Simultaneous prediction of vapour–liquid and liquid–liquid equilibria (VLE and LLE) of aqueous mixtures with the SAFT-γ group contribution approach
Highlights
► SAFT-based group contribution method. ► Focus on study of phase behaviour of aqueous solutions. ► Interaction parameters from limited experimental data. ► Transferability of interaction parameters. ► Accurate predictions of VLE and LLE for wide range of systems and conditions.
Introduction
Aqueous solutions of hydrocarbons are of great interest in many applications ranging from the petrochemical industry to biological processes and waste water treatment. The thermodynamic modelling of systems of this type is particularly challenging due to the highly non-ideal behaviour that they exhibit over a wide range of thermodynamic conditions. Characteristics of the fluid phase equilibrium of these systems include heterogeneous azeotropes bounding regions of vapour–liquid and liquid–liquid equilibria, where the respective solubilities in the two liquid phases can differ by many orders of magnitude. The extreme nature of the fluid phase behaviour exhibited by these systems is a direct consequence of the strong hydrogen bonding interactions between the water molecules. It is therefore clear that the key to a successful description of aqueous solutions requires the application of a thermodynamic treatment that accounts explicitly for the effects of association. Examples of such approaches include the statistical associating fluid theory (SAFT) [1], [2] and the cubic plus association (CPA) [3] equations of state (EoSs) which have been used to describe the fluid phase equilibria in water–hydrocarbon mixtures [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16]. For a more complete review the reader is directed to the book of Kontogeorgis and Folas [17].
Though powerful thermodynamic tools have been developed to deal with systems exhibiting a highly non-ideal behaviour, the successful application of these techniques usually requires information of both the pure component fluids and the mixture. The need for experimental data for the mixture stems from the fact that one has to determine the binary interaction parameter(s) for all pairs of components in a mixture. One should emphasise that the use of experimental data for the estimation of binary parameters is the standard, despite the fact that some efforts have been directed to predicting these interaction parameters based on theoretical considerations [18], [19], [20]. This often limits the applicability of the EoS to cases where experimental data is available for a mixture.
A popular approach to overcome the reliance on experimental data and increase the predictive capability of a thermodynamic methodology is its formulation within a group contribution (or solutions of groups) approach. Within the scope of group contribution (GC) methods, molecules are deconstructed into distinct functional groups that characterise their chemical composition. These groups are assumed to give rise to the same thermodynamic contribution independently of the molecule in which they appear. The contribution that each functional group makes to the properties of the system is traditionally obtained by regression to experimental data. Once the parameters for an existing group have been determined then this functional group can be used as a building block to form a molecule, and by appropriate use of the GC method to predict the property of the system of interest. In this sense, group contribution methods are essentially predictive, since there is only a dependency of experimental data at the early stage of obtaining the group parameters from a set of selected systems.
Group contribution methodologies were initially developed for the determination of pure component properties [21], [22], [23] but have also been widely applied to the prediction of the phase behaviour of binary (and multicomponent) mixtures within different thermodynamic theories. The formulation of an activity coefficient treatment as a group contribution approach has lead to the most widely known methodology: UNIFAC [24]. The UNIFAC approach was presented over 35 years ago [24], and has since been extended and revisited [25], [26], [27], and also modified at the level of the underlying theory [28], [29], [30]. The parameters of each group characterise its size and like attractive interaction, and the unlike interactions with other groups. They are obtained by simultaneous estimation to fluid phase equilibrium data for a large number of mixtures; the type of data included in the determination of the group parameters determines the applicability of the method. As an example of this, and of particular relevance to our current work, different parameter sets are required within the original UNIFAC approach for an adequate representation of the different types of fluid phase behaviour (e.g., see the work on the development of parameters for vapour–liquid [26] and liquid–liquid [27] equilibria); the appropriate parameters are obtained by regression to the corresponding experimental data. This is not the case however for the more recent modified UNIFAC approach (Dortmund) [28], where vapour–liquid equilibria (VLE), liquid–liquid equilibria (LLE), and solid-liquid equilibria (SLE) data sets are included in the regression procedure so that different types of phase behaviour can be treated using the same group parameters. The broad applicability of the method stems from the extensive list of available group parameters, from which the phase behaviour of a wide range of systems can be predicted. However, the formulation of UNIFAC within an activity coefficient approach leads to a number of limitations, the most important being the limited pressure and temperature ranges of reliable application [31] and the inability to treat pure components.
In an effort to overcome the limitations associated with activity coefficient methods, group contribution approaches have also been used in conjunction with equations of state. In EoS-gE models, for example, the excess Gibbs energy of mixing, gE, of a system is equated with that obtained from a predictive group contribution method (such as UNIFAC). One of the most widely applied predictive EoS-gE approaches is the predictive Soave–Redlich–Kwong (PSRK) method [32] based on the well-known SRK-EoS [33], where the existing parameter table of UNIFAC is employed for the calculation of gE. Models of this type are essentially predictive, since the only information required are the pure component parameters used in the equation of state; the use of UNIFAC (in this case) for the calculation of gE introduces implicitly information obtained by estimating the group parameters from experimental data for mixtures. Other approaches of this type are the UNIWAALS [34], LCVM [35], the predictive EoSs of Lermite and Vidal [36], the work of Orbey et al. [37] as well as the more recent volume-translated Peng–Robinson (VTPR) EoS [38], [39], [40]. Apart from the methods mentioned thus far, where a group contribution formalism is employed mainly to obtain a relation between the excess Gibbs energy and the parameters appearing in the equation of state, group contribution approaches have also been implemented directly at the level of calculating the molecular parameters used within the EoS in question. Approaches of this type include the parameters-from-group-contributions [41], CORGC [42], GCLF EoS [43], and finally the work of Coniglio et al. [44], [45] based on the Peng–Robinson EoS. More recent examples include the approach of Jaubert and Mutelet [46] and the GCA-EoS of Gros et al. [47], which is based on the GC-EoS of Skjold-Jørgensen [48] with the introduction of the association term of Wertheim [49], [50], [51], [52], which is also employed within SAFT [1], [2].
Of particular relevance to our current work are group contribution approaches within the general framework of SAFT [1], [2]. This versatile approach has been shown to describe accurately the phase behaviour of highly asymmetric mixtures and of mixtures that deviate markedly from ideal behaviour. For a thorough description of the applications and advances of the SAFT method, the reader is directed to recent reviews [53], [54], [55], [56], [57], and also the book of Kontogeorgis and Folas [17]. Most frequently, a homonuclear model is employed within the SAFT formalism, where each molecule is modelled as a chain consisting of identical segments; each segment is then described using the same set of parameters that represent the intermolecular interactions. One of the first applications of a group contribution methodology within SAFT was presented by Lora et al. [58], where calculations for the parameters of polyacrylates were performed based on the available parameters for low molecular weight propanoates. Following this work, a predictive implementation of the SAFT-EoS was presented by Tobaly and co-workers [59], [60], where pure component parameters were obtained by fitting to experimental data (vapour pressure and saturated liquid density) and subsequently these parameters were related to molecular properties, such as the molecular weight. This approach was the basis for the development of a more sophisticated implementation of a group contribution scheme within the SAFT-0 [1] and SAFT-VR [61], [62] EoSs, presented later by the same group [20], [63], [64], [65], [66]. At this stage, functional groups were clearly identified and the parameters for each group were obtained by examining a series of compounds belonging to the same chemical family, but the focus was restricted to the properties of pure components. The predictive capability of the method was also tested in the prediction of the phase behaviour of mixtures [67]; in this case however the description was based on the use of a combining rule (e.g., Lorentz–Berthelot) without correction. This GC-SAFT methodology cannot be used to determine unlike group interaction parameters based on pure component data alone since the application of an “average” homonuclear model smears out the specific group interactions. Following the ideas of Haslam et al. [18] for the a priori determination of unlike binary interaction parameters in the case of highly non-ideal mixtures (where mixing rules are expected to fail), GC-SAFT approaches have also been presented where the binary interaction parameters of mixtures are calculated at the group contribution level [19], [68], [69]. Group contribution approaches have also been developed within other versions of SAFT [70], such as the PC-SAFT EoS [71], whereas different approaches that take into account proximity effects [72] and second-order groups [73], [74], [75] have also been presented.
Apart from these GC-SAFT approaches, which employ a homonuclear model, group contribution methodologies within SAFT have been proposed in which a heteronuclear representation of the molecules is employed; here each segment (or “group” of segments) corresponds to a functional group. Methods of this type include SAFT-γ [76], [77], the approach used in our current work, and hetero GC-SAFT-VR [78], [79]. These methods are discussed in the following section. A more detailed discussion of the application of group contribution methodologies is available in our recent review [80].
We should also mention that the concept of group contribution methods is also widely adopted in the area of molecular simulation. From the all-atom OPLS [81] and TraPPE force fields [82] to the coarse-grained MARTINI force field [83] and models developed by Potoff and Bernard-Brunel [84], intermolecular potentials are developed where the parametrisation is made on the basis of the functional groups in the molecule. The group contribution spirit has also been combined with quantum mechanical calculations such as in the COSMO-RS approach [85].
The fluid phase equilibria of aqueous solutions of hydrocarbons has been studied with various group contribution approaches. The performance of the GCA-EoS [47] in the prediction of the phase behaviour of these systems has been presented in [86], [87]. Group contribution methods cast within the framework of SAFT have however not yet been assessed in the description of the phase behaviour of water + hydrocarbon mixtures. To our knowledge, the only predictive study of this type presented in the literature is based on the sPC-SAFT [88] approach where generalised parameters are used to represent the family of 1-alkanols [89], and the performance of the method in predicting the phase behaviour of aqueous solutions of 1-alkanols is discussed.
In our current work we assess the performance of the SAFT-γ group contribution approach in the prediction of the fluid phase behaviour of aqueous solutions including hydrocarbons. The ability of the method to describe accurately the extreme phase behaviour that these systems exhibit over a wide range of thermodynamic conditions is examined in detail. The predictive capability of the method lies mainly in the fact that the predictions of the thermodynamic properties of mixtures are based on pure component experimental data alone. Although such an approach is possible for a broad class of systems, it is not appropriate in the case of molecules that are described as a single functional group. Since the most appropriate model for water is as a single functional group, the extension of the method to aqueous solutions requires the determination of unlike group parameters between the water molecule and the other groups making up the solute molecule. We demonstrate how this can be undertaken based on a minimal set of experimental data, and assess the transferability of the estimated group interactions.
A brief outline of the SAFT-γ group contribution approach and the parameter estimation procedure employed for the determination of the group parameters is given in the following section. In Section 3, the parameters used in this work are presented, including a discussion of the appropriate functional groups for the representation of the 1-alkanols and the determination of cross group parameters between previously developed functional groups and the group for water, based on experimental data for mixtures. Finally, in Section 4, the adequacy of the method in predicting the vapour–liquid and liquid–liquid phase equilibria of aqueous solutions of n-alkanes and 1-alkanols as well as ternary mixtures of water + n-alkane + 1-alkanol is discussed.
Section snippets
The SAFT-γ group contribution approach
The SAFT-γ method [76] is a generalisation of the SAFT-VR EoS [61], [62] to treat molecules formed of fused heteronuclear segments. Each segment, or group of segments, represents a functional group; the method has been extended to include functional groups that comprise multiple identical segments [77]. An example of this is shown in Fig. 1, where a model for 1-butanol is presented as comprising one CH3, two CH2 and one CH2OH functional groups, with the latter featuring three association sites.
Pure component parameters: 1-alkanols
The key to group contribution methodologies is that molecules are decomposed into functional groups. The identification of groups is in most cases, however, based on heuristics, with the final choice being usually the combination of groups that results in the best representation of the experimental data. The combination of atoms chosen to represent the functional groups identified on a molecule is chosen based on a balance between the predictive capability of the method and the number of
Pure components: 1-alkanols
A preliminary step in the validation of the parameters obtained for the functional groups is the examination of the performance of SAFT-γ in predictions of the VLE of pure compounds that were not included in the regression procedure. In the case of pure 1-alkanols the adequacy of the parameters obtained for the CH2OH functional group is tested by examining long-chain 1-alkanols. The predictions for the pure component VLE of C12H25OH, C14H29OH and C18H37OH are depicted in Figs. 4(a) and (b).
Conclusions
In this work, the performance of the SAFT-γ group contribution approach in the simultaneous prediction of vapour–liquid and liquid–liquid equilibria of aqueous solutions of hydrocarbons and alkanols is examined in detail. New interaction parameters for the description of the family of 1-alkanols by means of a CH2OH functional group are obtained, and the improved accuracy of the method in the prediction of the fluid phase behaviour of systems comprising alkanes and 1-alkanols is discussed. For
Acknowledgements
V.P. is very grateful to the Engineering and Physical Sciences Research Council (EPSRC) of the UK for the award of a PhD studentship. 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 is also gratefully acknowledged.
References (145)
- et al.
Fluid Phase Equilib.
(1989) - et al.
Fluid Phase Equilib.
(1999) - et al.
Fluid Phase Equilib.
(1999) - et al.
Fluid Phase Equilib.
(2009) - et al.
Fluid Phase Equilib.
(2004) - et al.
Fluid Phase Equilib.
(2008) - et al.
Fluid Phase Equilib.
(2008) - et al.
Fluid Phase Equilib.
(1985) - et al.
Fluid Phase Equilib.
(1991) Chem. Eng. Sci.
(1972)
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Chem. Eng. Sci.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Fluid Phase Equilib.
Ind. Eng. Chem. Res.
Ind. Eng. Chem. Res.
J. Chem. Soc., Faraday Trans.
J. Phys. Chem.
Ind. Eng. Chem. Res.
Ind. Eng. Chem. Res.
Ind. Eng. Chem. Res.
Ind. Eng. Chem. Res.
Ind. Eng. Chem. Res.
J. Phys. Chem. B
Thermodynamic Models for Industrial Applications. From Classical and Advanced Mixing Rules to Association Theories
Ind. Eng. Chem. Res.
Ind. Eng. Chem. Res.
Chem. Eng. Commun.
AIChE J.
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