This research presents a new method, the decoupled overlapping grids method, for the numerical modelling of transient pressure and rate properties of oil wells. The method is implemented in two stages: a global stage solved in the entire domain with a point or line source well approximation, and a local (post-process) stage solved in the near-well region with the well modelled explicitly and boundary data interpolated from the global stage results. We have carried out simulation studies in two- and three- dimensions to investigate the accuracy of the method. For homogeneous case studies in 2D, we have demonstrated the convergence rate of the maximum error in the quantities of interest of the global and local stage computations by numerical and theoretical means. We also proposed a guideline for the selection of the relative mesh sizes of the local and global simulations based on error trends. Comparison to other methods in the literature showed better performance of the decoupled overlapping grids method in all cases. We carried out further investigations for heterogeneous case studies in 2D and partially-penetrating wells in 3D which show that the error trends observed for the 2D homogeneous case deteriorate only slightly, and that a high level of accuracy is achieved. Overall the results in this thesis demonstrate the potential of the method of decoupled overlapping grids to accurately model transient wellbore properties for arbitrary well con gurations and reservoir heterogeneity, and the gain in computational e ciency achieved from the method.