Adaptive Control of Bottom Hole Pressure in High-Pressure Brine Layer

With the continuous deepening of exploration and development, the problem of saltwater overflow is inevitable. Overflow of high-pressure brine leads to stratification and settlement of drilling fluid, which can damage the performance of the drilling fluid and cause wellbore pressure instability. Therefore, a class of first-order linear $2 \times 2$ hyperbolic PDE systems is established, and an adaptive observer based on the swapping design method is derived to identify the drilling fluid density and related unknown parameters after saltwater intrusion into the wellbore. Next, an adaptive controller based on infinite dimensional backstepping is designed for the identified PDEs system. Finally, This method is applied to cases of saltwater overflow. It is found that the identification results of density can converge to the actual value within 10 s, and the controller has stronger robustness.