Fluid surfaces and interfaces

• Two immiscible fluids in contact -> surface
• Liquid/liquid: interface, otherwise surface
• Interfacial tension gives rise to force/energy per area
• Interfaces are attractive for impurities

Why crude oil/water interfaces?

• Crude oil is never produced without water
• Separating water from oil can be surprisingly tricky

Why is it hard to separate?

• Tiny water drops suspended in oil: emulsion

Modern coalescer

• Integrated into gravity separators (below), or inline

It works, now what?

• Research has been ongoing since 1911
• Current aims of research:
  • More compact equipment
  • More efficient equipment
  • Less use of chemicals and energy for heat-treating
  • Ability to predict coalescer performance

What is actually crude oil?

-> natural gas, gasoline, diesel, engine oil, wax; glue, asphalt

What are really asphaltenes?

• National High Magnetic Field Lab, FSU

What are really asphaltenes?

• IBM Zürich group, AFM with functionalized CO-tip

MD simulation to the rescue?

• Molecular dynamics (MD):
  • Determine some force field (resolution)
  • Put N particles in a box
  • Solve Newton’s second law for many small timesteps

Levels of resolution for MD

• Molecular simulations have varying resolution, from quantum to coarse-grained

SAFT-γ Mie approach

• One-to-one correspondence between Equation of State (EoS) and MD
  • Can fit EoS to experimental data -> MD parameters
  • Tune MD parameters to match experiments -> EoS
  • Also have correlation using critical properties
• Helmholtz energy based EoS
  • \(A(\rho,T) = A^{ideal} + A^{mono} + A^{chain} + A^{assoc}\)
  • Can get all other properties by partial derivatives
• Coarse-grained molecular force field

Bottled SAFT

• With SAFT-\(\gamma\) Mie we can simulate almost any chemical
• We made a database with 6000+ chemicals
• Let’s make an app for that! http://www.bottledsaft.org

\(^1\) Å. Ervik, A. Mejía, E.A. Müller. Journal of Chemical information and modeling, 2016

Polymer phase transitions

• Coarse-grained model for polystyrene in heptane

\(^2\) Å. Ervik, G.J. Serratos, E.A. Müller. Computer Physics Communications, (2016)
\(^3\) G.J. Serratos et al. Macromolecules 50 (12) (2017)

Liquid-liquid equilibrium

• Alkane+toluene mixture in equilibrium with water
  • Water: model by Lobanova\(^1\)
  • Heptane, Dodecane: M&M model\(^2\)
  • Toluene: ring-SAFT\(^3\)
• Parwise cross-interactions need to be fitted w. experiments \(^4\) O. Lobanova, C. Avendaño, T. Lafitte, E. A. Müller and G. Jackson. Molecular Physics 113, (2015)
  \(^5\) A. Mejía, C. Herdes, and E. A. Müller. Industrial & Engineering Chemistry Research, 53(10) (2014)
  \(^6\) A. Mejía and E. A. Müller. Langmuir, 33(42) (2017)

Liquid-liquid equilibrium

• Prediction at high \(T, P\) of interfacial tension
  • winners of 9th Industrial Fluid Properties Simulation Challenge
  • Challenging system with interfacial adsorption

\(^7\) C. Herdes, Å. Ervik, A. Mejía, E.A. Müller. Fluid Phase Equilibria (2017)

Molecular models for crude oil/water

• Heptane/toluene oil, water model as before
• Asphaltene
  • Interfacially active, coats water drops
  • ~50 C atoms, complexity is combinatorially huge
  • Extremely polydisperse mixture
  • “Coarse-graining in” the complexity

Asphaltene models used here

• We developed three coarse-grained model asphaltenes

• Definition of asphaltenes is vague:
  • Cluster in heptane
  • Do not cluster in toluene

• Only our final model actually does this

\(^8\) A multiscale method for simulating fluid interfaces covered with large molecules such as asphaltenes,
Å. Ervik, M.O. Lysgaard, C. Herdes, G.J. Serratos, E.A. Müller, S.T. Munkejord, B. Müller.
J. Comp. Phys. 327 (2016)

Do they behave like asphaltenes?

Asphaltenes at interfaces

Asphaltenes at interfaces

Link to the macroscale

• From molecular simulations we can compute
  • interfacial tension \[ \gamma = \frac{L_z}{2}(P_{zz} - \frac{1}{2}(P_{xx}+P_{yy}))\]
  • interfacial elasticity \[ E_d = \frac{\Delta \gamma}{A/A_0 - 1}\]
• Gives one-way link to macroscale

Macroscale: new method for contaminated interfaces

• MSc thesis of Morten Olsen Lysgaard (2015)
• level-set/ghost-fluid/immersed-boundary
• Can have an arbitrary tension on interfacial elements \[ T = E_d (d-1) + \gamma \]
• \(E_d\) and \(\gamma\) parameters from MD
• Important: non-Gibbsian elasticity
• Gives interfacial force in Navier-Stokes \[\vec{f} = \frac{\partial T}{\partial s}\vec{t} + T\,d\,\kappa\,\vec{n}\]

The multiscale method

Pulling water out of an asphaltene-covered drop

• Very interesting case: crumpling of the interface
• Have identified two regimes in the literature, based on Eötvös number \[Eo = \Delta\rho g R^2/\gamma\]
• Very small \(Eo\): symmetric crumpling
• Moderate \(Eo\): axisymmetric crumpling

Small Eötvös number

Moderate Eötvös number

• Suggests new interpretation/understanding of crumpling

Implications for separation

• As the elasticity decreases total tension to zero, driving force for coalescence disappears
• All “emulsion-breaking” techniques are somehow increasing the total tension

• The usual experimental measurements of elasticity give wrong results

• Next step: experiments to confirm these hypotheses

Crude oil / water interfaces

• Dynamics of fluid interfaces still poorly understood
• Coarse-grained MD enables study of many systems
• With CFD: multiscale analysis of complex interfaces
• Elastic hypothesis is promising step forwards
• Work is needed on experimental validation
• Could spur new methodologies for separation equipment

Session info

Written in R Markdown and rendered with reveal.js.

print(sessionInfo(), locale = FALSE)

## R version 3.4.2 (2017-09-28)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 10 x64 (build 14393)
## 
## Matrix products: default
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base     
## 
## loaded via a namespace (and not attached):
##  [1] compiler_3.4.2  backports_1.1.1 magrittr_1.5    rprojroot_1.2  
##  [5] tools_3.4.2     htmltools_0.3.6 revealjs_0.9    yaml_2.1.14    
##  [9] Rcpp_0.12.13    stringi_1.1.5   rmarkdown_1.6   knitr_1.17     
## [13] stringr_1.2.0   digest_0.6.12   evaluate_0.10.1