Impulsive optimal control model for the trajectory of horizontal wells

Abstract

MSC: 34A37 49J55 90C31Keywords: Horizontal well Impulsive control system Nonlinear parametric programming Uniform design a b s t r a c t This paper presents an impulsive optimal control model for solving the optimal designing problem of the trajectory of horizontal wells. We take fully into account the effect of unknown disturbances in drilling. The optimal control problem can be converted into a nonlinear parametric optimization by integrating the state equation. We discuss here that the locally optimal solution depends in a continuous way on the parameters (disturbances) and utilize this property to propose a revised Hooke-Jeeves algorithm. The uniform design technique is incorporated into the revised Hooke-Jeeves algorithm to handle the multimodal objective function. The numerical simulation is in accordance with theoretical results. The numerical results illustrate the validity of the model and efficiency of the algorithm.

Dynamic optimization for robust path planning of horizontal oil wells

“…Given an optimal solution (τ * , ξ * ) for Problem (A) and the dynamic systems (1)- (2) and 17- (18) with ξ = ξ * , choose an admissible switching point vector τ ∈ Γ such that the target error sensitivity function (28) is minimized subject to the continuous state inequality constraints (8) and the additional inequality constraint (9).…”

“…We are only aware of two papers (references [7] and [8]) that consider the issue of target error sensitivity with respect to inaccuracies in the curvatures and tool-face angles. In reference [7], the dispersion between the actual path and the optimal path is modelled by a stochastic perturbation in the dynamic system describing the path trajectory.…”

“…In reference [7], the dispersion between the actual path and the optimal path is modelled by a stochastic perturbation in the dynamic system describing the path trajectory. In reference [8], the dispersion is instead modelled by a series of stochastic impulsive jumps applied at the turn segment end-points. Both references [7] and [8] apply the Hookes-Jeeves algorithm to solve a series of nonlinear optimization problems generated by realizations of the random variables modelling the dispersion.…”

“…In reference [8], the dispersion is instead modelled by a series of stochastic impulsive jumps applied at the turn segment end-points. Both references [7] and [8] apply the Hookes-Jeeves algorithm to solve a series of nonlinear optimization problems generated by realizations of the random variables modelling the dispersion. Thus, the methods proposed in these references require solving multiple optimization problems, not just one.…”

“…Thus, the methods proposed in these references require solving multiple optimization problems, not just one. Moreover, the cost and constraint gradients for these optimization problems are not provided in references [7] and [8], and hence fast gradient-based optimization algorithms such as sequential quadratic programming are not applicable.…”