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Fractal structure of asphaltene aggregates
Journal of Colloid and Interface Science 285 (2005) 599–608 www.elsevier.com/locate/jcis
Fractal structure of asphaltene aggregates Nazmul H.G. Rahmani a , Tadeusz Dabros b , Jacob H. Masliyah a,∗ a Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 2G6, Canada b CANMET, Devon, AB T9G 1A8, Canada
Received 13 July 2004; accepted 30 November 2004 Available online 21 February 2005
Abstract A photographic technique coupled with image analysis was used to measure the size and fractal dimension of asphaltene aggregates formed in toluene–heptane solvent mixtures. First, asphaltene aggregates were examined in a Couette device and the fractal-like aggregate structures were quantified using boundary fractal dimension. The evolution of the floc structure with time was monitored. The relative rates of shear-induced aggregation and fragmentation/restructuring determine the steady-state floc structure. The average floc structure became more compact or more organized as the floc size distribution attained steady state. Moreover, the higher the shear rate is, the more compact the floc structure is at steady state. Second, the fractal dimensions of asphaltene aggregates were also determined in a free-settling test. The experimentally determined terminal settling velocities and characteristic lengths of the aggregates were utilized to estimate the 2D and 3D fractal dimensions. The size–density fractal dimension (D3 ) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This relatively low fractal dimension suggests that the asphaltene aggregates are highly porous and very tenuous. The aggregates have a structure with extremely low space-filling capacity. 2004 Elsevier Inc. All rights reserved. Keywords: Asphaltene; Bitumen; Structure; Fractal; Couette; Aggregation; Fragmentation; Floc; Settling
1. Introduction Petroleum asphaltenes have been the subject of extensive research. On the basis of solubility, asphaltenes are defined as the part of petroleum that is insoluble in n-alkanes and completely miscible in aromatic hydrocarbons such as toluene or benzene [1]. This property is used for the separation of asphaltenes. The above definition is in some sense arbitrary, as the molecular structure of asphaltenes varies significantly depending on their origin, method of oil recovery, and history of extraction [2]. According to their chemical structure, asphaltenes are aromatic multicyclic molecules surrounded and linked by aliphatic chains and heteroatoms; published molar mass data for petroleum asphaltenes range from 500 g/mol to as high as 50,000 g/mol [3]. The polar* Corresponding author. Fax: +1-780-492-2881.
E-mail address: [email protected] (J.H. Masliyah). 0021-9797/$ – see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.11.068
ity and complex structure of asphaltenes lead to their selfassociation, flocculation, and precipitation during the course of heavy-oil processing. The formation of colloidal asphaltene associations in several organic solvents and in crude oil was observed for the first time more than half a century ago [4]. It is postulated that in aromatic solvents, asphaltenes can form micelle-like aggregates above a certain concentration, known as the critical micelle concentration (CMC). The CMC data for asphaltenes in toluene have been determined using a variety of methods, such as measurement of surface tension [5] and calorimetric titration [6,7]. Sheu and Storm [8] have noted that asphaltenes in a good solvent below the CMC are in a molecular state, whereas above the CMC, asphaltene micelle formation occurs in a manner similar to that in surfactant systems but with less uniformity in their structure and more polydispersity. According to other investigations, the structure and the shape of asphaltenic micelle-like associates appear to be much more complicated than those of
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classic surfactant micelles [9,10]. These studies indicate that asphaltene micelle-like associates are formed as a result of multiple interactions: aggregates about 2–5 nm in size either are present in a molecular form or are formed by strong intermolecular attractive forces, while the larger particles are self-associates, formed from these small aggregates by weaker interaction forces. Though many studies have been conducted on the growth of colloidal asphaltene particles in hydrocarbon solutions, the flocculation of asphaltene particles under hydrodynamic shear flow has not been investigated. It bears a significant implication in industrial applications. A mixture of toluene and n-heptane is often used to investigate the stability and the precipitation of asphaltenes. At a certain threshold value of the ratio of n-heptane to toluene, the asphaltenes in solution becomes unstable and asphaltene particles start to precipitate. It is found that when a concentrated solution of asphaltenes in toluene is added to excess heptane, the precipitated asphaltene grows from micrometer-sized primary particles to aggregates that are orders of magnitude larger within a few minutes. The objective of this paper is to study asphaltene aggregates’ settling behavior in order to understand their structural properties. Aggregate structure and size distribution have been known to be of great importance in solid–liquid separation processes such as filtration, sedimentation, and dewatering. The aggregate structure and consequently its density influence the strength of the aggregates [11]. This, in turn, indicates whether an aggregate can sustain the shear experienced during the flocculation process and determines the final characteristic of the aggregates after they undergo growth, breakup, and possible restructuring [12,13]. Image analysis techniques yield data on the basis (in the form) of two-dimensional images of the aggregates being studied, so that once the area and length have been calculated the most interesting feature is the irregularity of the perimeter. In general, there are two basic methods of characterizing aggregates from two-dimensional image data [14]. The first method is to measure the fractal dimension of the aggregate boundary, and the second method is to consider the scaling relationship between either the perimeter and area, or the number density and radius. The first method employs such techniques as variable magnification, mosaic amalgamation, structured walk, dilation logic, and the equispaced method, all of which measure perimeter length as a function of resolution. A summary of the procedures involved and a comparison of the relative merits of these methods is given by Kaye et al. [15]. The second method utilizes perimeter/area measurement [16], nested squares, radius of gyration, and direct correlation, which are all indirect techniques of measuring the density fractal dimension. All these latter techniques have been used by Robinson and Earnshaw [17] to characterize twodimensional aggregates and were found to be in good agreement. Indeed, the majority of the studies using fractal characterization in the current literature utilize one or several
of these techniques. It should be noted that the fractal dimension measured by the boundary method and the density method do not necessarily describe the same physical property of the aggregate, and so may have different values. In particular, they diverge at the morphological extremes of space-filling and tenuous aggregates. Fractal dimensions relate aggregate size to some property in n-dimensions, where n = 1, 2, or 3 and Dn is the fractal dimension in n dimensions. For example, fractal dimensions of aggregates imbedded in one, two, and three dimensions are P ∝ l D1 , A∝l
D2
V ∝l
D3
(1)
,
(2) or
V ∝l , D
(3)
where l is the characteristic length scale, which can be taken either as the shortest, longest, geometric mean, or equivalent radius (based on area) of an aggregate [18], P is the aggregate perimeter, A is the aggregate cross-sectional area (i.e., including the space between particles of an aggregate), and V is the total solid volume of all particles in the aggregate. The subscript on Dn indicates the integer value of Dn for Euclidean geometry. If the subscript is omitted, it is understood that its value is 3, or D = D3 . The fractal dimensions can be obtained from the slopes of log–log plots of the respective aggregate properties in Eqs. (1)–(3) and aggregate length. For Euclidean objects (e.g., a sphere), D1 = 1, D2 = 2, and D3 = 3. The perimeter of irregular objects is larger and the crosssectional area is smaller than the corresponding properties for a spherical object of the same length. As the perimeter of fractal objects increases with particle size, their D1 > 1. Similarly, fractal aggregates become less dense and more irregular as they increase in size and their D2 < 2. These two fractal dimensions therefore quantify the rates of change at which the aggregate perimeter and projected area increase with respect to the characteristic length. Properties of aggregates that affect sedimentation rates, such as porosity, average density, and hydrodynamic radius, are primarily functions of D2 and D3 . Aggregates tend to become more porous with increasing size, resulting in two- and three-dimensional fractal dimensions that are usually less than their corresponding Euclidean values; i.e., D2 < 2 and D3 < 3. If measurement of the perimeter (P ) of an aggregate is performed with an accuracy defined by the smallest length of the measurement (i.e., the resolution), a fractal relationship between the measured perimeter and the projected area (A) of the floc is written as A ∝ P 2/Dpf ,
(4)
where Dpf is the perimeter-based fractal dimension of the floc [19]. This equation is used to investigate the geometry of asphaltene aggregates. Heterogeneously (nonuniformly) packed objects with irregular boundaries can be defined by nonlinear relationships
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where the properties of the object scale with a characteristic length dimension raised to a power called the fractal dimension [20–22]. For example, the aggregate porosity (or effective density) and characteristic length are consistent with power-law relationships, 1 − ε ∼ laD3 −3 ,
(5)
ρeff = (ρa − ρl ) = (1 − ε)(ρp − ρl ) ∝ laD3 −3 ,
(6)
where ε is the aggregate porosity; (1 − ε) is the solid volume fraction in an aggregate; la is the aggregate longest dimension; ρeff is the aggregate effective density; ρa is the aggregate density; ρl is the density of the liquid; ρp is the density of the primary particles used to build the aggregate; and D3 is the three-dimensional fractal dimension for a self-similar structure. If the fractal relationship between aggregate size D −3 and porosity (i.e., (1 − ε) ∼ la 3 ) is included in Stokes’ equation, then this equation leads to the scaling relationship between settling velocity (U ) and aggregate longest dimension (la ) [22] U ∼ laD3 −1 .
(7)
Hence the fractal dimension, D3 , can also be derived from the slope of the log–log plot of settling velocity and aggregate longest dimension. Another fractal geometrical assumption is also important and should be included in Stokes’ law. Logan and Wilkinson [23] used the area–length equation, Eq. (2), in the derivation of Stokes’ law, which produced the scaling relationship U ∼ laD3 −D2 +1 .
(8)
When D3 < 2, a colloidal aggregate viewed in two dimensions is transparent since all particles are visible, and D2 = D3 . However, when D3 2, then D2 = 2 [24]. Thus for D3 < 2, Eq. (8) would predict U ∼ la1 ; but this linear relationship between U and la is not observed experimentally. A few more scaling relationships between U and la were reported for different ranges of Reynolds numbers and fractal dimensions [25]. It was concluded by Johnson et al. [25] that using Eq. (7) is only valid when D3 > 2. If D3 < 2, D2 must be included in the scaling relationship (Eq. (8)). If D2 is not included, the magnitude of D3 will be overestimated. However, in the present study, though the experimentally observed aggregate settling velocities fall into the Stokes regime (Re 1) and D2 < 2, Eq. (8), which includes D2 , cannot be used, as it gives D3 < 1, which is impossible. Hence Eq. (7) is used to determine the 3D fractal dimension of the aggregates. For rapid coagulation, particles with small D3 may be desirable, while for gravity settling a large D3 is preferred [22]. As indicated by Eqs. (7) and (8), both aggregate size and fractal dimension influence the settling velocity, U . Recently, fractal concepts have been used to explain higher observed settling velocities for large aggregates, relative to Stokes settling [25–27]. It was suggested that the internal
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flow through large pores within the fractal aggregates contributes to faster settling velocities. Johnson et al. [25] scrutinized this effect and indicated that the actual settling velocity of a real aggregate is several times faster (on the average 4–8.3 times) than one predicted by Stokes’ law for aggregates of identical size, mass, and primary particle density. On the other hand, Logan and Hunt [28] calculated that the power in a size–settling velocity relationship was only increased slightly from U ∼ d 0.40 to Uperm ∼ d 0.44 after aggregate permeability is accounted for. Others have also found similarly small changes in the aggregate size–settling velocity relationship due to aggregate permeability [29]. Hence by neglecting the flow through the aggregates (i.e., the permeability effect), the three-dimensional fractal dimensions calculated from the settling velocity will be slightly underestimated. The main reason for larger deviation of the experimentally observed settling velocity from Stokes’ velocity is thought to be a result of nonlinear relationships between aggregate size and porosity [28]. In the present experimental studies, the asphaltene aggregates are formed using the Couette device and the jar tester (four-pitched-blade-type flocculator). In the first set of experiments in Couette flow, photographic technique and image analysis are employed to monitor the dynamic evolution of the aggregates structure at different shear rates in terms of the 2D fractal dimension. The structure of the asphaltene aggregates at steady state is found to depend on rotational speed, but not on the solvent composition or particle concentration. In the second set of experiments, asphaltene aggregates are formed in a stirred tank under different experimental conditions and transferred to a quiescent glass settling column having the same solvent mixture. Photographic technique and image analysis are used to determine the aggregate size and settling velocity in the bottom section of the glass column after the aggregates reach the terminal settling velocity. The 2D and 3D fractal dimensions of the aggregates are then determined from the slopes of size–projected area and size–settling velocity regression lines.
2. Materials Asphaltene aggregation in toluene and heptane mixtures was studied with two different feed sources: • Solid asphaltenes that was previously extracted and purified from Athabasca bitumen as described in Section 2.1. The Athabasca bitumen is obtained from a commercial plant. • Athabasca bitumen containing a natural level of asphaltenes that was extracted from oil sands using toluene in the laboratory. It is known as solvent-extracted bitumen. Reagent-grade toluene and heptane were purchased from Fisher Scientific and used as delivered.
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2.1. Preparation of solid asphaltenes The solid asphaltenes used in this study are extracted from Syncrude vacuum-distillation-tower-feed Athabasca bitumen (bitumen that has been treated to remove most of the solids and water). However, the bitumen still contains mineral solids, which make up about 1 wt% of the bitumen [30]. The “solids,” which include fine clays, are insoluble in toluene. To remove the solids, the bitumen is first dissolved in toluene and centrifuged at 35,000g for 30 min. The supernatant liquid is recovered and evaporated until dry, “solids-free” bitumen remains. Asphaltenes are extracted from the “solids-free” bitumen with a 40:1 volume ratio of heptane to bitumen (solids-free). The mixture is stirred for 4 h and left standing to allow the precipitated asphaltenes to settle overnight. Then the supernatant liquid is removed and the remaining precipitate is further diluted with heptane at a 4:1 volume ratio of heptane to asphaltenes. After 4 h, the final mixture is filtered using 0.22-µm Millipore filter paper and the remaining asphaltenes are washed thoroughly with heptane until the filtrate (i.e., heptane) becomes colorless. The precipitated asphaltenes are dried in a vacuum oven dryer at absolute pressure 23 kPa and 50 ◦ C. The drying process usually requires 1 wk. The asphaltenes recovered in this method make up about 16 wt% of the original bitumen. 2.2. Preparation of asphaltene aggregate suspension For the first set of aggregation experiments conducted in a Couette apparatus, dry asphaltene powder is mixed with toluene and is subjected to high-speed stirring for proper mixing. This is retained as a stock of asphaltene–toluene solution. For the aggregation experiments, samples of this stock solution are diluted in toluene and then n-heptane is added to provide the desired solvent composition (i.e., the volume ratio of toluene to heptane in the solution, T:H) and initial asphaltene concentration and a constant stirring speed is then employed to allow floc formation. In the second set of aggregation experiments conducted in a stirred tank, both solid asphaltenes and solvent extracted bitumen were used. Similarly to the procedure described above, bitumen, instead of solid asphaltenes, was dissolved in toluene and the solution was added to excess heptane to investigate asphaltenes aggregation. 3. Experimental apparatus 3.1. Couette device A schematic view of the Couette device (where the asphaltenes–solvent mixture is introduced) is shown in Fig. 1. This device is used because under certain conditions it generates a well-defined shear field. The inner cylinder, with a diameter of 50 mm, is made of Teflon to provide better optical reflection. The outer cylinder, with an inner diameter of
Fig. 1. Schematic of the experimental set-up for the Couette device.
60 mm, is made of Pyrex glass to allow the suspension to be observed. The asphaltene suspension in a toluene–heptane solvent mixture is completely mixed at 300 rpm with a marine propeller for 15 s and is placed into the outer glass cylinder, which is quickly snapped into the Couette device. The rotation of the inner cylinder begins at a required rpm (see Fig. 1). This is considered as the starting time for aggregation. The experiments are carried out at a constant shear rate (G) ranging from 1.2 to 12.7 s−1 . Because of the limited optical resolution, the small asphaltene aggregates and their structural details became visible when the aggregates reached approximately 30 µm in size [31]. For these experiments, the location of the observation area or control volume is 50 mm above the bottom of the cylinders. Images of asphaltene aggregates in suspension are obtained using a microscope (Carl Zeiss Canada Ltd.) coupled with a CCD camera and a video recorder. Image analysis software (Sigma ScanPro 4) is used to calculate the geometrical properties of the aggregates from the captured images. 3.2. Settling column The aggregates used in the free-settling tests were produced in a bench-scale continuously stirred tank of 1.0 L in volume at different fluid shear rates—36, 75, and 160 rpm [32]. In performing the flocculation test, the sample suspension of pure asphaltenes/bitumen in a 1:5 ratio toluene– heptane solvent mixture is first mixed at 660 rpm for 15 s to break up any agglomerates. The impeller, which is a standard 45◦ -angle four-blade pitch turbine positioned at 1/3 of the tank height from the bottom, is then set to the desired speed to produce a constant average fluid shear and allow floc formation. The experimental apparatus for the settling of asphaltene aggregates consists of a Pyrex glass column (Fig. 2). The column is 350 mm in height to ensure that the terminal settling velocity could be reached, and 30 mm in width to neglect the wall effect on aggregate settling. After the average aggregate diameter reached a steady-state size (which is known from the previously performed growth kinetics experiments by PDA [32]), samples were withdrawn
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asphaltene aggregates have rugged, irregular structures and statistical self-similarity, which resemble the shape of cloud and snowflakes. Table 1 shows the one- and two-dimensional fractal dimensions obtained from the log–log plots of aggregate longest dimension (or major axis) versus perimeter and projected area, respectively, based on the analysis of several aggregates formed in a Couette device, and reached steady state at all the employed shear rates. The standard error is applied in determining the slopes from the regression lines. A higher D2 fractal dimension with increasing shear indicates that the aggregates became less amorphous and more compact at higher shear rates. However, the one-dimensional fractal dimension did not show any significant dependence on shear rate. Since the one-dimensional fractal dimension increases with the irregularity of a boundary, the fractal nature of the aggregate perimeter was not correlated with changes in the aggregate area. A similar lack of correlation between D2 and D1 fractal dimensions has previously been found for synthetic as well as marine snow aggregates [35]. From the measurement of the properties of individual aggregates, it is possible to measure the fractal dimension of a population of aggregates having different sizes. As there are several aggregates in each experiment, the perimeter-based fractal dimension, Dpf , of the flocs can be estimated from Eq. (4) using a log–log plot of the floc perimeter and crosssectional area. The value of Dpf is related to the floc surface morphology since Dpf varies between 1 (the projected area of a solid sphere, a circle) and 2 (a line, e.g., a chain of particles). Values of Dpf greater than one have been found for synthetic fractals [19] and a variety of natural objects such as clouds, lakes, and snow patches during melt [36]. The interpretation of Dpf > 1 is that as the objects become larger, i.e., as A increases, P increases more rapidly than for Euclidean objects, so that the boundary becomes more convoluted [37]. Therefore larger values of Dpf represent irregular floc structures. Fig. 3 shows the relation between the projected area (A) of the flocs with their perimeter (P ) on logarithmic coordinates. The perimeter-based fractal dimension of the flocs at steady state (Dpfss ), based on Eq. (4), was derived individually for three different shear rates (i.e., 1.2, 3.8, and 12.7 s−1 ) from Fig. 3 and are shown together for all employed shear rates (i.e., 1.2–12.7 s−1 ) in Fig. 4. The standard error bar is shown on the average Dpfss values in Fig. 4. It shows that at a higher shear rate, G = 12.7 s−1 , the flocs are small and the Dpfss values are smaller (= 1.17 ± 0.02), indicating more
Fig. 2. Experimental arrangement for aggregate settling velocity measurement.
from the stirred tank at certain time intervals (every 15 min) and placed in the settling column. A small amount (about 3 ml) of suspension containing aggregates is gently transferred into the top of the settling column using a rubber dropper bulb with a 10-ml pipette tip cut midway to minimize breakup of the aggregates. The column was filled with the same solvent composition as the original system (i.e., toluene:heptane = 1:5). But this solvent mixture is not saturated with asphaltenes, and hence, small parts of the aggregates added will dissolve during settling. In the present study, this minute loss is neglected due to experimental constraint. Images of asphaltene aggregates, while passing through the observation region in the glass-settling column, were obtained using a microscope objective connected with a CCD camera and a video recorder [33]. A cold fiber-optic light was placed on the same side of the column as the camera to provide reflected lighting from the white background on the other side of the column, which produces clear and sharp pictures. Snappy Video Snapshot, installed under Windows XP, was used to grab and digitize the chosen frames of the recordings. Image analysis software was used to determine the shape, size, and settling velocity of the aggregates from the captured images.
4. Results and discussion 4.1. Determination of aggregate fractal dimension in Couette device The concept of fractal nature proposed in 1975 by Mandelbrot [34] is useful to describe the ruggedness of flocs. The
Table 1 The steady state power law fractal dimensions as a function of shear rate for asphaltene aggregates formed at toluene-to-heptane solvent ratio (T:H) of 1:15 and asphaltene particle concentration of 12.8 mg/L Equation number
Fractal dimension
1 2
D1 D2
Average shear rate (s−1 ) 1.2
2.5
3.8
8.4
12.7
1.08 ± 0.03 1.61 ± 0.03
1.05 ± 0.02 1.80 ± 0.03
1.09 ± 0.03 1.82 ± 0.04
1.06 ± 0.03 1.80 ± 0.03
1.06 ± 0.03 1.90 ± 0.03
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Fig. 3. Determination of perimeter-based fractal dimension for asphaltene aggregates at steady-state (Dpfss ) from image analysis measurements of aggregate cross-sectional area and perimeter.
Fig. 4. Evolution of steady-state perimeter-based fractal dimension (Dpfss ) for asphaltene aggregates as a function of shear rate at a toluene-to-heptane solvent ratio of 1:15 and a particle concentration of 12.8 mg/L. Reducing shear produces more open and irregular aggregate structures at constant particle concentration.
compact and regular structures, while at a lower shear rate (e.g., 1.2 s−1 ), the flocs became more porous and irregular (understood from a higher Dpfss value, about 1.31 ± 0.02). There is a tendency to a smaller Dpfss value at a higher shear, at which the increased amount of fragmentation or erosion and/or restructuring of the floc results in more compact floc structures at steady state. The value of Dpf is a quantitative measure of floc structure that is directly related to the surface fractal dimension, Ds , of the floc [38]. Image analysis of floc structure projections is a more direct and rapid measure of floc structure than light scattering and size or sedimentation velocity measurements, and thus has potential for on-line application in the processing industry. The mass fractal dimension of a floc, Df , is also a measure of floc structure and varies from 1 for a line of particles to 3 for a sphere [38]. However, the Dpf derived from image analysis is a two-dimensional fractal dimension and is not directly related to Df [24].
Fig. 5. Dynamic evolution of the perimeter-based fractal dimension (Dpf ) for asphaltene aggregates for three different shear rates at a toluene-toheptane solvent ratio of 1:15 and an asphaltene particle concentration of 12.8 mg/L. After sufficiently long times, Dpf approaches an asymptotic, steady state value.
Fig. 5 shows the time evolution of Dpf for three different shear rates. The various shear rates (i.e., G) within the Couette device produce a distribution of floc structures as a result of simultaneous shear-induced growth, breakage, and/or restructuring. The Dpf values were determined from the log– log plot of flocs perimeter and projected area, obtained from the analysis of the images taken at a specific time. The graph shows that Dpf increases from its initial value (Dpf = 1, assuming spherical “primary” particles when the experiment starts) and reaches a maximum value as the flocs grow and become more porous. When fragmentation and possibly restructuring begin to dominate, the Dpf value decreases until it reaches a steady-state value. Tambo and Watanabe [39] and Oles [40] suggested that decreased floc porosity (as indicated here by the decreasing perimeter-based fractal dimension) results from the production of strong, dense fragments by preferential breakage of the flocs at weak points. For all cases, Dpf values are obtained using regression analysis. Since a whole population of aggregates is used in these calculations, the calculated fractal dimensions represent a statistical average for the population of aggregates. Individual aggregates may have higher or lower fractal dimensions. The measured steady-state perimeter-based fractal dimensions, Dpfss , for different asphaltene particle concentrations and toluene-to-heptane ratios in the solvent mixture are shown in Table 2. Error limits represent the standard error of the measured values of Dpfss during the experiment. The Dpfss values were not affected significantly at the lower shear rate of 2.5 s−1 by asphaltene particle concentration or toluene-to-heptane ratios in the solvent. A problem arises when the aggregates of interest are three-dimensional objects, which is the case with real systems. The images are two-dimensional projected areas of the actual shape. Consequently, some of the detail of the original shape will be obscured in the projection of the resultant profile. Between 33 and 36% [41,42] of the particles will
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Table 2 The steady-state perimeter-based fractal dimensions (Dpfss ) of asphaltene aggregates as a function of particle concentration and solvent composition for a shear rate of 2.5 s−1 Asphaltene particle concentration (mg/L) Toluene-to-heptane solvent ratio (T:H) Dpfss
4.1 1:7 1.15 ± 0.03
5.3 1:7 1.17 ± 0.03
be hidden. Fractal dimensions measured by image analysis techniques are therefore intrinsically lower than the actual D values for three-dimensional flocs. The maximum permitted value of fractal dimension for both boundary and scaling methods is 2, since in both cases this corresponds to a curve that fills the plane completely; therefore, any object with a mass fractal dimension D > 2 will be underestimated by image analysis techniques. However, Jullien and Thouy [43] have proposed that for D < 2 the values measured from the two-dimensional projected areas concur with the actual value of D and that the perimeter fractal dimension of the two-dimensional objects is a non-trivial continuously varying function of D. According to Rogak and Flagan [41], any object with fractal dimension D > 2 is underestimated by
10.3 1:7 1.16 ± 0.02
8.8 1:3 1.15 ± 0.03
10.3 1:7 1.16 ± 0.02
12.8 1:15 1.17 ± 0.03
10–20% compared to the values obtained using techniques that are sensitive to three-dimensional structure, such as dynamic light scattering [44] and settling velocities [45]. The comparison of values measured by image analysis with values measured by the above techniques should, therefore, be used with caution. 4.2. Derivation of fractal dimension from settling velocity of the aggregates From settling experiments, the 2D and 3D fractal dimensions of the aggregates are calculated from the log–log plot of aggregate projected area vs the longest dimension (Fig. 6), and aggregates settling velocity vs the longest dimension
(a)
(b)
(c)
(d)
Fig. 6. Determination of two-dimensional fractal dimension (D2 ), based on Eq. (2) (A ∝ l D2 ), from image analysis measurements of aggregate projected area and longest dimension. In (a) and (b), the tests were conducted to evaluate the settling velocity of asphaltene aggregates that were formed in a stirred tank with pure asphaltenes at a toluene-to-heptane ratio (T:H) of 1:5 in solvent mixtures and an asphaltene particle concentration of 62.5 mg/L. In (c) and (d), asphaltene aggregates were formed in a stirred tank with bitumen at a toluene-to-heptane ratio (T:H) of 1:5 and a bitumen concentration of 1000 mg/L. In (a), stirring rate = 36 rpm, and in (b), stirring rate = 75 rpm. In (c), stirring rate = 75 rpm, and in (d), stirring rate = 160 rpm.
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(a)
(b)
(c)
(d)
Fig. 7. Determination of three-dimensional fractal dimension (D3 ), based on Eq. (7) (U ∝ l D3 −1 ), from the slopes of the log–log plot of aggregate settling velocity and longest dimension. In (a) and (b), the aggregates were formed in a stirred tank with pure asphaltenes at a toluene-to-heptane ratio (T:H) of 1:5 in solvent mixtures and asphaltene particles concentration of 62.5 mg/L. In (c) and (d), the aggregates were formed in a stirred tank with bitumen at a toluene-to-heptane ratio (T:H) of 1:5 and bitumen concentration of 1000 mg/L. In (a), stirring rate = 36 rpm, and in (b), stirring rate = 75 rpm. In (c), stirring rate = 75 rpm, and in (d), stirring rate = 160 rpm.
(Fig. 7), based on Eqs. (2) and (7), respectively. Alternatively, the 3D fractal dimension can also be obtained using Eq. (5), which was shown in another communication [33]. For asphaltene aggregates formed at different shear rates and particle concentrations, the size of the aggregates varied in a narrow range of 20–200 µm. In summarized form, Table 3 shows that the 2D fractal dimensions fall in the range from 1.57 to 1.71 and the 3D fractal dimensions fall in the range from 1.06 to 1.41. The fractal dimensions obtained from size and settling velocity measurement are statistically analyzed. In the regression analysis, the precision of parameter estimation using standard error [46] is applied to identify whether the results are statistically different for the aggregates formed under four different conditions having different combinations of stirring speed and particle concentration. However, no statistically significant difference is found in fractal dimensions among different groups of asphaltene aggregates studied (Table 3). The large standard error in 3D fractal dimension from experimental data may be caused either by the limitations of the experimental method used or by the real shape distribution of asphaltene aggregates within
the same characteristic length. For such a narrow range of smaller size aggregate (20–200 µm), a large scatter in the experimental observations between aggregate settling velocity and size is also found in Refs. [18,47,48]. Table 4 summarizes the 3D fractal dimension for various aggregates obtained from free-settling experiments. Inorganic flocs usually exhibit higher fractal dimensions, while for the microbial and organic flocs they are smaller. Activated sludge flocs show fractal dimensions ranging from 1.0 to 2.0. Inorganic flocs have fractal dimensions in a higher range, from 1.59 to 2.85. Fractal dimensions of asphaltene aggregates are at the lower limit of the range for activated sludge flocs. The lower fractal dimension derived for this work indicates that the asphaltene aggregates possess a highly porous structure. Moreover, the observation that the 3D fractal dimension of the three-dimensional aggregate structure is less than 2 (which is the Euclidean dimension of a surface) strongly implies that the aggregates have extremely low space-filling capacity. Theoretically, the solid portion in such a structure is so low that it would not fill completely its own projected area. This implication by the
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Table 3 Fractal dimensions obtained from settling tests for asphaltene aggregates formed at toluene-to-heptane solvent ratio (T:H) of 1:15 in the solution Variables of aggregate formation (shear rate; particle concentration)
2D fractal dimension (D2 ± std. error)
3D fractal dimension (D3 ± std. error)
36 rpm; 62.5 mg/L solid asphaltenes 75 rpm; 62.5 mg/L solid asphaltenes 75 rpm; 1000 mg/L bitumen 160 rpm; 1000 mg/L bitumen
1.57 ± 0.08 1.71 ± 0.10 1.71 ± 0.05 1.68 ± 0.05
1.29 ± 0.16 1.41 ± 0.36 1.06 ± 0.11 1.23 ± 0.07
Table 4 Fractal dimensions obtained from free-settling experiments of other studies for inorganic and microbial aggregates and aggregates formed in organic medium Type of aggregate
3D fractal dimension (D3 )
References
Inorganic aggregates Alum Clay–iron Clay–magnesium Alum
1.59–1.97 1.92 1.91 1.55–1.66
Tambo and Watanabe [39]a Tambo and Watanabe [39]a Tambo and Watanabe [39]a Gorczyca and Ganczarczyk [50]
Microbial aggregates Activated sludge Activated sludge Activated sludge Sludge from BFc Sludge from ASBFd Digested sludge
1.0–1.3 1.44–1.49 1.55–2.0 1.79 1.85 1.63–1.66
Tambo and Watanabe [39]b Magara et al. [52]a Li and Ganczarczyk [49] Zahid and Ganczarczyk [53] Park and Ganczarczyk [54] Namer and Ganczarczyk [47]
Aggregates formed in organic medium Asphaltenes
1.06–1.41
This study
a b c d
Calculated by Li and Ganczarczyk [49]. Calculated by Logan and Wilkinson [51]. BF = biological filter. ASBF = aerated submerged biological filter.
fractal dimension of the aggregates is in qualitative agreement with the high porosity of the aggregates reported in another communication [32]. Because fractal dimension may vary with the aggregates generated under different conditions, it can be used to study the factors that affect the process of aggregation. In this study, it can be observed from Table 3 that at the same stirring speed of 75 rpm, asphaltene aggregates formed with solid asphaltenes produced 3D fractal dimension considerably higher than that formed with bitumen. This implies that the presence of other compounds (such as resins, aromatics, and saturates) in bitumen makes the asphaltene aggregates more tenuous and more irregular. Hence, the fractal dimension can link the affecting factor directly to the process of aggregation and the structure of the aggregates. Besides, the fractal nature of the aggregates suggests that the aggregates are filled with gaps of all sizes. It seems possible to quantitatively characterize the gaps in the aggregates by using fractal theory once the fractal dimension of a sample of asphaltene aggregates is determined.
5. Conclusions It has been demonstrated that asphaltene aggregates generated in the flocculation/coagulation process possess fractal features. Several morphological properties of these aggre-
gates are characterized by fractal dimension. In this study, the asphaltene aggregates are formed using a four-pitch blade-type mixing vessel and a Couette apparatus. It can be noted that the experimental standard error in the fractal dimensions obtained for aggregates produced in Couette device are considerably smaller. Basically, flows in a mixing vessel are far from homogeneous with very high shear produced near the blade tip and generally low shear elsewhere. Hence a larger experimental standard error is observed in free-settling tests, where aggregates produced from a jar tester are used. The 2D fractal dimensions observed in the Couette device became higher with increasing shear, indicating that the aggregates became less amorphous and more compact at higher shear rates. The dynamic evolution of asphaltene aggregate structure was monitored by image analysis of the digitized images. The perimeter-based fractal dimension, Dpf , of the flocs was initially found to increase (more open structure) and then to decrease slightly (more compact structure) and reach a steady state as a result of shear-induced breakage and/or restructuring. Shear-induced restructuring also narrows the range of Dpf values as steady state is attained. The steady-state perimeter-based fractal dimensions, Dpfss , of the flocs formed at the lower shear rate of 2.5 s−1 , exhibit no significant dependence on asphaltene concentration or solvent composition.
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In the free-settling test, the size–density fractal dimension (D3 ) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This value is low but comparable with fractal dimensions for activated sludge flocs. This indicates that the asphaltene aggregates are highly porous and more tenuous. Though 3D fractal dimensions determined from settling velocities vary over a wide range, nearly all of the reported values for D in the literature are less than 2.0 (Table 4). In this study, due to experimental constraints the size and density of primary particles, and porosity of the aggregates could not be determined, and hence, the permeability of fractal aggregates was not taken into account for settling velocities. Moreover, depending on the scaling relationship used, the fractal dimension can be underestimated. Thus, while the 3D fractal dimensions reported here may be slightly low, the experimental data of Table 4 reported by other researchers do suggest that fractal dimensions of different type of particles are low, less than 2. From a practical viewpoint, the present study provides quantitative information on the significance of shear rate, particle concentration, and solvent composition on the shape/structure, and consequently density/compactness, of asphaltene aggregates. The fractal dimension (D) values provide an insight into the structure/porosity/density of the aggregates, which can aid in predicting the settling velocity of asphaltene aggregates. This knowledge is significant for proper process design and material handling. Acknowledgments We express our gratitude to the Alberta Department of Energy and Albian Sands Energy Inc. for financial support of this project.
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[12] P.T. Spicer, W. Keller, S.E. Pratsinis, J. Colloid Interface Sci. 184 (1996) 112. [13] C. Selomulya, R. Amal, G. Bushell, T.D. Waite, J. Colloid Interface Sci. 236 (2001) 67. [14] C. Bower, C. Washington, T.S. Purewal, Colloids Surf. A Physicochem. Eng. Aspects 127 (1997) 105. [15] B. Kaye, G.G. Clark, Y. Kydar, Part. Part. Syst. Charact. 2 (1994) 411. [16] S. Lovejoy, Science 216 (1982) 185. [17] D.J. Robinson, J.C. Earnshaw, Phys. Rev. A 46 (1992) 2045. [18] B. Gorczyca, J. Ganczarczyk, Environ. Technol. 17 (1996) 1361. [19] B.B. Mandelbrot, D.E. Passoja, A.J. Paullay, Nature 308 (1984) 721. [20] Q. Jiang, B.E. Logan, Environ. Sci. Technol. 25 (1991) 2031. [21] M.R. Wiesener, Water Res. 26 (1992) 379. [22] B.E. Logan, Environmental Transport Processes, Wiley, New York, 1999. [23] B.E. Logan, D.B. Wilkinson, Biotechnol. Bioengin. 38 (1991) 389. [24] P. Meakin, Adv. Colloid Interface Sci. 28 (1988) 249. [25] C.P. Johnson, X. Li, B.E. Logan, Environ. Sci. Technol. 30 (1996) 1911. [26] R.K. Chakraborti, J.F. Atkinson, J.E. Van Benschoten, Environ. Sci. Technol. 34 (2000) 3969. [27] X.Y. Li, B.E. Logan, Water Sci. Technol. 42 (2000) 253. [28] B.E. Logan, J.R. Hunt, Limnol. Oceanogr. 32 (1987) 1034. [29] K. Stolzenback, Deep-Sea Res. 40 (1993) 359. [30] H.W. Yarranton, Asphaltene Solubility and Asphaltene Stabilized Water-in-Oil Emulsions, Ph.D. thesis, University of Alberta, 1997, pp. 20–66. [31] N.H.G. Rahmani, T. Dabros, J.H. Masliyah, AIChE J. 49 (2003) 1645. [32] N.H.G. Rahmani, T. Dabros, J.H. Masliyah, Ind. Eng. Chem. Res. 44 (2005) 75. [33] N.H.G. Rahmani, T. Dabros, J.H. Masliyah, Energy & Fuels, 2005, in revision. [34] B.B. Mandelbrot, J. Fluid Mech. 72 (1975) 401. [35] B.E. Logan, J.R. Kilps, Water Res. 29 (1995) 443. [36] G. Korvin, Fractal Models in the Earth Sciences, Elsevier, Amsterdam, 1992. [37] D.H. De Boer, M. Stone, L.M.J. Levesque, Hydrol. Process. 14 (2000) 653. [38] B.B. Mandelbrot, Proc. R Soc. London Ser. A Mat. 423 (1989) 1864. [39] N. Tambo, Y. Watanabe, Water Res. 13 (1979) 409. [40] V. Oles, J. Colloid Interface Sci. 154 (1992) 351. [41] S.N. Rogak, R.C. Flagan, J. Colloid Interface Sci. 151 (1992) 203. [42] R.H. Gray, G.M. Kanapilly, Y.S. Cheng, R.K. Wolf, J. Aerosol Sci. 16 (1985) 211. [43] R. Jullien, R. Thouy, Phys. Rev. E 50 (1994) 3878. [44] J. Cai, N. Lu, C.M. Sorensen, Langmuir 9 (1993) 2861. [45] I. Colbeck, Z.F. Wu, J. Phys. D 27 (1994) 670. [46] G.E.P. Box, W.G. Hunter, J.S. Hunter, Statistics for Experiments: An Introduction to Design, Data Analysis, and Model Building, Wiley, New York, 1978. [47] J. Námer, J.J. Ganczarczyk, Water Pollut. Res. J. Canada 29 (1994) 441. [48] D.J. Lee, G.W. Chen, Y.C. Liao, C.C. Hsieh, Water Res. 30 (1996) 541. [49] D. Li, J. Ganczarczyk, Environ. Sci. Technol. 23 (1989) 1385. [50] B. Gorczyca, J. Ganczarczyk, Influence of the nature of the turbidity on some properties of alum coagulation flocs, presented at the 1992 AWWA Annual Conference, Vancouver, Canada, 1992. [51] B.E. Logan, D.B. Wilkinson, Limnol. Oceanogr. 35 (1990) 130. [52] Y. Magara, S. Nambu, K. Utosawa, Water Res. 10 (1976) 71. [53] W.M. Zahid, J.J. Ganczarczyk, Water Res. 24 (1990) 215. [54] J.W. Park, J.J. Ganczarczyk, Environ. Technol. 15 (1994) 945.
Fractal structure of asphaltene aggregates Nazmul H.G. Rahmani a , Tadeusz Dabros b , Jacob H. Masliyah a,∗ a Department of Chemical and Materials Engineering, University of Alberta, Edmonton, AB T6G 2G6, Canada b CANMET, Devon, AB T9G 1A8, Canada
Received 13 July 2004; accepted 30 November 2004 Available online 21 February 2005
Abstract A photographic technique coupled with image analysis was used to measure the size and fractal dimension of asphaltene aggregates formed in toluene–heptane solvent mixtures. First, asphaltene aggregates were examined in a Couette device and the fractal-like aggregate structures were quantified using boundary fractal dimension. The evolution of the floc structure with time was monitored. The relative rates of shear-induced aggregation and fragmentation/restructuring determine the steady-state floc structure. The average floc structure became more compact or more organized as the floc size distribution attained steady state. Moreover, the higher the shear rate is, the more compact the floc structure is at steady state. Second, the fractal dimensions of asphaltene aggregates were also determined in a free-settling test. The experimentally determined terminal settling velocities and characteristic lengths of the aggregates were utilized to estimate the 2D and 3D fractal dimensions. The size–density fractal dimension (D3 ) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This relatively low fractal dimension suggests that the asphaltene aggregates are highly porous and very tenuous. The aggregates have a structure with extremely low space-filling capacity. 2004 Elsevier Inc. All rights reserved. Keywords: Asphaltene; Bitumen; Structure; Fractal; Couette; Aggregation; Fragmentation; Floc; Settling
1. Introduction Petroleum asphaltenes have been the subject of extensive research. On the basis of solubility, asphaltenes are defined as the part of petroleum that is insoluble in n-alkanes and completely miscible in aromatic hydrocarbons such as toluene or benzene [1]. This property is used for the separation of asphaltenes. The above definition is in some sense arbitrary, as the molecular structure of asphaltenes varies significantly depending on their origin, method of oil recovery, and history of extraction [2]. According to their chemical structure, asphaltenes are aromatic multicyclic molecules surrounded and linked by aliphatic chains and heteroatoms; published molar mass data for petroleum asphaltenes range from 500 g/mol to as high as 50,000 g/mol [3]. The polar* Corresponding author. Fax: +1-780-492-2881.
E-mail address: [email protected] (J.H. Masliyah). 0021-9797/$ – see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.11.068
ity and complex structure of asphaltenes lead to their selfassociation, flocculation, and precipitation during the course of heavy-oil processing. The formation of colloidal asphaltene associations in several organic solvents and in crude oil was observed for the first time more than half a century ago [4]. It is postulated that in aromatic solvents, asphaltenes can form micelle-like aggregates above a certain concentration, known as the critical micelle concentration (CMC). The CMC data for asphaltenes in toluene have been determined using a variety of methods, such as measurement of surface tension [5] and calorimetric titration [6,7]. Sheu and Storm [8] have noted that asphaltenes in a good solvent below the CMC are in a molecular state, whereas above the CMC, asphaltene micelle formation occurs in a manner similar to that in surfactant systems but with less uniformity in their structure and more polydispersity. According to other investigations, the structure and the shape of asphaltenic micelle-like associates appear to be much more complicated than those of
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classic surfactant micelles [9,10]. These studies indicate that asphaltene micelle-like associates are formed as a result of multiple interactions: aggregates about 2–5 nm in size either are present in a molecular form or are formed by strong intermolecular attractive forces, while the larger particles are self-associates, formed from these small aggregates by weaker interaction forces. Though many studies have been conducted on the growth of colloidal asphaltene particles in hydrocarbon solutions, the flocculation of asphaltene particles under hydrodynamic shear flow has not been investigated. It bears a significant implication in industrial applications. A mixture of toluene and n-heptane is often used to investigate the stability and the precipitation of asphaltenes. At a certain threshold value of the ratio of n-heptane to toluene, the asphaltenes in solution becomes unstable and asphaltene particles start to precipitate. It is found that when a concentrated solution of asphaltenes in toluene is added to excess heptane, the precipitated asphaltene grows from micrometer-sized primary particles to aggregates that are orders of magnitude larger within a few minutes. The objective of this paper is to study asphaltene aggregates’ settling behavior in order to understand their structural properties. Aggregate structure and size distribution have been known to be of great importance in solid–liquid separation processes such as filtration, sedimentation, and dewatering. The aggregate structure and consequently its density influence the strength of the aggregates [11]. This, in turn, indicates whether an aggregate can sustain the shear experienced during the flocculation process and determines the final characteristic of the aggregates after they undergo growth, breakup, and possible restructuring [12,13]. Image analysis techniques yield data on the basis (in the form) of two-dimensional images of the aggregates being studied, so that once the area and length have been calculated the most interesting feature is the irregularity of the perimeter. In general, there are two basic methods of characterizing aggregates from two-dimensional image data [14]. The first method is to measure the fractal dimension of the aggregate boundary, and the second method is to consider the scaling relationship between either the perimeter and area, or the number density and radius. The first method employs such techniques as variable magnification, mosaic amalgamation, structured walk, dilation logic, and the equispaced method, all of which measure perimeter length as a function of resolution. A summary of the procedures involved and a comparison of the relative merits of these methods is given by Kaye et al. [15]. The second method utilizes perimeter/area measurement [16], nested squares, radius of gyration, and direct correlation, which are all indirect techniques of measuring the density fractal dimension. All these latter techniques have been used by Robinson and Earnshaw [17] to characterize twodimensional aggregates and were found to be in good agreement. Indeed, the majority of the studies using fractal characterization in the current literature utilize one or several
of these techniques. It should be noted that the fractal dimension measured by the boundary method and the density method do not necessarily describe the same physical property of the aggregate, and so may have different values. In particular, they diverge at the morphological extremes of space-filling and tenuous aggregates. Fractal dimensions relate aggregate size to some property in n-dimensions, where n = 1, 2, or 3 and Dn is the fractal dimension in n dimensions. For example, fractal dimensions of aggregates imbedded in one, two, and three dimensions are P ∝ l D1 , A∝l
D2
V ∝l
D3
(1)
,
(2) or
V ∝l , D
(3)
where l is the characteristic length scale, which can be taken either as the shortest, longest, geometric mean, or equivalent radius (based on area) of an aggregate [18], P is the aggregate perimeter, A is the aggregate cross-sectional area (i.e., including the space between particles of an aggregate), and V is the total solid volume of all particles in the aggregate. The subscript on Dn indicates the integer value of Dn for Euclidean geometry. If the subscript is omitted, it is understood that its value is 3, or D = D3 . The fractal dimensions can be obtained from the slopes of log–log plots of the respective aggregate properties in Eqs. (1)–(3) and aggregate length. For Euclidean objects (e.g., a sphere), D1 = 1, D2 = 2, and D3 = 3. The perimeter of irregular objects is larger and the crosssectional area is smaller than the corresponding properties for a spherical object of the same length. As the perimeter of fractal objects increases with particle size, their D1 > 1. Similarly, fractal aggregates become less dense and more irregular as they increase in size and their D2 < 2. These two fractal dimensions therefore quantify the rates of change at which the aggregate perimeter and projected area increase with respect to the characteristic length. Properties of aggregates that affect sedimentation rates, such as porosity, average density, and hydrodynamic radius, are primarily functions of D2 and D3 . Aggregates tend to become more porous with increasing size, resulting in two- and three-dimensional fractal dimensions that are usually less than their corresponding Euclidean values; i.e., D2 < 2 and D3 < 3. If measurement of the perimeter (P ) of an aggregate is performed with an accuracy defined by the smallest length of the measurement (i.e., the resolution), a fractal relationship between the measured perimeter and the projected area (A) of the floc is written as A ∝ P 2/Dpf ,
(4)
where Dpf is the perimeter-based fractal dimension of the floc [19]. This equation is used to investigate the geometry of asphaltene aggregates. Heterogeneously (nonuniformly) packed objects with irregular boundaries can be defined by nonlinear relationships
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where the properties of the object scale with a characteristic length dimension raised to a power called the fractal dimension [20–22]. For example, the aggregate porosity (or effective density) and characteristic length are consistent with power-law relationships, 1 − ε ∼ laD3 −3 ,
(5)
ρeff = (ρa − ρl ) = (1 − ε)(ρp − ρl ) ∝ laD3 −3 ,
(6)
where ε is the aggregate porosity; (1 − ε) is the solid volume fraction in an aggregate; la is the aggregate longest dimension; ρeff is the aggregate effective density; ρa is the aggregate density; ρl is the density of the liquid; ρp is the density of the primary particles used to build the aggregate; and D3 is the three-dimensional fractal dimension for a self-similar structure. If the fractal relationship between aggregate size D −3 and porosity (i.e., (1 − ε) ∼ la 3 ) is included in Stokes’ equation, then this equation leads to the scaling relationship between settling velocity (U ) and aggregate longest dimension (la ) [22] U ∼ laD3 −1 .
(7)
Hence the fractal dimension, D3 , can also be derived from the slope of the log–log plot of settling velocity and aggregate longest dimension. Another fractal geometrical assumption is also important and should be included in Stokes’ law. Logan and Wilkinson [23] used the area–length equation, Eq. (2), in the derivation of Stokes’ law, which produced the scaling relationship U ∼ laD3 −D2 +1 .
(8)
When D3 < 2, a colloidal aggregate viewed in two dimensions is transparent since all particles are visible, and D2 = D3 . However, when D3 2, then D2 = 2 [24]. Thus for D3 < 2, Eq. (8) would predict U ∼ la1 ; but this linear relationship between U and la is not observed experimentally. A few more scaling relationships between U and la were reported for different ranges of Reynolds numbers and fractal dimensions [25]. It was concluded by Johnson et al. [25] that using Eq. (7) is only valid when D3 > 2. If D3 < 2, D2 must be included in the scaling relationship (Eq. (8)). If D2 is not included, the magnitude of D3 will be overestimated. However, in the present study, though the experimentally observed aggregate settling velocities fall into the Stokes regime (Re 1) and D2 < 2, Eq. (8), which includes D2 , cannot be used, as it gives D3 < 1, which is impossible. Hence Eq. (7) is used to determine the 3D fractal dimension of the aggregates. For rapid coagulation, particles with small D3 may be desirable, while for gravity settling a large D3 is preferred [22]. As indicated by Eqs. (7) and (8), both aggregate size and fractal dimension influence the settling velocity, U . Recently, fractal concepts have been used to explain higher observed settling velocities for large aggregates, relative to Stokes settling [25–27]. It was suggested that the internal
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flow through large pores within the fractal aggregates contributes to faster settling velocities. Johnson et al. [25] scrutinized this effect and indicated that the actual settling velocity of a real aggregate is several times faster (on the average 4–8.3 times) than one predicted by Stokes’ law for aggregates of identical size, mass, and primary particle density. On the other hand, Logan and Hunt [28] calculated that the power in a size–settling velocity relationship was only increased slightly from U ∼ d 0.40 to Uperm ∼ d 0.44 after aggregate permeability is accounted for. Others have also found similarly small changes in the aggregate size–settling velocity relationship due to aggregate permeability [29]. Hence by neglecting the flow through the aggregates (i.e., the permeability effect), the three-dimensional fractal dimensions calculated from the settling velocity will be slightly underestimated. The main reason for larger deviation of the experimentally observed settling velocity from Stokes’ velocity is thought to be a result of nonlinear relationships between aggregate size and porosity [28]. In the present experimental studies, the asphaltene aggregates are formed using the Couette device and the jar tester (four-pitched-blade-type flocculator). In the first set of experiments in Couette flow, photographic technique and image analysis are employed to monitor the dynamic evolution of the aggregates structure at different shear rates in terms of the 2D fractal dimension. The structure of the asphaltene aggregates at steady state is found to depend on rotational speed, but not on the solvent composition or particle concentration. In the second set of experiments, asphaltene aggregates are formed in a stirred tank under different experimental conditions and transferred to a quiescent glass settling column having the same solvent mixture. Photographic technique and image analysis are used to determine the aggregate size and settling velocity in the bottom section of the glass column after the aggregates reach the terminal settling velocity. The 2D and 3D fractal dimensions of the aggregates are then determined from the slopes of size–projected area and size–settling velocity regression lines.
2. Materials Asphaltene aggregation in toluene and heptane mixtures was studied with two different feed sources: • Solid asphaltenes that was previously extracted and purified from Athabasca bitumen as described in Section 2.1. The Athabasca bitumen is obtained from a commercial plant. • Athabasca bitumen containing a natural level of asphaltenes that was extracted from oil sands using toluene in the laboratory. It is known as solvent-extracted bitumen. Reagent-grade toluene and heptane were purchased from Fisher Scientific and used as delivered.
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2.1. Preparation of solid asphaltenes The solid asphaltenes used in this study are extracted from Syncrude vacuum-distillation-tower-feed Athabasca bitumen (bitumen that has been treated to remove most of the solids and water). However, the bitumen still contains mineral solids, which make up about 1 wt% of the bitumen [30]. The “solids,” which include fine clays, are insoluble in toluene. To remove the solids, the bitumen is first dissolved in toluene and centrifuged at 35,000g for 30 min. The supernatant liquid is recovered and evaporated until dry, “solids-free” bitumen remains. Asphaltenes are extracted from the “solids-free” bitumen with a 40:1 volume ratio of heptane to bitumen (solids-free). The mixture is stirred for 4 h and left standing to allow the precipitated asphaltenes to settle overnight. Then the supernatant liquid is removed and the remaining precipitate is further diluted with heptane at a 4:1 volume ratio of heptane to asphaltenes. After 4 h, the final mixture is filtered using 0.22-µm Millipore filter paper and the remaining asphaltenes are washed thoroughly with heptane until the filtrate (i.e., heptane) becomes colorless. The precipitated asphaltenes are dried in a vacuum oven dryer at absolute pressure 23 kPa and 50 ◦ C. The drying process usually requires 1 wk. The asphaltenes recovered in this method make up about 16 wt% of the original bitumen. 2.2. Preparation of asphaltene aggregate suspension For the first set of aggregation experiments conducted in a Couette apparatus, dry asphaltene powder is mixed with toluene and is subjected to high-speed stirring for proper mixing. This is retained as a stock of asphaltene–toluene solution. For the aggregation experiments, samples of this stock solution are diluted in toluene and then n-heptane is added to provide the desired solvent composition (i.e., the volume ratio of toluene to heptane in the solution, T:H) and initial asphaltene concentration and a constant stirring speed is then employed to allow floc formation. In the second set of aggregation experiments conducted in a stirred tank, both solid asphaltenes and solvent extracted bitumen were used. Similarly to the procedure described above, bitumen, instead of solid asphaltenes, was dissolved in toluene and the solution was added to excess heptane to investigate asphaltenes aggregation. 3. Experimental apparatus 3.1. Couette device A schematic view of the Couette device (where the asphaltenes–solvent mixture is introduced) is shown in Fig. 1. This device is used because under certain conditions it generates a well-defined shear field. The inner cylinder, with a diameter of 50 mm, is made of Teflon to provide better optical reflection. The outer cylinder, with an inner diameter of
Fig. 1. Schematic of the experimental set-up for the Couette device.
60 mm, is made of Pyrex glass to allow the suspension to be observed. The asphaltene suspension in a toluene–heptane solvent mixture is completely mixed at 300 rpm with a marine propeller for 15 s and is placed into the outer glass cylinder, which is quickly snapped into the Couette device. The rotation of the inner cylinder begins at a required rpm (see Fig. 1). This is considered as the starting time for aggregation. The experiments are carried out at a constant shear rate (G) ranging from 1.2 to 12.7 s−1 . Because of the limited optical resolution, the small asphaltene aggregates and their structural details became visible when the aggregates reached approximately 30 µm in size [31]. For these experiments, the location of the observation area or control volume is 50 mm above the bottom of the cylinders. Images of asphaltene aggregates in suspension are obtained using a microscope (Carl Zeiss Canada Ltd.) coupled with a CCD camera and a video recorder. Image analysis software (Sigma ScanPro 4) is used to calculate the geometrical properties of the aggregates from the captured images. 3.2. Settling column The aggregates used in the free-settling tests were produced in a bench-scale continuously stirred tank of 1.0 L in volume at different fluid shear rates—36, 75, and 160 rpm [32]. In performing the flocculation test, the sample suspension of pure asphaltenes/bitumen in a 1:5 ratio toluene– heptane solvent mixture is first mixed at 660 rpm for 15 s to break up any agglomerates. The impeller, which is a standard 45◦ -angle four-blade pitch turbine positioned at 1/3 of the tank height from the bottom, is then set to the desired speed to produce a constant average fluid shear and allow floc formation. The experimental apparatus for the settling of asphaltene aggregates consists of a Pyrex glass column (Fig. 2). The column is 350 mm in height to ensure that the terminal settling velocity could be reached, and 30 mm in width to neglect the wall effect on aggregate settling. After the average aggregate diameter reached a steady-state size (which is known from the previously performed growth kinetics experiments by PDA [32]), samples were withdrawn
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asphaltene aggregates have rugged, irregular structures and statistical self-similarity, which resemble the shape of cloud and snowflakes. Table 1 shows the one- and two-dimensional fractal dimensions obtained from the log–log plots of aggregate longest dimension (or major axis) versus perimeter and projected area, respectively, based on the analysis of several aggregates formed in a Couette device, and reached steady state at all the employed shear rates. The standard error is applied in determining the slopes from the regression lines. A higher D2 fractal dimension with increasing shear indicates that the aggregates became less amorphous and more compact at higher shear rates. However, the one-dimensional fractal dimension did not show any significant dependence on shear rate. Since the one-dimensional fractal dimension increases with the irregularity of a boundary, the fractal nature of the aggregate perimeter was not correlated with changes in the aggregate area. A similar lack of correlation between D2 and D1 fractal dimensions has previously been found for synthetic as well as marine snow aggregates [35]. From the measurement of the properties of individual aggregates, it is possible to measure the fractal dimension of a population of aggregates having different sizes. As there are several aggregates in each experiment, the perimeter-based fractal dimension, Dpf , of the flocs can be estimated from Eq. (4) using a log–log plot of the floc perimeter and crosssectional area. The value of Dpf is related to the floc surface morphology since Dpf varies between 1 (the projected area of a solid sphere, a circle) and 2 (a line, e.g., a chain of particles). Values of Dpf greater than one have been found for synthetic fractals [19] and a variety of natural objects such as clouds, lakes, and snow patches during melt [36]. The interpretation of Dpf > 1 is that as the objects become larger, i.e., as A increases, P increases more rapidly than for Euclidean objects, so that the boundary becomes more convoluted [37]. Therefore larger values of Dpf represent irregular floc structures. Fig. 3 shows the relation between the projected area (A) of the flocs with their perimeter (P ) on logarithmic coordinates. The perimeter-based fractal dimension of the flocs at steady state (Dpfss ), based on Eq. (4), was derived individually for three different shear rates (i.e., 1.2, 3.8, and 12.7 s−1 ) from Fig. 3 and are shown together for all employed shear rates (i.e., 1.2–12.7 s−1 ) in Fig. 4. The standard error bar is shown on the average Dpfss values in Fig. 4. It shows that at a higher shear rate, G = 12.7 s−1 , the flocs are small and the Dpfss values are smaller (= 1.17 ± 0.02), indicating more
Fig. 2. Experimental arrangement for aggregate settling velocity measurement.
from the stirred tank at certain time intervals (every 15 min) and placed in the settling column. A small amount (about 3 ml) of suspension containing aggregates is gently transferred into the top of the settling column using a rubber dropper bulb with a 10-ml pipette tip cut midway to minimize breakup of the aggregates. The column was filled with the same solvent composition as the original system (i.e., toluene:heptane = 1:5). But this solvent mixture is not saturated with asphaltenes, and hence, small parts of the aggregates added will dissolve during settling. In the present study, this minute loss is neglected due to experimental constraint. Images of asphaltene aggregates, while passing through the observation region in the glass-settling column, were obtained using a microscope objective connected with a CCD camera and a video recorder [33]. A cold fiber-optic light was placed on the same side of the column as the camera to provide reflected lighting from the white background on the other side of the column, which produces clear and sharp pictures. Snappy Video Snapshot, installed under Windows XP, was used to grab and digitize the chosen frames of the recordings. Image analysis software was used to determine the shape, size, and settling velocity of the aggregates from the captured images.
4. Results and discussion 4.1. Determination of aggregate fractal dimension in Couette device The concept of fractal nature proposed in 1975 by Mandelbrot [34] is useful to describe the ruggedness of flocs. The
Table 1 The steady state power law fractal dimensions as a function of shear rate for asphaltene aggregates formed at toluene-to-heptane solvent ratio (T:H) of 1:15 and asphaltene particle concentration of 12.8 mg/L Equation number
Fractal dimension
1 2
D1 D2
Average shear rate (s−1 ) 1.2
2.5
3.8
8.4
12.7
1.08 ± 0.03 1.61 ± 0.03
1.05 ± 0.02 1.80 ± 0.03
1.09 ± 0.03 1.82 ± 0.04
1.06 ± 0.03 1.80 ± 0.03
1.06 ± 0.03 1.90 ± 0.03
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Fig. 3. Determination of perimeter-based fractal dimension for asphaltene aggregates at steady-state (Dpfss ) from image analysis measurements of aggregate cross-sectional area and perimeter.
Fig. 4. Evolution of steady-state perimeter-based fractal dimension (Dpfss ) for asphaltene aggregates as a function of shear rate at a toluene-to-heptane solvent ratio of 1:15 and a particle concentration of 12.8 mg/L. Reducing shear produces more open and irregular aggregate structures at constant particle concentration.
compact and regular structures, while at a lower shear rate (e.g., 1.2 s−1 ), the flocs became more porous and irregular (understood from a higher Dpfss value, about 1.31 ± 0.02). There is a tendency to a smaller Dpfss value at a higher shear, at which the increased amount of fragmentation or erosion and/or restructuring of the floc results in more compact floc structures at steady state. The value of Dpf is a quantitative measure of floc structure that is directly related to the surface fractal dimension, Ds , of the floc [38]. Image analysis of floc structure projections is a more direct and rapid measure of floc structure than light scattering and size or sedimentation velocity measurements, and thus has potential for on-line application in the processing industry. The mass fractal dimension of a floc, Df , is also a measure of floc structure and varies from 1 for a line of particles to 3 for a sphere [38]. However, the Dpf derived from image analysis is a two-dimensional fractal dimension and is not directly related to Df [24].
Fig. 5. Dynamic evolution of the perimeter-based fractal dimension (Dpf ) for asphaltene aggregates for three different shear rates at a toluene-toheptane solvent ratio of 1:15 and an asphaltene particle concentration of 12.8 mg/L. After sufficiently long times, Dpf approaches an asymptotic, steady state value.
Fig. 5 shows the time evolution of Dpf for three different shear rates. The various shear rates (i.e., G) within the Couette device produce a distribution of floc structures as a result of simultaneous shear-induced growth, breakage, and/or restructuring. The Dpf values were determined from the log– log plot of flocs perimeter and projected area, obtained from the analysis of the images taken at a specific time. The graph shows that Dpf increases from its initial value (Dpf = 1, assuming spherical “primary” particles when the experiment starts) and reaches a maximum value as the flocs grow and become more porous. When fragmentation and possibly restructuring begin to dominate, the Dpf value decreases until it reaches a steady-state value. Tambo and Watanabe [39] and Oles [40] suggested that decreased floc porosity (as indicated here by the decreasing perimeter-based fractal dimension) results from the production of strong, dense fragments by preferential breakage of the flocs at weak points. For all cases, Dpf values are obtained using regression analysis. Since a whole population of aggregates is used in these calculations, the calculated fractal dimensions represent a statistical average for the population of aggregates. Individual aggregates may have higher or lower fractal dimensions. The measured steady-state perimeter-based fractal dimensions, Dpfss , for different asphaltene particle concentrations and toluene-to-heptane ratios in the solvent mixture are shown in Table 2. Error limits represent the standard error of the measured values of Dpfss during the experiment. The Dpfss values were not affected significantly at the lower shear rate of 2.5 s−1 by asphaltene particle concentration or toluene-to-heptane ratios in the solvent. A problem arises when the aggregates of interest are three-dimensional objects, which is the case with real systems. The images are two-dimensional projected areas of the actual shape. Consequently, some of the detail of the original shape will be obscured in the projection of the resultant profile. Between 33 and 36% [41,42] of the particles will
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Table 2 The steady-state perimeter-based fractal dimensions (Dpfss ) of asphaltene aggregates as a function of particle concentration and solvent composition for a shear rate of 2.5 s−1 Asphaltene particle concentration (mg/L) Toluene-to-heptane solvent ratio (T:H) Dpfss
4.1 1:7 1.15 ± 0.03
5.3 1:7 1.17 ± 0.03
be hidden. Fractal dimensions measured by image analysis techniques are therefore intrinsically lower than the actual D values for three-dimensional flocs. The maximum permitted value of fractal dimension for both boundary and scaling methods is 2, since in both cases this corresponds to a curve that fills the plane completely; therefore, any object with a mass fractal dimension D > 2 will be underestimated by image analysis techniques. However, Jullien and Thouy [43] have proposed that for D < 2 the values measured from the two-dimensional projected areas concur with the actual value of D and that the perimeter fractal dimension of the two-dimensional objects is a non-trivial continuously varying function of D. According to Rogak and Flagan [41], any object with fractal dimension D > 2 is underestimated by
10.3 1:7 1.16 ± 0.02
8.8 1:3 1.15 ± 0.03
10.3 1:7 1.16 ± 0.02
12.8 1:15 1.17 ± 0.03
10–20% compared to the values obtained using techniques that are sensitive to three-dimensional structure, such as dynamic light scattering [44] and settling velocities [45]. The comparison of values measured by image analysis with values measured by the above techniques should, therefore, be used with caution. 4.2. Derivation of fractal dimension from settling velocity of the aggregates From settling experiments, the 2D and 3D fractal dimensions of the aggregates are calculated from the log–log plot of aggregate projected area vs the longest dimension (Fig. 6), and aggregates settling velocity vs the longest dimension
(a)
(b)
(c)
(d)
Fig. 6. Determination of two-dimensional fractal dimension (D2 ), based on Eq. (2) (A ∝ l D2 ), from image analysis measurements of aggregate projected area and longest dimension. In (a) and (b), the tests were conducted to evaluate the settling velocity of asphaltene aggregates that were formed in a stirred tank with pure asphaltenes at a toluene-to-heptane ratio (T:H) of 1:5 in solvent mixtures and an asphaltene particle concentration of 62.5 mg/L. In (c) and (d), asphaltene aggregates were formed in a stirred tank with bitumen at a toluene-to-heptane ratio (T:H) of 1:5 and a bitumen concentration of 1000 mg/L. In (a), stirring rate = 36 rpm, and in (b), stirring rate = 75 rpm. In (c), stirring rate = 75 rpm, and in (d), stirring rate = 160 rpm.
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(a)
(b)
(c)
(d)
Fig. 7. Determination of three-dimensional fractal dimension (D3 ), based on Eq. (7) (U ∝ l D3 −1 ), from the slopes of the log–log plot of aggregate settling velocity and longest dimension. In (a) and (b), the aggregates were formed in a stirred tank with pure asphaltenes at a toluene-to-heptane ratio (T:H) of 1:5 in solvent mixtures and asphaltene particles concentration of 62.5 mg/L. In (c) and (d), the aggregates were formed in a stirred tank with bitumen at a toluene-to-heptane ratio (T:H) of 1:5 and bitumen concentration of 1000 mg/L. In (a), stirring rate = 36 rpm, and in (b), stirring rate = 75 rpm. In (c), stirring rate = 75 rpm, and in (d), stirring rate = 160 rpm.
(Fig. 7), based on Eqs. (2) and (7), respectively. Alternatively, the 3D fractal dimension can also be obtained using Eq. (5), which was shown in another communication [33]. For asphaltene aggregates formed at different shear rates and particle concentrations, the size of the aggregates varied in a narrow range of 20–200 µm. In summarized form, Table 3 shows that the 2D fractal dimensions fall in the range from 1.57 to 1.71 and the 3D fractal dimensions fall in the range from 1.06 to 1.41. The fractal dimensions obtained from size and settling velocity measurement are statistically analyzed. In the regression analysis, the precision of parameter estimation using standard error [46] is applied to identify whether the results are statistically different for the aggregates formed under four different conditions having different combinations of stirring speed and particle concentration. However, no statistically significant difference is found in fractal dimensions among different groups of asphaltene aggregates studied (Table 3). The large standard error in 3D fractal dimension from experimental data may be caused either by the limitations of the experimental method used or by the real shape distribution of asphaltene aggregates within
the same characteristic length. For such a narrow range of smaller size aggregate (20–200 µm), a large scatter in the experimental observations between aggregate settling velocity and size is also found in Refs. [18,47,48]. Table 4 summarizes the 3D fractal dimension for various aggregates obtained from free-settling experiments. Inorganic flocs usually exhibit higher fractal dimensions, while for the microbial and organic flocs they are smaller. Activated sludge flocs show fractal dimensions ranging from 1.0 to 2.0. Inorganic flocs have fractal dimensions in a higher range, from 1.59 to 2.85. Fractal dimensions of asphaltene aggregates are at the lower limit of the range for activated sludge flocs. The lower fractal dimension derived for this work indicates that the asphaltene aggregates possess a highly porous structure. Moreover, the observation that the 3D fractal dimension of the three-dimensional aggregate structure is less than 2 (which is the Euclidean dimension of a surface) strongly implies that the aggregates have extremely low space-filling capacity. Theoretically, the solid portion in such a structure is so low that it would not fill completely its own projected area. This implication by the
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Table 3 Fractal dimensions obtained from settling tests for asphaltene aggregates formed at toluene-to-heptane solvent ratio (T:H) of 1:15 in the solution Variables of aggregate formation (shear rate; particle concentration)
2D fractal dimension (D2 ± std. error)
3D fractal dimension (D3 ± std. error)
36 rpm; 62.5 mg/L solid asphaltenes 75 rpm; 62.5 mg/L solid asphaltenes 75 rpm; 1000 mg/L bitumen 160 rpm; 1000 mg/L bitumen
1.57 ± 0.08 1.71 ± 0.10 1.71 ± 0.05 1.68 ± 0.05
1.29 ± 0.16 1.41 ± 0.36 1.06 ± 0.11 1.23 ± 0.07
Table 4 Fractal dimensions obtained from free-settling experiments of other studies for inorganic and microbial aggregates and aggregates formed in organic medium Type of aggregate
3D fractal dimension (D3 )
References
Inorganic aggregates Alum Clay–iron Clay–magnesium Alum
1.59–1.97 1.92 1.91 1.55–1.66
Tambo and Watanabe [39]a Tambo and Watanabe [39]a Tambo and Watanabe [39]a Gorczyca and Ganczarczyk [50]
Microbial aggregates Activated sludge Activated sludge Activated sludge Sludge from BFc Sludge from ASBFd Digested sludge
1.0–1.3 1.44–1.49 1.55–2.0 1.79 1.85 1.63–1.66
Tambo and Watanabe [39]b Magara et al. [52]a Li and Ganczarczyk [49] Zahid and Ganczarczyk [53] Park and Ganczarczyk [54] Namer and Ganczarczyk [47]
Aggregates formed in organic medium Asphaltenes
1.06–1.41
This study
a b c d
Calculated by Li and Ganczarczyk [49]. Calculated by Logan and Wilkinson [51]. BF = biological filter. ASBF = aerated submerged biological filter.
fractal dimension of the aggregates is in qualitative agreement with the high porosity of the aggregates reported in another communication [32]. Because fractal dimension may vary with the aggregates generated under different conditions, it can be used to study the factors that affect the process of aggregation. In this study, it can be observed from Table 3 that at the same stirring speed of 75 rpm, asphaltene aggregates formed with solid asphaltenes produced 3D fractal dimension considerably higher than that formed with bitumen. This implies that the presence of other compounds (such as resins, aromatics, and saturates) in bitumen makes the asphaltene aggregates more tenuous and more irregular. Hence, the fractal dimension can link the affecting factor directly to the process of aggregation and the structure of the aggregates. Besides, the fractal nature of the aggregates suggests that the aggregates are filled with gaps of all sizes. It seems possible to quantitatively characterize the gaps in the aggregates by using fractal theory once the fractal dimension of a sample of asphaltene aggregates is determined.
5. Conclusions It has been demonstrated that asphaltene aggregates generated in the flocculation/coagulation process possess fractal features. Several morphological properties of these aggre-
gates are characterized by fractal dimension. In this study, the asphaltene aggregates are formed using a four-pitch blade-type mixing vessel and a Couette apparatus. It can be noted that the experimental standard error in the fractal dimensions obtained for aggregates produced in Couette device are considerably smaller. Basically, flows in a mixing vessel are far from homogeneous with very high shear produced near the blade tip and generally low shear elsewhere. Hence a larger experimental standard error is observed in free-settling tests, where aggregates produced from a jar tester are used. The 2D fractal dimensions observed in the Couette device became higher with increasing shear, indicating that the aggregates became less amorphous and more compact at higher shear rates. The dynamic evolution of asphaltene aggregate structure was monitored by image analysis of the digitized images. The perimeter-based fractal dimension, Dpf , of the flocs was initially found to increase (more open structure) and then to decrease slightly (more compact structure) and reach a steady state as a result of shear-induced breakage and/or restructuring. Shear-induced restructuring also narrows the range of Dpf values as steady state is attained. The steady-state perimeter-based fractal dimensions, Dpfss , of the flocs formed at the lower shear rate of 2.5 s−1 , exhibit no significant dependence on asphaltene concentration or solvent composition.
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In the free-settling test, the size–density fractal dimension (D3 ) of the asphaltene aggregates was estimated to be in the range from 1.06 to 1.41. This value is low but comparable with fractal dimensions for activated sludge flocs. This indicates that the asphaltene aggregates are highly porous and more tenuous. Though 3D fractal dimensions determined from settling velocities vary over a wide range, nearly all of the reported values for D in the literature are less than 2.0 (Table 4). In this study, due to experimental constraints the size and density of primary particles, and porosity of the aggregates could not be determined, and hence, the permeability of fractal aggregates was not taken into account for settling velocities. Moreover, depending on the scaling relationship used, the fractal dimension can be underestimated. Thus, while the 3D fractal dimensions reported here may be slightly low, the experimental data of Table 4 reported by other researchers do suggest that fractal dimensions of different type of particles are low, less than 2. From a practical viewpoint, the present study provides quantitative information on the significance of shear rate, particle concentration, and solvent composition on the shape/structure, and consequently density/compactness, of asphaltene aggregates. The fractal dimension (D) values provide an insight into the structure/porosity/density of the aggregates, which can aid in predicting the settling velocity of asphaltene aggregates. This knowledge is significant for proper process design and material handling. Acknowledgments We express our gratitude to the Alberta Department of Energy and Albian Sands Energy Inc. for financial support of this project.
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