An
analysis of the fundamental equation for countercurrent spontaneous imbibition (SI) for water-wet
porous media has been performed based on a generalized mobility term
MTGEN accounting for fluid–solid and fluid–fluid
interaction developed by Andersen et al. (10.3997/2214-4609.201700303IOR 201719th European Symposium
on Improved Oil RecoveryEuropean Association of Geoscientists & Engineers (EAGE)Houten, The Netherlands2017). MTGEN contains an additional term in the denominator,
compared to the standard mobility term for two-phase flow, resulting
from fluid–fluid interaction effects, which is proportional
to both fluid viscosities. Evaluating MTGEN at a characteristic
water saturation S*w chosen as 0.5; a characteristic generalized
mobility term, MT*GEN, was developed. MT*GEN gives rise to a new dimensionless time (tDNew) for scaling
of oil recovery vs time for spontaneous countercurrent imbibition
specifically addressing the impact of fluid viscosities on the rate.
tDNew has been tested and compared with the standard dimensionless
time tDMZM derived by Ma, Zhang and Morrow and the dimensionless
time expression tDMFMR due to Mason-Fischer-Morrow-Ruth
by scaling 2 extensive sets of experimental data by Fischer and Morrow
from 2006 where fluid viscosities were varied in the range 1–1647
and 4–43 cP for the aqueous and oleic phases, respectively.
Comparison has also been performed for 1 data set reported by Zhang
et al. (10.2118/30762-PASPE Reservoir Eng.199611280285) where oil viscosity was varied from 4 to 156 cP keeping
aqueous phase viscosity constant at 1 cP. The results show that tDNew in general can account for variations in fluid viscosities
over the wide ranges in a better way than the two expressions tDMMZ and tDMFMR as it gives significantly less spread
in the scaled oil recovery curves. Particularly, for two of the data
sets reported by Fischer and Morrow (10.1016/j.petrol.2006.03.003J. Pet. Sci. Eng.2006523553), where oil viscosity was kept constant and water phase viscosity
was varied over several orders of magnitude, the reference scaling
approaches, using tDMZM or tDMFMR, showed a
systematic delay at increased water viscosity. The new time scale
could capture this variation and scale all the tests to one curve
due to the fluid–fluid interaction term, indicating that viscous
coupling effects could impact the time scale at high viscosities.
Compared to the reference time scales, tDNew incorporates
the following additional data for numerical computations: End-points
of the relative permeability functions (1/Iw and 1/Io), curvature of the relative permeability functions (α
and β) and a fluid–fluid interaction coefficient (I).
tDNew should in principle be universally valid for estimating
fluid mobilities at countercurrent flow for all fluid viscosities
and all relative permeability shapes. Hence, further testing on more
empirical SI data where relative permeability data is available (end-points
and shapes) for large variations in fluid viscosities (e.g., water
gas systems) is recommended for further corr...