US 12,442,286 B1
Nonlinear model predictive control for directional drilling applications
Jiamin Xu, Houston, TX (US); He Zhang, Singapore (SG); Kaixiao Tian, Singapore (SG); Nazli Demirer, Tomball, TX (US); Yang Liu, Singapore (SG); Ketan C. Bhaidasna, Houston, TX (US); Robert P. Darbe, Tomball, TX (US); and Dongmei Chen, Austin, TX (US)
Assigned to HALLIBURTON ENERGY SERVICES, INC., Houston, TX (US); and BOARD OF REGENTS, THE UNIVERSITY OF TEXAS SYSTEM, Austin, TX (US)
Filed by Halliburton Energy Services, Inc., Houston, TX (US); and Board of Regents, The University of Texas System, Austin, TX (US)
Filed on Jun. 18, 2024, as Appl. No. 18/747,079.
Claims priority of provisional application 63/632,116, filed on Apr. 10, 2024.
Int. Cl. E21B 44/00 (2006.01); E21B 7/10 (2006.01); E21B 17/10 (2006.01)
CPC E21B 44/00 (2013.01) [E21B 7/10 (2013.01); E21B 17/1078 (2013.01)] 20 Claims
OG exemplary drawing
 
1. A method comprising:
accessing well plan data associated with a drill string during a wellbore drilling operation, wherein the well plan data is accessed by one or more processors executing code that simulates a mathematical model of the drill string as the dill string moves during the drilling operation;
identifying a nonlinear delayed differential equation (DDE) based on one or more parameters associated with a wellbore segment, wherein the nonlinear DDE is a differential equation where a derivative of a function at a certain time is expressed in terms of values of the function at previous times;
converting the nonlinear DDE associated with the portion of the wellbore into a linear time varying DDE;
converting the linear time varying DDE into a continuous time varying ordinary differential equation (ODE) that is a differential equation where a derivative of a function at a certain time is expressed linearly in terms of values of the function at a current time and one or more varying inputs;
converting the time varying ODE into a discrete ODE;
implementing, by the one or more processors, the mathematical model to compute one or more control inputs for the drill string based on the discrete-time ODE; and
adjusting the one or more control inputs of the drill string based on one or more constraints of the well plan data to control movement of the drill string.