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Monte Carlo Modeling of Asphaltene AggregationCoupled with SedimentationKian Safaie a & Ali Reza Solaimany Nazar aa Chemical Engineering Department , University of Isfahan , Isfahan , IranAccepted author version posted online: 15 Oct 2012.Published online: 23 Jul 2013.

To cite this article: Kian Safaie & Ali Reza Solaimany Nazar (2013) Monte Carlo Modeling of Asphaltene Aggregation Coupledwith Sedimentation, Journal of Dispersion Science and Technology, 34:8, 1173-1182, DOI: 10.1080/01932691.2012.735926

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Monte Carlo Modeling of Asphaltene AggregationCoupled with Sedimentation

Kian Safaie and Ali Reza Solaimany NazarChemical Engineering Department, University of Isfahan, Isfahan, Iran

GRAPHICAL ABSTRACT

In this article, simultaneous occurrences of aggregation and sedimentation processes of asphal-tene particles in toluene and n-heptane mixture are studied. Image processing technique is appliedin a settling column setup to evaluate the size distribution evolution at three sections. Each sectionconsists of three distinct zones that are introduced on the aggregate size evolution: the stable,ascending and the descending zones. The effect of the toluene to n-heptane volume ratio (T:H)and the structure of asphaltenes on the size distribution are investigated. The asphaltene aggre-gates with higher aromaticity factor have more tendencies to aggregate with one another. Atime-driven Monte Carlo (MC) model is proposed to predict asphaltene aggregate size distri-bution during sedimentation in toluene and heptane media. The results of this model are in goodagreement with experimental results. By increasing the aggregation probability, the fractaldimension becomes smaller in the simulated case studies.

Keywords Aggregation, asphaltene, modeling, Monte Carlo, sedimentation

INTRODUCTION

Asphaltene is defined as one of the heaviest fractions ofcrude oil, soluble in aromatic solvent but no insoluble in n-alkanes.[1] Asphaltenes are composed of polyaromatic andpolycyclic rings with short aliphatic chain and heteroatomssuch as nitrogen, oxygen, sulfur, and metals.[1–4] Ancheytaet al. found that asphaltene content is related to theamount of sulfur, nitrogen, nickel and vanadium presencein crude oil. By changing the thermodynamic conditionof the crude oil, asphaltenes coalesce and form a colloiddisperse phase.[5] These colloids can further agglomerate

and become deposited in oil wells, oil processing equip-ments, and transportation lines. Asphaltene depositionleads to a significant loss of productivity and a high costof remediation.[6–8] Asphaltenes are stabilized in oil bythe resin molecules that act as peptizing agents for emulsi-fying the asphaltene. In fact, asphaltene colloids are morestable in high resin content oil types.[9]

For the first time, Smoluchowski modeled an aggre-gation as a rate process. In his model, first the particlesare transferred and then the attachment process takesplace.[10] Here, the two important factors are the aggre-gation kernel and the collision efficiency. These factorsdepend on the hydrodynamic conditions imposed on parti-cles in a macroscopic scale in addition to the interactingforces between particles in a microscopic scale. The parti-cles collide with one another through three mechanisms:

Received 21 August 2012; accepted 26 August 2012.Address correspondence to Ali Reza Solaimany Nazar,

Chemical Engineering Department, University of Isfahan,Isfahan, Iran. E-mail: asolaimany@eng.ui.ac.ir

Journal of Dispersion Science and Technology, 34:1173–1182, 2013

Copyright # Taylor & Francis Group, LLC

ISSN: 0193-2691 print=1532-2351 online

DOI: 10.1080/01932691.2012.735926

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perikinetic, orthokinetic, and differential settlingaggregation.[11] Small particles in suspension undergo con-tinuous random movements called Brownian motion andcollide with one another through the perikinetic mech-anism. This mechanism gains importance gradually whenparticles size are one or smaller than 1 mm.[12] Particlemovement, due to fluid motion can cause an enormousincrease in the interparticles collision rate; this mechanismis called orthokinetic. The particles of different sizes havedifferent settling velocities and can coagulate during colli-sion with one another. The settling mechanism becomesrelevant at particle size 10–100 mm.[13] Smoluchowskiassumed that all particle collisions lead to coagulation.Stochastic approach is used as a procedure in coagulationprocess where particles stick to one another. If the stickingprobability is one, the mechanism of aggregation is dif-fusion limited aggregation (DLA), on the contrary, thereaction limited aggregation (RLA) is considered whensticking probability is near zero. The clusters have porousstructure and are not impermeable; therefore, fractaldimension (df) value is defined for them. In RLA mech-anism, particles coagulate one another with a very lowprobability. So, these clusters have a compact structureand a higher fractal dimension value. All collisions leadto coagulation in DLA mechanism and the clusters haveless fractal dimension in comparison with the RLA mech-anism.[14–16] Some researchers have obtained relationswhich correlate the collision efficiency with total interac-tion forces between particles. In fact, if two particles havemore intermolecular forces, they are apt to coagulate withone another.[17,18] In addition to all these claims, thereexists a fractal approach that is used in defining the colli-sion diameter concept. The collision diameter is describedwith the reversal of the fractal dimension by a power lawrelation. In some studies the diameter of the particles isreplaced by collision diameter, and modified kernel aggre-gation is acquired, where the interparticle forces could becalculated.[19,20]

There are several methods in studying aggregation size:scattering methods,[21,22] Coulter counter method,[23] ultra-sonic methods,[24] etc. Each of these techniques have someadvantage and disadvantages and final selection dependson the experimental conditions, cost and the range of par-ticles size, which is investigated. One of the experimentalinvestigation methods of particulate system is the imageprocessing technique through which asphaltenes aggre-gation could be studied. The main weakness of the imageprocessing technique is the necessity of the transparencyof the under liquid media study. The n-heptane and toluenemixture already were selected for studying the asphalteneaggregation and breakage processes in atmospheric con-dition by image processing analysis.[25–27] This could be areasonable selection, due to the fact that destabilization

of asphaltene in crude oil depends on the type and amountof asphaltene solvent and precipitant agent.[28]

Asphaltene aggregates have a fractal structure. Rah-mani et al. evaluated the fractal dimension value of asphal-tene, by using an image analysis technique.[25] In theirstudy, they allow first, some asphaltenes to becomeagglomerated in shear induced petroleum solution andthen a little amount of the suspension is delivered to a set-tling column. They measured the asphaltene fractal dimen-sion by allowing the aggregate to settle in a column, andconcluded that an increase in shear rate leads to an increasein the fractal dimension.

In dealing with a particulate system, the particle size dis-tribution (PSD) is applied, and its evolution is examined.One of the common methods for prediction of PSD ispopulation balance modeling. Several developments on thismethod apply deterministic solution methods such asmoment, sectional, discrete and discrete-sectionalmethod.[29–34] Another method is Monte Carlo (MC) mod-eling; this technique applies stochastic approach thatincludes the terms of the population balances equation.Recently many researchers used MC technique in agglom-eration, multicomponent aerosols and crystallization pro-cesses.[35–38] The dynamic evolution of particulate systemwith MC falls into three main categories: time-drivenMC, event-driven MC and multi MC. Time-driven MCmodel is developed by Liffman,[39] here the step time isfixed and all probable events are unfolded. This techniqueis applied in the phase separation where the colloidal aggre-gation and breakage takes place in sheared induced mix-ture like dynamic evolution of asphaltene aggregatesize.[36–40] In the event-driven MC model, an event unfoldsinitially and then time passes through the related time step.This method is developed by Garcia et al.[41] The Multi MC(MMC) is a new technique that applies statistical weightconcept, which in a scene shades more light on the real par-ticulate system. This MC method is developed by Zhaoet al. in order to model the coagulation and condensationin the dispersed systems.[42] Despite many studies conduc-ted on asphaltenes aggregation modeling, still advancedunderstanding of the evolution of the aggregation and sub-sequent sedimentation of these compounds is necessarywith further investigation. Sedimentation of asphaltenesparticles in storage reservoirs causes some problems suchas decreasing the capacity or obstructing the outgoing linesof the reservoirs.

In this article, the aggregation and subsequent sedimen-tation of asphaltene particles are investigated as simul-taneous phenomena. Image processing technique isapplied in the experimental study. A time-driven MCmodel is presented and the effects of toluene volume ratioand asphaltenes structure on the size of settling asphalteneparticles are investigated.

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EXPERIMENTAL SECTION

Materials

Asphaltenes are extracted from two types of Iraniancrude oil. Table 1 shows the properties of these crude oiltypes that come from SARA analysis.

Asphaltene Solid Preparation and Analysis

Initially the crude oil residue was obtained followingASTM D86-01 and then, n-heptane insoluble asphaltenes(C7 asphaltene) were extracted from the obtained residuesthrough ASTM D6560-00. The extracted asphaltenes werecharacterized through x-ray diffraction (XRD). The XRDmeasurements were carried out through an XRD diffract-ometer (D8ADVANCE. Bruker, Ltd., Germany). Here,CUKa radiation (k¼ 1.5406 A) was applied. The scanrange (2�h), scan rate and count time were set on 5–45,0.005�=s and 2 sec=step, respectively.

Apparatus

The experimental setup used in this study is shown inFigure 1. This setup consists of a cylindrical cell as a set-tling column with a 20 cm height. This cell contains twocoaxes cylinders: the inner one has a 50mm diameter and

can rotate by the means of an electromotor (IKA); theouter glassy cylinder has a 60mm diameter and non-rotating. The asphaltene aggregates were observed by amicroscope (Labomed CZM6) with a charge coupleddevice camera (Labomed 1500ic). A microscope is attachedto the CCD camera and placed on a telescopic camerastand in order to capture the image of asphaltene aggre-gates at three sections of the cell. The positions of the threeimage capturing sections are called A, B, and C, and arelocated at 4.5, 10.5, and 18 cm from the top of the cylinder.A cold light source was used to brighten the space of theimage capturing. Since the image width is smaller thanthe cylinder radial, the optical correction for its curvaturecan be neglected. Image processing technique was appliedfor asphaltene aggregate size evaluation during the agglom-eration and the sedimentation. In this process the Digi Pro4.0 software is used for capturing the image of asphalteneaggregates in the three sections of cylindrical cell. The geo-metrical properties of asphaltene particles were calculatedby Sigma Scan Pro 5 software.

Sample Preparation and Test Procedure

To prepare two stock solutions, asphaltene powder weredissolved in toluene solvent (Merck, Ltd., Germany). Twoconcentrations of 320 and 200mg=liter asphaltene wereprepared in this solvent. These values are applied accordingto upper and lower limits in our image processing system inorder to indicate clearly the effect of parameters T:H ratioon asphaltene aggregation.

A 25mL of stock sample with 320mg=liter concen-tration was poured in the cylindrical cell then 175ml ofn-heptane (Merck, Ltd.) was added to the cell as asphalteneprecipitation agent. The inner cylinder was rotated at 6 rpmfor 45 minutes in order to increase the clustering processbetween colloidal asphaltene particles. This low speedrotation was applied for obtaining larger detectable aggre-gates with our image processing device. Through the sys-tem adopted in this study we were able to measure theasphaltenes aggregate size over 20 mm diameter. After theinitial rotation, the electro motor was turned off and themixture was allowed to stay at static situation for 50 sec-onds. The image capturing was performed on the assignedsections in 2 minute intervals between each section bychanging the camera position from the top to the bottomof the cell. The average size of the asphaltene aggregatesare not continuously measured with time and an intervalis needed to adjust telescopic camera in front of sections.Due to the high required computation time for modelrun, each experiment took 60 minutes at maximum. In asimilar manner, a 40ml of stock sample with 200mg=literconcentration is used to investigate the T:H ratio effect.This experimental study was carried out at room tempera-ture of approximately 25�C.

TABLE 1SARA analysis of crude oil samples

Saturate(wt %)

Aromatics(wt %)

Resins(wt %)

Asphaltenes(wt %)

Crude oiltype 1

24.8 58.8 13.8 2.4

Crude oiltype 2

27 56.5 11.9 3

FIG. 1. Schematic diagram of the experimental setup: (1) electro-

motor, (2) gear box, (3) outer cylinder, (4) inner cylinder, (5) cold light

source, (6) microscope, (7) CCD camera, (8) telescopic camera stand, (9)

computer. (Figure available in color online.)

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MODEL DESCRIPTION

Physical System

A physical schematic of the system applied in the mod-eling is shown in Figure 2. A volume of 20 cm H� 1500 mmW� 5mm D is considered as the simulation system. Thesurface of capturing images is 1500 mm� 2000 mm. Theobtained asphaltene particles in the first captured imageare randomly distributed in the image surface withoutoverlapping. The length of the simulation system is 100times of the captured images length.

Model Assumptions

The following assumptions are considered in themodeling:

1. The particle movements are assumed as two dimen-sional.

2. The particles distribution is uniform at the initial stageof measurement.

3. The periodic binary condition is considered in the direc-tion perpendicular to settling movement (horizontalaxis).

4. An average fractal dimension is used for the asphalteneparticles.

5. Due to the asphaltene low concentration the collisionbetween more than two particles is ignored.

Model Formulation

The time driven MC was developed by Liffman forcoagulation.[39] Zhao et al. extended this model to (MMC)and applied it to coagulation and condensation in dispersedsystem.[42] Faraji and Solaimany Nazar applied atime-driven MC model for asphaltene agglomeration and

breakage in the shear induced particulate systems.[43] In thisstudy a time-driven MC is developed to evaluate asphalteneaggregation and sedimentation process. Two aggregationmechanisms due to differential settling and Brownianmotion are considered here. It is assumed that each mech-anism contributes independently to the aggregation rate.In general, Brownian motion is important for small particlesizes (<0.5 mm, radius), while differential fall velocities affectparticles larger than 0.5 mm. Aggregation kernel is expressedas the constant rate of collision. For binary collisions ofparticles with rigid diameters di and dj, the total aggregationkernel is defined as:

bij ¼2kBT

3lðdi þ djÞ2

didj

!þ p

4ðdi þ djÞ2ðvi � vjÞ; ½1�

where first and second terms correspond to the differentialsettling and Brownian mechanisms, respectively, vi and vjare the settling velocity of particles i and j, kB is the Boltz-mann constant, T and m are the temperature and the viscosityof the mixture, respectively. The collision diameter for a frac-tal aggregate is associated to the number of primary particleswith diameter dp and fractal dimension df, defined by:

dci ¼ dpðNiÞ1=df ; ½2�

where Ni is the number of the rigid particle inside theaggregate i and e is the aggregate porosity which is deter-mined by Equations (3) and (4):

Ni ¼ ð1� 2Þ Vi

Vp; ½3�

2¼ 1� dcidp

� �d�3f : ½4�

Equation (1) often appears in this form particularly in caseswhen interparticle and fluid forces are neglected. The sumkernel does not account for the enhanced collision ratedue to diffusive processes in the wake of falling particlesand the relative motion of particles. No theory exists forthe calculation of the collision efficiency of aggregatedgrowth from doublets to triplets and larger aggregatesbecause of the complexity of the hydrodynamics involved.Moreover, irregular aggregate shapes can increase theefficiency of aggregate contacts. Hence, the exact kernelis greater than the sum kernel. The individual contributionsof the mentioned factors to the aggregate size are unclear.Few theoretical and experimental studies have investigatedto investigate these effects.[44,45] Moreover, due to themeasurement limitations in this study the presence of thefine particles could not be detected by the CCD camera.The particles that had not reached the detectable sizerequired by the experimental system at the beginning of

FIG. 2. Schematic view of the simulation system.

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the process should be included in the calculation strategy.However, as the time passes these particles coagulate withone another and could be detected by the CCD camera. Allthat is needed for modeling is to include a correction fac-tor, X, into the total kernel rate expression (Equation(1)). The mixture composition to a great extent affectsthe aggregation of the asphaltenes and the subsequent sedi-mentation; therefore, the correction factor is compositiondependent. If a particle tends to coagulate strongly, thevalue of the correction factor will be high. The kernelbetween particles i and j is proposed as:

bij ¼ X2kBT

3lðdci þ dcjÞ2

dci

!þ p

2ðdci þ dcjÞ2ðvi � vjÞ

" #: ½5�

The aggregation and sedimentation times for each par-ticle are estimated as:

tagg ¼VsPnj¼1 bij

: ½6�

tsed: ¼h� yivi

; ½7�

where h is the height of the simulation volume which isequal to the height of the liquid mixture inside the cylinder;yi is the downward distance from the free surface of themixture and vi is the sedimentation velocity. Gonzalez,used particle sedimentation velocity for carbonate calciumclusters in his MC model, defined as [46]:

vi ¼qppd

3p 1� q

qp

� �gNi

18ldci; ½8�

where g is the earth gravitational acceleration. In this pro-posed model qp is the density of asphaltene rigid particlesin the clusters which is assumed to be equal 1200 kg=m3;q indicates the density of solution and dp is assumed tobe 3 mm in this case studies. This value is found by compar-ing the experimental result with the model result. The timestep should be less than or equal to both the minimumaggregation and minimum sedimentation times.

Dt � minftagg; tsedg: ½9�

So the time step is defined as:

Dt ¼ a �minftagg; tsedg; ½10�

where a is fixed at (a¼ 0.1). Due to the high computationtime of MC method, choosing a smaller value for a is sub-ject to limitation. By setting the time step on smaller thanthe fastest process that takes place in the simulation,

assures that at the most one aggregation occurs withintime, Dt, for each particle in the simulation volume. In eachMC time step the aggregation occurrence for particle i, wasevaluated by the following inequality expression:

R1 < CiVs; ½11�

where Ci is the summation of aggregation kernel betweenparticle i and other particles overlapping on it.

Ci ¼Xn

j¼1bij; ½12�

where R1 is a random number from uniform distributionbetween 0 and 1 and Vs is the simulation volume(Vs¼ 1.5�10�6m3). The partner for a binary aggregationis chosen with the following probability:[47]

P0i;j ¼

bðVi;VjÞPj bðVi;VjÞ

½13�

Asphaltenes particles are assumed to be spheres withequivalent diameters. These asphaltene particles are ran-domly arranged in a volume without overlapping withone another. The particles in the simulation volume aremoved according to Brownian and settling motions. Parti-cles can move in two axial directions by horizontal (x) andvertical (y) movement steps which are denoted as Dx andDy in each step, respectively.

Dx ¼ffiffiffiffiffiffiffiffiffiffiffiffiffi2DtDi

p½14�

Dy ¼qppd

3p 1� q

qp

� �gNi

18ldciDtþ

ffiffiffiffiffiffiffiffiffiffiffiffiffi2DtDi

p; ½15�

where the diffusion coefficient of aggregate i, (Di), isdefined by the Stokes-Einstein equation:

Di ¼kBT

3pl dci½16�

In each time step the aggregation condition is examinedfor each particle. If two particles i and j coagulate with eachother the new particle will be substituted with diameter as:

dnew ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffid3i þ d3

j3

q: ½17�

The number average of particles is calculated by:

davs ¼P

nidciPni

; ½18�

where ni is the number of aggregates of size i.During the simulation the particle number decreases

continuously with respect to time and so does the precision

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of MC method. If the particle number in the simulationvolume decreases by a factor of two of its initial value,the simulation volume is doubled in a way that anothersimilar volume is added where the total and the arrange-ment of the particles are the same as the previous volume.This is a common procedure in Monte Carlo methods.[48]

The results were averaged over four numbers of simula-tions in order to reduce the stochastic noise inherent inMonte Carlo methods.

Simulated Cases Studies

Three case studies are modeled here. The initial distri-bution of asphaltene particles is determined by the firstimage captured at the initial time of measurement; theinitial number average diameter is obtained from this firstimage. The numbers of particles which are applied in MCmodeling are listed in Table 2. These values are obtainedaccording to the first captured images.

RESULT AND DISCUSSION

XRD Measurement

The x-ray patterns for two types of extracted asphal-tenes are presented in Figure 3. The determined results ofx-ray patterns are listed in Table 3. Aromaticity and otherstructural variables were designated according to Shirokoffet al.’s procedure.[49] In this study, the important parameteris the aromaticity factor (fa) which is the ratio of the aro-matic carbon number to the total number of both the ali-phatic and aromatic carbons in asphaltenes. Extractedasphaltenes from crude oil type 2 have low aromaticity;therefore, these asphaltenes have no more tendency tocompose large aggregates. However, in Table 1, the SARAtest results show that the two types of crude oil are similarin fractional composition. Although, these two types ofcrude oil are similar, there is a difference in their asphal-tenes aromaticities. This study revealed a pattern to com-pare the model results with the experimental results.

Asphaltene Nature Effect

The predicted and measured average asphaltene diam-eter (dave) evolution in three sections A, B and C for asphal-tene extracted from crude oil type 1 are illustrated in

Figure 4 Toluene to n-heptane volume ratio is T:H¼ 1:7.The MC modeling performs with initial particle size atT:H¼ 1:7, the adjustable parameter (X¼ 12) and(df¼ 1.81). The results point to an attracting trend, thatis, in all sections the results indicate the three distinct stagesof the process. The average asphaltene diameter begins todecline after a stable zone reaches its peak. The balancebetween the behaviors of the aggregation and sedimen-tation between asphaltene particles contributes to theapproximate stability of the average diameter. Both the

FIG. 3. The x-ray patterns of extracted asphaltene from crude oil type

1 (top) and crude oil type 2 (bottom).

TABLE 2Number of particles in cases studies according to the

obtained results of the first captured images

T:H ratio Extracted asphaltene Number of particles

T:H¼ 1:7 Crude oil type 1 1400T:H¼ 1:4 Crude oil type 1 2600T:H¼ 1:7 Crude oil type 2 1700

TABLE 3Aromaticity and crystallite parameters, the XRD

measurement outcome

Structuralparameters

Asphaltene ofcrude oil type 1

Asphaltene ofcrude oil type 2

fa 0.11 0.075dm (A) 3.58 3.58dgama (A) 3.66 4.43Lc (A) 24.4 29.2M 7.8 9.1

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phenomena have contributed to the particle diameterincrease. The more progress in aggregation, the moredominant sedimentation process. Big particles subsidemore rapidly than the small ones; thus, the average sizeat the final zone decreases. It can be presumed that theextension of the stable zone can occur if the particles arevery tiny and small. In section A, there is no significantchange in the average diameter size over a long period oftime. Here the particles do not have enough time to coagu-late with one another. The trend in section B shows that thevalue of the dave increases, reaches its maximum and thendecreases. An increase in aggregate size is due to particleaggregation. The aggregates have enough time forfurther aggregation during subsidence from section A tosection B. As a result of the average aggregate diameteraugmentation, the slope intensity in the descending zoneat section B is greater than section A. The descending zoneslope increases because of high settling rate of the big par-ticles. Eventually, the biggest average size of particle couldbe observed in section C where the particles are in average

diameter 95 mm. Here, the opportunity of aggregationprocess is high, due to an average particle size increase.A comparison between the model prediction and theexperimental results for each section is drawn in Figure 4.A good quantitative agreement existed between the experi-ments and MC model for the three mentioned zones.

The aggregate size evolution for asphaltenes extractedfrom crude oil type 2 is shown in Figure 5. The MC model-ing was implemented at T:H¼ 1:7 with the correction para-meter (X¼ 8.5) and fractal dimension (df¼ 1.83). The threementioned zones were observed; however, the slope inten-sity in the ascending zone in crude oil type 2 is lower thanthat of the one in crude oil type 1. In the descending zone, alow slope intensity of decrease is observed. In fact, theasphaltenes extracted from crude oil type 2, form smallaggregates; here the largest average aggregate size is60 mm. It should be noted that due to inhibition effect oftoluene, the formation of asphaltenes aggregates fromcrude oil type 2 at T:H¼ 1:4 is not measurable with ourexperimental system. Thus, it is concluded that the crude

FIG. 4. Average diameter evolution for asphaltene of crude oil type 1

at T:H¼ 1:7 in sections A, B, and C of the settling column. FIG. 5. Average diameter evolution for asphaltene of crude oil type 2

at T:H¼ 1:7 in sections A, B, and C of the settling column.

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oil type 2 asphaltenes have less tendency to coagulate withone another.

As it was expected from XRD results, asphaltenes ofcrude oil type 1 have more aromatic zone within theirstructure and these asphaltenes could be highly bridgedtogether and form larger aggregate. The correction factorof for asphaltene crude oil type 2 decreased and the fractaldimension augmented in comparison with that of theasphaltene of crude oil type 1. The high intermoleculartendency is responsible for an enhanced aggregation andformation of larger aggregates at the early stage of floccu-lation process. Further studies need to be conducted inrecognizing the intermolecular and interparticle forcesbetween asphaltene molecules and particles in order toinvestigate their effects on the aggregation of asphalteneprocess.

T:h Volume Ratio Effect

The effect of toluene to n-heptane ratio was investigatedon aggregation and subsequent sedimentation of the parti-cles. The initial particle distributions of asphaltenes ofcrude oil type 1 at T:H¼ 1:7 and T:H¼ 1:4 are shown inFigure 6. Here, it is clearly observed that an increase inthe toluene volume ratio, affects the initial particle distri-bution. The best normal distribution fitted the data withthe table curve software. The particle size was discretizedaccording to the Batterham et al. method and the lengthof the first zone of ASD and the smallest particle size areassumed 1 and 20 um, respectively.[50] As observed inFigure 6 the normal distribution is shifted towards smallersizes for (T:H¼ 1:4) due to the dissolution of asphaltene inthe toluene solvent.

The evolution of the number average size of particles forcrude oil type 1 at T:H¼ 1:4 is shown in Figure 7. In theearly time, no significant change is noticed and the steadyzone in section A of the cylinder cell extends. For settlingparticles in section B no average diameter change was

observed before almost 34 minutes after which averagediameter began to decrease very slowly. A decrease inaggregate size decreases the settling rate. A similar exten-sion of stable zone is noticeable for section C of the settlingcell in Figure 7. No significant change was observed in theaverage diameter of asphaltenes particles. Kraiwattana-wong et al. have also encountered this extension of stablezone.[51] They investigated the effect of inhibitors onasphaltene aggregate size by turbidity measurement. Themodeling is performed with initial particle size based onT:H¼ 1:4 and adjustable parameters of (X¼ 2) and(df¼ 1.92) that could precisely predict the experimentalresults. By comprising the values of these parameters, itis revealed that as the asphaltenes aggregation decreasesin higher toluene volume, the correction parameter andthe fractal dimension decreases and increases, respectively.

FIG. 6. Initial particle size distribution for asphaltene of crude oil type

1 at T:H¼ 1:4 and T:H¼ 1:7.

FIG. 7. Average diameter evolution for asphaltene of crude oil type 1

at T:H¼ 1:4 in sections A, B, and C of the settling column.

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The experiments are conducted on the asphaltenes ofcrude oil type 2 at T:H¼ 1:4 where no particle is seen dis-tinctly in this image processing technique.

For all experiments, it is concluded that the adjustableparameters (X, df) are related to the initial distribution.Two important factors of initial distribution including themaximum size of particle (g) and the number average ofparticle diameter are listed for each one of the three experi-ments in Table 4.

CONCLUSIONS

In this article, image processing technique is used tostudy asphaltene aggregation coupled with sedimentationin toluene and n-heptane mixture inside an annulus cylin-drical cell. The objective here is to investigate aggregationbetween asphaltenes’ particles during sedimentation pro-cess. It is noticed that in the lower position of the cell,the asphaltene particles are more apt to coagulate, whilewith particles larger size are observed. In the average aggre-gate diameter evolution three zones are observed: thestable, the ascending and the descending zone. Stable zoneis established when the aggregation and sedimentationphenomena have the same value order and while compet-ing with each other; ascending zone is the result of thedomination mechanism of aggregation and finally descend-ing zone is observed due to the particles sedimentation. Atime-driven MC model was applied for predicting theaggregate size evolution in each section of the cylindricalcell. The two adjustable parameters of the fractal dimen-sion and the correction factor were applied for aggregationkernel. As the aggregation probability increases the aver-age fractal dimension decreased, that is, more porousparticle is formed.

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