Abstract
Spontaneous imbibition experiments are usually carried out on All Faces Open or One End Open cores and this severely limits the information that can be obtained because imbibition can be approximately described with a square root of time function, which involves only a single variable. Two Ends Open with one end in contact with the brine and the other end in contact with oil (at the same pressure) offers much more varied behaviour because imbibition is partly co-current and partly counter-current. Previously, an analysis and experiments were described for primarily co-current imbibition when the viscosities of the oil and brine were close to equal. Small deviations from the square root of time relationship allowed parameters such as the capillary back pressure (bubble pressure) to be determined. In the present paper, the situation when the oil is significantly more viscous than the brine is analysed and compared with experiments. The results show that counter-current imbibition continues for almost the entire imbibition period. They also show that the relative permeability to oil behind the front varies as the viscosity ratio is changed. Very viscous oil gives higher relative permeability than less viscous oil.
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Abbreviations
- \(A\) :
-
Cross-sectional area of cylindrical core (m\(^{2}\))
- \(D\) :
-
Parameter involved in the ratio of co-current to counter-current production of non-wetting phase
- \(k_{\mathrm{nw}}\) :
-
Co-current relative permeability to the non-wetting phase ahead of the imbibition front
- \(k_{\mathrm{nw}}^{*}\) :
-
Counter-current relative permeability to the non-wetting phase behind the imbibition front
- \(k_\mathrm{w} \) :
-
Co-current relative permeability to the wetting phase behind the imbibition front
- \(K\) :
-
Rock permeability \((\hbox {m}^{2})\)
- \(L_{\mathrm{core}} \) :
-
Length of cylindrical core (m)
- \(P_{\mathrm{c,f}} \) :
-
Capillary pressure at the imbibition front (Pa)
- \(P_{\mathrm{c,o}}\) :
-
Capillary back pressure at the core face in contact with wetting phase (Pa)
- \(P_{\mathrm{w,f}}\) :
-
Pressure in the wetting phase at the imbibition front (Pa)
- \(P_{\mathrm{nw,f}}\) :
-
Pressure in the non-wetting phase at the imbibition front (Pa)
- \(P_{\mathrm{nw,pt}}{(t)}\) :
-
Pressure in the non-wetting phase measured at the pressure port at time \(t\)
- \(q_{\mathrm{nw}}\) :
-
Co-current flow of the non-wetting phase (m\(^{3}\)/s)
- \(q_{\mathrm{nw}}^{*}\) :
-
Counter-current flow of the non-wetting phase (m\(^{3}\)/s)
- \(q_\mathrm{w}\) :
-
Co-current flow of the wetting phase (m\(^{3}\))
- \(S_{\mathrm{wi}}\) :
-
Initial wetting phase saturation
- \(S_{\mathrm{wf}}\) :
-
Wetting phase saturation behind the front
- \(t\) :
-
Time for the front to reach distance \(X_\mathrm{f}\) from the core face in contact with the wetting phase (s)
- \(V_{\mathrm{nw}}(t)\) :
-
Cumulative volume of oil produced co-currently at time \(t\) (m\(^{3}\))
- \(V_{\mathrm{nw}}^{*}(t)\) :
-
Cumulative volume of oil produced counter-currently at time \(t\) (m\(^{3}\))
- \(V_{\mathrm{w}}(t)\) :
-
Cumulative volume of water that has entered the core co-currently at time t (m\(^{3}\))
- \(V_{\mathrm{w}}^*(t)\) :
-
Cumulative volume of water that has entered the core counter-currently at time t (m\(^3\))
- \(x_\mathrm{f}\) :
-
Normalised distance from face in contact with wetting phase to the imbibition front (m)
- \(x_{\mathrm{pt}}\) :
-
Normalised distance from the WP face to the pressure port
- \(X_\mathrm{f}\) :
-
Distance from face in contact with wetting phase to the imbibition front (m)
- \(X_{\mathrm{pt}}\) :
-
Distance from face in contact with wetting phase to the pressure port (m)
- \(\mu _{\mathrm{nw}}\) :
-
Viscosity of the non-wetting phase (Pa \(\cdot \) s)
- \(\mu _\mathrm{w}\) :
-
Viscosity of the wetting phase (Pa \(\cdot \) s)
- \(\varphi \) :
-
Rock porosity
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Funding for this work has been provided by BP, Chevron, Statoil, and the University of Wyoming Enhanced Oil Recovery Institute.
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Haugen, Å., Fernø, M.A., Mason, G. et al. The Effect of Viscosity on Relative Permeabilities Derived from Spontaneous Imbibition Tests. Transp Porous Med 106, 383–404 (2015). https://doi.org/10.1007/s11242-014-0406-4
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DOI: https://doi.org/10.1007/s11242-014-0406-4