Spontaneous imbibition is one of the most important processes in enhanced oil recovery in fractured reservoirs. Although Imbibition plays a significant role in oil production in such reservoirs, it can be performed only if the rocks become water-wet. Recently, wettability changes from oil-wet to the water are new approaches in cracked carbonate reservoirs. Researches in Nano-science showed great advantages of Nano-materials related to higher oil recovery and interesting results are reported through nanoparticle applications. Wettability change which is one the most important parameters in enhanced oil recovery, have been reported by nanoparticle application in injection oil recovery methods. However, sufficient information and researches are not available for the case of nanoparticles effects on rock flow properties (e.g. relative permeability and capillary pressure) during spontaneous imbibition. In this study, relative permeability and capillary pressure estimations have been offered in presence of nanoparticles. A comparison between the results in absence of nanoparticles has been presented in order to investigate the wettability change and its effects on related parameters (e.g. relative permeability and capillary pressure). First, numerical modeling of flow equations for a cylindrical core was presented using MATLAB software and the results are compared with the ECLIPSE100 simulation results. History match was done by relating the spontaneous imbibition model to ant-colony optimization algorithm, unknown parameters (relative permeability and capillary pressure) were estimated matching oil production information. Then the relative permeability and capillary pressure were investigated by using experimental data of spontaneous imbibition in presence of nanoparticles. Results comparisons confirmed relative permeability and capillary pressure changes to the water-wet in presence of nanoparticles. KEYWORDS Relative Permeability, Capillary Pressure, Optimization, Enhanced oil Recovery, nanoparticles, Spontaneous imbibition