Spontaneous counter-current imbibition outwards from a hemi-spherical depression

Mason, Geoffrey; Fernø, Martin A.; Haugen, Åsmund; Morrow, Norman R.; Ruth, Douglas

doi:10.1016/j.petrol.2012.04.017

Cited by 19 publications

(12 citation statements)

References 8 publications

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“…Previous analyses of imbibition have shown that the assumption that there is a saturation front moving inwards from the face in contact with brine gives a reasonable description of events (Wickramathilaka et al 2011;Mason et al 2012) and permits tractable analysis. The key assumption that can be made is that the saturation does not vary with distance behind the front (piston-like displacement).…”

Section: Theorymentioning

confidence: 99%

“…For linear imbibition, a relatively straightforward mathematical analysis predicts that the volume of oil produced will depend on the square root of time. This is useful for correlation purposes (Ma et al 1997). However, this behaviour only allows determination of a single parameter which involves a group of core and liquid properties (Schmid and Geiger 2012).…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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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

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Section: Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

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“…1b) (Harimi et al, 2019;Zhang et al, 2019). For the first boundary condition, oil could only be produced by counter-current imbibition (Rangel-German and Kovscek, 2006a;Mason et al, 2012). For the second boundary, oil is produced by combination of counter-and co-current imbibition (Khan et al, 2018).…”

Section: Introductionmentioning

confidence: 99%

Recent advances in spontaneous imbibition with different boundary conditions

Meng¹,

Cai²

2018

Capillarity

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Spontaneous imbibition plays an important role in many practical processes, such as oil recovery, hydrology, and environmental engineering. The past few years have witnessed a rapid development in the mechanism analysis and industry applications of spontaneous imbibition. In this paper, we focus on boundary conditions of spontaneous imbibition, which has important effects on the imbibition rate and efficiency. Various boundary conditions are first generated using different capillary model and introduced focusing on the fundamental physical mechanisms. Then, the studies of spontaneous imbibition in core scale are reviewed. The feature is discussed and the relative permeability for coand counter-current imbibition is analyzed. The scaling of imbibition data with different boundary conditions is also presented by combination of experimental and numerical methods. An analytical model to describe spontaneous imbibition is provided at the end.

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“…The mathematical model for AFO imbibition was established by separating the flow pattern into linear imbibition and radial imbibition by Mason et al (2009b). Mason et al (2012) developed a model for imbibition outwards from a hemispherical depression and reported that oil production was linear with the imbibition time. The models for OEO and TEO imbibition are established by Fischer et al (2008) and Mason et al (2009a) and they reported that the oil production was linear with the square root of imbibition time.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2016

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Spontaneous imbibition experiments with two ends open (TEO) boundary condition showed that oil production from each open face of core is asymmetrical while the invasion of water is symmetrical. Investigating the asymmetry characteristics of oil production is helpful to understand the imbibition displacement mechanisms. In this paper, a mathematical model considering the difference in capillary back pressure for TEO imbibition is established by assuming piston-like advance of the imbibition front. Based on the model, the reason for asymmetry in oil production is discussed and the effect of the viscosity ratio, relative permeability ratio, average capillary back pressure and the difference in capillary back pressure on the asymmetry in oil production is investigated as well. The simulated results show that asymmetry in oil production depends on the ratio of the difference in capillary back pressure to the pressure drop in oil between the imbibition front and the open face of the core. As capillary driving pressure dissipated in oil is very small, a small difference in capillary back pressure will cause a significant asymmetric production of oil. Furthermore, the asymmetry in oil production decreases with increasing viscosity ratio (μ o /μ w ) and relative permeability ratio (k rw /k rnw ) and increases with increasing average capillary back pressure and the difference in capillary back pressure. This work gives us a comprehensive insight into the spontaneous imbibition with TEO boundary condition. Keywords Spontaneous imbibition · Two ends open · Asymmetry in oil production List of symbolsA Cross-sectional area of the core (cm 2 ) k rw,L Relative permeability to wetting phase behind the left imbibition front k rnw,L Relative permeability to non-wetting phase behind the left imbibition front B Qingbang Meng 123 736 Q. Meng et al.k rw,R Relative permeability to wetting phase behind the right imbibition front k rnw,R Relative permeability to non-wetting phase behind the right imbibition front K Absolute permeability (×10 −3 µm 2 ) L Length of the core (cm) P w,L Pressure in the wetting phase at the left imbibition front (atm) P nw,L Pressure in the non-wetting phase at the left imbibition front (atm) P w,R Pressure in the wetting phase at the right imbibition front (atm) P nw,R Pressure in the non-wetting phase at the right imbibition front (atm) P cf,L Capillary driving pressure at the left imbibition front (atm) P cf,R Capillary driving pressure at the right imbibition front (atm) P cb,L Capillary back pressure at the left open face (atm) P cb,R Capillary back pressure at the right open face (atm) q w,L Flow rate of wetting phase behind the left imbibition front (cm 3 /s) q w,R Flow rate of wetting phase behind the right imbibition front (cm 3 /s) q nw,L Flow rate of non-wetting phase behind the left imbibition front (cm 3 /s) q nw,R Flow rate of non-wetting phase behind the right imbibition front (cm 3 /s) q nw,M Flow rate of non-wetting phase across the middle of the core (cm 3 /s) R qw Ratio of water invasion fro...

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Spontaneous counter-current imbibition outwards from a hemi-spherical depression

Cited by 19 publications

References 8 publications

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

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

Recent advances in spontaneous imbibition with different boundary conditions

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

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