  Three-phase flows through a pore network of Berea sandstone are studied
numerically under critical interfacial tension condition. Results show that the
relative permeability of each fluid increases as its own saturation increases.
The specific interfacial length between wetting and non-wetting fluids
monotonously decreases with increasing the saturation of intermediate-wetting
fluid, while the other two specific interfacial lengths exhibit a
non-monotonous variation. As the wetting (non-wetting) fluid becomes less
wetting (non-wetting), the relative permeability of wetting fluid monotonously
increases, while the other two relative permeabilities show a non-monotonous
trend. Due to the presence of spreading layer, the specific interfacial length
between wetting and non-wetting fluids always stabilizes at a low level. As the
viscosity ratio of wetting (non-wetting) to intermediate-wetting fluids
increases, the relative permeability of wetting (non-wetting) fluid increases.
With the viscosity ratio deviating from unity, the phase interfaces become
increasingly unstable, leading to an increased specific interfacial length.
