The numerical simulation is an important tool for development of oil and gas reservoirs that can be used for production planning. One of the key parameters required for the reservoir simulation is relative permeability (kr) curve as a function of fluid saturation. The kr curve directly governs the fluid flow through the reservoir and thus significantly influences the oil recovery. The relative permeability curves are generally determined from the core-flood experiments (steady-state or unsteady-state) performed on the small core plug (around 5 cm). A valid question may arise here, how the relative permeability of a small core plug can be scaled up to a huge and heterogeneous reservoir block (order of 100 meters)? First, in this study, the unsteady-state core-flood experiments were performed using different rocks type to obtain the relative permeability of the oil-water and oil-gas systems for each rock type. Then a cubic reservoir block with a specific pattern of heterogeneity (using experimental data) was built in a reservoir simulator. The injection and production wells were allocated to the model and the fluid flow in the reservoir block was simulated using fine grid model. The recovery and pressure data of the wells resulted from simulation was considered as the actual data. In the next stage, the reservoir block was considered as a homogenous model such that the uniform rock properties (i.e. porosity and permeability calculated by volumetric averaging) were assigned to each grid cells. The kr curve of homogenous model was assumed as an unknown parameter. Therefore, the unknown kr was estimated by history matching of the actual data (results of heterogeneous simulation). The kr curve resulted from history matching is representative (or equivalent) of the various kr curves in the homogenous model. This procedure was repeated with the different heterogeneity patterns for the oil-water and oil-gas system. The kr resulted from history matching was assessed against kr obtained from capillary limit (CL) and viscous limit (VL) up-scaling methods. The reservoir conditions, in which each of CL and VL methods can adequately predict relative permeability of the reservoir scale, were presented. The range of validity for using of CL and VL methods were demonstrated using dimensionless number group. Finally, a technical protocol for scaling up of relative permeability from core scale to the reservoir scale was presented. KEYWORDS Scale up, Heterogeneity, Relative permeability, Capillary equilibrium method, Viscous limit method
