This paper discusses the implementation of a discretized well-bore simulator fully implicitly coupled with the grid cells in a thermal compositional simulator. The computation of pressure losses due to multiphase frictional effects and flow regimes in the wellbore cells is handled with the Beggs and Brill correlation, but the formulation is general enough to use with any other correlation. Wellbore configurations, such as partial or complete tubing in casing, uninsulated/insulated tubing, partial or complete casing perforations, and variations in skin damage along the well, can be modelled. The resulting simulator has been applied to simulate circulating startup in SAGD processes with steam trap control. The model's calculated horizontal wellbore pressure losses compare favourably with a process simulator. The simulator SAGD oil rates for 2D cases with steam trap control match published results from another simulator. The simulator can be used for SAGD well design to redirect tubing and annular flows to try to affect steam chamber development. The effects of tubing insulation and pressure drop are shown in 3D cases. The simulation cases have reasonable execution times, thus showing the efficiency of the coupled wellbore model.