Model Predictive Control for Mud Motor Operation in Directional Drilling

This paper is concerned with autonomous drilling using a mud motor to follow a predefined well plan for hydrocarbon exploration. The well plan contains curve & straight sections, possibly including a horizontal section that is common for non-conventional oil & gas drilling. We first introduce a steering model describing wellbore propagation response of a mud motor in the vertical plane, which contains multiple distributed delays in the depth domain. Later we address the three-dimensional well plan tracking problem by designing and combining two controllers. The first one is based on the idea of Model Predictive Control (MPC) for well-plan tracking in the vertical plane, while the second one performs Azimuthal corrections. Because mud motor control inputs comprise both continuous and binary quantities due to its physics and operation principles, the MPC problem is formulated as a Mixed-Integer-Quadratic-Programming (MIQP) problem with the goal of minimizing certain quadratic cost function. The proposed autonomous drilling method utilizes the same information available to the directional driller for feedback, which includes depth, inclination and azimuth angles at survey points. The MIQP problem is solved online each time a new survey result is available to provide optimal mud-motor control input up to the next survey in the future. The method has been field tested and proven to be both effective and reliable. Testing results are presented at the end of this paper to demonstrate the effectiveness of proposed method.