Page 308 - Enhanced Oil Recovery in Shale and Tight Reservoirs

Spontaneous imbibition 281

according to Eq. (10.1); initially the fluid imbibes into larger pores and later
into smaller pores; therefore, the imbibition velocity becomes slower at late
time. Another fact that can cause slow imbibition rate at late time is that the
pressure inside the core builds up; this built pressure serves as a resistance to
the imbibition. The late flat portion of the curve is not caused or represented
by diffusion as Shen et al. (2016) interpreted.
Again from Eq. (10.1), we can see that the imbibition velocity into a
smaller pore is lower than that into a larger pore; as the imbibition takes a
longer time (longer l), the imbibition velocity becomes lower. Tagavifar
et al.’s (2019) simulation results also approve this fact. Yang et al.’s (2016)
experimental data showed that imbibition velocities were lower for lower
porosity and permeability cores; their experimental velocities were lower
than what the theory (Eq. 10.1) predicted; the lower their porosity and
permeability, the lower their experimental velocity was, compared with
the theoretical velocity.
Real experimental data in log(V) versus log(t) may not show the slope of
0.5. Hu et al. (2012) suggested the change of the slope of the curve repre-
sented the change in pore connectivity. Cai and Yu (2011) suggested the
slope change was caused by pore tortuosity. Yang et al. (2016) suggested
that the slopes reflected the pore distribution and pore connectivity, with
the early slope reflected macropores (>50 nm), the middle and late slopes
reflected meso- and micropores, as shown in Fig. 10.1.
For type “B,” the linearity appears in the early time, suggesting relatively
high permeability and good pore connectivity. The macropores are well-
developed, and the pore size distribution is of a single-peak type. For type
“S,” the initial position has an “arc-shaped tail” which suggests n i > 0.5 at
the early imbibition stage and good pore connectivity. The macropores
and mesopores are well developed, and the pore size distribution is of the
two-peak-type. For type “A,” the arc-shaped and convex behavior suggests
a low initial time exponent (n i < 0.5) and poor pore connectivity; the late
time exponent (n L ) appears to be above 0.1 which suggests well-developed
meso/micropores. The pores are narrowly distributed. For type “M,” with
complex multiporosity feature, the initial imbibition rate becomes lower,
which suggests microfractures are embedded in the rock matrix, representing
good-connected microfractures to poor-connected matrix pores. The macro-
pores, mesopores, and micropores are developed, and the pore size distribu-
tion is of the multipeak type. Here macropores are >50 nm diameter,
mesopores are between 2 and 50 nm, and micropores are <2 nm, according