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[en] Steam injection is an integral and a crucial element of the steam-assisted gravity drainage (SAGD) process that has emerged as a leading technology to recover heavy crude oil from oil sands. In this contribution, we have developed a simulation algorithm for an unsteady state nonisothermal two-phase wellbore model to predict the downward flow of a wet steam. This numeric model is reconstructed by incorporating the mass and energy conservation equations, and a pressure drop relationship, along with a couple of algebraic equations/correlations. A drift-flux model is used to consider the slipping occurred between the phases inside the wellbore. Further, the existence of four flow regimes in the wellbore is also taken into account. This dynamic wellbore flow model is attempted to simulate by developing a numerical algorithm. Furthermore, an analytical expression for wellbore pressure is determined to derive a semi-analytic model. Formulating a computer-assisted simulation algorithm for this, it is shown that the semi-analytic model offers a reduced complexity and computational time over the numeric model. A series of numerical and analytical results are presented to validate the wellbore models against the real field data. Subsequently, both the models are extended to predict the transient behavior of the steam injection system. It is investigated that both the solution methods provide similar results. - Highlights: • An unsteady state nonisothermal two-phase wellbore model is reconstructed. • A numeric and a semi-analytic structures of the model are derived. • Two computer-assisted simulation algorithms are formulated. • Both the model structures are validated with real field data. • The models are compared in predicting the dynamic behavior of the wellbore.