Horizontal well path planning and correction using optimization techniques

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.