Interfacial behavior of the decane + brine + surfactant system in the presence of carbon dioxide, methane, and their mixture † Soft Matter

Molecular dynamics simulations are carried out to get insights into the interfacial behavior of the decane + brine + surfactant + CH 4 + CO 2 system at reservoir conditions. Our results show that the addition of CH 4 , CO 2 , and sodium dodecyl sulfate (SDS) surfactant at the interface reduces the IFTs of the decane + water and decane + brine (NaCl) systems. Here the influence of methane was found to be less pronounced than that of carbon dioxide. As expected, the addition of salt increases the IFTs of the decane + water + surfactant and decane + water + surfactant + CH 4 /CO 2 systems. The IFTs of these surfactant-containing systems decrease with temperature and the influence of pressure is found to be less pronounced. The atomic density profiles show that the sulfate head groups of the SDS molecules penetrate the water-rich phase and their alkyl tails are stretched into the decane-rich phase. The sodium counterions of the surfactant molecules are located very close to their head groups. Furthermore, the density profiles of water and salt ions are hardly aﬀected by the presence of the SDS molecules. However, the interfacial thickness between water and decane/CH 4 /CO 2 molecules increases with increasing surfactant concentration. An important result is that the enrichment of CH 4 and/or CO 2 in the interfacial region decreases with increasing surfactant concentration. These results may be useful in the context of the water-alternating-gas approach that has been utilized during CO 2 -enhanced oil recovery operations.

observed favorable CO 2 -fluorinated surfactant tail interactions at the interface in the water + surfactant + CO 2 system. 50 The high density of CO 2 in the bulk enabled strong interaction between CO 2 and the hydrocarbon tail of SDS at the interface. 56,57 However, the interfacial behavior of the decane + brine + surfactant + CH 4 + CO 2 system has not been studied yet.
Molecular simulations have emerged as important tools for accurately predicting the bulk and interfacial properties. 9,[12][13][14]38,[59][60][61][62] Here, we perform molecular dynamics (MD) simulations to get insights into the interfacial behavior of the decane + brine + surfactant system in the presence of CH 4 and CO 2 at reservoir conditions.

Simulation details
MD simulations of decane + water + surfactant and decane + brine + surfactant two-phase systems in the presence of CH 4 and CO 2 at 323 and 443 K, and pressure up to 100 MPa were carried out using the GROMACS package. 63 The salt (NaCl) concentration is 2.7 mol kg À1 and the amounts of surfactant adsorbed at the interface are 0.008 and 0.016 SDS per Å 2 . The method is similar to that used previously by us. 39,64,65 In short, the TraPPE force field was used to model normal decane, methane, and carbon dioxide. [66][67][68] Water is represented by the TIP4P/2005 model 69 and the Na + and Cl À ions are described using the Smith and Dang 70 parameters. As in the case of, e.g., decane, the hydrocarbon tail of SDS (C12) was also modeled using the TraPPE united atom force field. The sulfate head group of SDS was modeled using the all-atom CHARMM36 forcefield. 71 The Lennard-Jones energy (e) and distance (s) parameters, and the charges (q) of the SDS molecules are given in Table 1. The number of each species employed in our simulations is given in Table 2. For example, all the systems had 2048 water and 200 decane molecules. Also, all the systems had the dimensions of 36 Â 36 Å parallel to the interfaces (Fig. 1). The cell size in the z-direction (perpendicular to the interfaces) L z was about three times this value. The system sizes used here ensure that the finite-size effects are negligible. 38,[40][41][42][43][72][73][74] Each system was equilibrated for 5 ns in the NPT ensemble (only L z varied) and we ran a 5 ns production under NVE conditions. The temperature was controlled using the Nosé-Hoover thermostat and pressure using the Parrinello-Rahman barostat.
The IFT was estimated from the below equation: 38,39,64,65,72-75 where the diagonal components of the pressure tensor are represented by P xx , P yy , and P zz . The radial distribution function (RDF) was determined as described previously. 14 The validation of models and a detailed analysis of the interfacial behavior of decane + H 2 O and decane + brine (NaCl) systems in the presence of CH 4 , CO 2 , and their mixture can be found in our previous studies. 38,39 The amounts of surfactant chosen in our simulations (0.008 and 0.016 SDS per Å 2 ) seem to be well below the critical micelle concentration (CMC). The overlap of the simulated IFTs of the water + SDS and water + SDS + CH 4 systems with the corresponding experimental data 46,47 is shown in Fig. 2.
To achieve the overlap, the bulk concentration of surfactant reported in the experiments was multiplied by a constant (same value used in both systems). It is important to mention that these estimates could be further improved by using the Gibbs adsorption isotherm. 55,58 For these systems, the CMC is about 8 mM (about 0.025 SDS per Å 2 76,77 ). Note, however, that higher surfactant concentrations might be considered by using coarsegrained models. 78 3 Results

Interfacial tension
The simulated IFTs of the decane + water + surfactant and decane + brine + surfactant systems in the presence of CH 4 (x CH 4 = 0.5), CO 2 (x CO 2 = 0.5), and their equimolar mixture (x CH 4 = x CO 2 = 0.25) at 443 K are provided in Fig. 3. The salt (NaCl) concentration was 2.7 mol kg À1 and the amounts of surfactant adsorbed at the interface were 0.008 and 0.016 SDS per Å 2 . The corresponding simulation results at 323 K are provided in Fig. S1 (ESI †). Note that our previous results of the simulated IFTs of the decane + water 38 and decane + brine (NaCl) 39 systems in the presence of CH 4 , CO 2 , and their mixture compared well with the corresponding experimental 25,35 and density gradient theory (DGT) 38,39 results. Past studies have shown that the IFT of the alkane + water + CH 4 /CO 2 systems is more similar to that of the corresponding alkane + water system alone. 25,35,36,[38][39][40][41][42][43]45 Also, the IFT of the decane + brine + CH 4 / CO 2 systems was more similar to that of the corresponding decane + brine system alone. 26,29,39,44,45 The IFTs of all these systems decreased with temperature. For instance, the simulation value of the IFT of the decane + water system (20 MPa) decreased from about 47.8 mN m À1 at 323 K to about 36.5 mN m À1 at 443 K. 39 It was found that the IFTs of these systems generally increased with pressure. The influence of pressure was, however, found to be less pronounced at lower temperatures and higher values of x CH 4 /x CO 2 . Note that the IFT of the water + CH 4 /CO 2 and brine + CH 4 /CO 2 systems depends nonmonotonically on pressure. [72][73][74][75][79][80][81][82][83][84][85][86][87][88] Furthermore, the IFTs of the alkane + water + CH 4 /CO 2 and alkane + brine + CH 4 /CO 2 systems increased with decreasing x CH 4 /x CO 2 . Here, the influence of methane was found to be less pronounced than that of carbon dioxide. This can be attributed to the fact that the interface was highly enriched with CO 2 molecules than with methane molecules. It was found that the IFTs of the alkane + brine and alkane + brine + CH 4 /CO 2 systems increase with salt concentration. 26,27,29,39,44,45 Here, the linear slope in the IFT versus salt (NaCl) concentration plot was about 2 mN (m mol kg À1 ) À1 under all conditions. This value was similar to that reported for the brine + CH 4 /CO 2 systems. 72,73,79 However, higher slopes were reported for the corresponding systems containing divalent ions. 73,79 Previous studies 47,55 have also shown that the IFTs decreased with increasing SDS concentration, e.g., at the methane/water interface (see Fig. 2). Our current results show that the addition of the SDS surfactant reduces the IFTs of the decane + water and decane + water + CH 4 /CO 2 systems. Similar behavior is also observed for the decane + brine and decane + brine + CH 4 /CO 2 systems. For example, the IFT of the decane + water + surfactant (0.016 SDS per Å 2 ) system is about 16.5 mN m À1 at 20 MPa and 443 K. As in the case of, for example, the alkane + water system, the IFTs of these surfactant containing systems decrease with temperature and the influence of pressure is found to be less pronounced. We see that the IFTs of the decane + water + surfactant + CH 4 /CO 2 and decane + brine + surfactant + CH 4 / CO 2 systems decrease with increasing x CH 4 /x CO 2 . Again the influence of methane is found to be less pronounced than that of carbon dioxide. For example, the IFTs of the decane + water + surfactant (0.016 SDS per Å 2 ) system in the presence of CH 4 (x CH 4 = 0.5) and CO 2 (x CO 2 = 0.5) were about 13.7 and 11.5 mN m À1 , respectively, at 20 MPa and 443 K. It can be seen that the IFT of, for instance, the decane + water + surfactant + CH 4 + CO 2 system is more similar to that of the corresponding decane + water + surfactant + CO 2 system. Furthermore, the addition of salt increased the IFTs of the decane + water + surfactant and decane + water + surfactant + CH 4 /CO 2 systems. For example, the IFT of the decane + brine + surfactant (0.016 SDS per Å 2 ) system is about 25.2 mN m À1 at 20 MPa and 443 K.

Atomic density profiles
The atomic density profiles may provide insights into the bulk and interfacial properties of the studied systems. The simulated density profiles for the decane + brine + surfactant + CH 4 + CO 2 (x CH 4 = x CO 2 = 0.25) system at 443 K and 20 MPa are provided in Fig. 4. These profiles at other conditions are provided in Fig. S2-S4 (ESI †). Note that our simulation results of the atomic density  profiles for the decane + water 38 and decane + brine (NaCl) 39 systems in the presence of CH 4 , CO 2 , and their mixture compared well with the corresponding DGT 38,39 results. Previous studies of the alkane + water + CH 4 /CO 2 and alkane + brine + CH 4 /CO 2 systems 36,[38][39][40][41][42][43]45 have shown that the presence of CH 4 and CO 2 hardly affects the density profiles of water, alkane, and salt. It was found that, in general, the density profiles of water and alkane vary monotonically across the interfacial region. These profiles might be approximated by a hyperbolic tangent function. 89 The salt ions were excluded from the interfacial region and distributed homogenously within the H 2 O-rich phase. However, water is enriched at the interfacial region with the addition of salt. 39,73,86,90 This can be  explained by the enhanced ionic desorption from the interfacial region at high salt concentrations. Also, at high x CH 4 , the interfacial region was enriched with decane in the alkane + water + CH 4 system. 38 It is worth noting that the simulated distributions of alkane exhibited artificial oscillations in the interfacial region due to finite-size effects. 89,91 The interfacial region was enriched with CH 4 and CO 2 molecules for the alkane + water + CH 4 /CO 2 and alkane + brine + CH 4 /CO 2 systems. 36,[38][39][40][41][42][43]45 This enrichment was found to decrease with temperature and increase with pressure. Also, in general, this enrichment increased with increasing x CH 4 / x CO 2 . Here, the enrichment of methane was found to be less pronounced than that of carbon dioxide. The presence of salt had no significant effect on the CH 4 /CO 2 enrichment. 39 At low pressures, however, the enrichment of the interfacial region with CO 2 (CH 4 ) depends nonmonotonically on x CO 2 (x CH 4 ). 38,40 Details of the interfacial behavior of the water + CH 4 /CO 2 and brine + CH 4 / CO 2 systems have been described by us and others. [72][73][74][75][80][81][82][83][84][86][87][88] Here the enrichment of the interfacial region with CH 4 and CO 2 depends nonmonotonically on pressure.
Note that the behavior of the IFT can be further understood by means of the Gibbs adsorption equation: where G i and m i are the surface excess and the chemical potential of component i, respectively. The surface excesses could be calculated using the density profiles. 38,39,64,65,73,74,84,85 A detailed description of the surface excess of different species in the decane + water + CH 4 /CO 2 and decane + brine + CH 4 /CO 2 systems is provided in our previous reports. 38,39 For these systems, it was found that the IFTs increase with pressure (salt concentration) due to the negative surface excesses of alkanes (salt). 38,39 For the water + CH 4 /CO 2 and brine + CH 4 /CO 2 systems, a minimum was found in the IFT versus pressure plot when the surface excess of CH 4 /CO 2 changes sign from positive to negative. 73,75,84,85 Furthermore, for the alkane + water and alkane + water + CH 4 /CO 2 systems, the solubilities of decane/ CH 4 /CO 2 in the water-rich phase and water in the decane-rich phase were very low. 38,92,93 The solubility of CH 4 /CO 2 in the water-rich phase was found to decrease with the addition of salt (salting-out effect). 39 Our current results show that the sulfate head groups (see, e.g., sulfur atoms) of the SDS surfactant molecules penetrate the water-rich phase and their alkyl tails are stretched into the decane-rich phase. The Na + counterions of the SDS surfactant molecules are located very close to their head groups (see, e.g., Fig. S2, ESI †). Furthermore, the distributions of water and Cl À ions are independent of the surfactant concentration for the Fig. 5 Simulated surface excess (symbols) of (a) CH 4 , (b) CO 2 , and (c) decane for the decane + brine + surfactant + CH 4 + CO 2 (x CH 4 = x CO 2 = 0.25) system at 323 K and NaCl concentration of 2.7 mol kg À1 . The corresponding surface excess at 443 K is shown in (d), (e), and (f), respectively. The lines denote the DGT results. 39 studied systems (see also Fig. S5, ESI †). However, the interfacial thickness between water and decane/CH 4 /CO 2 molecules increases with increasing surfactant concentration. We estimated the interfacial thickness between water and decane by applying the ''90-90'' interfacial thickness criterion (distance between positions where densities of decane and H 2 O were 90% of their own bulk densities). 51 The results are provided in Fig. S6-S9 (ESI †). The interfacial thickness between water and decane is in the range of about 1.1-1.7 nm for the studied systems. This interfacial thickness shows an opposite trend to that seen for the IFT. For example, the interfacial thickness decreases with the addition of salt and increases with the addition of CH 4 /CO 2 . Interestingly, the enrichment of CH 4 and/or CO 2 in the interfacial region decreases with increasing surfactant concentration. It seems that the enrichment is followed by a minimum in the density profile of CO 2 at high surfactant concentrations. This minimum is found near the location of the surfactant tails.
We calculated the surface excess 38,39,64,65,73,74,84,85 by using these density profiles. Our results show that the surface excess of CH 4 , CO 2 , and decane decreases with increasing surfactant concentration (Fig. 5). The surface excess of CH 4 /CO 2 changes sign from positive to negative as surfactant concentration increases. The addition of SDS surfactants has a more pronounced effect on the surface excess of decane. For example, at 443K and 20 MPa, the surface excess of decane in the decane + brine + CH 4 + CO 2 39 and decane + brine + surfactant + CH 4 + CO 2 (0.016 SDS per Å 2 ) systems is about À0.47 Â 10 À6 mol m À2 and À2.7 Â 10 À6 mol m À2 , respectively. The corresponding surface excess of CH 4 is about 0.19 Â 10 À6 mol m À2 and À 0.73 Â 10 À6 mol m À2 , respectively, and that of CO 2 is about 0.57 Â 10 À6 mol m À2 and À0.03 Â 10 À6 mol m À2 , respectively. Here the effects of pressure, temperature, and mole fraction on the surface excess are similar to those observed for the decane + water + CH 4 /CO 2 and decane + brine + CH 4 /CO 2 systems. 38,39 For example in all cases, we see that the surface excess of decane decreases with pressure, whereas the surface excess of CH 4 and CO 2 increases with pressure.

Radial distribution functions
The RDFs may give further insights into the interfacial properties of the surfactant-containing systems. The simulated RDFs for the decane + brine + surfactant + CH 4 + CO 2 system at 443 K and 20 MPa are provided in Fig. 6. We see that water molecules and counterions are nearest to the SDS headgroups. The first peak in the RDF of S-H (water), S-Na + , and S-O (water) is around 0.29, 0.36, and 0.38 nm, respectively. These peak positions obtained here are consistent with the previous simulation results. [52][53][54]58 The presence of water molecules near the SDS headgroups is possibly due to the hydrogen bonding between SDS headgroups and water molecules. 49 Whereas, CO 2 , CH 4 , decane, and Cl À are further away from the SDS headgroups. The first peak in the RDF of S-O (CO 2 ), S-CH 4 site, and S-Cl À is around 0.40, 0.46, and 0.49 nm, respectively. The RDFs show that the interactions of the surfactant headgroups with methane are weaker than those with CO 2 . This is expected due to the quadrupole moment of CO 2 molecule. 94 Similar positions of these peaks were found in all studied systems. It is worth mentioning that here the RDFs may not go to unity at large distances due to the inhomogeneous nature of the system. [52][53][54]58 In comparison, the alkyl tails of SDS interact strongly with decane molecules leading to peaks, for example, at 0.55 nm (Fig. S10, ESI †). Furthermore, it is found that the alkyl tails of SDS interact similarly with CH 4 and CO 2 . For both these interactions the first peak in the RDF plot is around 0.47 nm and its magnitude is about 1.7. A similar result is obtained for the interactions between alkane and CH 4 /CO 2 . 64, 65 We calculated the end-to-end distance and radius of gyration 62,64,65 of the alkyl tails of SDS molecules for the decane + water + surfactant system (Table 3). Here the end-to-end distance is in the range of about 1.12 to 1.18 nm. This endto-end distance decreases with temperature and increases with the amount of surfactant. We found that pressure has no effect on the end-to-end distance. Similar trends were observed for the radius of gyration. Furthermore, these sizes were not affected by the presence of salt/CH 4 /CO 2 under the studied conditions.
Regarding the SDS force field (see Table 1), it was shown that the difference among the force fields does not have much effect on the overall structure of small aggregates of surfactant. 54 Among different water models, the surface tension simulated using TIP4P/2005 model was close to the experimental data. 72 Moreover, our simulated RDF peaks for SDS-water spatial correlations are consistent with previous studies. [52][53][54]58 It will be challenging to obtain the relevant activity coefficients of, e.g., salt from molecular simulations for these multi-component Fig. 6 RDFs between the S-atom of SDS and different species in the decane + brine + surfactant + CH 4 + CO 2 (x CH 4 = x CO 2 = 0.25) system at 443 K and 20 MPa. The NaCl concentration is 2.7 mol kg À1 and the amount of surfactant adsorbed at the interface is 0.016 SDS per Å 2 .  (2)). 38,39 Note that we did not consider any SDS in the bulk and the salting-out of SDS to the interface. 48 Therefore, further studies are necessary to fully understand the effects of surfactants on the decane + brine + CH 4 /CO 2 systems.

Conclusions
The interfacial behavior of the decane + brine + surfactant + CH 4 + CO 2 two-phase system was studied using MD simulations at 323 and 443 K, and pressure up to 100 MPa. Note that our previous results 38, 39 of the simulated IFTs of decane + brine + CH 4 /CO 2 systems compared well with the corresponding experimental 25,35 and DGT 38,39 results. Our current results show that the addition of CH 4 , CO 2 , and the presence of SDS surfactant at the interface reduced the IFTs of the decane + water and decane + brine (NaCl) systems. Notably, the influence of methane was observed to be less pronounced than that of carbon dioxide. For example, the IFT of the decane + water + SDS + CH 4 + CO 2 (x CH 4 = x CO 2 = 0.25) system is more similar to that of the corresponding decane + water + SDS + CO 2 (x CO 2 = 0.5) system. This may be attributed to the fact that the interface was highly enriched with CO 2 molecules than with CH 4 molecules.
As expected, at a fixed surface concentration of SDS, the addition of salt increases the IFTs of the decane + water + SDS and decane + water + SDS + CH 4 /CO 2 systems. The IFTs of these surfactant-containing systems decreased with temperature and the influence of pressure was found to be less pronounced.
The atomic density profiles show that the sulfate head groups of the SDS molecules penetrate the water-rich phase and their alkyl tails are stretched into the decane-rich phase. The Na + counterions of the surfactant molecules are positioned very close to their head groups. Furthermore, the density profiles of water and salt ions are independent of the surfactant concentration. However, the interfacial thickness between water and decane/CH 4 /CO 2 molecules increases with increasing surfactant concentration. For instance, the interfacial thickness between water and decane is in the range of about 1.1-1.7 nm for the studied systems. This interfacial thickness decreased with the addition of salt and increased with the addition of CH 4 /CO 2 . An important finding is that the enrichment of CH 4 and/or CO 2 in the interfacial region decreases with increasing surfactant concentration. The calculated RDFs show that the interactions of the surfactant headgroups with methane are weaker than those with CO 2 .

Conflicts of interest
There are no conflicts to declare.