Improving thermal efficiency of steam injection wells is an important goal in the process of steam injection for heavy oil recovery. The main objectives of this paper are to establish a comprehensive mathematical model for estimating the thermal efficiency of steam injection wells and to make some suggestions on how to achieve the above goal.

The mathematical model is composed of four sections. The first one is about prediction of thermophysical properties of injected steam considering phase change. In this section, if wet steam is not cooled to liquid water, slippage between gas and liquid phases is taken into account in calculating pressure drop based on momentum balance principle. In addition, a complete expression for steam quality distribution in wellbores is derived in detail. However, if phase change occurs, we can obtain an implicit equation for fluid temperature by combining energy balance and Coulter-Bardon equations. In the second section, steady-state heat transfer inside the wellbore and transient radial conduction in the formation are coupled at the cement/formation interface, based on which the wellbore heat loss rate is determined. Next, the thermal efficiency is estimated by using both direct and indirect methods. Finally, the mathematical model is solved iteratively for each segment and a detailed calculation flowchart is also provided.

The proposed model is validated by comparing simulated steam pressure, temperature and quality with measured field data from Liaohe Oilfield, and the direct and indirect methods of estimating the thermal efficiency prove to be reliable. Then, using the validated model, we analyze the effects of wellhead steam quality, injection rate and thermal conductivities of insulation materials on thermal efficiency of steam injection wells. The results indicate that enhancing the wellhead injection rate and using low thermal conductivities of insulation materials can greatly improve the thermal efficiency. But it is not a good choice to achieve this goal by improving the wellhead steam quality. Moreover, the paper shows that our methods for estimating the thermal efficiency of steam injection wells can also be applied to concentric-dual tubing steam injection wells.

In this paper, the comprehensive mathematical model for estimating the thermal efficiency of steam injection wells may be worthy of more attention, because it has not been widely reported in the literature. More important, phase change from steam/water two-phase flow to liquid water single-phase flow in deep wells is also considered in our study.