Summary
Scaling the experimental data of spontaneous imbibition without serious
limitations has been difficult. To this end, a general approach was developed
to scale the experimental data of spontaneous imbibition for most systems
(gas/liquid/rock and oil/water/rock systems) in both cocurrent and
countercurrent cases. We defined a dimensionless time with almost all the
parameters considered. These include porosity, permeability, size, shape,
boundary conditions, wetting- and nonwetting-phase relative permeabilities,
interfacial tension (IFT), wettability, and gravity. The definition of the
dimensionless time was not empirical; instead, it was based on theoretical
analysis of the fluid-flow mechanisms that govern spontaneous imbibition. The
general scaling method was confirmed against the experimental data from
spontaneous water imbibition conducted at different IFTs in oil-saturated rocks
with different sizes and permeabilities. A general analytical solution to the
relationship between recovery and imbibition time for linear spontaneous
imbibition was derived. The analytical solution predicts a linear correlation
between the imbibition rate and the reciprocal of the recovery by spontaneous
imbibition in most fluid/fluid/rock systems.
Introduction
An important fluid-flow phenomenon during water injection or aquifer
invasion into reservoirs is spontaneous water imbibition. Scaling the
experimental data of spontaneous water imbibition in different fluid/fluid/rock
systems is of essential importance in designing the water-injection projects
and predicting the reservoir production performances. Ignoring the effects of
relative permeability, capillary pressure, and gravity in the dimensionless
time might be the reason that the existing scaling methods do not always
function successfully. It is known that these parameters influence the
spontaneous imbibition in porous media significantly. For that reason, these
parameters should be honored properly in the scaling.
Many papers have been published to characterize and scale spontaneous water
imbibition in both oil/water/rock systems (Li et al. 2002; Tong et al. 2001;
Zhou et al. 2001; Babadagli 2001; Kashchiev and Firoozabadi 2002; Civan and
Rasmussen 2001; Akin et al. 2000; Cil et al. 1998; Perkins and Collins 1960;
Mattax and Kyte 1962; Du Prey 1978; Hamon and Vidal 1986; Reis and Cil 1993;
Cuiec et al. 1994; Ma et al. 1995; Chen et al. 1995; Zhang et al. 1996;
Al-Lawati and Saleh 1996; Babadagli 1997; Li and Horne 2002) and
gas/liquid/rock systems (Li and Horne 2001, 2004a; Li et al. 2006; Handy 1960).
However, few have included the effects of capillary pressure, relative
permeability (both wetting and nonwetting phases), wettability, and gravity
simultaneously. This is important because all the parameters may play an
important role in many cases and may not be ignored. For example, a number of
enhanced-/improved-oil-recovery processes relate to low IFT. In these cases,
capillary pressure as a driving force may be small, and gravity may not be
neglected. In some cases, gravity may also be a driving force, as pointed out
by Schechter et al. (1991).
© 2006. Society of Petroleum Engineers
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History
- Original manuscript received:
14 January 2003
- Revised manuscript received:
17 February 2006
- Manuscript approved:
26 February 2006
- Version of record:
20 June 2006
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