Development Of Efficient Constraint-Handling Approaches For Well Placement Optimization

Abstract

Efficient constraint-handling methodology is developed to solve for a set of concurrent geometric well placement constraints. This implementation enhances constraint-handling capability such that expert knowledge may more easily be incorporated into well placement problem formulations through realistic geology- and engineering-based nonlinear constraints. A well-defined collection of constraint definitions may, besides enforcing minimum feasibility, also make the optimization process more efficient by limiting the search to highly-relevant solution spaces. This is particularly important for well placement problems that commonly rely on time-consuming reservoir simulations for objective function evaluation. Constraints are imposed on parameters determining the configuration of multiple deviated wellbores in reservoir space, e.g., well length and inter-well distance. A constraint-handling repair approach based on an alternating projections methodology that solves each restriction as an independent constraint-handling subproblem is implemented. The subproblems are solved in sequence, i.e., the solution from one subproblem is used as the initial point for solving the next feasibility problem. The entire sequence is performed in a loop until feasibility is achieved for all constraints. Results from two optimization procedures that implement algorithms with very distinct search characteristics are presented. Though the repair method is external to the sequential quadratic programming and differential evolution algorithms implemented, this work provides a practical framework for how to adapt and couple the constraint-handling methodology to these different types of algorithms in an efficient manner. Results show the standalone optimization procedures provide feasible solutions while performing effective searches of the solution space, both in terms of cost function evolution growth and progression of well configuration.