A numerical fully-implicit non-isothermal wellbore/reservoir simulator is developed. The model entails simultaneous solution of transient coupled mass, momentum, and energy balance equations within the wellbore; energy balance equations for the tubular and cement materials and the formation surrounding the wellbore; and mass balance and flow rate-pressure equations for the reservoir formation. A wellbore heat loss model that is a strong feature of this study is developed and employed into the model to improve the accuracy of the simulator as well as to be able to estimate the casing temperature and formation temperature distribution. The model formulation is completed with an equation of state (EOS) to estimate fluid properties and appropriate friction-factor correlations in the wellbore tubing to compute the frictional pressure drop for different flow regimes.

The developed model has several applications in the petroleum industry, particularly in the gas well testing design and interpretation of both isothermal and non-isothermal gas reservoirs.

This non-isothermal simulator is validated through comparisons to both analytical models and an equivalent numerical isothermal coupled wellbore/reservoir simulator that is also developed in this paper. Applications of this simulator to analyzing gas well testing problems, in addition to several important observations, are extensively studied in Part II of this research work (Bahonar et al. 2010).