Transport in Porous Media

, Volume 114, Issue 3, pp 777–793

Effect of Surfactant Partitioning Between Gaseous Phase and Aqueous Phase on \(\hbox {CO}_{2}\) Foam Transport for Enhanced Oil Recovery


DOI: 10.1007/s11242-016-0743-6

Cite this article as:
Zeng, Y., Ma, K., Farajzadeh, R. et al. Transp Porous Med (2016) 114: 777. doi:10.1007/s11242-016-0743-6


\(\hbox {CO}_{2}\) flood is one of the most successful and promising enhanced oil recovery technologies. However, the displacement is limited by viscous fingering, gravity segregation and reservoir heterogeneity. Foaming the \(\hbox {CO}_{2}\) and brine with a tailored surfactant can simultaneously address these three problems and improve the recovery efficiency. Commonly chosen surfactants as foaming agents are either anionic or cationic in class. These charged surfactants are insoluble in either \(\hbox {CO}_{2}\) gas phase or supercritical phase and can only be injected with water. However, some novel nonionic or switchable surfactants are \(\hbox {CO}_{2}\) soluble, thus making it possible to be injected with the \(\hbox {CO}_{2}\) phase. Since surfactant could be present in both \(\hbox {CO}_{2}\) and aqueous phases, it is important to understand how the surfactant partition coefficient influences foam transport in porous media. Thus, a 1-D foam simulator embedded with STARS foam model is developed. All test results, from different cases studied, have demonstrated that when surfactant partitions approximately equally between gaseous phase and aqueous phase, foam favors oil displacement in regard to apparent viscosity and foam propagation speed. The test results from the 1-D simulation are compared with the fractional flow theory analysis reported in the literature.


Nonionic surfactant Partition coefficient \(\hbox {CO}_{2}\) Foam Gas breakthrough Mobility control Enhanced oil recovery (EOR) IMPES Fractional flow theory 

List of Symbols

\(C_\mathrm{sg} \)

Surfactant concentration in gas phase

\(C_\mathrm{ss} \)

Surfactant concentration on the solid phase

\(C_\mathrm{sw} \)

Surfactant concentration in water phase

\(C_\mathrm{threshold} \)

Threshold concentration for surfactant in water phase


Foam model parameter in F2


Foam model parameter in F1

F1 to F6

Dependent functions in the range of 0 to 1 in STARS model


Average foam quality


Mobility reduction factor


Foam model parameter in F2


Reference to the maximum gas mobility reduction that can be achieved


Foam model parameter in F1

\(k_\mathrm{rg}^\mathrm{f} \)

Relative permeability of gas phase in the state of foam

\(k_\mathrm{rg}^\mathrm{nf} \)

Relative permeability of gas phase in the absence of foam

\(k_\mathrm{rg}^\mathrm{o} \)

End point relative permeability of gas phase

\(k_\mathrm{rw} \)

Relative permeability of water phase

\(k_\mathrm{rw}^\mathrm{o} \)

End point relative permeability of water phase


Dispersion tensor of species i in phase j


Dispersion tensor of species surfactant in gas phase


Dispersion tensor of species surfactant in water phase

\(K_\mathrm{sgw} \)

Partition coefficient of surfactant between gas phase and water phase


Length of 1-D formation

\(n_\mathrm{g} \)

Corey exponent for gas phase

\(n_\mathrm{w} \)

Corey exponent for water phase

\(\overrightarrow{N_\imath }\)

Flux of species i

\(N_p \)

Number of phases


Number of grid blocks



\(p_\mathrm{g} \)

Gas pressure

\(p_\mathrm{w} \)

Water pressure

\(\hbox {Pe}_\mathrm{g} \)

Peclet in gas phase

\(\hbox {Pe}_\mathrm{w} \)

Peclet number in water phase

\(S_\mathrm{gr} \)

Residual gas saturation

\(S_j \)

Saturation of phase j

\(S_\mathrm{w} \)

Water saturation

\(S_\mathrm{wr} \)

Residual water saturation


Total pore volume of injection

\(R_i \)

Generation and consumption term in conservation equation



\(\overrightarrow{u_\jmath }\)

Superficial velocity of phase j

\(u_\mathrm{g} \)

Superficial velocity of gas phase

\(u_\mathrm{w} \)

Superficial velocity of water phase


Interstitial velocity

\(W_i \)

Total mass of i in bulk volume

\(W_\mathrm{g} \)

Total mass of gas in bulk volume

\(W_\mathrm{w} \)

Total mass of water in bulk volume



\(\phi \)


\(\rho _j \)

Density of phase j

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

Density of gas phase

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

Density of solid phase

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

Density of water phase

\(\omega _{ij} \)

Mass fraction of species i in phase j

\(\omega _{is} \)

Mass fraction of species i in phase solid phase

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

Apparent viscosity of foam

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

Viscosity of gas

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

Viscosity of water

Funding information

Funder NameGrant NumberFunding Note
Shell (NL)Global Solutions
    Rice University Consortium for Processes in Porous Media

      Copyright information

      © Springer Science+Business Media Dordrecht 2016

      Authors and Affiliations

      • Yongchao Zeng
        • 1
      • Kun Ma
        • 1
        • 4
      • Rouhi Farajzadeh
        • 2
        • 3
      • Maura Puerto
        • 1
      • Sibani L. Biswal
        • 1
      • George J. Hirasaki
        • 1
      1. 1.Department of Chemical and Biomolecular EngineeringRice UniversityHoustonUSA
      2. 2.Shell Global Solutions InternationalRijswijkThe Netherlands
      3. 3.Delft University of TechnologyDelftThe Netherlands
      4. 4.Total E&P Research and Technology USA, LLCHoustonUSA

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