The efficiency of hydrocarbon recovery from oil and gas reservoirs is mainly controlled by our ability to understand and define fluid transport properties, such as relative permeability and capillary pressure. This study focuses on the development and implementation of a numerical model of multiphase flow in a fractured core sample by establishing a proper physical framework that describes the capillary pressure-relative permeability characteristics. An automated history matching approach is proposed to determine relative permeability and capillary pressure curves consistent with a core flood reservoir model performance. The automated history matching approach relies on a commercial reservoir simulator coupled with an optimization protocol. A large-scale 'Trust Region Method' that minimizes the objective function is implemented for the adjustment of parameters controlling the relative permeability and capillary pressure curves. The objective function is defined as the non-linear least square representation of the difference between estimated and obtained fluid saturation distributions from a core flood reservoir model. The results indicate that the proposed approach successfully predicts relative permeability and capillary pressure curves of a fractured core sample which provides a foundation for field-scale history matching with simultaneous estimation of transport properties.