Energy Fuels 2010, 24, 1917–1924 Published on Web 02/17/2010
: DOI:10.1021/ef9012328
Kinetics of Asphaltene Precipitation in a Heptane-Toluene Mixture Ali Khoshandam and Abdolmohammad Alamdari* Chemical Engineering Department, School of Chemical and Petroleum Engineering, Shiraz University, Shiraz 7134851154, Iran Received October 28, 2009. Revised Manuscript Received January 22, 2010
The enlargement of asphaltene particles precipitated in a heptane-toluene mixture (Heptol) was mechanistically modeled using mass and population balance equations. The kinetic parameters used in the model equations were optimized through fitting of the model predictions to the experimental data. The significance of this study is the investigation of growth mechanism of asphaltene particles based on supersaturation not reported in the literature. Agglomeration and growth mechanisms of asphaltene precipitation were quantitatively related to the supersaturation as a driving force in the form of rate equations. Using a fractal dimension for asphaltene particles found in the literature resulted in a better consistency between the model predictions and experimental data. Size analysis was carried out using a Horiba LB-550 nanoparticle size analyzer, which uses a dynamic laser scattering technique to measure the size of the asphaltene particles in the range of 1 nm to 6 μm. The concentration of asphaltene in the liquid mixture during the development of flocs was measured using the spectrophotometry technique. Particle enlargement from about 8 nm to 2 μm lasted about 2 h in a mixture of asphaltene-toluene containing 115.3 mg of asphaltene/kg of toluene when 0.79 kg of n-heptane/kg of toluene was added as an antisolvent.
to enlarge particles to reach the onset point depends on the nature of the oil and on the volume of resins in the oil.5,6 Heptol (heptane-toluene) as a mixture of solvent-antisolvent of asphaltene is usually used for the study of asphaltene precipitation. This is because the behavior of asphaltene in crude oil depends on the interaction between asphaltene, solvents, and antisolvents in the oil and, hence, on the composition.7,8 The composition and temperature have simple effects on the asphaltene precipitation. Both a higher concentration of light hydrocarbons and a lower temperature will increase the precipitation of asphaltene.9 In order to solve the blockage problems induced by asphaltene precipitation, a deep understanding of the size enlargement mechanism of asphaltene particles is necessary. A model for aggregate size evolution may help to anticipate the process conditions and solution compositions at which the petroleum mixture will be unstable, and settling of asphaltene aggregates will occur. This kind of model may also be helpful in the design of the process equipment and petroleum pipe lines. Available literature on the investigation of the size enlargement of asphaltene precipitates in a Heptol mixture as synthetic oil is limited. The particle size of asphaltene in the range of 0.5-12 μm in precipitation from a toluene-heptane mixture was investigated
1. Introduction Asphaltene precipitation originates blockage and pressuredrop problems in the petroleum industry. Asphaltene may precipitate on the rock surface and damage the formation, reducing the rock permeability and porosity. It may alter the wettability properties of formation and reduce the recovery and productivity because of an increase in the fluid viscosity and precipitation in crude oil.1 Therefore, knowledge of the asphaltene precipitation mechanism and an understanding of the effect of factors such as pressure, temperature, and composition of crude oil on asphaltene precipitation are essential in the prevention of asphaltene deposition. Asphaltenes are defined as materials soluble in aromatics such as benzene, toluene, and xylene and insoluble in light n-alkanes such as heptane.2 Asphaltenes comprise polycondensed aromatic sheets and aliphatic chains, charged with transition metals V, Ni, and Fe and heteroatoms O, N, and S.3 Asphaltene appears in crude oil as soluble compounds and as colloidal particles stabilized by resins.4 The addition of antisolvents such as n-heptane will weaken bonds between resin molecules and the surface of asphaltene particles. When asphaltene particles contact each other from areas uncovered by resin, the particles may join together and start to agglomerate. Progress of agglomeration enlarges the particles to a visible size (onset point). The quantity of antisolvent necessary to remove resins from the surface of asphaltene particles and
(5) Ferworn, K.; Svrcek, W.; Mehrotra, A. Measurement of Asphaltene Particle Size Distributions in Crude Oils Diluted with n-Heptane. Ind. Eng. Chem. Res. 1993, 32 (5), 955–959. (6) Jianjun, L.; Zhang, L.; Masliyah, J.; Xu, Z. Colloidal Interactions between Asphaltene Surfaces in Aqueous Solutions. Langmuir 2006, 22 (4), 1485–1492. (7) Wang, S.; Liu, J.; Zhang, L.; Masliyah, J.; Xu, Zh. Interaction Forces between Asphaltene Surfaces in Organic Solvents. Langmuir 2010, 26 (1), 183–190. (8) Arteaga-Larios, F.; Sheu, E. Y.; Perez, E. Asphaltene Flocculation, Precipitation, and Liesegang Ring. Energy Fuels 2004, 18, 1324– 1328. (9) Hirschberg, A.; Schipper, B. A.; Meijer, J. G. Influence of Temperature and Pressure on Asphaltene Flocculation. Soc. Pet. Eng. J. 1984, 24 (3), 283–293.
*To whom correspondence should be addressed. E-mail: alamdari@ shirazu.ac.ir. (1) Speight, J. The Chemical and Physical Structure of Petroleum: Effect on Recovery Operations. J. Pet. Sci. Eng. 1999, 22 (1), 3–15. (2) Anderson, S.; Stenby, E. Thermodynamics of Asphaltene Precipitation and Dissolution Investigation of Temperature and Solvent Effects. Fuel Sci. Technol. 1996, 14 (1/2), 261–287. (3) Mullins, O. C.; Sheu, E. Y. Structures and Dynamics of Asphaltenes; Plenum Press: New York, 1998. (4) Mansoori, G. A. Modeling of Asphaltene and Other Heavy Organic Depositions. J. Pet. Sci. Eng. 1996, 17, 101–111. r 2010 American Chemical Society
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Energy Fuels 2010, 24, 1917–1924
: DOI:10.1021/ef9012328
Khoshandam and Alamdari
10
by Anisimow et al. The population balance equation was used to model the asphaltene agglomeration in the crude oil due to antisolvent addition by Mansoori and Al-Ghannam.11 Using a size-independent porosity for particles, Rahmani et al. modeled the agglomeration of asphaltene in Heptol in the range of 30-400 μm.12 Rastegari et al. investigated the agglomeration of asphaltene particles larger than 1 μm using a fractal dimension of 1.6 and found an appropriate kernel function for agglomeration.13 Solaimani-Nazar and Rahimi used a population balance equation and a fractal dimension of 1.6 for asphaltene particles to model their agglomeration in Heptol under shear and at different concentrations of n-heptane.14 All of these studies did not consider the growth of primary particles in their model development. Investigation of the size enlargement of asphaltene particles in the nanometer range is very limited in the available literature. Almost no report was found on the study of the growth mechanism of asphaltene particles considering supersaturation release from a solution on particles due to antisolvent addition. In the present study, the enlargement of asphaltene particles in Heptol in the size range of 1 nm to 2 μm at room temperature was experimentally examined. Using both population and mass balances, the kinetic parameters of growth and agglomeration were optimized, and a growth equation in terms of supersaturation was developed for asphaltene particles.
of 200 g of the bottom product (bitumen) was dissolved in 1 L of toluene, and the mixture was well agitated for about 1 h. The mixture was centrifuged at 7000 rpm for 30 min to remove any probable entrained solid from the distillation process. Then, the supernatant from the centrifuge was heated up, and toluene was vaporized until a viscous concentrate remained. The remaining materials were mixed with enough heptane (40 volume times) to dissolve heptane-soluble materials such as waxes and resins. The mixture was agitated for about 4 h and was kept unagitated for 24 h. The supernatant including nonasphaltene materials dissolved in heptane was separated. The remaining solid was again mixed with further n-heptane (4 volume times) and agitated for about 1 h. After 4 h, the settled material was filtered using Whatman No. 42 filter paper. The filter cake was thoroughly washed with heptane until the filtrate became clear and colorless.12 In order to further purify the produced asphaltene and to release any probable resin adsorbed on or included in particles, a reprecipitation process of asphaltene was carried out and the above procedure was repeated once again. The washed filter cake was dissolved in 0.5 L of toluene. No turbidity was observed in the resultant solution, indicating assurance of no solid impurity in asphaltene prepared from the previous stage. The solution was well mixed and then centrifuged at 7000 rpm. The supernatant was concentrated and then well mixed with 3 L of n-heptane. The solution was stirred for 1 h, and then the precipitates were allowed to settle for 12 h and filtered using Whatman filter paper (No. 42). The precipitates were washed by n-heptane on the filter until a clear colorless filtrate was observed. The precipitates were kept in an oven at 70 C for more than 1 week until no weight loss was noticed. The stock solution of 0.1 g of asphaltene/L of toluene (115.3 mg of asphaltene/kg of toluene) was prepared using the precipitates obtained through the above procedure. A schematic diagram of the procedure is shown in Figure 1. Toluene and n-heptane used in the asphaltene preparation procedure were high-performance liquid chromatography (HPLC) grade supplied by Merck Company, Germany. 2-3. Particle Size Analysis. The nanoparticle size analyzer LB-550 was used to measure the size distribution of asphaltene precipitates. The instrument measures the particle size in the range of 1 nm to 6 μm and the solid concentration of 1 ppm to 40 wt % based on dynamic laser light scattering. The response time of the instrument is about 30 s, and the temperature of the measuring sample can be adjusted in the range of 5-70 C. The temperature of the sample in the present study was adjusted at 20 C, and the response time was in the range of 30-40 s. 2-4. Measurement of the Asphaltene Concentration. A GENESYS 10 spectrophotometer was used to measure the asphaltene concentration in the mixture. Spectrophotometers measure the solute concentration based on the absorption or transmission of light with a specific wavelength. The instrument was calibrated with carefully prepared samples of 0, 10, 20, 30, 40, and 50 ppm of asphaltene in a Heptol mixture (50-50 vol %) at 20 C. The maximum wavelength absorbed by the asphaltene particles was determined as 295 nm in the present study. The calibration curve based on the absorption of 295 nm light was used to determine the asphaltene concentration for unknown samples.
2. Experimental Section The enlargement of asphaltene particles was monitored during batch precipitation from toluene as the solvent at 1 atm, room temperature (20 C), and using n-heptane as an antisolvent. 2-1. Experimental Method. A solution containing 0.1 g of asphaltene/L of toluene was prepared and stored as a stock solution. A specified volume (200 mL) of the stock solution was gently mixed with 200 mL of n-heptane to obtain a mixture of 0.79 kg of n-heptane/kg of toluene (50 vol %) containing 115.3 mg of asphaltene/kg of toluene. At different time intervals after mixing, the mixture was sampled for both the particle size analysis and concentration measurement. The size analysis was carried out immediately after sampling. However, the time of solution mixing with heptane was considered as the start time of the size development. The sampling process was continued until the size of the biggest particles exceeded the maximum measurable size of the analyzer (6 μm). The sampling times for the asphaltene concentration were the same as the sampling times for the size measurements. In order to prevent the interference of the precipitated asphaltene particles with the measurement of soluble asphaltene in the solution, the samples were immediately filtered using Whatman 0.2 μm syringe filters. The filtrate was analyzed for the asphaltene concentration using the spectrophotometry method. 2-2. Asphaltene Preparation. The asphaltene necessary for this study was prepared from the bottom product of the distillation tower of Shiraz Oil Refinery located in South Iran. An amount (10) Anisimov, M. A.; Yudin, I.; Nikitin, V.; Nikolaenko, G. Asphaltene Aggregation in Hydrocarbon Solutions Studied by Photon Correlation Spectroscopy. J. Phys. Chem. 1995, 99 (23), 9576–9580. (11) Mansoori, G. A.; Al-Ghannam, K. Investigations into Asphaltene in Heavy Oils: Effect of Temperature on Precipitation by Alkane Solvent. Fuel 1981, 60, 1045–1048. (12) Rahmani, N.; Dabros, T.; Masliyah, J. H. Evolution of Asphaltene Floc Size Distribution in Organic Solvents under Shear. Chem. Eng. Sci. 2003, 59 (3), 685–697. (13) Rastegari, K.; Svrcek, W. Y.; Yarranton, H. W. Kinetics of Asphaltene Flocculation. Ind. Eng. Chem. Res. 2004, 43 (21), 6861–6870. (14) Solaimany-Nazar, A.; Rahimi, H. Dynamic Determination of Asphaltene Aggregate Size Distribution in Shear Induced Organic Solvents. Energy Fuels 2008, 22 (5), 3435–3442.
3. Modeling Size evolution of the asphaltene particles results from mechanisms of growth and aggregation. If the behavior of the asphaltene species such as growth and aggregation in a petroleum production system can be well predicted in the design stages of a project through model development, the necessary schemes and facilities may be provided in advance to reduce plugging problems and to maintain flow assurance in later operations. 1918
Energy Fuels 2010, 24, 1917–1924
: DOI:10.1021/ef9012328
Khoshandam and Alamdari
Figure 1. Schematic diagram of the procedure for preparation of the stock solution of 115.3 mg of asphaltene/kg of toluene.
population density of the particles during the course of enlargement is determined through the simultaneous solution of mass and population balances. Fitting the model predictions of size distributions to the experimental data at the corresponding times may be used to estimate the kinetic parameters. The initial conditions are the initial concentration of asphaltene in the liquid phase and the initial magma density.
Aggregation of the particles due to their impact increases the size, and breakage of the aggregates due to shear stress reduces the size; therefore, the size evolution depends on the dominance of either mechanism.13 The breakage was assumed to be negligible because of the lack of shear stress actions on the fluid in the present study. 3-1. Population Balance. The population balance equation represents a number balance of particles in a specified size interval. The equation includes terms for particle convection to the interval due to growth, accumulation of the particles in the size interval, and rates of appearance and disappearance of the particles in the interval due to the agglomeration mechanism.15 The population balance equation for the nonagitated batch system of the present study without input and output streams in the size range v to v þ dv based on a unit mass of Heptol is
þ
1 2
Z 0
Fðu, v - uÞ nðt, uÞ nðt, v - uÞ du - nðt, vÞ Z
¥
Fðu, vÞ nðt, uÞ du
MT ðt ¼ 0Þ ¼ MT0
ð4Þ
GL ¼ ð1Þ
dL ¼ kg0 S a dt
ð5Þ
where S is the relative supersaturation, L is the particle size, kg0 is the growth rate constant, and a is the supersaturation order of the growth rate. The growth rate defined based on the change in the particle volume is
0
where n is the population density of the particles, t is the time, v is the volume of the particles as sized, u is a dummy size, Gv is the growth rate of the particles based on volume, and F is a kernel function representing the effective impacts between the different sized particles in a unit mass of mixture. 3-2. Mass Balance. The mass balance relates the mass of solute asphaltene in the liquid to the asphaltene mass deposited on the solids suspended in the mixture as dCA dMT þ ¼0 dt dt
ð3Þ
3-3. Particle Growth Rate. Particle enlargement due to mass deposition from the liquid phase to the solid phase by supersaturation release was also considered in the present study of asphaltene precipitation. The growth rate function based on the diffusional step of mass transfer and surface integration of solute molecules was presented by the following semiempirical equation:16
Dnðt, vÞ D½nðt, vÞGv ¼ Dt Dv v
CA ðt ¼ 0Þ ¼ CA0
Gv ¼
dv ¼ KG S a v2=3 dt
ð6Þ
where Gv is the volume change of the particle with time and v is the volume of the particle as sized. It is notable that 3kg0kv1/3 =KG, where kv is the volume shape factor. The relative supersaturation is defined as
ð2Þ
S ¼
where CA is the asphaltene concentration in the liquid phase and MT is the magma density of asphaltene particles. The (15) Randolph A. D.; Larson, M. A. Theory of Particulate Processes, 2nd ed.; Academic Press, Inc.: London, 1988; Chapter 4.
c - c c
ð7Þ
(16) Mullin, J. W. Crystallization, 3rd ed.; Butterworth-Heinemann: Oxford, U.K., 1993,
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Energy Fuels 2010, 24, 1917–1924
: DOI:10.1021/ef9012328
Khoshandam and Alamdari
where c is the specific concentration of asphaltene in the mixture and c* is the specific concentration at equilibrium. The specific concentration of asphaltene, here, was defined as c ¼
mheptane masphaltene mtoluene
asphaltene particles in the present study was assumed to be constant and equal to 1.65.13,14 γ was assumed to be 2.6.13 The fractal dimension is defined as
ð8Þ
Df ¼
where m denotes for mass of the components present in the mixture. Because heptane behaves in the mixture as an antisolvent, its mass in the numerator increases the asphaltene potential for precipitation from a mixture, and because toluene behaves as a solvent in the mixture, its mass in the denominator decreases the asphaltene potential for precipitation. However, it is necessary that the supersaturation that directly presents the solute potential for precipitation be defined in comparison with equilibrium conditions, as seen in eq 7. It is worth noting that c*, the specific concentration at equilibrium, represents the capacity of a solventantisolvent mixture to retain asphaltene at equilibrium. Therefore, the c* value depends on the chemical nature of the solvents, antisolvents, and asphaltenes. Different solvent-antisolvent combinations exhibit different values of c* at a certain temperature for a certain type of asphaltene. 3-4. Agglomeration Kernel. Kernel functions demonstrate the probability of particle attachments according to their size and their frequency of impacts that result in successful aggregation. The function is substantially dependent on the flow regime.17 For porous pervious asphaltene particles, the kernel function depends additionally on the fractal structure and dimension.13,18 A fractal structure is defined as an irregular and rough structure having self-similarity. In a fractal, the local configuration and the whole configuration have a kind of similarity and resemblance but they do not coincide. The fractal dimension of an agglomerate particle may be measured by the turning radius method in which the number of primary particles contained in a circle of radius R drawn from the center of the agglomerate is counted (N). Then the radius R is changed, and N is counted again. The fractal dimension is the slope of N versus R on a log-log scale plot.19 The fractal particles may have a higher chance of successful impact with each other because they possess larger diameters compared to their counterpart nonporous impervious particles with equivalent weight. The following equation has been reported to represent the kernel function of asphaltene particles:13 γ Iu Iv 1=Df 1=Df Fðu, vÞ ¼ KF Iv þ Iu ðS b Þ ð9Þ Iv þ Iu Iv þ Iu
logðIp Þ ! ds log dp
ð10Þ
where Ip is the number of primary particles that form a secondary particle and ds and dp are the diameters of secondary and primary particles, respectively. The ratio ds/dp represents a kind of magnification factor between the sizes of the secondary and primary particles. The kernel function in the present study was also considered as dependent on supersaturation in order to take into account the role that the supersaturation level may have in the success of impacts to agglomeration. 3-5. Model Solution and Parameter Estimation. The solution of population balance (eq 1) will predict the particle size distribution of asphaltene particles at different times. The boundary and initial conditions, the function of birth and death for agglomeration, and the growth and kernel functions need to be represented. 3-5-1. Initial Condition. In the present study, the initial conditions n(0,v) and CA0 were determined by the first measurements of the particle size distribution and the asphaltene concentration. The population density of the particles was extracted from the number distribution presented by the size analyzer. The dependency of the total mass of particles on the population density is Z vmax vnðt, vÞdv ð11Þ MT ¼ ð1 - εÞFA VT ¼ ð1 - εÞFA vmin
where MT is the magma density of particles, FA is the skeletal density of secondary particles equal to the density of primary particles, which is 1200 kg/m3,12 ε is the porosity of secondary particles, and v is the volume of secondary particles. The relationship between the volumes of primary and secondary particles is π vð1 - εÞ ¼ Ip dp 3 6
ð12Þ
where Ip is the number of primary particles of diameter dp that agglomerate together to form a secondary particle of volume v. Because of the lack of enough accuracy of the gravimetry method at a very low value of the magma density, the mass of asphaltene particles precipitated from the mixture, MT, was calculated through the concentration measurements of asphaltene in the clear mixture by the spectrophotometry method. 3-5-2. Boundary Conditions. The boundary conditions of the model equation are
where F(u,v) is the kernel function for the agglomeration of two particles with volumes of u and v, KF is the agglomeration rate coefficient, Iv and Iu are the number of primary particles in v and u volume secondary particles, respectively, γ is a constant in the range of 2-3, and Df is the fractal dimension of asphaltene particles. The fractal dimension of
nðt, vmin Þ ¼
B Gðv ¼ vmin Þ
nðt, v ¼ vmax Þ ¼ 0
(17) Hartel, R. W.; Randolph, A. D. Mechanisms and Kinetic Modeling of Calcium Oxalate Crystal Aggregation in a Urinelike Liquor. AIChE J. 1986, 32 (7), 1186–1195. (18) Valter, A.; Branco, M.; Mansoori, G. A.; Cristina De Almeidaavier, L.; Park, S. J.; Manafi, H. Asphaltene Flocculation and Collapse from Petroleum Fluids. J. Pet. Sci. Eng. 2001, 32 (2-4), 217. (19) Hosokawa M.; Nogi, K.; Naito, M.; Yokoyama, T. Nano Particle Technology Handbook, 1st ed.; Elsevier: Amsterdam, The Netherlands, 2007.
ð13Þ ð14Þ
where B is the nucleation rate and Gv(vmin) is the growth rate of nuclei. 3-5-3. Parameter Estimation. The values of the parameters in the functions F, Gv, D, and B were initially guessed, and using the initial and boundary conditions, the equations were 1920
Energy Fuels 2010, 24, 1917–1924
: DOI:10.1021/ef9012328
Khoshandam and Alamdari
solved and the model predictions for size distribution at corresponding sampling times were calculated. The method of Crank-Nickolson and the software of MATLAB were used in the model solution. The size evolution continued to be predicted during depletion of the main fraction of supersaturation (Sinitial = 0.461 and Sfinal = 0.328). The guessed values of the parameters were corrected by minimizing the difference between the model predictions and the experimental data obtained from both liquid and solid phases. The minimization problem was arranged as min ΦðNexp , N, Sexp , S; θÞ
ð15Þ
where S and Sexp are the relative supersaturations calculated by the model and calculated from experimental measurements of the asphaltene concentration, respectively, N and Nexp are the number of asphaltene particles smaller than specified size, predicted by the model, and measured by the nanoparticle size analyzer at different times. θ is the set of kinetic parameters (KG, KF, a, and b), and Φ is the objective function defined as
Figure 2. Size evolution of asphaltene particles at different times and at 20 C in an unagitated mixture of asphaltene-toluene containing 115.3 mg of asphaltene/kg of toluene when 0.79 kg of n-heptane/kg of toluene was added as the antisolvent.
4-2. Particle Size Evolution of Asphaltene. After the addition of n-heptane to the asphaltene-toluene mixture, the precipitated asphaltene particles appeared at about 8 nm and started to grow and enlarge. Figure 2 shows the size distribution of particles at different times of the agglomeration process at 20 C in the mixture of asphaltene-toluene after the addition of n-heptane. The agglomeration experiment was carried out at 0.79 kg of n-heptane/kg of tolueneasphaltene mixture. Note that the stock mixture (tolueneasphaltene) contained 115.3 mg of asphaltene/kg of toluene. Checking both liquids of n-heptane and the asphaltenetoluene solution by a nanoparticle size analyzer for probable background particles resulted in no background particles present in the liquids before intermingling. The first measurement of size distribution after 5 min from the moment of n-heptane addition to the asphaltene-toluene mixture showed precipitated asphaltene particles in the range of 8-22 nm. This indicated an enlargement of primary particles to secondary particles during the period of 5 min. The nucleation rate B was assumed to be zero during the course of the size enlargement of this study because of the results of monitoring of the distribution around the size of 1 nm. Apart from the generation of 1 nm particles at the precipitation onset, the appearance of these nuclei was not detected by the instrument during the course of the experiment. The agglomeration process may be controlled by different mechanisms at different concentrations of asphaltene in toluene. It has been suggested that at concentrations of asphaltene micelles less than the critical micelle concentration of 3-4 g of asphaltene/L of toluene the process of agglomeration is controlled by diffusion of asphaltene micelles,22 while at higher concentrations of asphaltene micelles, the agglomeration will be controlled by impact.21 Under the conditions of the present study, the diffusion and contact of asphaltene particles with each other seem to control the agglomeration process because of the low concentration of asphaltene in the mixture (115.3 mg/kg of toluene). A low diffusion rate of particles toward each other and a high probability of sticking together after their contact are assumed here. The experimental data recorded at 20 min was used as the initial condition for size evolution and the experimental data recorded at 60 and 80 min was used for fitting of the model
ΦðθÞ ¼ Φ1 ðθÞ Φ2 ðθÞ 2 !2 3 !2 Ns Ne Ns X X X N ðjÞ -NðjÞ Sexp ðiÞ -SðiÞ exp 4 5 ¼ Nexp ðjÞ Sexp ðiÞ i ¼1 j ¼1 i ¼1 ð16Þ where Φ1 is the information obtained from the solid phase and Φ2 is the information obtained from the liquid phase. Ns is the number of measurements of the asphaltene concentration and size distribution during the course of the experiment equal to 4, and Ne is the number of size intervals in the distribution equal to 100. 3-5-4. Comparison of Analytical and Numerical Solutions. The validity of the numerical solution of model equations was examined by a comparison of the numerical solution with the analytical solution for those limited cases where the analytical solutions of a simplified population balance equation were found in the literature.20 4. Results and Discussion 4-1. Precipitation Onset. The precipitation onset for a mixture containing 0.1 g of asphaltene/L of toluene (115.3 mg of asphaltene/kg of toluene) was found by the progressive addition of n-heptane to the mixture and attempts to detect the appearance of particles by size analysis using the nanoparticle size analyzer. A total of 20 mL of the asphaltene-toluene mixture was mixed with 6.7 mL of n-heptane (25 vol %) and tested for particle appearance, where no generation of the particles was detected. Further tests were carried out by the addition of progressively more n-heptane (1 vol %) and checking for particle appearance. The experiment was repeated three times, and it was found that the composition at which the precipitation onset occurred was 115.3 mg of asphaltene and 0.64 kg of n-heptane/kg of toluene (45 vol %). Yudin et al. reported a precipitation onset at a heptane concentration of 52-55 vol %.21 (20) Gelbard, F.; Seinfeld, J. H. Numerical Solution of the Dynamic Equation for Particulate Systems. J. Comput. Phys. 1978, 28, 357–375. (21) Yudin, I. K.; Nikolaenko, G. L.; Gorodetskii, E. E.; Markhashov, E. L.; Agayan, V. A.; Anisimov, M. A.; Sengers, J. V. Crossover Kinetics of Asphaltene Aggregation in Hydrocarbon Solutions. Physica A 1998, 251, 235–244.
(22) Andersen, S. I.; Birdi, K. S. Aggregation of Asphaltene as Determined by Calorimetry. J. Colloid Interface Sci. 1991, 142 (2), 497–502.
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Energy Fuels 2010, 24, 1917–1924
: DOI:10.1021/ef9012328
Khoshandam and Alamdari
Figure 3. Number distribution of asphaltene particles precipitated from a mixture containing 115.3 mg of asphaltene/kg of toluene and 0.79 kg of n-heptane/kg of toluene at 20 C and under nonagitated conditions after 110 min from the commencement of agglomeration. The solid line represents the model predictions, and the points represent the experimental data.
Figure 4. Number distribution of asphaltene particles precipitated from a mixture containing 115.3 mg of asphaltene/kg of toluene and 0.79 kg of n-heptane/kg of toluene at 20 C and unagitated conditions at different times. The solid lines represent the model predictions, and the points represent the experimental data.
predictions and adjustment of the values of the kinetic parameters in the model functions. An accurate measurement of the asphaltene concentration in the liquid phase necessitated filtration of precipitated asphaltene particles before spectrophotometry. The unavailability of a syringe filter finer than 0.2 μm restricted the use of experimental data for model fitting to those data corresponding to particles larger than 0.2 μm. In other words, only the experimental data when particles grew larger than 0.2 μm was used in the parameter estimation (Figure 5). This resulted in more accuracy of parameters calculated by the optimization process because of the use of more accurate data points for the model fitting. However, information obtained during the first 20 min, when particles were smaller than 0.2 μm, was used for onset determination. In order to examine the model validity, the model was allowed to run for 110 min after the commencement of agglomeration and to predict the size distribution of asphaltene particles. The model predictions at 110 min were compared with experimental data at the corresponding time. The consistency of these two sets of data represented the validity of the model. Note that this set of experimental data was excluded from the data given to the model for the parameter estimation. In other words, the model predictions beyond the range in which parameters have been optimized were used for determination of the model validity. Thus, the model ability for extrapolation was examined. The relative average deviation between the experimental data and the model predictions was 10%. The following equation was used to calculate the relative average deviation: ! Ne 1 X Mexp ðjÞ - MðjÞ ð17Þ deviation ¼ Ne j ¼1 Mexp ðjÞ
Figure 5. Concentration variations of asphaltene in the mixture initially containing 115.3 mg of asphaltene/kg of toluene and 0.79 kg of n-heptane/kg of toluene at 20 C and under nonagitated conditions. The solid line represents the model predictions, and the points represent the measured concentrations by the spectrophotometry method.
n-heptane addition to the mixture decreases as the asphaltene particles precipitate from the liquid phase (points in Figure 5). The initial concentration of asphaltene was 115.3 mg/kg of toluene. After 20 min, the concentration reduced to 104.6 mg/ kg of toluene, and thereafter the rate of the concentration reduction diminished. The final concentration of asphaltene after several days approached 71.5 mg/kg of toluene due to supersaturation release on particles of asphaltene present in the liquid. This concentration was assumed as the final equilibrium concentration of asphaltene. It is worth noting that the consecutive size measurements showed that after 20 min no particle smaller than 200 nm was generated in the mixture during the course of concentration depletion in the experiment (Figure 2). Particles larger than 200 nm were separated from the liquid in the sampling process by syringe filters; therefore, the concentration measured through the method of spectrophotometry is free from the error of measuring solid asphaltene particles smaller than 200 nm as the solute and solely includes soluble asphaltene in the liquid phase. The absence of fine particles smaller than 200 nm continued the entire time, indicating no generation of primary and secondary nuclei after the initial burst of nuclei
The model predictions (solid line) after 110 min from the commencement of agglomeration and the corresponding experimental data (points) are shown in Figure 3. The closeness of the model predictions to experimental data indicates the validity of the model. As shown in Figure 4, the total number of particles decreases as the agglomeration process progresses during the course of the experiment. 4-3. Concentration Depletion of Asphaltene in the Liquid Phase. The asphaltene concentration in the mixture after the 1922
Energy Fuels 2010, 24, 1917–1924
: DOI:10.1021/ef9012328
Khoshandam and Alamdari
Table 1. Optimum Values of the Kinetic Parameters for the Enlargement of Asphaltene Particles through the Precipitation Process from a Mixture Initially Containing 115.3 mg of Asphaltene/kg of Toluene and 0.79 kg of n-Heptane/kg of Toluene at 20 C and under Nonagitated Conditions parameter
value
KF (kgsolution #-1 μm-3 s-1) KG (μm s-1) a b
1.03 10-17 1.83 10-4 1.7 0.85
Figure 7. Sensitivity of the objective function to changes in the values of supersaturation exponents around the optimum points, while the other parameters were kept constant at their optimum values reported in Table 1 (above, exponent in the growth rate function; below, exponent in the agglomeration kernel function).
through the difference between the asphaltene concentrations in the filtrate and in the initial mixture obtained by the addition of 200 mL of n-heptane to 200 mL of 0.1 g of asphaltene/L of toluene. In order to illustrate the sensitivity of the model predictions to the parameter values, the objective function was depicted against the parameter values. The parameters under consideration were changed around the optimum points, while the values of other parameters were kept constant at optimum values. The results of sensitivity analysis carried out for all parameters have been shown in Figures 6 and 7.
Figure 6. Sensitivity of the objective function to changes in the values of coefficients around the optimum points, while the other parameters were kept constant at their optimum values reported in Table 1 (above, coefficient of the growth rate function; below, coefficient of the agglomeration kernel function).
5. Conclusions
at the onset point. On the other hand, measurement of the concentration showed continuous reduction in the asphaltene concentration after 20 min. Because the agglomeration process does not consume supersaturation, the reduction in the concentration is necessarily attributed to the growth of primary and secondary particles in the agglomerates. No report was found in the literature about the growth of asphaltene particles; however, many workers have reported the agglomeration of asphaltene particles. The growth, here, considers joining the soluble species in the liquid phase to already agglomerated particles. The population balance in the present study includes the growth term, considering this phenomenon of particle enlargement in addition to agglomeration. 4-4. Parameter Estimation and Sensitivity Analysis. Estimation of the kinetic parameters was carried out based on a model fitting to experimental data of asphaltene concentrations in the liquid phase and size distributions of solid particles both measured at 60 and 80 min after heptane addition. Table 1 shows the optimum values of the parameters corresponding to a minimum value of the objective function. Note that the mass of particles was calculated
The enlargement of asphaltene particles precipitated from a toluene mixture by the antisolvent addition of n-heptane was investigated in the present study. The onset of nucleation at 20 C for a Heptol mixture containing 115.3 mg of asphaltene/kg of toluene was found to be at a concentration of 0.61 kg of n-heptane/kg of toluene. Supersaturation and dependency of the growth mechanism to supersaturation for the particle enlargement of asphaltene was defined and developed. Both growth and agglomeration mechanisms of the particle enlargement were considered in the model development. These mechanisms were considered as an exponent function of supersaturation generated through heptane addition to the mixture. The kinetic parameters of agglomeration and growth mechanisms of size enlargement were estimated by a model fitting to the experimental data. The model was able to predict the size evolution beyond the range at which the model was adjusted and tuned. The relative deviation of the model predictions to experimental data was 10%. Acknowledgment. The authors are grateful to the Nanotechnology School of Shiraz University for their permission to use the 1923
Energy Fuels 2010, 24, 1917–1924
: DOI:10.1021/ef9012328
Khoshandam and Alamdari
L = particle size, μm dL = particle size interval, μm Mexp = experimental cumulative mass undersize, mgparticle kgsolution-1 MT = magma density of the particles, mgparticle kgsolution-1 N = number of particles smaller than size, # kgsolution-1 n(v,t) = population density of v-sized particles, # kgsolution-1 μm-3 Ip = number of primary particles that form secondary particles dp = diameter of primary particles, μm ds = diameter of secondary particles, μm S = relative supersaturation, dimensionless t = time, s u = dummy particle size, μm3 v = particle volume as sized, μm3 vmax = maximum size in distribution, μm3 vmin = minimum size in distribution, μm3
nanoparticle size analyzer and to Shiraz Refinery for providing of samples from the bottom product of the distillation tower.
Nomenclature Symbols a = supersaturation order of the growth rate, dimensionless B = nucleation rate, # kgsolution-1 s-1 B(v,t) = birth function, # kgsolution-1 s-1 μm-3 F = agglomeration kernel, #-1 s-1 kgsolution c = specific concentration of asphaltene, gasphaltene gheptane gtolune-1 c* = specific concentration of asphaltene at saturation, gasphaltene gheptane gtolune-1 C = concentration of asphaltene in the mixture, mgasphaltene gsolution-1 D(v,t) = death function, # kgsolution-1 s-1 μm-3 Df = fractal dimension, dimensionless Gv = volumetric growth rate of the particles, μm3 s-1 i = counter of solid-phase sampling operations j = counter of sieves KF = agglomeration rate coefficient, kgsolution #-1 μm-3 s-1 Kg = coefficient of the growth rate, μm s-1 kv = volume shape factor of the particles
Greek Letters Φ = objective function FA = skeletal density of the particles, kg m-3 γ = adjustable parameter, dimensionless ε = porosity of the secondary particles, dimensionless
1924
