Effects of Asphaltene Content and Temperature on Viscosity of Iranian

Article pubs.acs.org/EF

Effects of Asphaltene Content and Temperature on Viscosity of Iranian Heavy Crude Oil: Experimental and Modeling Study Mahdi Ghanavati, Mohammad-Javad Shojaei, and Ahmad Ramazani S. A.* Department of Chemical and Petroleum Engineering, Sharif University of Technology, Azadi Avenue, Tehran, Iran ABSTRACT: Heavy and extra heavy crude oils usually have a high weight percentage of asphaltene, which could induce many problems during production to refining processes. Also, asphaltene has the main role on the high viscosity of the heavy and extra heavy crude oils. In this paper, the effects of asphaltene characteristics on the crude oil rheological properties have been experimentally and theoretically investigated using different classes of the suspension models. For experimental investigation, the asphaltene was first precipitated from the original heavy crude oil and then 10 well-defined reconstituted heavy oil samples are made by dispersing the asphaltene into the maltene (i.e., deasphalted heavy crude oil) for measuring viscosity at a wide range of temperatures from 25 to 85 °C. Then, the viscosity of the prepared reconstituted heavy oil samples was measured using a rotational rheometer at seven different temperatures. Moreover, for modeling the viscosity behavior of the heavy oil samples versus different asphaltene contents (0−12.22 vol %) at different temperatures (25−85 °C), six equations from three groups of suspension models are used, including Pal−Rhodes (with parameters of the shape factor ν and solvation constant K), Mooney, Krieger−Dougherty, and Brouwers (with parameters of the intrinsic viscosity [η] and the maximum packing volume fraction φmax), and Bicerano et al. and Santamaria-Holek and Mendoza (with parameters of the intrinsic viscosity [η] and the critical volume fraction φc). The results of experimental study indicate that the viscosity of the reconstituted heavy oil samples increases exponentially as the asphaltene content increases at a constant temperature. Also, the viscosity of the heavy oil samples decreases significantly with increasing the temperatures from 25 to 85 °C at a constant asphaltene volume fraction.

1. INTRODUCTION Crude oil plays an important role in the energy supply all over the world. The global demand for crude oil has increased in the first years of the 21th century in comparison to the last years of the 20th century.6−9 On the basis of these reasons, crude oil will remain as the essential source of energy supply of the world’s demand. Among different types of crude oils, the attentions have been focused on the recovery of heavy and extra heavy crude oils, because the conventional light and medium crude oil resources have been reduced globally.10−12 The heavy and extra heavy crude oils are defined as the petroleum with American Petroleum Institute (API) gravity equal or lower than 20° and equal or lower than 10°, respectively. The heavy crude oils have been found in the different regions of the world, such as the Orinoco Belt in Venezuela, Alberta in Canada, some regions of the Gulf of Mexico, and northeastern China.8,13−16 Also, Iran as one of the main producers of crude oil in the world has various varieties of crude oil resources from light crude oils to extra heavy crude oils. Currently, Iran’s developed oil reserves are estimated at 560 billion barrels, of which 140 billion barrels are recoverable, including 70 billion barrels of heavy and extra heavy crude oils. Despite the importance and high volumes of the heavy oil reserves, the development and production from these resources are low and difficult, unfortunately. The composition complexity and high viscosity of the heavy and extra heavy crude oils cause many problems and challenges in the production chains, such as extraction, transportation, and refining.17,18 Moreover, these types of crude oils usually have a great percentage of heavy components, such as asphaltene and wax, in their composition.17−20 In addition, other compounds, such as sulfur, salts, and metals (such as nickel and vanadium) may exist in the heavy crude oil.16,21 © 2013 American Chemical Society

Asphaltene is regarded as the heaviest fraction of the crude oil, which is insoluble in normal alkanes (such as n-pentane, n-hexane, and n-heptane) and soluble in aromatic solvents (such as benzene and toluene).22−28 Asphaltene has an essential role on the high viscosity of crude oils, and therefore, the heavy oils are not pumped easily via pipelines.29−31 Asphaltene causes many challenges through different operations of the crude oil from reservoir to refining processes.32−36 Asphaltene deposition leads to the blocking the pore throats, permeability reduction of rocks, and alteration the wettability of rocks from water wet to oil wet, which all have negative effects on oil production.37−42 Moreover, the asphaltene precipitation in surface facilities, such as separators and pipelines, causes various problems in the transportation and refining of the crude oils and, thus, wastes time and cost during the operation, and asphaltene should be cleaned from these equipment.43−45 The chemical, thermal, mechanical, electromagnetic, and biological methods or a combination of them has been used for solving the problems of the asphaltene precipitation, but these methods usually have environmental and personal hazards and lead to high costs.46−48 Asphaltenes are polar aromatic compounds with high molecular weight, which partly dissolved and partly dispersed in the crude oil.22,23,49−52 The nonpolar resins that exist in the crude oil are strongly adsorbed by asphaltene, and therefore, the adsorbed resins around asphaltene prevent their aggregation. However, under various conditions, the layers of resins can desorb from asphaltene particles, which enable the asphaltenes to Received: April 27, 2013 Revised: September 14, 2013 Published: September 17, 2013 7217

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come in contact and precipitate.19 Also, resins enhance the size of asphaltene particles and decrease the coagulation and precipitation of asphaltenes in crude oil. Generally, the crude oils with higher resin content are more stable.47 Among different parameters, pressure, temperature, and compositional changes are more effective factors that result in asphaltene deposition.53−58 Pressure and compositional changes may occur during primary depletion or enhanced oil recovery (EOR) processes.19,59−64 The experimental investigations show that the most severe asphaltene precipitation takes place in the reservoirs at the bubble point pressure.28,65−69 Many researchers have investigated that the asphaltene precipitation occurred during thermodynamic changes, such as CO2 and natural gas injection.22,70−74 Also, many papers have focused on the modeling of the asphaltene precipitation behavior under different conditions with various approaches.75−81 The different effects of the temperature on the deposition of asphaltene are observed. Results show that, usually at higher temperatures, resins have greater solubility in n-alkanes, and thus, asphaltenes aggregate in the crude oil because of less solubility.47,82−85 Also, because the asphaltene precipitation increases the operational costs, the effect and performance of some inhibitors are studied for inhibition of asphaltene precipitation from crude oils during various processes.86−88 Despite the influence of asphaltene on crude oil viscosity, few experimental studies have been conducted on this case. Therefore, in this study, the effects of asphaltene contents on the viscosity of heavy crude oil are investigated at different temperatures. For this purpose, 10 reconstituted heavy oil samples were prepared with the addition of different precipitated asphaltenes from Iranian heavy crude oil. Then, the viscosities of the reconstituted heavy oil samples were measured at seven temperatures in the ranges of 25−85 °C. Furthermore, to evaluate the effect of asphaltene contents on the viscosity behavior of the reconstituted heavy oil samples, six suspension equations from three groups of models were used. The parameters of these models were determined and analyzed to better understand the effect of asphaltene on the viscosity of heavy oil.

and density of the original oil sample are 2638 cP and 963 kg/m3 at the atmospheric pressure and 25 °C, respectively. In this study, n-hexane (Merck, Germany) was used for measuring the asphaltene content of the original heavy crude oil and precipitating the asphaltene for preparing the reconstituted heavy oil samples. 2.2. Asphaltene Content and Heavy Oil Sample Preparation. For experimental study, it is necessary to determine the asphaltene content and prepare the reconstituted heavy crude oil samples with various asphaltene contents. For these goals, first, the asphaltene must be precipitated from the original heavy crude oil using the ASTM D2007 method.89 The procedure of this method is described as follows: (1) The given volume of the heavy crude oil was injected into the beaker (1000 mL, SCHOTT, DURAN, Germany). (2) The weight of the added heavy crude oil was recorded accurately with an electronic laboratory balance (Sartorius, Germany), which is denoted as w1. (3) A total of 1 volume of heavy crude oil was mixed with 40 volumes of n-hexane that was used as a precipitant in this work. (4) The mixture of heavy oil and precipitant was agitated using a magnetic stirrer (SP46925, Barnstead/Thermolyne Corporation, Dubuque, IA) for approximately 10 h. After agitation, the beaker was closed, and then the mixture remained in the dark for 7 days to ensure the whole asphaltene particles precipitate at the bottom of the beaker. (5) After these steps, the mixture was filtered through a filter paper (Whatman No. 42), and the filter cake was rinsed with n-hexane until n-hexane remained colorless. (6) The filtrate mixture containing deasphalted heavy crude oil and precipitated asphaltenes was separately dried until their weight did not change with the reading of an electric laboratory balance. The weight of precipitated asphaltene is denoted as w2. Knowing the weight of the initial heavy crude oil (w1) and precipitated asphaltene (w2), the asphaltene content of the original crude oil is calculated as follows: w weight percent (%) = 2 × 100% w1 (1) These stages were performed for the original heavy crude oil, and the asphaltene content was measured to be Wasp = 14.86 wt %. To prepare the reconstituted heavy crude oil samples with different asphaltene contents, stages 1−6 were carried out, which were described previously. After these steps, the precipitated asphaltene were ground and shifted through a 75 μm sieve. Then, the reconstituted heavy oil samples with various asphaltene contents were supplied by dispersing different values of shifted asphaltenes into the maltenes (i.e., deasphalted heavy oil) and were homogenized by agitating the mixture to ensure that the physical properties of the reconstituted samples are the same. Figure 1 shows the images of precipitated asphaltene before and after shifting through a 75 μm sieve. 2.3. Density and Volume Fraction Calculation. The density of the heavy crude oil was measured using a digital Anton Paar densitometer (Anton Paar, DMA 35N). The weight percentage of asphaltenes can be converted to the volume fraction by obtaining the density of asphaltene and densities of the samples with different asphaltene contents. The density of asphaltene can be calculated from the following equation:

2. EXPERIMENTAL SECTION 2.1. Materials. The heavy crude oil was supplied from one of the major Iranian oil fields. The heavy crude oil components are listed in Table 1. As seen in Table 1, the used heavy crude oil does not have light components under C9. The asphaltene content of the original heavy crude oil is 14.86 wt % (n-hexane insoluble). Also, the viscosity

Table 1. Compositional Analysis of the Heavy Crude Oil carbon number

mol %

C1 C2 C3 C4 C5 C6 C7 C8 C9 C10 C11 C12+

0 0 0 0 0 0 0 0 3.25 4.77 3.84 88.14

ρasp =

Wasp 1 ρoil

−

1 − Wasp ρmal

(2)

where Wasp, ρmal, and ρoil are the weight percentage of the asphaltene in the original heavy crude oil, density of maltene, and density of heavy crude oil at the atmospheric pressure and 25 °C, respectively. The density of maltene was measured to be 919 kg/m3 at the atmospheric pressure and 25 °C. Having Wasp, ρmal, and ρoil and considering eq 2, the density of asphaltene was calculated to be ρasp = 1327 kg/m3. Also, the weight percentage (w) of asphaltene can be converted to the volume fraction φ by the following equation: φ=

7218

ρsample ρasp

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Figure 1. Images of precipitated asphaltene (a) before and (b) after shifting through a 75 μm sieve. where ρsample is the density of each reconstituted heavy crude oil sample. ρsample was calculated from the weight percentage of each reconstituted heavy oil by linear interpolation of the measured densities of the original heavy crude oil and maltene at the atmospheric pressure and 25 °C. A simple design of the experiment has been summarized in a flowchart in Figure A1 of Appendix A. 2.4. Experimental Setup. The measurements of the prepared samples were carried out using a Physica MCR 301 rheometer from Anton Paar, which operates by the Rheoplus software. The measurements were conducted using a plate−plate geometry setup. This geometry includes a fixed lower plate and an upper plate that can

rotate with a diameter of 25 mm. To investigate the influence of the temperature on the viscosity of the crude oil samples, a great control on the temperature is needed during viscosity measurements, because the temperature strongly affects the viscosity behavior of the heavy crude oils.90 The rheometer controls the temperature in the range from −40 to 200 °C with an accuracy of 0.01 °C by a Peltier plate at the bottom of the rheometer. Also, an active Peltier hood was used as a cover, which controls the temperature within the hood to match that of the bottom Peltier plate. This technique controls the temperature accurately and minimizes temperature gradients in horizontal and vertical directions during the tests. It should be noted that the rheometer is equipped with an air compressor system, which is used for increasing the 7219


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temperature by heating air using an element inside the rheometer (Anton Paar Physical MCR technical specifications). For viscosity measurements, a thin layer of prepared crude oil samples was placed on the fixed plate of the rheometer. Then, the upper plate was adjusted to obtain the desired gap width. The measurement gap was set to 0.8 mm for all prepared crude oil samples. Figure 2 shows the schematic diagram of the Anton Paar rheometer in

and

[η] = Kν

(7)

kH = k1K 2

(8)

where [η] and kH are known as intrinsic viscosity and Huggins coefficient, respectively. These values are related to the physical properties of the solid particles, such as size and rigidity, and also the interaction between particles and the continuous phase. The coefficients of higher order terms in eq 6 do not have particular names and have not been considered as effective as [η] and kH. The first equation for modeling the suspension viscosity was suggested by Einstein in linear approximation.92 ηr =

η = 1 + 2.5φ η0

(9)

In comparison of eqs 9 and 6, the intrinsic viscosity in the Einstein equation is equal to 2.5. However, for many suspensions and colloid dispersions, the Einstein equation is not valid for the concentrate dispersion. This equation indicates that the dispersion particles are spherical and without solvation effect (i.e., K = 1). However, in reality, many dispersion particles are non-spherical in shape, and the solvation effect exists.93 On the basis of these reasons, the various forms of the models have been derived to modify the Einstein equation. Pal and Rhodes1 proposed a viscosity model considering the solvation effect, but in the Pal and Rhodes equation, the solid particles are assumed spherical. To account for the nonspherical shapes of the dispersed solid particles, the shape factor was entered in this equation. Thus, the generalized Pal−Rhodes equation is expressed as94

Figure 2. Schematic diagram of the rheometer in the plate−plate geometry. the plate−plate geometry, which has been used for the viscosity measurements. In this work, the viscosity measurements are conducted in a wide range of shear rates from 0.1 to 100 s−1 and the samples represent constant viscosity at low shear rate (γ̇ < γ̇c) and shear thinning behavior at high shear rate (γ̇ > γ̇c). Thus, the reported viscosities of the samples in this paper are related to the Newtonian region of the reconstituted heavy oil samples. The viscosity measurements were carried out 3 times, and the maximum relative error in the viscosity measurements was found to be 2.68%. It should be noted that the phase change was not observed for the sample during the temperature rise for experimental measurement by the rheometer.

3. VISCOSITY MODELING OF THE SUSPENSION The viscosity of the solid particles in a liquid can be generally expressed as power series terms. The relative viscosity of the suspension can be written as91 η = 1 + νφeff + k1φeff 2 + ... ηr = η0 (4)

ηr = (1 − Kφ)−ν

(10)

In the above equation, if the effective volume fraction (i.e., φeff = Kφ) of the solid particles is equal to unity, the suspension viscosity approaches infinity. This behavior may happen for high densely dispersed particles. In this case, the effective volume fraction of the dispersed solid particles is less than unity and is termed the maximum packing volume fraction φmax. With this methodology, Mooney2 suggested the semi-empirical equation, which is expressed in the following form:

where η is the relative viscosity, which is defined as the ratio of the viscosity of the suspension to the viscosity of the continuous phase, ν indicates the shape factor of the dispersed solid particles, which depends upon the spherical or nonspherical shape of the solid particles, k1 is a constant, and φeff represents the effective volume fraction of the dispersed phase in the colloid dispersion after it is solvated in the continuous phase. In addition, the solvation constant K is defined as the ratio of the effective volume fraction (φeff) of the solvated phase to its original dry volume fraction (φ) before dispersion to a continuous phase, which is expressed as follow:89 φ K = eff φ (5)

⎛ [η]φ ηr = exp⎜ ⎜1 − φ φmax ⎝

⎞ ⎟ ⎟ ⎠

(11)

Also, according to this concept, Krieger and Dougherty95,96 proposed another equation considering the crowding effect, which was introduced by Mooney. The Krieger and Dougherty equation is as follows: −[η]φmax ⎛ φ ⎞ ⎟⎟ ηr = ⎜⎜1 − φmax ⎠ ⎝

With substitution of eq 5 into eq 4, the relative viscosity can be written as a function of the dry volume fraction of the solid particles.91 η = 1 + [η]φ + kHφ 2 + ... ηr = η0 (6)

(12)

In addition, Brouwers3 has proposed another equation, which can relate the relative viscosity of the suspension to the dispersed volume fraction. 7220


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⎞[η]φmax /1 − φmax ⎟ ⎟ ⎠

where c1 and c2 are defined by (13)

Mooney, Krieger-Dougherty, and Brouwers equations have been used for modeling the viscosity behavior of the reconstituted heavy oil samples. Moreover, Douglas and Garboczi4 suggested a different approach for calculating the suspension viscosity based on the expected theoretical divergence of viscosity near the percolation threshold. −2 ⎛ φ⎞ ⎜ ⎟ ηr ∼ ⎜1 − ⎟ φc ⎠ ⎝

(16)

c 2 = kHφc 2 − 2[η]φc + 1

(17)

kH =

⎞ 1 ⎛ 2 [η]⎜⎜[η] + − 1⎟⎟ 2 ⎝ φc ⎠

(18)

where φc in this equation is defined as the critical volume fraction at which the suspension losses its fluidity. SantamariaHolek and Mendoza5 modified and extended the Bicerano et al.4 equation as follows: −2 ⎡ ⎛ ⎛φ⎞ ⎛ φ ⎞2 ⎛ φ ⎞3 ⎤ φ⎞ ⎢ ηr = ⎜⎜1 − ⎟⎟ 1 + c1⎜⎜ ⎟⎟ + c 2⎜⎜ ⎟⎟ + c3⎜⎜ ⎟⎟ ⎥ φc ⎠ ⎢⎣ ⎝ ⎝ φc ⎠ ⎝ φc ⎠ ⎝ φc ⎠ ⎥⎦

(14)

In the above equation, the relative viscosity is independent of the shape of the dispersed particles in suspension. Thus, Bicerano et al.4 using the Douglas and Garboczi approach proposed their equation, which provides a smooth transition between the dilute and concentrate regimes. −2 ⎡ ⎛ ⎛φ⎞ ⎛ φ ⎞2 ⎤ φ⎞ ⎢ ⎜ ⎟ ⎜ ⎟ ηr = ⎜1 − ⎟ 1 + c1⎜ ⎟ + c 2⎜⎜ ⎟⎟ ⎥ φc ⎠ ⎣⎢ ⎝ ⎝ φc ⎠ ⎝ φc ⎠ ⎥⎦

c1 = [η]φc − 2

(19)

where constants c1 and c2 are defined as the Bicerano et al. model,4 which is given by eqs 16−18. Also, constant c3 is determined by c3 =

(15)

φc 3 6

[η]([η]2 − 2[η] + 2)

(20)

Table 2. Summary of the Suspension Models Used in the Paper viscosity model

equation

consideration K and ν are the solvation constant and shape factor, respectively

Pal and Rhodes1

ηr = (1 − Kφ)−ν

Mooney2

⎛ [η]φ ηr = exp⎜⎜ φ 1− φ ⎝ max

Krieger and Dougherty96

⎛ 1−φ ηr = ⎜⎜ φ 1− φ ⎝ max

⎞[η]φmax /1 − φmax ⎟ ⎟ ⎠

Brouwers3

⎛ 1−φ ηr = ⎜⎜ φ 1− φ ⎝ max

⎞[η]φmax /1 − φmax ⎟ ⎟ ⎠

Bicerano et al.4

−2 ⎡ ⎛ ⎛φ⎞ ⎛ φ ⎞2 ⎤ φ⎞ ηr = ⎜⎜1 − ⎟⎟ ⎢1 + c1⎜⎜ ⎟⎟ + c 2⎜⎜ ⎟⎟ ⎥ φc ⎠ ⎢⎣ ⎝ ⎝ φc ⎠ ⎝ φc ⎠ ⎥⎦

⎞ ⎟ ⎟ ⎠

[η] and φmax are the intrinsic viscosity and maximum packing volume fraction, respectively

φc is the critical volume fraction at which the suspension loses its fluidity, and [η] and kH are the intrinsic viscosity and Huggins coefficient, respectively

c1 = [η]φc − 2 c 2 = kHφc 2 − 2[η]φc + 1 ⎞ 1 ⎛ 2 − 1⎟⎟ [η]⎜⎜[η] + φc 2 ⎝ ⎠

kH =

c3 = Santamaria-Holek and Mendoza5

φc 3 6

[η]([η]2 − 2[η] + 2)

−2 ⎡ ⎛ ⎛φ⎞ ⎛ φ ⎞2 ⎛ φ ⎞3⎤ φ⎞ ηr = ⎜⎜1 − ⎟⎟ ⎢1 + c1⎜⎜ ⎟⎟ + c 2⎜⎜ ⎟⎟ + c3⎜⎜ ⎟⎟ ⎥ φc ⎠ ⎣⎢ ⎝ ⎝ φc ⎠ ⎝ φc ⎠ ⎝ φc ⎠ ⎥⎦

c1 = [η]φc − 2 c 2 = kHφc 2 − 2[η]φc + 1 kH =

c3 =

⎞ 1 ⎛ 2 − 1⎟⎟ [η]⎜⎜[η] + φc 2 ⎝ ⎠

φc 3 6

[η]([η]2 − 2[η] + 2) 7221


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⎡ (η )i − (η )i ⎤ r,exp r,est ⎥ × 100 Ei = ⎢ ⎢⎣ ⎥⎦ (ηr,exp)i

The equations used in this study for the modeling of the relative viscosity versus asphaltene volume fraction of the heavy oil samples are summarized in Table 2. It must be noted that all of the suspension models used in this study have two adjustable parameters and can be determined using the nonlinear regression among the measured relative viscosity and dispersed volume fraction data. In addition, because the temperature has a strong effect on the viscosity of the heavy crude oil, its influence should be investigated on the viscosity of the reconstituted heavy oil samples with different asphaltene contents. To achieve this purpose, the Arrhenius equation95 was used as follows: ⎡E⎛ 1 1 ⎞⎤ η(T ) = η(T0)exp⎢ ⎜ − ⎟⎥ T0 ⎠⎦⎥ ⎣⎢ R ⎝ T

(26)

where Ei is the relative deviation of the experimental data from the estimated value by models. 4.5. Average Absolute Percent Relative Error (AAPRE). AAPRE determines the relative absolute deviation from the experimental data. It is calculated from the equation below.

Ea =

n

∑ ((ηr,exp)i − (ηr,est)i )2

(22)

i=1

ηr,exp and ηr,est are the experimental and estimated values of the relative viscosities, respectively. 4.2. Standard Deviation (SD). This parameter calculates the dispersion, and a low value of this error is indicative of a smaller degree of scatter. It is determined by 1 n−1

SD =

⎛ (η )i − (η )i ⎞2 r,exp r,est ⎟ ∑ ⎜⎜ ⎟ η ( ) i ⎠ r,exp i=1 ⎝ n

(23)

2

4.3. Coefficient of Determination (R ). This parameter indicates how good the model matches the data and shows a measure of the utility of the model. It is calculated from following equation: n

R2 = 1 −

∑i = 1 ((ηr,exp)i − (ηr,est)i )2 n

∑i = 1 ((ηr,est)i − ηr̅ )2

(24)

where η̅r is the mean of the experimental data value as in the above equation. Also, It should be noted that the better fitting of data with models is observed when the value of R2 is closer to 1. 4.4. Average Percent Relative Error (APRE). APRE calculates the relative deviation from the experimental data and is as follows: Er =

1 n

n

∑ Ei i=1

n

∑ |Ei| i=1

(27)

5. RESULTS AND DISCUSSION 5.1. Viscosity Measurement at Different Temperatures. To investigate the effect of the asphaltene content on the heavy oil viscosity, 10 reconstituted heavy oil samples were provided with dispersion of the prepared dry asphaltene in the range of 0−16.74 wt % (i.e., φ = 0−12.22 vol %). Also, considering the influence of the temperature on the viscosity of heavy oil, viscosity of the reconstituted heavy oil samples was measured at seven different temperatures from 25 to 85 °C. For analysis of the experimental data, the measured viscosities of the reconstituted heavy oil samples versus the asphaltene volume fraction at seven different temperatures are shown in Figure 3. Figure 3 illustrates that, with an increase in the asphaltene content at a constant temperature in the samples, the viscosity of the reconstituted heavy oil increases, particularly at low temperatures. For example, the viscosity of heavy oil increases from 283 to 5960 cP with increasing the asphaltene content from 0 to 12.22 vol % at 25 °C. However, the viscosity increases from 29 to 124 cP at 85 °C and in the same asphaltene volume fraction range. Moreover, when the temperature increases at a constant asphaltene content, the viscosity reduces, particularly at higher temperatures. In summary, the viscosity of the reconstituted heavy oil samples increases quickly with asphaltene volume fractions at a constant temperature and decreases quickly with the temperature at a constant asphaltene volume fraction. For example, the viscosity of heavy oil at 12.22 vol % asphaltene content is 256 cP at 25 °C, but this value is 124 cP at 85 °C. For modeling the viscosity measurements, the relative viscosities of the reconstituted heavy oil samples versus the asphaltene volume fraction at seven different temperatures are plotted in Figure 4. The relative viscosity is defined as the ratio of the viscosity of the reconstituted heavy oil sample to the maltene, which has zero asphaltene content at the constant temperature. As depicted in Figure 4, three regions are observed in the 10 added asphaltene volume fractions. In the first region (φ = 3.93 vol %), the relative viscosity of each reconstituted heavy oil sample increases slowly and approximately linearly versus the asphaltene volume fraction. As seen in Figure 4, in this region, the relative viscosity does not have strong dependency upon the temperature and the effect of the temperature is negligible. In the diluted region, the asphaltene particles are much far away from each other and the interactions between them are negligible. Also, the longrange hydrodynamic interactions among the maltenes and the asphaltene particles lead to a small increase in relative viscosity.100

4. PERFORMANCE EVALUATION To investigate the accuracy and performance of models, the statistical errors have been used for analysis of data. These statistical errors include the mean square error, standard deviation of error, coefficient of determination, average percent relative error, and average absolute relative error.97−99 These statistical errors are expressed as follows. 4.1. Root Mean Square Error (RMSE). RMSE calculates the data dispersion around zero deviation and is defined by 1 n

1 n

AAPRE is noted as the main criterion in the statistical analysis in this work.

(21)

where η(T) and η(T0) are the viscosity of samples at the temperature T and reference temperature T0, respectively, and R and E are the universal gas constant (kJ mol−1 K−1) and the activation energy of viscous flow (kJ/mol), respectively.

RMSE =

i = 1, 2, 3, ..., n

(25)

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Figure 3. Measured viscosities of 10 reconstituted heavy oil samples versus the asphaltene volume fraction at seven temperatures.

Figure 4. Measured relative viscosities of 10 reconstituted heavy oil samples versus the asphaltene volume fraction at seven temperatures.

5.2. Solvation Constant K and Shape Factor ν. In this section, the generalized Pal−Rhodes94 equation is used to determine the solvation constant K and the shape factor ν in the ranges of K = 1−5 and ν = 2.5−10. The obtained results from the generalized Pal−Rhodes equation are presented in Table 3. This table includes the solvation constant K, the shape factor ν, and statistical errors in seven different temperatures. Also, the intrinsic viscosity [η], which is the product of the solvation constant K and the shape factor ν, is reported in Table 3. As seen in Table 3, the solvation constant K reduces from 3.714 to 3.139 with increasing the temperature from 25 to 85 °C. In addition, the shape factor ν quickly reduces from 5.027 to 2.995 with increasing the temperature from 25 to 85 °C. The shapes of asphaltene particles in the heavy oil sample are classified in three groups,101−103 namely, disk-like (ν > 2.5), spherical (ν = 2.5), and ellipsoidal (ν < 2.5). With this definition, it is clear that the dispersed asphaltene particles in the reconstituted heavy oil samples in this work are nonspherical in all temperatures. However, the obtained results show that the asphaltene particles tend to be spherical (ν =2.5)

In the second region, the relative viscosity begins to deviate from the linear behavior and increases more clearly than that in the diluted region at the same temperature. In the medium region (3.93−9.40 vol %), the relative viscosity increases as the asphaltene volume fraction increases. This is because of the fact that the amount of asphaltene particles increases and shortrange interactions between asphaltene particles are more than that in the diluted region.89 On the other hand, the influence of the temperature on the relative viscosity is observed more in the first region. After the medium region, the relative viscosity increases most rapidly versus the asphaltene volume fraction, and thus, this increase is the most obvious trend. Also, the separations of the relative viscosity at different temperatures are indicative of the greater influence of the temperature in the concentrate region (φ ≥ 9.4 vol %). When the asphaltene volume fraction is bigger than φ = 9.4 vol %, the strong interparticle interactions are observed between the dispersed asphaltene particles in the concentrate region.100 In summary, the increase of the relative viscosity is much larger at lower temperatures and higher asphaltene volume fractions. 7223


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Table 3. Curve Fitting Results Using the Generalized Pal−Rhodes Equation T (°C)

K

ν

[η] = Kν

AAPRE

APRE

RMSE

SD

R2

25 35 45 55 65 75 85

3.714 3.625 3.379 3.269 3.207 3.172 3.139

5.027 4.753 4.350 3.933 3.541 3.227 2.995

18.67 17.23 14.70 12.86 11.36 10.24 9.40

6.397 3.493 3.373 1.624 1.015 0.519 0.306

−1.268 −2.430 1.138 0.467 −0.031 −0.117 0.029

29.859 10.388 9.901 4.331 3.301 1.770 0.767

8.519 6.475 4.908 2.223 1.284 0.658 0.473

0.9975 0.9995 0.9988 0.9995 0.9996 0.9998 0.9999

Table 4. Curve Fitting Results Using the Mooney Equation T (°C)

[η]

φc

AAPRE

APRE

RMSE

SD

R2

25 35 45 55 65 75 85

18.33 16.91 14.49 12.70 11.22 10.12 9.302

0.465 0.476 0.519 0.541 0.551 0.559 0.567

6.380 3.349 3.361 1.633 1.022 0.522 0.298

−1.039 −2.168 1.278 0.549 0.025 −0.063 0.072

30.360 10.075 9.986 4.448 3.211 1.698 0.825

8.437 6.292 4.971 2.282 1.277 0.630 0.504

0.9974 0.9995 0.9988 0.9995 0.9996 0.9998 0.9999

Table 5. Curve Fitting Results Using the Krieger and Dougherty Equation T (°C)

[η]

φmax

AAPRE

APRE

RMSE

SD

R2

25 35 45 55 65 75 85

18.67 17.23 14.70 12.86 11.36 10.23 9.402

0.269 0.276 0.296 0.306 0.312 0.315 0.319

6.399 3.495 3.375 1.630 1.023 0.507 0.305

−1.268 −2.408 1.132 0.445 −0.061 −0.072 0.025

29.858 10.378 9.901 4.338 3.308 1.772 0.766

8.519 6.474 4.908 2.223 1.288 0.654 0.473

0.9975 0.9995 0.9987 0.9996 0.9996 0.9998 0.9999

shows that the generalized Pal−Rhodes equation94 is more accurate at higher temperatures. Because the interactions among asphaltene particles and resin−asphaltene are weaker at higher temperatures with respect to lower temperatures, the prediction of the generalized Pal−Rhodes equation94 is better. The result shows the percent relative error versus asphaltene volume fraction at 25, 55, and 85 °C (see Figure B1 in Appendix B). 5.3. Intrinsic Viscosity [η] and Maximum Packing Volume Fraction φmax. In this part, other classes of suspension models, including Mooney, Krieger−Dougherty, and Brouwers equations2,3 are used to find the best fitting with experimental data. These three equations have two parameters of the intrinsic viscosity [η] and the maximum packing volume fraction φmax, which are selected in the ranges of [η] = 5−20 and φmax = 0.2−1, respectively. Tables 4−6 illustrate regression results obtained from three equations at different temperatures. The intrinsic viscosities [η] determined from the three equations are close to the intrinsic viscosity [η] calculated from the generalized Pal−Rhodes equation, but among the three equations, the Krieger−Dougherty equation gives the best agreement compared to the other two equations. Generally, in the three equations, the maximum packing volume fraction φmax increases as the temperature increases. Because at higher temperatures, more resins at the outmost layers are desorbed, the effective volumes of the solvated asphaltene particles can be dispersed in the reconstituted heavy oil samples.104 A larger intrinsic viscosity [η] = Kν implies a larger solvation constant K with equality of the shape factor ν of the asphaltene particles. The bigger intrinsic viscosity at lower temperatures in the three equations applied indicates that greater interactions exist

at higher temperatures. This behavior of the asphaltene particles may be attributed to the fact that more resins at the outmost layers are desorbed from the asphaltene particles with increasing the temperature, and thus, the shapes of asphaltene particles tend to be spherical.104 According to the shape factors in Table 3, the largest and lowest desorption of the resins from asphaltene particles happens at 25 and 85 °C, respectively. Table 3 indicates that solvation constant K reduces from 3.714 to 3.139 as the temperature increases. Moreover, the intrinsic viscosity [η] decreases with increasing the temperature from 25 to 85 °C. At higher temperatures, in comparison to lower temperatures, a weaker solvation effect exist and the effective volume of the solvated asphaltene particles becomes insignificant, but at lower temperatures, the stronger solvation effect leads to a greater effective volume.105 In this work, the solvation constant K is defined as the ratio of the volume of the solvated asphaltene particles after dispersion to the volume of the dry asphaltene particles before dispersion. Therefore, if the asphaltene particles are assumed to be spherical, the ratio of the average diameter of the solvated asphaltene particles to the diameter of the dry asphaltene particles can calculated with K1/3. For example, at 25−85 °C, the average diameters of the solvated asphaltene particles are 3.7141/3 = 1.549 and 3.1391/3 = 1.464 times larger than the diameter of the dry asphaltene particles, respectively. This is due to the breaking hydrogen bonds and charge-transfer π−π bonds between resins and asphaltene particles, and thus, resins easily desorbed.104 As shown in Table 3, the AAPRE error decreases from 6.397 to 0.306% with increasing the temperature. This observation 7224


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Table 6. Curve Fitting Results Using the Brouwers Equation T (°C)

[η]

φmax

AAPRE

APRE

RMSE

SD

R2

25 35 45 55 65 75 85

18.44 17.01 14.54 12.73 11.25 10.14 9.322

0.321 0.331 0.366 0.385 0.395 0.402 0.409

6.379 3.388 3.357 1.637 1.016 0.509 0.297

−1.133 −2.237 1.269 0.575 0.026 −0.031 0.067

30.195 10.160 9.962 4.419 3.226 1.711 0.810

8.462 6.347 4.954 2.271 1.276 0.631 0.496

0.9974 0.9995 0.9988 0.9995 0.9996 0.9998 0.9999

Table 7. Curve Fitting Results Using the Bicerano et al. Equation T (°C)

[η]

φc

AAPRE

APRE

RMSE

SD

R2

25 35 45 55 65 75 85

17.48 16.03 13.70 12.05 10.7 9.701 8.962

0.199 0.209 0.235 0.257 0.277 0.295 0.311

6.287 3.188 3.394 1.670 1.033 0.531 0.396

−1.135 −2.061 1.475 0.758 0.233 0.111 0.192

29.065 10.003 10.262 4.759 3.191 1.679 1.049

8.291 6.057 5.160 2.471 1.356 0.668 0.636

0.9977 0.9995 0.9987 0.9994 0.9995 0.9998 0.9999

Table 8. Curve Fitting Results Using the Santamaria-Holek and Mendoza Equation T (°C)

[η]

φc

AAPRE

APRE

RMSE

SD

R2

25 35 45 55 65 75 85

16.48 15.34 13.42 11.95 10.69 9.736 9.014

0.220 0.234 0.269 0.298 0.323 0.344 0.361

6.231 2.929 3.461 1.703 1.021 0.525 0.419

0.030 −1.230 1.829 0.961 0.337 0.147 0.213

31.383 9.606 10.726 5.175 3.108 1.661 1.134

8.187 5.681 5.387 2.653 1.389 0.691 0.672

0.9974 0.9996 0.9985 0.9993 0.9996 0.9998 0.9999

particles and resin−asphaltene particles are weaker at higher temperatures, and thus, the models predict better measured viscosities. 5.4. Intrinsic Viscosity [η] and Critical Volume Fraction φc. At the end, two equations are applied for modeling the measured relative viscosity. The Bicerano et al.4 and SantamariaHolek and Mendoza5 equations have two parameters of the intrinsic viscosity [η] and critical volume fraction φc, which

between the asphaltene particles and resins in maltene in the heavy oil samples. Also, the other studies prove that a stronger solvation effect exists between asphaltene particles with maltene than with organic solvents, such as toluene and xylene.106,107 This is because the interaction among asphaltene particles and organic solvents is weaker than those with resins.104 Moreover, the differences among the maximum packing volume fraction φmax in the three equations at different temperatures may have various reasons. The asphaltene particles in this work are nonspherical (ν > 2.5) and, thus, have diverse sizes. Also, great interactions exist between the asphaltene particles. In addition, solvation of the asphaltene particles in maltene makes the effective volume fraction much higher than their dry volume fraction.89 However, at higher temperatures, the determined φmax is higher because of a weaker solvation effect. When the solvation effect of the asphaltene particles becomes stronger at lower temperatures, their effective volumes are higher, so that the maximum packing volume fraction φmax becomes smaller, and this behavior is conversely observed at higher temperatures. In three equations, the AAPRE error reduces as the temperature increases. This behavior is similar to the generalized Pal−Rhodes equation,94 shown in Table 3. The results show the percent relative error versus different asphaltene volume fractions at 25, 55, and 85 °C (see Figures B2−B4 in Appendix B). As observed in Tables 4−6, AAPRE decreases with increasing the temperature for the three equations, and thus, it is clear that the Mooney, Krieger−Dougherty, and Brouwers2,3 equations are more applicable at higher temperatures when the interactions between asphaltene particles are weaker than lower temperatures. In this case, the interactions between asphaltene

Figure 5. Activation energy of 10 reconstituted heavy oil samples versus the asphaltene volume fraction. 7225


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equations of the Bicerano et al.4 and Santamaria-Holek and Mendoza5 equations, respectively. Decreasing the intrinsic viscosity with increasing the temperature is also observed in these two equations. As mentioned above, at higher temperatures, most resins at outmost layers desorbed from asphaltene particles and the weaker interactions conducted among them. The intrinsic viscosities obtained from the two equations are lower than the two previous groups of the equations. The differences between the intrinsic viscosities at lower temperatures are bigger than higher temperatures with respect to the generalized Pal−Rhodes94 equation. The critical volume fraction in the two equations increases as the temperature increases from 25 to 85 °C. According to the definition of the critical volume fraction φc, these values show that the reconstituted heavy oil sample loses its fluidity at a higher volume fraction with increasing the temperature. It is because of the fact that, at higher temperatures, the interactions among the asphaltene particles in the reconstituted heavy oil samples reduce. In addition, the kinetic energy of the heavy oil samples increases at higher temperatures, and the flowability of the reconstituted heavy oil samples increases too. Because of these three reasons, the flowability of the reconstituted heavy oil samples increases, and thus, with increasing the temperature, the sample loses its fluidity at higher volume fractions. It is obvious that the AAPRE error decreases with increasing the temperature. However, the Bicerano et al. and SantamariaHolek and Mendoza models similar to other equations are more accurate at higher temperatures because of weaker interactions between asphaltene particles. This behavior is similar to the previous models; this class of suspension models estimates the viscosity better at higher temperatures (see Figures B5 and B6 in Appendix B). 5.5. Temperature Dependence of the Reconstituted Heavy Oil Samples. To evaluate the temperature dependency of the reconstituted heavy oil samples at a constant asphaltene volume fraction, the Arrhenius equation95 is used, which introduced the activation energy (E). To calculate the activation energy for 10 reconstituted heavy oil samples with different asphaltene volume fractions (0−12.22 vol %), the slope of the plot of ln(η(T)/η(85 °C)) versus (1/R)((1/T) − (1/385.15))

Figure A1. Simple design of experiments.

are chosen in the ranges of 5−20 and 0.1−1, respectively. Tables 7 and 8 list the results of regression using the two

Figure B1. Percent relative error distribution at different asphaltene volume fractions using the Pal and Rhodes equation. 7226


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gives the activation energy of viscous flow. Figure 5 shows the activation energy of viscous flow for 10 reconstituted heavy oil samples versus different asphaltene volume fractions. As seen in Figure 5, the activation energy increases linearly from 34.14 to 58.53 kJ/mol with increasing the asphaltene contents from 0 to 12.22 vol %. At a lower asphaltene volume fraction, the weaker attraction interparticle interaction exists between the dispersed asphaltene particles. Moreover, as the asphaltene content increases, the interactions among asphaltene particles increase, and thus, higher activation energy is needed to overcome the attractive interparticle interactions and allow for the heavy oil samples to flow.108 5.6. Correlation Development. As observed, despite the important effect of the temperature on the viscosity of the heavy crude oil, the temperature has not been considered in the suspension models. Hence, according to nonlinear multiple regressions, a new correlation form was developed on the basis of minimization of AAPRE error, which has been considered as

the objective function of this regression. For this correlation development, the genetic algorithm (GA) has been used from MATLAB software. In this correlation, two parameters of temperature and asphaltene content have been used. This new correlation is as follows:

μ(T , φ) = 10 AT B

(28)

and A = a1 + a 2φ̃

(29)

B = a3 + a4φ̃

(30)

φ̃ = 1 − φ

(31)

where μ(T,φ) represents the heavy oil viscosity in centipoises, T is the temperature in degrees Fahrenheit, and φ is the asphaltene content volume fraction. The AAPRE error of the new correlation is 1.13%, and the values of constants a1−a4 are given as follow:

Figure B2. Percent relative error distribution at different asphaltene volume fractions using the Krieger and Dougherty equation.

Figure B3. Percent relative error distribution at different asphaltene volume fractions using the Mooney equation. 7227


Energy & Fuels a1 = 0.081, a4 = 0.0699

Article

a 2 = −2.904,

and shape factor ν), Moony, Krieger−Dougherty, and Brouwers (with intrinsic viscosity [η] and maximum packing volume fraction φmax), and Bicerano et al. and SantamariaHolek and Mendeza (with intrinsic viscosity [η] and critical volume fraction φc) equations. The obtained solvation constant K and shape factor ν from the generalized Pal−Rhodes equation indicate that the asphaltene particles are non-spherical at different temperatures. Also, the solvation constant K and shape factor ν reduce as the temperature increases, because the resins at the outmost layers desorbed from asphaltene particles with increasing the temperature. The intrinsic viscosity [η] and maximum packing volume fraction φmax were calculated by applying the Moony, Krieger− Dougherty, and Brouwers equations. In all models, the intrinsic viscosities are in accurate agreement with [η] = Kν, which has been obtained from the generalized Pal−Rhodes equation. Also, the maximum packing volume fraction φmax increases as the temperature increases, because resin desorption from

a3 = 7.062, (32)

6. CONCLUSION In this work, the effects of asphaltene contents on the viscosity of Iranian heavy crude oil were investigated. For this goal, 10 reconstituted heavy oil samples were prepared with dispersion of the precipitated asphaltene on maltene (i.e., deasphalted heavy crude oil) at seven different temperatures. The results from the measured viscosities show that the viscosities exponentially increase with increasing asphaltene volume fractions. Also, the viscosity decreases as the temperature increases. For modeling the viscosity behavior of the reconstituted heavy oil samples versus the asphaltene volume fraction, three groups of suspension models were applied at different temperatures, including generalized Pal−Rhodes (with solvation constant K

Figure B4. Percent relative error distribution at different asphaltene volume fractions using the Brouwers equation.

Figure B5. Percent relative error distribution at different asphaltene volume fractions using the Bicerano et al. equation. 7228


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Figure B6. Percent relative error distribution at different asphaltene volume fractions using the Santamaria-Holek and Mendoza equation.

asphaltene particles decreases the effective volumes of asphaltene particles. Moreover, the intrinsic viscosity [η] and critical volume fraction φc are determined using the Bicerano et al. and Santamaria-Holek and Mendeza equations. In both models, the intrinsic viscosity [η] reduces as the temperature increases. Also, as the temperature increases, the critical volume fraction φc increases because the flowability of the reconstituted heavy oil samples increases, and thus, the samples lose their fluidity at higher volume fractions. In addition, the activation energy is obtained using the Arrhenius equation at constant asphaltene volume fractions. The activation energy increases with increasing the asphaltene volume fraction because the interaction between asphaltene particles enhances. Also, it should be noted that all suspension model predictions improve as the temperature increases.

■

■ ■

APPENDIX A A simple design of experiments is provided in Figure A1.

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APPENDIX B Percent relative error distributions at different asphaltene volume fractions are provided using the Pal and Rhodes equation (Figure B1), Krieger and Dougherty equation (Figure B2), Mooney equation (Figure B3), Brouwers equation (Figure B4), Bicerano et al. equation (Figure B5), and Santamaria-Holek and Mendoza equation (Figure B6).

■

Ei = relative deviation RMSE = root mean square error ν = shape factor γ̇ = shear rate (s−1) K = solvation constant SD = standard deviation T = temperature R = universal gas constant (kJ mol−1 K−1) η = viscosity (cP) φ = volume fraction w2 = weight of precipitated asphaltene for measuring the asphaltene content w1 = weight of the added heavy crude oil for measuring the asphaltene content

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

NOMENCLATURE E = activation energy of viscous flow (kJ/mol) AAPRE = average absolute percent relative error APRE = average percent relative error ρ = density (kg/m3) kH = Huggins coefficient [η] = intrinsic viscosity 7229


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Effects of Asphaltene Content and Temperature on Viscosity of Iranian

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