Water-alternating-macroemulsion reservoir simulation through capillary number-dependent modeling

  • Ranena V. Ponce F.
  • Vladimir Alvarado
  • Marcio S. CarvalhoEmail author
Technical Paper


Experimental observations clearly show that dispersed-phase pore-scale flow effects of emulsion flow are responsible for drop entrapment at pore throats and this strongly depends on local capillary number. As a result, this dimensionless number is key to parametrize emulsion flooding for EOR purposes. In this work, we incorporate capillary number effects that influence two well-known oil recovery mechanisms observed in continuous emulsion flooding, namely a microscopic increased pore-level efficiency, and a macroscopic mobility control or flood conformance. These mechanisms can be advantageously exploited in a newly proposed process denominated water-alternated-emulsion (WAE) injection, which is the focus of this article. To this end, a capillary number dependence was added to our initial model [17]. The resulted parametrization of relative permeability curves as functions of the capillary number was implemented in a Matlab open-source code. A parametric analysis of a 1/4 five-spot geometry used on the first layer of the Tabert Formation shows that capillary number can significantly impact emulsion mobility control potential that has been shown to contribute to the observed oil recovery enhancement. Emulsions with adequate drop-to-pore size ratio and interfacial properties optimize emulsion mobility reduction and sweep efficiency. Results show that timing of the emulsion injection can promote conformance improvement and accelerate oil production. Mitigation of high injection pressure observed in continuous emulsion flooding is possible during cyclic WAE injection without significant oil recovery impairment.


Emulsion flooding Capillary effects Mobility control Enhanced oil recovery 

List of symbols


Capillary number


Emulsion dispersed drop concentration (vol\(\%\) )


Injected emulsion dispersed drop concentration (vol\(\%\) )


Emulsion’s displacement efficiency mechanism


Drop-to-pore size distribution


Fractional flow


Injector bottom-hole pressure (KPa)


Absolute permeability tensor (\(\mathrm{m}^{2}\))


Aqueous-phase relative permeability


Oil-phase relative permeability


Emulsion relative permeability endpoint at residual oil saturation


Emulsion relative permeability endpoint at irreducible emulsion saturation


Oil relative permeability endpoint at irreducible water phase saturation


Emulsion’s mobility control mechanism


Corey’s exponent for water phase with emulsion’s dispersed drop as component


Corey’s exponent for oil phase (oil-emulsion system)


Corey’s exponent for oil phase (oil–water system)


Corey’s exponent for water phase


Original oil in place (m\(^3\))


Recovery factor


Pressure (Pa)


Pore volume


Total flow rate (m\(^3\)/s)


Flow rate of the water phase (m\(^3\)/s)


Flow rate at the injector well (m\(^3\)/s)


Residual oil saturation to emulsion


Residual oil saturation to water phase


Water saturation


Irreducible water saturation


Time (s)


Water-alternating emulsion


Water cut


Variable X parametrized by capillary number


Variable X parametrized by dispersed drop concentration


Maximum value of the variable X


Minimum capillary of the variable X

Greek symbols

\(\Delta S_\mathrm{w}\)

Difference in water saturation between waterflooding and WAE injection


Total mobility (1/Pa.s)


Displacing fluid viscosity (Pa.s)

\(\mu _\mathrm{o}\)

Oil viscosity (Pa.s)

\(\mu _\mathrm{w}\)

Water viscosity (Pa.s)


Reservoir domain

\(\partial \Omega\)

Frontier of the reservoir domain

\(\Omega _\mathrm{i}\)

Cell frontier of the injector well

\(\Omega _\mathrm{p}\)

Cell frontier of the producer well



\(\rho _\mathrm{o}\)

Oil density (Kg/m\(^3\))

\(\rho _\mathrm{w}\)

Water density (Kg/m\(^3\))


Oil–water interfacial tension (mPa.s)


Darcy velocity (m/s)



We would like to acknowledge the Chevron Corporation, Petrobras, and the Enhanced Oil Recovery Institute (EORI) at the University of Wyoming for financial support.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2017

Authors and Affiliations

  • Ranena V. Ponce F.
    • 1
  • Vladimir Alvarado
    • 2
  • Marcio S. Carvalho
    • 1
    Email author
  1. 1.Department of Mechanical EngineeringPUC-RioRio de JaneiroBrazil
  2. 2.Department of Chemical and Petroleum EngineeringUniversity of WyomingLaramieUSA

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