We study the kick and loss detection and attenuation problem in managed pressure drilling by modeling the well as a distributed parameter system. Two cases are considered, distinguished by whether down-hole pressure measurements are available or not. The main contribution of the paper is a theoretical result on adaptive stabilization and set-point regulation by boundary control for a general 2 × 2 linear hyperbolic system in the case of measurements taken at both boundaries, with stability proven in the $L_2$-sense. The design is applied to the drilling system and shown to solve the kick and loss problem with sensing at both boundaries. An earlier result on adaptive set-point regulation for 2 × 2 hyperbolic systems is also applied to the drilling system and shown to solve a kick and loss problem with sensing restricted to the actuated boundary only. The two designs are compared in a simulation of a loss incident, showing a significant reduction in convergence time and total accumulated loss for the design with sensing allowed at both boundaries.

我们通过对油井建模以及分布式参数系统的研究，研究了有管理压力钻井中的反冲和损失检测及衰减问题。考虑两种情况，根据是否可以进行井下压力测量来区分。本文的主要贡献是在两个边界都进行测量的情况下，对于一般的2×2线性双曲系统，通过边界控制进行的自适应稳定和设定点调节的理论结果，其稳定性已得到验证。${\mathrm{大号}}_2$-感。该设计已应用于钻井系统，并显示为通过在两个边界处感应来解决反冲和损失问题。关于2×2双曲系统的自适应设定点调节的早期结果也被应用到了钻井系统中，并显示了仅在驱动边界范围内进行传感即可解决反冲和损失问题。在损失事件的仿真中对这两种设计进行了比较，结果表明，在两个边界都允许感应的情况下，设计的收敛时间和总累积损耗显着减少。