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

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## Abstract

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.

## Keywords

Emulsion flooding Capillary effects Mobility control Enhanced oil recovery## List of symbols

- Ca
Capillary number

- \(C_\mathrm{d}\)
Emulsion dispersed drop concentration (vol\(\%\) )

- \(C_\mathrm{d_\mathrm{inj}}\)
Injected emulsion dispersed drop concentration (vol\(\%\) )

- DE
Emulsion’s displacement efficiency mechanism

- Dd/Dp
Drop-to-pore size distribution

- \(f_\mathrm{w}\)
Fractional flow

- IBP
Injector bottom-hole pressure (KPa)

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

- K\(_\mathrm{rw}\)
Aqueous-phase relative permeability

- K\(_\mathrm{ro}\)
Oil-phase relative permeability

- \(K_\mathrm{reor}\)
Emulsion relative permeability endpoint at residual oil saturation

- \(K_\mathrm{roei}\)
Emulsion relative permeability endpoint at irreducible emulsion saturation

- \(K_\mathrm{rowi}\)
Oil relative permeability endpoint at irreducible water phase saturation

- MC
Emulsion’s mobility control mechanism

- \(n_\mathrm{e}\)
Corey’s exponent for water phase with emulsion’s dispersed drop as component

- \(n_\mathrm{oe}\)
Corey’s exponent for oil phase (oil-emulsion system)

- \(n_\mathrm{ow}\)
Corey’s exponent for oil phase (oil–water system)

- \(n_\mathrm{w}\)
Corey’s exponent for water phase

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

- ORF
Recovery factor

- p
Pressure (Pa)

- PV
Pore volume

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

- \(q_\mathrm{w}\)
Flow rate of the water phase (m\(^3\)/s)

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

- \(S_\mathrm{or_\mathrm{e}}\)
Residual oil saturation to emulsion

- \(S_\mathrm{or_\mathrm{w}}\)
Residual oil saturation to water phase

- \(S_\mathrm{w}\)
Water saturation

- \(S_\mathrm{w_\mathrm{i}}\)
Irreducible water saturation

- t
Time (s)

- WAE
Water-alternating emulsion

- WCUT
Water cut

- \(X^{*}\)
Variable

*X*parametrized by capillary number- \(X^{**}\)
Variable

*X*parametrized by dispersed drop concentration- \(X_\mathrm{max}\)
Maximum value of the variable

*X*- \(X_\mathrm{min}\)
Minimum capillary of the variable

*X*

## Greek symbols

- \(\Delta S_\mathrm{w}\)
Difference in water saturation between waterflooding and WAE injection

- \(\lambda\)
Total mobility (1/Pa.s)

- \(\mu\)
Displacing fluid viscosity (Pa.s)

- \(\mu _\mathrm{o}\)
Oil viscosity (Pa.s)

- \(\mu _\mathrm{w}\)
Water viscosity (Pa.s)

- \(\Omega\)
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

- \(\phi\)
Porosity

- \(\rho _\mathrm{o}\)
Oil density (Kg/m\(^3\))

- \(\rho _\mathrm{w}\)
Water density (Kg/m\(^3\))

- \(\sigma\)
Oil–water interfacial tension (mPa.s)

- \(\upsilon\)
Darcy velocity (m/s)

## Notes

### Acknowledgements

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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