A model has been developed to simulate multiphase flow in the wellbore and heat transfer processes between the well and formations. The model is capable of handling dynamic well depth during drilling, varying flow regimes in multiphase flow, phase change between liquid and gas, and kicks or lost circulation depending on the pressure difference between the wellbore annulus and formation. The model requires simple data input and is able to handle complicated drilling cases such as casing installation, changing drilling fluids, and drillpipe/coiled tubing connections during drilling operations. [S0195-0738(00)00303-4].