As more and more wells have been put in operation, an accurate modeling 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 due to phase or flow regime changing. A black oil multi-phase multi-segment dynamical wellbore flow model has been coupled into Stanford's General Purpose Research Simulator (GPRS), which has the capability to simulate the isothermal black oil reservoir model to obtain detailed information on 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 simulation of several cases on dynamical local mesh refinement isothermally, 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.