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Effect of resins on asphaltene self-association and solubility.


Mineable oil sands and in situ heavy oil remaining reserves are estimated to be in the order of 5 and 23 billion cubic metres, respectively (Alberta Energy and Utilities Board, 2006). Current oil sands extraction and most heavy oil production processes use hot water and steam, respectively. However, the available water supply for oil sands operations has almost entirely been committed to current projects. The water supply for heavy oil projects is also limited and steam generation costs are a significant expense. Hence, there is a growing interest in solvent-based process alternatives such as VAPEX for heavy oil production and solvent-extraction for oil sands bitumen. Data on the phase behaviour and physical properties of heavy oil and solvent mixtures are required to develop, select, and optimize these potential processes. At first glance, heavy oil and solvents may seem an unusual topic with which to commemorate Jacob Masliyah, who is best known for his contributions to the optimization of the hot water extraction process. In fact, it is a testament to the breadth of Masliyah's work that one of the authors (Yarranton) started his research into bitumen-solvent systems under Masliyah's guidance.

Recent research in this area has focused largely on modelling asphaltene precipitation from mixtures of heavy oils and hydrocarbon solvents using either regular solution (Hirschberg et al., 1984; Griffith and Siegmund, 1985; Kawanaka et al., 1991; Yarranton and Masliyah, 1996; Andersen and Speight, 1999; Wang and Buckley, 2001; Alboudwarej et al., 2003; Akbarzadeh et al., 2005; Correra and Merino-Garcia, 2006) or equation of state models (Gupta, 1986; Nghiem and Coombe, 1997; Qin et al., 2000; Ting et al., 2003). In this study, the focus is on regular solution theory. Regular solution theory was first applied to asphaltene precipitation from crude oils by Hirschberg et al. (1984) and Griffith and Siegmund (1985), while Andersen and Speight (1999) used this approach for mixtures of asphaltenes, toluene, and heptane. Kawanaka et al. (1991) was the first to use a molar mass distribution for the asphaltenes. More recently, Yarranton and Masliyah (1996) modelled asphaltene precipitation in solvents by treating asphaltenes as a mixture of components of different density and molar mass. Alboudwarej et al. (2003) and Akbarzadeh et al. (2005) extended Yarranton and Masliyah's model to asphaltene precipitation from several different heavy oils and bitumens over a range of temperatures and pressures. Correra and Merino-Garcia (2006) confirmed that the regular solution model successfully fitted and predicted asphaltene precipitation from other crude oils as well.

While progress has been made, these and other recent models all contend with uncertainty in the fluid characterization. For example, in previous studies (Alboudwarej et al., 2003; Akbarzadeh et al., 2005), the heavy oil is divided into pseudo-components based on a SARA analysis; that is, saturates, aromatics, resins, and asphaltenes. The asphaltenes are treated as a mixture of self-associated species with a distribution of aggregation numbers or apparent molar mass. The average aggregation number of an isolated asphaltene fraction can be determined with vapour pressure osmometry (VPO). However, it has been shown that resins alter the aggregation of the asphaltenes (Speight, 1999; Yarranton et al., 2000); hence, the size distribution of the asphaltenes in a heavy oil is not the same as asphaltenes in a pure solvent. There is currently no established method for measuring the aggregation number of the asphaltenes in a heavy oil. In the model described above, the average aggregation number of the asphaltenes in the oil is used as a fitting parameter. A more predictive model could be constructed if the asphaltene aggregation number could be predetermined from the fluid characterization data.

Another model assumption is that resins can be characterized as a single, distinct pseudo-component. However, if resins participate in asphaltene self-association, a better approach may be to treat asphaltenes and resins as a single mixture of self-associated species. To date, this distinction has not been important because most studies have focused on asphaltene precipitation from heavy oils or bitumens diluted with n-pentane or higher carbon number n-alkanes. By definition, only asphaltenes are precipitated by these solvents. However, the lower carbon number n-alkanes generally precipitate a deeper cut of the heavy oil including components that are usually defined as resins. Hence, the model predictions are expected to be sensitive to the resin characterization. This issue is of current interest because the lower n-alkanes, such as propane, are potentially usable as the solvent for solvent-based recovery processes.

The objective of this study is to model the self-association and precipitation of asphaltenes and resins as a group. The self-association was assessed using VPO measurements of asphaltene and resin mixtures. A previously developed asphaltene self-association model (Agrawala and Yarranton, 2001) was adapted to fit and interpret the data. The output from the model is a molar mass distribution of the asphaltene-resin aggregates. Precipitation of asphaltenes and resins was measured in solutions of asphaltenes, resins, toluene, and heptane. The precipitation data was fitted using a modified version of a previously developed regular solution model (Akbarzadeh et al., 2005). The asphaltene-resin aggregate molar mass distribution is an input to the regular solution model.



Athabasca bitumen was obtained from Syncrude Canada Ltd. Toluene, n-heptane, n-pentane, and acetone were obtained from Aldrich Chemical Company and were 99%+ pure. Asphaltenes, saturates, aromatics and resins were extracted according to ASTM D2007M (Alboudwarej et al., 2002). The asphaltenes were "filter-washed" asphaltenes as defined by Alboudwarej et al. (2002). The composition of this Athabasca bitumen sample is 19.6 wt.% saturates, 45.4 wt.% aromatics, 16.4 wt.% resins, 16.9 wt.% asphaltenes, and 1.7 wt.% non-asphaltene solids.

Most asphaltene samples contain non-asphaltenic solids including sand, clay and adsorbed organics. To remove the solids, asphaltenes were dissolved in excess toluene and centrifuging for 5 min at 900 RCF. The supernatant was decanted and the solvent evaporated to recover "solids-free" asphaltenes. All experiments in this study were performed with solids-free asphaltenes. Note, a small quantify of fine solids may remain in these asphaltenes.

Molar Mass Measurements

Molar masses of the asphaltenes, resins, and their mixtures were measured using a Jupiter Model 833 vapour pressure osmometer, as described elsewhere (Yarranton et al., 2000). All measurements were made in toluene at 50[degrees]C. Asphaltenes self-associate and the apparent molar mass at any given concentration increases with decreasing temperature. Therefore, when the molar mass data was used as input to the regular solution model, the measured molar masses of self-associating mixtures were increased by 20% (Akbarzadeh et al., 2005) from the measured value to account for the change in molar mass between the vapour pressure osmometry (VPO) measurement at 50[degrees]C and the solubility experiments at 23[degrees]C. The molar mass measurements were repeatable to [+ or -] 800 g/mol.

Precipitation Measurements

Asphaltene precipitation and solubility measurements were performed gravimetrically in solutions of 10 kg/[m.sup.3] of asphaltenes in toluene and n-pentane. Resins were added if required to a specified mass ratio of asphaltenes-to-resins. All measurements unless otherwise indicated were taken at 23[degrees]C and atmospheric pressure. The solutions were sonicated for 45 min and left to settle for 24 h. Then the solutions were centrifuged at 3500 rpm (900 RCF) for 5 min. The supernatant was decanted and then approximately 30 [cm.sup.3] of the same solvent was added to the precipitate. The mixture was shaken for 5 min, sonicated for 15 min, and centrifuged for 5 min at 3500 rpm. Note, the supernatant was only slightly discoloured in all cases indicating that little if any asphaltenes and resins redissolved. The supernatant was decanted and the precipitate dried. Precipitation is reported on a fractional basis; that is, the mass of precipitate per total mass of asphaltenes plus resins. The precipitation data were repeatable to [+ or -] 0.03 w/w.



In the Agrawala and Yarranton (2001) model, asphaltenes are treated as molecules that contain active sites (heteroatoms or aromatic clusters) through which they can interact with other similar molecules to form aggregates. This van der Waals interaction is assumed to be analogous to polymerization even though the "bonding" forces are much weaker than for free-radical polymerization. Some molecules may have multiple sites that can link with other molecules and hence act as propagators in an oligomerization-like reaction. Other molecules may have a single active site and can be treated as terminators. Yet other molecules may be inert. Asphaltenes are assumed to consist mainly of propagators with a small proportion of terminators, while resins are assumed to consist mainly of terminators with a small proportion of propagators.

Recent experimental data supports an oligomerization-like model of asphaltene association. Calorimetery data (Merino-Garcia et al., 2004; Merino-Garcia and Andersen, 2005) have confirmed step-wise addition of asphaltenes and the measured heats of association and reaction constants are reasonably consistent with those predicted by the Agrawala and Yarranton model. Atomic force microscopy measurements of asphaltene aggregates pulled from mica surfaces appear to confirm linear oligimerization of asphaltenes (Long et al., 2006).

Single-End Termination Model

Agrawala and Yarranton (2001) proposed a linear oligomerization type scheme involving propagation and single-end termination, as follows:










where [[P.sub.1]] is the concentration of propagator monomers, [[P.sub.k]] is the concentration of propagator aggregates consisting of k monomers, [T] is the concentration of terminators, K is the association constant, and i is a "diminution" parameter that has a value between zero and unity. Propagator aggregates are free to react with monomers and grow larger. Aggregates containing a terminator are assumed to stop reacting. Only termination of one end of the "polymer" is considered.

In the original model (Alboudwarej et al., 2002), it was assumed that the association constant is the same for all "reactions"; that is, i = 1. This means that the probability of a propagator or terminator monomer forming a link with an aggregate was the same as that of forming a link with another monomer. In fact, structural effects may reduce the probability of monomers joining large aggregates. In the revised model shown above (Agrawala, 2001), the probability of a monomer joining a larger aggregate is monotonically decreased when the diminution parameter is set to less than unity.

The "reaction" schemes are solved in the same manner as a polymerization reaction; that is, with mass balance equations for both propagators and terminators, Equations (1) to (8). When i = 1, the equilibrium concentration of propagator monomers is given by:


and the equilibrium concentration of terminators is given by:

[T] = [[T].sub.0] (1 - K [P.sub.1]) (10)

where [[[P.sub.1]].sub.0] and [[T].sub.0] denote the initial mole fractions of propagators and terminators, respectively. When i < 1, the system of equations must be solved numerically. In either case, the molar mass distribution can be obtained from the mole fraction of each aggregate ([P.sub.k] from Equations (1) to (8)).

Double-End Termination Model

One of the more unrealistic assumptions in the above model is that an aggregate chain stops growing when a single terminator caps one end of the chain. Even with linear polymerization, the chain can continue to grow until capped at both ends. Therefore, the following reaction equations were added to the model:


Note, all of the proposed reaction schemes are almost certainly gross oversimplifications. The purpose here is to find a model that can adequately fit the molar mass and precipitation data.

Regular Solution Theory

Details of the regular solution theory model are given elsewhere (Alboudwarej et al., 2003; Akbarzadeh et al., 2005) and only a brief summary is provided here. A liquid-liquid equilibrium is assumed between the heavy liquid phase (asphaltene-rich phase including asphaltenes and resins) and the light liquid phase (solvent-rich phase including all components). The equilibrium ratio, [] hl, for any given component is given by:


where [x.sup.h.sub.i] and [x.sup.l.sub.i] are the heavy and light liquid phase mole fractions, R is the universal gas constant, T is temperature, [v.sub.i] and [[delta].sub.i] are the molar volume and solubility parameter of component i in either the light liquid phase (l) or the heavy liquid phase (h), and [v.sub.m] and [[delta].sub.m] are the molar volume and solubility parameter of either the light liquid phase or the heavy liquid phase. It was assumed that only asphaltenes and resins partitioned to the heavy phase. Once the equilibrium ratios are known the phase equilibrium is determined using standard techniques (Rijker and Heidemann,

1986; Alboudwarej et al., 2003).

To use this model, the mole fraction, molar volume, and solubility parameter of each component in the mixture must be specified. In this case, the mixture was divided into pure components (the solvents) and pseudo-components (the asphaltenes and resins). The properties of the pure components are known or can be determined using well-established techniques (Reid et al., 1989; Perry, 1997). The issue in this study is how best to describe the asphaltenes and resins.


Previous Asphaltene and Resin Characterization

The asphaltenes are assumed to be macromolecular aggregates of monodisperse asphaltene monomers. Therefore, the asphaltene fraction was divided into pseudo-components based on the aggregation number:

r = M/[M.sub.m] (13)

where r is the number of monomers in an aggregate, M is the molar mass of the aggregate (g/mol), and [M.sub.m] is the monomer molar mass of the asphaltenes. The gamma distribution function (Whitson, 1983), Equation (14), was used to describe the molar mass distribution of the aggregates:

f(M) = 1/[M.sub.m][GAMMA]([beta]) [[[beta]/([bar.r] -[r.sub.m]].sup.-[beta]] x [(r -[r.sub.m]).sup.[beta]-1] exp [[beta](r -[r.sub.m])/([bar.r] - [r.sub.m])] (14)

where [bar.r] is the average aggregation number and is given by M/[M.sub.m] and [bar.M] is the average molar mass of the self-associated asphaltenes. [beta] is a parameter that determines the shape of the distribution and is given by the following correlation for mixtures of asphaltenes in solvents:

[beta](T) = -0.0259 T + 10.178 T < 373 K (15)

where T is the temperature (Kelvin). As discussed elsewhere (Alboudwarej et al., 2003), the asphaltenes were discretized into 30 pseudo-components ranging up to 30 000 g/mol.

The molar volume and solubility parameter are required for each pseudo-component. The molar volume of an asphaltene pseudo-component was determined from the following correlation (Alboudwarej et al., 2003):

v = 1.493 [M.sup.0.9361] (16)

where [upsilon] is the asphaltene molar volume ([cm.sup.3]/mol). The molar mass of an asphaltene pseudo-component is the associated molar mass (r[M.sub.m]) of that pseudo-component as determined from the gamma distribution. The solubility parameter of the asphaltene pseudo-component was determined from the following correlation (Yarranton and Masliyah, 1996; Akbarzadeh et al., 2005):

[[delta].sub.a] = [(1000A(T) M/[upsilon]).sup.1/2] (17)


AT = 0.579 - 0.00075T (18)

and [[delta].sub.a] is the solubility parameter ([MPa.sup.0.5]) of asphaltenes and A is approximately equal to the monomer heat of vaporization (kJ/g). Note, Equation (18) has been modified slightly from previous work.

The resins were considered to be a single non-aggregating pseudo-component with a molar mass of 1000 g/mol. The molar volume and solubility parameter were also determined using Equations (16) and (17), respectively.

Proposed Asphaltene and Resin Characterization

An alternative approach is to model the resins and asphaltenes as a single distribution of aggregates. This distribution was estimated using two different methods. In the first case, the gamma function was used as before but with some adjustment to the monomer molar mass and the shape factor. In the second case, the distributions were obtained from the self-association model, discretized, and input directly into the regular solution model.



Figure 1 also shows the apparent molar mass of mixtures of 4:1, 2:1, and 1:2 mass ratios of asphaltenes-to-resins. As the proportion of resins increases, the apparent molar masses decreases. The decrease in average molar mass may simply be a result of averaging the asphaltene molar mass with a relatively low but constant resins molar mass. To test this hypothesis, the asphaltene molar mass data were fitted with an average molar mass was calculated for the mixtures assuming that the resin molar mass was constant at 1220 g/mol. The calculated molar masses are shown as dashed lines on Figure 1a. The averaging method does not fit the data well, consistently underpredicting the measured molar masses, particularly at a 4:1 ratio of asphaltenes-to-resins. An alternative explanation is that asphaltenes and resins both participate in self-association reactions.

Each self-association model was fitted to the "pure" asphaltene and "pure" resin molar mass data by adjusting the T/P ratio. An association constant of 130 000 was used in all cases and a variety of monomer molar masses in the range of 500 to 1500 g/mol were assumed for terminators and propagators. Neither the association model nor the regular solution model predictions were very sensitive to the choice of monomer molar masses. Nonetheless, better results were achieved with monomer molar masses of 750 and 1000 g/mol for terminators and propagators, respectively. Interestingly, these molar masses are similar to those of model compounds found to replicate many properties of resins and asphaltenes (Gray, 2006) and are near the values recently determined using low ionization mass spectrometry (Groenzin and Mullins, 1999; Kim et al., 2006). Although the resins are assumed to self-associate, their apparent molar mass reaches a plateau at concentrations below 2 kg/[m.sup.3]. Hence, the transition from monomers to aggregates cannot be detected with VPO.

Once the asphaltene and resin data were fitted, the number of terminators and propagators in the mixtures of asphaltenes and resins was calculated. The average molar masses of the aggregated mixtures were then predicted. In all cases, the models matched the data within experimental error of [+ or -] 800 g/mol, as shown in Figure 1b for the diminution model with i = 0.95. The fitted and calculated T/P ratios for the single termination, double termination, and diminution models are given in Table 1.

The VPO data are better fitted when the asphaltenes and resins are modelled as a single distribution of self-associating species rather than distinct fractions. However, the molar mass data is not sufficiently accurate to be used to distinguish one self-association model from another. The absolute average deviations, AAD, for each model are reported in Table 2.

The distribution of aggregate molar masses is required to model asphaltene and resin precipitation. The cumulative mass frequency distribution was fitted with a mathematical function and then discretized. The distributions predicted for "pure" asphaltenes at a concentration of 10 kg/[m.sup.3] at 23[degrees]C are shown in Figure 2. The gamma function distribution used in a previous study (Akbarzadeh et al., 2005) to model the solubility of these asphaltenes at 10 kg/[m.sup.3] at 23[degrees]C is shown for comparison. The distributions from the single and double termination models are broader than the gamma distribution. If a diminution parameter of 0.95 is used, the distribution from the self-association model matches the gamma distribution closely and hence is expected to provide the best predictions of asphaltene precipitation.


Figure 3 shows the fractional yield of precipitate from solutions of asphaltenes, 4:1, 2:1, and 1:2 asphaltenes-to-resins in toluene and n-pentane. Recall that resins are soluble in n-pentane (by definition, by separation method, and from solubility tests). As expected, the fractional precipitation decreases as the proportion of resins increases. However, for the 1:2 asphaltenes-to-resin mixture, asphaltenes make up 33% of the mixture and yet approximately 50% of the mixture precipitates. Hence, at least some resins become insoluble in n-pentane in the presence of asphaltenes. One possible explanation is that the resins associate with the asphaltenes.

To test this hypothesis, the data were fitted with the regular solution model with the following alternative assumptions:

1. asphaltenes and resins are separate fractions and only asphaltenes self-associate (old model), Figure 3a. The monomer molar mass of the asphaltenes and was set to 1000 g/mol and the average molar mass of the asphaltenes at 23[degrees]C was 6313 g/mol. The resin molar mass was set to 1000 g/mol and [beta] to 2.5;

2. asphaltenes and resins are a single distribution, represented by a gamma function, Figure 3b. The average molar mass was taken from VPO data corrected to 23[degrees]C, the monomer molar mass was set to 750 g/mol, and [beta] to 2.5;

3. asphaltenes and resins are a single distribution, represented by a gamma function using an average molar mass from VPO data corrected to 23[degrees]C and [beta] was adjusted to fit the data, Figure 3c.

Figure 3a shows that characterizing asphaltenes and resins as separate fractions resulted in a poorer fit as the proportion of resins increases. Note, no resins are predicted to precipitate at any of the conditions of this study. In fact, the most serious flaw with this approach is that it cannot be tuned to predict that resins, alone, will not precipitate in n-pentane but that resins can precipitate from a solution of asphaltenes, toluene, and n-pentane.

Figure 3b shows that when resins and asphaltenes are treated as a single distribution, resin precipitation can be predicted from solutions of asphaltenes, resins, toluene, and n-pentane. However, the results in Figure 3b also show that the model over predicts the fractional yield from the asphaltene-resin mixtures at high n-pentane volume fractions. In fact, some resins are predicted to precipitate in pure n-pentane. One possible explanation is that the shape of the distribution depends on the ratio of asphaltenes-to-resins (A:R). If wider distributions (smaller [beta]) occur at lower A:R ratios, then earlier onset of precipitation and lower ultimate yields can be expected. Figure 3c shows that the fit to the data can be improved if the shape factor of the distribution is adjusted ([beta] = 2.5, 1.5, 1.5, 1.25, and 1.25 for asphaltenes, 4:1 A:R, 2:1 A:R, 1:2 A:R, and resins, respectively). The onset of precipitation is fit quite well but the fractional yields at high n-pentane volume fractions are still over predicted.


Overall, the models that incorporate a combined distribution of asphaltenes and resins fit the data with approximately the same AAD's as the model that used separate fractions, Table 3. Only the grouped distribution models are capable of predicting that resins alone will not precipitate while resins with asphaltenes can precipitate. Hence, treating the asphaltenes and resins as a single distribution appears to be a viable approach for modelling both the molar mass and precipitation data. One significant challenge is that the model predictions are very sensitive to the shape of the molar mass distributions. One purpose of this study was to develop the self-association model to the point that it can be used to predict the molar mass distributions of mixtures of asphaltenes and resins, not just the average molar mass. These distributions could be input directly into the regular solution model and the gamma function and ? tuning would not be required. To test this approach, the precipitation data were remodelled with a single distribution of asphaltenes and resins predicted from the following self-association models:

1. single-end termination model, diminution parameter of unity;

2. double-end termination model, diminution parameter of unity;

3. single-end termination model with diminution parameter of 0.95.

Figure 4 compares the three model predictions for the fractional precipitation of asphaltenes from n-pentane. As anticipated from the molar mass distributions of Figure 2, the model with the diminution parameter of 0.95 provides the best fit. The predictions for the asphaltene-resin mixtures from the diminution model with i = 0.95 are shown in Figure 5. This model predicts the onsets of precipitation reasonably well except for the 1:2 R:A ratio. The ultimate yields are well matched except again for the 1:2 A:R ratio. Resins are predicted to be almost completely soluble in n-pentane. While not perfect, the predictions are considerably improved from those obtained with the gamma function, see also the AAD's in Table 4. Given the gross oversimplifications made in the self-association model and the sensitivity of the regular solution model to the shape of the asphaltene-resin molar mass distribution, the predictions are acceptable. It appears that the asphaltenes and resins are better characterized as a single distribution of self-associated species.


The molar mass of mixtures of asphaltenes and resin were measured in toluene at 50[degrees]C using VPO. The average apparent molar masses of mixtures of asphaltenes and resins were best fit when the asphaltenes and resins were modelled as mixture of self-associating species. The results suggest that resins participate in asphaltene self-association.

The predicted molar mass distributions of the aggregates were input into the regular solution model and used to predict the fractional yield of precipitate from mixtures of asphaltenes and resins in solutions of toluene and n-pentane. The model predictions were compared with experimental data and the fit to the data was improved from the case where asphaltenes and resins were treated as distinct fractions. However, the predictions deviated because the regular solution model predictions were sensitive to the shape of the asphaltene-resin molar mass distribution.

The data and modelling indicate that the asphaltenes and resins can best be characterized as a combined pseudo-component with a single molar mass distribution of the aggregated species. In this study, the best fits of average molar mass fractional precipitation were obtained with a "monomer" molar mass of 750 g/mol and with a decreasing probability of self-association for larger aggregates.





We thank our Consortium--Asphaltenes and Emulsions Research (C-AER) sponsors and in particular Shell International for financial support. We are also grateful to the Natural Sciences and Engineering Research Council (NSERC) for financial support and to Syncrude Canada Ltd. for providing the bitumen samples.

Manuscript received February 23, 2007; revised manuscript received April 18, 2007; accepted for publication June 4, 2007.


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Harvey W. Yarranton *, William A. Fox and William Y. Svrcek

Department of Chemical and Petroleum Engineering, University of Calgary, 2500 University Drive N.W., Calgary, AB, Canada, T2N 1N4

* Author to whom correspondence may be addressed. E-mail address:
Table 1. T/P Ratios used to model the VPO molar mass data

 Single-end Double-end Diminution

Asphaltenes (a) 0.18 0.33 0.13
4:1 A:R (b) 0.354 0.706 0.335
2:1 A:R (b) 0.495 1.07 0.487
1:2 A:R (b) 0.976 2.73 1.02
Resins (a) 1.8 20 2.0

(a)--fitted, (b)--calculated

Table 2. Comparison of AAD's (g/mol) for the average molar masses
of asphaltenes and resins predicted from averaging the resin and
asphaltene molar mass, and from the three self-association

 Averaging Single-end Double-end Diminution

Asphaltenes (a) 560 740 870 830
4:1 A: R (b) 574 300 200 200
2:1 A: R (b) 207 200 240 130
1:2 A: R (b) 411 230 30 260
Resins (a) 80 120 300 80

(a)--fitted, (b)--predictions

Table 3. Comparison of AAD's for the fractional precipitation of
asphaltenes and resins predicted with the regular solution model
using the gamma function and assuming asphaltenes and resins
are: (1) distinct fractions, (2) grouped, (3) grouped with a
modified shape factor

 Distinct Grouped Grouped modified

Asphaltenes 0.058 0.063 0.059
4:1 A:R 0.064 0.083 0.067
2:1 A:R 0.146 0.121 0.122
1:2 A:R 0.083 0.135 0.133

Table 4. Comparison of AAD's for the fractional precipitation of
asphaltenes and resins predicted with the regular solution model
using the molar mass distributions from: (1) the single-end
termination model, (2) the double-end termination model,
(3) the diminution model

 Single-end Double-end Diminution

Asphaltenes 0.120 0.140 0.154
4:1 A:R 0.009 0.016 0.015
2:1 A:R 0.070 0.094 0.064
1:2 A:R 0.066 0.059 0.073
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Author:Yarranton, Harvey W.; Fox, William A.; Svrcek, William Y.
Publication:Canadian Journal of Chemical Engineering
Date:Oct 1, 2007
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