Molecular Weight and Density Distributions of Asphaltenes from Crude

Article pubs.acs.org/EF

Molecular Weight and Density Distributions of Asphaltenes from Crude Oils D. M. Barrera, D. P. Ortiz, and H. W. Yarranton* Department of Chemical and Petroleum Engineering, Schulich School of Engineering, University of Calgary, 2500 University Drive Northwest, Calgary, Alberta T2N 1N4, Canada S Supporting Information *

ABSTRACT: Asphaltenes self-associate, and the molecular weight and density distributions are a factor in asphaltene precipitiation. To determine these distributions, heptane-extracted asphaltenes from four crude oils were fractionated into solubility cuts. The asphaltenes were dissolved in toluene and then partially precipitated at specified ratios of heptane/toluene to generate sets of light (soluble) and heavy (insoluble) cuts. The molecular weight and density were measured for each cut. The asphaltenes were found to include both associating and non-associating asphaltenes. The content of non-associating components was up to 15 wt % of the asphaltenes. The density distributions were determined directly from the data. The molecular weight data were fitted with a self-association model to predict the distributions at any given concentration. Then, a guideline was developed to represent the molecular weight distribution of non-associated and associated asphaltenes with a Γ distribution function. Finally, the density of asphaltene cuts was correlated to their molecular weight. This correlation fit the data with an average absolute deviation of 11 kg/m3.

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INTRODUCTION An ongoing flow assurance issue in the petroleum industry is deposition and fouling associated with asphaltene precipitation. Precipitated asphaltenes can foul pipes and process equipment, cause catalyst deactivation during upgrading, and in general, reduce production.1−3 Asphaltene precipitation can occur when highly undersaturated oils are depressurized,4 when heavy oils are diluted with paraffinic solvents,5 and when incompatible crude oils are blended during transportation and refining.6 While there is a need to predict asphaltene precipitation to anticipate and mitigate potential fouling and deposition problems, the ill-defined nature of asphaltenes presents a challenge for phase behavior models. Asphaltenes are the heaviest and most polar components present in heavy oils and bitumens. They are defined as a solubility class insoluble in n-alkanes, such as pentane and heptane, and soluble in aromatic solvents, such as toluene. They are an ill-defined polydisperse mixture in terms of molecular weight, chemical composition, and structure. In addition to their molecular polydispersity, some asphaltenes self-associatiate to form molecular nanoaggregates over a broad range of sizes.7−10 The nature of this aggregation is still debated, but it appears that the aggregates can be treated as macromolecules at least for the purpose of phase behavior modeling.11−14 Asphaltene molecular weight measurements from a variety of methods and sources are consistent with average monomer molecular weights on the order of 1000 g/mol.15−19 Vapor pressure osmometry (VPO) data suggest average nanoaggregate molecular weights of less than 10 000 g/mol.15,20,21 These results are consistent with molecular film22 and gel permeation chromatography23 measurements. Note that gel permeation chromatography data are qualitative because of the tendency of asphaltenes to adsorb on the medium and © 2013 American Chemical Society

aggregate, both of which affect the validity of the calibration curve at high molecular weights. VPO data also indicate that nanoaggregate molecular weights range from approximately 1000 to at least 30 000 g/mol.15,22 Recent time-of-flight data are consistent with this range of molecular weights.24 On the other hand, Eyssautier et al.25 observed a range of aggregates an order of magnitude larger than the VPO data based on a combination of ultracentrifugation and X-ray scattering measurements. This difference can only partially be attributed to the difference between molar averages (VPO) and mass averages (scattering) but could be explained by flocculation of the aggregates, which would not be detected by VPO measurements. Many other methods, such as ultracentrifugation,26 filtration,27 and diffusion,28 focus on the size of the nanoaggregates, and the molecular weight can only be determined if the porosity or effective density of the nanoaggregates is assumed. There is considerable uncertainty in the density of the nanoaggregates given the probability of solvent partitioning or occlusion within the nanaoggregate.14,29 Nonetheless, the different methods indicate a distribution of aggregate sizes that must be accounted for in phase behavior modeling. The most successful modeling approaches for asphaltene precipitation to date are the statistical associating fluid theory (SAFT) model15,30,31 and variations on regular solution theory.22,32−38 Most SAFT models treat the asphaltenes as an associated molecular system with an average molecular weight found from data fitting. This approach has been successfully applied to modeling the onset of asphaltene precipitation. Recent regular solution-based models treat the asphaltene Received: January 24, 2013 Revised: March 26, 2013 Published: March 26, 2013 2474

dx.doi.org/10.1021/ef400142v | Energy Fuels 2013, 27, 2474−2487

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western Canadian oil sands extraction process. The WC_BIT_B1 sample was from a western Canadian steam-assisted gravity drainage (SAGD) process and had been stored for approximately 10 years, and therefore, some alteration of the crude oil may have occurred. WC_BIT_C1 is another western Canadian bitumen sample recovered from a cold production process. The Arabian medium crude oil sample was marketed by Saudi Aramco from Saudi Arabia and was sampled from a cargo ship on route to a refinery. Asphaltene precipitations, solids removal, solubility experiments, and asphaltene fractionations were performed using n-heptane and toluene (ACS grade) obtained from VWR International. Asphaltene molecular weight measurements were carried out with Omnisolv highpurity toluene (99.99%) obtained from VWR International; sucrose octaacetate (98%) and octacosane (99%) were obtained from SigmaAldrich Chemical Co. Reverse-osmosis water was provided by the University of Calgary physical plant. Asphaltene Precipitation from Crude Oil. Asphaltenes were precipitated from crude oil or bitumen using a 40:1 ratio (mL/g) of nheptane/heavy oil. The mixture was sonicated in an ultrasonic bath for 60 min at room temperature and left to settle without disturbing for a total contact time of 24 h. The supernatant was filtered through a Whatman no. 2 filter paper until approximately 20% of the solution remained in the beaker. A total of 10% of the original volume of the solvent was added to the remaining asphaltenes in the beaker, and then it was sonicated for 60 min and left to settle overnight for a contact time of approximately 18 h. The remaining mixture was filtered through the same filter paper. The filter cake was washed using 25 mL of n-heptane each time at least 3 times per day over 5 days until the effluent from the filter was almost colorless. The filter cake was dried in a closed fume hood until the weight of the filter did not change significantly. The dry filter cake consists of asphaltenes and inorganic solids, which are collected with the precipitated asphaltenes. The material extracted with n-heptane is termed “C7-asphaltenes + solids”. Asphaltenes + solids yields were reported as the mass of asphaltenes recovered after the washing and drying stages divided by the original mass of heavy oil used. Material referred to as solids corresponds to mineral material, such as sand, clay, ashes, and adsorbed organics, that precipitates along with the asphaltenes without affecting the onset or percentage of precipitated asphaltenes.39 Solids were removed from asphaltenes dissolving the C7-asphaltenes + solids in toluene and centrifuging to separate out the solids. A solution of asphaltenes in toluene was prepared at 10 kg/m3 and room temperature. The mixture was sonicated in an ultrasonic bath for 20 min or until all asphaltenes were dissolved, and then the solution was settled for 60 min. The mixture was divided into centrifuge tubes and centrifuged at 4000 rpm for 6 min. The supernatant (solids-free asphaltene solution) was decanted into a beaker and set into the fume hood to dry for 4 days or until constant weight, and then solids-free asphaltenes were recovered and stored in a jar. The non-asphaltenic solids, corresponding to the remaining material in the centrifuge tubes, were dried and weighed to calculate the solids content as the mass of solids divided by the mass of the original asphaltene sample. The asphaltenes extracted with nheptane and treated with toluene to remove solids are termed “C7asphaltenes”. Asphaltene Fractionation. C7-asphaltenes were divided into two fractions based on solubility: a light cut corresponding to the soluble asphaltenes in the specified solution of n-heptane and toluene (Heptol) and a heavy cut with the asphaltenes precipitated from the same Heptol mixture (Figure 1). The asphaltene cuts are termed “H##L” or “H##H”, where ## is the volume percent of n-heptane in the Heptol solution, “L” indicates the light soluble asphaltenes, and “H” indicates the heavy insoluble asphaltenes. Unless otherwise indicated, the Heptol ratios were chosen such that 25, 50, and 75% of precipitated asphaltenes were recovered in each experiment. The C7asphaltenes are termed “whole”, indicating that they have not been fractionated. The fractionations were performed in 10 kg/m3 solutions of asphaltenes with Heptol. Asphaltenes were first combined with toluene and sonicated for 20 min, then the corresponding amount of n-

aggregates as a distribution of macromolecules. Hence, asphaltene property distributions are model inputs. This approach has been successfully applied to modeling asphaltene yields from diluted heavy oils. To see how these distributions are used, consider the regular solution approach. The inputs to a regular solution model are the mole fractions, molar volume, and solubility parameters of each component or pseudo-component. Asphaltenes can be divided into a number of pseudo-components to represent their property distributions. For example, Akbarzadeh et al.37 used a Γ distribution function to represent the apparent molecular weight of the associated asphaltenes and correlations to relate the asphaltene density and solubility parameter to molecular weight. The distribution and correlations were then used to assign properties to asphaltene pseudo-components. However, these property distributions were based on very limited data. Because uncertainty in the property distributions within the asphaltene fractions can lead to significant uncertainty in the model predictions, it is desirable to construct property distributions based on more complete data for asphaltenes from more sources. The main objective of this work is to measure the density and molecular weight of asphaltenes (and solubility fractions of the asphaltenes) and to use these data to construct more accurate density and molecular weight distributions. The following approach was taken: (1) Fractionate the asphaltenes into solubility cuts by dissolving them in toluene and precipitating a portion of the asphaltenes by adding n-heptane to a specified ratio of heptane/toluene. Using different ratios, obtain three sets of solubility cuts, each set consisting of a soluble (light) cut and a corresponding insoluble (heavy) cut. (2) Construct density distributions directly from the density measurements of the cuts and whole asphaltenes. (3) Model the apparent molecular weights of the cuts using the termination−propagation association model.26 Reconstruct the distribution of whole asphaltenes at any given concentration with the model. Note that this approach was required because asphaltenes self-associate, so that the apparent molecular weights of the cuts may differ from their apparent molecular weight when part of the whole asphaltenes; therefore, the molecular weight distribution cannot be determined directly from the data. Finally, the density of the asphaltene cuts is correlated to their molecular weight. Note that the molecular weight distributions are determined in toluene and guidelines are provided to estimate the distribution in a crude oil.

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EXPERIMENTAL SECTION

Chemicals and Materials. Samples from four crude oils were obtained for this study (Table 1). WC_BIT_A1 was provided by Syncrude Canada, with the remainder provided from Shell Global Solutions. The WC_BIT_A1 sample was a topped bitumen from a

Table 1. Asphaltene and Solids Contents for the Samples Used in This Study

sample

API

asphaltene (wt %)

WC_BIT_A1 bitumen WC_BIT_B1 bitumen WC_BIT_C1 bitumen Arabian medium crude oil

9 8 9 31

16.50 16.30 11.76 6.44

solids (wt %) in asphaltenes

solids (wt %) in crude oil

7.67 3.85 1.82 0.54

1.27 0.63 0.21 0.03 2475


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possible to isolate self-association and non-ideality of the asphaltenes based on asphaltene VPO data alone. However, aromatics and resins are chemically similar to asphaltenes but show little or no association. These fractions appeared to form nearly ideal solutions in toluene40−42 as per eq 3, and therefore, the asphaltene molecular weights were also determined with eq 3. Density Measurement. Densities were measured at 20 °C and atmospheric pressure with an Anton Paar DMA 46 density meter. Reverse-osmosis water and air were used for the calibration. The instrument precision was ±0.0005 g/cm3. Asphaltene densities could not be measured directly and were only measured in solutions of toluene. The repeatability of the indirectly determined densities (calculated assuming no excess volume of mixing) was found to be ±10 kg/m3. If the mixture of asphaltenes and solvent forms a regular solution, the density of the solution is given by w w 1 = 1 + 2 ρmix ρ1 ρ2

Figure 1. Fractionation of WC_BIT_A1 asphaltenes based on solubility in Heptol solutions. Lines indicate fractions obtained at a heptane mass fraction of 60% (H60L and H60H).

where ρ is the density (kg/m ), w is the mass fraction, and subscripts mix, 1, and 2 denote the mixture, solvent, and asphaltene, respectively. The density of asphaltene can be determined indirectly from a plot of the specific volume (the inverse of the mixture density) versus the asphaltene mass fraction, as follows:

heptane was added and the mixture was sonicated for 45 min. After settling for 24 h, the solution was centrifuged at 4000 rpm for 6 min. The supernatant was transferred to a beaker, and the precipitated material (corresponding to the heavy cut) was washed with the same solvent until the supernatant was colorless and then dried in a vacuum oven at 60 °C. The supernatant material (corresponding to the light cut) was recovered and dried in a fume hood until the weight change was negligible. The fractional yield of each cut was calculated as the mass of the cut divided by the total mass of asphaltenes. The repeatability of the yield was approximately ±6 wt %. Molecular Weight Measurement. Molecular weights were measured in toluene at 50 °C using a Jupiter model 833 vapor pressure osmometer. The instrument was calibrated with sucrose octaacetate (679 g/mol), and the calibration was confirmed with octacosane (395 g/mol). The measured molecular weight of octacosane was within 3% of the correct value. The repeatability of the asphaltene molecular weight measurements was approximately ±15% for all of the samples. Note at least two repeats were performed at each concentration. VPO is based on the change in vapor pressure when a solute is added to a solvent. Two separate thermistors are set in a chamber saturated with pure solvent vapor. Because the droplets have a difference composition, there is a difference in temperature in the liquid phases in equilibrium with the same vapor phase. The temperature difference causes a resistance change (or voltage difference) in the thermistors, which is related to the molecular weight of the solute, M2, as follows:15

⎛ 1 ⎞ ΔV = K⎜ + A1C2 + A 2 C 2 2 + ...⎟ C2 ⎝ M2 ⎠

ρ2 =

K (ΔV /C2)

(5)

⎛1 w w 1 1⎞ = 1 + 2 − wSw2⎜⎜ + ⎟⎟β12 ρmix ρ1 ρ2 ρ2 ⎠ ⎝ ρ1

(6)

where β12 is a binary interaction parameter between the asphaltene component and the solvent. The last term in the expression is the excess volume of mixing. Excess mixing volumes could not be determined directly because only up to approximately 7 wt % of asphaltenes could be readily dissolved in toluene. At these low mass fractions, the difference between a regular solution (no excess volume of mixing) and an irregular solution cannot be distinguished beyond the experimental error. Sanchez43 examined the densities of several distillation cuts from a western Canadian bitumen. She confirmed that the heavy distillation cuts formed irregular solutions with toluene and found that the value of β12 increased toward the heavier cuts. She extrapolated the trend of β12 versus mass fraction distilled and estimated a β12 of 0.015 for asphaltenes. Table 2 shows WC_BIT_B1 asphaltene densities calculated on the basis of both the regular mixing rule and the excess volume mixing rule, with β12 = 0.015. Note that the value calculated using the regular mixing rule is approximately 40 kg/m3 higher than the value obtained with the excess volume mixing rule. The same behavior occurs for all

(1)

Table 2. Density of Cuts for WC_BIT_B1 Asphaltenes Using Both Regular and Excess Volume Mixing Rules

(2)

For an ideal system, the second term in eq 2 is zero and ΔV/C2 is constant. In this case, the molecular weight is determined from the average ΔV/C2 as follows:

M2 =

1 S+I

where S and I are the slope and intercept, respectively, in the specific volume plot. If the mixture does not form a regular solution; that is, there is an excess volume of mixing, then the mixture density can be expressed as follows:

where ΔV is the voltage difference between the thermistors, C2 is the solute concentration, K is the proportionality constant, and A1 and A2 are coefficients arising from the non-ideal behavior of the solution. In most cases, the solutions are at a low concentration, most of the higher order terms become negligible, and eq 1 reduces to

⎛ 1 ⎞ ΔV = K⎜ + A1C2⎟ C2 ⎝ M2 ⎠

(4) 3

(3)

The calibration standard formed non-ideal solutions with toluene, and the voltage differences could be fitted with eq 2 to find K. It is not 2476

cut

ρA regular mixing rule (kg/m3)

ρA excess volume mixing rule (kg/m3)

HT92L HT77L HT60L whole HT92H HT77H HT60H

1078.4 1137.9 1162.1 1170.8 1184.3 1187.1 1189.6

1044.1 1101.2 1124.4 1132.5 1145.3 1146.0 1150.4


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of the asphaltene cut data, which are shifted similarly when the excess volume mixing rule is used instead of the regular mixing rule. The value of β12 for asphaltenes used in the excess volume mixing rule is a preliminary estimation that has not yet been confirmed with additional experimental data. Even though it is necessary to account for the non-regularity of the asphaltene−toluene mixtures, there is uncertainty about the correct β12 parameter to use, and for now, the density of asphaltenes was calculated with the regular mixing rule. These values will be used for the determination of the density correlations for all of the samples. Note that the models and conclusions presented in this study are not qualitatively affected by the mixing rule assumption. Only the values of asphaltene density and model parameters will be affected.

P1 + P3 ↔ P4 K

P1 + Pn ↔ Pn + 1

[P2] = K[P1]2

(7)

K

[P3] = K[P1][P2] = K 2[P1]3

(8)

P1 + P2 ↔ P3

[Pn + 1] = K[P1][Pn] = K n[P1]n + 1

(10)

Termination reactions occur when a terminator monomer T links up with a monomer P1 or an existing aggregate Pn, terminating the association. For this case, it is also assumed that reactions are first-order with respect to both the terminator molecules and the aggregate molecules and are characterized by an association constant K. It is also assumed that the association constant is the same for all of the reactions and has the same value as the constant from the propagation reactions. Another assumption of this model is that association stops when termination occurs at only one site of the aggregate. It was found that a model capping both ends of a linear aggregate gave similar results.40 The concentration of terminator aggregates [PnT] can be expressed in terms of the association constant and the equilibrium concentration of propagators [P1] as shown below

SELF-ASSOCIATION MODEL The asphaltene association developed by Agrawala and Yarranton40 was adapted to interpret the molecular weight data. In this model, self-association is assumed to be analogous to polymerization or oligomerization, except that the molecules are assumed to link by van der Waals forces rather than covalent bonding. The asphaltenes (and resins) are considered to be free molecules in solution with multiple functional groups that interact with other molecules to form aggregates. The asphaltenes plus resins are divided into two classes of molecules: propagators and terminators. A propagator was defined as a molecule with multiple active sites that is capable of linking with other similar molecules or aggregates and promoting additional association. A terminator is defined as a molecule with a single active site that is capable of linking with other molecules but terminates further association. This model defines any mixture in terms of its content of propagators and terminators, and the proportion of each type of molecule determines the extent of association. The aggregates are, in effect, macromolecules of asphaltenes and resins as observed in asphaltene phase behavior and molecular weight measurements.40,44,45 Note that the model is almost certainly a gross oversimplification of the true aggregation behavior of asphaltenes. However, it has been proven to fit the available molecular weight data of associated asphaltenes and resins in a self-consistent and physically plausible manner.41 In addition, there are insufficient data to justify constructing a more complex model. Original Model Formulation. Only two reaction schemes are required for the model: propagation and termination. Unlike polymerization reactions, an initiation step is not required because association is not a free radical reaction.40 Propagation reactions occur when a monomer P1 links up with another monomer P1 or an existing aggregate Pn (where n is the number of monomers in the aggregate). Propagator monomers can link freely with other molecules and grow in each subsequent step of the polymerization. Reactions are assumed to be first-order with respect to both the propagator monomer and the aggregate molecules. The kinetics is described by the association constant, K, that represents the equilibrium between forward and reverse association. The association constant is assumed to be the same for all of the reactions. The concentration of aggregates [Pn] can be expressed as a function of the association constant and the equilibrium concentration of propagators [P1] as follows: K

(9)

The general equation for propagation is given by

■

P1 + P1 ↔ P2

[P4] = K[P1][P3] = K3[P1]4

K

P1 + T ↔ PT 1 K

P2 + T ↔ P2T

[PT 1 ] = K[P1][T ]

(11)

[P2T ] = K[P2][T ] = K 2[P1]2 [T ] (12)

K

P3 + T ↔ P3T

[P3T ] = K[P3][T ] = K3[P1]3 [T ]

(13)

The general equation for termination is given by K

Pn + T ↔ PnT

[PnT ] = K[Pn][T ] = K n[P1]n [T ] (14)

The assumption of equal association constant for all of the reactions indicates that the probability of a monomer of any class forming a link with an aggregate of any size is the same as that of linking up another monomer. This model does not consider aggregate−aggregate association. The set of reactions is solved simultaneously like a polymerization reaction, starting with the mass balance for both propagators and terminators. The equilibrium concentrations of propagator and terminator monomers are given by [P1] = (1 + K ([P1]0 + [T ]0 ) − (((1 + K (2[P1]0 + [T ]0 ))2 − 4K[P1]0 ([P1]0 + [T ]0 ))1/2 )/(2K 2([P1]0 + [T ]0 ))

[T ] = [T ]0 (1 − K[P1])

(15) (16)

where [P1]0 and [T]0 are defined as the initial concentration of propagator and terminator monomers, respectively. The concentration of aggregates of any size can be calculated using eqs 7−14 as long as the initial concentration of monomers [P1]0 and [T]0 and the association constant are defined. Note that the maximum number of aggregates n for both propagation and termination reactions must be set high enough to include the largest predicted aggregates in the system (determined by trial and error with different n). Note that the bracketed terms are concentrations but, because the asphaltenes are dilute, the concentrations are proportional to the mole fractions. Therefore, the bracketed terms are treated as mole fractions from this point forward. 2477


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Application to Asphaltenes with Associating and Nonassociating Components. The original version of the selfassociation model assumed that all of the asphaltene (plus resin) monomers have at least one active site that promotes association with aggregates or with other monomers. As will be shown later, some asphaltenic material (neutrals) may be present that does not participate in the association but must be included in the model to complete the material balance. These non-associating components are defined as “neutrals”. The propagation and termination reactions are not affected by the presence of neutrals. However, the amount of neutrals must be accounted for when calculating the initial concentration of propagators and terminators and the final molecular weight. The inputs for the model are the molecular weights for terminators, propagators, and neutrals. The model is underconstrained, and many combinations of monomer molecular weights can provide a similar fit to the data. As will be shown later, the asphaltenes consist mostly of propagators, and the lightest cuts exhibited little association. Therefore, the molecular weight of propagators was initially set equal to the molecular weight of the lightest cut for each sample. The best results were found when terminators and neutrals were assumed to be smaller molecules than propagators. Their molecular weights were assumed to be the same and were initially set to equal the lowest observed molecular weights. All of the monomer molecular weights were then adjusted to optimize the fit to the data. For all of the cases, the molecular weight of propagator and terminator (and neutral) monomers was lower than 2000 and 1600 g/mol, respectively. An initial ratio of terminators/propagators (T/P)0 and an association constant K are assumed, and then the initial mole fraction x of each monomer in asphaltenes is calculated as follows: xT0 ⎛T ⎞ ⎜ ⎟ = ⎝ P ⎠0 x P0 xT0 =

MWmono = xT0 MWT + (1 − xT0 − xN )MWP + xN MWN (22)

The average molecular weight of the aggregated system at a given concentration is given by n

MWavg = (1 − xN ,final)( ∑ (x[Pn]MW[Pn] + x[PnT ]MW[PnT ])) n=0

+ xN ,final MWN

where x and MW are the mole fraction and molecular weight of a propagator aggregate [Pn], terminator aggregate [PnT], or neutral molecule N, respectively. Note xN,final is the concentration of neutrals in the aggregated system and is different from xN because the average molecular weight of the system has changed through aggregation. The output from the model is the molecular weight and mass fraction of propagator (Pn) and terminator (PnT) aggregates. The model is run with the selected fitting parameters and the calculated values of [P1]0 and [T0], and equilibrium mole fractions are determined from eqs 19 and 20. The value of (T/ P)0 and the association constant K are modified until the model fits the experimental average molecular weight. The (T/P)0 ratio determines the value of the molecular weight at a high concentration while the association constant K determines the concentration at which the limiting molecular weight is reached. Molecular Weight Distribution. The concentration of each aggregate is determined from the solution of eqs 7−14. Then, the neutrals are incorporated into the distribution as a mole fraction of fixed molecular weight. Because a distribution of monomer sizes is not taken into account, the predicted distribution is discrete. However, a continuous form is more convenient for the precipitation models. A continuous mass frequency distribution for the molecular weight of asphaltenes is determined by sorting in ascending order the mass fraction and molecular weight data for all of the aggregates and fitting those values with the least-squares method to a frequency distribution with the following form:

(17)

(T /P)0 (1 − xN ) 1 + (T /P)0

and

x P0 = 1 − xT0 − xN

⎛ ⎛ C − MW ⎞⎞ ⎟⎟ cumf = A + B exp⎜ −exp⎜ ⎝ ⎠⎠ ⎝ D

(18)

where xN is the mole fraction of neutrals in the asphaltenes (plus resins if present) prior to any aggregation (monomers only). The initial mole fraction of propagators and terminators in the solution depends upon the mass concentration of asphaltenes CA and the molar volume of the solvent υs and is calculated as follows:

(19) (20)

The initial mole fraction of neutrals in solution is given by [N ]0 =

■

xN

(1 +

MWmono CAυs

)

(24)

where cumf is the calculated cumulative mass fraction, MW is the aggregate molecular weight, and the other terms are fitting parameters. The terms A and B modify the upper limit of the distribution, and the terms C and D change the slope and point at which the maximum value is reached.41 After determination of the equation for the cumulative mass fraction of aggregates, the function can be divided into intervals to determine the molecular weight distribution. Figure 2 shows a typical cumulative molecular weight distribution, in this case the results from fitting WC_BIT_A1 C7-asphaltene VPO data to the self-association model and the fitting curve to the form of eq 24. For this case, the error in the fitting is 0.003. In all cases, eq 24 fits the discrete distributions with an error less than 0.013.

⎞ ⎛⎛ MWmono ⎞ [P1]0 = 1/⎜⎜1 + ⎟(1 + (T /P)0 )⎟⎟(1 − xN ) CAυs ⎠ ⎝⎝ ⎠

[T ]0 = [P1]0 (T /P)0

(23)

RESULTS AND DISCUSSION First, asphaltene molecular weight and density data for the solubility cuts from the four crude oils are presented. The WC_BIT_A1 asphaltenes are used as an example. Density distributions are reconstructed on the basis of the measured

(21)

The average molecular weight MWmono of the non-aggregated system is calculated as 2478


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To simplify the comparison of samples, only the molecular weight for the lightest cut, the whole asphaltenes, and the heaviest cut at 60 kg/m3 for each sample are considered here (Table 3). Similar comparisons were observed at other concentrations. Considering that we are examining selfassociating materials from different sources, there is surprisingly little difference in the molecular weight distributions. The WC_BIT_A1 and WC_BIT_C1 asphaltenes have a higher average molecular weight than the other two samples, perhaps indicating that they experienced more biodegradation in the reservoir. If asphaltenes did not self-associate, their molecular weights would be additive and the molecular weight of the whole asphaltenes could be calculated from the molecular weight of its cuts as follows:

Figure 2. Cumulative mass frequency versus molecular weight for WC_BIT_A1 C7-asphaltenes in toluene at 23 °C using the selfassociation model with neutrals.

MWwhole = x H ## L MWH ## L + (1 − x H ## L)MWH ## H

(25)

where MW is the molecular weight data at a specific asphaltene concentration, H##L and H##H are the light and heavy cuts, respectively, separated with a common Heptol solution (H##). Figure 4 shows the calculated molecular weight for the whole

densities assuming no excess volumes of mixing. Because asphaltenes self-associate, the terminator−propagator selfassociation model is used to interpret the measured data for the molecular weight of the aggregates. Measured Molecular Weights. Figure 3 shows the molecular weight for WC_BIT_A1 asphaltenes and a pair of

Figure 4. Recalculation of WC_BIT_A1 molecular weight assuming additive molecular weights. Figure 3. Molecular weight for WC_BIT_A1 whole asphaltenes and cuts precipitated using HT70 and HT77, respectively.

WC_BIT_A1 and WC_BIT_B2 asphaltenes. For all of the cuts, the calculated molecular weight was significantly less than the measured value. The same behavior was observed for WC_BIT_B2 and WC_BIT_C1 asphaltenes. For the Arabian asphaltenes, the calculated molecular weight exceeded the measured values. Therefore, in most cases, self-association must be accounted for when interpreting the molecular weight distributions. When asphaltenes are divided into two solubility cuts, the lower molecular weight aggregates tend to remain soluble and report to the light cuts, while the high molecular weight aggregates tend to precipitate and report to the heavy cut, as observed in Figure 5. Then, when each cut is dissolved in

solubility cuts. The molecular weight of all but the lightest cuts increased with an increasing asphaltene concentration, as expected for a self-associating material. The molecular weight of the lightest cut increased little with the concentration, suggesting that it contained little self-associating material. The molecular weight of the heaviest cut increased significantly, indicating that it contained a high proportion of self-associating molecules or that its components self-associated more strongly. A similar behavior for molecular weight was observed for all of the other samples (see the Supporting Information).

Table 3. Molecular Weight at 60 kg/m3 in 50 °C Toluene and Density at 23 °C of Whole, Lightest Cut, and Heaviest Cut of Asphaltenes from Different Sources whole

lightest cut

heaviest cut

sample

MW (g/mol)

density (kg/ m3 )

mass fraction of asphaltene

MW (g/mol)

density (kg/ m3)

mass fraction of asphaltene

MW (g/mol)

density (kg/ m3)

WC_BIT_A1 WC_BIT_B1 WC_BIT_C1 Arabian medium

6800 4000 11000 4200

1175.4 1170.7 1179.8 1183.4

0.15 0.21 0.30 0.27

1300 900 4300 2200

1132.6 1078.4 1146.7 1122.2

0.42 0.19 0.24 0.30

27000 12300 38000 24000

1197.4 1189.6 1202.5 1209.0

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average density of the components between that point and a mass fraction of 1. It appears that the heaviest (and highest molecular weight) asphaltenes precipitate first and the lightest (lowest molecular weight) asphaltenes precipitate last. Similar results were obtained for the other oil samples (see the Supporting Information). To determine the density distribution, the increment in the density from one cut to the next was calculated from both the light cut data and the heavy cut data. Then, the average density for each interval in the distribution was determined from the incremental densities. Figure 7 shows the density distributions

Figure 5. Illustration of partitioning of asphaltene aggregates into solubility cuts and self-association into new molecular weight distributions.

toluene for a molecular weight measurement, it will reassociate but not necessarily to the same distribution as it had in the original asphaltene mixture when in equilibrium with all of the other asphaltene molecules and aggregates. Therefore, the measured molecular weights are not necessarily additive. Instead, a self-association model is used to fit the data to determine the number of monomers of different types of asphaltene molecules in each cut (such as non-associating neutrals, propagators, and terminators). Then, a material balance can be performed on the monomers, with the molecular weight distribution calculated for any cut or combination of cuts using the self-association model. Before the self-association model was applied, the density data are examined as help to assess the amount of non-associating and associating monomers in the asphaltenes. Measured Density Distributions. The densities of the whole asphaltenes for the four oil samples were very similar, with an average density of approximately 1176 kg/m3 (Table 3). These densities are typical for asphaltenes; asphaltene densities from a variety of sources generally fall within a range of 1130−1200 kg/m3.37 The density distribution within the asphaltenes was determined from the density of the asphaltene solubility cuts. Figure 6 shows the density of the light and heavy cuts of WC_BIT_A1 asphaltenes versus the mass fraction of the whole asphaltenes. Each data point for a light cut is the average density of the components between 0 and the mass fraction of that point. Each data point for a heavy cut is the

Figure 7. Comparison of the density distributions of the four asphaltene samples.

for all of the asphaltene samples. In almost every case, the density distributions of the asphaltenes showed two distinct trends: a steep rise in density, followed by a shallow rise or plateau. The steep rise corresponded to the lightest lowest molecular weight cuts, where little or no self-association was observed in the molecular weight data. The shallow rise or plateau corresponded to cuts exhibiting self-association. Therefore, it is likely that some of the asphaltenes do not self-associate, and these asphaltenes are found predominantly in the most soluble fraction of the asphaltenes. Similar to any other molecules in the crude oil, there is a distribution of densities and, therefore, a relatively steep slope versus mass fraction. Note that the lower end of this trend was similar to the density of resins; for example, the lowest density of the WC_BIT_B2 asphaltenes was 1078 kg/m3 compared to a resin density of 1075 kg/m3.42 Self-associated asphaltenes are aggregates likely formed from a number of molecules of

Figure 6. (a) Density of WC_BIT_A1 asphaltene cuts, where lines are the cumulative density distribution calculated from the density distribution, and (b) density distribution of WC_BIT A1 asphaltenes. 2480


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(T/P)0 that best fit the molecular weight data for each cut was determined. Second, the model was used to determine the optimum (T/P)0 value for the whole asphaltenes, with the constraint that the molecular weight at 10 kg/m3 was approximately the same as the measured value. Next, the initial moles of propagators and terminators were determined for each of the light and heavy cuts, and the moles in the whole asphaltenes were calculated from each corresponding pair of cuts (e.g., H60L and H60H) with a material balance. The (T/ P)0 value was calculated for the whole asphaltenes and compared to the fitted (T/P)0 value. If the difference between both fitted and calculated values was less than 15%, the asphaltene molecular weight distribution was determined from the fitted amounts of neutrals, propagators, and terminators. Otherwise, the values of (T/P)0 for all of the cuts were modified until the error in fitting the molecular weight data was minimized. Table 5 presents the calculated (T/P)0 ratio for all WC_BIT_A1 asphaltene cuts and the fitted value for the

varying density. The density of the aggregates will tend to the average density of the monomers. Hence, the density does not change significantly across the mass fraction of self-associated asphaltenes. Table 4 summarizes the minimum and maximum densities of each sample as well as the point where the slope changes. The Table 4. Minimum and Maximum Densities and Proposed Mass Fraction of Non-associating Material for All of the Asphaltene Samples sample

minimum density (kg/m3)

maximum density (kg/m3)

mass fraction of non-associating material

WC_BIT_A1 WC_BIT_B1 WC_BIT_C1 Arabian medium

1133 1078 1146 1122

1197 1190 1203 1209

7 15 8 15

mass fraction where the slope changes is a preliminary measure of the mass fraction of non-associating asphaltenes in each sample. The non-associated zone ranges from 7 to 20 wt % of the asphaltenes, indicating that the majority of these asphaltenes tend to associate. The density distributions are very similar to each other, with a maximum density of approximately 1200 kg/m3. There are some differences in the minimum density, which may indicate some property differences but could also reflect the uncertainty in fitting the density data or slight differences in washing the asphaltenes in the preparation of the samples. Similarly, the differences in the mass fraction of non-associating material are sensitive to washing, experimental error, and fitting errors. It other words, the differences between the samples are within the uncertainty of the analysis. Modeling Molecular Weight Data. Fitting Data with the Self-Association Model. The self-association model adapted to include neutrals was used to model the molecular weight data. On the basis of the molecular weight and density data, it was assumed that, during fractionation, neutrals partitioned only into the lightest asphaltene cut. The methodology for the implementation of the model is shown in Figure 8. First, the model was run for each light and heavy cut, and the value of

Table 5. (T/P)0 of WC_BIT_A1 Whole Asphaltenes, Fitted for the Whole Asphaltene Sample and Calculated by Recombination for Each Pair of Light and Heavy Cuts cut

(T/P)0

error (%)

whole HT60 HT70 HT80 HT90

0.235 0.260 0.259 0.259 0.259

11 10 10 10

whole asphaltenes. Note that error is approximately 10% for all of the cuts. The quality of the fit is very good considering the high scatter in the molecular weight measurements and that the self-association model is a simplified representation of asphaltene association. For all of the other samples, the error in the recalculated (T/P)0 value was lower than 17%, except for Arabian asphaltenes, where the error values were approximately 27% (see the Supporting Information). The reason for the higher error for the Arabian asphaltenes is not known.

Figure 8. Algorithm to fit the self-association model to molecular weight data. 2481


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Figure 9. Fitting of molecular weight data using the self-association model for (a) light cuts and (b) heavy cuts of WC_BIT_A1 asphaltenes.

Table 6. Inputs and Parameters of the Self-Association Model for All of the Samples at 50 °C sample

MWT (g/mol)

MWP (g/mol)

MWN (g/mol)

(T/P)0

mol % N monomers

K (mol−1)

mass % N

WC_BIT_A1 WC_BIT_B1 WC_BIT_C1 Arabian

900 700 1600 1200

1800 900 1900 2000

900 700 1600 1200

0.235 0.26 0.135 0.592

5 5 5 3

55000 55000 55000 55000

2.8 4.1 4.3 2.1

Figure 9 shows the fitting for WC_BIT_A1 cuts and whole asphaltenes. Similar results were obtained for the other samples (see the Supporting Information). The model successfully represented the main features of asphaltene self-association: the increase in molecular weight with asphaltene concentration, the change in self-association from light cuts to heavy cuts, and the lack of self-association in the lightest cut. Note that the model overestimated the molecular weight for the light cuts at low concentrations possibly because the reaction constant, K, was assumed to be the same for all of the cuts. Table 6 summarizes the fitting parameters and inputs of the single-end termination model for the different samples. The value of K was 55 000 mol−1 in all cases. This similarity suggests that asphaltenes self-associate following similar mechanisms in asphaltenes from different sources. The observation is not surprising if one considers that the elemental composition of asphaltenes does not vary significantly between crude oils.9 In fact, the reason most asphaltenes are part of the asphaltene solubility class may well be that they are nanoaggregates and, therefore, less soluble than single molecules. The similarity in the chemistry and behavior of asphaltenes from different sources may occur because they have self-association in common. The molecular weight of terminators and neutrals ranged from 700 to 1800 g/mol, and for the propagators, it was between 900 and 2000 g/mol. Note that for all cases, the propagator monomer molecules are larger than the terminator molecules. Apart from this systematic difference. the variation in monomer sizes may reflect the inaccuracies of the data and data fitting as much as any real differences between the samples. The size range of the monomers is consistent with recent highresolution mass spectrometry data.18 For all of the samples, the molar percentage of neutral monomers ranged between 3 and 5 mol %. The mass fraction of neutrals was calculated and ranged between 2.1 and 4.3 wt %. These values are lower than the values obtained from the density distribution but confirm the presence of non-associated molecules. Note that the amount of neutrals determined from the model is a fit parameter, while the amount determined from

the density distributions is an experimental observation and, therefore, likely to be more accurate. Molecular Weight Distributions. Once the parameters of the self-association model were determined and adjusted so that the mass balances for all of the samples were achieved, the molecular weight distribution was determined. The output of the model was the molecular weight and mass fraction for all of the associated species in the system as well as neutrals. The cumulative mass fraction was plotted as a function of the molecular weight, and the values were fitted using eq 24. Figure 10 shows the fitting of the modeled cumulative distribution for

Figure 10. Cumulative molecular weight distribution for WC_BIT_A1 asphaltenes at 50 °C and 10 g/L asphaltene concentration.

WC_BIT_A1 whole asphaltenes. The calculated average molecular weight of the distribution was matched to the molecular weight measured experimentally at 10 kg/m3 for the whole asphaltenes. For this case, the error in the fitting was 0.3%, and for all cases, the error was less than 1.3%. To generate a frequency distribution of the molecular weight distribution for each asphaltene sample, the cumulative distribution was discretized into 40 fractions of constant step 2482


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we propose guidelines for representing asphaltene properties based on a Γ function. The Γ distribution function46 is given by

size and the average molecular weight was calculated for each interval. Note that the neutral material was also including the fitted distribution. Figure 11 shows the molecular weight distribution for WC_BIT_A1 asphaltenes at 50 °C.

f (MW) =

⎛ MWmono − MW ⎞ (MW − MWmono)α − 1 exp⎜ ⎟ α β Γ(α) β ⎝ ⎠ (27)

where MWmono is the molecular weight of the monomer, MW is the average associated molecular weight for the whole asphaltenes, Γ(α) is the Γ function, α is a parameter that defines the shape of the distribution, and β is given by β = MWavg − MWmono

Two alternatives are considered: (1) lump the neutrals with the aggregates, and (2) separate the neutrals and the aggregates. In both cases, the first step is to fit the Γ distribution to match the T/P distributions. The cumulative Γ distribution is discretized into the same molecular weight steps as in the T/P distribution for consistent comparisons; the average molecular weight must be the same as in the T/P distribution; and the shape factor (α) is tuned until both distributions closely match. Then, a generalized guideline is recommended. Lumped Distribution of Neutrals and Aggregates. Figure 13 shows the mass and mole fraction T/P distributions and its corresponding fitted Γ distributions for WC_BIT_A1 C7asphaltenes. The Γ distribution follows a similar shape as the T/P distribution, but it was not possible to provide a perfect fit possibly because the inclusion of neutral species distorts the shape of the distribution. The difference is most evident at the lowest molecular weights of the molar distributions (Figure 13b), exactly where the neutrals appear in the distribution. Similar results were obtained for the other crude oil samples (see the Supporting Information). Table 8 shows the value of the shape factors (α) used to fit the Γ distribution to the T/P distribution. In three of four cases, the value of α was 2.0. The only exception was the WC_BIT_B1 asphaltenes, with an α of 2.2. Given the 15% uncertainty in the molecular weight data, we conclude that an α of 2.0 represents the molecular weight distribution of native petroleum asphaltenes within the error of the data. Distribution of Aggregates without Neutrals. The inclusion of non-associated components, the amount of which may vary from sample to sample, may distort the shape of the distributions. Therefore, the neutrals were represented as a single non-associated component and only associated components considered when fitting the association model molecular weight distribution. The cumulative distribution from the T/P model (without neutrals) at 23 °C was again fitted with eq 24, with the parameters given in Table 9. Note only the value C and in some cases B were changed to fit the distribution. The average molecular weight when excluding neutrals is higher because the relatively low-molecular-weight neutrals were excluded. Figure 14 shows the mass and mole fraction T/P distributions and its corresponding fitted Γ distributions for

Figure 11. Molecular weight distribution for WC_BIT_A1 asphaltenes at 23 and 50 °C and 10 g/L asphaltene concentration.

To be consistent with the density data, the distribution was corrected to 23 °C to account for the effect of the temperature on asphaltene molecular weight. The average molecular weight of the distribution was recalculated at 23 °C as follows:15 MW23 ° C = MW50 ° C exp(0.0073(50 °C − 23 °C))

(28)

(26)

Then, the self-association model was run again, changing only the (T/P)0 ratio until the average molecular weight of the new distribution corresponded to the corrected value at 23 °C. The new cumulative distribution was again fit with eq 24 with the constraint that MWcumf = 0 was the same as at 50 °C. The error in the fitting of the model results at 23 °C for WC_BIT_A1 asphaltenes is 0.08% and, for all cases, is less than 0.56%. Table 7 shows the (T/P)0 value and eq 24 parameters used to obtain the molecular weight distribution at 23 °C for each sample. The frequency distribution was then calculated, as was described above. Figure 11 shows the molecular weight distributions for WC_BIT_A1 asphaltenes at 23 and 50 °C with average molecular weights of 6488 and 5250 g/mol, respectively. Figure 12 shows the molecular weight distributions at 23 °C for the four asphaltene samples. All of the distributions have a similar shape and show that asphaltenes consist mostly of material with molecular weight lower than 15 000 g/mol, with a lesser amount of aggregates ranging up to 50 000 g/mol or more. As noted previously, the molecular weight distributions are similar for most samples. The WC_BIT_A1 and WC_BIT_C1 samples have a broader distribution than the other samples, perhaps indicating more biodegraded oils. Representing Asphaltene Molecular Wieght Distributions with the Γ Distribution Function. It is not practical to obtain cut data and use a self-association model to determine asphaltene property distributions for every crude oil. Instead,

Table 7. Parameters for the Asphaltene Molecular Weight Distributions at 23 °C sample

A

B

C

D

MWavg at 23 °C

(T/P)0 at 23 °C


1.164 1.632 1.208 1.366

8984 5710 11549 5900

6533 282 7501 2550

−0.164 −0.627 −0.208 −0.366

6489 3586 8636 4846

0.125 0.164 0.040 0.374

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Figure 12. Comparison of molecular weight distributions of four asphaltene samples at 23 °C and 10 g/L asphaltene concentration.

Figure 13. Comparison of T/P and Γ molecular weight distributions in (a) mass faction and (b) mole fraction for Athabasca asphaltenes at 23 °C and 10 g/L asphaltene concentration.

Table 8. Mass Percent Neutrals in Asphaltenes and α Parameter for the Γ Function Based on Molecular Weight Data at 23 °C and 10 g/L Asphaltene Concentration mass percent neutrals α with neutrals α no neutrals

WC_BIT_A1

WC_BIT_B1

WC_BIT_C1

Arabian

2.7

4.1

4.3

2.0

2.0 1.85

2.2 1.80

2.0 1.90

2.0 1.70

Guidelines for Representing Asphaltene Molecular Weight Distributions. If the amount of neutrals is known or can be estimated, then it is recommended to represent the asphaltene aggregates with a Γ distribution function centered on the average molecular weight of the aggregates with a minimum molecular weight of 900 g/mol and an α of 1.8. However, if, as in most cases, the mass fraction of neutrals is unknown, then it is recommended to use the average molecular weight of the asphaltenes with a minimum molecular weight of 900 g/mol and an α of 2.0. Note that these values were developed for C7-asphaltenes. Pentane-extracted asphaltenes (C5-asphaltenes) are a larger fraction of the crude oil and, consequently, include more of the lower molecular weight components and possibly more neutrals than C7-asphaltenes. Their average molecular weight will be lower. On the basis of observations from mixtures of asphaltenes and resins,11 the minimum molecular weight is expected to be similar to those of C7-asphaltenes but the α value will be lower, tending toward 1.5. There is more uncertainty in applying the Γ distribution function to asphaltenes in crude oils because the medium is no longer toluene and the extent of self-association may change. The monomer size must be the same, and the amount of neutrals is not expected to change. However, an independent measurement of the average asphaltene molecular weight measurement is required, and there is no reliable method to do so. Therefore, the molecular weight must be estimated or adjusted to fit solubility data in a given phase behavior

Table 9. Parameters Adjusted To Fit the Asphaltene Molecular Weight Distributions, Excluding Neutralsa

a

parameter

B

C

MWavg, no neutrals


8983 5700 11549 6200

7000 400 8300 2700

7610 4087 9440 5082

Parameters A and B are the same as in Table 7.

WC_BIT_A1 C7-asphaltenes. While not perfect, a better fit to the T/P model is obtained when the neutrals are excluded. Not surprisingly, the fit is improved most at the lowest molecular weights of the molar distributions (Figure 13b), where the neutrals appear in the distribution. Similar results were obtained for the other crude oil samples (see the Supporting Information). Table 8 shows the value of the shape factors (α) used to fit the Γ distribution to the T/P distribution. The average of the fitted α values was 1.81. 2484


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Figure 14. Comparison of T/P and Γ molecular weight distributions in (a) mass faction and (b) mole fraction for Athabasca asphaltenes at 23 °C and 10 g/L asphaltene concentration.

⎛ ⎛ MW ⎞⎞ ⎟⎟ ρ = 1100 + 100⎜1 − exp⎜ − ⎝ 3850 ⎠⎠ ⎝

model.12,30,31,36−38 Once the average molecular weight is estimated, the guidelines provided above can be applied. Correlation of Density to Molecular Weight. It is convenient to correlate asphaltene density to the molecular weight distribution rather than determining the distribution experimentally. Many similar correlations have been developed for distillation fractions32 but do not extrapolate well to asphaltenes because asphaltene molecular wieghts vary more by self-association than differences in the chemical structure. Yarranton et al.11 developed a power law correlation of asphaltene density to molecular weight, but the correlation was based on a small data set for one bitumen. The correlation can now be updated using a more extensive data set. The densities were determined at 23 °C, and therefore, all of the molecular weights were corrected to 23 °C, as described previously. Also, because the molecular weight of the aggregates depends upon the concentration, the correlation was developed using molecular weights at a fixed asphaltene concentration of 10 g/L. Figure 15 shows the density as a function of the molecular weight for WC_BIT_A1 asphaltenes. The original Yarranton et

(29)

where ρ is the density (kg/m ) and MW is the molecular weight (g/mol) of the asphaltene cut at 10 g/L asphaltene concentration. Figure 15 shows that the fit to the WC_BIT_A1 asphaltenes is considerably improved. Figure 16 compares the correlation to density data from all of the samples. The correlation does not provide an exact match 3

Figure 16. Density correlation (eq 29) compared to density of asphaltene cuts from four samples at 23 °C.

to all of the experimental data, partly because the correlation does not explicitly account for the mass fraction of nonassociating components. If this mass fraction was used as an input to the correlation, a more accurate correlation could be developed. However, because there is currently no simple method to determine this mass fraction, this approach was not pursued further. Nonetheless, the densities calculated with the correlation are within a maximum error of 40 kg/m3 (for the lowest density cuts) and an average absolute deviation (AAD) of 11 kg/m3.

Figure 15. Density at 23 °C as a function of the molecular weight at 10 g/L for WC_BIT_A1 asphaltenes.

al. correlation provides a good estimate of the average density but does not accurately fit the trend in the density data. Instead, the following new correlation is proposed on the basis of the density data for all of the asphaltenes considered in this study 2485


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(8) Asphaltenes, Heavy Oils and Petroleomics; Mullins, O. C., Sheu, E. Y., Hammami, A., Marshall, A. G., Eds.; Springer: New York, 2007; pp 329−352. (9) Speight, J. G. The Chemistry and Technology of Petroleum; CRC Press (Taylor and Francis Group): Boca Raton, FL, 2007. (10) Birdi, K. S. Handbook of Surface and Colloid Chemistry, 3rd ed.; CRC Press (Taylor and Francis Group): Boca Raton, FL. 2008; Chapter 13, pp 703−718. (11) Yarranton, H. W.; Masliyah, J. H. AIChE J. 1996, 42, 3533− 3543. (12) Ting, P. D.; Hirasaki, G. J.; Chapman, W. G. Pet. Sci. Technol. 2003, 21−3 (4), 647−661. (13) Wang, J. X.; Buckley, J. S.; Burke, N. E.; Creek, J. L. SPE Prod. Facil. 2004, 19, 152−160. (14) Gray, M. R.; Tykwinski, R. R.; Stryker, J. M.; Tan, X. Energy Fuels 2011, 25, 3125−3134. (15) Yarranton, H. W.; Alboudwarej, H.; Jakher, R. Ind. Eng. Chem. Res. 2000, 39, 2916−2924. (16) Qian, K.; Edwards, K. E.; Siskin, M.; Olmstead, W. N.; Mennito, A. S.; Dechert, G. J.; Hoosain, N. E. Energy Fuels 2007, 21, 1042− 1047. (17) Guzman, A.; Bueno, A.; Carbognani, L. Pet. Sci. Technol. 2009, 27, 801−816. (18) McKenna, A. M.; Blakney, G. T.; Xian, F.; Glaser, P. B.; Rodgers, R. P.; Marshall, A. G. Energy Fuels 2010, 24, 2939−2946. (19) Mullins, O. C.; Sabbah, H.; Eyssautier, J.; Pomerantz, A. E.; Barré, L.; Andrews, A.; Ruiz-Morales, Y.; Mostowfi, F.; McFarlane, R.; Goual, L.; Lepkowicz, R.; Cooper, T.; Orbulescu, J.; Leblanc, R. M.; Edwards, J.; Zare, R. N. Energy Fuels 2012, 26 (7), 3986−4003. (20) Moschopedis, S. E.; Fryer, J. F.; Speight, J. G. Fuel 1976, 55, 227−232. (21) Acevedo, S.; Gutierrez, L. B.; Negrin, G.; Pereira, J. C. Energy Fuels 2005, 19, 1548−1560. (22) Sztukowski, D. M.; Jafari, M.; Alboudwarej, H.; Yarranton, H. W. J. Colloid Interface Sci. 2003, 265 (1), 179−186. (23) Peramanu, S.; Pruden, B. B.; Rahimi, P. Ind. Eng. Chem. Res. 1999, 38, 3121−3130. (24) McKenna, A. M.; Donald, L. J.; Fitzsimmons, J. E.; Juyal, P.; Spicer, V.; Standing, K. G.; Marshall, A. G.; Rodgers, R. P. Energy Fuels 2013, 27 (3), 1246−1256. (25) Eyssautier, J.; Frot, D.; Barré, L. Langmuir 2012, 28, 11997− 12004. (26) Indo, K.; Ratulowski, J.; Dindoruk, B.; Gao, J.; Zuo, J.; Mullins, O. C. Energy Fuels 2009, 23, 4460−4469. (27) Amundarían, J. L.; Chodakowski, M.; Long, B.; Shaw, J. M. Energy Fuels 2011, 25 (11), 5100−5112. (28) Dechaine, G. P.; Gray, M. R. Energy Fuels 2011, 25, 509−523. (29) Verruto, V. J.; Kilpatrick, P. K. Energy Fuels 2007, 21, 1217− 1225. (30) Vargas, F. M.; Gonzalez, D. L.; Hirasaki, G. J.; Chapman, W. G. Energy Fuels 2009, 23 (3), 1140−1146. (31) Gonzalez, D. L.; Hirasaki, G. J.; Creek, J.; Chapman, W. G. Energy Fuels 2007, 21, 1231−1242. (32) Fussell, L. T. Soc. Pet. Eng. J. 1979, 203−208. (33) Hirschberg, A.; DeJong, L. N. J.; Schipper, B. A.; Meijer, J. G. SPE J. 1984, 283−293. (34) Kawanaka, S.; Park, S. J.; Mansoori, G. A. SPE Reservoir Eng. 1991, 185−192. (35) Wang, J. X.; Buckley, J. S. Energy Fuels 2001, 15 (5), 1004− 1012. (36) Alboudwarej, H.; Akbarzadeh, K.; Beck, I.; Svrcek, W. Y.; Yarranton, H. W. AIChE J. 2003, 49, 2948−2956. (37) Akbarzadeh, K.; Dhillon, A.; Svrcek, W. Y.; Yarranton, H. W. Energy Fuels 2004, 18, 1434−1441. (38) Manshad, A. K.; Edalat, M. Energy Fuels 2008, 22, 2678−2686. (39) Mitchell, D. L.; Speight, J. G. Energy Fuels 1973, 52, 149−152. (40) Agrawala, M.; Yarranton, H. W. Ind. Eng. Chem. Res. 2001, 40, 4664−4672.

CONCLUSION Asphaltenes were fractionated into solubility cuts (pairs of light and heavy fractions), and the molecular weight and density were measured for each cut. The asphaltenes were found to include both associated and non-associated asphaltenes. The proportion of non-associating species could not be determined precisely but was on the order of 10 wt % of the asphaltenes. The average molecular weights of the solubility cuts ranged from 1000 to 30 000 g/mol, equivalent to approximately 1−30 molecules per nanoaggregate. The apparent molecular weight of the associating material increased with the asphaltene concentration, while it was almost constant for non-associating asphaltenes. In contrast, the density increased from non-associating to associated asphaltenes but became almost constant across the mass fraction of associated asphaltenes. This observation suggests that asphaltene aggregates contain a variety of asphaltene species, which tends to average properties, such as density. The data were used to construct molecular weight and density distributions. The molecular weight data were fitted with a self-association model to predict the distributions at any given concentration. Then, the following guideline was developed to represent the combined distribution of nonassociated and associated asphaltenes with a Γ distribution function: minimum molecular weight = 900 g/mol, average molecular weight as measured or input, and α = 2.0. Finally, the density of asphaltene cuts was correlated to their molecular weight (as measured in toluene at 50 °C). This correlation fit the data more accurately (AAD of 11 kg/m3) than the previously used correlation (AAD of 36 kg/m3).

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ASSOCIATED CONTENT

* Supporting Information S

Molecular weight and density data provided for each sample. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: (403) 220-6529. Fax: (403) 282-3945. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The authors thank Shell Global Solutions for financial support and Zhongxin Huo and Frans van den Berg for their input.

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REFERENCES

(1) Mullins, O. C. SPE J. 2008, 13 (1), 48−57. (2) Sheu, E. Y. Energy Fuels 2002, 16, 74−82. (3) Macchietto, S.; Hewitt, G. F.; Coletti, F.; Crittenden, B. D.; Dugwell, D. R.; Galindo, A.; Jackson, G.; Kandiyoti, R.; Kazarian, S. G.; Luckham, P. F.; Matar, O. K.; Millan-Agorio, M.; Muller, E. A.; Paterson, W.; Pugh, S. J.; Richardson, S. M.; Wilson, D. I. Heat Transfer Eng. 2011, 32 (3−4), 197−215. (4) Hammami, A.; Phelps, C. H.; Monger-McClure, T.; Little, T. M. Energy Fuels 2000, 14 (1), 14−18. (5) Andersen, S. I. Energy Fuels 1999, 13, 315−322. (6) Wiehe, I. A.; Kennedy, R. J. Energy Fuels 2000, 14 (1), 56−59. (7) Yen, T. F.; Chilingarian, G. V. Asphaltenes and Asphalts, 1; Elsevier: Amsterdam, The Netherlands, 1994. 2486


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(41) Yarranton, H. W.; Fox, W. A.; Svrcek, W. Y. Can. J. Chem. Eng. 2007, 85, 635−642. (42) Okafor, J. Personal communication, University of Calgary, Calgary, Alberta, Canada, Dec 2012. (43) Sanchez, C. Personal communication, University of Calgary, Calgary, Alberta, Canada, Dec 2012. (44) Merino-Garcia, D.; Murgich, J.; Andersen, S. I. Petr. Sci. Technol. 2004, 22 (7 and 8), 735−758. (45) Riazi, M. R. Characterization and Properties of Petroleum Fractions; ASTM International: West Conshohocken, PA, 2006. (46) Whitson, C. H.; Brulé, M. R. Phase Behavior; Society of Petroleum Engineers, Inc.: Richardson, TX, 2000; Monograph Vol. 20, Henry L. Doherty Series.

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