Impact of Natural Gas Adsorption on the Surface Tension of Liquid Water Eboni Collins1, Olivia Allen2, Yang Wang3, Hank Ashbaugh3 1Department of Physics, Dillard University, New Orleans, LA, 2Department of Chemistry, University of Arkansas at Pine Bluff, Pine Bluff, AR, 3Department of Chemical and Biomolecular Engineering, Tulane University, New Orleans, LA

AcknowledgementsWe thank the Ashbaugh group for their help over the summer. HSA thanks

Brian Pethica (Princeton). We also thank the National Science Foundation for financial support through grantsDMR-1460637 and DMR-1852274

Surface Virial CoefficientSimulation Methods

Methane Adsorption on Water Methane Surface ExcessIntroductionAdsorption phenomenon plays a significant role applications ink printing,pesticides spraying, emulsification, and oil recovery. The natural gas-waterinterfacial tension (IFT) has impact on gas production and transportation aswell as hydrate formation, because during processing, gas is frequently incontact with water while flowing through porous media and the gas-water IFTcan affects the capillary pressure which can cause serious pore blockingproblems during two-phase flow, especially in tight gas reservoirs. Whileexperiments can measure the IFT from macroscopic perspective, a molecular-level picture of adsorption interfacial phenomena is less clear.

Figure 3 shows methane positivelyadsorbs on the planar surface of water.This is indicated by the peak in themethane density just to the right of thewater density profile. Following theadsorption peak, methane’s densityquickly decays to the bulk gas density.The results in this figure were obtainedat 20°C with 1044 methane included.The measured pressure in thesimulation box is 82 bar. While detailsvary, the density profiles in the othersimulations are qualitatively similar.Quantities like the surface excess (the“extra” amount of methane adsorbedon the surface per unit area) can beextracted from these results.

The surface excesses determinedfrom GAI and the methanedensity profiles at 25°C usingsimulation are illustrated in Figure5. We observe excellentagreement between resultsobtained from the adsorptiondensity (e.g., Figure 3) and theadsorption isotherm (e.g., Figure4) giving us confidence in thephysical picture that methaneadsorption drives the surfacetension drop.

For comparison, we include thesurface excess determined byapplying GAI to the experimentsby Sachs and Meyn1. Overall, theresults agree qualitatively,although greater adsorption isfound experimentally.

Conclusions

Impact of Adsorption on Surface TensionThe surface tension can by evaluated by integration of differences in the componentsof the pressure tensor across the water/methane interface. Figure 4 shows thesurface tension determined from our simulations at 5°C, 25°C, and 45°C as a functionof the system pressure. This data shows that the surface tension is reduced by 15 to20 mN/m by increasing the methane pressure. This data is in qualitative agreementwith the experimental results reported by Sachs and Meyn3 (Figure 4 inset).

References

The impact of methane adsorptionon the surface tension can beexpressed as a virial expansion𝛾𝛾0 − 𝛾𝛾 = 𝑅𝑅𝑇𝑇𝑇𝑇 + 𝑅𝑅𝑇𝑇𝑏𝑏2𝑇𝑇2 + ⋯,

where 𝛾𝛾0 is the surface tension ofthe neat water surface, 𝑅𝑅𝑇𝑇 is theproduct of the ideal gas constantand temperature, and 𝑏𝑏2 is thesecond surface virial coefficient.𝑏𝑏2 is a measure of the interactionsbetween pairs of methane onwater’s surface. Figure 6compares 𝑏𝑏2 determined fromsimulation, experiment, and fromstatistical theory. The overallagreement between these isexcellent, providing confidence weare capturing surface interactions.

Figure 3. Density profile of water (blue) and methane(red) with 1,044 methane particles at 20°C

Thermodynamics connects thechanges in the surface tensionand the surface excess, Γ ,through the Gibbs’ AdsorptionIsotherm (GAI)

�𝜕𝜕𝜕𝜕𝜕𝜕𝜇𝜇𝑚𝑚𝑚𝑚 𝑇𝑇

= −Γ.

Here 𝜇𝜇𝑚𝑚𝑚𝑚 is the chemical potentialof methane. The chemicalpotential is generally an increasingfunction of pressure. Hence, forsystems that exhibit positiveadsorption (Γ > 0) we expect thesurface tension to be a decreasingfunction of pressure as observed.If we can evaluate the derivative inthe GAI, we can compare surfaceexcesses determined from thesurface tension (e.g., Figure 4)against those from the density(e.g., Figure 3).

Figure 4. Surface tension with respect to the methanepressure and temperatures of 5°C, 25°C, and 45°C(symbols defined in legend). The inset figure showsexperimental results from ref. 3 at 25°C.

Figure 5. Surface excess with respect to pressure at25°C. Symbols are defined in the figure legend. Toapply GAI the surface tension results in Figure 4were fitted to an empirical equation for the isotherm,while the chemical potential was determined frommethane’s equation-of-state.

Figure 6. Comparison between surface 𝑏𝑏2 as afunction of temperature determined from simulation,experiment3,4, and statistical theory. Symbols aredefined in the figure legend. From statisticalmechanics 𝑏𝑏2 ≈ 𝜋𝜋 ∫0

∞ 1 − exp(−𝜑𝜑/𝑅𝑅𝑇𝑇 𝑟𝑟 d𝑟𝑟

methane adsorptionpeak

bulk methane

1. Abascal, Jose LF, and Carlos Vega. "A general purpose model for the condensed phases of water: TIP4P/2005." The Journal of Chemical Physics 123 (2005):234505.

2. Martin, Marcus G., and J. Ilja Siepmann. "Transferable potentials for phase equilibria. 1. United-atom description of n-alkanes." The Journal of Physical ChemistryB 102 (1998): 2569-2577.

3. W. Sachs and V. Meyn, “Pressure and temperature dependence of the surface tension in the system natural gas/water. Principles of investigation and the firstprecise experimental data for pure methane /water at 25°C up to 46.8 MPa Colloids and Surfaces A 94 (1995): 291-301.

4. Jho, C., et al. "Effect of pressure on the surface tension of water: Adsorption of hydrocarbon gases and carbon dioxide on water at temperatures between 0 and 50C." Journal of Colloid and Interface Science 65 (1978): 141-154.

• Simulations capture the drop in water’s surface tension due tomethane adsorption.

• Surface excesses determined from methane’s density and the Gibbs’Adsorption Isotherm agree quantitatively.

• Surface virial coefficients determined for first time from simulation.

Figure 2. a) 336 Methane at 20 ℃. b) 1516 Methane at 50 ℃.

The Molecular Dynamics (MD) simulationsGROMACS 2016.3.Water Model:TIP4P/20051.Methane Model: TraPPE-UA2.

Canonical ensemble (NVT)1500 water in the center.Methane ranging from 0 to 4820 (22different amount of methane).Temperature ranging from 0 ℃ to 50 ℃ withincrement of 5 ℃.

Simulation box (4 nm × 4 nm × 30 nm). Simulation: 1 minimization, 1 equilibration

and 1 production (100 ns).

TIP4P/2005 Water

United Atom Methane

Figure 1. a) water droplet not wetting the surface due to thesurface tension. b) illustration of the gas-water interface.

a) b)Over the summer, wehave performedmolecular dynamicssimulations to examinemethane adsorption, thesimplest natural gas, onthe air-water interface todevelop a microscopicand thermodynamicperspective onadsorption.