Guide to Asphaltene Solubility - Energy & Fuels (ACS Publications)

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Guide to Asphaltene Solubility Paul C. Painter, Boris A. Veytsman, and Jack Youtcheff Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/ef502918t • Publication Date (Web): 28 Apr 2015 Downloaded from http://pubs.acs.org on April 29, 2015

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Guide to Asphaltene Solubility Paul Painter, Boris Veytsman† and Jack Youtcheff†† The EMS Energy Institute, The Pennsylvania State University, University Park, PA 16802. †

School of Systems Biology & Computational Materials Science Center, George Mason University, MS 6A12, Fairfax, VA 22030 ††

Turner Fairbanks Highway Research Center, McLean, VA 22101.

CORRESPONDING AUTHOR: Paul Painter AUTHOR EMAIL ADDRESS [email protected] ABSTRACT A guide to the solubility of asphaltenes in a range of solvents is constructed through the use of an association model to account for asphaltene nanoaggregation and its effect on phase behavior and Hildebrand solubility parameters to model interactions between aggregates and solvent. Solvents are classified according to their polarity and ability to self-associate (e.g., through hydrogen bonds). In addition, estimates of the contribution of free volume terms to interaction parameters indicate that a further distinction must be made between solvents with flexible molecules (such as the n-paraffins) and those that are relatively inflexible (such as toluene). A “bare” interaction parameter ( ) is calculated and it is this parameter that is related to Hildebrand solubility parameters. For non-polar and weakly polar solvents, a critical value of the

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solubility parameter difference ( ∆ ) between an asphaltene or asphaltene component and solvent is calculated to be ±3.5 MPa0.5 at 25˚C for a non-polar or weakly polar solvents with largely inflexible molecules and a molar volume of 100 cm3/mol. For flexible solvents such as the n-paraffins, free volume effects are larger and ∆ is about ±2.8 MPa0.5. For strongly polar solvents that have limited flexibility the equivalent critical value of the solubility parameter difference is also calculated to be ±2.8 MPa0.5. Hydrogen bonded solvents like methanol are calculated to be immiscible with asphaltenes, with miscibility being defined as forming a single phase across the composition range (at 25 ˚C). Miscibility maps are constructed in terms of the calculated phase boundary at the critical point, ± ∆ , where is the asphaltene component solubility parameter, plotted as a function of solvent molar volume. The solubility of asphaltenes and asphaltene components in various solvents is discussed. The solvent that defines asphaltene identity, toluene, is predicted to dissolve only a limited range of asphaltene components. This is consistent with various reported experimental observations. However, solubility is often defined in terms of an absence of a visible precipitate and based on recent work in the literature toluene solutions may contain some microphase-separated material stabilized against further aggregation by steric and kinetic factors.


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INTRODUCTION Solubility parameters have been widely used to model the solubility of asphaltenes.1-11 More than 40 years ago Mitchell and Speight1 obtained a correlation of asphaltene solubility (or lack thereof) to the Hildebrand solubility parameters of a set of (largely) hydrocarbon solvents. The excellent correlation they obtained was probably because they were using solubility parameters as they were originally intended – to describe non-polar or weakly polar interactions. However, many solvents used in asphaltene studies are strongly polar and/or hydrogen bond and it was recognized that a single component solubility parameter may not capture interactions in these solutions. Wiehe2,3 developed a two component solubility parameter approach, while other workers5-11 have used the three component model developed by Hansen.12 In recent work, Dechaine et al.13 and Nikooyeh and Shaw14,15 have cast serious doubts on the applicability of regular solution theory to asphaltene mixtures. They concluded that even when the Flory Huggins theory is used to account for size disparities between asphaltene and solvent molecules, solubility parameters do not provide a good description of interactions in these mixtures. As mentioned above, solubility parameters were originally developed to describe interactions involving dispersion and weak polar forces. Because of the assumptions made in relating solution and pure component properties, they do not apply to interactions that lead to association, such as hydrogen bonds and the more complicated collection of interactions that are probably central to asphaltene association.16 In addition, for mixtures where there are large disparities in thermal expansion coefficients there are free volume differences that contribute to the free energy of mixing.


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In a recent paper we have used an association model to account for the effect of asphaltene nanoaggregation on the free energy of mixing17 and subsequently expanded the treatment to also account for free volume effects18 using an approximation described by Graessely19 and Milner et al.20 This accounts at least in part for some of the problems in applying the Flory-Huggins theory to asphaltene mixtures referenced above and results in the definition of a bare χ parameter that is more appropriately related to solubility parameters. Here we will apply this approach to see if it is capable of providing a broad picture of asphaltene solubility. It is similar but not identical to the “rule of thumb” developed by Blanks and Prausnitz21 to describe polymer solubility. These authors used solubility parameters to estimate the enthalpic component of the Flory interaction parameter ( ) for a range of polymer solutions and found empirically that the entropic

component ( ) had an average value of 0.34. Earlier, Small22 had calculated a value for of

about 0.3. This led to the estimate that for a polymer to dissolve in a solvent, the solubility parameter difference between the two should be less than ±1 (cal/cm3)0.5. This is a result of using the critical value of = 0.5 for polymer solutions and applying: = + = 0.34 +

( − ) (1)

The quantity is the molar volume of the solvent and it was assumed that at 25 ˚C Vs/RT ~ 1/6 cm3/cal (the units these authors used). The solubility parameters and refer to the polymer

and solvent, respectively. The quantity is an effective interaction parameter and in this

empirical model is assumed to be independent of composition.


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As mentioned above, Graessley19 and Milner et al.20 have discussed and applied a simplified form of the equations describing the contribution of free volume effects to ( ). They demonstrated that the difference in thermal expansion coefficients between polymers and solvents gave a value of ~ 0.3, close to that determined by Blanks and Prausnitz21 and by Small.22 We will use this approach to estimate contribution of free volume effects to in

asphaltene solutions and use an association model to capture the effect of strong interactions that lead to the formation of identifiable associated species, both in asphaltenes and in strongly polar and hydrogen bonded solvents. This will allow us to calculate a “bare” parameter, which will be used to model the weaker interactions between associated asphaltene species and solvent molecules or their associated species. This bare parameter will be related to Hildebrand solubility parameters in order to determine if this approach provides a guide to the solubility of asphaltenes in a range of solvent types. In what follows we will first make some general points concerning the nature of asphaltene solutions and how we will define miscibility. We will then briefly review the effect of association on phase behavior, focusing on the critical value of the Flory parameter and its relationship to solubility parameters. Self-association of solvents through hydrogen bonding and strong dipolar interactions will also be treated. We will then provide visual guides to asphaltene solubility based on the model. THE MISCIBILITY OF ASPHALTENE SOLUTIONS It is now widely accepted that asphaltenes associate to form nanoscale aggregates, even in very dilute solutions of good solvents like toluene. However, experimental data describing the nature of the aggregates and the aggregation process remain open to interpretation and are the subject of


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various disagreements. One school of thought considers these nanoscale aggregates to be colloidal structures.23,24 A second view is that aggregation does not necessarily imply colloid formation and that a liquid/liquid phase separation can result in the formation of a solvent rich phase in equilibrium with asphaltene rich clusters.25-29 It has also been shown that the coalescence of nanoscale asphaltene particles into macroscopic phase separated domains can be limited by kinetic30-33 and steric factors.34,35 As this very limited citation of a very large literature suggests, asphaltene solutions and their phase behavior can be frustratingly difficult to describe unambiguously. In considering the literature on asphaltene aggregation, it is therefore important to clearly define what type of aggregates are being discussed. In some studies, particles in the size range 5–10 nm are referred to as both aggregates and nanoaggregates,36-38 which of course they are. However, in scattering work a clear distinction has been made between an initial, limited association to form nanoaggregates approximately 2–3 nm in size and a subsequent aggregation of these particles to form mass fractal clusters in the size range 5-10 nm.32-34,39-41 In keeping with this latter literature, we will refer to nanoaggregates as the smaller particles formed initially by the self-association of asphaltene molecules and refer to the larger aggregates of these particles as clusters. Following earlier work that applied an association model to asphaltene nanoaggregation by Yarranton et al.,27-29 we showed that the (attenuated) association of asphaltenes to form nanoaggregates has a significant effect on the critical value of an “effective” Flory interaction parameter (see below), such that phase separation occurs more readily (i.e., at lower temperatures) than in solutions of similar molecules that do not self-associate.17,18 On the basis of the calculation of spinodal and binodal phase boundaries, we argued that the aggregation of nanoaggregates to form clusters was a microphase separation process where the subsequent


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coalescence of these phase separated entities was inhibited by the kinetic and steric factors cited above. We will maintain that view here, but now turn to a discussion of a broad range of solvents. Solubility will depend upon concentration, so here we will define a miscible system as one that at a particular temperature or value of the Flory interaction parameter is single phase across the entire composition range. We will briefly expand on this before considering how we will use solubility parameters. THE CRITICAL VALUE OF As derived and discussed in our previous studies,17,18 the free energy of mixing (ΔG) asphaltenes with non-associating solvents is superficially in the form of a Flory-Huggins equation with additional terms to account for the association of asphaltene molecules to form nanoaggregates. The general form of the free energy per mole of lattice sites for mixing asphaltenes (A) with a second component (B) is given by: Δ ΔG =

=!

" "* ln&"' ⁄"' ) + +,"* # #* 3

" (/01 21' − 1) (/01 21' − 1) +. − + " "* 6 5 # 5 # (2) V is the total volume of the mixtures and the reference volume, Vref, is equal to the molar volume of a lattice site (equation (2) is derived using a Flory lattice model). VA and VB are the molar volumes of an (average) asphaltene molecule and the second component of the mixture,


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respectively. R and T have their usual definitions. Also, rA = VA/Vref and rB = VB/Vref. For asphaltene solutions we will initially put rB =1 and use the molar volume of the solvent to define the lattice cell size. This will bring up some subtleties in calculating the critical value of that

we will address later. The quantities "' and "' are the volume fractions of (unassociated)

asphaltene “monomer” molecules in the mixture and pure state, respectively, that are in equilibrium with associated i-mers. The volume fraction of asphaltene present in solution is " , while for a non-self associating solvent "* is the volume fraction of the second component of the

mixture. KA is the equilibrium constant describing the self-association of asphaltene molecules. We have shown previously that because asphaltenes associate strongly and KA is large, there is little variation in the degree of association and the calculated critical value of over a very wide range of KA values. Self-association of asphaltenes has a significant effect on calculated phase behavior.17,18 The critical value of the effective interaction parameter, ( )c, decreases from a value of about 0.92 (at 25 ˚C) for a non self-associating material whose molar volume and whose chemical character (i.e., solubility parameter) is the same as an asphaltene, to a value of about 0.64 in a solution of self-associating asphaltenes (calculated using a value of KA = 11000 and rA, the ratio of the molar volume of an individual asphaltene molecule to that of the solvent, equal to 8). In a corresponding fashion, self-associating solvents (such as those that hydrogen bond and to a lesser extent solvents that interact through strong dipolar forces) also have an effect on the critical value of . Simplistically, if the solvent self-associates, it is less likely to mix with asphaltenes that are also self-associating. This brings up the question of how we define a self-associating solvent.


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Solvents that hydrogen bond are easily identified through their well-known functional groups (e.g., hydroxyls) and equilibrium constants describing their association can be measured spectroscopically. Solvents with strong dipoles, such as n-methyl pyrrolidone (NMP), also associate to a measureable extent, but interactions in solvents with weaker dipoles can be insufficient to overcome thermal motion. Table 1 lists many of the solvents we will consider here (although common non-polar ones such as the alkanes are omitted). They are separated into four categories, separated by empty rows in the table, and listed roughly in order of increasing dipole moments. The first four solvents in the table can be considered to be weakly polar and all have dipole moments less than 1.15 D. Following Israelachvili,44 it can be shown that their interaction strength is less than kT at 25 ˚C and they do not self-associate to any measureable extent. Skipping the second set of solvents for now, the third set consists of solvents with strong dipoles that have measureable self-association constants. For example, acetone has a dipole moment of 2.69 D45 and Tiffon et al.46 used NMR to determine that this solvent weakly self-associates to form dimers with a self-association equilibrium constant of about 0.09 l mol-1. In terms of the dimensionless equilibrium constants we have used previously17,18 and will use below, this is equal to a value of about 1.2. Dipole moments alone cannot be used to determine self-association. For example, the four solvents segregated at the bottom of the table all form hydrogen bonded chains, but have dipole moments between 1 and 2 D. However, these liquids also have high dielectric constants, also listed in this table. We therefore somewhat arbitrarily define strongly polar solvents as those with larger dipole moments and/or higher dielectric constants than acetone. This leaves a group of solvents of “intermediate” polarity between those we have classified as “weakly” polar and “strongly” polar – the second group down in table 1. Solvents with intermediate polarity do not


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have measureable association constants, presumably because of the randomizing effect of thermal motion. For solvents that self-associate, the terms in the free energy for the second component of the mixture, B, also have to be expressed in terms of the equilibrium volume fraction of monomers found in the solution. The derivation of these expressions can be found in the literature42,43 and the form of the equations depends on the mode of association. So as not to clutter the main body of the paper with too many equations, these are provided as supplementary information. We will be calculating the critical value of using minima in plots of the spinodal, which for the general case is given by: 1 7"' 1 7"*' 7 (Δ ⁄) = − − 2 =0 # "' 7" #* "*' 7" 7" (3) In equation (3), "*' is the equilibrium volume fractions of (unassociated) solvent “monomer”

molecules in the mixture. For non self-associating solvents (e.g., toluene) "*' = "* . is the

term determined from the second derivative of the free energy. We are using a model where the interaction parameter is independent of concentration, so = = +

(4) The term accounts for free volume effects and a “bare” parameter, , is related to solubility parameters in the usual way:


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=

( − ) = (∆) (5)

The solubility parameters and refer to the asphaltene and solvent, respectively. We will be defining miscibility in terms of forming a single phase mixture across the composition range and therefore need to calculate

) for solutions of various types. The

self association of asphaltenes was modeled by assuming they have a molar volume of 800 cm3/mol and a self-association constant KA = 11000 (at 25˚C), as in previous work.17,18 The contribution of self-association of two polar solvents to the spinodals was calculated using KB values of 1.2 and 6 for acetone and NMP, respectively, thus covering the range for strongly polar solvents listed in table 1. For hydrogen bonding solvents, self-association is much stronger and KB values of 300, 200 and 60 for methanol, ethanol and 2-propanol were used. These values of the equilibrium constants were taken from the literature.46-53 Figure 1 shows spinodals plotted as calculated values vs. asphaltene concentration (volume fraction). Equation (3) and the stoichiometric equations given in supplementary materials were used to perform these calculations. It can be seen that for asphaltene solutions,

) is

reduced from a value near 0.65 for non-polar solvents to a value of about 0.45 in weakly selfassociating polar solvents such as acetone. These are the values at the minimum in the spinodal plot and any solution with a value of smaller than these respective values for non-polar and polar solvents will form a single phase across the composition range and be miscible in terms of the definition used here. The value of

) for somewhat more polar solvents such as NMP

is about 0.4, while in strongly hydrogen bonding polar solvents such as methanol the value of


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) is about 0.13. (Only the methanol curve is labeled in figure 1, because the spinodals for ethanol and 2-propanol lie very close to this curve.) In what follows, we will define three limiting conditions characterized by values of solvents,

) ~ 0.65 for non-polar or weakly polar

) ~ 0.45 for strongly polar but weakly associating solvents and

) ~ 0.13

for strongly self-associating (hydrogen bonding) solvents. This latter value is particularly small suggesting that once free volume effects are taken into account the model will predict that solvents such as methanol will be immiscible with asphaltenes. FREE VOLUME EFFECTS AND THE CRITICAL VALUE OF In order to calculate a critical value of the bare parameter, , from , the contribution of free volume ( ) needs to be estimated (equation 4). As described in our previous publication,

we used the approximation described by Graessley19 and Milner et al.20 This requires that we have values of the (liquid state) volumetric thermal expansion coefficient (9) of asphaltene, which are used to calculate a characteristic temperature, ∗ , as described previously.18 Here we will assume a value of 7.0 x 10-4 K-1. If we were to follow the methodology used to develop a “rule of thumb” solubility guide for polymers, described in the introduction to this paper, we would use an average value of characteristic temperatures, ∗ , for a number of solvents together

with the assumed value for asphaltenes to calculate an average value of . This is a very crude approach, because of the wide range of values that result (see below). However, using values of ∗ calculated from the thermal expansion coefficients listed by Graessely19 and other data in the literature,54 we found an interesting trend that we could use. Figure 2 shows values of

calculated for a range of solvents and color coded according to type. The red filled squares show the calculated values for the n-paraffins, while the blue filled squares show calculated values for


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more compact, less flexible or rigid molecules. Free volume is related to molecular dynamics and above the glass transition temperature involves coupled vibrational, rotational and translational motions of a molecule in a fluctuating cage of its neighbors. For a flexible molecule such as heptane, translational motion is in turn related to coupled bond rotations. The ends of even short chains have more freedom of motion than those segments in the middle of a chain. Accordingly, in the n-paraffins free volume decreases as chain length increases (fewer ends per unit volume) and the free volume difference between long chain paraffins and asphaltenes becomes less as chain length increases. As a result, the n-paraffins show a systematic decrease in on going from the smallest molecules to the largest. Similar arguments apply to other flexible molecules such as diethyl ether (open red squares in figure 2). Less flexible or rigid molecules such as methylene chloride and toluene also show a systematic decrease in free volume differences relative to asphaltene with increasing solvent molar volume. However, the calculated values are more scattered, in part because freedom of motion and hence free volume is influenced by other factors, such as intermolecular interactions. Nevertheless, figure 3 suggests that as a crude approximation we use values of calculated as a function of molar volume of the solvent, Vs. We used a linear fit to the data for less flexible or rigid molecules: = 0.466 − 0.00327 (6) All the polar, non-hydrogen bonding molecules considered here are included in this category. We used a second order polynomial for flexible molecules:


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= 0.82 − 0.0062 + 0.0000133 (7) Hydrogen-bonding solvents like ethanol and methanol have large calculated values of (see figure 2) and are considered separately. To illustrate the approach we are taking, calculated values of and were used to

determine spinodals plotted in terms of vs. composition. These were constructed for hypothetical non-associating solvents, polar but weakly associating solvents and hydrogen-

bonded solvents, as defined above, all assumed to have molar volumes of 100 cm3/mol. For selfassociating solvents, we considered two limiting cases, using self-association equilibrium constants characteristic of solvents like acetone at one extreme and those characteristic of strongly hydrogen bonding solvents like methanol at the other. A value of = 0.14 was used for both relatively inflexible non-polar and polar but non-hydrogen bonding solvents. A value of = 0.33 was used for both flexible non-polar solvents and hydrogen bonding solvents. The spinodals shown in figure 3 are then obtained. It can be seen that for non self-associating solvents the critical value of , , for asphaltene solutions has a value near 0.51 for molecules such as toluene, but is significantly smaller than this for solutions involving flexible molecules such as the n-alkanes, about 0.32. These values correspond to solubility parameter differences, ∆ , of about ±3.6 MPa0.5 and ±2.8 MPa0.5, respectively (at 25 ˚C). For weakly associating (but

strongly polar) solvents, the value of is about 0.31 and ∆ is ±2.8 Mpa0.5. The vs.

composition spinodal for hydrogen bonded solvents like methanol was determined to have minima at negative values. A negative value of the second derivative of the free energy means the system is grossly phase separated. Essentially, strongly hydrogen-bonding solvents such as


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methanol, ethanol, etc., are immiscible with asphaltenes. (Keep in mind that even in grossly phase-separated systems there are single-phase regions at the composition extremes.) Clearly, the calculated value of is significantly affected by , which in turn depends on the molar volume of the solvent. We will consider this in more detail below. ASPHALTENE SOLUBILITY PARAMETERS Given a value of we can calculate a critical value of the solubility parameter difference, ∆ .

Those asphaltenes within the range ± ∆ for a given asphaltene/solvent pair are then predicted to be miscible. For purposes of illustration and to preview what will be more complicated plots later, this is illustrated schematically in figure 4, with miscible and immiscible regions labeled. In order to construct a guide to solubility, we now need an estimate of asphaltene solubility parameters. However, unlike synthetic homopolymers, which have single, well-defined solubility parameters (even if they are not easy to determine), asphaltenes are a solubility class. Asphaltenes from different sources have different average solubility parameters and a given asphaltene has components that also span a range of values. We previously used an atomic group contribution method (using data from materials that do not self-associate strongly) to obtain a correlation of calculated average solubility parameters to H/C ratios,17,18 and determined average values for asphaltenes that ranged from ~ 20–25 MPa0.5. Most asphaltenes from bitumen and oils clustered between values of 20–24 MPa0.5, but there are a few calculated to have much higher average values.18 The part of the plot relevant to the work described here is reproduced in figure 5 for the convenience of the reader. Rogel55 also estimated the solubility parameter distribution of asphaltenes using an additive group method applied to a large number of hypothetical asphaltene molecules constructed to reflect known structural parameters. Rogels’s calculated average solubility parameters for individual asphaltenes are somewhat larger


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than what we calculate for the same samples, but there are doubtless uncertainties in both estimates and each calculate that most values lie between 20.0 and 25.0 MPa0.5. Even asphaltenes from a single, well-defined source encompass a broad range of materials and this will have to be taken into account when we discuss miscibility, but a rough estimate of the distribution of solubility parameter values within a given sample can be obtained from solvent fractional precipitation studies. For example, Yang et al.56 separated an asphaltene into six subfractions whose H/C ratios varied from about 1.3 to 1.1. On the basis of figure 5, this would suggest solubility parameter values ranging from about 20 to 22 MPa0.5. Kharrat57 obtained eight fractions of two Canadian heavy oils with H/C ratios ranging from 1.30 to 1.15 (suggesting varies from about 20.0 to 21.5 MPa0.5). Of course, each of these sub-fractions is no doubt also characterized by a distribution of values, albeit one that is narrower than the parent asphaltene. In this respect, Gawrys et al.58 attempted to obtain a better estimate of the statistical distribution of properties by separating three different asphaltenes into 20—30 fine fractions. Two asphaltenes with average H/C ratios near 1.2 consisted of sub-fractions with H/C ratios ranging from about 1.3 to 1.1, which according to figure 5 corresponds to values ranging from about 20 to 22 MPa0.5. An asphaltene with an average H/C ratio of 1.04 had sub-fractions with H/C ratios ranging from 1.2 to 0.97 ( ~21 to about 23-24 MPa0.5), but with the lower values H/C

asphaltenes (higher ) more heavily weighted. This latter sample appeared to have a bimodal

distribution of H/C ratios, while the other two had close to a Gaussian distribution about the mean. All suggest solubility parameter values that cover a range of at least 2 MPa0.5. GUIDE TO ASPHALTENE SOLUBILITY – NON-POLAR AND WEAKLY POLAR SOLVENTS


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Hildebrand solubility parameters were originally formulated to deal with dispersion or weakly polar interactions, so we will first consider solvents that are non-polar or only weakly polar. We would also reemphasize that because we will be using the critical value of the solubility parameter difference, our guide to solubility is based on whether or not an asphaltene is miscible with a given solvent across the entire composition range. This sounds straightforward, but as mentioned above asphaltene solubility is not easy to characterize unambiguously. Neglecting such complications for now, we have constructed visual guides to solubility, miscibility maps, using plots of ± ∆ vs. solvent molar volume. For non-polar and weakly polar solvents (i.e.,

non-associating) we used ~ 0.51 (figure 3), resulting in a “miscibility window” or “miscibility

band” of ∆ ±3.6 MPa0.5 at 25˚C for a hypothetical solvent consisting of relatively inflexible molecules having a molar volume of 100 cm3/mol. However, we are considering a range of solvents whose molar volumes vary by more than a factor of two and this affects the free energy. Variations in solvent molar volume can be accounted for in two different ways. We could define an arbitrary lattice cell size (recall that we are using a Flory type lattice model), say in terms of the smallest solvent considered, such that larger solvents then consist of segments defined by the molar volume of this solvent. Alternatively, we can calculate

) as a function of solvent

molar volume then simply calculate the critical value of the solubility parameter difference, ∆ , which normalizes for the effect of molar volume differences through the Vs/RT term in equation 5. We used this latter approach, because we calculate parameters such as using equations defined in terms of individual solvent molar volumes. Hildebrand solubility parameter values for selected solvents (as compiled from various sources by Yaws59) are plotted as a function of their molar volume in figure 6. Those that interact largely


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through dispersion and weak polar forces are shown as filled circles. The solvents that we identify as on the borderline in terms of polarity (i.e., polar but probably not self-associating) are identified separately on this plot as open squares. These values would be subject to larger errors. The lower miscibility limit (corresponding to − ∆ in figure 4) for asphaltenes having a

solubility parameter of = 20 MPa0.5 was then calculated and is also plotted in figure 6. The

+ ∆ curve (c.f. figure 4) is off the scale of the plot. To construct this plot, values of

)

and (equation 6) were calculated as a function of solvent molar volume, Vs, then in turn and ∆ (at 25 ˚C).

It can be seen that many of the solvents considered here are predicted to be miscible with asphaltene components having solubility parameters near 20 MPa0.5 – they lie above the lower miscibility limit curve and within the miscibility band defined by ± ∆. The n-alkanes and one or two other solvents with solubility parameter values less than about 16 MPa0.5 lie below the curve and are calculated to be immiscible. The calculated lower miscibility limit moves to higher solubility parameter values as the assumed value of the asphaltene solubility parameter increases. Figure 7 shows a busier plot using five assumed values of between 20 MPa0.5 and 24 MPa0.5. It can be seen that only a few of the solvents considered here, namely pyridine, quinolone, o-dichlorobenzene and carbon disulfide, are predicted to be miscible with asphaltene fractions having calculated solubility parameters of 24 MPa0.5 or less. Other solvents that are considered to be “good” for asphaltenes, such as methylene chloride (dichloromethane) are predicted to form miscible mixtures with asphaltene components that have smaller values of , which for methylene chloride is less than about 23.6 MPa0.5. Benzene, THF and chloroform are predicted to dissolve asphaltene or


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asphaltene components with solubility parameters less than about 22.5 MPa0.5. The experimental observation of solubility will therefore depend on the composition of the asphaltene being considered, its solubility parameter spectrum and also the concentration of the solutions being considered. Asphaltenes with average H/C ratios near 1.2 considered by Gawrys et al.,58 for example, with fractions calculated to span the solubility parameter range from 20 to 22 MPa0.5, are predicted to be miscible with these solvents, while the asphaltene with an average H/C ratio of 1.04 and hence components with solubility parameters calculated in the range 22–23 MPa0.5 would have an insoluble fraction. Intriguingly, the solvent that defines the identity of asphaltenes, toluene, is calculated to be on the edge of miscibility with asphaltenes or asphaltene components that have solubility parameters of about 21.7 MPa0.5 and immiscible with asphaltene components that have solubility parameters larger than this value. In this regards, Gutierrez et al.60 reported that an asphaltene fraction with an H/C ratio of ~0.9, hence an estimated solubility parameter of about 25 MPa0.5, was only sparingly soluble in toluene, consistent with the results displayed in figure 7. Wiehe61, Acevedo et al.9 and Sato et al.10 have reported solubility data for asphaltenes and asphaltene fractions in a range of solvents. Acevedo et al.9 studied an asphaltene from Hamaca oil with an H/C ratio ~1.13, which on the basis of the correlation shown in figure 5 suggests an average solubility parameter of about 21.5 MPa0.5. Assuming a range of values around this average, figure 7 suggests that toluene and xylene may not dissolve some components. In earlier work, Sato et al.10 also reported that asphaltenes with H/C ratios of 1.01 and 1.05, which according to our calculations would have components with solubility parameters larger than 22 MPa0.5. These asphaltenes were also reported to be soluble in toluene. However, two things need to be kept in mind. The first factor is concentration. Many solubility studies are conducted in


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dilute solutions. The volume fraction of asphaltene at the critical point is about 0.14 and the critical point defines our calculations of miscibility. The solubility studies reported by Acevedo et al.9 were based on the visual identification of the solvents ability to dissolve 5% or more of the asphaltene (volume fraction ~0.042). At these lower concentrations the value of ∆ at the phase boundary will be larger. Sato et al.10 used dynamic light scattering to determine solubility and this technique required the use of much more dilute solutions, 1 g/L (volume fraction asphaltene a bit less than 0.001). According to the binodal presented in our previous study,18 at this concentration ∆ has a value of 4.6 MPa0.5 and miscibility with asphaltene components with solubility parameter values less than about 22.8 MPa0.5 are predicted. Accordingly, at these concentrations toluene would be miscible with a broader range of asphaltene fractions than those indicated in figure 7. Nevertheless, on the basis of the calculations presented here we would have anticipated the detection of at least some phase-separated material for those asphaltenes with H/C values ~1.0. Leaving aside toluene solutions for now, the solubility guide shown in figure 7 is broadly consistent with the results of Acevedo et al.9 and Sato et al.10 Ethyl acetate, for example, was found to be a “borderline” solvent by Acevedo et al.9 Figure 6 indicates that this solvent will only dissolve components with calculated solubility parameters less than 22 MPa0.5. Benzene and methylene chloride were found to be good solvents by these authors, but Sato et al.10 found these solvents dissolved one asphaltene, but were poor solvents for another. This latter sample had an average H/C ratio of 1.01 and hence probably had components with solubility parameter values greater than ~22.5 MPa0.5. Both asphaltenes were found to be soluble in carbon disulfide, however, which is in agreement with the miscibility guide shown in figure 7, provided that the


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asphaltene components with a low H/C ratio have solubility parameters that are less than about 24.3 MPa0.5. Toluene remains an apparent anomaly and this brings up the second factor – what is the nature of a single-phase or miscible asphaltene solution? Yarranton et al.62 recently reported a multilaboratory study that applied a broad range of analytical techniques to a single source asphaltene. Vapor pressure osmometry (VPO) measurements indicated “monomer” asphaltene molecular weights of the order of 850 g/mol, with nanoaggregates having a number average molecular weight less than 10,000. On the other hand, small angle X-ray scattering (SAXS) data indicated weight average molecular weights twenty times higher than this. The authors discussed a number of possible reasons for this result, including the formation of flocs of nanoaggregates, which would not be detected by VPO measurements but would significantly affect SAXS measurements. The authors suggested that the aggregation of nanoaggregates to form clusters or larger flocs could be a manifestation of a phase change and the results of applying our attenuated association model suggest the same thing.18 If clusters are stabilized against further coalescence by steric and kinetic factors, as mentioned above, then visual or other macroscopic determinations of solubility would not necessarily indicate the presence of a thermodynamic, single-phase solution. In this regard, the presence of fractal clusters would be a better guide. Eyssautier et al.39-41 have applied various scattering techniques to toluene solutions of an asphaltene with a H/C atomic ratio near 1.1. According to figure 5, this asphaltene would have at least some components with a solubility parameter in excess of 22 MPa0.5 and there would be asphaltene components that would undergo a microphase separation to form clusters. Similarly, the scattering work of Hoepfner et al.32-34 used solutions of asphaltenes with H/C rations close to 1.0.63 According to our calculations, these asphaltenes would have even larger solubility


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parameter values, near 24 MPa0.5. Both groups reported that the asphaltenes were present as fractal clusters and interpreted their results in terms of a clustering of nanoaggregates. An intriguing question is whether or not the steric factors35 that apparently stabilize toluene dispersions against further aggregation occur in solutions involving other “good” solvents (e.g., pyridine) or are perhaps unique to toluene as a result of asphaltene aggregate structure and the nature of surfaces that are exposed to solvent. The miscibility guide shown in figure 7 also suggests an explanation for the variation in molecular weight determined by VPO measurements using different solvents. Yarranton et al.,27 for example, found that the degree of association of Athabasca and Cold Lake asphaltenes was less in o-dichlorobenzene than in toluene. Acevedo et al.64 found that the extrapolated value of asphaltene molecular weights determined by VPO was also lower in o-dichlorobenzene than in toluene (and also in nitrobenzene, considered in the next section). One explanation for this would be a dependence of the association constant KA on solvent. However, we have shown that except at very low concentrations, large changes in KA do not result in large variations in the degree of association or the critical value of .18 Of course, molecular weight measurements are made in dilute solutions, but the results presented here suggest another possibility. If there are some asphaltene components present with low H/C ratios and hence high solubility parameters, larger than ~22–23 MPa0.5, these could phase separate into clusters in toluene, thus influencing the measured molecular weight. Depending on concentration, such material could persist to very low concentrations (see calculated binodals in reference 18). However, in solvents with a higher solubility parameter value than toluene, such as dichlorobenzene, there could be fewer clusters or even none. We suggest that a crucial part of such experiments in the future would be the


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determination of atomic H/C ratios to at least get an indication of which solvents are least likely to give anomalous results as a result of cluster formation. Finally, it is interesting that the model also predicts that cyclic paraffins such as cyclohexane are better solvents than the n-alkanes and will dissolve asphaltene fractions that are characterized by solubility parameters in the range 20-21 MPa0.5. This result is consistent with the results of Schabron and Rovani,65 who found that about 40% of the heptane asphaltenes from unpyrolized residua were soluble in this solvent. GUIDE TO ASPHALTENE SOLUBILITY – STRONGLY POLAR AND HYDROGEN BONDING SOLVENTS. We will now consider solvents that are polar to the extent that they have a measureable degree of association, where we would anticipate that there would be larger errors in the use of Hildebrand solubility parameters. However, some systems with strong dipole moments only show small deviations in experimental estimates of interaction parameters (based on miscibility) from those calculated using solubility parameters.66 But there is a notable exception. Hildebrand and Scott67 noted that molecules with “dipoles capable of forming hydrogen bonds or bridges - - - - are so exceptional in their behavior as to require separate consideration.” We can do no less and we will deal with solvents like methanol as a separate class. We will use an approach applied to studies of the miscibility of polymer blends68,69 and also the swelling of coal.70 In this work, group contributions were determined using data from molecules that do not hydrogen bond (but included many weakly polar solvents), both in terms of functional group68,69 and atomic group contributions.70 The latter was used to calculate the solubility parameters for asphaltenes shown in figure 5, while the former was used to calculate non-associating solubility parameters for the


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hydrogen bonded solvents shown in table 1. These values are reported in parentheses next to the values determined from heats of vaporization. Errors are no doubt significant, but the difference is extremely large, 15.0 MPa0.5 vs. 29.7 MPa0.5 for methanol, for example. If we use the same approach68,69 to calculate solubility parameters for polar molecules like acetone and acetonitrile, the differences are relatively small, 19.2 MPa0.5 vs. 20.1 MPa0.5 for acetone and 23.8 MPa0.5 vs. 24.3 MPa0.5 for acetonitrile. Hildebrand solubility parameter values may therefore be somewhat larger than non-associating values for polar but non-hydrogen bonding solvents, but given that errors and uncertainties that also surround the use of functional group contributions, we decided to use the Hildebrand values. However, the conclusion of Hildebrand and Scott67 that hydrogen bonded systems must be handled differently is in our view appropriate. Fortunately, because they were determined to be immiscible with asphaltenes just on the basis of calculations of , there

is no need to try and calculate ∆ for these solvents. As for non-polar solvents, values of

) and (equation 6) were calculated, then in turn

and ∆ (at 25 ˚C), all as a function of solvent molar volume, Vs. Values of ± ∆ were

then determined using assumed values of the asphaltene solubility parameter, , in the range

20–24 MPa0.5. A miscibility map for an assume value of = 20 MPa0.5 is shown in figure 8 superimposed on a plot of solvent Hildebrand solubility parameters plotted as a function of solvent molar volume. Solubility parameters for strongly polar (but non hydrogen-bonding) solvents are shown as filled red squares. Because the solvents self-associate,

) is now

smaller and there is a much narrower “miscibility band” (defined by ± ∆ ) than for nonpolar or weakly polar solvents. Accordingly, both the lower and upper miscibility limits are shown in the plot. It can be seen that for asphaltene components with the lowest calculated solubility parameters (~20 MPa0.5), a number of polar solvents are predicted to be miscible, but


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some strongly polar solvents like n-methyl pyrrolidone (NMP) and dimethyl formamide (DMF), are not, with solubility parameter values that lie above the upper miscibility boundary. Nitrobenzene also lies very close to this upper boundary. A similar figure calculated using = 24 MPa0.5 is shown in figure 9. Strongly polar solvents

like NMP and DMF now lie within the miscibility band. Plots for other assumed values of in

the range 21-23 MPa0.5 are provided as supplementary information. Only two strongly polar solvents are predicted to form miscible mixtures with all asphaltene components with calculated solubility parameters in the range 20–24 MPa0.5. These are nitrobenzene and dimethyl acetamide (DMAC). Cyclohexanone is predicted to form miscible mixtures with asphaltene components with solubility parameters in the range 20–23 MPa0.5, while NMP (n-methyl pyrrolidone) and DMF (dimethyl formamide) are predicted be immiscible with asphaltene components that have solubility parameter values less than about 21 MPa0.5, but form miscible mixtures with asphaltene components that have a higher range of values (21–24 MPa0.5). These higher solubility parameter asphaltene components are presumably more polar. Acetone is predicted to be not quite as good a solvent as cyclohexanone, in the sense that only those asphaltene components with solubility parameters smaller than 22.5 MPa0.5 are predicted to be miscible. DMAC was not considered by Acevedo et al.,9 but cyclohexanone was identified as a good solvent for the asphaltene they studied, as was nitrobenzene. Acetone was not. Sato et al.10 did not consider DMAC or cyclohexanone, but identified nitrobenzene and acetone as poor solvents. However, it can be seen from figure 7 that nitrobenzene is very close to the upper phase boundary for asphaltene fractions with solubility parameters near 20 MPa0.5. Given the errors and


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assumptions that have gone into this guide, this solvent could easily lie on the other side of this line, so that in general this miscibility map is consistent with experimental observations. NMP is an interesting case. This solvent is predicted to form miscible mixtures with asphaltene fractions that have solubility parameters greater than about 21 MPa0.5. Those with smaller values than this are predicted to phase separate. Both Morgan et al.70 and Ascanius et al.71 have shown that the asphaltenes they studied have both NMP soluble and insoluble components, but there did not seem to be any large difference in the structural parameters of the soluble and insoluble fractions. However, Daaou et al.,72,73 used extraction and precipitation experiments with solvents of systematically varying polarity and showed that the most polar fraction of the asphaltenes that they studied were soluble in NMP, but insoluble in mildly polar or non-polar solvents. This is consistent with the miscibility guides shown in figures 6-8. Also shown in figure 8 and 9, for completeness, are two solvents that we identified as being polar but probably not self-associating, pyridine and quinoline. They were included because even with the more limited miscibility windows that are a result of solvent self-association, these solvents are still predicted to dissolve asphaltene components having calculated solubility parameters across the 20–24 MPa0.5 range. Overall, our calculations suggest that these are the best solvents for a wide range of asphaltenes. Turning to hydrogen-bonding solvents, methanol has often been used in mixed solvents in order to dissolve polar species. However, on the basis of the calculations presented here methanol is predicted to be a very poor solvent and immiscible with asphaltenes. Andersen74 examined the extraction of asphaltenes from a crude oil using methanol/toluene mixtures. Methanol alone did not extract any asphaltenes (but did dissolve a large fraction of the crude oil). Significant


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quantities were obtained only when toluene concentrations in mixed toluene/methanol solvents exceeded 60%. This also impacts the results of time-of-flight mass spectrometry (TOF-MS) studies of asphaltenes, where 50/50 toluene/methanol solutions have been used. In their study of asphaltene aggregation, for example, McKenna et al.75 noted that the use of such mixed solvents can destabilize asphaltene solutions. Nevertheless, they determined that at very low concentrations (up to 500 ng/ml) asphaltenes are largely unassociated or weakly associated. This is consistent with calculations of the degree of association calculated in our previous studies.17,18 We also determined that for asphaltenes mixed with non-polar/weakly polar solvents, the phase diagram is skewed, closely approaching the pure solvent composition limit. We have not calculated binodals for asphaltene/methanol mixtures, but the spinodal shown in figure 4 indicates that the same behavior must hold. So, in extremely dilute solutions one could get a single-phase solution, but phase separation into (very) dilute and concentrated phases at higher concentrations would occur upon crossing the phase boundary. TOF-MS spectra would then show at least a bimodal distribution. At concentrations of 500 µg/ml McKenna et al.74 observed a multimodal distribution, with monomers and dimers together with a broad aggregate peak centered near m/z values of 9500, but extending up to m/z values near 25,000. We suggest that monomers and dimers are in the dilute phase, while the more concentrated phase is a mixture of soluble nano-aggregates and clusters of microphase-separated material. CONCLUSIONS Asphaltene solubility is a complicated business. The material is heterogeneous and samples obtained from different sources can have very different average solubility parameters. Individual asphaltenes contain components that span a range of values. In this paper we have defined miscibility in terms of forming a single-phase system across the composition range. This allows


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the calculation of “miscibility maps” based on the critical value of the solubility parameter difference between asphaltenes or asphaltene components and a range of solvents. The critical factors that affect asphaltene and asphaltene component miscibility with a particular solvent are the self-association of the asphaltene; the degree of self-association of strongly polar and hydrogen-bonding solvents; free volume differences between asphaltene components and solvents. Free volume differences depend on both solvent molar volumes and the flexibility of the solvent molecules. Strongly self-associating solvents like methanol are predicted to be immiscible with asphaltenes. For weakly self-associating polar solvents, a particular solvent may be “good” for asphaltenes with one distribution of solubility parameter values, but poor for one with a different average value and distribution. The best solvents overall appears to be pyridine and quinoline. The solvent that defines asphaltene identity, toluene, only dissolves asphaltene components with calculated solubility parameters less than about 21.7 MPa at the critical point, but would dissolve components with higher solubility parameters in dilute solutions, where many experimental studies are performed. However, solubility is often (but not always) measured in terms of an absence of a visible precipitate. Based on recent work in the literature, toluene solutions may contain some microphase-separated material stabilized against further aggregation by steric and kinetic factors. They would thus be a complex mixture of dissolved nanoaggregates and a dispersed phase. ACKNOWLEDGEMENT The authors gratefully acknowledge the support of the Federal Highway Administration under Subcontract SES#12-01 SUPPORTING INFORMATION


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51. Dyrkacs, G. Energy Fuels 2001, 15, 918-929. 52. Letcher, T. M.; Naicker, P.K. J. Chem. Thermodynamics 1999, 31, 1585-1595. 53. Shikata, T.; Sugimoto, N. J. Phys. Chem. A 2012, 116, 990-999. 54. Data has been published on-line at http://www.scribd.com/doc/184781900/Coefficient-ofThermal-Expansion-of-Liquid. 55. Rogel, E. Energy Fuels 1997, 11, 920-925. 56. Yang, X.; Hamza, H.; Czarnecki, J. Energy Fuels 2004, 18, 770-777. 57. Kharrat, A. M. Energy Fuels 2009, 23, 828-834. 58. Gawrys, K. L.; Blankenship, G. A.; Kilpatrick, P. K. Energy Fuels 2006, 20, 705-714. 59. Yaws, C. L. Thermophysical Properties of Chemicals and Hydrocarbons. William Andrews Inc., Norwich, NY. 2008. 60. Gutierrez, L. B.; Ranaudo, M. A., Mendez, B.; Acevedo, S. Energy Fuels 2001, 15, 624-628. 61. Wiehe, I. A.; Fuel Sci. and Tech. Int. 1996, 14, 289-312. 62. Yarranton, H. W.; Ortiz, D. P.; Barrera, D. M.; Baydak, E. N.; Barre, L.; Frot, D.; Eyssautier, J.; Zeng, H.; Xu, Z.; Dechaine, G.; Becerra, M.; Shaw, J. M.; McKenna, A. M.; Mapolelo, M. M.; Bohne, C.; Yang, Z.; Oake, J. Energy Fuels 2013, 27, 5083-5106. 63. Hoepfner, M. P. Investigations into Asphaltene Deposition, Stability, and Structure. PhD Thesis, University of Michigan, 2013. 64. Acevedo, S.; Guzman, K.; Ocanto, O. Energy Fuels 2010, 24, 1809-1812.


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65. Schabron, J. F.; Rovani Jr. J. F. Fuel 2008, 87, 165-176. 66. Zhu, S.; Paul. D. R. Macromolecules 2002, 35, 8227-8238. 67. Hildebrand, J; Scott, R. The Solubility of Non-electrolytes, 3rd edition, Reinhold, N.Y., 1950. 68. Coleman, M. M.; Serman, C. J.; Bhagwagar, D. E.; Painter, P. C. Polymer 1990, 31, 11871203. 69. Coleman, M. M.; Graf, J. F.; Painter, P. C. Specific Interactions and the Miscibility of Polymer Blends; Technomic Publishing: Lancaster, PA, 1991. 70. Painter, P. C.; Graf, J.; Coleman, M. M. Energy Fuels 1990, 4, 379-384. 71. Morgan, T. J.; Alvarez-Rodrigues, P.; George, A.; Herod, A. A.; Kandiyoti, R. Energy Fuels 2010, 24, 3977-3989. 72. Ascanius, B. E.; Garcia, D. M.; Andersen, S. I. Energy Fuels 2004, 18, 1827-1831. 73. Daaou, M.; Modarressi, A.; Bendedouche, D.; Bouhadda, Y.; Krier, G.; Rogalski, M. Energy Fuels 2008, 22, 3134-3142. 74. Daaou, M.; Bendedouche, D.; Modarressi, A.; Rogalski, M. Energy Fuels 2012, 26, 56725678. 75. Andersen, S. I. Pet. Sci. Tech. 1997, 15, 185-198. 76. 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, 1246–1256.


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Table 1: Solvent Properties. DM is the dipole moment; DC is the dielectric constant; is the

Hildebrand solubility parameter; > is the non-associating solubility parameter (see text).

SOLVENT

Vs

DM

cc/mol

(D)

106.9

0.31

1-Methyl naphthalene (MeN)

142

0.51

Trichloroethylene (TCE)

90

0.81

3.42

19.0

Methylene chloride (MeCl2)

63.9

1.14

8.93

20.4

Diethyl ether

105

1.15

4.33

15.5

Tetrahydrofuran (THF)

81.9

1.75

7.58

18.7

Ethyl Acetate (EA)

98.2

1.88

6.02

18.4

n-Propyl bromide (n-PB)

85.7

2.12

8.44

18.1

o-Dichlorobenzene

112.6

2.14

9.13

20.3

Quinoline

118.5

2.25

9

21.9

Pyridine

80.5

2.37

12.4

21.8

Acetone

73.4

2.69

20.7

20.1

Methyl ethyl ketone (MEK)

89.6

2.76

18.51

19.0

Cyclohexanone

103.5

3.06

18.2

20.2

Acetonitrile

52.1

3.44

24.3

Dimethyl acetamide (DMAC)

92.7

3.72

22.4

Dimethyl formamide (DMF)

77.8

3.86

24.0

n-Methyl pyrrolidone (NMP)

96.2

4.09

32.2

22.9

Dimethyl Sulfoxide (DMSO)

71.4

4.1

46.68

26.3

Nitrobenzene

102.9

4.28

34.8

22.6

Methylamine

44.7

1.33

11.4

23.1 (13.8)

Methanol

40.5

2.87

32.7

29.7 (15.0)

Ethanol

58.4

1.66

24.55

26.2 (15.3)

Toluene


DC

δH MPa0.5

2.38

18.2 20.5

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Energy & Fuels

Figure 1: Calculated spinodals plotted as vs. the volume fraction of asphaltenes for non-

associating solvents, weakly associating polar solvents and strongly hydrogen bonding polar solvents.


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Figure 2: The calculated value of for various asphaltene/solvent pairs plotted as a function of the molar volume of the solvent. Red data points are the n-paraffins and flexible molecules; blue data points, solvents with limited flexibility. (1-MeN = 1-methyl naphthalene; MeCl2 = methylene chloride; MeCN = acetonitrile; MEK = methyl ethyl ketone.)


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Energy & Fuels

Figure 3: Spinodals calculated as plots of the bare parameter, vs. asphaltene concentration. The two curves for non-associating solvents were calculated for flexible molecules such as the n-paraffins (open blue squares) and less flexible or rigid solvents (filled blue squares).


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Energy & Fuels

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Figure 4: Schematic “miscibility map” showing the upper and lower limits of miscibility for a hypothetical asphaltene. This defines a miscibility band of solubility parameter values, ± ∆ .


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Energy & Fuels

Figure 5: Solubility parameters for asphaltenes from reference 18 plotted as a function of the atomic H/C ratio of the material.


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Energy & Fuels

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Figure 6: Plot of the solubility parameters of various solvents vs. their molar volumes. Solubility parameter values for non-polar and weakly polar solvents are identified by filled circles, while values for somewhat polar solvents are identified by open squares. Miscibility limits for

asphaltene solubility in non-associating solvents are plotted as − ∆ curves calculated for

= 20 MPa0.5 and a critical value of the solubility parameter difference (∆ ) calculated as a

function of solvent molar volume. (Abbreviations defined in Table 1, with the exception of carbon tetrachloride (CCl4) and chloroform (CHCl3).)


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 7: Plot of the solubility parameters of various solvents vs. their molar volumes. Solubility parameter values for non-polar and weakly polar solvents are identified by filled circles, while values for somewhat polar solvents are identified by open squares. Miscibility limits for

asphaltene solubility in non-associating solvents are plotted as − ∆ curves calculated for

four different values of between 20 and 24 MPa0.5 and a critical value of the solubility parameter difference (∆ ) calculated as a function of solvent molar volume.


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Figure 8: Plot of the solubility parameter values of polar solvents vs. their molar volumes. Superimposed on this plot are the miscibility limits for asphaltene solubility plotted as a ± ∆

curve calculated for a value of = 20 MPa0.5. Weakly self-associating but strongly polar solvent solubility parameter values are identified by filled squares, while somewhat polar solvents are identified by open squares. (Abbreviations given in Table 1.) Hydrogen bonding solvents are shown as green squares.


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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Figure 9: Plot of the solubility parameter values of polar solvents vs. their molar volumes. Superimposed on this plot are the miscibility limits for asphaltene solubility plotted as a ± ∆

curve calculated for a value of = 24 MPa0.5. Weakly self-associating but strongly polar solvent solubility parameter values are identified by filled squares, while somewhat polar solvents are identified by open squares. (Abbreviations given in Table 1.) Hydrogen bonding solvents are shown as green squares.


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Guide to Asphaltene Solubility - Energy & Fuels (ACS Publications)

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