0.7

0.8

0.9

Heptane concentration, mass fraction Figure 5. The amplitude of the aggregate-radius growth as a function of heptane concentration. Arrow marks a rough estimate of the threshold concentration: xonset = 0.48 mass fraction of heptane.


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8 7 6

c

Characteristic time τ , ms

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5 4 3 2 1 0 0.6

0.7

0.8

0.9

Heptane concentration, mass fraction

Figure 6. Exponential decay of the DLA characteristic time for the asphaltene aggregation upon increase of heptane concentration. Solid curve is the approximation given by Eq. (5).


33

Energy & Fuels

60

Amplitude A, nm·s-1/α

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 40

50 40 30 20 10 0 0.5

0.6

0.7

0.8

0.9

Heptane concentration, mass fraction Figure 7. Determination of precipitation threshold. Black solid curve is obtained by substitution of

τc (given by Eq. (5)) into A = R0 τ cα

.

Arrow marks the suggested definition of the threshold

concentration: xonset = 0.505 mass fraction of heptane.


34

Page 35 of 40

1000 800

1000 800

a

Radius, nm

Radius, nm

b

600

600 400

200 k= 0 k= 2 k= 6 k=10

100

60

600

400

200 k= 0 k= 2 k= 6 k=10

100

60

6000

600

c

1000 800

6000

Time, s

Time, s

d

1000 800

600

600

Radius, nm

Radius, nm

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

400

200 k= 0 k= 2 k= 6 k= 10

100

60

600

6000

400

200 k= 0 k= 2 k= 6 k=10

100

60

600

Time, s

6000

Time, s

Figure 8 Time dependence оf the size оf asphaltene aggregates in resin-containing samples at fixed heptane concentrations (mass fraction): (a) 0.65 heptane,

(b) 0.70 heptane, (c) 0.75 heptane, (d)

0.80 heptane.


35

Energy & Fuels


0.25

Characteristic time τC , ms

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 40

0.20 0.15 0.10 0.05 0.00 0

2

4

6

8

10

Resin-asphaltene mass ratio k

Figure 9. DLA characteristic time as a function of the resin/asphaltene ratio at fixed amounts of heptane. Solid curves are approximations given by Eq. (8).


36

Page 37 of 40

1.4 1.2 ∂τc /∂k, ms

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

1.0 0.8 0.6 0.4 0.2 0.0 0.6

0.7

0.8

0.9


Figure 10. Response of the DLA characteristic time to the addition of resins as a function of heptane concentration. Solid curve is the approximation given by Eq. (9).


37

Energy & Fuels

14

Characteristic time τC , ms

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 38 of 40

k=0 k=2 k=6 k=10

12 10 8 6 4 2 0 0.5

0.6

0.7

0.8

0.9

Heptane concentration, mass fraction Figure 11. Characteristic DLA times of the asphaltene aggregation for fixed resin/asphaltene ratios. Solid curves are approximations given by Eq. (8).


38

Page 39 of 40

60

Amplitude A, nm⋅s-1/α

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

50

k=0 k=2 k=6 k=10

40 30 20 10 0 0.5

0.6

0.7

0.8

0.9


Figure 12. DLA amplitudes of the asphaltene aggregation for fixed resin/asphaltene ratios. Approximations for the amplitudes are obtained by substitution of τc , given by Eqs. (5) and (7), into

A = R0 τ cα . Aggregation onsets are obtained by the same method (tangents to the inflection points) as shown in Fig. 7 for the resin-free samples.


39

Energy & Fuels

0.55

Threshold, heptane mass fraction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 40 of 40

0.54

0.53

0.52

0.51

0.50 0

2

4

6

8

10

12

Resin-asphaltene mass ratio k

Figure 13. Estimated asphaltene precipitation threshold as a function of the resin/asphaltene mass ratio. Solid curve is approximation by an exponential function, xonset = a ⋅ e

−k

k0

+ x0 with x0 =

0.54308, a = - 0.03906, k 0 = 1.96981.


40

Effects of Resins on Aggregation and Stability of Asphaltenes - Energy

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