Horizontal Well Path Planning and Correction Using Optimization Techniques

Abstract

We present a procedure that uses nonlinear optimization theory to plan complex, three-dimensional well paths and path corrections while drilling. The problem of hitting a 3-D target is posed as seeking a profile that optimizes some well-defined objective function (the optimality criterion) subject to equality and inequality constraints. The well path is idealized to contain a finite combination of turn and straight sections. Operational restrictions translate into inequality constraints, and target restrictions translate into equality constraints. Several optimality criteria may be chosen, and appropriate choices are discussed. In this work, we choose optimization with respect to user preferred parameters as the criterion. The resulting nonlinear optimization problem is solved using a sequential gradient-restoration algorithm (SGRA), with scaling and optimal step-size selection. The optimization problem formulation and the solution procedure are described. The procedure is robust, efficient, and clearly superior to trial-and-error heuristic techniques that are commonly used to plan well paths today. A computer program based on this technique has been developed and successfully used. Two examples are included to illustrate the procedure. It is concluded that nonlinear optimization is a powerful and versatile mathematical tool that can be used for planning better, optimal well paths, and can be extended to several other drilling and production problems.

Stochastic optimal control and algorithm of the trajectory of horizontal wells

“…Unlike the approaches in [6,9], the presented model in the paper specifies the effects of random perturbations while drilling. Therefore, the results of this research are much more rational and practical.…”

“…In recent years, very few references have discussed the horizontal well planning in the mathematical literature. Foreign and domestic experts mainly put forward nonlinear programming models [2,4,6], a fuzzy model [9] and an optimization model [8]. In fact, there are more unknown parameters for complete well than there are defining equations.…”

Impulsive optimal control model for the trajectory of horizontal wells

“…Since it is difficult to achieve the gradient of our objective function, these algorithms are not appropriate for our nonlinear parametric optimization problem. The sequential unconstrained minimization technique (SUMT) in [6] and sequential gradient-restoration algorithm (SGRA) in [8,11] have a similar drawback. The Hooke-Jeeves algorithm is a pattern search method for unconstrained optimization problems.…”

“…Due to the effect of some unknown factors such as stratum and tools, the trajectory of horizontal wells will deviate from the theoretically optimal one while drilling. But such unknown disturbances have been ignored or only given a little qualitative consideration in the previous designs [5][6][7][8][9][10][11]. If the control parameters provided by the optimal design are applied in practice, the trajectory may not achieve optimality, or even fail to hit the target.…”

“…Helmy et al [6] use a sequential unconstrained minimization technique (SUMT) to design a well path with minimal length for a two-dimensional S-shaped well. As demonstrated in [8,11], the authors use a sequential gradient-restoration algorithm (SGRA) to plan the threedimensional well path and path correction. The criterion in these two papers is that of minimizing the distance between the solution parameters and preferred values.…”