8The two-phase flow behaviour in porous media is determined on the basis of capillary pressure-saturation-relative 9 permeability relationships (P c -S-K r ). These relationships are highly non-linear and obtained by laboratory 10 experiments on porous samples, typically around 10-12cm in length. It is normally assumed that these samples are 11 homogenous; however it is well known that this is in fact not the case and that even at this scale micro-scale 12 heterogeneities exist. Two-phase flow experiments on soils with different properties (e.g., particle and pore size 13 distribution, permeabilities, etc) result in different P c -S relationships. These cause non-uniqueness in the P c -S 14 curves. Recent work has shown that the presence of these micro-heterogeneities has a significant effect on the 15 measured P c -S-K r relationships and they also cause non-uniqueness in these relationships. In the previous work in 16 this area, the micro-heterogeneity effects on the P c -S-K r relationships have been analysed in a number of contexts, injecting on horizontal plane. On the other hand, injection from the bottom (vertically upwards) leads to a higher 31 iw S . As expected, the distribution of heterogeneity has a significant effect on the saturation distribution and the 32 shape of the P c -S-K r curves. However, we show that if the heterogeneities are distributed in such a way that they 33 are closer to the boundary of injection, the irreducible wetting phase saturation is higher.

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