The capillary pressure is the key parameter to affect
the inversion
accuracy of the water–oil relative permeability curve. The
existing analytical inversion methods have neglected the influence
of capillary pressure, which may cause low precision for the estimated
relative permeability curve in some cases. On the basis of the numerical
inversion method for the water–oil relative permeability curve
established in part 1 (10.1021/ef300018w),
taking the one-dimensional radial numerical experiment for example,
the rules of relative permeability variation and influence of different
displacement conditions on relative permeability deviation when neglecting
the capillary pressure are investigated. With regard to water-wet
cases whose oil–water viscosity ratio is greater than 1.5,
it indicates that the estimated water-phase relative permeability
curve is higher and the estimated oil-phase relative permeability
curve is lower compared to the true relative permeability curve when
the capillary pressure is neglected. The main displacement conditions
influencing the inversion accuracy of the relative permeability curve
include the injection rate, average permeability, and shape factor
of the core sample. As the injection rate increases, the degree of
relative permeability deviation caused by neglecting the capillary
pressure becomes smaller. Moreover, the deviation trends of the water–oil
relative permeability curve are the same as those of the increasing
injection rate when average permeability decreases or the shape factor
of the core sample increases. Finally, the orthogonal experimental
design technique is used to establish the experimental conditions
considering the combined effect of multiple factors, and then the
water–oil relative permeability curve under every experimental
condition is estimated implicitly. On this basis, the multivariate
analysis is performed to obtain the threshold value charts of radial
displacement experimental parameters, such as the injection rate,
average permeability, and shape factor of the core sample, and their
corresponding rational value domains are also achieved, which can
be used to reduce the influence of neglecting capillary pressure data
as much as possible and provide a calculation theory for estimation
of the water–oil relative permeability curve accurately.