Summary
Spontaneous-imbibition data for Berea sandstone cores, which are very
strongly wetted by the aqueous phase and initially 100% saturated with mineral
oil, are reported for linear, radial, and all-faces-open boundary conditions.
Oil viscosities were 4, 63, and 173 cp, and aqueous-phase viscosities ranged
from 1 to 495 cp. Oil-/aqueous-phase-viscosity ratios were varied by more than
four orders of magnitude (0.01 to 173.1). Near-linear relationships (with
slopes close to one-half), between the frontal position and imbibition time on
a log-log scale, were obtained for both linear and radial countercurrent flow.
Behavior is consistent, with near piston-like displacement by the imbibing
aqueous phase. The results are analyzed by a new mathematical model that
accounts for countercurrent spontaneous imbibition with symmetrical flow
patterns. The model assumes that saturation and permeabilities to
counterflowing phases behind the front are constant and that any effect of
local change in interfacial curvature with distance is negligible. The results
from the model are used to extend scaling to include the measured effect of
viscosity ratio for linear and radial flow. For the all-faces-open boundary
condition, commonly used in core-analysis studies, oil recovery vs. imbibition
time is estimated by a combination of spherical and radial flow. Consistently
close agreement was obtained between experiments and behavior predicted by the
model.
Introduction
Laboratory spontaneous-imbibition experiments are used commonly to
investigate the mechanism of oil recovery from fractured reservoirs. The rate
of oil transfer from the rock matrix into the fractures determines oil
production. Although capillary force is the dominant driving mechanism for
spontaneous imbibition, the rate of oil recovery depends on many factors,
including relative permeability, fluid viscosities, sample size and shape, and
surfaces open to imbibition (Ma et al. 1997). A model of spontaneous imbibition
is needed that can be verified by laboratory experiments and has predictive
capability.
Differential equations of mass balance and extension of Darcy’s equation to
two-phase flow in porous media (Blair 1964) often serve as the basis for
modeling countercurrent spontaneous imbibition. For countercurrent flow, the
rate of water imbibition is assumed to be equal to the rate of oil production
and in the opposite direction. If boundary conditions, relative permeability,
and capillary pressure functions are specified, the progress of saturation and
pressure profiles can be calculated. The effect of relative permeability and
capillary pressure functions may be lumped together as a single saturation
function (Pooladi-Darvish and Firoozabdi 2000; Kashchiev and Firoozabadi 2002;
Li et al. 2003; Wo 2002) to reduce the number of function parameters. However,
determination of relative permeabilities and capillary pressures that pertain
to spontaneous imbibition is highly problematic. In practice, saturation
functions have to be tuned to match either the measured saturation profiles or
the imbibition rate calculated by integration of the saturation profiles. When
cores are very strongly water-wet, it can be difficult to tune the saturation
functions to match the sharp imbibition front. More significantly, because of a
lack of experimental data, the traditional approach has not been tested fully
against imbibition experiments under different flow patterns and a wide range
of viscosity ratios.
Another approach to prediction of the rate of imbibition involves
development of dimensionless scaling groups that compensate for the effects of
sample size and shape, boundary conditions, and rock and fluid properties. A
scaling group proposed by Mattax and Kyte (1962) was later modified by Ma et
al. (1997) to give a dimensionless time tD defined by
[Equation], (1)
where t is the imbibition time; k is the rock permeability;
ø is rock porosity; σ is the water/oil interfacial tension;
µw and µo are the water and oil
viscosities, respectively; and Lc is the characteristic
length, which depends on the sample size and shape and the boundary conditions.
The scaling group (Eq. 1) correlated available oil/water imbibition data
satisfactorily (Ma et al. 1997; Zhang et al. 1996).
Use of the geometric mean of the oil and water viscosities was based on
experiment and, particularly for the complex process of spontaneous imbibition,
cannot be safely assumed to hold outside the range of measurement conditions.
Extension of experimental data to three-orders-of-magnitude variation in
aqueous-phase viscosity showed a large systematic increase in
tD for oil-/water-viscosity ratios smaller than 0.25 (Fischer
and Morrow 2005). These results indicate that correlation of imbibition data
can be extended to a wider range of conditions simply by inclusion of a
viscosity-ratio term. In addition, mainly on the basis of extensive scaled
imbibition data for fluid-viscosity ratios of unity, small differences in the
shapes of the recovery curves have been identified for radial vs. linear flow
and should be taken into account as well (Fischer and Morrow 2005). This paper
presents correlations of new data for a wide range of viscosity ratios for
linear and radial imbibition and for imbibition into cylindrical cores with all
faces open.
© 2008. Society of Petroleum Engineers
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History
- Original manuscript received:
28 June 2006
- Meeting paper published:
24 September 2006
- Revised manuscript received:
29 October 2007
- Manuscript approved:
17 February 2008
- Version of record:
20 June 2008
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