An excellent design of steam injection projects requires accurate prediction of bottomhole steam pressure, temperature and quality. However, it is not always easy to meet the requirement when we design concentric dual-tubing steam injection schemes due to the complexity of downward steam/water flow in annuli. Also, previous methods for estimating pressure gradient in annuli, such as mechanistic models and empirical correlations, are either time-consuming or inaccurate.
In this study, we present a new semi-analytical model to predict steam pressure and temperature in annuli. It is based on Coulter-Bardon equation and on mass and energy balances in the wellbore. A more rigorous thermodynamic behavior of steam/water mixture is taken into account. More importantly, one-to-one correspondence between pressure gradient and temperature gradient of saturated steam is reasonably developed and applied in our further derivation and simplification. It is because of the simplification that we do not have to use mechanistic models or empirical correlations to separately calculate the pressure drop in annuli, which is significantly different from previous work, including Sagar et al. (1991), Alves et al. (1992) and Hasan et al. (1994) models. Our solution procedure is straightforward, the equations of steam pressure, temperature, quality, steady-state heat transfer in the wellbore and transient heat transfer in the formation just need to be coupled and solved iteratively for each segment.
Our model is validated by comparison with measured field data from Liaohe Oilfield, Petro China. The results indicate that the direction of heat transfer between inner and outer tubing depends on wellhead conditions and temperature drop in each tubing. We also show that the equivalent hydraulic diameter is not always a suitable characteristic dimension for steam/water flow in annuli. Moreover, the paper shows that our method can also be applied to single-tubing steam injection design. The predicted results from our modified model are also compared with those from CMG simulator and previous work in our study.