Investigation on AgglomerationâFragmentation Processes in Colloidal

Energy & Fuels 2009, 23, 967–974

967

Investigation on Agglomeration-Fragmentation Processes in Colloidal Asphaltene Suspensions Ali Reza Solaimany-Nazar* and Hassan Rahimi Department of Chemical Engineering, UniVersity of Isfahan, Hezarjarib Street, Isfahan, Iran ReceiVed August 30, 2008. ReVised Manuscript ReceiVed NoVember 26, 2008

In situ image analyzing measurements are applied in determining the evolution of crude oil asphaltene aggregate size distribution in toluene solutions. The experimental data are compared to the predictions of a population balance model. The effect of different asphaltenes nature on the fractal-like aggregate size is investigated as a function of shear rate and toluene to n-heptane volume ratio. Good agreement is found for the average size evolution of asphaltene aggregate size distribution, assuming a fractal approach for model discretization. Initially, the average-number asphaltene aggregate size increases with time and then beyond a maximum value decreases to an almost constant steady-state size. The aggregates fractal dimension value can strongly affect the evolution kinetics of aggregation.

Introduction It is well known that asphaltene precipitation and deposition from crude oils may give rise to a number of problems1,2 including formation damage3,4 and fouling of the production and surface handling facilities.5 Asphaltenes in crude oil are partly dissolved and partly in colloidal and/or micellar form stabilized by resins adsorbed on their surface.6 The low molecular weight part of the asphaltene distribution is dissolved, and its high molecular weight fraction is in the form of colloidal suspension in paraffinic oils and in micellar format in aromatic oils. These components are defined as the portion insoluble in n-heptane but soluble in toluene.7,8 Disruption of the equilibrium conditions of this colloidal system may result in irreversible aggregation of asphaltenes. As noted in the literature, asphaltene aggregates are permeable and have fractal-like structure. In general, fractals can be defined as disordered self-similar systems with a noninteger dimension. Proper analysis of the scattering intensity curves can provide aggregate size, shape, molecular weight, and fractal aggregate dimension.9-12 The fractal dimension value of an aggregate gives a quantitative description of the packing of the particles within the aggregates and is expected to explain the rheological and mechanical aggregate properties. * To whom correspondence should be addressed. Telephone: 0098-3117934027. Fax: 00983117934031. E-mail: [email protected]. (1) Garcia, M. C.; Carbognani, L. Energy Fuels 2001, 15, 1021–1027. (2) Mansoori, G. A. J. Pet. Sci. Eng. 1997, 17, 101–111. (3) Islam, M. R. In Asphaltenes and Asphalts; Yen, T. F., Chilingarian, G. V., Eds.; Elsevier: Amsterdam, 1994; pp 249-298. (4) Reyadh, A. A. J. Pet. Sci. Eng. 2004, 42, 152–170. (5) Garland, E. SPE Annual Technical Conference and Exhibition, SPE No.19731, San Antonio, TX, Oct 1989. (6) Hirschberg, A.; deJong, L. N. J.; Schipper, B. A.; Meijer, J. G. Soc. Pet. Eng. 1984, 24, 283–293. (7) Sheu, E. Y.; Storm, D. A. In Asphaltenes: Fundamentals and Applications; Sheu, E. Y., Mullins, O. C., Eds.; Plenum Press: New York, 1995; pp 1-52. (8) Sahimi, M.; Rassamdana, H.; Dabir, B. SPE J. 1997, 2, 157–169. (9) Rassamdana, H.; Sahimi, M. AIChE J. 1996, 42, 3318–3332. (10) Sahimi, H.; Rassamdana, H. Physica A 1997, 240, 419–431. (11) Fenistein, D.; Barre’, L.; Brosseta, D.; Espinat, D.; Livet, A.; Roux, J. N.; Scarsella, M. Langmuir 1998, 14, 1013–1020. (12) Roux, J. N.; Broseta, D.; Deme’, B. Langmuir 2001, 17, 5085– 5092.

The fractal nature of asphaltene aggregates was defined first in 1980s.13,14 Those authors determined the asphaltene fractal dimensions. They have fractal dimensions in the range of df ) 1.06-2.5 based on the aggregation mechanism.8-10,15-18 Diffusion-limited particles aggregation and diffusion-limited cluster-cluster aggregation are introduced as the main mechanisms of asphaltene aggregation processes, when a solvent is injected into a system containing crude oil, for small and large nonsettling aggregates, respectively. The mass to particle size scaling relationship for diffusion-limited cluster-cluster aggregates with a nanoparticle fractal dimension of 2.5 is estimated to be consistent with a primary particle size of ∼5.8 Å.9 A good way to understand how asphaltene aggregates cause foregoing difficulties is simultaneous modeling of asphaltene particles coagulation and fragmentation processes. Results of such models can include asphaltene aggregate size distribution and its evolutions. One of the common methods for modeling of particulate processes to predict the particle size distribution (PSD) and its evolution is population balance (PB) modeling. The population balance is widely used to model aggregation processes in fields such as crystallization,19 polymerization,20 coagulation of colloid,21 and aerosol coalescence.22 A limited number of papers have discussed the dynamic prediction of asphaltnene aggregation using a population balance,23,24 and fundamental experimental data on PSD of asphaltene aggregates (13) Park, S. J.; Mansoori, G. A. Proceedings of the UNITAR/UNDP 4th International Conference on HeaVy Crudes and Tar Sands, Edmonton, Alberta, Aug 1988. (14) Park, S. J.; Mansoori, G. A. Int. J. Energy Sources 1988, 10, 109– 125. (15) Dabir, B.; Nematy, M.; Mehrabi, A. R.; Rassamdana, H.; Sahimi, M. Fuel 1996, 75, 1633–1645. (16) Rastegari, K.; Svrcek, W. Y.; Yarranton, H. W. Ind. Eng. Chem. Res. 2004, 43, 6861–6870. (17) Rahmani, N. H. G.; Dabros, T.; Masliyah, J. H. J. Colloid Interface Sci. 2005, 285, 599–608. (18) Rahmani, N. H. G.; Dabros, T.; Masliyah, J. H. Energy Fuels 2005, 19, 1099–1108. (19) Randolph, A. D.; Larson, M. A. Theory of Particulate Processes, 2nd ed.; Academic Press: New York, 1988. (20) Stockmayer, W. H. J. Chem. Phys. 1943, 11, 45–55. (21) von Smoluchowski, M. Z. Phy. Chem. 1916, 17, 129–168. (22) Friedlander, S. K. Smoke, Dust and Haze; Wiley: New York, 1977.

10.1021/ef800728h CCC: $40.75  2009 American Chemical Society Published on Web 02/02/2009

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Solaimany-Nazar and Rahimi

are few.23-25 In a more recent paper, a population balance model was developed to determine the evolution of the crude oil asphaltene fractal aggregate size distribution.24 The model predictions have good accuracy in comparison with the experimental results that were obtained by the image processing method. Effects of shear rate, solvent composition, and initial particle size were studied on the evolution of the number-average diameter. Accurate experimental studies on asphaltenes of different crudes sources needed to be carried out in order to check the predictive capacity of this model. The main aim of this paper was to provide new asphaltene aggregate size distribution data in diluted colloidal asphaltene suspensions of the three different Iranian crudes to study the hydrodynamic effects and extracted asphaltene nature on results. The population balance model developed by Solaimany Nazar and Rahimi24 was used as a kinetic framework to analyze the experimental results. Theoretical Section Basic Theory. A population balance model based on the fractal discretization of aggregates size domain is used in this paper. The unsteady-state model considering both the aggregation and the breakage processes may predict the dynamic evolution of the asphaltene aggregates size distribution in shearinduced petroleum solutions. A simplified form of PBE in a system with constant volume and without supersaturation is as follows (1)

where n is the particle number density of size L (or volume V) and is defined as the particle number per unit size in unit volume of suspension or solution (e.g., n, no/(m · .m3) or no/(m3 · m3)). BA and DA are19 1 2

∫

V

0

C(u, V - u)n(u)n(V - u)du

DA(V) ) n(V)

∫

∞

0

(2)

C(V, V′)n(V ′ )dV′

(3)

The function C(V,V′) is the aggregation kernel that describes the rate at which particles of volumes V and V′ collide and coalesce. BB and DB are presented as follows26 BB(V) )

∫

∞

V

γ(V, V″)S(V″)n(V″)dV″

(4)

DB(V) ) -S(V)n(V)

(5)

S(V) is the breakup rate function of aggregates of size V, and γ(V,V″) is the breakup distribution function defining the volume fraction of the fragments of size V breaking from the larger aggregates of size V″. Model Description. A discretized form of eq 1 is used to determine PSD27 i-1 dNi i-2 j-i+1 1 2 ) 2 Ci-1,jNi-1Nj + Ci-1,i-1Ni-1 - Ni 2j-iCi,jNj dt 2 j)1 j)1

∑

∑

imax

- Ni

∑C

i,jNj - SiNi +

j)1

Ci,j ) Ri,jβi,j

imax

∑Γ

i,jSjNj

(6)

j)i+1

(23) Rahmani, N. H. G.; Dabros, T.; Masliyah, J. H. Chem. Eng. Sci. 2004, 59, 685–697. (24) Solaimany Nazar, A. R.; Rahimi, H. Energy Fuel 2008, 22, 3435– 3442.

(7)

where Ri,j is the collision efficiency of particles of volumes Vi and Vj. As aggregation proceeds, particles grow as porous objects with highly irregular and open structures. They are usually referred to as fractal aggregates, characterized by their fractal dimension df. The collision efficiency of unity appears realistic for fractal structure aggregates such as asphaltene.29 For a fractal aggregate with mass equivalent volume of Vi, the collision diameter dc,i is related to the number of primary particles xi of diameter dp in it as follows30 1

dc,i ) dpxi ⁄df

(8)

The collision frequency of fractal aggregates is given as follows29 1

dn(V) ) BA - DA + BB - DB dt

BA(V) )

where Ni is the number of particles of characteristic size Vi in unit volume of suspension or solution (e.g., Ni: no/m3), Ci,j is the aggregation kernel that describes the rate at which particles of volumes Vi and Vj collide and coalesce, Si is the breakup rate function of aggregates of size Vi, and Γi,j is the breakup distribution function defining the volume fraction of the fragments of size Vi breaking from the larger aggregates of size Vj. Aggregation Kernels. The orthokinetic aggregation mechanisms and asphaltene fractal-like aggregate structure approach are considered in modeling. The aggregation kernel of this approach is based on the idea that all collisions form larger aggregates. The aggregation kernel is expressed as28

1

3

βi,j ) 0.31GVP(xi ⁄df + xj ⁄df)

(9)

Particles Nature Effect on Aggregation. The nature of the particles has no direct effect on the collision efficiency. The particles nature influences the fractal dimensions and in turns the aggregate collision diameter, which affects the aggregation kernel magnitude. The existing velocity gradient in suspension is considered the only effective transfer mechanism of a particle to an aggregate or another particle surface by assuming orthokinetic aggregation. If there is a possible relationship between the asphaltene aggregate fractal dimension and the structural parameters, the effect of crude nature on orthokinetic aggregation will be determined. Brownian motion causes fine particles to collide with each other in a perikinetic mechanism. The collision efficiency depends on the particles thermal energy and physical properties of particles and surrounding media. The effect of the perikinetic aggregation mechanism is neglected as the large aggregates form in suspension. Besides, aggregates rapidly collide with each other in the shear-induced condition. Brownian motion may be ignored in comparison with the rapid particles motion in suspension under shear rate.29 Fragmentation Kernel. The fragmentation kernel for fractal aggregates in dilute suspensions (that the viscosity of suspension is not affected by solid particles) is given by as follows29 1

Si ) A′GqVp⁄3

( ) dc,i dp

3⁄ df

(10)

(25) Nielsen, B. B.; Svreck, W. Y.; Mehrotra, A. K. Ind. Eng. Chem. Res. 1994, 33, 1324–1330. (26) Zhang, J.; Li, X. AIChE J. 2003, 49, 1870–1882. (27) Hounslow, M. J.; Ryall, R. L.; Marshall, V. R. AIChE J. 1988, 34, 1821–1832. (28) Kusters, K. A.; Wijers, J. G.; Thoenes, D. Chem. Eng. Sci. 1997, 52, 107–121. (29) Barthelmes, G.; Pratsinis, S. E.; Buggisch, H. Chem. Eng. Sci. 2003, 58, 2893–2902. (30) Matsoukas, T.; Friedlander, S. K. J. Colloid Interface Sci. 1991, 146, 495–506.

Agglomeration-Fragmentation Processes

Energy & Fuels, Vol. 23, 2009 969

Table 1. Properties of Crude Oils Come from SARA Test, Elemental Analysis33 samples properties

Bangestan

Mansoori

Maroon

% wt asphaltene % wt resin % wt aromatic % wt aliphatic asphaltene N mass% C mass% H mass% H/C resin N mass% C mass% H mass% H/C

17.7 2.4 19.7 30.5

15.2 3.7 7.9 29.6

10.4 2.0 31.4 33.8

0.5 82.4 7.6 1.11

1.2 83.3 7.8 1.12

1 83.6 7.6 1.09

2.6 82.1 9.2 1.34

2.6 81.4 9.3 1.37

2.7 81.7 9 1.32

G)

where A′ and q are the fragmentation parameters which are determined experimentally. A binary fragmentation (or aggregate splitting) model was accepted in the modeling, which has a distribution form Γi,j )

{

2 (Vi ) Vj ⁄ 2) 0 (Vi * Vj ⁄ 2)

nonsupersaturated state. Images from the samples were captured using the CCD camera every 2 min. During image capturing the speed of the motor was fixed on constant values corresponding to appropriate shear rates. The first image was used as the initial conditions of the run. The induced shear rate was computed from following relation

(11)

Initial Condition. The initial number-average diameter was obtained from the first image experimentally, and a binary distribution of asphaltene aggregates was assumed for the initial condition. Further details of modeling have been reviewed elsewhere.24 Experimental Section Materials. Measurements were performed on the three different extracted asphaltene of Iranian crude samples. They were sampled from Bangestan, Mansoori, and Maroon Oil Fields located south of Iran. Initially, residues of crude oils were obtained following ASTM method D86.31 Then, insoluble normal heptane asphaltenes were isolated as specified in ASTM-D6560-00.32 Finally, asphaltenes were dried and their powders used to prepare samples for experiments. Toluene and normal heptane solvents were obtained from Merck Co. and were 99%+ pure. Table 1 shows the properties of crude oils come from the SARA test and elemental analysis.33 Apparatus. The evolution of the asphaltene aggregate size distribution in shear-induced suspensions was determined by an image processing method. The experimental apparatus, which has been described in a previous paper,24 is composed essentially of a two coaxis cylinders, a charge-coupled device (CCD) camera, a microscope, a cold light source, and image analysis software. The inner Teflon cylinder can rotate by means of an electromotor. The outer cylinder is made of glass and is static. The samples were poured in the small annulus gap between two cylinders. Rotation of the inner cylinder induces a velocity gradient in suspension. This device allows capturing of asphaltene aggregates images and calculation of their geometrical properties using image analysis software. Sample Preparation and Test at Different Shear Rates. Asphaltene powders were dissolved in toluene to prepare stock solutions with a concentration of 1 g/L. Experiments carried out with stock solution samples were reflocculated by adding n-heptane on various toluene-n-heptane volume ratios (T:H). Each experimental run involved 10 min preinduction of a vigorous shear rate on the samples transferred to the device cell to achieve a (31) Annual Book of ASTM Standards; American Society for Testing and Materials: Philadelphia, PA, 2005; Standard No. D86-01, Vol. 05.01. (32) Annual Book of ASTM Standards; American Society for Testing and Materials: Philadelphia, PA, 2005; Standard No. D6560-00, Vol. 05.03. (33) Solaimany Nazar, A. R.; Bayandory, L. Iranian J. Chem. Eng 2008, 5, 3–12.

riω ∆U ) td ro - ri

(12)

where∆Uis the linear velocity difference of two cylinders, ω is the rotational speed of the inner cylinder, and td, ri, and roare annulus radial distance and inner and outer cylinders radiis, respectively.

Results and Discussion Asphaltene Precipitation by Flocculent Titration. Figure 1 presents the heptane-insoluble asphaltene solid volume fraction, φs, versus the heptane to toluene volume ratio for the three studied crude asphaltenes. Increasing the heptane to toluene volume ratio increases asphaltene solid, but because of total solution volume magnification, φs cannot increase higher than a maximum. Asphaltene Aggregate Size Distribution. All of the experimental data were obtained using an image processing method. This technique is an in situ and nonintrusive technique.23 Figures 2, 3, and 4 show the effect of the solvent ratio on the kinetics of asphaltene aggregate growth in terms of the number-average diameter as a function of time for Bangestan, Mansoori, and Maroon extracted asphaltene under a constant shear, respectively. Experiments are carried out at various solvent compositions, i.e., T:H in solvent mixture varied between 1:3 and 1:9. The shear rate is kept fixed at 3.76 s-1 for Bangestan asphaltene suspensions and 5.64 s-1 for the other two asphaltene crude suspensions. One should notice that the trends of the kinetics results of are very alike, indicating, in principle, that the aggregation fragmentation mechanisms are identical for the three samples. The kinetics behavior of aggregation weakly depends on the solvent composition. As shear induction starts the number-average diameter of aggregates rapidly increases with time and peaks at a certain time. This behavior is related to the dominant kinetics of orthokinetic aggregation of aggregates. After passing through this maximum size the average aggregate size is followed by a decrease region before reaching the final plateau value. The fragmentation rate of aggregates is very high during the declining period, and it can inhibit further growth of aggregates. In general, results concerning the ultimately steadystate particles size would suggest that the dynamic balance between the aggregation and fragmentation rates rules the kinetics of the asphaltene evolution process. It can be inferred from Figure 4 that the aggregate average size depends on the asphaltene content out of solution which is presented in Figure 1. As the asphaltene out of solution concentration increases there is an observable increase in the average size value. A lower asphaltene volume fraction leads to a decrease in the average size value. The kinetics behavior of aggregates obeys the trend of asphaltene solubility in solution. This behavior is in good qualitative agreement with the experimental literature data.34 The results in Figures 2 and 3 do not seem to follow the trends of Bangestan and Mansoori asphaltene solubility, appearing in Figure 1, in the whole time range. The effect of the media nature on the aggregation evolution and other fragmenta(34) Rahmani, N. H. G.; Dabros, T.; Masliyah, J. H. Ind. Eng. Chem. Res. 2005, 44, 75–84.



Figure 1. Asphaltene solid volume fraction of the three crude samples vs n-heptane to toluene volume ratio.

Figure 2. Evolution of asphaltene number diameter at different values of T:H under G ) 3.76(1/s) for Bangestan crude.

Figure 3. Evolution of asphaltene number average diameter at different values of T:H under G ) 5.64(1/s) for Mansoori crude.

tion mechanisms like restructuring may be responsible of observed results, mainly in the higher asphaltene concentrations. Although the T:H volume ratio of solvent affects the asphaltene solubility in solution, the influence of the media on intermo-

lecular forces between asphaltene particles in various T:H ratios and asphaltene concentrations may not be neglected. The model prediction has been examined successfully for Bangestan crude oil before.24 In Figures 5 and 6 a comparison



Figure 4. Evolution of asphaltene number average diameter at different values of T:H under G ) 5.64(1/s) for Maroon crude.

Figure 5. Cumulative asphaltene aggregate size distribution of Mansoori crude at various stages of growth under a shear rate of 3.76 (1/s) at T:H ) 1:9 (a, b, c, d, e, and f correspond to 3, 9, 15, 19, 24, and 29 min, respectively): symbols, experimental results; solid line, model prediction.

of the cumulative aggregate diameter distribution predicted by the PB model and those obtained by experiment are presented for Mansoori and Maroon, respectively. The vertical axis shows the relative number frequency (Ni/Ntotal) that is the ratio of the number concentration of particles in ith size domain to the total number concentration of particles in all bins.23 As can be clearly seen, in both considered crudes, the predicted values are in a satisfactory agreement with the experimental results. The appropriate evaluated fractal dimension values for the asphaltenes samples are listed in Table 2. The fractal dimensions given in Table 2 are very close together for the three crudes, with an average of 1.65, but not the same.

Effect of the Fractal Dimension of Asphaltene on the Asphaltene Aggregate Size Distribution. There is no direct parameter in the population balance model with respect to the nature and composition of crude oil and, consequently, its influence on the asphaltene aggregate size distribution. It is a fact that structural parameters have effects on the fractal dimension value. The crude oil nature and composition affects the fractal dimension value, out of solution concentration, and initial aggregates size distribution of asphaltene. The predicted evolution results of the number-average aggregate diameters of the three asphaltene different sources are presented in Figure 7 for T:H ) 1:9 and G ) 5.64 s-1 with 100 µm initial mean



Figure 6. Cumulative asphaltene aggregate size distribution of Marroon crude at various stages of growth under a shear rate of 3.76 (1/s) at T:H ) 1:9 (a, b, c, d, e, and f correspond to 2, 6, 10, 15, 20, and 30 min, respectively): symbols, experimental results; solid line, model prediction. Table 2. Fractal Dimension Values of Asphaltenes Samples asphaltene sample

fractal dimension value

Bangestan Mansoori Maroon

1.6 1.7 1.64

aggregate sizes. The Bangestan asphaltene has a greater average aggregates size compared with the other two samples during the aggregate evolution process except for a sufficiently short initial time. At T:H ) 1:9 the out of solution asphaltene concentration for all crude samples is almost the same. The different evolution processes are due to the different fractal dimensions of asphaltene aggregates in the three sources. It should be noted that the evaluated fractal dimensions listed in Table 2 are average values during aggregation proceeding with time. Moreover, the results shown in Figure 7 show that beyond the maxima of curves the average size of the aggregates approach a nearly constant value. Fragmentation and restructuring processes produce smaller and more compact aggregates after a sufficiently long time within the same fractal dimension. The aggregates fractal dimension value can strongly affect the evolution trend of agglomeration. Figure 8 depicts the predicted results of the variation of asphaltene fractal dimension values in the range from 1.5 to 3 on the number-average aggregate diameter for hypothetical suspensions. The required time for achieving maximum aggregate size is illustrated in the figure as a function of the fractal dimension. The initial numberaverage aggregate diameter has been chosen to be 100 µm, and the induced shear rate on suspension is set to be equal, G ) 5.64 s-1. The lower the fractal dimension (which may correspond to the more porous and brittle aggregates) the shorter the time it takes to peak and the higher the value of eventually steady-state aggregate average sizes. It means that the effects of the aggregation and breakage processes on the evolution kinetics are considerably rapid for aggregates with a lower fractal dimension value as compared to the higher value.

Aggregates Fractal Dimension Variation in Evolution Kinetic. The aggregation mechanism affects strongly the aggregate morphology and magnitudes of structural parameters. Recently, a descriptive model for asphaltene association and precipitation was proposed based on the idea that these phenomena are controlled by different intermolecular forces.35 It was suggested that asphaltenes aggregate through 2-D stacking interactions in which the highly flexible monomolecular sheets spontaneously bend out of the aromatic plane forming hollow spherical vesicles.35 This vesicle model was quantitatively consistent with both scattering and viscosity data. In this model aggregation is proposed to drive by strong specific forces (hydrogen bonds, for instance) at the periphery of the asphaltene molecules, and precipitation of asphaltene aggregates is determined by the weaker and nonspecific van der Waals attractions between aggregates. It is then to be expected that the fractal dimensions of aggregates may appreciably differ if the aging time is included through the path from asphaltene association to its precipitation. The scattering data of ref 11 is verified by the effect of the aging time on the aggregation mechanism alterationfromdiffusion-limitedparticlestodiffusioncluster-cluster aggregation, which leads to a variation of the fractal dimension values. It was interpreted that some mechanisms like, a sticking probability lower than one, breakage of the clusters above a certain size would increase the fractal dimension of aggregates in a colloidal system. Experimentally, aggregation coupled with sedimentation has been studied more extensively by Allain and collaborators,36,37 who found an increase in the fractal dimension of the large, settling aggregates (reaching values as high as 2.2).36,37 It is conceivable that also a restructuring of the large (35) Porte, G.; Zhou, H.; Lazzeri, V. Langmuir 2003, 19, 40–47. (36) Allain, C.; Cloitre, M.; Wafra, M. Phys. ReV. Lett. 1995, 74, 1478– 1481. (37) Allain, C.; Cloitre, M.; Parisse, F. J. Colloid Interface Sci. 1996, 178, 411–416.



Figure 7. Comparison of the model predicted evolutions of number-average diameter of the three crude asphaltene for T:H ) 1:9 and G ) 5.64(1/ s) with initial average aggregate sizes ) 100 µm.

Figure 8. Model prediction of number-average diameter of a hypothetical suspension for solid volume fraction ) 8.0938 × 10-5 and G ) 5.64 s-1 (1/s) with initial average aggregate sizes ) 100 µm at different fractal dimension values.

clusters would make them still more compact, helping to push its the fractal dimension up to about 2.2. They attributed this increase in the fractal dimension of the large clusters to a restructuring mechanism due to the hydrodynamic stresses felt by their branches when they drift downward. It was investigated that the fractal dimension value of asphaltene aggregate differs in the free settling and orthokinetic aggregation mechanisms by about 40%.17 The effect of inclusion of the hydrodynamic interactions on the fractal dimension is unclear. Agglomeration of aggregates under shear is controlled by the van der Waals intermolecular forces which yield stack-like aggregates. In this work, PSD measurements show the effects of mechanical forces on the dynamic evolution of asphaltene agglomeration-fragmentation to an established mechanical equilibrium size of aggregate distribution. This process mainly depends on the weaker intermolecular forces between aggregates. On the other hand, restructuring or breakage seems to be the direct effect of the mechanical forces on the aggregates structure. It is emphasized that under constant shearing large open aggregates become more compact as the aggregates restructure or fragment and reform more durable structures.34,38,39 Restructuring is likely the most prevalent compaction mechanism when a steady state is reached

between aggregation and fragmentation during flocculation.40 Therefore, the dynamical quantity of the fractal dimension describing the aggregates in a colloidal system under shear should depend on the effects of both aggregation due to van der Waals intermolecular forces and breakage or restructuring of aggregates. This mechanism causes the fractal dimension of aggregates is not established at a constant value and would change during shearing the suspension. In future research the effect of aggregates restructuring should be considered to achieve a realistic model for prediction of the asphaltene size distribution in simple suspensions. The other hydrocarbons components of the crude media have a considerable influence on the interaction of asphaltene aggregates and their size distribution. Further details regarding intermolecular interactions of crude components molecules remain to be studied. Since real petroleum mixtures, which have asphaltene precipitation problems, are so compositionally complicated, (38) Spicer, P. T.; Keller, W.; Pratsinis, S. E. J. Colloid Interface Sci. 1996, 184, 112–122. (39) Bouyer, D.; Line, A.; Cockx, A.; Do-Quang, Z. Chem. Eng. Res. DeV. 2001, 79, 1017–1024. (40) Spicer, P. T.; Pratsinis, S. E.; Raper, J. A.; Amal, R.; Bushell, G.; Meesters, G. M. H. Powder Technol. 1998, 97, 26–34.


further developments of both theoretical and experimental approaches on the agglomeration and fragmentation of the asphaltene aggregates will be necessary. Conclusions The image processing technique of a petroleum mixture could be a useful method for the study of the effects of hydrodynamic factors and asphaltene nature on the asphaltene aggregates size distribution. The aggregation evolution of asphaltenes upon addition of n-heptane and under shear rate was investigated for Bangestan, Mansoori, and Maroon dead crude oils using an image processing apparatus. The proposed population balance model provided a fairly good prediction of the asphaltene aggregates evolution measurements. The results were confirmed that the crude oil nature and composition affects the fractal dimension value, the out of solution concentration of asphaltene. The aggregates fractal dimension value has a strong effect on prediction of the aggregates evolution trends. Abbreviations A′ ) fragmentation parameter ASD ) aggregate size distribution BA ) rate of birth due to aggregation BB ) rate of birth due to breakage Ci,j ) aggregation kernel of particles of diameters Vi and Vj DA ) rate of death due to aggregation DB ) rate of death due to breakage dc,i ) collision diameter of aggregates in bin i df ) fractal dimension di ) diameter of rigid sphere mass equivalent aggregates in bin i dp ) diameter of a spherical primary particle, µm


G ) shear rate, s-1 imax ) number of classes or bins n ) particle number density Ni ) number concentration of aggregates in bin i having characteristic volume Vi, m-3 Ntotal ) total number concentration of particles in all bins, m-3 PBE ) population balance equation PSD ) particle size distributions q ) fragmentation parameter ri,ro ) inner and outer cylinders radius Si ) fragmentation or breakup rate of aggregates of size i, s-1 T:H ) toluene-to-heptane ratio in solvent mixtures (or solvent composition) t ) time, s td ) annulus radial distance V ) volume of particle, m3 Vi ) mean characteristic mass-equivalent particle volume of bin i, m3 Vp ) volume of a spherical primary particle, m3 xi ) sectional spacing Greek Letters Ri,j ) collision efficiency of particles of diameters Vi and Vj or the fraction of collisions that result in aggregation βi,j ) collision frequency of particles of diameters Vi and Vj Γi,j ) breakup distribution function γ(V,V′) ) breakup distribution function defining the volume fraction of the fragments of size V originating from V′-sized particles φs ) solid particle contents (i.e., volume fraction of particles) ω ) rotational speed of inner cylinder ∆U ) linear velocity difference of two cylinders EF800728H

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