In this study, a Pore Network (PN) tool was developed in order to obtain two and three phase relative permeability values. It has been found that the observed results agree with published data. It has also been found that as contact angle increased, irreducible water saturation decreased, and oil relative permeability increased for two phase oil-water imbibition simulations. During the three phase displacement simulation by pore network simulation it was observed that water and gas relative permeabilities are only dependent on their own saturations, but oil relative permeability is dependent on its initial and own saturations in addition to water and gas saturations. It was also observed that as contact angle increased, the three phase region enlarged, and as relative permeability of oil increased, the oil isoperms became linear from concave towards the 100% oil apex.