Understanding the fluid phase behaviour of crude oil: Asphaltene precipitation

Understanding the fluid phase behaviour of crude oil: Asphaltene precipitation

Fluid Phase Equilibria 306 (2011) 129–136 Contents lists available at ScienceDirect Fluid Phase Equilibria journal homepage: www.elsevier.com/locate...

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Fluid Phase Equilibria 306 (2011) 129–136

Contents lists available at ScienceDirect

Fluid Phase Equilibria journal homepage: www.elsevier.com/locate/fluid

Understanding the fluid phase behaviour of crude oil: Asphaltene precipitation Pierre-Arnaud Artola 1 , Frances E. Pereira, Claire S. Adjiman, Amparo Galindo, Erich A. Müller, George Jackson, Andrew J. Haslam ∗ Department of Chemical Engineering and Centre for Process Systems Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK

a r t i c l e

i n f o

Article history: Received 29 October 2010 Received in revised form 25 January 2011 Accepted 26 January 2011 Available online 11 March 2011 Keywords: SAFT-VR Liquid–liquid instability Crude-oil phase diagrams Crude-oil bubble curve Asphaltene precipitation boundary Lumping Modelling crude oil Multicomponent mixtures

a b s t r a c t We present a simplified but consistent picture of asphaltene precipitation from crude oil from a thermodynamic perspective, illustrating its relationship to the familiar bubble curve via the calculation of constant-composition p–T phase diagrams that incorporate both the bubble curve and the asphaltene precipitation boundary. Using the statistical associating fluid theory (SAFT) we show that the position of the precipitation boundary can be explained using a very simple fluid model including relatively few components. Our results support the view that the precursor to asphaltene precipitation is a liquid–liquid phase separation due to a demixing instability in the fluid. Moreover, the bubble curve for these systems is seen to represent a boundary between regions of two-phase (liquid–liquid) and three-phase (vapour–liquid–liquid) equilibria. © 2011 Elsevier B.V. All rights reserved.

1. Introduction Crude oil is a complicated mixture typically comprising a very large number of components. Many of these myriad individual components fall into one of three classes. Alkanes (paraffins) typically predominate, however cycloalkanes (usually referred to as naphthenes) are present, along with aromatic components. High-molecular-weight polyaromatic components, usually called asphaltenes, are thought to be responsible for precipitation and fouling during the processing of crude oil [1–3]. The precipitation of these heavy molecules during production and processing increases costs dramatically in terms of the prevention and mitigation of fouling. Asphaltenes are defined operationally to be the (toluene soluble) fraction precipitated from oil upon the addition of n-heptane, however, analogous precipitation from the oil can also be induced by addition of other precipitants or, in particular, by changes in the thermodynamic conditions (temperature and/or pressure); such precipitates are also often referred to as asphaltenes. A detailed description of an asphaltene-containing crude oil is an experimental and theoretical challenge, mainly due to the striking complexity of the mixture, both from the point of

∗ Corresponding author. Tel.: +44 20 7594 5618. E-mail address: [email protected] (A.J. Haslam). 1 Current address: LCP, Université de Paris Sud, 91405 Orsay Cedex, France. 0378-3812/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2011.01.024

view of the number and size distribution of components and from the complex interactions involved. Though thermodynamic treatments of this problem date back as far as the late 1970s and early 1980s [4,5], the problem is as yet unresolved. This is partly because of a lack of experimental data, but also because the asphaltene fractions of crude oils are far from being well characterised. This lack of a precise characterisation is reflected by a limited understanding of the physical phenomena leading to the instability of the fluid phase, aggregation and posterior precipitation of some of the asphaltenes. However, it is this open problem that is particularly important in crude-oil production, transport and refining, since the economic cost associated with either reservoir, production pipe or pipeline blockage due to asphaltene deposition is significant. Clearly, any insight into the precipitation phenomenon that could be provided by an improved understanding of the phase behaviour of crude oil would be of great value. Developing such an understanding of the phase behaviour of crude oil involves, first of all, a strategy for studying multicomponent mixtures. In chemical and petroleum engineering practice, it is common to group together components of similar chemical composition and molecular weight into individual “pseudocomponents”, thereby decreasing the complexity of phaseequilibrium calculations. Nevertheless, accurate prediction of the phase behaviour of crude oils generally involves a large number of adjustable parameters that are estimated based on experimental data or obtained from correlations. Cubic equations of state, such

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as the Peng–Robinson [6] and Soave–Redlich–Kwong [7] equations and their many variants, are widely employed in this area. These equations of state can provide accurate correlations of data (albeit over restricted intervals of phase space) but provide little physical insight. In general, methods involving many adjustable parameters, though of great accuracy, are strongly system dependent and give little physical understanding of the overall phase behaviour of complex mixtures. To provide a representation of the distribution of chemical compositions and molecular weights, workers in this field have regularly increased the number of components in their model systems from a few (6 or 7) [8,9] to almost a hundred in more-recent studies [10–13]. Notwithstanding this, we note that Prausnitz and co-workers [14,15] have shown that such large numbers of components should not be required in order to obtain a satisfactory description of the phase behaviour. Use of statistical associating fluid theory (SAFT) in modelling alkane and oil-like systems is well established. For some representative examples of the description of the fluid phase behaviour of hydrocarbon systems with the SAFT-VR version of the theory, which is employed in our current paper, the reader is directed to Refs. [16–27]. In particular, SAFT has been applied with some success in modelling the onset of asphaltene deposition from crude oil [28–37]. By capturing experimental onset and bubble-point data, these studies have demonstrated the applicability of SAFT for the study of crude-oil systems. Experimental asphaltene-precipitation and bubble-point data for the same oil are extremely scarce in the open literature and, in the studies that are available, just a few data points across a small region of phase space are given, providing only a restricted view of the overall phase behaviour. In view of this paucity of experimental data, rather than carrying out a system-dependent study, the aim of our current work is to present a physically based analysis of the fluid phase behaviour of these complex mixtures, with minimal adjustment of parameters. Pedersen et al. [8] have warned of the dangers of tuning equation-of-state parameters to specific properties; by extension one might suppose it to be similarly dangerous to rely heavily on parameters tuned to capture experimental data over only a narrow region of phase space. In this work therefore we choose simple models of generic crude-oil systems comprising alkanes with a heavier (asphaltene) component. The emphasis lies on the simplicity of the molecular description, whereby the general features of the phase diagram can be reproduced and understood, and factors influencing the individual features probed. A potential difficulty in studies of this type is the selection of a molecular model to represent asphaltene, since (as yet) there remains no clear consensus concerning its exact nature. Even an apparently trivial property, such as its average molecular weight is a subject of considerable debate. Buch et al. [38] have estimated asphaltene molecular weight to range from ∼700 to ∼3000 g mol−1 , while Morgan et al. [39] have recently reported estimated molecular weights of up to ∼10,000 g mol−1 from a sample of asphaltene from Mayan crude of average molecular weight ∼1300 g mol−1 (number-average molecular weight, Mn ∼ 1300 g mol−1 ; weight-average molecular weight, Mw ∼ 2700 g mol−1 ). Asphaltene molecules contain a large number of aromatic rings, alkyl chains as well as heteroatoms such as nitrogen or sulphur [40], however the actual morphology of a “prototypical” molecule is still unclear [41]. If one neglects the possibility of heteroatoms, a plausible model molecule suitable to represent an asphaltene would be one that contains aromatic rings and alkyl chains and, in addition, can be tuned to account for the polydispersity and possible differences in molecular weight. Polystyrene (PS) is a simple prototypical example of such a molecule. It becomes more attractive as a model considering that, while there are several factors which induce the precipitation of asphaltenes from crudes, one of the most impor-

tant issues may be the size asymmetry between the components of the mixture; even in the case of athermal mixtures (where no cohesion effects are in place) extreme differences in molecular size can induce a fluid–fluid phase separation [42]. The use of a polymer model in this context is not a new idea. In 1984 Hirschberg et al. [5] treated the problem using a modified Flory–Huggins theory and subsequently this and related approaches have been used in a number of studies of the asphaltene precipitation problem, for example, Refs. [43–52]. Vargas et al. [33] have pointed out that the phase behaviour of mixtures of PS, cyclohexane and CO2 shows many qualitative similarities with the phase behaviour reported for asphaltenes in crude oil. For example, both PS and asphaltenes are stable at reservoir pressure but, in both cases, with analogous changes in thermodynamic conditions (p or T) or gas content, the fluid mixture becomes unstable by demixing, leading to precipitation. Accordingly, in this work, we represent asphaltenes as PS oligomers or polymers of the corresponding molecular weight; we refer to this approach as a polystyrene–asphaltene mapping (PAM). As a further justification for this model, the choice of polystyrene to represent asphaltene may be considered analogous to the use of polystyrene standards for calibrating molecular weight range in size exclusion chromatography. The lighter components in the crude oil are represented simply as alkanes. 2. Theory and models All our calculations are carried out using SAFT-VR (statistical associating fluid theory for potentials of variable range) [53,54]. SAFT is a molecular-based theory based on the thermodynamic perturbation theory of Wertheim [55–60]. The initial developments of SAFT were made in the late 1980s [61–64]. Subsequently the theory has been further developed, and today many different variations of the theory are in use by a variety of groups world-wide. Several reviews on the method have been published, e.g., [65–69]. In SAFT-VR [53,54] molecules are modelled as chains of m spherical segments interacting via a potential of variable range. Here the square-well (SW) potential is used:

 ij (rij ) =

+∞ −εij 0

rij < ij ij ≤ rij < ij ij , rij ≥ ij ij

(1)

where rij is the segment–segment distance,  ij is the hard-core diameter, εij is the depth of the potential well and ij represents the range of the potential. The theory is based on a decomposition of the Helmholtz free energy into an ideal contribution, Aideal , a contribution due to the monomer segments, Amono , a contribution due to connecting the segments into chains (of length m), Achain , and (in the case of associating molecules) a contribution due to association, Aassoc : A Aideal Amono Achain Aassoc = + + + ; NkB T NkB T NkB T NkB T NkB T

(2)

N represents the total number of particles, kB the Boltzmann constant, and T the absolute temperature. In this work all molecules are assumed to be non-associating, so that the last term in Eq. (2), Aassoc /NkB T = 0. (It has been demonstrated previously in SAFT treatments of ashpaltenic systems [31–36] that asphaltene can be successfully modelled without association and we prefer this simpler option to avoid introducing extra parameters.) Pure components are completely specified by their SW-potential parameters, ,  and ε, together with the number of segments m, which can be thought of as a representation of molecular weight. For example, in the case of n-alkanes, m can be related to the number of carbons, Cn , via m = (Cn − 1)/3 + 1 [70], e.g., m = 2 for butane.

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Table 1 Pure-component model parameters. For the PS model used to represent asphaltene, m is related to molecular weight, MW, via mPS = 0.0205 (MW/(g mol−1 )) [71,72]. Species

Alkane

m ε/kB (K) ˚  (A) 

C1

Cn ; n > 1

1 167.30 3.6847 1.4479

2–7 259.56 3.9332 1.4922

Asphaltene (PS) 21–63 348.2 4.152 1.49

In this work, the alkane SW-potential parameters are identical for all alkanes, except for methane; in this way all the alkane–alkane unlike interactions (excepting those involving methane) are kept the same, obviating any need for combining rules. The SWpotential-parameter values used are those of the butane model of Paricaud et al. [22]; m = 2 thereby corresponds exactly to nbutane whereas, for example, m = 4 corresponds to a “decane-like” molecule. The explicit (optimal) model for methane [22] is retained since the behaviour of methane generally does not follow the trend of the homologous series of alkanes. For asphaltene we use the polystyrene model of Kao [71], which is based on a similar model used in the PC-SAFT approach by Kouskoumvekaki et al. [72], and is expressed as a function of molecular weight. All the model parameters are summarised in Table 1. Mixtures are treated using a van der Waals one-fluid approximation, implemented [54] with the following combining rules:



εij = (1 − kij ) ij = ij =

εii εjj ,

1 ( + jj ), 2 ii ii ii + jj jj ii + jj

(3) (4)

.

(5)

The binary-interaction parameter kij is 0 for i = j and for all alkane–alkane interactions, i.e., kij = / 0 only for alkane–asphaltene interactions. Kao [71] employed kij = 0.01 for the interaction between polystyrene and a hydrocarbon (cyclohexane); this value was taken as a guide for the alkane–asphaltene interaction in our work, and is used except where otherwise indicated. We note that a similar value was used by Kouskoumvekaki et al. in their studies using the PC-SAFT approach [72].

Fig. 1. Constant-composition, p–T phase diagrams of binary mixtures of a light oil (C10 ) + 1 mol% asphaltene of molecular weight (a) MW ∼ 485 g mol−1 (m = 10) and (b) MW ∼ 485, 975, 1465, 1950, 2680 and 3410 g mol−1 (m = 10, 20, 30, 40, 55 and 70 (respectively)). In (a) the pure-C10 vapour-pressure curve is indicated in addition, as a continuous red curve, terminating at the C10 critical point (filled circle). Note that the solid phase is not considered. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)

4. Results 3. Methodology We build an understanding of the general features of the phase diagrams of asphaltene-containing crude-oil-type systems by considering first binary mixtures of a light component (“oil”) + asphaltene, then examining the effect on the phase diagram of gradually increasing the number of components in the model mixture, effectively increasing the sophistication of the oil model. For each system of interest, the pressure–temperature (p–T) space was divided up into a grid in p and T, and flash calculations were performed across the whole space at each (p, T) point on the grid, to establish the number of phases and their composition at each point. The calculations were carried out using the (p, T) flash algorithm of Pereira et al. [73,74]. This is a robust, multicomponent, multiphase-flash algorithm that identifies the number of stable fluid phases present at equilibrium, along with their properties, without need of initial guesses or a priori knowledge of the phase behaviour of the system. The algorithm is based on the general framework for phase stability and phase equilibrium calculations presented in Ref. [75] and is applicable to the calculation of any kind of fluid phase behaviour (e.g., vapour–liquid equilibrium (VLE), liquid–liquid equilibrium (LLE), vapour–liquid–liquid equilibrium (VLLE), etc.). Constant-composition, p–T phase diagrams were thereby constructed for each system of interest.

We consider first the simplest possible representations of the crude-oil system, as binary mixtures comprising an oil (alkane) plus a small amount of ashpaltene. In Fig. 1 we present p–T phase diagrams of C10 + 1 mol% asphaltene, for increasing molecular weights of asphaltene. In Fig. 1(a), to illustrate the different regions in the phase diagram, the generic phase diagram is presented using an “asphaltene” represented by m = 10 (molecular weight ∼ 485 g mol−1 ) as an example. (This molecular weight is too low to genuinely represent an asphaltene; nevertheless we choose this value to provide the qualitative limiting phase behaviour for this class of mixture.) For a binary mixture comprising two components but containing a tiny amount of one of the components, one would expect a p–T (bubble and dew) curve falling close to the pure-component vapour-pressure curve of the majority component, demarking only a small region of VLE; this is exemplified in this figure, wherein the calculated pure-C10 vapour-pressure curve is also presented for reference. The bubble curve in this case appears to extend out of the pure-C10 vapour-pressure curve. In addition, at very low temperature, a region of liquid–liquid immiscibility is indicated; in reality this phase boundary would be metastable relative to the solid phase (not considered here), however we retain the boundary in the diagram for illustrative purposes. In Fig. 1(b), the effect of increasing the molecular weight of the asphaltene is illus-

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Fig. 2. Constant-composition, p–T fluid phase diagrams of binary mixtures of a light oil Cn (n = 4, 7, 10, 13, 16 and 19) + 1 mol% asphaltene (MW = 3066 g mol−1 ).

trated. As the asphaltene molecular weight becomes larger and the mixture accordingly more asymmetric, the liquid–liquid boundary moves to higher temperature. Simultaneously, the bubble curve departs from the pure-C10 vapour-pressure curve at progressively lower temperature (and pressure). For mixtures with asphaltenes of very high molecular weight, the LLE boundary and the bubble curve merge and these two phase-equilibrium regions meet; there is then a continuous transition from a LLE-like region to a VLE-like region. The shape of the phase boundary has a characteristic “sideways-S” shape. For these highly asymmetric mixtures, the phase diagram no longer reflects the vapour-pressure curve of the pure majority component (C10 ). We consider next the effect on the binary-mixture phase diagram of changing the molecular weight of the oil. In Fig. 2 we present p–T phase diagrams of Cn + 1 mol% asphaltene, for n = 4, 7, 10, 13, 16 and 19. For these calculations, a moderately high molecular weight of 3066 g mol−1 was chosen for the asphaltene; this corresponds to m ∼ 63. A higher molecular weight is preferred here since this brings out more clearly the features of the phase diagrams that we seek to explain. This value of molecular weight corresponds to that used in a SAFT treatment of a Mexican crude oil [30], and represents an estimate of the aggregated molecular weight of asphaltene, considered as a cluster of three molecules. The phase diagrams illustrated in this figure take the same qualitative form as those of the more asymmetric systems in Fig. 1(b), with the characteristic “sideways-S” shape; for none of these mixtures can one easily infer the position of the pure-Cn vapour-pressure curve from the mixture phase diagram. Instead, the phase diagram is characterised by a low-temperature region of LLE instability with a continuous transition, on increasing temperature, to a region of VLE. We seek now to improve our simple crude-oil model to the next level of sophistication and treat the system as a ternary mixture. The previous representation as a binary mixture is the simplest representation of asphaltene-containing crude oil. Within this analogy, the addition of a third component may be thought of as analogous to the addition of a precipitant. Commensurate with the general definition of asphaltene as the precipitate following addition of n-heptane, for the mixtures including heavier oils (Cn , with n = 13, 16 and 19), C7 was added as the third component (recall that our model for C7 corresponds to an “n-heptane-like” molecule). For the mixtures including one of the three lighter oils, methane was added as the third component, so that in each case the precipitant was represented by a lighter molecule than the oil. In either case, the composition of the added precipitant was 10 mol%; the composition of the asphaltene remained at 1 mol%. (Of course, we do not seek here to model a typical precipitation

Fig. 3. Constant-composition, p–T fluid phase diagrams of several ternary mixtures comprising the previous binary systems (see Fig. 2) with 10 mol% of either methane or C7 as precipitant; methane was used for n < 11 and C7 for n > 11. The presence of the third component results in the appearance of a three-phase (VLLE) region at low pressure; see text for details.

experiment, in which one would add a much larger quantity of precipitant.) In Fig. 3 we present the p–T phase diagrams of these ternary mixtures. Several important observations can be made. The first of these is that in all cases, the characteristic “sideways-S”-shaped phase boundaries seen for the corresponding (asymmetric) binary mixtures remain; the maximum temperature of the phase boundary is hardly affected by the precipitant and is therefore essentially dependent on the heavier component. (Although the effect is small, one can discern that this maximum temperature is lowered by increasing n.) The next important observation is that all the phase diagrams display the same qualitative features. Following an isotherm in the mid-T range (e.g., ∼500 K) from high pressure, the system passes from a single-phase region into a two-phase region (exactly as would be the case for the corresponding binary system), however at low p a three-phase region is observed. The existence of this region may be rationalised as follows: when the system passes from the single-phase to the two-phase region, the two phases that appear are effectively one that contains practically all the asphaltene and a second that is essentially a binary mixture containing only the “lights” and is almost free of any heavy (asphaltene). On further lowering the pressure the system reaches the p–T coexistence curve of this “binary”, which is clearly expected to feature a region of VL equilibrium. In this context, the small size of this region is to be expected: as described earlier, the p–T curve of a binary mixture of two fluids of similar molecular weight, rich in one of the fluids, lies close to the pure-component vapour-pressure curve of the majority component. From these results we can begin to explain the main features of the phase behaviour of many-component mixtures encountered in crude oils. To illustrate this, we model first the Mexican crude oil described in Ref. [30]. Buenrostro-Gonzalez et al. [30] used a SAFT-VR treatment (including association) for their theoretical description of asphaltene precipitation. These authors coupled SAFT-VR with a McMillan–Mayer-type solution theory in which the oil itself was treated as a continuum. Accordingly, the bubble curve for the oil could not be obtained using the same model and was calculated independently using the Peng–Robinson equation of state [6] with many components (up to 16). Calculations were made only across the narrow range of p and T for which experimental data were measured. The precipitation-boundary (liquid phase instability) and the bubble curves were each (independently) adjusted to fit the experimental data, whereby one cannot easily relate the two curves. Here we consider a simple description of the same system, with no association, in which the bubble and

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Table 2 Composition of the 5-component mixture based on the crude oil of Ref. [30]. The asphaltene molecular weight is taken as 1022 g mol−1 (corresponding to m ∼ 21); see text for details. Component

Composition

1 (C1 ) 2 (C4 ) 3 (C7 ) 4 (C10 ) 5 (asphaltene)

0.4008 0.2029 0.2752 0.1151 0.0060

precipitation-boundary curves are both obtained with the same model and theory. We represent the asphaltene-containing oil using only five components: four alkane-like (m = 1, 2, 3, 4, corresponding to C1 , C4 , C7 and C10 ) with the same SW-potential parameters as previously (see Table 1) plus one component for the asphaltene. For the asphaltene molecular weight we take the value of 1022 g mol−1 (corresponding to m ∼ 21); this is one third of the molecular weight used by Buenrostro-Gonzalez et al. Their model described an aggregate or cluster of three molecules and the value of 3066 g mol−1 used is therefore, more properly, a “cluster molecular weight”; our value of molecular weight was chosen to represent that of the individual molecules. The composition of the mixture is given in Table 2; this was obtained from Table 3 of Ref. [30] for oil “C1”, which comprises 11 explicit components and 6 specified pseudo-components based on a lumping of the C7+ fraction. Our lumping of this characterisation is performed as follows: • Component 1: the light gases (CO2 , H2 S, N2 , C1 and C2 ) are represented as C1 (see Table 1); • Component 2: low-molecular-weight alkanes (C3 , iC4 , nC4 , iC5 and nC5 ) are represented as nC4 (see Table 1); • Component 3: intermediate-molecular-weight alkanes (C6 and the first three of the grouped pseudo-components for C7+ (detailed in Ref. [30])) are represented by C7 (see Table 1); • Component 4: heavy end (the last three C7+ of the grouped pseudocomponents for C7+ (detailed in Ref. [30])) are represented by C10 (see Table 1). With this lumping we obtain directly the mole fractions of each component from a simple sum. Our model of the crude is thus a very simple one consisting of four alkane-like components plus asphaltene. The guide value of the asphaltene-alkane cross interaction (kij = 0.01) was obtained from a study of PS + cyclohexane [71]. According to a recent predictive approach [76] a higher value is expected for mixtures of PS with lighter alkanes, in particular, for PS + C1 . The kij value used in modelling this oil should represent a weighted (by concentration) average of the kij values for each of the binary interactions; a higher value of kij ∼ 0.02 is indicated by the theory. Indeed, a value of kij = 0.015 was found to provide for a slightly improved description of the experimental data than that obtained using the guide value (kij = 0.01), and accordingly used in preference. In Fig. 4 we present our calculated p–T phase diagram; we purposely extend our calculations well beyond the range of p and T spanned by the experimental data (depicting the bubble curve and the asphaltene-precipitation boundary), which are also indicated in the figure for comparison. The appearance of this diagram is qualitatively similar to those seen in Fig. 3, and may be explained analogously. The principal difference is that the three-phase region is expanded in comparison to those seen in Fig. 3; this is to be expected as it now corresponds, by analogy, to the p–T curve for the four-component mixture representing the oil. The experimental precipitation data are seen to lie close to the turning point of the characteristic “sideways-S-shaped” phase boundary. This suggests

Fig. 4. Calculated constant-composition, p–T fluid phase diagram of a simple model of an oil (continuous curves) compared to experimental data [30] (symbols). See Table 2 for details of the oil composition.

that for slightly different systems one might encounter experimental precipitation boundaries with a turning point or, indeed, with positive (rather than negative) slope in the region of p and T investigated. It is important to stress that the object here is not to correlate precisely the experimental data depicted in Fig. 4; one would not expect to do so with models as simple as those used here and with little adjustment of parameters. Such correlation is possible, as has been demonstrated by Gonzalez et al. [31], who modelled the crude oil described in Ref. [77] using PC-SAFT [78,79] (without association); these authors obtained also both the precipitation boundary and the bubble curve using the same model oil, in their case comprising seven components. The asphaltene-model (PCSAFT) parameters were tuned to meet the onset of asphaltene precipitation at a reference pressure (3800 psia ≡ 26.2 MPa). These authors demonstrated that both the precipitation boundary and bubble curve can be captured using a relatively simple model of the oil, however they did not extend their calculations beyond the region spanned by the experimental data, illustrating only this narrow portion of the phase diagram. In our work, a key point is that the model of the asphaltenecontaining crude has been restricted to a very basic description consisting of only five components, three of which are described with the same SW-potential parameters and distinguished only by their different size (m), and that the phase diagram is not obtained as a result of a fitting procedure. We seek to demonstrate how the bubble-point and precipitation data fit within a complete phase diagram. In Fig. 4, the general trends of the experimental data are clearly reproduced. The bubble curve is seen to be a boundary delimiting a three-phase region of VLLE, while the location of the precipitation boundary is closely related to the LLE boundary, clearly supporting the interpretation of the onset of precipitation of the asphaltene as a liquid–liquid instability. In addition, one can understand how the precipitation boundary would be affected by changes in the nature of the crude oil. Of course, it is important to keep in mind that in reality, the precipitation boundary would be expected to be very sensitive to the precise distribution of asphaltenic species and not just the average molecular weight. For example, a sample with a long-tail distribution of larger molecules would be more prone to be unstable than a system with an equivalent average molecular weight, but a sharper distribution; such sensitivity is well-known in polymer-solvent phase equilibria [80]. Nevertheless, it is interesting to note that the asphaltene modelled here has a molecular weight of ∼1000 g mol−1 , and that this appears to provide a good representation of the precipitation boundary; a much larger molecular weight would not provide a description of the same quality.

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5. Discussion and conclusions

Fig. 5. Composition dependence of (a) C10 and (b) asphaltene in the different phases at T = 450 K. The horizontal dotted lines represent the global mole fractions of C10 and asphaltene (respectively). The two vertical dashed lines represent the positions of the boundaries of the three-phase region.

Analogous to the explanation of the three-phase region in Fig. 3, the crude-oil bubble curve is expected to be essentially that of the asphaltene-free liquid phase; this is supported by close coincidence between this phase boundary and the bubble-dew curve of the four-component oil (without asphaltene). To confirm this, we have calculated the composition of the components in all phases across the whole p–T space for our model of the Buenrostro-Gonzalez oil. This reveals that, in terms of the light (or oil) components, the composition of the two liquids inside the (LLE) two-phase region is essentially the same. This is illustrated in Fig. 5(a) for the case of the C10 (“n-decane-like”) component, in which xC10 is presented as a function of p for the isotherm at 450 K. In contrast if one considers instead the composition of the asphaltene, a marked difference in the phases is apparent, as is illustrated in Fig. 5(b). At low pressure two phases are present, one in which the mole fraction of asphaltene is close to unity, and one (a gaseous phase) in which there is, essentially, no asphaltene (note that, for clarity, the scale of the figure is logarithmic). At ∼3.5 MPa, a third phase appears in which there is still very little asphaltene; the composition of asphaltene in this dense fluid phase is several orders of magnitude lower than that of the asphaltene-rich phase, reaching a minimum at the boundary between the three-phase and two-phase regions (at ∼14 MPa). (In this three-phase region, the content of lights (in particular C1 ) in the liquid phases increases with pressure, while that of the heavier components decreases accordingly.) At higher pressure, once again only two phases are observed and although asphaltene is present in both phases, the composition of asphaltene in the asphaltene-rich phase remains at least an order of magnitude higher than that in the other phase. This analysis of the two phases, one of them largely free of any asphaltene, provides a physically relevant picture of the phase behaviour.

We have presented a general method for modelling complex many-component oil mixtures using molecular-based equations of state such as SAFT. This method proves very useful not only for the usual correlation or fitting of experimental data but provides a full and consistent picture of the asphaltene-precipitation phenomenon in relation to the familiar crude-oil phase behaviour. It is important to reiterate that it was not our aim to accurately correlate experimental data in this study; this could have been achieved by introducing more components with, correspondingly, more unlike interactions (acting as potential fitting parameters). From such a starting point one is restricted to system-dependent predictions; moreover, since available experimental data tend to lie only in narrow regions of p–T space such an approach becomes similarly focussed. Our simpler approach allows us to understand the underlying physical behaviour – in particular because we considered the entire p–T space. The central feature of our model is its simplicity, wherein the same potential parameters are used in representing three of the five components used to model the asphaltene-containing oil, with just a single adjustable parameter (kij ) invoked to tune the alkane–asphaltene unlike interaction. The position of the LLE phase boundary is sensitive to this parameter and so its value is the key in this (or any related) study of asphaltene precipitation. Of course, the nature of the components present in the crude will impact the value of kij ; for example, a lower value would be expected for crudes with higher aromatic content, which would lead to a larger region of miscibility in the phase diagram (with the liquid–liquid boundary shifted to lower temperature). Accordingly it is important to keep in mind also that this parameter was not treated as fully adjustable and that its value was required to be consistent with a theoretically calculated value. This provides confidence that the underlying physics has been captured and not, simply, that the experimental behaviour has been correlated by a fitting procedure. The importance of this lies in the capacity for understanding and judging the effect on the phase behaviour of changes in thermodynamic conditions or addition of additives, which could be of great help in anticipating or mitigating precipitation. In similar fashion, the effect of differences in the molecular weight of asphaltene on the phase behaviour may be investigated; thereby, in future, the asphaltene molecular weight need not be known a priori and may, instead, be inferred by obtaining the best description of experimental data. Another important consequence of the simplicity of our oil model, upon which we have not commented hitherto, is that all of the component species are treated using models defined by integer values of the parameter m, which denotes the number of segments in the chain representing the molecule. Together with the low number of components in the model, this will allow the same system to be studied using molecular-simulation techniques, such as molecular dynamics. By contrast, had our crude-oil model comprised many components or (as would be usual in SAFT-type studies) any components been characterised by non-integer m (i.e., the model molecules consisted of a non-integer number of segments), such a complementary study would not be straightforward. In future work, it is our intention to extend our study of these systems using a group-contribution approach, SAFT-␥ [81,82]. Compared with polystyrene, asphaltene molecules have lower flexibility due to the presence of fused aromatic cores, which would be expected to play a role in the conformational entropy of the system. The advantage of the SAFT-␥ approach is that it will enable study of the possible impact of this lower flexibility on the positions of the phase boundaries in the constant-composition p–T diagrams that have been the focus of this study. In addition, the degree of flexibility in molecules has a direct influence on the types of ori-

P.-A. Artola et al. / Fluid Phase Equilibria 306 (2011) 129–136

entationally ordered phases that are observed. It is interesting to note that asphaltenic crude-oil systems are known to exhibit liquidcrystalline phase equilibria (e.g., see the recent paper by Bagheri et al. [83]). This type of orientational ordering behaviour can be modelled by coupling a SAFT description with Onsager-like forms of the free energy [84–88]. In future work we plan also to pursue this line of study to investigate possible links between liquid-crystal ordering of the asphaltenic fluid (following phase separation) and agglomeration of the asphaltene into the viscous residue that is so deleterious in crude-oil processing. In summary, we have shown that the position of the asphalteneprecipitation boundary of crude oil can be explained from a thermodynamic perspective using a very simple fluid model including relatively few components, differentiated almost exclusively by their molecular size. In a single series of calculations using this model we have calculated a p–T phase diagram that is in good agreement with experimental data, including both the bubble curve and asphaltene-precipitation boundary, using minimal fitting. Our results indicate that the bubble curve for such heavy-oil systems represents a boundary between regions of two-phase (LLE) and three-phase (VLLE) equilibrium. In particular, our results support the view that asphaltene precipitation is initiated by a thermodynamic instability to liquid–liquid phase separation.

List of symbols A Helmholtz free energy iCn iso-alkane Boltzmann’s constant kB kij binary interaction parameter for well depth of unlike (mixture) intermolecular potential Mn number average molecular weight weight average molecular weight Mw MW molecular weight m number of segments in SAFT model of a molecule n carbon number for alkane or alkane-like molecule N total number of particles nCn normal alkane p pressure r segment–segment separation for intermolecular potential T absolute temperature x mole fraction ε well depth of (square-well) intermolecular potential  range of (square-well) potential  (square-well) intermolecular potential  hard-core diameter of (square-well) intermolecular potential

Acknowledgements The authors would like to acknowledge: Prof Alejandro Gil-Villegas for many helpful discussions; Dr Edo Boek for a critical appraisal of the manuscript; Mr Edwin Teik Goh for preliminary calculations on some of the binary systems. PAA gratefully acknowledges Shell International Exploration for funding a research fellowship; AJH gratefully acknowledges the Engineering and Physical Sciences Research Council (EPSRC) for funding a research fellowship (grant EP/D503051/1); FEP gratefully acknowledges the EPSRC for funding a PhD studentship (EP/E016340/1). We are also very thankful for additional funding to the Molecular Systems Engineering Group from the EPSRC (grants GR/T17595, GR/N35991, and EP/E016340), the Joint Research Equipment Initiative (JREI) (GR/M94427), and the Royal Society-Wolfson Foundation refurbishment scheme.

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