Page 410 - Petrophysics 2E

378 PETROPHYSICS: RESERVOIR ROCK PROPERTIES

As the system becomes more oil-wet, the rate of imbibition decreases.
Therefore, a graph of recovery versus dimensionless time indicates
differences of wettability from strongly water-wet to mixed or neutral
wettability.
Curves of oil recovery versus dimensionless time can be fit to the
Aronofsky equation [541:

(6.16)

Equation 6.16 may be used to obtain an average curve of several
repeated tests to examine the effect of the initial saturation on imbibition.
Ma et al. proposed a wettability index based on the pseudo work of
imbibition, WR [53]. A dimensionless curve of pseudo imbibition capillary
pressure (versus water saturation) that indicates the effect of wettability
on the relative rate of imbibition was defined:

pc,p = a& (6.17)

The pseudo work of imbibition, W, is the area under the Pc,p vs. S,
curve. The relative pseudo work of imbibition, WR, was defined as the
ratio of the pseudo work of a sample to the pseudo work of a very strongly
water-wet system. The constant, a, in Equation 6.17 was set equal to 1.0;
thus the pseudo work is:

(6.17)

Zhou et al. obtained a correlation between WR and the Amott
wettability index [55].

FLUID DISPLACEMENT ENERGY

If two immiscible phases (water and oil) are initially distributed equally
throughout a column of porous material, they will adjust to capillary
equilibrium and will coexist throughout the column. If an elemental
volume, AV, of one of the phases is raised from height h to h + dh,
the isothermal reversible work (the total free energy change), 6F, is zero
because capillary equilibrium is assumed to exist within the system. The
total free energy change is a composite of two parts:

1. the free energy change accompanying the transfer of the fluid (say,
water) from h to h + dh, and