Transport in Porous Media

, Volume 115, Issue 1, pp 189–207 | Cite as

Experimental and Analytical Investigation of Spontaneous Imbibition in Water-Wet Carbonates

  • Nayef Alyafei
  • Ali Al-Menhali
  • Martin J. Blunt


We perform co-current spontaneous imbibition ambient-condition experiments in three carbonates with a wide range of permeability under strongly water-wet conditions. We measure water saturation profiles as a function of distance and time in air-filled rocks with no initial water saturation using X-ray CT scanning. We demonstrate that the saturation profiles are functions of distance divided by the square root of time. We also demonstrate that the profiles are consistent with analytical solutions for imbibition in one dimension, and using reasonable estimates of relative permeability and capillary pressure, we can match the experimental results. We discuss how, in combination with conventional measurements of relative permeability (steady-state or using Buckley–Leverett theory in an unsteady-state experiment), the capillary pressure can be determined, or how the relative permeability can be determined from the spontaneous imbibition experiment and the capillary pressure.


Spontaneous imbibition Analytical solution Relative permeability Capillary pressure Capillary-dominated flow Carbonates 

List of Symbols

\(\alpha \)

Capillary pressure exponent

\(\lambda _\mathrm{{nw}}\)

Mobility of the non-wetting phase

\(\lambda _\mathrm{{t}}\)

Total mobility

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

Mobility of the wetting phase

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

Density of the non-wetting phase

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

Density of the wetting phase

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

Viscosity of the non-wetting phase

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

Viscosity of the wetting phase

\(\phi \)


\(\omega \)

Imbibed distance over square root of time


Proportionality constant used in the analytical solution


Capillary dispersion coefficient


Fractional flow for viscous-dominated flow

\(f^{\prime }\)

First derivative of f


Fractional flow for capillary-dominated flow

\(F^{\prime }\)

First derivative of F

\(F^{\prime \prime }\)

Second derivative of F


Gravitational acceleration




Relative permeability


Gas relative permeability

\(k_{\mathrm{{rg}}, \mathrm{{max}}}\)

Maximum gas relative permeability


Water relative permeability


Maximum water relative permeability


Corey gas exponent


Corey water exponent


Capillary pressure


Entry capillary pressure


Non-wetting phase pressure


Wetting phase pressure


Total Darcy velocity


Non-wetting phase Darcy velocity


Wetting phase Darcy velocity


Residual gas saturation


Water saturation


Initial water saturation


Irreducible water saturation




Shockfront moving speed


Dimensionless shockfront moving speed





We would like to acknowledge funding from the Qatar Carbonates and Carbon Storage Research Centre, QCCSRC, which is supported jointly by Qatar Petroleum, Shell and the Qatar Science & Technology Park.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Nayef Alyafei
    • 1
  • Ali Al-Menhali
    • 1
  • Martin J. Blunt
    • 1
  1. 1.Qatar Carbonates and Carbon Storage Research Centre, Department of Earth Science and EngineeringImperial CollegeLondonUK

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