Because more and more wells have been put in operation, an accurate modelling of wellbore flow plays a significant role in reservoir simulation. One requirement of a wellbore model is its ability to trace various flow boundaries in the tubing, such as those created by phase or flow regime changing. An algorithm of dynamic gridding is applied to the wellbore flow model coupled with Stanford's general purpose research simulator (GPRS), which has the capability to simulate the isothermal black oil reservoir model to obtain detailed information that explains such important quantities as flow pattern and mixture velocity in any specific location of wellbore. A significant problem in this case is how to calculate fluid and velocity properties with a fine grid (segment) on the boundaries of different flow regimes in the wellbore. Local dynamical segment refinement in the well can accurately and effectively handle this problem. This wellbore model includes mass conservation equations for each component and a general pressure drop relationship. The multiphase wellbore flow is represented using a drift-flux model, which includes slip between three fluid phases. The model determines the pressure, mixture flow velocity, and phase holdups as functions of time and the axial position along the well or alleviation depth. In addition, this model is capable of generating automatically adaptive segment meshes. We apply the black oil model to the simulation of several cases of isothermal dynamical local mesh refinement, and compare the results with fixed coarse and fine meshes. The experiments show that using local segment refinement can yield accurate results with acceptable computational time.