In this paper, a new compositional mechanistic wellbore model, including gas lifting parameters, is presented. In the governing equations of this model, new terms for mass transfer between phases and the enthalpy of phase change which are important in non-isothermal gas lift systems have been considered. These terms have been ignored in some recent research studies and subsequent results show that by ignoring them, serious errors may arise. In the current research study, using a mechanistic drift-flux approach, the pressure distribution in a wellbore was modeled. To verify the new simulator, the results were compared with those of commercial simulators. They were also verified against the phase behavior analysis of the fluid flowing in the wellbore. In addition, in order to show the novel aspects of the new simulator, the results of the presented simulator were compared with the results of a recently proposed model found in the literature. It was concluded that neglecting phase change effects may cause significant errors in calculating pressure and temperature values along wellbores. This error could be significant, up to 24% depending on conditions, when flowing fluid pressure is close to its saturation point or in the case of simulating gas lift operation.