comprehensive characterization of interfacial behavior for the mixture co 2 + h 2 o + ch 4 :...

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The Journal of Physical Chemistry C is published by the American Chemical Society.1155 Sixteenth Street N.W., Washington, DC 20036Published by American Chemical Society. Copyright American Chemical Society.However, no copyright claim is made to original U.S. Government works, or worksproduced by employees of any Commonwealth realm Crown government in the courseof their duties.

Article

A Comprehensive Characterization of Interfacial Behavior for theMixture CO

2

+ H2

O + CH4

: Comparison Between Atomistic and CoarseGrained Molecular Simulation Models and Density Gradient Theory

Jos Manuel Mguez, Jos Matas Garrido, Felipe JimenezBlas, Hugo Segura, Andrs Meja, and Manuel M. Pieiro

J. Phys. Chem. C, Just Accepted Manuscript DOI: 10.1021/jp507107a Publication Date (Web): 29 Sep 2014

Downloaded from http://pubs.acs.org on September 30, 2014

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A Comprehensive Characterization of Interfacial

Behavior for the Mixture CO2 + H2O + CH4:

Comparison between Atomistic and Coarse Grained

Molecular Simulation Models and Density Gradient

Theory

Jos Manuel Mguez, Jos Matas Garrido, Felipe J. Blas, Hugo Segura,

Andrs Meja, and Manuel M. Pieiro,

Laboratoire des Fluides Complexes et leurs Rservoirs, UMR5150, Univ. de Pau et des

Pays de LAdour, B.P. 1155, Pau, Cedex 64013, France, Departamento de Fsica Aplicada,

Univ. de Vigo, E36310, Vigo, Spain, Departamento de Ingeniera Qumica, Univ. de

Concepcin, POB 160-C, Concepcin, Chile, Departamento de Fsica Aplicada, Facultad de

Ciencias Experimentales, Univ. de Huelva, E21071 Huelva, Spain, and Centro de

Investigacin de Fsica Terica y Matemtica FIMAT, Univ. de Huelva, E21071 Huelva,

Spain

E-mail: [email protected]

To whom correspondence should be addressedLaboratoire des Fluides Complexes et leurs Rservoirs, UMR5150, Univ. de Pau et des Pays de LAdour,

B.P. 1155, Pau, Cedex 64013, FranceDepartamento de Fsica Aplicada, Univ. de Vigo, E36310, Vigo, SpainDepartamento de Ingeniera Qumica, Univ. de Concepcin, POB 160-C, Concepcin, ChileDepartamento de Fsica Aplicada, Facultad de Ciencias Experimentales, Univ. de Huelva, E21071

Huelva, SpainCentro de Investigacin de Fsica Terica y Matemtica FIMAT, Univ. de Huelva, E21071 Huelva, Spain

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The Journal of Physical Chemistry

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KEYWORDS: Water, methane, carbon dioxide, interfacial behavior, molecular simula-

tion, three phase equilibruim

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Abstract

The accurate description of the phase equilibria and interfacial behaviour of the

ternary mixture H2O + CO2 + CH4 is of fundamental importance in processes related

with enhanced natural gas recovery, CO2 storage, and gas-oil miscibility analysis. For

this reason, the physical understanding and theoretical modelling of this remarkably

complex mixture, in a wide range of thermodynamic conditions, constitutes a challeng-

ing task both for scientists and engineers. This work focuses on the description of the

interfacial behaviour of this mixture, with special emphasis on several regions that yield

different scenarios (vapour-liquid, liquid-liquid and vapour-liquid-liquid equilibria) and

in pressure and temperature ranges related with the practical applications previously

mentioned. A comparison between three alternative approaches has been performed:

atomistic Monte Carlo simulations (MC), Coarse Grained Molecular Dynamics (CG-

MD) simulations and Density Gradient Theory (DGT) have been used to characterize

the interfacial region, describing in detail complex phenomena, including preferential

adsorption and wetting phenomena even in the ternary triphasic region. Agreement

between the results obtained from different methods indicate that the three alternative

approaches are fully equivalent to analyze the interfacial behaviour. It has been also

found that the preferential adsorption of CO2 over H2O interface is greater if compared

to CH4 in all conditions characterized. In fact, we have also demonstrated that CH4

under triphasic conditions has very limited influence on the complete wetting of the

binary system H2O + CO2.

Introduction

In the last few years, the precise theoretical description of the interfacial properties of inho-

mogeneous fluid systems, including H2O, CH4, and CO2, has received much attention due to

its relevant industrial and environmental implications. These fluids are greatly involved, for

instance, in processes of enhanced natural gas recovery from the so-called non conventional

sources, and they are also matter of great interest in studies concerning geological CO2 stor-

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age.13 In these two applications, the interactions between the fluid and the solid substrate

play an essential role, and the conditions of adsorption, wetting, or confinement effects are

determined by the interfacial interactions, which are closely related to molecular scale inter-

actions. In this context, obtaining an accurate description of the interfacial behaviour (i.e

density profiles, interfacial tensions, Gibbs adsorption, etc.) is a key step towards a better

understanding of the physics of the problem. Experimental data for these properties are still

scarce due to the considerable technical difficulties associated to the design and operation of

experimental setups working especially in ranges of high pressure and/or temperature. This

handicap makes theoretical estimation even more important, and the critical evaluation of

existing theories and the development of new approaches are undoubtedly highly desirable

goals.

For these reasons, a number of new and interesting works are being published in this

field, proposing different approaches. For instance, Jackson and co-workers have presented

remarkable results48 studying the interfacial properties for this type of fluid systems with a

combination of the Density Functional Theory (DFT) and the SAFT-VR9,10 molecular equa-

tion of state (EoS), applied to CO2 mixtures,11 or in a more general perspective to reservoir

fluids.12 With a similar approach, Lafitte et al.13 have combined the Density Gradient The-

ory (DGT) with the original SAFT-VR Mie14 EoS to describe the interfacial behaviour of

the CO2 + H2O binary mixture. Other recent works have successfully used the same scheme,

combining DGT and different SAFT versions to study the interfacial behaviour of this latter

binary mixture, and the papers of Amzquita et al.15 and Li et al.16 are good represen-

tatives of this. Additionally, Hu et al.17 have studied the interfacial tension of the same

mixture using DFT. Recently, Ghobadi and Elliott18 combined DFT, considering the modi-

fied fundamental measure theory, with the SAFT- WCA EoS19 and analyzed the interfacial

properties of confined fluids and fluid interfaces. These inhomogeneous media theories, DGT

and DFT, have proved to be versatile and reliable, and their ability to describe different types

of interfacial behaviour, combined with their solid physical foundations, is to be underlined.

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Molecular Simulation (MS) is another valuable approach to study complex fluid systems.

Although much slower than other estimation techniques, a constraint which does not allow

to explore wide thermodynamic condition ranges, the capability to obtain a precise charac-

terization of the microscopic fluid structure for a given molecular model offers an important

added value. The possibility of obtaining a link between the details on the molecular models

and the influence of every variable on the macroscopic interfacial structure and properties

is to be pointed out as well. Despite this potentiality, it must be reminded that the quan-

titative interfacial properties results depend not only on the molecular models selected to

describe the fluids but also on the precise treatment of all variables involved in the simula-

tion. For instance, a rigorous treatment of the long-range corrections (LRCs) of both the

coulombic and dispersive terms of the intermolecular potential determines to a great extent

the quantitative results obtained from the calculation, as shown recently.20,21

The cited molecules have been widely studied using various MS techniques either in bulk

homogeneous conditions, or for inhomogeneous fluids presenting interfaces. For instance,

da Rocha et al.22 have described the structure of the interface between CO2 and H2O us-

ing Molecular Dynamics (MD) and atomistic models similar to those used in this work.

Kuznetsova and Kvamme23 study the liquid-liquid (LL) and liquid-vapour (LV) interfaces

involving mixtures of between CO2 and H2O using also MD. The same authors24 have ex-

tended their work to the ternary mixture obtained by adding CH4, focusing on the hydrate

formation conditions. They have developed a Gibbs free energy thermodynamic model to

describe the triphasic coexistence region and characterize the hydrate phase transitions, ob-

taining accurate results even for density profiles across the interfaces. In a recent work,

Miqueu et al.25 studied the interface of the CH4 + H2O binary mixture using inhomoge-

neous Monte Carlo (MC) simulation and the DGT + SAFT VR Mie14 approach obtaining

a detailed description of the microstructure formed at different pressures and temperatures.

Nielsen et al.26 have also focused on this binary mixture using MD simulations over the

entire range of pressures (545 MPa) and temperatures (298383 K) relevant to geologic

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carbon storage. Neyt et al.27 used byphasic MC and Gibbs Ensemble Monte Carlo (GEMC)

simulations to analyze the interfacial properties of mixtures of CO2 with several alkanes.

Recently, the work of Mller and Meja28 contributed with an innovative and interesting

characterization to the interfacial tension of the CO2 + H2O binary system, describing two-

and three-phase equilibrium at 298.15 K in a wide range of pressures by performing MD

simulations using a molecular Coarse Grained (CG) model. Finally, Garrido et al.29 have

proposed a methodology for characterizing the component density profiles, molar fractions,

equilibrium pressure, and interfacial tensions in a ternary system at the three-phase equilib-

rium state using MD and DGT for the case of monomeric LennardJones (LJ) mixtures.

From an experimental point of view, high-pressure interfacial tension data have been

reported3033 for the H2O + CO2 binary mixture at conditions at which different phases

coexist and also including paths crossing the triphasic line, which gives a good description

of the macroscopic behaviour of the interfaces. Nevertheless, many features of the interfaces

at molecular-scale level are not well studied yet. As an example, the reported preferential

adsorption of CO2 at the interfaces with water-rich phases under certain conditions (see e.g.

Lafitte et al.,13 or Mller and Meja28) has important implications in practical applications,

as enhanced natural gas recovery or CO2 geological storage. A study of the modification

of CH4 adsorption on fluid-fluid or solid-fluid interfaces upon the injection of an external

aqueous fluid at real reservoir conditions is then a matter of industrial relevance, and the need

to critically test the performance and reliability of the existing theoretical tools is a must.

This interest is enhanced by the very limited amount of experimental data on interfacial

properties of multicomponent systems. This lack of information is due to the technical

difficulties associated to this type of measurements. In this situation, both inhomogeneous

fluid theories and MS become extremely valuable estimation tools in the field of Process and

Chemical Engineering.

The main goal of this work is to analyze the capability of both, the atomistic and CG

models, as well as the DGT formalism in predicting the interfacial properties of the H2O +

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CH4 + CO2 ternary mixture. We pay special attention on regions of the phase diagram at

which different interfacial scenarios exist. This also includes the pressure and temperature

working conditions for the practical applications described above. This paper is organized

as follows; we first summarize the different molecular models, simulation techniques and the

main expressions of the Density Gradient Theory used to calculate the properties of interest

(section 2). In section 3 we present and discuss the main results obtained for the interfa-

cial properties of systems under investigation. Finally, we summarize the main conclusions

obtained in section 4.

Molecular Model and Theory

Atomistic Monte Carlo simulation

The MC calculation methodology used in this paper is related to the one used in a previous

work.25 We study here the interfacial properties of the coexisting fluid phases of two different

systems: the H2O + CO2 and H2O + CH4 + CO2 mixtures. In the latter case, we pay special

attention on the triphasic liquid-liquid-vapour (LLV) region of the phase diagram.

CH4 is modelled, following the united-atom approach, as a single LennardJones (LJ)

sphere using the parametrization proposed by Mller et al.34 This model, albeit simple, offers

accurate results in the calculation of interfacial properties, as shown by several authors.25,35,36

Concerning CO2, many different molecular models have been proposed in literature, but the

most widely used geometry is a rigid-linear chain molecule with three overlapped segments,

representing each of the atoms. In these rigid non-polarizable models each segment or inter-

acting site consists of a combination of a LJ site plus an electric point charge. This structure

mimics the typical anisotropic feature of CO2, including the large quadrupole moment value

accounted for the three partial charges. The parametrization selected in this case for this

molecular structure is the one proposed by Harris and Yung,37 the so-called EPM2 model,

which was optimized to reproduce accurately thermophysical properties, such as the critical

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point37 or VLE of binary mixtures.38 In the case of H2O, the well-known rigid non-polarizable

TIP4P/200539 model has been selected. This model considers four interacting sites placed

on the oxygen atom O, on each of the hydrogen atoms H, and along the HOH bisector on

the so called M-site. The TIP4P/2005, which has been shown to provide accurate estimates

of H2O bulk properties if compared with other similar versions, it is also remarkably profi-

cient in the estimation of interfacial properties, as shown by Vega and de Miguel.40 Table 1

summarizes the characteristic parameters for these molecular models.

Table 1: Lennard-Jones well depth and size , partial charges q, and geometry,of the CH4, H2O and CO2 models used.

Atom /kB (K) i () q(e) GeometryLennardJones CH4 149.92 3.7327 0TIP4P/2005 H2O

O 93.20 3.1589 0.0 O-H:0.9572 ()H 0.0 0.0 0.5564 O-M:0.1546 ()M 0.0 0.0 1.1128 H-O-H:104.52

EPM2 CO2C 28.129 2.757 0.6512 C-O:1.149 ()O 80.507 3.033 0.3256 O-C-O:180

The interactions between i and j molecular sites of different molecules are treated ac-

cording a pairwise additive Lennard-Jones (LJ) and Coulombic potential:

u (rij) = 4ij

[

(

ijrij

)12

(

ijrij

)6]

+qiqj

40rij(1)

where rij is the distance between sites, qi and qj are the partial charges on these sites, and

ij and ij are the LJ cross-parameters computed from pure molecular parameters i and j,

and i and j, respectively, using the Lorentz-Berthelot combining rules.

The LJ contribution to the internal energy is computed with a spherical cut-off radius

(rc), and inhomogeneous LRCs are evaluated with the method proposed by Janecek,41 and

later modified by MacDowell and Blas.42 The Janeceks method accounts accurately for the

LRCs in inhomogeneous systems along the whole range of temperatures in which the sys-

tem exhibits vapour-liquid coexistence,43 and what is more important, using this method

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the calculated values of interfacial properties obtained with a cut-off distance rc = 2.5

are identical to those obtained using any other larger cut-off distance.41,43 Consequently,

the cut-off radius is set to 3 in this case. The coulombic interactions are dealt with the

Reaction Field (RF) methodology, instead of the widely used Ewald summation technique.

Previous works have shown that the use of the RF method yields analogous results to the

computationally much more demanding Ewald sum method in the calculation of the in-

terfacial tension and coexistence densities of diverse systems: liquid-vapour simulations of

H2O,20 liquid-liquid simulations of CH4 + H2O binary mixture25 or even much more complex

biomolecular systems.44

The procedure used to simulate multiphasic interfaces, which was first introduced by

Liu,45 can be summarized as follows. In the case of two-phase equilibria, the first step is

the equilibration of two independent simulation boxes, in the isothermal-isobaric (NPT )

ensemble at the estimated coexistence temperature and pressure. The dimensions Lx and

Ly of these boxes are kept constant with a value Lx = Ly = 35 and volume variations are

performed by changing only the Lz distance with the aim to facilitate the posterior assembly

of a two-phase box. The usual periodic boundary conditions and minimum image convention

are applied. The number of molecules of each specie in the two boxes depends obviously

on the composition of the involved equilibrium phases, which has been estimated for MC

calculations using the SAFT-VR equation of state.9,10 In a recent paper, a detailed phase

equilibria study of the ternary mixture H2O + CH4 + CO2, and the involved binaries has

been performed using this approach.46 A similar strategy has been recently used by Forte et

al.47 to describe accurately the phase diagram of ternary mixtures containing water, carbon

dioxide, and several alkanes, and also Garrido et al.29 have applied this technique for ternary

systems under three-phase equilibrium at constant temperature. The number of molecules,

N , is adjusted in every case depending on the system composition, but always having at least

1024 water molecules present in the system (see Table 2 for distribution of molecules in MC

approach). It must be emphasized here that this initial guess of the equilibrium conditions

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is essential for the posterior correct development of the molecular simulation calculation.

If the initial values of the involved variables (equilibrium temperature, pressure, and phase

compositions) are far from the coexisting conditions predicted by the molecular models, the

boxes will not develop a stabilized interface after they have been put into contact. At this

point, it is very important to remind that although the molecular model on which the EoS

is grounded is not similar at all to the one considered during MC simulations, the guess

provided by the auxiliary thermodynamic model will be an essential and useful guide if the

model is reliable enough, as it is the case here. The use of the EoS as auxiliary model in this

case to obtain a guess of the coexistence conditions is to be underlined. Without this support,

obtaining an equilibrium configuration using MS only to describe coexistence conditions for

a multicomponent and multiphasic fluid is a remarkably cumbersome and time consuming

task. The excellent correspondence between the quantitative equilibrium results obtained

using the two theoretical routes explored must also be emphasized, despite the fact that both

approaches have little to do with each other. For practical purposes, this combined strategy

reveals itself here as a very useful alternative, but it needs an EoS and MS molecular models

which are realistic enough to provide a similar description of the real system involved. If this

is the case, the guess of equilibrium conditions obtained from the EoS may be used in a fully

transferable manner as input to guide the molecular simulations with successful results.

Once both simulation boxes have been equilibrated separately, an inhomogeneous bipha-

sic simulation box is constructed assembling along the z direction the simulation box corre-

sponding to the denser phase in the middle (to optimize CPU time), and two replicas of the

other box at both ends. Then, this biphasic simulation box is allowed to evolve at constant

temperature and volume (NV T ) conditions until two parallel explicit interfaces are fully

equilibrated. The NPT and NV T MC simulations are organized in cycles. Each cycle con-

sists of N attempts to either displace or rotate a randomly chosen molecule (both movements

with equal probability) in the case of canonical ensemble simulations. In addition to this, an

attempt to change the volume is used in bulk canonical ensembe or NPT simulations. The

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Table 2: Temperature (K), pressure (MPa) and number of molecules used in theinhomogeneous multiphasic simulation box for the CO2 + H2O and H2O + CH4+ CO2 mixtures.

T (K) P (MPa) N (Atomistic MC) N (Coarse Grained MD)CH4 34 H2O39 CO2 37 CH4 48 H2O28 CO2 49

H2O + CO2287.00 4.0 1024 100287.00 4.5 1024 120287.00 5.0 1024 500287.00 5.5 1024 600298.15 2.0 1024 50298.15 10.0 1024 864

CH4 + H2O + CO2275.00 6.3 260 1024 1120 628 3436 2936298.15 10.0 250 1024 250 378 6243 379298.15 10.0 150 1024 350 221 6241 538298.15 10.0 350 1024 150 526 6245 229550.00 30.0 154 1182 252 203 5433 364550.00 30.0 238 1136 74 423 5437 140

acceptance ratios for translational, rotational moves and volume changes are adjusted along

the run to approximately 30%. After the initial equilibration period, consisting in approxi-

mately 106 cycles, 2 106 cycles are used to accumulate averages of the desired interfacial

properties.

Coarse Grained Molecular Dynamics simulations

Coarse Grained Molecular Dynamics (CGMD) simulations are performed on ternary mix-

tures containing more than 6000 molecules at conditions of temperature and pressure where

the liquidvapour and liquidliquidvapour interface is present (see more details in Ta-

ble 2). The number of molecules of each species in the mixture is set according to the mole

fraction desired and the systems are set up in such a way that the volume fractions of the bulk

phases and bulk densities are comparable. The methodology is composed by two standard

parts: in the first part, CGMD simulations of the liquidvapour and liquidliquidvapour

equilibria are started from an initial configuration consisting of two and three single slabs

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of the different phases obtained from SAFT- Mie EoS48 located in a rectangular box. A

simulation in the isothermal-isobaric or NPT ensemble is then carried out at a pressure cor-

responding to the different liquid and vapour phases to equilibrate the system and establish

the equilibrium box dimension to be used in the subsequent simulations in the canonical

or NV T ensemble. In our particular case, the approximate dimensions of the simulation

box are chosen as Lx = Ly = 14CH4 . For the case of Mie interactions, a spherical cut-off

equal to half the simulation box was used (rcut = 7CH4) which was carefully calibrated

in order to avoid any significant size effect on results.50 The system is then simulated in

the NV T ensemble using the modified version of DL_POLY package51 at different temper-

atures listed in Table 2. A Nos-Hoover thermostat with a relaxation constant of 1.0 ps

and a Verlet leapfrog algorithm with a time step of 3 fs have been used. After the initial

NPT equilibration, simulations up to 30 ns were carried out, using the last 15 ns for data

acquisition.

For the case of CGMD simulations, molecules interact according to the Mie potential52

force field:

uMie (rij) = C[

(

ri,j

)r

(

ri,j

)a]

(2)

In this latter expression, r and a are the repulsion and attraction parameters of the

intermolecular potential, respectively, rij is the center-to-center distance of the interacting

segments, is the energy scale corresponding to the potential well depth, and is the length

scaling unit, corresponding to the effective segment diameter. C is a constant defined as:

C = rr a

(

ra

)a

ra

(3)

Table 3 summarizes the characteristic parameters used in this approach, taken from

Lafitte et al.48 for CH4, from Mller and Meja28 for H2O, and from Avendao et al.49 for

CO2. It is interesting to note that, as shown in Table 3, these molecules are represented

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Table 3: SAFT- Mie Force Field Parameters for pure fluids

Molecule msi /kB (K) i () ri ai 1020 cii (Jm5mol2)CG CH4 48 1 153.36 3.7412 12.65 6.00 1.981

CG H2O28 1312.39 (275.00 K) 2.9195 (275.00 K)

8.000 6.00 1.816320.99 (298.15 K) 2.9068 (298.15 K)370.51 (550.00 K) 2.8712 (550.00 K)

CG CO2 49 1 353.55 3.7410 23.00 6.66 2.811

as single isotropic CG beads interacting through a Mie potential. Particularly, the single

soft Mie potential for H2O, as a function of temperature, has been used to reproduce the

experimental value of the interfacial tension, the liquid density, and the experimental PT

projection of the phase diagram of the CO2 + H2O binary mixture28,49 using only a constant

interaction parameter. In this latter work, the authors provide valuable information on the

interfacial behavior using MS in the region close to the three-phase coexistence region, at

298.15 K, obtaining an excellent agreement between experimental data3033 and theoretical

descriptions of density profiles through DGT.13 In the case of CH4 and CO2, Aimoli et al.53

have presented recently a comparison of different force fields using MD for both molecules

analyzing the estimation of pure fluid density over wide pressure and temperature ranges.

This first criterium is then used by the authors as a filter to select the best performing

approaches, that are subsequently used for a complete study of second derivative properties

in the same range, including compressibilities, speeds of sound, heat capacities, and Joule-

Thomson coefficient. This remarkable extended study yielded very interesting conclusions.

For instance, in the particular case of CO2, the authors show that the simplified SAFT-

Mie49 molecular model is able to provide accurate results, improving clearly the performance

of other CO2 purely dispersive single site or even dimer models, and standing very close

to the performance of the widely used three site molecular models with explicit charges

-as EPM2, the one used in this case-. This relevant conclusion by Aimoli et al.53 is a

supplementary motivation for the study presented here, that extends the comparison between

performance of molecular models with different degree of detail from the estimation of pure

bulk thermodynamic properties to complex mixture interfacial behaviour.

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The CG-MD is extended to mixtures by using a number of unlike binary parameters

which are defined by applying the combination rules described by Lafitte et al.48 in the

SAFT-VR Mie EoS. The unlike size parameter, ij, is obtained using an arithmetic mean:

ij =ii + jj

2(4)

while the unlike Mie attractive interaction energy (or cross potential well depth), ij, is

obtained using a Berthelot-like geometric average:

ij = (1 kij)

3ii3jj

3ij

iijj (5)

where kij is a binary interaction parameter which can be obtained from experimental data

of phase equilibria. In this work, a unique binary interaction parameter kij = 0.08 has been

used for the mixture H2O + CO2,28 kij = 0.015 for the mixture H2O + CH4, and kij = 0.032

for the mixture CO2 + CH4. The supplementary material shows the PT projection of the

phase diagram of these mixtures calculated using SAFT- Mie. As can be seen, agreement

with calculations obtained by Mguez et al.46 is remarkable.

Finally, the cross attractive (a,ij) and repulsive (r,ij) parameters48 involved in the Mie

potential are calculated as:

(k,ij 3) =

(k,ii 3) (k,jj 3) ; k = a, r (6)

The expresion for k,ij has been initially proposed by Lafitte et al.54 This approach provides

a great performance in predicting the thermodynamic behaviour of mixtures of alcohols

with hydrocarbons, including second derivative properties. A more detailed and generalized

expression for different combinations of the Mie potential can be analyzed in the work of

Lafitte et al.48

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Molecular simulation of interfacial behaviour

In order to characterize the interfacial behavior from MC and MD, concentration profiles are

calculated by dividing the system in 250 slabs along the z direction. The molecular density

profiles, i (z), are obtained by assigning the position of each interacting site, zi, to the

corresponding slab and constructing the molecular density from mass balance considerations.

Additionally, these profiles are displaced so that the center of mass of the system lies at the

center of the simulation cell, avoiding smearing of the profiles due to fluctuations of the center

of mass. From the density profiles, i (z), it is possible to evaluate the surface activity of

each species along the interfacial region. Excluding the interface, coexisting phase densities

are computed as the average of the 25 central slabs in each phase using the final density

profile.

The surface tension is computed using two methods: the mechanical and thermodynamic

routes. In the first case, the interfacial tension is determined by using the Irving-Kirkwood

methodology according to which the interfacial tension is calculated from the components

of the pressure tensor and the Hulshof55 expression:

=1

2

+Lz/2

Lz/2

[pN (z) pT (z)] dz (7)

where pN(z) and pT (z) are the normal and tangential components of the pressure tensor,

respectively, and Lz is the size of the simulation box in the z direction, defined along the

longitudinal dimension across the interface. In this method, the profiles of the pressure

tensor diagonal elements are calculated employing the virial expression.56

In the second case, the Test-Area (TA) technique proposed by Gloor et al.,57 is used. The

TA method has been applied by different authors to determine the vapour-liquid interfacial

properties of several H2O models,20,40 binary fluid mixtures,25 and recently it has been also

used to determine the solid-fluid interfacial tension of a confined LJ fluid.58 In the TA

method, the interfacial tension, , can be obtained from the change in the Helmholtz free

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energy, A, in the limit of an infinitesimal perturbation in the interfacial area, A, in the NV T

ensemble. Within the scope of this approach, is given by

=

(

A

A

)

NV T

= limA0

(

A

A

)

NV T

= kBTA ln exp (U/kBT )0 (8)

where A is the infinitesimal perturbation in the interfacial area A. U denotes the change

in the configurational energy due to a small change of free energy A and 0indicates

an ensemble average carried out over an equilibrated state.

In the case of triphasic phase equilibrium the methodology followed is roughly the same,

with only minor adjustments. In the first step, three independent simulation boxes are equi-

librated, with the corresponding number of molecules of each type in each phase determined

using in this case the auxiliary SAFT-VR for Monte Carlo simulations and SAFT- Mie

for Molecular Dynamics simulations. In the second step, a small change is introduced in

the construction of the inhomogeneous triphasic simulation box. This box is constructed by

assembling five, instead of three, equilibrated boxes. The denser phase lies at the center of

the box, with the second liquid and vapour phases placed at each side, respecting periodic

boundary conditions in every case.29 The calculation of interfacial tension for the triphasic

systems is always carried out using the Irving-Kirkwood56 method, as the Test-Area method

has been developed for simulation boxes containing only two coexisting fluid phases.

Theoretical approach to interfacial behavior: Density Gradient The-

ory

The application of the DGT to different EoS models has been described by several au-

thors,13,25,5963 so here we only briefly outline the specific details considered for the calcu-

lation of the interfacial tensions and density profiles. According to the DGT formalism,

the inhomogeneous fluid between two bulk phases (, ) in equilibrium obeys the condition

of minimum energy. For a planar interface, the indicated condition is given by the

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following set of ordinary differential equations (ODEs)6467

nc

j=1

cijdjdz2

= 0i i (9)

i , i = 1, 2, . . . , nc

The boundary conditions associated to the ordinary differential equations are given by

the homogeneous bulk phase (, ): i (z z) = i and i(

z z)

= i . In Equation (9),

i corresponds to molar concentration or density of the i -th component defined in terms of

mole fraction xi as i = xi. Furthermore, z is the normal coordinate to the interface, nc is

the number of components, cij is the cross influence parameter, i is the chemical potential

of the i -th component, and the superscript 0 denotes the evaluation of a given property at

equilibrium state. The chemical potential (i) can be calculated from any EoS model by

considering the following definition

i =

(

a0i

)

T,V,j 6=i

(10)

where a0 is the Helmholtz energy density of the homogeneous system obtained from the

SAFT- Mie EoS.48 This equation of state is a modified version of the original SAFT VR Mie

equation14,54 in which a r and a variable Mie potential is used as a reference intermolecular

potential to describe chain and associating molecules. The generic SAFT-like approach68

is written in terms of the Helmholtz free energy, which can be expressed as a sum of the

following three microscopic contributions: an ideal gas contribution (aIDEAL) that allows

to obtain the ideal gas asymptotic behavior of the fluid phase in the low density limit, a

monomer term (aMONO) that takes into account the attractive and repulsive forces between

the segments that form the molecules, and a chain contribution (aCHAIN) that accounts for

the connectivity of segments within the molecules. The expression of the Helmholtz energy

density of SAFT-VR Mie EoS for a nonassociating chain fluid is given by

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a0 =(

aIDEAL + aMONO + aCHAIN)

Nav

(11)

where a = A/ (NkBT ), A is the total Helmholtz free energy, N is the total number of

molecules, Nav is the Avogadro constant, T is the absolute temperature, kB is the Boltzmann

constant, = 1/ (kBT ) , and is the molar density of the mixture. For further details and

description of the Helmholtz free energy density see the work Lafitte et al.48

Following the original work proposed by Carey,69 the cross-influence parameters (cij =

cji) are related to the geometric mean of the pure component influence parameters, as follows:

cij = (1 ij)ciicjj (12)

where ij is a symmetric adjustable parameter that, in turn, may be obtained from the

fit of experimental data of mixtures. In this case we have set the correcting parameter

ij equal to zero in our calculations, and considered a temperature-independent influence

parameter (cii is constant) fitted to experimental data of pure fluids,70 as explained by sev-

eral authors.13,25,5963 Table 3 summarizes the values of constant influence parameter using

the SAFT- Mie EoS. The interfacial tension modeled by the DGT+ SAFT- Mie EoS lies

within the experimental data uncertainties, providing an accurate estimation of the surface

tension over a wide temperature range, as shown in the supplementary information. The

approximation of constant influence parameter provides a good representation, as previously

shown by Garrido et al.,29 for a complex ternary system and greatly simplifies the math-

ematical solution. In this case, the set of ordinary differential equations simplifies to the

following algebraic equations:

css(

k () 0k)

=ckk(

s () 0s)

; k = 1, 2, . . . , s 1, s+ 1, nc (13)

It is important to recall that special care should be taken for solving Equation (13), which

is applied from the - to the - bulk phase, or vice versa, by appropriately selecting s as

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the independent variable. This selection is conditioned by the topolgy of the s function,

whose mathematical behavior should be monotonically defined along the interfacial region.

A practical rule of selection is to consider the pure fluid with the highest interfacial tension

as the independent s variable.69,7173 Then, from the i j projection, it is possible to

characterize the interfacial tension and distribution of species along the interfacial length by

considering the following relationships:

=

s

s

[

2

(

a0 nc

i=1

ii + p0

)

nc

i,j=1

cij

(

dids

)(

djds

)

]

(14)

(

dsdz

)2

=2 (a0

nci=1 ii + p

0)nc

i,j=1 cij

(

dids

)(

djds

) ; k = s

dkdz

=

(

dkds

)(

dsdz

)

; k = 1, 2, . . . , s 1, s+ 1, nc

where p0 is the equilibrium pressure. At this point, it is important to mention an special

case affecting the application of Equation (14), related with the calculation of interfacial

behaviour (interfacial tension and density profiles) involving three phases. Note that the

condition given by Equation (14) still remains valid and each one of the different density

profiles, together with their corresponding tensions, can be calculated by using appropriate

integration limits. These limits are obtained by the bulk phase condition given by the EoS

model.

Results

H2O + CO2

The simulation technique that considers biphasic boxes with contact between the coexist-

ing phases has the advantage of providing direct access to the structure of the interface,

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allowing the simultaneous determination of coexistence densities, interfacial properties, and

microscopic structural properties, as the case of density profiles, across the interface. As

an example, Figure 1 shows the density profile of the H2O + CO2 binary mixture across a

single interface at 298.15 K and two different pressures, 2 and 10 MPa. The density pro-

file of H2O increases monotonically across the interface with the traditional shape of the

hyperbolic tangent function. Note that no change in its shape is observed with increasing

pressure. However, the density of CO2 presents an adsorption peak located on the CO2-rich

side of the interface due to the low solubility of CO2 in the H2O-rich phase at these pressure

and temperature conditions. This behaviour is in agreement with the findings reported by

Miqueu et al.25 and Biscay et al.35 for the case of the CH4 + H2O mixture, and also for

mixtures made up of hydrocarbon with N2, CO2 or CH4.7476

Figure 1 also serves to illustrate the effect of the treatment of the LRCs to the inter-

molecular potential on the interface structure. Although the coulombic interactions are pre-

dominant for these models if compared with the dispersive LJ interactions, a recent work21

has shown that interfacial properties are very sensitive to the rigorous treatment of LRCs.

In this work, the coulombic interactions have been treated with the Reaction Field method20

and the Janeceks method41 -in the formulation of Blas and MacDowell,42- is used to deal

with dispersive interactions. Since the DGT approach with constant influence parameter is

accurate for describing vapour-liquid interfaces mainly, it is difficult to unambiguously judge

the physical reliability of our predictions. Consequently, results for interfacial density pro-

files are compared with Monte Carlo results. Particularly, Figure 1 shows the performance

of this combined treatment. The obtained results are in a good agreement with the mixture

density profiles across the interface determined using an alternative theoretical approach, the

Density Gradient Theory, applied to the new version of SAFT developed by Lafitte et al.48

On one hand, agreement between density profiles obtained from MC and DGT calculation

is remarkable. Although MC underestimates the height of the peak in density profiles when

compared with the DGT, it successfully predicts preferential adsorption of CO2 at the inter-

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face. This fact is also observed in the recent work of Mller and Meja,28 in which density

profiles calculated by CG-MD shown that CO2 is strongly adsorbed in the H2O interface.

On the other hand, the use of a pure truncation of the LJ potential and no further treat-

ment of LRCs results in a different estimation of interfacial mixture density profiles, in the

same direction of the case of pure liquid vapour interfacial properties shown in the previous

work.21

Figure 2 depicts the vapour-liquid density profiles of the CO2 + H2O binary mixture

just below the saturation pressure of CO2 at 287 K. We have decided to explore these

thermodynamic conditions because they evidence interesting phenomena from a fundamental

point of view near the three-phase equilibrium. As shown in Figure 2, CO2 accumulates at

the interface creating a thin liquid film that perfectly wets the interface with the liquid H2O.

As pressure increases at constant temperature, this adsorbed layer grows thicker continuously

just below the saturation pressure of CO2. This represents a prewetting transition,77 which

means that Tcw < T < Tc, where Tcw represents the critical wetting temperature at this

thermodynamic condition. This effect is obtained by the imminent appearance of a three-

phase equilibrium (the prediction by SAFT- Mie shown in Figure 2c), where the CO2

adsorption at the interface of the H2O-rich phase changes from a gas-liquid equilibrium

(GLE) to a liquid-liquid equilibrium (LLE). In fact, Figure 2c shows the DGT calculations

at 287 K and 5 MPa where density profiles of CO2 and H2O clearly predicts the appearance

of a new liquid phase. Here, the density profiles of CO2 obtained using inhomogeneous

LRCs provide also the best agreement with those obtained with DGT calculation in this

work and in perfect agreement to the theoretical calculation reported by Lafitte et al.13

using the original SAFT-VR Mie EoS and = 0.085. In fact, we have tested 6= 0 values

but a marginal and non-statistically significant improvement of predictions is found. At

this point, it is important to note that with a value of = 0 the DGT with SAFT model is

a fully predictive scheme. This result demonstrates that LRCs are fundamental to compute

accurately not only the CO2 interfacial behaviour, but the phase equilibria itself, as Figure 2

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shows that the pure truncation of the potential leads to an incorrect location of the CO2

saturation transition for the molecular model selected in this case.

Once the density profiles of the system are investigated, we have obtained the interfacial

tension of the H2O + CO2 binary mixture at different thermodynamic conditions. Figure 3

shows the interfacial tension of the mixture as obtained from MC and DGT+SAFT- at

298.15 and 287 K. We have also included literature experimental data.3033 In this particular

case, interfacial tension is obtained from MC simulation using the Test-Area57 and Irving-

Kirkwood56 methods. Since the interfacial tension values obtained using both alternatives

are fully equivalent, only TA values are plotted in Figure 3 for clarity. Agreement between

MC values, experimental, theoretical values, and Coarse-Grained Molecular Dynamics (CG-

MD) simulations28 is remarkably satisfactory. Nevertheless, interfacial tension is much more

sensitive to LRCs in the prewetting transition conditions, if compared to liquid-liquid or

vapour-liquid equilibria, as shown in Figure 3b. This is in agreement with the fact that

the vapour-liquid phase transition at 287 K is only adequately estimated using LRCs in

MC simulations. Interfacial tension values computed using inhomogeneous LRCs are in this

case in much better agreement with both DGT and experimental values. Once again, these

results are in excellent agreement with CG-MD obtained by Mller and Meja.28

H2O + CO2 + CH4

Once we have analyzed the interfacial behavior of the CH4 + H2O25 and CO2 + H2O binary

mixtures using MC simulation, the next objective is to analyze the interfacial behaviour

of the ternary mixture. Pseudo-binary diagrams depicting the boundary limits of invariant

equilibrium points have been typically applied to determine the main features of phase

behavior of the ternary system, as described in detail in a previous work.46 The global phase

diagram of this ternary mixture is rather complex, with a combination of two systems that

exhibit type-III phase behaviour, the H2O containing binary mixtures, and the last system,

CH4 + CO2, that behaves as type-I according to the classification of van Konynenburg and

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Scott.78 As in the case of the binary mixture studied in the previous section, we use SAFT-

VR9,10 as theoretical input for MC simulations and SAFT- Mie48 for CG-MD calculations

for the analysis of the interfacial properties and fluid phase equilibria of this ternary mixture.

In particular, we consider different types of interfacial behavior, as well as the analysis of

the triphasic liquid-liquid-vapour (LLV) region of the phase diagram.

The phase behaviour of the ternary system is dominated at high pressures by relatively

large VL and LL immiscibility regions as consequence of the transition from the phase

behaviour of the CH4 + H2O mixture (vapour-liquid equilibrium) to that of the CO2 + H2O

system (liquid-liquid equilibrium). This complex phenomenology is depicted in Figure 4a. As

can be seen, SAFT- Mie underestimates the coexistence region along the H2O-poor phase

compared with the predictions of SAFT-VR, while both models are able to provide the same

description of the region phase in the H2O-rich liquid phase. Note that the composition here

is nearly constant (xH2O 0.999). This difference is due mainly to the use of the CG model

for H2O since the main objective of the parametrization of this model has been to represent

the interfacial tension and the condensed phase density in a wide range of temperature and

pressure conditions.28

At higher temperature and pressure conditions (550 K and 30 MPa), as shown in Fig-

ure 4b, the two-phase LL immiscibility region shrinks. Once again we can see that SAFT-

Mie underestimates the size of the coexistence region of the H2O-poor phase. Note that

this is true for the predictions of both EoS. Equivalent to Figure 4a, the phase envelope

corresponding to the H2O-rich liquid phase remains essentially at the same position in the

triangular phase diagram. From the quoted figure it is possible to observe a new H2O-poor

liquid phase whose composition varies between xH2O 0.33 0.4 and xH2O 0.68 0.65,

as predicted by SAFT-VR and SAFT- Mie respectively, while CO2 and CH4 composition

changes inversely in the models selected.

Figure 4c depicts the triangular diagram of the ternary mixture at 275 K and 6.3 MPa.

Now, the topology of the phase diagram is completely different than that shown in Figure 4a

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or Figure 4b, since it displays one triangular central LLV three-phase region, where two

liquid phases coexist in equilibrium with a vapour phase. The compositions of each phase

are defined by the coordinates of the central triangle in the phase diagram. It is important to

remark that the same position in the triangular phase diagram is observed for H2O-rich liquid

phase (nearly constant at xH2O 0.999) predicted by both EoS. The fundamental difference

is observed in the region composed by the two liquids and the vapour phase, namely VL1E

and VL2E, for the same reason noted for the case of Figure 4a. In summary, although there

is a difference between the predictions obtained from both SAFT models, the results allow to

obtain global concentrations along the ternary diagram (pseudo-binary systems), and hence,

to compare the predictions obtained from both MS calculations.

Table 4: Phase equilibrium and interfacial tension results calculated for H2O +CO2 + CH4 ternary mixture at 298.15 K and 10 MPa. The subscripts give theaccuracy of the last decimal(s), i.e., 1017.31.4 means 1017.3 1.4

Global concentrations L kg/m3 V kg/m3 mN m1

MCxCH4 0.3 and xCO2 0.7

9924 164.51.4 422CG-MD 1017.31.4 153.10.9 37.21.4DGT 1022.6 193.71 35.61



9915 142.20.9 503CG-MD 1012.21.1 125.90.9 44.81.1DGT 1022.72 131.79 42.22



9924 103.30.8 573CG-MD 1013.71.3 127.30.8 51.20.9DGT 1019.96 107.91 49.71

The reason to choose these three PT conditions is that the interfacial behavior is in

each case different, as it will be shown later, and will serve to demonstrate the ability of the

tested molecular models (SAFT-VR and SAFT- Mie) and molecular simulations techniques

(MC and MD) with the setting described above, in the description of the different interfacial

scenarios for this complex mixture. The comparison of the location of the different phase

equilibria boundaries -molar fraction and bulk densities- as initial guesses for MS calculations

are provided by the selected molecular EoS. This constitutes the strategic plan in the present

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work, i.e., guiding MS calculations based on accurate molecular based EoS.29

Ternary density profiles across the interface computed by MC and CG-MD simulations

at 298.15 K and 10 MPa, are plotted in Figure 5 for the tie lines depicted in Figure 4a.

The first comment to be noted is that MC simulation provides an excellent agreement with

the prediction of the phase behavior obtained from CG-MD, as the bulk phase and density

behaviors of the coexisting phases are very close to each other (results are summarized in

Table 4). As we discussed in Figure 4a, a H2O-rich liquid phase composed almost of pure

H2O coexists with one H2O-poor phase whose composition varies between different global

composition selected: Figure 5a (xCH4 0.3 and xCO2 0.7), Figure 5b (xCH4 0.5 and

xCO2 0.5), and Figure 5c (xCH4 0.7 and xCO2 0.3). The selection of global concentrations

is not random, as it allows to analyze how the interfacial behavior is modified between the

constituent binaries. The density profile of H2O shows the same trend as before, observing

that density values of H2O in the ternary system are very close to experimental data70 of

pure H2O. The densities of CO2 and CH4 present an adsorption peak located on the waterless

phase side, due to the low solubility of the coexisting phases at these PT conditions. The

preferential adsorption peak of CO2 is much higher than that of CH4 because H2O molecules

are more likely to interact with CO2 than with CH4. Moreover, the adsorption of CO2 and

CH4 decreases and increases, respectively, when the ternary system transits from the H2O

+ CO2 LLE to the H2O + CH4 VLE at this particular thermodynamic condition. As in

previous cases, quantitative agreement between theory and MS is observed. In summary,

the DGT+SAFT- Mie approach provides a reliable description of the interfacial properties

of these systems.

Figure 6 shows the density profiles across the interface for the mixture at 550 K and

30 MPa, and at concentrations corresponding to the two tie lines shown Figure 4b. Ta-

ble 5 summarizes the coexistence densities and the interfacial tensions obtained from the

approaches used. At these high-pressure conditions, the mixture shows phase equilibria be-

tween a H2O-rich phase and a H2O-poor phase. Density profiles in this figure reveal the

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Table 5: Phase equilibrium and interfacial tension results calculated for H2O +CO2 + CH4 ternary mixture at 550 K and 30 MPa. The subscripts give theaccuracy of the last decimal(s), i.e., 780.51.6 means 780.5 1.6


MCxCH4 0.56, xCO2 0.18, xH2O 0.26

7383 120.81.2 171.7CG-MD 772.81.3 200.61.1 13.91.5DGT 802.03 171.17 11.93


MCxCH4 0.25, xCO2 0.45, xH2O 0.30

7352 1772 191.4CG-MD 780.51.6 239.91.2 12.61.8DGT 809.1 227.29 11.01

difference produced on the prediction of equilibrium in Figure 4b due to the overestimation

of the vapour density of H2O, at 550 K, as obtained from the CG-MD approach. Now,

contrarily to the case shown previously, only a very slight adsorption of CO2 and CH4 at

the interface (region highlighted in the inset of Figure 6a and Figure 6b) is obtained from

the MC, CG-MD, and DGT predictions. The difference between this and the previous case

is to be underlined, and it was predictable from the results obtained by Miqueu et al.25 for

CH4 + H2O.

It is interesting to analyze the discrepancies obtained in the interfacial tension values of

the ternary mixture using different approaches. As shown in Tables 4 and 5, atomistic models

(TIP4P2005/EPM2/LJ) overpredict the interfacial tensions about 5 mNm1 compared with

the results obtained from the CG-MD and DGT approaches. This result is consistent with

the analysis obtained by Liu et al.79 for simulations of the vapour-liquid interface and values

of the interfacial tension in the CO2 + H2O + NaCl ternary mixture. In fact, we can observe

in Figure 3 that the simulations of the atomistic TIP4P2005 and EPM2 models are also found

to overpredict the experimental interfacial tension, and also estimations obtained from CG-

MD and DGT calculations. However, as pointed out before, the interfacial behaviour (i.e

interfacial tension, adsorption phenomena, and density profiles) obtained from the three

methodologies used are mutually consistent.

Finally, it is important to remark that all approaches used in this work are able to predict

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Table 6: Interfacial Tensions () and bulk densities () at 275 K and 6.3 MPafor the mixture H2O + CO2 + CH4 at triphasic condition. The subscripts givethe accuracy of the last decimal(s), i.e., 1023.41.2 means 1023.4 1.2

L1 kg/m3 L2 kg/m

3 V kg/m3 L1L2 mN m1 V L2 mN m

1 V L1 mN m1

MC 9944 8242 142.21.3 382 70.8 462CG-MD 1023.41.2 865.21.2 143.60.8 31.20.9 5.20.5 36.50.6DGT 1033.62 842.88 160.12 30.02 4.81 34.85

the existence of triphasic LLV phase equilibrium for this ternary mixture, as described by

the SAFT-VR and SAFT- Mie bulk EOS at conditions around 275 K and 6.3 MPa, as

shown in Figure 7 (results for the three approaches are summarized in Table 6). It has been

possible to demonstrate as well a good coherency between both EoS models, if the ternary

three-phase surfaces shown as Supplementary Material are compared with the results of

Mguez et al.46 These profiles are in excellent agreement with all the methods considered,

and also show positive excess adsorption, very similar to the binary case discussed by Mller

and Meja28 for CO2 + H2O mixture at 298.15 K. This situation reveals that CH4 does not

have a great significance in the interfacial behavior of the ternary mixture. It is evident that

the H2O-poor vapour phase (V) and H2O-rich liquid 1 phase (L1) have been separated by

the appearance of a CO2-rich liquid 2 phase (L2). As demonstrated in a previous work,29

a binary or ternary system under three-phase condition is characterized by three different

values of interfacial tensions (L1L2 , V L1 , and V L2), which are related through the following

inequality.80

V L1 V L2 + L1L2 (15)

It has been well established that this inequality, also known as Neumman inequality,

implies that the L2phase is in partial contact or, equivalently, the L2 phase partially wets

the interface formed by the V and L1 phases. The case of equality in Equation (15), denoted

as Antonow rule, implies that the L2-phase completely wets the interface formed by the

V and L1 phases. The results summarized in Table 6 show that the wettability pattern

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(V L1 = V L2 + L1L2) corresponds to a total wetting of the L2 bulk phase at the V L1

interface. This fact is very important for this kind of system, because it reveals that CH4

under the conditions of pressure and temperature selected has no influence on the complete

wetting of the binary system CO2 + H2O.

Conclusions

In this work, two different approaches using molecular simulation (MC and CG-MD) and

DGT have been applied to predict the fluid phase coexistence and interfacial behavior of two

different systems, the CO2 + H2O binary mixture and the CO2 + H2O + CH4 ternary mix-

ture. MC molecular simulation provides an accurate description of the CO2 + H2O interfacial

tension and density profiles of each component across the interface, in good agreement with

theoretical predictions from DGT + SAFT- Mie and experimental data available, which

confirms the consistency of this method. Nevertheless, it must be reminded that calculation

of interfacial properties is very sensitive to the inhomogeneous LRCs of the intermolecular

interactions. The results obtained evidence that only a careful and complete treatment of

these LRCs yields quantitatively correct values and interfacial behavior.

As a combination of two molecular simulation approaches, MC and CG-MD have been

applied to describe the interfacial behavior of the CO2 + H2O + CH4 ternary mixture

using SAFT-VR and SAFT- Mie as auxiliary models for MC and CG-MD, respectively,

with the aim to obtain an estimation of the phase boundary locations and initial guesses

for conditions able to generate stable molecular simulation calculations. Trying to obtain

equilibrium coexistence states from simulation of a mixture that exhibits a complex phase

diagram, as the one shown here, without a reliable input of these involved variables is a

nearly improbable task. Coexisting fluid phases are examined through interfacial density

profiles of each component at different thermodynamic conditions. A nearly systematic

adsorption of CH4 and CO2 at the interface with the H2O-richer phases, clearly affected by

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pressure, is observed. The competitive adsorption between both species can be discussed and

quantitatively characterized in this case, which is very relevant for any practical application.

The ability to describe the region of the phase diagram of the system at which three

phases coexist, including the knowledge of pressure, temperature, and coexisting phase com-

positions, can be regarded as the most stringent proof showing the ability of the rigid non-

polarizable molecular models and single isotropic CG model selected for the three species

treated. On one hand, it is important to recall again that the molecular parameters of the

models used in this work are tuned originally to describe pure fluid saturation data. Here,

we use the same parameters, without any type of higher order parameter or spurious mixing

rule, to predict accurately and simultaneously the complex mixture phase behaviour and

interfacial properties from MS. On the other hand, CG-MD simulation provides a symbiotic

route between a rigorous model equation of state and molecular simulations. Since both

approaches are based on the same potential model, this allows to analyze the coherency

of molecular simulation results (mixing rules, appropriate molecular parameter of pure flu-

ids) and to understand the interfacial behavior of the mixtures studied, including interfacial

tension, adsorption phenomena, wetting, etc.

Acknowledgement

The authors thank Dr. Christelle Miqueu (Universit de Pau et des Pays de LAdour, France)

for stimulating discussions concerning this work. J.M.M. acknowledges Fundacin Barri de

la Maza (Spain), for a postdoctoral grant, and J.M.G acknowledges doctoral scholarship

from Conicyt, Chile and from Red Doctoral REDOC.CTA, MINEDUC project UCO1202 at

U. de Concepcin. H. S and A. M acknowledges partial support financed by FONDECYT,

Chile (Projects 1120228 & 1100938). M.M.P. acknowledges CESGA (www.cesga.es) and

MCIA (AVAKAS cluster, Univ. of Bordeaux) for providing access to computing facilities,

and Ministerio de Economa y Competitividad, (Proj. Ref. FIS2012-33621, cofinanced with

EU FEDER funds). F.J.B. also acknowledges Ministerio de Economa y Competitividad

29

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123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960

(Proj. Refs. FIS2010-14866 and FIS2013-46920-C2-1-P, cofinanced with EU FEDER funds).

Additional funding from Junta de Andaluca and Universidad de Huelva is also acknowledged.

Supporting Information Available:

The Supporting Information provided includes first a description of the calculation method

used to estimate the DGT influence parameter. Then, the temperature dependence of inter-

facial tension, , estimated using SAFT- Mie EoS and the coarse grained molecular models

described for H2O (Fig. S1), CH4 (Fig. S2), and CO2 (Fig. S3) is included. Also, the

plot of the P-T projection of the global phase diagrams estimated using the same theory,

for the binary mixtures H2O + CO2 (Fig. S.4), H2O + CH4 (Fig. S.5) and CH4 + CO2

(Fig. S.6) have been included. Finally, a tridimensional plot of the triphasic region of the

ternary mixture, estimated again using the same theory at 275 K, is shown in Fig. S.7. This

material is available free of charge via the Internet at http://pubs.acs.org.

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