The Effect of Viscosity on Relative Permeabilities Derived from Spontaneous Imbibition Tests

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. ACross-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 nw Co-current relative permeability to the non-wetting phase ahead of the imbibition front k * nw Counter-current relative permeability to the non-wetting phase behind the imbibition front k w Co-current relative permeability to the wetting phase behind the imbibition front K Rock permeability (m 2 ) L core Length of cylindrical core (m) P c,f Capillary pressure at the imbibition front (Pa) P c,o Capillary back pressure at the core face in contact with wetting phase (Pa) P w,f Pressure in the wetting phase at the imbibition front (Pa) P nw,f Pressure in the non-wetting phase at the imbibition front (Pa) P nw,pt (t)Pressure in the non-wetting phase measured at the pressure port at time t q nw Co-current flow of the non-wetting phase (m 3 /s) q * nw Counter-current flow of the non-wetting phase (m 3 /s) q w Co-current flow of the wetting phase (m 3 ) S wi Initial wetting phase saturation S wf Wetting phase saturation behind the front t Time for the front to reach distance X f from the core face in contact with the wetting phase (s) V nw (t)Cumulative volume of oil produced co-currently at time t (m 3 ) V * nw (t) Cumulative volume of oil produced counter-currently at time t (m 3 ) V w (t)Cumulative volume of water that has entered the core co-currently at time t (m 3 ) V * w (t) Cumulative volume of water that has entered the core counter-currently at time t (m 3

A critical review on fundamental mechanisms of spontaneous imbibition and the impact of boundary condition, fluid viscosity and wettability

“…However, many matrix blocks are partly covered by water in fractured reservoirs (Bourblaux, 1990;Pooladi-Darvish and Firoozabadi, 2000). Haugen et al (2014Haugen et al ( , 2015 designed a special experimental setup to study SI in the core partly covered by water, in which one end of the core was in contact with water and the other end of the core was in contact with oil. In these experiments, initially oil was produced by combination of counter-and cocurrent imbibition from inlet and outlet of the end face.…”

“…A little time later, oil production from inlet end face ceased and oil was only produced from the outlet end face by co-current imbibition. The fractions of oil production by co-and countercurrent imbibition depend on the oil-water viscosity ratio (Haugen et al, 2015;. Meng et al (2015 and Hauglan (2016) conducted the similar imbibition experiments with unconsolidated porous media (Fig.…”

“…However, the model did not consider the counter-current imbibition at the beginning of the imbibition under TEO-OW boundary condition. Haugen et al (2015) developed a mathematical model for SI under TEO-OW boundary condition by assuming that all the pressure would be in the non-wetting phase. However, this assumption may cause serious error with the practical case at the end stages of imbibition.…”

Asymmetry Characteristics of Oil Production by Spontaneous Imbibition from Cores with Two Ends Open

“…Li et al (2006) reported that the capillary back pressure in oil/air case is about 2/5 down to 1/3 and in the water/oil case about 1/4 down to 1/9 of the capillary driving pressure at the imbibition front for Berea sandstone. Haugen et al (2014Haugen et al ( , 2015 reported that capillary back pressure for Portland chalk in brine/oil case is almost half of the capillary driving pressure at the imbibition front. Fernø et al (2015) reported that the capillary back pressure for chalk is 1/3 and 2/5 of the capillary driving pressure at the imbibition front.…”

“…Recently, many research groups have investigated various aspects of spontaneous imbibition by experimental (Zhang et al 2014;Meng et al 2015), analytical (Cai et al 2010;MirzaeiPaiaman and Masihi 2013) and numerical method (Wang et al 2008;Mirzaei-Paiaman et al 2011b). The specific items include the form of imbibition front (Akin et al 2000;Zhou et al 2002;Fernø et al 2013), the capillary driving pressure at the imbibition front (Li et al 2009(Li et al , 2011b, the capillary back pressure at the open face of the core (Li et al 2006;Haugen et al 2014), the relative permeability to wetting and non-wetting phase (Mason et al 2010a;Haugen et al 2015;Meng et al 2015), initial water saturation (Baldwin and Spinler 2002), geometric shape of core (Yildiz et al 2006) and boundary condition (Mason et al 2009a). For the investigation of spontaneous imbibition, the selection of which boundary conditions to apply is a significant problem.…”