A comprehensive mathematical model for estimating oil drainage rate in SAGD process considering wellbore/formation coupling effect

The aim of this work is to present a comprehensive mathematical model for estimating oil drainage rate in Steam-assisted gravity drainage (SAGD) process, more importantly, wellbore/formation coupling effect is considered. Firstly, mass and heat transfer in vertical and horizontal wellbores are described briefly. Then, a function of steam chamber height is introduced and the expressions for oil drainage rate in rising and expanding steam chamber stages are derived in detail. Next, a calculation flowchart is provided and an example is given to introduce how to use the proposed method. Finally, after the mathematical model is validated, the effects of wellhead steam injection rate on simulated results are further analyzed. The results indicate that heat injection power per meter reduces gradually along the horizontal wellbore, which affects both steam chamber height and oil drainage rate in the SAGD process. In addition, when production time is the same, the calculated oil drainage rate from the new method is lower than that from Butler's method. Moreover, the paper shows that when wellhead steam injection rate is low enough, the steam chamber is not formed at the horizontal well's toe position and enhancing the wellhead steam injection rate can increase the oil drainage rate.