Influence of Temperature on Aggregation and Stability of Asphaltenes

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Catalysis and Kinetics

Influence of Temperature on Aggregation and Stability of Asphaltenes: II. Orthokinetic Aggregation Mohammad Torkaman, Masoud Bahrami, and Mohammad Reza Dehghani Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.7b03601 • Publication Date (Web): 18 Apr 2018 Downloaded from http://pubs.acs.org on April 18, 2018

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Low temperature

High temperature

Black Box - Phase dominated by nucleation & aggregation (I)

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Average Diameter

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Kinetic phenomeno n dominated by aggregation (II)

Kinetic phenomeno n dominated by fragmentati on (III)

First measurement

Time ACS Paragon Plus Environment

Balance of aggregation & fragmentatio n (IV)

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Influence of Temperature on Aggregation and Stability of Asphaltenes: II. Orthokinetic Aggregation †

Mohammad Torkaman, Masoud Bahrami, †

1,†

Mohammad Reza 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 The effect of temperature on asphaltene aggregation has not been investigated at different shear rates. Following our previous work, the effects of temperature and shear rate on the evolution of asphaltene aggregate size distribution in a heptane-toluene mixture are experimentally studied within a Couette flow device. At fixed temperature and shear rate, the average diameter of flocs initially increased with time until it reached a maximum value and then declined to a constant steady state size as a result of the balance between the aggregation and fragmentation. Increasing the temperature resulted in a smaller steady state average diameter. Results of experiments indicated that the agitation rate affects the evolution kinetics of asphaltene aggregates less than temperature. The effect of shear rate on the fragmentation rate was found higher than that on aggregation which is resulted in a maximum in the average steady state diameter versus shear rate. A fractal geometric population balance model was developed to simulate the experimental results and to extract the kinetics of the aggregation and fragmentation processes. In the proposed model, three fitting parameters, including the collision efficiency, the fractal dimension, and the breakup rate coefficient were used to match the model on experimental data. The calculated collision efficiency was strongly dependent on temperature. The results showed that the collision efficiency decreases with increase in temperature in both perikinetic and orthokinetic aggregations. Based on the obtained breakup rate coefficients, the floc strength decreases with temperature.

1

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

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1. Introduction 1.1. Background. Crude oils are complex mixtures of hydrocarbons generally divided into four major fractions with different degrees of solubility in a solvent. These fractions are saturates, aromatics, resins, and asphaltenes (SARA).1 Asphaltene consists of polycondensed aromatic sheets and aliphatic chains, charged with transition metals like nickel, iron, and vanadium and heteroatoms like nitrogen, oxygen, and sulphur.1–3 Asphaltenes are not dissolved in n-heptane, however, toluene can easily dissolve them.4–6 Typically, asphaltenes are precipitated from crude oils or bitumens by adding n-alkanes (e.g., n-pentane, n-heptane, etc.) as precipitant to oil with a volume ratio 40:1.3,7 The behavior of asphaltene in crude oil highly depends on the composition, meaning the interaction between asphaltene, solvents, and anti-solvents. So the precipitation of asphaltenes is usually investigated using a synthetic solution consists of heptane, toluene and asphaltene.8,9 At each step of crude oil production, transportation, and refinery, asphaltene will be precipitated with significant changes in hydrocarbon composition, pressure, and temperature.10 Asphaltene precipitation can cause serious damages to equipment applied in crude oil production or it can cause formation damage by partially or completely plugging of the pore spaces at near the wellbore region.11 The plugging of the subsurface and surface tubing is another consequence of asphaltene precipitation.12 In the refineries, the precipitation of asphaltene can cause malfunction of distillation columns, fouling the heat exchangers and deactivation of the catalyst.13 A deep comprehension of the size augmentation mechanism of asphaltene particles and its modeling are exigent in order to reduce the problems caused by asphaltene precipitation. The population balance modeling is one of the common methods applied for modeling of particulate processes to predict the evolution of PSD. The literature demonstrates lots of development in using population balance model for determining PSD.14–19 Meanwhile the number of researchers considered population balance equation for describing the asphaltenes behavior has been increased.20–24

1.2. Previous Studies on the Kinetics of Asphaltene Aggregation. Nielsen et al.25 observed that the average diameter of particles slightly decreases with increasing of temperature in a range of 0 to 150 °C. Anisimov et al.26 used photon correlation spectroscopy and found that the kinetics of asphaltene aggregation and the stability of aggregates within hydrocarbon solutions are significantly affected by the nature of the solvent. Rahmani et al.20,27 have studied the effects of


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shear rate, solvent composition, and asphaltene concentration on the aggregate size distribution of asphaltenes within a Couette device. It was observed that the broadness of the size distribution of asphaltene particles in a mixture of toluene and n-heptane is independent of shear rate (in the range of 1.2−12.7 s-1) while final steady state diameter decreases with shear rate. Also, it was seen that the average size of aggregates increases more rapidly during the initial stages of shear-induced flocculation. They applied population balance modeling to simulate the results considering aggregation and fragmentation processes. It was found that the aggregation has a dominant role in controlling the kinetics of asphaltene particles enlargement at initial stages of flocculation. With increasing the size of asphaltene particles, the hydrodynamic stresses exerted on aggregates increases and its order of magnitude reaches that of the yield strength of aggregates and consequently, the fragmentation will find the dominant contribution to the enlargement of particles. The competition between two aggregation and fragmentation processes passes the average diameter through a maximum at a specific time. The average size declines at longer times and approximates to a constant value. Additionally, the enlargement rate of asphaltene flocs is increased with increasing of asphaltene and precipitant concentrations. Espinat et al.28 used smallangle neutron scattering (SANS), dynamic light scattering (DLS), and Small-angle X-ray scattering (SAXS) methods for measuring the size of particles in toluene at different temperatures and concluded that the average diameter increases with a decrease in temperature. The authors observed that the aggregation process accelerates as a consequence of the decrease in temperature due to the generation of fractal-like aggregates. The fractal structures result in more collisions which cause the average diameter to increase. Rastegari et al.29 studied the growth kinetics of asphaltene particles in mixtures of toluene and heptane at mixing rates of 110, 230, and 600 rpm. The authors indicated that the rate of aggregation increases with increasing of asphaltene and heptane concentrations, and with decreasing of shear rate. In addition, they developed a fractal population balance model to simulate the evolution of particle-size distributions and volume-based average diameter. The fractal dimension of asphaltene aggregates was obtained about 1.6. Solaimany-Nazar and Rahimi30–32 showed that the fractal dimension of the asphaltene aggregates within toluene and heptane mixture is not constant during aggregation process and increases from an initial value of 1.6 to a final steady state value. The final value of fractal dimension was found to depend on the shear rate which was ranged from 1.87 to 13.15 s-1. Additionally, the authors observed that the maximum attainable diameter depends on the shear rate and initial average


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diameter of asphaltene particles and is independent of initial particle size distribution. Khoshandam and Alamdari22 tuned four coefficients of growth and agglomeration rates by fitting population balance model predictions on experimental data acquired by dynamic light scattering with a relative deviation of 10%. Eskin et al.33 developed a geometric population balance model to simulate the asphaltene aggregation in a Couette device under turbulent flows. They employed three fitting parameters; particle-particle collision efficiency, the particle-wall sticking efficiency, and the particle critical size. The value of collision efficiency in their study was considered to be constant and independent of the particle size. Mansur et al.34 observed that by temperature increase in the range of 10 to 50 °C, the solubility of asphaltene in n-heptane increases and final steady state distribution of particles size and its average become narrower and smaller, respectively. Maqbool et al.35,36 believed that the temperature increment has complex and various competing effects on the asphaltene stability, totally results in a reduction of the onset time of precipitation. Furthermore, they observed an increase in the size of asphaltene aggregates with increasing of the precipitant concentration. These authors also used population balance equation to predict the evolution of asphaltene particles size distribution and the onset time of precipitation at low concentrations of heptane. Nassar et al.23 applied population balance model using Smoluchowski’s kernels for aggregation and fragmentation processes in the presence of nanoparticles. They used a double exponential model to describe the adsorption kinetics of asphaltenes onto the three kinds of nanoparticles. The model fitted successfully on the experimental results with a relative deviation of 9%. The aforementioned studies separately disclose the effects of temperature and shear rate on the asphaltene aggregates. However, no report was found in these sources about the role of temperature on the aggregation kinetics of asphaltene in the presence of shear. The majority of the previous studies are based on this assumption that all of the collisions are successful and interaction forces between aggregating asphaltenes have not been considered. Additionally, assessment of the size evolution of asphaltene particles from nanometric scale to micrometric scale over a wide range of temperature is very limited. In the present study, both experimental and theoretical approaches are used to scrutinize the aggregation and fragmentation kinetics of the asphaltene particles within a Couette device at different fixed temperatures and shear rates. In population balance modeling, the fractal dimension is considered as a function of temperature.


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2. Experimental Section 2.1. Tests Conditions. To study the effects of temperature and agitation rate, experiments were carried out at 20, 40, 60, and 80°C and 100, 400, and 600 rpm. In all tests, the Couette device was completely sealed to prevent mixture evaporation.

2.2. Materials. The asphaltene required for this study was extracted from the bottom product of the distillation column of Abadan Oil Refinery located in the southwest of Iran. Details of the procedure used for solid asphaltene preparation can be found in the previous work.37 Toluene and n-heptane were high-performance liquid chromatography (HPLC)-grade and were supplied by Samchun Pure Chemical Company, Korea.

2.3. Apparatus. The tests were carried out within a Couette device which is schematically depicted in Figure 1. The Couette device mainly consists of two coaxial cylinders. The inner cylinder (48.5 mm OD) was made of Teflon to eliminate the corrosion of cylinder by the solvent. The outer one (58.0 mm ID) was made of Pyrex glass to provide visual observation of the tests. The height of both cylinders and the annular gap between them are 200 mm and 4.75 mm, respectively. The inner cylinder could be rotated with a rotation speed of 0-600 rpm by an electromotor equipped by a gear box while the outer cylinder is fixed. The annular gap with a capacity of 158.8 mL was used as experimental cell and was equipped with a thermocouple for controlling of temperature (±0.1 °C). The gap width is much smaller than the inner cylinder diameter and the spatially averaged velocity gradient (i.e. shear rate) across it is constant and homogeneous. For this reason, the Couette device is preferred to other devices such as blade impeller to investigate the effect of a homogeneous shear rate on aggregation and fragmentations processes which in turn affect the particle size distribution (PSD). Additional details of the Couette flow is included in the Supporting Information. The Couette device was placed within a thermostatic hot water bath for temperature adjustment of the cell. The input heat flux to water bath was controlled by a controller based on adjusted set point for cell temperature. Sampling was taken by an open-mouth pipette. The inner diameter of pipette mouth was sufficiently large (1 mm) to have a more representative sample. Size analysis of asphaltene particles in taken samples was carried out by using a Zetasizer Nano ZS-ZEN3600 (Malvern Instruments, UK)), which uses dynamic light scattering technique to analyze particles in the range of 0.3 nm to 10 μm.


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2.4. Solution Preparation and Sampling. The asphaltene powder obtained through the procedure explained in section 2.2 was dissolved in toluene to prepare stock solutions with a concentration of 50 mg/L. The solutions in all experiments were prepared by mixing 154 mL heptane and 22 mL of the stock solution (7/1 volume ratio) by a 3-blade impeller within a beaker to ensure complete mixing of the solutions. More information on the sample concentration before the start of a measurement can be found in the Supporting Information. Before mixing the stock solution and heptane, both liquids were separately analyzed by the Zetasizer for the presence of background particles and no particles were observed in the liquids. Then 158.8 mL of prepared solution was injected into the annular cell and motor speed and temperature were fixed at desirable values. The samples with a volume of 1.6 mL were taken by pipette at specified time intervals and size distributions of asphaltene particles were analyzed by Zetasizer. The first measured size distribution was considered as the initial condition in numerical solution.

2.5. Closure Properties. The refractive index and the viscosity of the sample are two properties that must be known and entered into the Zetasizer software. In doing so, the refractive indices and the viscosities of all the mixtures were measured at the prevailing temperatures by Bellingham & Stanley refractometer and a glass capillary viscometer, both equipped with a water bath, respectively. Recent studies have demonstrated that the value of asphaltene average refractive index lies in the range of 1.64-1.8, with an average of 1.72.38,39 So, the refractive index of asphaltene particles in the present work was assumed to be constant and equal to 1.72.

3. Population Balance Modeling The population balance equation (PBE) is an integro-differential equation that shows the number balance of particles in a specific size range. The accumulation of the particles in a size interval is obtained by the summation of terms expressing particle convection to/from the interval as a result of growth, birth and death of the particles in that interval due to the aggregation and fragmentation.40 In a particulate system, the four principal mechanisms of nucleation, growth, aggregation, and fragmentation could exist solely or together.40 Nucleation and growth occur where the solution is supersaturated. After generation of a nuclei, other phenomena could occur. Growth phenomenon is a mass transfers process by which the growth units are transferred from the bulk of solution to the kink sites on the surface of particles.20,30 In the present study, it could be proposed that the supersaturation is created by adding antisolvent(n-heptane) to stock solution


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and results in generation of nuclei. Therefore, 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. In the present study, a geometric discretization of the size domain with sectional spacing 𝑓 = 𝑣 𝑑𝑁 = 𝑑𝑡

2

𝐾 (𝑣

−𝑁

+

/𝑣 = 2 is applied:14

, 𝑣 )𝑁

2

1 𝑁 + 𝐾 (𝑣 2

𝐾 (𝑣 , 𝑣 )𝑁 − 𝑁

,𝑣

)𝑁

𝐾 (𝑣 , 𝑣 )𝑁 −

𝑆 𝑁

(1)

𝛤, 𝑆 𝑁

Where 𝑁 is the total number of particles within a section with characteristic volume of 𝑣 per unit volume of solution, KA(u, v-u) (in m3/sec) is the aggregation kernel and shows the formation rate of particles of volume v by cohesive collisions between particles of volumes u and v-u, 𝑣 is the characteristic volume, which is the arithmetic mean of lower and upper limits for particles volume at that section and is a function of that of previous section, 𝑆(𝑣 ) (in 1/sec) is the fragmentation rate of aggregates with volume 𝑣, and 𝛤 , is a modified distribution function for the fragmentation in order to conserve volume in discretized domain for the particular case of f = 2. It should be noted that particles volume conservation is respected in aggregation and fragmentation processes. In other words, when two particles of i and j collide with each other, the volume of the created particle, k, is equal to the sum of initial particles volume. 3.1. Aggregation Kernel The rate of aggregation (Ri,j) of particles i and j with sizes Vi and Vj, and number concentrations Ni and Nj, respectively, is expressed as:41 𝑅, =𝐾 𝑁𝑁

(2)

The aggregation kernel, KA, could be comprised of two parts: the collision efficiency (α) and the number of collisions or collision frequency (β):42


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(3)

𝐾 = 𝛼. 𝛽 ,

The collision efficiency is the fraction of collisions which lead to a bigger particle. The relations for aggregation kernel are often formulated based on collision mechanism (i.e. perikinetic, orthokinetic) to consider the physicochemical and fluid dynamic forces in the aggregation phenomenon. Thus, the aggregation kernel depends on certain factors such as particles size, colloidal interactions, viscous retardation, and applied shear stresses.42 3.1.1. Collision Frequency In General, aggregation is divided into two categories of primary and secondary. Primary aggregation caused by the inharmonic growth of particles and can be produced from a particle (as well as parallel growth or a tree growth in crystal) while secondary aggregation is caused by the collision of one particle with another particle.43 Secondary aggregation is divided into three subcategories: perikinetic aggregation and orthokinetic aggregation, and aggregation due to differential settling.42 Perikinetic aggregation is caused by Brownian motion (thermal movement) of particles and is usually considered dominant mechanism for particles smaller than 1 micron.43 Orthokinetic aggregation is caused by fluid velocity gradient and is usually considered for particles bigger than 1 micron. In this case, the movement of particles originates from external effects (mechanical, electrical and gravitational).43 The aggregation due to differential settling is a consequence of the considerable difference in settling velocities of particles.44 In the present study, the collision frequency function was considered as a superposition of the corresponding functions of Brownian motion and fluid shear, as expressed in Eq. (4): /

𝛽,

/

2 𝑘 𝑇 (𝑣 + 𝑣 ) = + 0.31𝐺(𝑣 / / 3 𝜇 𝑣 .𝑣

/

+𝑣

/

)

(4)

Where kB is the Boltzmann constant, T is the absolute temperature, µ is the dispersant viscosity, and G is the shear rate. It is postulated that the turbulent flow is distinguished by eddies of different sizes where the size of largest eddies is on the order of the container or impeller. During the energy transfer through a cascade of eddies, the energy is destroyed as heat below a certain length scale, known as the Kolmogoroff microscale.42,45 The energy dissipation above this length scale (inertial range) is


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negligible, whereas, below this scale (viscous sub-range), the energy is destroyed as heat. The Kolmogoroff microscale, 𝜂 , is calculated as:42,45 𝜐 𝜂 = ( ) 𝜀

(5)

/

Where υ and 𝜀 are the kinematic viscosity and power input per unit mass, respectively. For aggregates smaller than 𝜂 , transport by eddies is not important in the inertial range and the collision rate is proportional to 𝜀

/ 42,45 .

In the present study 𝜂

varies between 24.25 and

28.69µm depending on temperature, and is much higher than the size of aggregates. Therefore, the collision frequency of asphaltene aggregates can be reasonably well estimated using Smoluchowski’s expression for orthokinetic aggregation. 3.1.2. Collision Efficiency The collision efficiency is introduced in aggregation kernel to consider the effect of particle structure and its surface properties (like repulsive forces), hydrodynamic effects, and fluid viscosity on this process. Collision efficiency is the ratio of actual aggregation rate to aggregation rate presented by Smoluchowski.42 The application of presented equations for calculation of the collision efficiency is limited to laminar flow and organic solutions.44,46,47 The asphaltene particles have a fractal structure and the actual collisions between them are more than calculated values based on spherical shape. Therefore in many literatures, collision efficiency is assumed to equal to 1.20,22,23,27,29,31,32 Nevertheless, recent investigations indicated that this assumption is not realistic and a significant difference between models and experimental results is created by this hypothesis.24,33,35,48 Although Smoluchowski’s functions have a sound theoretical basis, recent works disclosed that there is the significant difference between these models and experimental results.24,33,35,48 Therefore, the applied kernel in present work is written based on Eq. (4) which is included the collision efficiency and the fractal dimension: /

𝐾 𝑣 ,𝑣

=𝛼

2𝑘 𝑇 (𝑣 . 3𝜇 𝑣

/

+𝑣

/

.𝑣

/

)

+𝛼

. 0.31𝐺(𝑣

/

+𝑣

/

)

(6)

The factors affecting the perikinetic and orthokinetic collisions are considered to be different from each other and so two separate efficiencies were considered for each type of collision in Eq. (6).


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There are several correlations in the literature for estimating the shear rate within the annular gap of a Couette device as a function of Reynolds number and the ratio of radii of cylinders.33,49–51 The non-dimensional torque, C, is calculated in the present work as follows:49,50

𝐶=

/ ⎧ 1.45 𝜆 ⎪ (1 − 𝜆)

𝜆/ ⎨ 0.23 ⎪ (1 − 𝜆) ⎩

.

𝑅𝑒

/

𝑅𝑒

/

.

𝑓𝑜𝑟 400 < 𝑅𝑒 < 10

(7)

𝑓𝑜𝑟 10 < 𝑅𝑒 < 10

Where λ is Ri/Ro and 𝑅 and 𝑅 are the inner and the outer radii of the Couette device, respectively. Re is Reynolds number and is calculated as:33,49–51 𝑅𝑒 =

𝑅 𝜔(𝑅 − 𝑅 ) 𝜐

(8)

Where ω is the angular velocity. The non-dimensional torque is used to determine the torque, T:49,50 𝑇 = 𝐶𝜌𝜐 ℎ

(9)

Where ρ is suspension density and h is the height of Couette device. The energy dissipation rate of a Couette device is related to the applied torque via the equation (Eq. 10):33 𝜀=

𝑇𝜔 𝜌𝜋𝑅 (1 − 𝜆 )ℎ

Finally, the absolute shear rate, G, is given by:33,42,50 𝜀 𝐺=( ) . 𝜐

(10)

(11)

The absolute shear rates, corresponding to rotation speeds applied in the present work, were calculated and shown in Table 1. 3.2. Fragmentation Rate The main mechanisms of fragmentation are (1) erosion of primary particles or releasing of particles from the surface of aggregates which occur when the size of eddies is comparable with the aggregate size and (2) rupture of the aggregate by pressure difference on its opposite sides.52 The Kapur’s kernel is the most applied kernel for fragmentation process. It is as a function of particle size as follows:53 Where b is the fragmentation rate coefficient and is considered a function of shear rate as follows:52


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𝑆 = 𝑏𝑣

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/

(12) (13)

𝑏=𝑏𝐺

The values of fitting constants y and 𝑏 are inversely related to the strength of the aggregate. The collision diameter dc,i of a fractal aggregate is a function of its fractal dimension (df) and also the number (xi) and diameter (dp) of primary particles involved in that aggregate:54 𝑑

,

= 𝑑 𝑥

/

(14)

The application of collision diameter of a fractal aggregate is more convenient than mass equivalent diameter, di, for representing the volume on which the disruptive shear force are acting:55 𝑑, ( ) 𝑑

𝑆 =𝑏𝑣

(15)

As aggregates become more porous (lower fractal dimension), they are broken more easily by shear forces. The simple power law relationship between aggregate size and shear rate (Eq. (15)) which is usually used as fragmentation kernel for fractal aggregates, shows that the fragmentation rate increases with decreasing of fractal dimension. 3.3. Fragmentation Distribution Function Three different types of breakup distributions are binary, ternary, and normal distributions. In the present work, the binary fragmentation function in which a particle of volume vj breaks down into two particles with equal volumes of vi was used:56,57 2

𝑖𝑓

0

𝑖𝑓

𝛤, =

𝑣 ) 2 𝑣 (𝑣 ≠ ) 2 (𝑣 =

(16)

4. Results and Discussion 4.1. Experimental Results. 4.1.1. Effect of Temperature. Figure 2 exhibits the effect of temperature on the average diameter of asphaltene particles as a function of time at 400 rpm. Depicted average diameter is the number average diameter (𝑑̅ , ). For all experiments, the first recorded PSD was 5 min after mixing heptane and stock solution. The initial average diameter varies from 68 to 421.3 nm as temperature decreases from 80 to 20°C.


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As seen, the average diameter passes through a maximum at all temperatures and the occurrence of this maximum value delays as temperature decreases. The presence of this maximum in average size is a strong evidence for competing at least two mechanisms in enlarging of particles within a shear-induced solution. After passing the peak, the asphaltene particles become smaller and reach a steady state value. The schematic variation of average diameter versus time is shown in Figure 3. Among aforementioned mechanisms, aggregation (orthokinetic) and fragmentation are supposed to be responsible for size variation at a fixed temperature. Due to nature of nucleation phenomenon, it is believed that nucleation is started and terminated at the initial black box (first 5 min, region I in Figure 3). The rapid size evolution of asphaltene particles in the second phase is supposed to be the result of aggregation (region II in Figure 3). When particles enlarge, the fragmentation induced by hydrodynamic stresses is increased (Eq. 12). Meanwhile, the aggregation rate is decreased mainly due to a reduction in the number of asphaltene particles (region III in Figure 3). It should be noted that with respect to the asphaltene particles concentration, the aggregation rate is a second order function while the fragmentation rate is a first order function (Eq. 1). Both the initial and steady state aggregate sizes were increased with decreasing temperature. This observation can be interpreted by temperature effect on asphaltene solubility in solution. Hildebrand et al. formulated the solubility parameter (δ) to take into account the solvent power of nonpolar liquids, as follows:7 ∆𝐻 − 𝑅𝑇 𝛿= 𝑉

/

(17)

Where ΔHV and 𝑉 are the heat of vaporization and molar volume, respectively, and R is the universal gas constant. The difference between the Hildebrand solubility parameters for a solution and the asphaltene shows the solubility of asphaltene within that solution. The solubility will increase with decreasing this difference. The difference in solubility parameters becomes smaller as temperature increases. In other words, increasing temperature will result in stabilizing asphaltenes within the solution and so a lower number of nuclei will originate at a higher temperature. The reduction in the number of the primary particles will decrease the collisions among them, and thus reduces the aggregation. Lower aggregation rate will reduce the size of aggregates which directly affects the fragmentation rate. At the highest temperature (80°C), it was not possible to record the size distribution after a certain time, because the size of the aggregates


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lies completely outside the detection limit of the current instrument. In summary, it can be concluded that the amount of precipitated asphaltene is increased as the temperature is decreased. 4.1.2. Effect of the Shear rate. Figure 4 shows the enlargement of asphaltene particles at a constant temperature (20 °C) and shear rates of 135.27, 764.87 and 1288.90 s-1. As observed in this figure, the shear rate has a significant effect on the enlargement of asphaltene particles. Both aggregation and fragmentation are affected by fluid shear, according to Eq. (6) and Eq. (7), respectively. As the shear rate is increased, the aggregation of particles is accelerated due to a higher number of collisions occurred between asphaltene particles. In addition, the increment of shear rate influences the fragmentation rate directly according to Eq. (13) and results in smaller particles. It is observed that the locus of maximum attainable average size shifts to occur earlier as the shear rate is increased. So it could be concluded that the effect of shear rate on fragmentation rate is higher than that on aggregation. The asphaltene particles have an open and porous structure that should be considered in the analysis of the effect of shear rate on the kinetics of the aggregation and fragmentation. In lower shear rates, aggregates have a more irregular structure which results in a higher number of collisions in comparison to spherical particles with equivalent mass. In other words, the restructuring phenomenon could occur for porous particles such as asphaltene and should be considered in the interpretation of observed results. At high shear rates, the branches of weak and fractal aggregates collapse and create a dense aggregate with lower porosity. This restructuring can reduce the particle size and increase the particle strength and so decrease the fragmentation. Additionally, with increasing shear rate, aggregates have more regular structures that increase viscous retardation and reduces the rate of aggregation. The effect of shear rate and temperature on both aggregation and fragmentation processes is shown in Figure 5a and 5b in term of steady state average size diameter of asphaltene particles (diameter of particles at phase IV in Figure 3). The opposite effects of shear rate on aggregation and fragmentation of asphaltene particles can be observed in Figure 5a in term of steady state average size diameter of particles. The steady state average particle size passes through a maximum as shear rate increases from 100 to 600 rpm. In the case of high shear rates, it is possible that the aggregates to be pulled out from the secondary minimum and broken into two smaller particles. On the other hand, the high shear rate may cause two particles overcome the potential energy barrier and form a large particle in a primary


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minimum, which is resistant to the shear rate. When the rotation speed is less than 400 rpm, the particles are formed in the secondary minimum, while in the case of 600 rpm, these particles are broken into smaller particles, which ultimately has decreased the steady state diameter of asphaltene particles. The experimental steady state average diameters obtained at different temperatures at both static and dynamic modes are shown in Figure 5b. The dynamic mode results were obtained in Couette device at 400 rpm and the static mode results are from our previous work.37 As seen in this figure, the steady state average diameters are decreased in both modes with an increase in temperature. The influence of temperature on steady state average diameter in dynamic mode is more severe than that in static mode. The steady state diameter in dynamic mode is reduced about 725 nm as temperature increases from 20 to 60 °C, while this variation is about 251 nm in static mode. This fact is attributed to the existence of fragmentation besides of aggregation in dynamic mode. Thus, it can be deduced that the kinetic behavior of asphaltene particles under shear rate have more dependency on the particle size than that in stationary systems. 4.2. Modeling and Simulation Results. For each test, the first PSD measurement was considered as the initial condition and the Eq. (1) was solved for 46 bins. In Figure 6, model predictions for the evolution of asphaltene particles are depicted at different temperatures. The hybrid kernel, including the orthokinetic kernel and the perikinetic kernel, was used in modeling and a significant improvement in results was obtained. As can be seen, there is a good match between the model and the experimental data. The values of four fitting parameters were obtained by using PSO algorithm and minimizing root-mean-square error (RMSE) and are shown in Table 2. It should be noted that the orthokinetic kernel was solely used and results showed that it was not successful to predict the evolution of PSD with acceptable accuracy. The better accuracy obtained by superposition of kernels in comparison to that of acquired by orthokinetic kernel alone, which could be an evidence for the role of perikinetic aggregation in the evolution of particles within a shear-induced suspension under laminar flow regime. In the present study, unlike previous studies carried out for particles larger than 20 μm, the PSD ranged from nanometers to micrometers. Therefore, it is expected that the perikinetic aggregation plays a considerable role beside of an orthokinetic aggregation. The previous studies43,44 stated that the orthokinetic mechanism is dominant for particles larger than one micrometer and particles smaller than this limit are affected by Brownian motion.


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The difference between the experimental data and the simulation results at the maximum point is higher than elsewhere. In Figure 7, the value of collision efficiencies for both perikinetic and orthokinetic mechanisms are plotted as a function of temperature. The values of both collision efficiencies are decreased with increasing temperature. According to the Fuch theory and empirical observations in the previous study37, the energy barrier between colliding particles is inversely proportional to temperature. In other words, the number of successful collisions (or collision efficiency) is decreased with increasing temperature. Fuchs theory is not applicable for large particles (about one micrometer) which their motion is considered to be a result of fluid shear. Although the effect of solution viscosity is not considered in Smoluchowski’s kernel, the results of present study indicate that it could have an impact on the aggregation process. The drainage of seized liquid within space between collided particles, called viscous effect or hydrodynamic resistance, have an important impact on the rate of aggregation. In other words, there is a fluid layer between particles that is not removed easily and interrupted the contact of two adjacent particles.47,57,58 The Brownian motion and the attractive interparticle forces can push particles toward and drain the seized fluid.42 The viscosity of liquids and the van der Waals forces are decreased with increasing temperature. Therefore, it can be concluded that decreasing the orthokinetic collision efficiency with increasing the temperature is a consequence of the reduction of the van der Waals forces. This conclusion is not consistent with the relation of Van de Ven and Mason59 who investigated the orthokinetic collision efficiency using trajectory analysis and by considering van der Waals forces. They introduced a limiting collision efficiency for monosized particles which is the value of collision efficiency in the absence of repulsive force. They presented a simple empirical expression to calculate it as follow:42,59 𝛼 = 𝑓(𝜆/𝑅)𝐶

.

(18)

Where 𝛼 is the limiting collision efficiency, 𝑓(𝜆/𝑅) is a function of the dispersion length () due to retardation effects, and CA is expressed as:42,59 𝐶 =

𝐴 36𝜋𝜇𝐺𝑅

(19)

Where A and R are Hamaker constant and particle radius, respectively. The value of liming collision efficiency is expected to increase with increasing temperature which in turn reduces the viscosity, while the results presented here show a different trend. In the presented relations, the


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Energy & Fuels

particle size is considered same, while the collision efficiency will be much lower for particles with different size. Because the separation distance between a large particle and a small particle is too much so that this separation distance is far greater than the range of the effects of the van der Waals forces and actually reduces the aggregation of particles. In addition, repulsive forces have not been considered in this regard that if they exist, the calculations will be much more complicated. Therefore, one of the factors that reducing the efficiency of the orthokinetic collision with increasing the temperature can be the increase of the repulsive forces compared to the attractive interparticle forces in a shear stress field. Asphaltene aggregates have an open structure that greatly reduces hydrodynamic resistance. Increasing temperature results in the more regular structure for asphaltene aggregates that have a less open structure which in turn increases the hydrodynamic resistance. This explanation is compatible with changing the fractal dimension with the temperature shown in Figure 8. It is well known that the aggregation acts contrary to the fragmentation and results in more irregular particles. Increasing the fractal dimension of asphaltene particles with increasing temperature at a constant shear rate certify that the rate of aggregation in comparison to fragmentation rate is reduced with temperature enhancement. This conclusion is compatible with previous finding (Figure 2) that the increase of temperature reduces the aggregation rate compare to the fragmentation rate. The applied concentration in the present study is much lower than critical micelle concentration (CMC) and aggregation is limited by diffusion (DLA). During aggregation process which is controlled by successful collisions (reaction-limited aggregation, RLA), particles impact each other several times before occurring a successful collision. Therefore the morphology of aggregates during RLA is more compact and regular than those formed by DLA. In other words, the fractal dimension of aggregates formed during RLA is higher than that in DLA. Calculated fractal dimensions are far from that of a spherical particle (df =3) and indicate that aggregation of asphaltene particles in a Couette device is controlled by diffusion.60–62 The Modeling of fragmentation process is more complex than other kinetic terms involved in PBE. Therefore the discrepancy between simulation results and experimental data could be primarily assigned to applied model for fragmentation. Figure 9 shows the variation of the fragmentation rate coefficient versus temperature at a constant shear rate. An increase in the value of b with an increase in temperature, reveals that the strength of the aggregates will reduce with temperature. The floc strength, in general, depends on the properties of primary particles (such as surface charge, the roughness of the surface) and also the number of particle-particle


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contacts per unit volume of aggregate. The number of particle-particle contacts depends on the density of the aggregates and specifies the effective coordination number. The fractal dimension of asphaltene particles is an indicator of particle density and it increases with temperature. Therefore the enhancement of temperature will increase the number of particle-particle contacts. In the previous study37, it was shown that zeta potential, an indicator of surface charge, of asphaltene particles is increased with increasing temperature. Therefore the reduction of b beside of increasing df, shows that the effect of van der Waals forces is predominant on the effect of the fractal structure of asphaltene particles This observation is compatible with findings of Spicer and Pratsinis57, who declared that the effect of the attractive forces is predominant on the effect of the aggregates density. The results shown in Figure 9 show that the breakup rate coefficient does not obey exactly a power law equation. In other words, its temperature dependency is not similar to the relation between the breakup rate coefficient and the shear rate, which is a power-law relationship. In the present study, aggregation and fragmentation kinetics of asphaltene aggregates are considered as forward and backward reactions of a reversible reaction, as illustrated in Figure 10. Following the above proposed model, the kinetic rate constants shown in Eq. (20) are used to describe the aggregation and fragmentation reactions:

I+J

𝐾 𝑉,𝑉

(20)

I.J 𝑆 𝑉.

For both aggregation and fragmentation reactions, an Arrhenius type equation is assumed for the dependency of reaction rate constants on temperature: 𝛼 = 𝑎 exp(−𝐸 /𝑅𝑇)

(21)

𝑏 = 𝑏 𝑒𝑥𝑝(−𝐸 /𝑅𝑇)

(22)

Where 𝐸 and 𝐸 are activation energies for the aggregation and fragmentation, respectively. The amounts of activation energy for perikinetic and orthokinetic aggregations were obtained -683.9 and -461.8 kJ/mol, respectively (Figure 11a). These result indicate that the perikinetic aggregation is more dependent on temperature than orthokinetic aggregation. Additionally, the amount of disruptive energy of fragmentation was determined 295.1 kJ/mol (Figure 11b) where its absolute


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Energy & Fuels

value is smaller than the activation energies obtained for perikinetic and orthokinetic aggregations. In other words, the obtained activation energies show that the fragmentation is affected by temperature less than both types of aggregations. Obtaining the positive value for activation energy of fragmentation shows that like an endothermic reaction, this process is accelerated with increase of temperature.

Conclusions The temperature was found to have a significant effect on PSD of fractal asphaltene particles within a Couette flow device through its effect on aggregation and fragmentation. The temperature effect on fragmentation was more than its effect on orthokinetic aggregation. The agitation rate had two opposite effects on PSD resulted in a maximum in the average steady state diameter versus shear rate. The effect of shear rate on fragmentation rate was higher than that on aggregation. Therefore, asphaltene particles can be stable over a certain range of shear rates, whereas they may precipitate at lower or higher values. Within a suspension under shear rate at laminar flow regime, the perikinetic aggregation existed, although its contribution was less than orthokinetic aggregation. Also, the aggregates of asphaltene were loose at high temperature due to high repulsive charge on the particle surface. Obtaining the higher values for fragmentation rate constant and fractal dimension at higher temperatures revealed that the resistance of asphaltene aggregates is decreased with increase in temperature.

 Acknowledgements The authors fully appreciate the kindness of the Research Center of Ahwaz Faculty of Petroleum for permission to use the laboratory facilities and also Abadan Oil Refinery for providing the bottom product from the distillation tower. The authors also express their gratitude to the National Iranian South Oil Company (NISOC) for technical and financial support of this project (Grant Number 93-DK-926).

 Associated Content Supporting Information. Section S1, Analysis of the Taylor-Couette flow in the annular gap; Section S2, Details of the sample preparation; Section S3, References.

 Author Information Corresponding Author


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*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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Energy & Fuels

Table 1: The values of rotation speed, angular velocity (ω), and absolute shear rate (G) in each test

Rotation Speed (rpm)

Temperature (°C)

ω (rad/s)

G (1/s)

100

20

10.47

135.27

400

20

41.87

764.87

400

40

41.87

771.09

400

60

41.87

819.14

600

20

62.8

1288.90

Table 2: Optimized kinetic parameters for the enlargement of asphaltene aggregates

𝜶𝒑𝒆𝒓𝒊𝒌𝒊𝒏𝒆𝒕𝒊𝒄

𝜶𝒐𝒓𝒕𝒉𝒐𝒌𝒊𝒏𝒆𝒕𝒊𝒄

𝟐𝟎

1.53 × 10

2.53 × 10

𝟒𝟎

1.35 × 10

𝟔𝟎

2.02 × 10

𝑻𝒆𝒎𝒑𝒆𝒓𝒂𝒕𝒖𝒓𝒆 (°𝑪)

𝒅𝒇

𝑹𝑴𝑺𝑬 %

2.11 × 10

1.49

7.33

4.68 × 10

4.88 × 10

1.61

19.12

2.59 × 10

3.56 × 10

1.79

17.30

𝒃


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Electromotor

Temperature probe

Gear box

Injection and removal of sample

Water bath

Inner cylinder

Outer cylinder

Annular gap

Sample discharge

Hotplate

Figure 1. The schematic of the experimental setup.


Page 25 of 29

1400

Average Diameter (nm)

1200

20°C

40°C

60°C

80°C

1000 800 600 400 200 0 0

20

40

60

80

100

120

140

160

180

200

220

Time (min) Figure 2. The enlargement of asphaltene particles in a mixture of toluene/heptane (1/7 v/v) containing 50 mg of

Black Box - Phase dominated by nucleation & aggregation (I)

asphaltene/liter of toluene under a constant rotation speed of 400 rpm.

Average Diameter

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

Kinetic phenomenon dominated by aggregation (II)

Kinetic phenomenon dominated by fragmentation (III)

Balance of aggregation & fragmentation (IV)

First measurement

Time Figure 3. Schematic representation of the asphaltene particle size enlargement under shear rate.


Energy & Fuels

Number Average Diameter (nm)

1400

135.27 1/s

1200

764.87 1/s 1269.70 1/s

1000 800 600 400 200 0 0

40

80

120

160

Time (min)

200

240

Figure 4. Size evolution of asphaltene particles at 20 °C in a mixture of toluene/heptane (1/7 v/v) containing 50 mg of asphaltene/liter of toluene.

(b)

(a) 1000 900 800 700 600 500 400 300 200 100 0

1000 900

0

200 400 600 800 1000 1200 1400

Shear Rate (1/s)

Final 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

Page 26 of 29

Static

800

Shear

700 600 500 400 300 200 100 0 290

300

310

320

330

340

Temperature (K)

Figure 5. Steady state average diameter of asphaltene aggregates in a mixture of toluene/heptane (1/7 v/v) containing 50 mg of asphaltene/liter of toluene (a) as a function of shear rate at 20°C (b) as a function of temperature at static and dynamic (400 rpm) modes.


Page 27 of 29

1400

Exp 20°C Exp 60°C Cal 40°C


1200

Exp 40°C Cal 20°C Cal 60°C

1000 800 600 400 200 0 0

20

40

60

80

100

120

140

160

180

200

220

Time (min) Figure 6. Comparison of experimental data and model predictions of asphaltene particles evolution in a mixture of toluene/heptane (1/7 v/v) containing 50 mg of asphaltene/liter of toluene under a constant rotation speed of 400 rpm.

(b)

(a)

1E+12

1E+16 1E+13

1E+09

α × 1028

α × 1017

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

1E+10 1E+07 y = 1E+125e-0/857x R² = 0/8514

1E+04

1E+06 y = 2E+84e-0/575x R² = 0/936

1E+03

1E+01

1E+00 290

1E-02 290

300

310

320

330

340

Temperature (K)

300

310

320

330

340

Temperature (K)

Figure 7. The optimized collision efficiencies at different temperatures under a constant rotation speed of 400 rpm (a) Perikinetic (b) Orthokinetic


Energy & Fuels

1/85

Fractal Dimension

1/8

y = 9E-05x2 - 0/0487x + 8/061 R² = 1

1/75 1/7 1/65 1/6 1/55 1/5 1/45 290

295

300

305

310

315

320

325

330

335

340

Temperature (K) Figure 8. The fractal dimension of asphaltene particles at steady state condition versus temperature (400 rpm).

1/0E+08

Breakup Rate Coefficient, b × 1010

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 29

1/0E+06 y = 3E-278x112/93 R² = 0/8645

1/0E+04

1/0E+02

1/0E+00 290

295

300

305

310

315

320

325

330

335

340

Temperature (K) Figure 9. The fragmentation rate coefficient versus temperature under a constant rotation speed of 400 rpm.

Collision & Capture

I

+

J

I

J

Rupture Figure 10. Conceptual model for asphaltene particle size enlargement.


Page 29 of 29

(a)

(b) 0

0 Perikinetic Orthokinetic

-10

y = 82258x - 282/88 R² = 0/8242

-30 -40

-30 -40

y = 55551x - 228/16 R² = 0/9168

-50 -60

-50 -70 0/0029 0/003 0/0031 0/0032 0/0033 0/0034 0/0035

-5 -10

ln (b)

-20 -20

0

ln (α_orthokinetic)

-10

ln (α_perikinetic)

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

-15 -20

y = -35499x + 100/29 R² = 0/8769

-25 0/0029 0/003 0/0031 0/0032 0/0033 0/0034 0/0035

1/T (1/K)

1/T (1/K)

Figure 11. The variation of the kinetic parameters with temperature by an Arrhenius-type relation: (a) collision efficiencies, and (b) breakup rate coefficient.


Influence of Temperature on Aggregation and Stability of Asphaltenes

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