Spontaneous Counter-Current Imbibition into Core Samples with All Faces Open

Abstract

Counter-current imbibition occurs when brine spontaneously displaces oil from a very strongly water-wet rock. Experiments are usually carried out on cylindrical core plugs which have all of their faces open, mainly because this is easiest to do and also because it appears to give the most reproducible results. The flow patterns are complex, but a reasonable approximation can be obtained by assuming piston-like advance of fronts from the radial outer face and both flat ends. This separates the flow pattern into two types: linear imbibition into cones and radial imbibition into the surrounding toroid ring. Production versus time curves have been calculated for cylinders of varying aspect ratios and other core shapes. The analytical results confirm the experimental observation that sample shape does not have much effect on the shape of the production versus time curves. Bearing in mind the inherent variability of experimental results for individual core samples, the differences would be difficult to detect in experiments. The time for imbibition to be completed scales as the characteristic length. The function given by Ma et al. (J Pet Sci Eng 18:165-178, 1997) requires only a small correction factor for agreement with the analytical result. The present analysis makes straightforward the comparison of results from the complex flow condition 123 200 G. Mason et al. of all-faces-open imbibition with results from linear and radial experiments. A comparison is made with published results. Nomenclature a L toroid − L cone (m) A Area (m 2 ) A f Area of the displacement front (m 2 ) A i Area open to imbibition in the ith direction (m 2 ) A R Area of the cylinder at a general radius, R(m 2 ) b L cone /R max C spread Factor determined by the breadth and shape of the pore size distribution d Core diameter (m) f Fraction of the core filled K Permeability (m 2 ) k rnw Relative permeability of the non-wetting phase k rw Relative permeability of the wetting phase L c Characteristic length (m) L cone Length of a cone (m) L core Core length (m) L c,Ma Characteristic length calculated from Ma's equation (m) L f Distance from the open face to the front for the cone (m) L max Length of the core for linear imbibition (m) L toroid Length of the toroid (m) M Mobility factor (Pa −1 s −1 )n Total number of surfaces open to imbibition P c Capillary pressure (Pa) P cf Capillary pressure at the imbibition front (Pa) P co Capillary pressure at the open face (Pa) P nw Pressure in the non-wetting phase (Pa) P w Pressure in the wetting phase (Pa) q nw Flow of non-wetting phase (m 3 /s) q w Flow of wetting phase (m 3 /s) q R w Flow passing through the surface of the cylinder, radius R (m 3 /s) R f Radial distance of the front from the axis (m) R end Radius of the final position of the front for the shorter toroid (m) R core Core radius (m) R sphere Radius of spherical core (m) S wf Wetting phase saturation behind the front S wi Initial wetting phase saturation t Time (s) t D Dimensionless time t end Time when imbibition ceases (s) t f Time when ...

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

“…This confirms that, in counter-current imbibition, the relative permeabilities to WP and NWP are not constant values but change with the viscosity ratio of the two fluids. It is the only plausible explanation for the most successful empirical correlation of the effect of viscosity ratio (Mason et al 2010). But just how reliable is the observed difference in k * nw for the two different viscosity oils?…”

“…The existence of the CBP was mentioned by Parsons and Chaney (1966), but its effect is usually omitted in analyses of the imbibition process. The CBP is determined by the largest pores at the surfaces where oil is produced as droplets (Li et al 2006;Mason et al 2009;Unsal et al 2009). It may be that small inhomogeneities at the rock surface have a significant effect on the CBP.…”

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

“…14). The most commonly used boundary condition in imbibition experiments is AFO, because it does not need to seal any surface of the core (Babadagli, 2002;Baldwin and Spinler, 2002;Mason et al, 2009;Rostami Ravari et al, 2011). However, the fluid flow patterns under AFO boundary conditions are complex even for homogeneous porous media, which results in that it is very difficult to simulate process of fluid flow by mathematical models.…”

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

“…In the past few years, various mathematical models have been established for spontaneous imbibition with different boundary conditions by assuming piston-like displacement. 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.…”