The application of Stefan problem in calculating the lateral movement of steam chamber in SAGD (Q1665507)

Summary: It is extremely important to monitor the development of steam chambers in reservoirs in the process of SAGD (Steam Assisted Gravity Drainage). By analyzing the temperature data of monitoring wells, the extending velocity and direction of steam chamber can be obtained, which helps to regulate and improve production effectively. Based on Stefan's inverse problem, a mathematical model is established in this paper for acquiring the extending velocity of steam chamber by using the temperature data of monitoring wells. Mathematical methods are utilized to solve the model such as Fourier transformation as well as an analytic solution using the moving velocity of steam chamber's edges. Finally, sensitivity analyses concerning some factors such as the formation heat transfer coefficient, the temperature of steam chamber, and the rate of temperature rise of monitoring wells are made. Field application showed that the model can be used to calculate the moving velocity in real time and determine the boundary scope of the steam chambers easily.