Influence of Temperature on Aggregation and Stability of Asphaltenes

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Influence of Temperature on Aggregation and Stability of Asphaltenes: Part I. Perikinetic Aggregation Mohammad Torkaman, Masoud Bahrami, and Mohammad Reza Dehghani Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b00417 • Publication Date (Web): 28 Aug 2017 Downloaded from http://pubs.acs.org on August 29, 2017

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Influence of Temperature on Aggregation and Stability of Asphaltenes: Part I. Perikinetic Aggregation Mohammad Torkaman,† Masoud Bahrami,*,†Mohammadreza Dehghani§ †

Department of Gas Engineering, Ahwaz Faculty of Petroleum, Petroleum University of Technology (PUT), Kout-Abdollah, Ahwaz, Iran

§

Department of Chemical Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran

Abstract Asphaltene deposition is one of the most challenging aspects of the petroleum industry that takes place through production, processing, and transportation. In the present study, first, the effect of temperature on the aggregation kinetics of asphaltene in a heptane-toluene mixture is investigated during a set of experiments done at different fixed temperatures. In spite of most previous works in which the collision efficiency is assumed to be constant and equal to one, the obtained experimental data in this study provide deep insights into the mechanism of aggregation of asphaltene particles within an organic medium. A population balance model considering the fractal structure for asphaltene aggregates and variable value for collision efficiency is developed to predict the enlargement of asphaltene floccules with the passage of time. The results show that the assumption of a constant value for collision efficiency is not realistic. The calculated value of collision efficiency decreases with the increase of average particle size during each experiment. Also, the value of collision efficiency decreases with the increase of temperature. In the second part of this work, the zeta potential of asphaltene aggregates in the mixture is measured during the evolution of floccules in separate tests. These results are applied to investigate the asphaltene stability and also to validate the size measurement data obtained in the first part. The measured zeta potentials of evolving particles indicate that the asphaltene aggregates are more stable at high temperatures than at low temperatures. Due to this fact, aggregates reach to a significantly smaller mean size at high temperatures in comparison to that at low temperatures.

*

Corresponding author. Telfax.: +98 61 35550868 E-mail address: [email protected]

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1. Introduction 1.1. Background. The basic constituents of the crude oil in petroleum industry are: saturates, aromatics, resins and asphaltenes (SARA).1 Asphaltenes are characterized as sticky and highly viscous material that precipitate in paraffinic solvents such as n-heptane, but are soluble in aromatic solvents such as toluene at room temperature. These polycyclic aromatic compounds contain heteroatoms (S, N, and O) and transition metals (Fe, V, and Ni).1–3 Serious problems including permeability and porosity reduction, wettability alteration, plugging of tubes, storage capacity loss and catalyst fouling are arisen by asphaltene deposition and it has been the subject of several controversial research.4–10 There are two lines of thinking about the state of asphaltene in petroleum (1) asphaltene particles are in micellar form and stay dispersed until the protective layer, consisting of resins, exists outside of them (colloidal thinking); (2) asphaltenes are dissolved species (thermodynamic thinking).2,10 In both approaches, asphaltenes are in equilibrium within petroleum, regardless of whether they are dissolved, or in colloidal form, or partly in both states. In an organic medium containing asphaltene, once the conditions for the evolution of asphaltene particles are provided, three main phenomena are believed to happen: nucleation, aggregation and breakage.11 Nucleation produces new fine particles which are primary particles for aggregation. The main process of enlargement of asphaltene particles is aggregation in which the fine particles collide with each other and stick together and constitute the larger particles. In the breakage process, the fragile particles are broken down into smaller parts due to shear stress and it could be ignored in a motionless system.12,13 Population balance modeling is a successful method which was applied by many researchers during the last three decades to forestall the variation of particle size distribution over time in particulate suspensions.12,14–20

1.2. Previous Studies on the Aggregation Kinetics of Asphaltene Particles. Nielsen et al.21 studied the effects of temperature and pressure on asphaltene particle size distribution in crude oils in the presence of n-pentane. They found that the mean size of asphaltene particles increases with pressure and is not significantly affected by temperature. Anisimov et al.22 determined the average particle size of asphaltene (in the range of 0.5 to 12µm) in heptane-toluene mixture. Rahmani et al.12,20 developed a mathematical model based on population balance equation to estimate the asphaltene floc size distribution (ranged between 30 and 400µm) in heptane-toluene mixture. They found that the shear rate has no effect on the variance of the distribution and also 2 ACS Paragon Plus Environment

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the rate of aggregation increases with increase of the solute (asphaltene) or antisolvent (n-heptane) concentrations. Rastegari et al.23 investigated the kinetics of asphaltene aggregation in heptanetoluene mixture and believed that it is a reversible process. They found an empirical function for aggregation rate and showed that it is improved by increase of heptane content and asphaltene concentration and decrease of shear rate. Their results indicate that asphaltene flocs have a fractal dimension of roughly 1.6. The evolution of asphaltene particles in a mixture of asphaltene, toluene and heptane was investigated by Solaimany-Nazar and Rahimi using an image analyzing technique. They concluded that the maximum diameter is significantly affected by shear rate and initial average diameter of asphaltene aggregates whereas the initial particle size does not have any effect on the steady state size.13,24,25 Additionally, the authors indicated that the fractal dimension of asphaltene particles is exponentially increased from 1.6 to 2.3 during the enlargement of particles.25 Khoshandam and Alamdari26 developed a population balance model considering the growth and aggregation mechanisms and using supersaturation as driving force. Maqbool et al.27– 29

studied the asphaltene precipitation in the mixtures of heptane and crude oil by using an optical

microscope. Asphaltene precipitation did not take place immediately after adding antisolvent (nheptane) and it started a few minutes or a number of months later, depending on the added volume of antisolvent. They reported that the increase in temperature would reduce the onset time of precipitation due to increase in solubility. Mansur et al.30 questioned experimentally the effect of temperature, flocculant, and additive on asphaltene particle size distribution. They deduced that the average particle size of asphaltene decreases with increase of temperature. Haji-Akbari et al.31– 33

investigated the roles of different parameters on the aggregation rate of asphaltenes in various

types of crude oils and asphaltenes. The authors found that the kinetics of asphaltene aggregation strongly depend on the properties of the crude oil and antisolvent. The difference between Hildebrand solubility parameters of surrounding solution and asphaltene versus detection time matches a universal curve. The collision efficiency was found to be proportional to square of this difference .31 Also maximum aggregation rate was obtained at asphaltene concentration 1 wt%.32 Moreover, Hildebrand solubility parameter and viscosity of the host fluid were found to be significantly increased with the rise of the chain length of antisolvent (normal alkane) thereby leading to higher aggregation rates.33 Chaisoontornyotin et al.34 studied the asphaltene aggregation and deposition in a capillary apparatus using various n-alkanes as antisolvent at fixed volume fraction of antisolvent and temperature. Their results were the same as previous studies and n3 ACS Paragon Plus Environment

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alkenes with higher carbon numbers or lower concentrations caused higher induction times. The collision efficiency was found by matching a geometric population balance model with experimental data. The obtained collision efficiency values for antisolvents with carbon number of 8, 9, and 10 were roughly 75, 60, and 20 percent of its value for n-heptane (C7), respectively. Chaisoontornyotin et al.34 declared that the difference between Hildebrand solubility parameters is a key parameter in the prediction of the asphaltene aggregation rate. Mohammadi et al.35–38 conducted a series of depressurization experiments of live oil at constant temperatures to study the asphaltene aggregation. A fractal geometric population balance model applying Smoluchowski’s kernel was used to predict the enlargement of asphaltene aggregates. Two adjustable parameters, including the collision efficiency and the mass fractal dimension, were employed in the model. Their studies showed that the mass fractal dimension of asphaltene aggregates is strongly dependent on temperature and pressure of the system as well as on the media nature.35 The prevailing mechanism of asphaltene coagulation was declared to change slowly from diffusion limited aggregation (DLA) to reaction limited aggregation (RLA) when the temperature of depressurization process is increased.37 It is evident that in the most of above studies the variation of collision efficiency was not considered in the estimation of the rate of asphaltene aggregation and a constant value one is assumed for it.

The collision efficiency was optimized as a function of the antisolvent

concentration and its value was in the order of magnitude of -6 in a few previous studies.29,34 It should be stated that no distinctive trend has been found about the influence of temperature on the collision efficiency in the available literature. The only available work on this subject is the study of Mohammadi et al.35, in which opposite trends were confirmed for different oil samples. In the present work, the effects of temperature on the enlargement of asphaltene particles in heptanetoluene mixture is experimentally scrutinized. A population balance model is employed to quantify the influence of temperature on the collision efficiency. Also, a series of zeta potential measurements are conducted beside particle size analysis for the interpretation of the obtained experimental results for the first time.

2. Experimental Section 2.1. Materials. The experiments of this study were carried out in a batch mixture of heptanetoluene at 20, 40, 60 and 80°C and 1 atm. Heptane and toluene with purity higher than 99.9%


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(HPLC grade) were purchased from Samchun Pure Chemical Company, Korea. Asphaltene used in the experiments was extracted from the distillation residue of Abadan Oil Refinery.

2.2. Preparation of Asphaltene Samples. Various techniques for extracting the asphaltene from crude oil or bottom product of the distillation tower were reported in the literature.39 In the present work, asphaltene was extracted from the residue of distillation tower according to a centrifugation-based technique.12,20,26 First, 10 grams (±0.1 mg) of the bitumen is weighted and dissolved in about 200 cc of toluene. In order to maximize the solubility of asphaltene, the liquor is completely mixed by a triple blade stirrer for 1hr. To separate the undissolved solids, comprising dust and fine clays, the mixture is centrifuged at 10,000 rpm for 60 minutes. After that, the supernatant liquid is decanted into a flask without disturbing the sediments. Then the toluene is removed from the liquor by evaporation until a highly viscous and dry residue remained. The residue in the flask is mixed with heptane (heptane- residue volume ratio is 40:1) and mixture is agitated for 4 h. At the end of this period, the flask is closed with a stopper and placed in a dark cupboard for 24 h for complete settlement of the asphaltenes particles. Thereafter, the supernatant liquid is separated and raffinate is diluted with heptane with volume equals to four times of raffinate’s and this mixture is stirred for 1 h. After resting for 4 h, the mixture is decanted on a Whatman Grade 42 filter paper and then the residue on the filter is rinsed with successive quantities of hot heptane until the heptane from the bottom of the funnel becomes colorless. Finally, the sample is placed in an oven at 90°C for one week which after that no variation in weight is observed. According to this procedure, the amount of obtained asphaltene was 10.1 weight percent of initial bitumen.

2.3. Particle Size Measurement. The particle size distributions of asphaltenes between 0.3nm and 10µm were analyzed by a Zetasizer Nano ZS-ZEN3600 (Malvern Instruments) in which a dynamic light scattering technique is applied. This instrument employs a 4 mW He-Ne 632.8 nm laser at a scattering angle of 173° (backscatter detection). In this technique, the particle size distribution is determined by measuring the Brownian motion of the particles in suspension in a few minutes. A prominent trait of Brownian motion is that large particles move considerably slower than smaller ones. The diffusion coefficient of a particle is related to its average-diameter through the Stokes-Einstein equation:1,40


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𝐷=

𝑘𝐵 𝑇 3𝜋𝜇𝑑

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(1)

where D, kB, T, and µ are diffusion coefficient, Boltzmann constant, temperature, and viscosity of the dispersant, respectively.

2.4. Zeta Potential Analysis. The zeta potential of the samples was measured by Zetasizer working based on electrokinetic effects and in the range of -250 mv to +250 mv. The effects of an applied electric field on charged and suspended particles within a solution are designated as the electrokinetic effects. The electrokinetic effects are divided into four distinct groups: electrophoresis, electroosmosis, streaming potential, and sedimentation potential.41 Zetasizer measures the electrophoretic mobility, which is the velocity of a particle in an electric field (UE), to determine the zeta potential of the particle. UE is a function of the dielectric constant of the medium (ε), the viscosity of the medium (µ), and the zeta potential (ξ) according to Henry’s correlation:41,42 𝑈𝐸 =

2 𝜀 𝜉 𝑓(𝐾𝑎 ) 3𝜇

(2)

where f(Ka) is Henry’s function and its value is generally estimated to be 1.0 (Huckel approximation) for non-aqueous media with low dielectric constant or 1.5 (Smoluchowski approximation) for aqueous media with moderate electrolyte concentration.41 Greater details on the technique of zeta potential measurement (M3-PALS) can be found in the Supporting Information.

2.5. Sample Preparation. The applied asphaltene concentration and toluene/heptane ratio vary over a fairly wide range of the previous studies: 4.1 mg/L to 1 g/L for asphaltene concentration and 1:0.4 to 1:15 for toluene/heptane ratio, depending on the employed particle size measurement techniques.12,13,23,26 Particle size analyzing is difficult at high and low concentrations of asphaltene due to multiple scattering and insufficient particles, respectively. Consequently, it is essential to determine the optimal range of asphaltene and heptane concentrations for experiments. Various asphaltene concentrations (ranging from 5 mg/L to 1 g/L) and heptane/toluene volumetric ratios (ranging from 0.5 to 13) were examined in order to specify the optimum conditions. The concentration of 50 mg of asphaltene per liter of toluene and volumetric ratio of 7 were found as the best conditions from the points of view of applied analyzer. Hence, the toluene/heptane ratio 6 ACS Paragon Plus Environment

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in all experiments was constant and equal 1/7. Asphaltene concentration was 50 mg per liter of toluene in most of the experiments and a few reported results were carried out at 100 and 200 mg/L. Due to the limitation of the DLS technique and rapid sedimentation of precipitates, the results at the concentrations of 500 and 1000 mg/L were not reliable to report. Samples were prepared by dissolving asphaltene in toluene and the solution was diluted by heptane. The mixing of the solution and heptane was conducted in the cuvette of the analyzer to eliminate the transferring time and so to record the evolution of changes as soon as possible. Before inserting the cell, the sample was gently shaken for a few seconds to minimize the localized high heptane concentrations. Since the particle size distribution varied rapidly at the initial minutes of the tests, the particle size was measured at shorter time intervals at the start of each experiment than that at the end. To prevent solvent evaporation and to enhance temperature stability, the cuvette was sealed with a suitable tightly stopper and also a thermal cap. The particle size and zeta potential were recorded for a relatively long time (about 150 min) to ensure that there is no remarkable change at the end of each test.

3. Population Balance Modeling Nowadays, the population balance equation is widely used in predicting the behavior of the particulate systems. It is well known that the variation of the size of particles is a direct consequence of nucleation, growth, aggregation, and breakage events. The general form of the population balance equation considering these four main processes in a suspension of volume V can be expressed as:43 𝜕𝑛𝑣 𝜕(𝐺𝑣 𝑛𝑣 ) 𝑛𝑣 𝜕𝑉 𝑛𝑣𝑝 − 𝑛𝑣𝑓 + + + 𝜕𝑡 𝜕𝐿 𝑉 𝜕𝑡 𝜏

(3)

= 𝐵𝐴 (𝑣) − 𝐷𝐴 (𝑣) + 𝐵𝑅 (𝑣) − 𝐷𝑅 (𝑣) + 𝐵0 𝛿(𝑣 − 𝑣0 ) where nv is the population density of particles with volume v at time t, G is the linear particle growth rate, nvp and nvf are population densities at product and feed streams, respectively, B(v) and D(v) are the birth and the death rates of particles with volume v due to aggregation and breakage, respectively, and subscripts A and R represent aggregation and rupture(breakage), B0 is the nucleation rate, and the Kronecker delta (δ (v-v0)) means that nucleation happens only at the lowest measurable particle volume v0. In the present study, it is believed that the breakage, growth


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and the nucleation will not occur because the system is stationary and in a non-supersaturated state. In other words, nucleation has not been considered in performed simulation based on this assumption that all of the nuclei are generated at times before the first measurement is performed. Therefore, the population balance equation can be simplified for a stationary batch system of constant volume as the following: 𝑑𝑛𝑣 = 𝐵𝐴 (𝑣) − 𝐷𝐴 (𝑣) 𝑑𝑡

(4)

BA and DA obtained from Eqs. (5) and (6):11 1 𝑣 𝐵𝐴 (𝑣) = ∫ 𝐾𝐴 (𝑢, 𝑣 − 𝑢) 𝑛𝑣 (𝑢, 𝑡) 𝑛𝑣 (𝑣 − 𝑢, 𝑡)𝑑𝑢 2 0

(5)

and ∞

𝐷𝐴 (𝑣) = 𝑛𝑣 (𝑣, 𝑡) ∫ 𝐾𝐴 (𝑢, 𝑣) 𝑛𝑣 (𝑢, 𝑡)𝑑𝑢

(6)

0

in which KA(u, v-u) (its unit in SI is m3/sec) is the aggregation kernel and quantifies the effective formation rate of particles of volume v by cohesive impacts between particles/aggregates of volumes u and v-u. In the most practical cases, the analytical solutions of these integrals are very difficult or even impossible and thereby the different numerical methods: discretized, moment or Mont Carlo are used for evaluating them.44,45 The discretized population balance equation is by far the most widely used method in the modeling of asphaltene flocculation. Hounslow et al.14 proposed a geometric discretization for the solution of population balance equation in a crystallizer including nucleation, growth, and agglomeration. This method is simplified in the present study in which the only aggregation is considered:14 𝑖−2

𝑖−1

𝑑𝑁𝑖 1 2 = ∑ 2𝑗−𝑖+1 𝐾𝐴 (𝑉𝑖−1 , 𝑉𝑗 )𝑁𝑖−1 𝑁𝑗 + 𝐾𝐴 (𝑉𝑖−1 , 𝑉𝑖−1 )𝑁𝑖−1 − 𝑁𝑖 ∑ 2𝑗−𝑖 𝐾𝐴 (𝑉𝑖 , 𝑉𝑗 )𝑁𝑗 𝑑𝑡 2 𝑗=1

𝑗=1

𝑖𝑚𝑎𝑥

− 𝑁𝑖 ∑ 𝐾𝐴 (𝑉𝑖 , 𝑉𝑗 )𝑁𝑗 𝑗=1


(7)

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Here Ni is the numbers of aggregates with the characteristic volume of Vi. It is noteworthy that Vi = (vi+vi-1)/2, where vi and vi-1 are particles volumes at the upper and lower boundaries of the ith compartment, respectively.

3.1. Aggregation Kernel. When two aggregates i and j with characteristic volumes Vi and Vj and number concentrations Ni and Nj collide with each other, the effective aggregation rate (Ri,j) is calculated from:46 𝑅𝑖,𝑗 = 𝐾𝐴 𝑁𝑖 𝑁𝑗

( 8)

where the aggregation kernel, 𝐾𝐴 , is comprised of two parts:47 𝐾𝐴 = 𝛼. 𝛽𝑖,𝑗

( 9)

Here α is the collision efficiency for doublet formation, and βi,j is the collision frequency between particles in ith and jth intervals. The collision efficiency is the number of successful collisions to the total number of collisions. The collision efficiency was set to a constant value of unity in the most previous studies on asphaltene aggregation.12,13,20,23,24,26 This assumption was based on this fact that the porous and irregular agglomerates collide each other more than nonporous and rigid particles. Besides this simplified approach, a few numbers of other researchers endeavored to improve the accuracy of their proposed models by applying the collision efficiency.29,34,35 The collision frequency, βi,j, represents all collisions between two particles with sizes Vi and Vj and a number of presented expressions for it in the literature are shown in Table 1. Owing to the irregular and the porous nature of asphaltene particles, the aggregation kernel is also a function of fractal dimension. Mandelbrot48 first introduced the mathematical theory of fractals where the relationship between the number of segments, N, and the system’s resolution, L, is just: 𝑁 ∝ 𝐿−𝑑𝑓

(10)

df is the mass fractal dimension and its average value is generally within the range from 1 to 3. The most kernels in Table 1 were obtained using nonporous and rigid spherical particles. This assumption is not valid for asphaltene aggregates with fractal particles. They have larger collision diameters than rigid particles with the same weight. This fact causes the collision frequency to be greater than the predicted value by these kernels. The Smoluchowski’s kernel has been widely applied for modeling the agglomeration of particles.28,29,31–35,49 Although this kernel has a sound


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theoretical basis, recent works found a significant difference between models and experimental results.29,34,35 In the present work, the Smoluchowski’s kernel was rectified to consider the fractal structure. Using volume instead of length and fractal dimension instead of the power of volume in Smoluchowski’s kernel results in the applied kernel in the present study: 1/𝑑𝑓

1/𝑑𝑓

+ 𝑉𝑗 )2 2𝐾𝑇 (𝑉𝑖 𝐾𝐴 (𝑉𝑖 , 𝑉𝑗 ) = 𝛼. 1/𝑑𝑓 1/𝑑𝑓 3𝜇 𝑉 .𝑉 𝑖

(11)

𝑗

According to the previous studies, the mass fractal dimension of asphaltene aggregates falls in the range from 1.06 to 2.0.23,50 In this study, the asphaltene fractal dimension was considered to be constant and equal to 1.65. Obviously, the aggregation of asphaltene clusters is generally a direct consequence of perikinetic, orthokinetic or differential settling mechanisms. The perikinetic, orthokinetic and differential settling mechanisms are considered to be the result of the Brownian motion of particles, sheared dispersions, and the difference in settling velocities of particles, respectively. The perikinetic flocculation is the dominant mechanism in this study for two reasons: (i) the influence of orthokinetic flocculation is trivial in the lack of fluid shear and (ii) in all tests, the maximum mean size of asphaltene clusters is less than 1μm for which the differential settling effect is negligible in comparison to thermal motion influence. 3.2. Numerical Solution. The evolution of asphaltene particle size distribution is predicted by the solution of the population balance equation. The first measurement of the aggregate size distribution was considered as the initial condition for numerical solution. The size distribution by number was used to obtain the cumulative numbers of aggregates in each size class. The output of the Zetasizer software is represented by the percentage of particle population, and thus it is necessary to convert these results into a cumulative particle size distribution. The total number of particles (NT) is a function of the total mass of asphaltenes (MT), the skeletal density of asphaltene particles (ρA), and the porosity of aggregates (ε), as follows: 𝑁𝑇 =

100𝑀𝑇 𝑖_𝑚𝑎𝑥 𝜌𝐴 ∑𝑖=1 𝑁𝑖 𝑉𝑖 (1

− 𝜀𝑖 )

(12)

The skeletal density of asphaltenes is assumed to be constant and equal to 1200 kg/m3.51 To improve the accuracy of the present model, the porosity is considered to be variable in the aggregates of different sizes. The porosity distribution of secondary particles is calculated from:


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𝜀𝑖 = 1 −

𝑥𝑖 𝑉𝑝 𝑉𝑖

(13)

where 𝑥𝑖 is the number of primary particles supposed to be sphere of volume 𝑉𝑝 in the floc with characteristic volume 𝑉𝑖 and is given by: 𝑑𝑠 𝑑 ) 𝑓 𝑑𝑝

𝑥𝑖 = (

(14)

Here, 𝑑𝑠 is the diameter of secondary particles and 𝑑𝑝 is the diameter of primary particles. The cubic spline interpolation is employed to find the values of the cumulative numbers of aggregates Ni within the interval with geometric mean particle volume Vi. Since the resultant discretized equations were nonstiff ordinary differential equations, the ode45 solver in MATLAB was used to provide a better accuracy in prediction of particle size distribution.

4. Results and Discussion 4.1. Characterization of Asphaltene Samples. In the determination of the asphaltene particle size by the Zetasizer, the dynamic viscosity of dispersant and the refractive index of both dispersion medium and asphaltene particles must be specified and imported to the software of Zetasizer. The glass capillary viscometers equipped with a thermostatic hot water bath were used to measure the sample kinematic viscosity at different temperatures. To convert kinematic viscosity to dynamic viscosity, fluid densities were accurately measured by a pycnometer, using distilled water as the reference fluid. The variation of measured values of mixture dynamic viscosity was found negligible during the aggregation (Figure 1). The behavior shown in Figure 1 is compatible with Einstein correlation (Eq. (15)). It is the volume of the asphaltene particles that affects the viscosity of the suspending fluid. Therefore, the particle size evolution during aggregation does not have a significant effect on the viscosity. Einstein52 derived an analytical equation for calculation of the viscosity of dilute suspensions containing a large number of rough, monosized and spherical particles, as follows: 𝜇 = 𝜇∗ (1 + 2.5Φ)

(15)

where µ is the viscosity of the mixture, µ* is the viscosity of the pure dispersant, and Φ is the volume fraction of dispersed particles present in the medium. The refractive index is the second


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parameter that must be specified experimentally for both dispersion medium and asphaltene. The refractive index of the sample is required for calculation of the average diameter, as follows:53,54 𝜃 2 1 𝑘𝐵 𝑇 4𝜋𝑛 sin (2) 𝑑= [ ] 𝑎 3𝜋𝜇 𝜆0

(16)

where n is the refractive index of the dispersion medium, θ is the scattering angle, 𝜆0 is the laser wavelength in vacuum, and a is a constant found by least square fitting of the intensity autocorrelation function. The refractive index of asphaltene particles is required to convert intensity distribution directly measured by Zetasizer to volume or number densities. As noted in the literature, the refractive index of asphaltene has a value of 1.72.55,56 The refractive indices of dispersion media (toluene-heptane mixture + evolving asphaltene particles) at different temperatures were measured by a Bellingham & Stanley refractometer and results are shown in Figure 2. The data in Figure 2 does not demonstrate significant variations in the refractive index of the mixture with time due to constant asphaltene volume and solution composition. With the decreasing temperature of the sample, there is a slight increase in the refractive index value of the mixture, and this may be attributed to the size and the fractal structure of asphaltene aggregates. As the temperature is decreased, the aggregates become larger and more porous leading to more propagation of light.

4.2. Effect of Temperature on Kinetics of Asphaltene Aggregation. At the start of the experiments, heptane and stock solution (toluene + asphaltene) were analyzed by the Zetasizer to check the presence of extraneous materials and no particles were detected before mixing. Verification of the instrument performance can be found in the Supporting Information. The experimental evolving size distributions during asphaltene aggregation at different temperatures are depicted in Figure 3a-d. Figure 4 presents the effect of temperature on the average diameter of asphaltene particles as a result of aggregation in asphaltene-heptane-toluene solution. As seen in Figure 4, at the initial time (less than 10 min) the mean diameter of asphaltene particles is slightly higher than that at a lower temperature and after 10 min this trend is reversed. The maximum attainable average diameter of particles is increased with the decrease of temperature. These results indicate that the aggregation kinetics of asphaltene particles and also their solubility in solution strongly depend on the temperature. The dependency of average diameter on the temperature is 12 ACS Paragon Plus Environment

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complicated due to several competing effects of temperature. The experimental data show that the solubility of asphaltenes in the toluene-heptane mixture is remarkably affected by temperature:57 1/2

∆𝐻 𝑉 − 𝑅𝑇 𝛿=[ ] 𝑉

(17)

where δ, ΔHv, V, R, and T are the solubility parameter, the heat of vaporization, the molar volume, the universal gas constant and the absolute temperature, respectively. As temperature increases, the difference between the solution solubility parameter and the asphaltene solubility parameter becomes smaller and so lesser amount of asphaltene comes out of the solution by nucleation to form primary asphaltene particles. Decreasing of primary particles results in a lower aggregation rate (see Eq. (7)) and so smaller particles. Various trends have been addressed in the refining literature for the effect of temperature on the asphaltenes solubility pertaining to the type of normal alkanes.3–5,28,58,59 It was observed by Maqbool et al.28, Mansur et al.30, and Espinat et al.60 that the difference between solubility parameters decreases with rising temperature while Nielsen et al.21 reported the increasing trend for the difference between solubility parameters with an increase in temperature. The aggregation process is generally classified into two mechanisms depending on the concentration of asphaltenes in toluene. The critical micelle concentration (CMC) is the concentration limit below which the asphaltenes in solution are in a molecular state (known as the asphaltene particles), while, beyond the CMC, the asphaltenes will start to form micelles by association with other asphaltenes in order to diminish the energy of the system.61 For concentrations less than the CMC, i.e. 3g of asphaltene per liter of toluene, the aggregation kinetics are controlled by the diffusion of asphaltene particles, while above the CMC the agglomerates are formed from asphaltene micelles. The former is called diffusion limited aggregation (DLA) and the latter is called reaction limited aggregation (RLA).62,63 All the experiments in the present study are examined below CMC and thereby the aggregation process is controlled by the impact of asphaltene particles. Under these circumstances and besides the number of available primary particles, the viscosity of surrounding fluid plays an important role in the effective diffusivity and so on the collision rate of asphaltene particles. Higher temperature provides a higher nucleation rate of the primary particles and also faster Brownian diffusion of these particles. These two synergetic effects at initial 10 min of experiments, results in the initial formation of larger flocs at 13 ACS Paragon Plus Environment

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a higher temperature. As the aggregation proceeds, the number of available primary particles decreases significantly and aggregates attain their final steady state size. Figure 5 represents the obtained aggregates size at asphaltene concentrations of 100 and 200 mg/L. The same as low asphaltene concentration (50 mg/L), the maximum attainable aggregate size decreases with the increase of temperature. Also with an increment of asphaltene concentration, the mean size of the asphaltene particles is increased, and it can be attributed to the increase in the number of generated primary particles. While the initial observed slope of results at 100 mg/L is the same as previous (50 mg/L), a different trend is revealed at high concentration (200 mg/L). The lower initial mean size of particles at high temperature than that at low temperature can be attributed to the dependency of the nucleation rate of primary particles on both temperature and concentration. In other words, beyond a certain limit (between 100 and 200 mg/L), the nucleation overshadows the aggregation.

4.3. Modeling the Asphaltene Flocculation. A discretized form of population balance equation is used to simulate the experimental results and predict the kinetic coefficient of asphaltene aggregation process. After extracting the initial distribution of particles from measurements, Eq. (7) was solved for 46 size bins and continued until a plateau value of average diameter is reached. The number of bins was sufficient to cover all particle sizes evolved during the process. The best fitted values of collision efficiencies at different fixed temperatures were found by matching the average diameter and the broadness of the asphaltene size distributions obtained from measurement and simulation. The broadness of distribution is quantified in terms of coefficient of variation, CV: 𝐶𝑉 =

𝜎 𝑑

(18)

where CV, σ, and d are the coefficient of variation, the standard deviation of a distribution and the average diameter, respectively. The results of population balance model are compared with experimental data in Figure 6, where the solid lines denote the numerical prediction, and the symbols exhibit the experimental data.

In order to find the mechanism of aggregation,

experimental data were matched corresponding relations exist for both DLA and RLA mechanisms. In the DLA process the relationship between the hydrodynamic radius, R, and time of agglomeration is power law, as follows:64 14 ACS Paragon Plus Environment

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𝑅 = 𝐴𝑅 𝑡 1/𝑑𝑓 + 𝑅0

(19)

where AR and R0 are the constant of aggregation rate and radius of primary particles, respectively. For the RLA mechanism, an exponential growth rate has been considered as Eq. (20):64 𝑅 = 𝑅0′ exp[𝑡/𝜏𝑅𝐿𝐴 ]1/𝑑𝑓

(20)

Here, 𝑅0′ is the radius of a primary particle and 𝜏𝑅𝐿𝐴 is the exponential characteristic time. Experimental data at all temperatures generally follow a power law relationship, indicating the governing influence of DLA mechanism on the flocculation process. When Eq. (19) was fitted to the experimental data, the R-squared values were 0.794, 0.919, 0.835, and 0.831 at four temperatures, 20, 40, 60 and 80°C, respectively. The results of fitting Eq. (20) to the same data were very poor (R-squared values were about 0.5). Figure 7 shows the effect of temperature on the broadness of the experimental size distributions. The comparison of calculated and measured values of CV shown in this figure reveals that the accuracy of the proposed model is reasonably good at all temperatures. 4.3.1. Collision Efficiency. A two-step procedure is used for analyzing the variations of collision efficiency with time and temperature: (1) in the first step, the best fitted value of collision efficiency at each temperature and time interval is found by matching the simulated data to experimental results (matching mean diameters and coefficients of variation of distributions) (Figure 8). (2) In the second step, the collision efficiency is found by matching the model to all of the experimental results obtained at different time intervals of each test done at a constant temperature by searching for a minimum of the mean squared error (MSE) (Figure 9). Table 2 presents the optimum values of the collision efficiencies at the minimum value of the objective function. Figure 8 exhibits that the collision efficiency extracted at each time interval. The collision efficiency declines from its maximum initial value to a plateau at each temperature. The reduction in the collision efficiency at larger aggregates can be associated to increase of surface charge of aggregates and will be discussed later. Reduction of the collision efficiency at a fixed temperature demonstrates that larger aggregates must impact more than smaller ones to attach together. This fact provides a higher chance for larger aggregates to explore other configurations and to attain a structure with lower porosity compared to smaller ones generated at early stages of flocculation. These findings are in good agreement with those obtained by Rahimi and Solaymani-Nazar25 who


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observed that fractal dimension increased from its initial value of 1.6 to 2.3 at the end of the experiment. The optimum values of the collision efficiency at different temperatures are presented in Table 2. In Figure 9, the optimized collision efficiency for the aggregation of asphaltenes at different temperatures is depicted. The temperature rise from 20 to 80°C caused 30 fold reduction in collision efficiency. The obtained values of collision efficiency in the present study are 1000 fold greater than that of Maqbool et al.29 The difference can be attributed to assumptions of Maqbool et al.29 who supposed asphaltene particles to be rigid and nonporous, without any consideration of the fractal structure of aggregates. To predict the collision efficiency for perikinetic aggregation, Fuchs developed a relationship between the stability ratio (W) and the total interparticle potential (𝜑 𝑇 ):65 𝜑𝑇 ) 𝑘𝐵 𝑇 𝑊 = 2∫ 𝑑𝑈 2 0 (𝑈 + 2) ∞ exp(

(21)

where 𝜑 𝑇 is the total energy between two aggregates (J), and U is a function of the radius of the particles (R) and particle separation distance (S), as follows:65 𝑈=

2𝑆 (𝑅1 + 𝑅2 )

(22)

Note that the stability ratio is the inverse of the collision efficiency. It can be shown that an exponential relationship between the stability ratio and temperature exists:65 𝛼=

1 𝜑𝑚𝑎𝑥 = 𝐶exp(− ) 𝑊 𝑘𝐵 𝑇

(23)

Here, C is a constant and 𝜑𝑚𝑎𝑥 is the maximum value of potential function. A detailed explanation of the approach and its mathematical validation can be found in the Supporting Information. This equation is valid if the value of collision efficiency is much smaller than one. The calculated value of the collision efficiency in the present study is in the range of 10-8 to 10-10 (Figure 9), and so Eq. (23) can be applied to investigate the stability of the system. The closeness of R-squared value to unity (R2=0.9661) indicates the validity of the model and the precision of experimental data (Figure 9). To better understand the effect of temperature on the kinetics of asphaltene aggregation, it is valuable to relate the collision efficiency to both temperature and difference in the solubility parameters. Recent investigations reveal that the energy barrier vary inversely with the difference between asphaltene and solution solubility, as follows:31,32,34,35 16 ACS Paragon Plus Environment

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𝜑𝑚𝑎𝑥 ∝

1 (𝛿𝑎𝑠𝑝ℎ. − 𝛿𝑠𝑜𝑙𝑛. )2

(24)

where 𝛿𝑠𝑜𝑙𝑛. and 𝛿𝑎𝑠𝑝ℎ. are the solution and asphaltene solubility parameters (Pa0.5), respectively. Using the above equation, the collision efficiency under various thermodynamic conditions of temperature, pressure and composition can be calculated. Using Eqs. (23) and (24) yields: −ln(𝛼) ∝

1 𝑇(𝛿𝑎𝑠𝑝ℎ. − 𝛿𝑠𝑜𝑙𝑛. )2

(25)

Due to the strong dependency of solubility parameters on temperature, it can be concluded from Eq. (25) that the aggregation rate of asphaltene particles is intimately controlled by temperature. Therefore, the increase of collision efficiency with decrease of temperature can be interpreted by this fact that the level of decrease in (𝛿𝑎𝑠𝑝ℎ. − 𝛿𝑠𝑜𝑙𝑛. )2 resulted from the increase in temperature is more significant than the level of increase in temperature itself. Hence the overall effect of these changes will be the increase in collision efficiency based on Eq. (25). In order to support this hypothesis, the internal pressure concept (π) was used to estimate the value of solubility parameter of heptane-toluene mixture, as follows:66 𝜕𝑈 𝜕𝑃 𝛼𝑃 ) 𝑇 = 𝑇( )𝑉 − 𝑃 = 𝑇 −𝑃 𝜕𝑉 𝜕𝑇 𝜅𝑇

2 𝜋 = 𝛿𝑠𝑜𝑙𝑛. =(

(26)

where 𝛼𝑃 is the volume expansivity (K-1) and 𝜅 𝑇 is the isothermal compressibility (MPa-1). The volume expansivity and isothermal compressibility of pure toluene and heptane were calculated from existing correlations in the literature.67,68 Then the solubility parameter of mixture is obtained from the volume-weighted average of pure solubility parameters. The correlation of Yarranton and Masliyah was employed to calculate the asphaltene solubility parameter.51 It is well known from recent studies that the asphaltenes are dominated by C50-C100 aromatics having molecular weights (MW) between 700 and 1400 kg.kmol-1.2 Because of the polydispersity nature of asphaltenes, the molecular weight of asphaltene is usually considered as an average value of the whole distribution and therefore a constant value of 1050 kg.kmol-1 is considered in this study to report the results. To check out the effect of MW of asphaltene on solubility parameter, calculations were repeated over a wide range of MW (700-1400 kg.kmol-1) and the same trends were obtained. Figure 10 shows the variation of collision efficiencies extracted from modeling in the present study besides the calculated value of 𝑇(𝛿𝑎𝑠𝑝ℎ. − 𝛿𝑠𝑜𝑙𝑛. )2 as a function of temperature. The squared value of the 17 ACS Paragon Plus Environment

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difference between solubility parameters is numerically smaller than absolute temperature by an order of magnitude and so its decrement by about 9 MPa makes up the temperature increment by 60 K. The trend of calculated difference between solubility parameters is compatible with the results of Mohammadi et al.35 Figure 11 presents the effect of temperature on the maximum energy barrier between asphaltene aggregates. The maximum energy barrier applied in this figure is calculated from Eq. (23). The energy barrier is generally composed of electrical repulsion and van der Waals attraction. The relative magnitude of these forces determines whether a collision is successful or not. At low temperatures, the van der Waals attraction increases, the structure of double layers compresses and the energy barrier decreases in the overlapping region of steric layers, hence the asphaltene particles destabilize. In other words, the magnitude of electrical repulsion is significantly descended by steric layers compaction, consequently, more fractions of impacts will have enough thermal energy to prevail over the energy barrier.

4.4. Consistency between the Zeta Potential Measurements and Results of Model. For validating the results of the model, a series of zeta potential measurements were carried out at different fixed temperatures. It has been proven experimentally that the surface charge on asphaltene particles within an organic mixture arises from the dissociation of basic or acidic surface functional groups. Surface groups such as pyridine(basic) and carboxylic(acidic) result in positive and negative zeta potentials, respectively.69 Organic dispersants with a low dielectric constant cannot form ionic species in solution, but proton transfer between the dispersant and the ionizable groups provides ions and forms an adsorbed films over the particles surface. The zeta potential of particles in nonaqueous liquids can be over ±100 mv as a result of strong acid-base interactions.70 It has been experimentally observed that asphaltenes will coagulate under influence of an electrical field, that is an evidence for the surface charge of asphaltene particles.9 For measuring the zeta potential, the dielectric constant, the viscosity and the refractive index of the mixture are needed to specify and entered into the Zetasizer software. The dielectric constant data for pure toluene and heptane were taken from data books.71 The dielectric constant of the mixture was calculated from the following formula:72 𝜀ℎ𝑒𝑝𝑡𝑎𝑛𝑒 − 𝜀𝑚𝑖𝑥𝑡𝑢𝑟𝑒 𝜀𝑡𝑜𝑙𝑢𝑒𝑛𝑒 1/3 Φℎ𝑒𝑝𝑡𝑎𝑛𝑒 = 1 − ( ) 𝜀ℎ𝑒𝑝𝑡𝑎𝑛𝑒 − 𝜀𝑡𝑜𝑙𝑢𝑒𝑛𝑒 𝜀𝑚𝑖𝑥𝑡𝑢𝑟𝑒

(27)

where ε is the dielectric constant and  is the volume fraction. A universal dip cell is used at which the temperature should not exceed 70°C, and therefore the experiments were conducted at 20, 40, 18 ACS Paragon Plus Environment

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60 and 70°C and 1 atm. The DLVO (Derjaguin-Landau and Verwey-Overbeek) theory relates the stability of a particle in suspension to its total potential energy. This theory states that the total potential energy is the sum of the van der Waals attraction (𝜑𝐴 ), electrical double layer repulsion (𝜑𝑅 ) and potential energy due to the solvent (𝜑𝑆 ):47 𝜑 𝑇 = 𝜑𝐴 + 𝜑𝑅 + 𝜑𝑆

(28)

In practice, the contribution of potential energy arising from the solvent is negligible at low separation distances (less than a few nanometers). Therefore the colloidal stability is characterized by the sum of electrical double layer repulsion and van der Waals attraction. Finding the relation between the attractive and repulsive potentials and the zeta potential is important due to the lack of direct measurement of them. Figure 12 shows the measured zeta potential of asphaltene particles in the mixture (toluene + heptane) during the aggregation process at a fixed temperature. The linear superposition approximation method assumes that the repulsive potential among two interacting surfaces obeys the linearized Poisson-Boltzmann equation:47 𝜑𝑅 = 𝜋𝑒𝑑𝜉 2 exp(−ҡℎ)

(29)

where ξ is the zeta potential, e is the electron or elementary charge, ҡ is the Debye-Huckel reciprocal length, and h is the surface to surface separation distance. According to Eq. (29) and results shown in Figure 12, large aggregates experience higher repulsive potential comparing to small aggregates. As aggregation proceeds, the energy barrier becomes larger and a smaller fraction of collisions will have sufficient energy to pass through a maximum of potential energy (Figure 13a). Figure 13 (panel a) shows that the energy barrier generally rises with particle size leading to smaller aggregation rate for larger aggregates. When two particles collide and form a larger aggregate, the exposed surface area is reduced while the total charge remains constant, resulting in an increase in surface charge density. This increase in surface charge density reinforces the repulsion against the attraction and results in a higher energy barrier retarding the flocculation (Figure 13a). During aggregation, the fractal aggregates with multilateral slender branches having more irregularities in their surface are generated. If the thickness of the roughness layer is very large compared to the surface-surface separation distance, the interactions decrease and so the rate of flocculation slows down. The slender branches collapse and the surface roughness decreases due to the restructuring, but in the present study, it seems to be negligible due to the lack of shear. These findings are in good agreement with calculated collision efficiencies (Figure 8), where the 19 ACS Paragon Plus Environment

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collision efficiency decreased during the aggregation phenomenon. Figure 14 demonstrates the effect of temperature on the time-averaged values of the measured zeta potential of the asphaltene particles. With increasing the temperature, the zeta potential of the asphaltene agglomerates increases. In other words, as the temperature rises the asphaltene aggregates become stable at lower diameters. It should be noted that, besides the formation of asphaltene aggregates at primary minimum, these aggregates can also be formed at a secondary minimum (Figure 13b). At the secondary minimum, two flocs form reversible weaker bonds than those at a primary minimum. The electrical repulsion and van der Waals attraction follow exponential and power law functions of separation distance, respectively. At adequately large surface to surface separation distances, the contribution of attractive forces is always greater than the repulsive forces that provide a secondary minimum in the potential energy profile. The weak bonds at secondary minimum are strong enough to prevent the breakup of the asphaltene aggregates by Brownian motion, while may disrupt under an external force such as vigorous stirring. The secondary minimum seems to have a pronounced effect on the stability and aggregation of asphaltenes and it can be the subject of a subsequent work. Additionally, the temperatures can affect the ratio of the thickness of the electric double layer to particle radius. At low temperatures, the double layer thickness becomes smaller compared to the diameter of particles, and so the van der Waals attraction outweighs repulsion and pulls asphaltene particles into an irreversible adhesion. These observations are in quite close agreement with the conclusions of population balance modeling, where it was seen that the collision efficiency decreases with particle size.

5. Conclusions It was observed that the average size of asphaltene aggregates decreases with an increment of temperature, and this is in good agreement with reviewed literature. Furthermore, the increase in temperature results in increasing the initial rate of flocculation at a low asphaltene concentration (50 mg/L) and the broadness of the size distribution. The effect of temperature on the initial rate of aggregation is justified by its effects on nucleation and aggregation rates. Also, according to the findings of the present research, it can be deduced that between two opposite effects of temperature, the increment of aggregates solubility was more important than decreasing of viscosity, and so resulting in a decrease of aggregation rate. The population balance model, regarding the fractal structure of asphaltene aggregates, predicted this trend with a reasonable accuracy. The calculated collision efficiency was exponentially declined with an increase of 20 ACS Paragon Plus Environment

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temperature. The model results were validated by measuring the zeta potential of asphaltene aggregates under different temperatures and a good consistency was observed in each case. Increasing the zeta potential by an increment of temperature means that the energy barrier becomes higher due to increasing surface charge density. In other words, the results of zeta potential showed that the van der Waals attraction outweighs the electrostatic repulsion at lower temperatures. At a specified temperature, the zeta potential of asphaltene particles increases as the aggregation proceeds. This finding proofed the direct dependency of the interaction energy to the particle size. The predominant mechanism of asphaltene aggregation in the applied organic medium was confirmed to be DLA by matching the experimental data to characteristic curves of both DLA and RLA mechanisms.

 Acknowledgements The authors are grateful to the Research Center of Ahwaz Faculty of Petroleum for their permission to use the laboratory facilities and to Abadan Oil Refinery for providing the distillation residue. Also, the authors gratefully acknowledge the National Iranian South Oil Company (NISOC) for its technical and financial support under Grant No. 93-DK-926.

 Author Information Corresponding Author *E-mail: [email protected] Present Address Department of Gas Engineering, Ahwaz Faculty of Petroleum, Petroleum University of Technology (PUT), Kout Abdollah, Ahwaz, Iran. Notes The authors declare no competing financial interest.

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Page 25 of 35

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

Energy & Fuels

Table 1. Some collision frequencies presented in the existing literature18,19,23,26,43,46,47,49,73–75 Motion type

Collision frequency β(𝑅1 , 𝑅2 ) =

Brownian motion

Reference

2𝐾𝐵 𝑇 (𝑅1 + 𝑅2 )(𝑅1−1 + 𝑅2−1 ) 3𝜇

Smoluchowski (1917) Hounslow and Paterson

𝛽0

Size-independent

4 β(𝑅1 , 𝑅2 ) = 𝐺(𝑅1 + 𝑅2 )3 3

Laminar Shear

Differential settling

Inertia and gravitational settling kernel,

Laminar Shear (Fractal structure)

β(𝑅1 , 𝑅2 ) = (

Smoluchowski (1917)

8𝜋 (𝑅 + 𝑅2 )7/3 𝜀 1/3 3 1

Saffman and Turner (1955) Kruis and Kusters (1996)

2𝜋𝑔 )(𝜌𝑠 − 𝜌𝐿 )(𝑅1 + 𝑅2 )3 (𝑅1 − 𝑅2 ) 9𝜇

Friedlander (1977)

β(𝑅1 , 𝑅2 ) = √

Turbulent Shear

Thompson empirical

(1994)

β(𝑅1 , 𝑅2 ) = 𝐶(𝑅12 − 𝑅22 )(𝑅1 + 𝑅2 )2 β(𝑑1 , 𝑑2 ) = 𝐶𝐴

𝛽𝑖,𝑗 =

(𝑑13 − 𝑑23 )2 𝑑13 + 𝑑23

1 𝑑𝑓 0.31𝐺𝑉𝑃 (𝑥𝑖

+

Thompson (1968)

1 𝑑𝑓 3 𝑥𝑗 )

1

Barthelmes et al. (2003)

1

Empirical kernel (Fractal structure)

𝐼𝑢 𝐼𝑣 𝐷 𝐷 β(𝑢, 𝑣) = 𝐾𝐹 ( 𝐼𝑣 𝑓 + 𝐼𝑢 𝑓 )𝛾 𝐼𝑢 + 𝐼𝑣 𝐼𝑢 + 𝐼𝑣

Empirical kernel (Fractal structure)

𝐼𝑢 𝐼𝑣 𝐷 𝐷 β(𝑢, 𝑣) = 𝐾𝐹 ( 𝐼𝑣 𝑓 + 𝐼𝑢 𝑓 )𝛾 (𝑆 𝑏 ) 𝐼𝑢 + 𝐼𝑣 𝐼𝑢 + 𝐼𝑣

Brownian Motion fluid shear

β(𝑑1 , 𝑑2 ) =

and

1

Drake (1972) & Schumann (1940)

1

2𝐾𝐵 𝑇 𝑑1 − 𝑑2 2 𝐺 ( ) + (𝑑1 + 𝑑2 )3 3𝜇 𝑑1 𝑑2 6


Rastegari et al. (2004)

Khoshandam and Alamdari (2010)

Nassar et al. (2015)

Energy & Fuels

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

Page 26 of 35

Table 2. Collision efficiencies at minimum MSE

Temperature (K)

Collision Efficiency

293.15

1.16 × 10-8

303.15

6.09 × 10-9

333.15

1.94 × 10-9

353.15

3.95 × 10-10


Page 27 of 35

0.5

Viscosity (cP)

0.45 0.4 0.35 0.3 0.25 20°C

40°C

60°C

80°C

0.2 0.15 0

20

40

60 80 Time (min)

100

120

140

160

Figure 1. Dynamic viscosity of toluene + heptane mixture during aggregation process of asphaltene (50 mg asphaltene per L of toluene)

1.4 1.395 1.39

Refractive Index

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

Energy & Fuels

1.385

1.38 1.375 1.37 1.365

20 °C

40 °C

60 °C

80 °C

1.36 0

20

40

60 80 Time (min)

100

120

140

160

Figure 2. The effect of temperature on the refractive index of mixture during aggregation of asphaltene


Energy & Fuels

(a)

30

Initial Time

25

20 min

20

Final Time

Initial Time

(b)

Number (percent)

Number (percent)

30

15 10 5

25

20 min

20

Final Time

15 10 5 0

0 10

100

1000

10

10000

Diameter (nm)

25 20

1000

10000

Diameter (nm)

(d)

Initial Time

25

Number (percent)

20 min Final Time

15

100

30

Initial Time

(c)

Number (percent)

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

Page 28 of 35

10 5 0

20 min

20

Final Time

15 10 5 0

10

100

1000

10000

10

Diameter (nm)

100

1000

10000

Diameter (nm)

Figure 3. The size distribution of the asphaltenes particles at different resting times in a mixture of toluene/heptane (1/7 v/v) containing 50 mg of asphaltene per liter of toluene at temperature of (a) 20; (b) 40; (c) 60 and (d) 80°C


Page 29 of 35

700

Average Diameter(nm)

600 500 400

300 20°C

40°C

60°C

80°C

200 100 0

50

100 Time(min)

150

200

Figure 4. Mean size of asphaltene particles at temperatures 20, 40, 60 and 80°C in a mixture of toluene/heptane (1/7 v/v) containing 50 mg of asphaltene per liter of toluene

1800 1600

Average Diameter (nm)

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

Energy & Fuels

1400 1200

1000 800 600 400 200 0 0

30

60

20°C(100mg/L)

60°C(100mg/L)

20°C(200mg/L)

60°C(200mg/L)

90

120

150

180

210

Time (min) Figure 5. Enlargement of average particle diameter at different concentrations of asphaltenes


Energy & Fuels

800


700 600 500 400 300 200

20°C 60°C 20°C 60°C

100

40°C 80°C 40°C 80°C

0 0

20

40

60

80

100 120 Time (min)

140

160

180

200

Figure 6. Model predictions for enlargement of asphaltene particles in a mixture of toluene/heptane (1/7 v/v) containing 50 mg of asphaltene per liter of toluene

4 3.5

Coefficient of Variation

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

Page 30 of 35

3 2.5 2 Experimental

1.5

Model

1 0.5 0 285

305

325

345

365

Temperature(K)

Figure 7. Comparison between experimental and calculated coefficient of variation data for different temperatures


Page 31 of 35

10 20°C

40°C

60°C

80°C

α × 109

1

0.1

0.01 0

20

40

60

80

100

120

140

160

Time(min)

Figure 8. Optimized collision efficiency versus time at various temperatures

14 12 10

α × 109

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

Energy & Fuels

8 6 y = 2E+08e-0.056x R² = 0.9661

4 2 0 280

290

300

310

320

330

340

350

360

Temperature (K)

Figure 9. Relationship between the optimized collision efficiency and temperature obtained by minimizing the MSE


Energy & Fuels

Extracted collision Efficiencies from Model Calculated values

8700

α × 109

2.00

8500 8300

1.50

8100

1.00 7900

0.50

7700

0.00

(K.MPa)

2.50

8900

T (δasph-δsolution)2

3.00

7500 280

300

320

340

360

Temperature (K) Figure 10. Variation of collision efficiency and 𝑇(𝛿𝑎𝑠𝑝ℎ. − 𝛿𝑠𝑜𝑙𝑛. )2 versus temperature

10

9

𝜑𝑚𝑎𝑥 × 1020(J)

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

Page 32 of 35

8 7 6 5

4 280

300

320

340

Temperature (K)

Figure 11. Maximum energy barrier versus temperature


360

Page 33 of 35

90 80

Zeta Potential (mv)

70 60 50 40 30 20

10

20°C

40°C

60°C

70°C

0 0

20

40

60 80 Time (min)

100

120

140

160

Figure 12. Increment of zeta potential of asphaltene particles during aggregation at different fixed temperatures

(a)

(b) Bigger Particles

Electrostatic Repulsion

Interaction Energy

Interaction Energy

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

Energy & Fuels

Smaller Particles

Energy Barrier

Primary Minimum

Secondary Minimum van der Waals Attraction

Separation Distance

Separation Distance

Figure 13. Total interaction energy of two asphaltene aggregates as a function of separation distance: (a) influence of particle size, and (b) the separate roles of attractive and repulsive forces


Energy & Fuels

80

Average Zeta Potential (mv)

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

Page 34 of 35

y = 1E-13x5.8485 R² = 0.9662

70 60 50 40 30 20 10 0

280

290

300

310

320

330

340

350

Temperature (K)

Figure 14. The effect of temperature on the zeta potential of asphaltene particles within toluene + heptane mixture (50 mg asphaltene per L of toluene)


Page 35 of 35

60 ˚C

700

140

600

120

500

100

400

80

300

60

200

40

100

20 ˚C

0

0

20

Diameter(20°C)

Diameter(60°C)

Zeta Potential(20°C)

Zeta Potential(60°C)

25

50

75

Time (min)

Van der Waals attraction tends to enhance asphaltene aggregation

ACS Paragon Plus Environment

100

125

150

0

Zeta Potential (mv)

Particles are stabilized against further aggregation by steric layers


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

Energy & Fuels

Influence of Temperature on Aggregation and Stability of Asphaltenes

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