Abstract
This paper reports experimental research on the flow behavior of oil-water surfactant stabilized emulsions in different pipe diameters along with theoretical and computational fluid dynamics (CFD) modeling of the relative viscosity and inversion properties. The pipe flow of emulsions was studied in turbulent and laminar conditions in four pipe diameters (16, 32, 60, and 90 mm) at different mixture velocities and increasing water fractions. Salt water (3.5% NaCl w/v, pH = 7.3) and a mineral oil premixed with a lipophilic surfactant (Exxsol D80 + 0.25% v/v of Span 80) were used as the test fluids. The formation of water-in-oil emulsions was observed from low water fractions up to the inversion point. After inversion, unstable water-in-oil in water multiple emulsions were observed under different flow regimes. These regimes depend on the mixture velocity and the local water fraction of the water-in-oil emulsion. The eddy turbulent viscosity calculated using an elliptic-blending k-ε model and the relative viscosity in combination act to explain the enhanced pressure drop observed in the experiments. The inversion process occurred at a constant water fraction (90%) and was triggered by an increase of mixture velocity. No drag reduction effect was detected for the water-in-oil emulsions obtained before inversion.
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Abbreviations
- [η]:
-
Krieger-Dougherty intrinsic viscosity parameter
- α c :
-
Averaged continuous phase volume fraction
- α d :
-
Averaged dispersed phase volume fraction
- α i :
-
Averaged phase i volume fraction
- \({\overline T _i}\) :
-
Average temperature of phase i
- β i :
-
Coefficient of thermal expansion of phase i
- \({\bf{\tau }}_i^t\) :
-
Phase i turbulent stress tensor
- τ c :
-
Continuous phase laminar stress tensor
- τ d :
-
Dispersed phase laminar stress tensor
- τ i :
-
Phase i laminar stress tensor
- D c :
-
Deformation rate tensor of the continuous phase
- D d :
-
Deformation rate tensor of the dispersed phase
- D i :
-
Deformation rate tensor of phase i
- F d :
-
Inter-phase drag force
- I :
-
Identity tensor
- n :
-
Wall normal vector
- u i :
-
Phase i velocity
- \(\dot \gamma \) :
-
Scalar shear rate
- η r (ϕ):
-
Dimensionless relative viscosity of the mixture
- γ :
-
Wall blending function
- \(\mu _i^t\) :
-
Turbulent eddy viscosity of phase i
- \(\mu _{tot}^t\) :
-
Total turbulent eddy viscosity of the mixture
- μ c :
-
Dynamic viscosity of the continuous liquid
- μ d :
-
Dynamic viscosity of the dispersed liquid
- μ i :
-
Phase i dynamic viscosity
- μ m :
-
Effective mixture viscosity
- μ lam :
-
Dynamic (laminar) viscosity of the mixture
- ν i :
-
Kinematic viscosity of phase i
- ϕ :
-
Dispersed phase volume fraction
- ϕ i′:
-
Elliptic blending function for phase i
- ϕ i :
-
Dispersed phase volume fraction inversion point parameter
- ϕ m :
-
Maximum packing dispersed phase volume fraction parameter
- ρ i :
-
Phase i mass density
- σ ε :
-
k-ε turbulence model constant
- σ κ :
-
k-ε turbulence model constant
- τ w :
-
Scalar wall shear stress
- ε 0 :
-
Ambient turbulence value constant
- ε i :
-
Turbulent dissipation rate of phase
- a‴ :
-
Symmetric interaction area density
- A D :
-
Linearized drag coefficient
- C D :
-
Particle drag coefficient
- c i :
-
Speed of sound in phase i
- C ε1 :
-
k-ε turbulence model constant
- C ε2 :
-
k-ε turbulence model constant
- C η :
-
k-ε turbulence model constant
- C μ :
-
k-ε turbulence model constant
- C κ :
-
Elliptic blending k-ε turbulence model constant
- C L :
-
k-ε turbulence model constant
- C M :
-
k-ε turbulence model constant
- C T :
-
k-ε turbulence model constant
- C t :
-
k-ε turbulence model constant
- d :
-
Particle diameter
- E i :
-
Elliptic blending k-ε turbulence model additional production
- \(G_i^b\) :
-
Standard k-ε buoyancy turbulence production term for phase i
- \(G_i^k\) :
-
Standard k-ε turbulence production term for phase i
- k i :
-
Turbulent kinetic energy per unit mass of phase i
- L i :
-
Characteristic turbulence length scale of phase i
- m ij :
-
Mass transfer term from phase i to j
- p :
-
Pressure
- \(P_i^k\) :
-
k-ε turbulence production term for phase i
- p i ϕ′ :
-
Elliptic blending k-ε production term for phase i
- \(Pr_i^t\) :
-
Turbulent Prandtl number of phase i
- Re :
-
Particle Reynolds number
- Re d :
-
Wall-distance Reynolds number
- Re m :
-
Mixture particle Reynolds number
- \(S_i^k\) :
-
Additional energy source term for phase i
- t 0 :
-
Specific turbulence time-scale
- t i :
-
Turbulent time-scale of phase i
- t ei :
-
Turbulent large eddy time-scale of phase i
- u * :
-
Wall velocity scale for phase i
- y :
-
Wall distance
- y i + :
-
Dimensionless wall distance for phase i
- Y i M :
-
Compressibility modification of Sakar and Balakrishnan for phase i
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Acknowledgements
Jose Plasencia’s work was funded by the Multiphase Flow Assurance Innovation Centre (FACE) — a research cooperation between Norwegian Universities and industry involving IFE, NTNU, and SINTEF. The centre was funded by The Research Council of Norway and industrial partners. The authors gratefully acknowledge Bjørnar Pettersen and Equinor for the FBRM probe. Nathanael Inkson would like to thank Dr. Mohit Tandon for building the emulsion model upon his multiphase code.
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Open access funding provided by NTNU Norwegian University of Science and Technology.
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Plasencia, J., Inkson, N. & Nydal, O.J. Research on the viscosity of stabilized emulsions in different pipe diameters using pressure drop and phase inversion. Exp. Comput. Multiph. Flow 4, 241–263 (2022). https://doi.org/10.1007/s42757-020-0102-2
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DOI: https://doi.org/10.1007/s42757-020-0102-2