Transient Nonisothermal Fully Coupled Wellbore/Reservoir Model for Gas-Well Testing, Part 1: Modelling

Summary A numerical fully implicit nonisothermal 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 in the model to improve the accuracy of the simulator and 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 nonisothermal gas reservoirs. This nonisothermal 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 2 of this research work (Bahonar et al. 2010). Currently, it has been well accepted that the applicability and significance of a reservoir simulator depend on the behaviour of the wellbore and interaction between the wellbore and reservoir. A robust, accurate coupled wellbore and reservoir simulator is an invaluable tool for the petroleum engineer to help the petroleum industry understand production behaviour, make a meaningful prediction, and make correct decisions in all field-development and production stages.