Visual investigation and modeling of asphaltene precipitation and deposition during CO2 miscible injection into oil reservoirs

Visual investigation and modeling of asphaltene precipitation and deposition during CO2 miscible injection into oil reservoirs

Fuel 160 (2015) 132–139 Contents lists available at ScienceDirect Fuel journal homepage: www.elsevier.com/locate/fuel Visual investigation and mode...

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Fuel 160 (2015) 132–139

Contents lists available at ScienceDirect

Fuel journal homepage: www.elsevier.com/locate/fuel

Visual investigation and modeling of asphaltene precipitation and deposition during CO2 miscible injection into oil reservoirs Peyman Zanganeh a,1, Hossein Dashti a,b,1, Shahab Ayatollahi c,⇑ a

Enhanced Oil Recovery (EOR) Research Center, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz, Iran Department of Chemical Engineering, School of Chemical and Petroleum Engineering, Curtin University, Kent Street, Bentley, WA, Australia c Department of Chemical and Petroleum Engineering, Sharif University of Technology, Tehran, Iran b

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

 Employing a high-pressure visual cell

to evaluate asphaltene precipitation.  Investigation of asphaltene

deposition during miscible CO2 injection at high pressure and temperature conditions.  Study the effect of temperature on asphaltene particle size distribution and aggregation.  Using the thermodynamic solid model in order to predict the amount of asphaltene precipitation.

a r t i c l e

i n f o

Article history: Received 5 February 2015 Received in revised form 15 July 2015 Accepted 21 July 2015 Available online 29 July 2015 Keywords: Asphaltene deposition Enhanced oil recovery CO2 flooding Pressure depletion Thermodynamic model Solid model

a b s t r a c t Miscible carbon dioxide (CO2) flooding has become the most commonly and favorable approach in Enhanced Oil Recovery (EOR) because of its high oil reservoir sweep efficiency and contribution to the reduction of greenhouse gas emissions. Despite this, it can significantly favor the asphaltene deposition, which leads to the wettability reversal and formation damage. A novel experimental setup was utilized to study asphaltene deposition on the model rock at reservoir condition. The evolution of asphaltene deposition was monitored by a microscope; then analyzed by image processing software to check the amount of deposited asphaltene and its size distribution at different conditions. The amount of asphaltene deposition during natural pressure depletion and CO2 injection was measured experimentally and modeled using the thermodynamic solid model. The results indicated that during the pressure depletion process, asphaltene particles tend to dissolve in the solution. It is shown that the amount of asphaltene deposition increases as more CO2 is injected. Further, the thermodynamic solid model used for this case study included many empirical parameters required to match the experimental data comprehensively. A range of sensitivity analysis is carried out to investigate the effects of dominant parameters in this study. The proposed model used in this study reasonably predicted the trend of the asphaltene precipitation process for both pressure depletion and CO2 injection processes as oil recovery processes. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction ⇑ Corresponding author. Tel./fax: +98 21 66166411. 1

E-mail address: [email protected] (S. Ayatollahi). The first two authors equally contributed to this work.

http://dx.doi.org/10.1016/j.fuel.2015.07.063 0016-2361/Ó 2015 Elsevier Ltd. All rights reserved.

Petroleum crude is a complex mixture consists of different hydrocarbons such as saturated hydrocarbons, aromatics, resins and asphaltenes (SARA). Saturates are nonpolar normal alkanes

P. Zanganeh et al. / Fuel 160 (2015) 132–139

133

Nomenclature APE ASTM CO2 EOR EOS g l MW OOIP P PR PVT SARA T

v V

asphaltene precipitation envelope American society for testing and materials carbon dioxide enhanced oil recovery equation of state gas liquid molecular weight original oil-in-place pressure Peng-Robinson pressure, volume, temperature saturated hydrocarbons, aromatics, resins and asphaltenes temperature vapor volume

Symbols bi equation of state parameter for component i CA+ non-precipitating component CB+ precipitating component

(n-paraffins), branched alkanes (iso-paraffins) and cyclo-alkanes (naphthenes). Aromatics are hydrocarbons which consist of one or more ring structures similar to benzene. The carbon atoms in aromatics are connected by double bonds [1–3]. Waxes contain linear paraffinic hydrocarbons with carbon chains of various lengths [4]. The resin fraction is a dark brown colored, thick viscous liquid to semi-solid which is completely miscible with light fractions of petroleum fluids, including light gasoline and petroleum ether [5,6]. Asphaltene is the heaviest part of the crude oil that is not soluble in light hydrocarbon solvents such as n-pentane, n-heptane, and n-decane, but can be dissolved in toluene, benzene, and xylene. This fraction contains aliphatic and aromatic structures with high molecular weight ranges from the order of 103 to 105g/mol [5–10]. Asphaltenes are generally incompatible with light petroleum fractions leading to undesirable effects in many stages of the petroleum industry. Asphaltene molecules’ tendency toward association and precipitation referred to their molecular structure [2,3,11]. However, it is not possible to verify it clearly due to the complex nature of asphaltene molecules. Asphaltene precipitation and deposition could be problematic in all steps of oil production. It can change the wettability of the formation rock from water wet to oil wet which hinders the oil recovery efficiency [3,12]. To maintain the well flow and avoid pressure reduction due to the asphaltene deposition and plugging, several mechanical and chemical methods have been proposed. These methods are mostly expensive and time-consuming. Therefore, the reduction of asphaltene precipitation is widely investigated in the literature [1–4,12–14]. The literature shows that beside the widespread study on the properties of asphaltene molecules in the last decades [2,15,16], there are still many limitations to model and predict asphaltene precipitation and deposition for the real cases, especially during the gas injection process. It is important to know that after the primary and secondary oil recovery stages, the typical residual oil saturation in many oil reservoirs is in the range of 50–60% of the original oil-in-place (OOIP) [17,18]. The results presented in the literature show that the EOR processes contribute significantly to more oil recovery efficiency from depleted oil reservoirs [19].

dik e fij fijeos fs fs⁄ nc P⁄ Pc  Pc Pci R si Tc T ci Vc

vci vck vs vjeos yi

Xb

interaction coefficient between i and k adjustable parameter fugacity of component i in phase j with translation fugacity of component i in phase j without translation fugacity of pure solid reference fugacity of pure solid number of components reference pressure critical pressure critical pressure of n-alkane critical pressure of component i gas constant dimensionless volume shift parameter for component i critical temperature critical temperature of component i critical volume critical volume of component i critical volume of component k molar volume of pure asphaltene EOS molar volume without volume shift mole fraction of component i dimensionless EOS parameter

CO2 injection is one of the most used enhanced oil recovery methods worldwide, and different studies have demonstrated that as much as 40% of the total oil can be recovered by CO2 miscible injection [20]. The main mechanisms contribute to oil recovery by CO2 flooding process are oil-viscosity reduction, oil-swelling effect, and changes in the interfacial properties of the crude oil–CO2 system, which results in high sweep efficiency [21,22]. Although the side effects of mutual interactions between the crude oil and CO2 in the CO2-EOR were not understood well, the mentioned main mechanisms are the results of CO2 dissolution into the crude oil [23]. The possibility of asphaltene precipitation during CO2 flooding and its effects on the reduction of oil production are known as a technical challenge for this favorable EOR technique. It is suggested that asphaltene precipitation causes the produced oil to be deasphalted and becomes lighter and less viscous compared to the original crude oil [24]. However, the precipitated asphaltene deposits on the rock surface may cause reservoir plugging and wettability alteration, which eventually leads to the decrease of enhanced oil recovery performance [25]. Asphaltene precipitation also can severely damage the wellbore region, plugging the production pipelines and reducing the capacity of surface facilities [26]. Therefore, for better prediction of the reservoir performance, it is important to find more on the effects of the main parameters such as pressure, temperature and composition on the asphaltene precipitation and deposition process in the reservoir and surface facilities for both production and CO2 injection processes. The size distribution of precipitated asphaltene would affect the deposition process and pore plugging mechanism as well as altering the main properties of the crude oil. The effects of temperature and pressure on asphaltene particle size distribution were investigated by Nielsen et al. [27] in several types of crude oils diluted with n-heptane. This process has been done at high-pressure laser cell apparatus to analyze the asphaltene particle size. According to their results, slight increase in the mean particle size of asphaltene was observed as the pressure was increased for all crude oil samples. Hung et al. [28] used confocal microscopy to study the kinetics of asphaltene precipitation in crude oils with different stability.

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They showed the physical nature of flocculated asphaltenes with the high-resolution micrographic images at ambient condition. According to their results, the nature of the crude oil and its asphaltene content determines colloidal structural evolution and aggregation process of asphaltene in the crude oil. Recently, Khoshandam and Alamdari [29] have modeled the enlargement of asphaltene particles precipitated in a heptane-toluene mixture mechanically using mass and population balance techniques. They have also analyzed the size distribution of flocculated asphaltene particles in a mixture of asphaltene–toluene and found particle enlargement from 8 nm to 2 lm. Srivastava et al. [15] indicated that higher CO2 concentration causes the asphaltene precipitation to increase linearly in the single-phase region. They used experimental evidence to verify the results. The lack of proper experimental data to study CO2-EOR is known as the main reason behind improper prediction methods and simulation tools. Besides, different thermodynamic approaches to model asphaltene precipitation were reported in the literature to make this process more predictive. Solubility model as a thermodynamic tool is based on simplified Flory–Huggins theory [30]. The others try to modify this theory to have a better prediction of asphaltene precipitation [31–33]. Regarding this model, there are two approaches: in the first scenario the micelles of asphaltene are assumed to be stabilized by resins and due to flocculation of these micelles the asphaltene precipitation occurs. In the other approach, the asphaltene is assumed as a free molecule and precipitated in the conventional manner [34]. The thermodynamic colloidal model is the other model which was based on statistical thermodynamics and colloidal science. In this model, asphaltene is assumed as a solid particle like colloidal suspension, which is absorbed to the resin surface [35]. The fourth model is solid model in which the solid phase is considered as two main parts, precipitating and non-precipitating asphaltene. There are too many matching parameters needed to tune this model with the experimental data [36]. The aim of this study is to investigate the asphaltene deposition mechanism during natural depletion and CO2 injection at different pressures. Most of the experimental works are challenging with very complicated phenomena such as the asphaltene deposition in the opening of microscopically heterogeneous rocks. A novel experimental setup was designed to utilize a high-pressure visual cell to study asphaltene deposition on the model rock at reservoir condition. The evolution of asphaltene deposition was monitored by a microscope; then analyzed by image processing software to check the amount of deposited asphaltene and its size distribution at different conditions. The process of asphaltene precipitation during pressure depletion and CO2 injection was modeled using the thermodynamic solid model. The PVT properties of the crude oil samples were utilized to characterize the asphaltene.

Table 1 SARA tests (wt %) of oil used in this work. Test name (wt %)

Bangestan field sample

Saturates Aromatics Resins Asphaltene

38.74 50.59 6.17 4.25

and deposition. The schematic diagram of this apparatus is illustrated in Fig. 1, which was described already in several publications [2,3,12,39]. The main part of the apparatus consists of a high-pressure cell which is filled with synthetic oil. A microscope (KRUSS, MBL2000) with an optical resolution up to 480X, was installed on the top of the cell to capture high-resolution images of asphaltene depositions on the substrates. Clear images of particles in the space between the substrate and side-glass were captured precisely by focusing closely into the cell through the opening. The geometric properties of asphaltene aggregation were determined by analyzing the captured images using Sigma Scan Pro 5 software. The calibration process applied in the software enables us to evaluate the size of deposited asphaltene particles according to the darkness and the area of each particle without interrupting the high-pressure and high-temperature conditions. A rotating metal disc as it is shown in Fig. 1 is placed horizontally inside the cell. Substrate plates of different types could be mounted on the disc in order to study the evolution of asphaltene deposition on different solid models. The tests were carried out at four different pressures: P1 = 140 bar, P2 = 100 bar, P3 = 60 bar and P4 = 30 bar. The temperature of the cell was adjusted using a high-accuracy controlled heater installed outside the cell. 3. Modeling part The solid model treats asphaltene as a single component residing the solid phase while both the oil and gas phases are modeled with a cubic equation of state (EOS). The precipitated asphaltene is represented as a pure solid in this model [41–43]. 3.1. Solid phase The fugacity of asphaltene in solid phase is given by [40]:

2. Experimental part 2.1. Materials Asphaltene used in this study was extracted from an Iranian oil field sample located in the south of Iran, based on the procedure described by ASTM-D86 [37]. To prepare the synthetic oil, toluene and normal heptane (Merk, high-performance liquid chromatography grade) were used. Glass substrates were utilized as the model solid surface to mimic the sandstone [38–40]. The SARA (Saturate, Aromatic, Resin, and Asphaltene) analysis of the crude oil samples is presented in Table 1. 2.2. Experimental apparatus The high-pressure cell was designed in the EOR Research Center, Shiraz University to study the asphaltene precipitation

Fig. 1. Schematic diagram of experimental apparatus including (1) peristaltic pump, (2) distilled water reservoir, (3) computer, (4) CCD camera, (5) microscope, (6) sight glass, (7) piston- cylinder, (8) cold light source, (9) heater, (10) magnetic mixer, (11) high pressure cell, (12) rotator, (13) metal disc, (14) fan, (15) magnetic device.

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ln f s ¼ ln f s þ

v s ðP  P Þ

ð1Þ

RT

3.2. Vapor and liquid phases Vapor and liquid phases are modeled with an equation of state (EOS) and volume shift parameters [43,44]. The fugacity of component i in phase j (j = 0, g) is [36]: eos

ln f ij ¼ ln f ij þ bi ¼

si bi P RT

i ¼ 1; . . . ; nc;

j ¼ v; 1

Xb RT ci

ð2Þ

ð3Þ

Pci

where fij and fijeos are the fugacities of component i in phase j with and without translation, si and bi are the dimensionless volume shift and EOS parameters for component i respectively. The molar volume of phase j with volume shift is calculated using the following equation:

v j ¼ v eos þ j

nc X yij si bi

j ¼ v;1

ð4Þ

¼1

3.3. Asphaltene component To represent the asphaltene component when the vapor, liquid, and solid phases exist, the following fugacity equations are solved to obtain vapor/liquid/solid equilibrium:

ln f iv ¼ ln f il

ð5Þ

ln f nc v ¼ ln f nc l ¼ ln f s

i ¼ 1; . . . ; nc

ð6Þ

In Nghiem et al. [45] approach the heaviest component in oil splits into non-precipitating (CA+) and precipitating component (CB+). These two pseudo-components have the same properties (e.g. critical temperatures, critical pressures, acentric factors and molecular weights) but they have different interaction coefficients with the light components. As the amount of light components in the solution increases, the higher interaction coefficient between the asphaltene and light components rather than the non-precipitating components, results in more asphaltene precipitation. The interaction coefficient is determined by following equation:

0

1 6

1 6

1e

2v v dik ¼ 1  @ 1 ci 1 ck A v 3ci þ v 3ck

i ¼ 2; . . . ; 12; k ¼ 2; . . . ; 12

ð7Þ

The reference fugacity could be calculated from a data point on the asphaltene precipitation envelope (APE) [46]. 3.4. Characterization of synthetic oil The lack of proper characterization parameters, especially in asphaltic petroleum fluids will lead to a non-accurate prediction of phase behavior [47]. In this study, to achieve an appropriate thermodynamic model, the thermodynamic fluid characterization has been examined. As it is shown in Table 2, the synthetic oil consists of three components: toluene (C7H8), n-heptane (n-C7) and the asphaltene. PR (Peng-Robinson, 1978) equation of state was chosen as an appropriate equation to predict the phase behavior. Calculations of saturation pressure were performed on a multi-component system to verify the capability of the EOS used at this stage. Three well-known correlations: Twu [48], Lee-Kesler [49] and Riazi [50] have been used to calculate the critical properties. The

Table 2 Specifications of synthetic oil components. Components

Synthetic oil (wt %)

C7H8 n-C7 Asphaltene

71.4 23.5 5.1

Total

100.00

results show that the Twu correlation could predict the experimental results more accurately. It may be explained by the fact that the Twu correlations are more suitable for heavy components like asphaltene. 3.5. Sensitivity analysis The next step is the specification of solid model parameters. According to the sensitivity analysis procedure, the main parameters to match the solid model with the experimental data were found as the molar volume of asphaltene component and the interaction coefficients between asphaltene and other components (toluene and n-heptane). In the CO2 injection scenario, the interaction coefficients between asphaltene and CO2 have been vigorously challenged. A sensitivity analysis performed with different runs using CMG simulator (WinProp module). The details of these analyses are presented in the results and discussion part. 4. Results and discussion The images were taken at different pressures showed that by increasing pressure the amount of deposition on the glass surfaces was increased. To investigate the effect of CO2 injection on the asphaltene deposition, the different mole percentage of CO2 was injected into the cell. Comparing the results showed that CO2 injection, lead to the increase of asphaltene deposition. The amount of the deposited asphaltene is the most desired parameter for any asphaltene study. This parameter must be measured in situ since by removing the substrates from the cell the pressure and temperature conditions change suddenly. To quantify the amount of deposited asphaltene as well as the diameter and the volume of asphaltene particles at the specified conditions, the image processing software has been used [2]. Using the density of extracted asphaltene, the total weight of asphaltene deposited on the glass surface was measured. Considering the total amount of dissolved asphaltene in the original synthetic oil and the measured deposited asphaltene, the weight fraction of asphaltene has been calculated. To ensure the accuracy and repeatability of the measurements, each test was repeated three times at the specified conditions. There were nine glass substrates mounted inside the cell in which the average amount of deposited asphaltene on each substrate was measured and assumed as the result of each experiment. Fig. 2 shows the effects of pressure changes on asphaltene deposition. In order to investigate the effect of CO2 injection on asphaltene deposition, 5% of CO2 on the molar basis was injected into the cell. The tests were repeated using different mole percents (10%, 15%, 20%) of CO2. Images which are taken at different pressures are shown in Figs. 3–6. The dark particles were shown on the images are aggregated asphaltenes deposited on the glass surfaces. To investigate the temperature effect, asphaltene particle size was measured at 35 and 90 °C. Fig. 7 demonstrates that asphaltene particles tend to stick together and make larger particles as the temperature increases. Results are presented in Table 3. In modeling part, after introducing the asphaltene component to the model, a sensitivity analysis was performed on two main

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Fig. 2. Asphaltene deposition at 90 °C (without CO2 injection).

Fig. 3. Effect of CO2 injection on asphaltene deposition at different pressure, 90 °C (5 mol% CO2 injection).

Fig. 4. Effect of CO2 injection on asphaltene deposition at different pressure, 90 °C (10 mol% CO2 injection).

Fig. 5. Effect of CO2 injection on asphaltene deposition at different pressure, 90 °C (15 mol% CO2 injection).

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Fig. 6. Effect of CO2 injection on asphaltene deposition at different pressure, 90 °C (20 mol% CO2 injection).

Fig. 7. Effect of temperature on asphaltene particle size, atmospheric pressure.

parameters to obtain the molar volume of asphaltene and the interaction coefficient between asphaltene and other components in synthetic oil. During different simulation tests, the amount of the asphaltene molar volume has been specified as 0.2 m3/kmol. This amount attained the best match for the final amounts of deposited asphaltene measured through the experimental tests and modeling results. The calculated value is in line with that of a previous study, 0.24 m3/kmol [51]. The same analysis on the interaction coefficients has fulfilled to find the tuned values in the solid model. The same sensitivity analysis was performed for the CO2 injection scenario. The striking result to emerge from the data is that in the pressure depletion scenario, the interaction coefficient between n-heptane and asphaltene is at least 20 times higher than that between toluene and asphaltene. It is assumed that the higher solubility of asphaltene particles in toluene is behind this unusual result. In CO2 injection scenario, the interaction coefficient between CO2 and asphaltene is much higher than other components with asphaltene. As the concentration of CO2 in different modeling test increases, the interaction coefficient between CO2 and asphaltene increases significantly. It seems that

they both are polar molecules, and it would be the main reason for higher interaction coefficient. The results of sensitivity analysis have been illustrated in Tables 4 and 5 according to the interaction Table 4 Interaction coefficient between different components of synthetic oil during pressure depletion. Components Interaction coefficient

C7H8/Asphaltene 0.005

n-C7/Asphaltene 0.12

Table 5 Interaction coefficient between CO2 and asphaltene precipitating of synthetic oil for different rate of CO2 injection. CO2 injection mole percent Interaction coefficient CO2/asphaltene

0.05 0.16

0.1 0.2

0.15 0.24

0.2 0.35

Table 6 Results of asphaltene deposition due to pressure depletion, 90 °C. Pressure (bar)

Table 3 Effect of temperature on asphaltene particle size (atmospheric pressure).

Experimental data

Modeling

Asphaltene deposited (wt %)

Temperature (°C)

35

90

Mean diameter of deposited asphaltene (lm) Mean area of deposited asphaltene (lm2)

0.211 1.104

2.54 7.82

30 60 100 140

0.0103 0.0150 0.0338 0.0588

0 0.0050 0.0413 0.0633

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Table 7 Results of asphaltene deposition due to CO2 injection at different pressures, 90 °C. Pressure (bar)

Experimental data Mole fraction of CO2 injection

Modeling

5%

10%

15%

20%

5%

10%

15%

20%

5%

10%

15%

20%

30 60 100 140

0.010 0.024 0.044 0.074

0.029 0.036 0.073 0.089

0.037 0.058 0.118 0.147

0.042 0.065 0.124 0.169

0 0.023 0.051 0.068

0.026 0.048 0.072 0.089

0.014 0.057 0.106 0.144

0 0.072 0.122 0.157

1 0.041 0.159 0.081

0.103 0.333 0.013 0

0.62 0.017 0.101 0.020

1 0.107 0.016 0.071

coefficients. Very few studies have investigated the interaction coefficients between asphaltene and synthetic oil. However, these results match those observed in the earlier study by Qin et al. [52]. After finding the main parameters in the solid model, the tuned model was used to predict the amount of asphaltene precipitation in comparison with the experimental data. A good agreement between experimental data and the tuned model was achieved. The modeling results of asphaltene precipitation due to pressure depletion and CO2 injection are presented in Tables 6 and 7. 5. Conclusions A high-pressure cell and image processing technique were successfully used to visualize asphaltene deposition process. Experimental results of asphaltene deposition at different pressures showed as the pressure increases, the amount of deposition increases too. Besides, the results demonstrated that CO2injection increases asphaltene deposition in all the pressure ranges comparing to the case of natural depletion. The results indicated that there are critical conditions for asphaltene deposition. For instance, asphaltene deposition at 140 bar and 90 °C is 5.8 times more than the case of 30 bar pressure and 90 °C for the synthetic oil used in this study. The results of CO2 gas injection revealed that the amount of asphaltene deposition was increased to a great extent as the CO2 mole fraction was increased. Changing CO2 injection from 5 to 20 mol% resulted in 56% more in asphaltene deposition at 140 bar and 90 °C condition. A thermodynamic solid model based on PR (Peng–Robinson, 1978) equation of state was presented which shows a satisfactory agreement between the developed model and experimental results. The main aim of this study was to investigate the effect of CO2 injection on the precipitation process of pure asphaltene molecules in the absence of other effective parameters such as other crude oil fractions at different pressures. It is worth mentioning that considering other parameters such as resins in the crude oil and the porous media as the main medium for the fluid flow could affect the precipitation and deposition process [53]. References [1] Hammami A, Ratulowski J. Precipitation and deposition of asphaltenes in production system: a flow assurance overview. New York: Springer; 2007. [2] Zanganeh P, Ayatollahi Sh, Alamdari A, Zolghadr A, Dashti H, Kord Sh. Asphaltene deposition during CO2 injection and pressure depletion: a visual study. Energy Fuels 2012;26:1412–9. [3] Soorghali F, Zolghadr A, Ayatollahi Sh. Effect of resins on asphaltene deposition and the changes of surface properties at different pressures: a microstructure study. Energy Fuels 2014;28:2415–21. [4] Mansoori GA, Barnes L, Glenn M. Petroleum waxes. West Conshohocken: ASTM Int’l; 2003. [5] Mansoori GA, Vazquez D, Shariaty-Niassar M. Polydispersity of heavy organics in crude oils and their role in oil well fouling. J Pet Sci Eng 2007;58:375–90. [6] Mansoori GA. A unified perspective on the phase behaviour of petroleum fluids. Int J Oil, Gas Coal Technol 2009;2(2):141–67. [7] Groenzin H, Mullins OC. Molecular size and structure of asphaltenes from various sources. Energy Fuels 2000;14(3):677–84. [8] Spiecker PM, Gawrys L, Kilpatrick PK. Aggregation and solubility behavior of asphaltenes and their subfractions. J Colloid Interface Sci 2003;267:178–93.

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