Lm. Hirsch et Ah. Thompson, SIZE-DEPENDENT SCALING OF CAPILLARY INVASION INCLUDING BUOYANCY AND PORE-SIZE DISTRIBUTION EFFECTS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(3), 1994, pp. 2069-2086
The effect of sample size on fluid saturation during capillary invasio
n is determined by modeling the invasion process on three-dimensional
cubic networks consisting of pore throats with radii randomly selected
from various pore size distributions. Without buoyancy, the threshold
saturation of the nonwetting fluid when it completes a connected path
across a sample decreases with the square root of sample size for all
the pore size distributions studied. Experiments on Berea sandstone s
amples ranging from 0.3 to 30 cm in size confirm the 1/root L scaling
relation. The 1/root L scaling is the prediction of percolation theory
without buoyancy. Large-aspect-ratio [(height):(diameter)] samples ha
ve greater threshold nonwetting phase saturations than low-aspect-rati
o samples. Relative permeability, which is dependent on the largest in
terconnected pores, also depends on sample size and shape. The pore si
ze distribution affects the pore occupancy when buoyancy is important.
To describe this effect we introduce a measure of the skewness of the
pore size distribution into the Bond number (the Bond number B is the
ratio of buoyancy to capillary pressures). For all the cases examined
, a universal scaling law for the threshold saturation has been found
based on the ratio of sample size L to Bond number correlation length
xi(B). xi(B) is proportional to B--0.47. This scaling relation incorpo
rates the effects of fluid density contrast, pore size distribution, s
urface tension, and contact angle while retaining the basic Bond numbe
r scaling previously predicted for percolation on lattices with unifor
m (flat) pore size distributions. The height of the critical pore that
must be filled to achieve breakthrough of the nonwetting phase is a u
seful parameter that also scales with L/xi(B) These finite-size scalin
g results have important implications for models of oil migration to r
eservoirs and models of pollutant migration in-ground water.