Effective treatment of geometric constraints in derivative-free well placement optimization

Abstract

A robust workflow for optimizing the placement of multiple deviated wells subject to challenging geometric constraints is presented and applied. The workflow entails the use of population-based global stochastic search algorithms in conjunction with a solution-repair method. The repair procedure, which involves a gradient-based optimization prior to flow simulation, reduces constraint violations via projection of the infeasible solutions onto (or toward) feasible space while minimizing the deviation between the repaired and original solutions. The constraints considered include well length, interwell distance, well-to-boundary distance, and the requirement that wells not cross faults. The repair procedure is implemented with three different core optimization algorithms — particle swarm optimization, iterative Latin hypercube sampling, and differential evolution. Through extensive numerical tests involving the placement of multiple deviated wells, we demonstrate that it is necessary to tune the hyperparameters associated with the core optimizers when these optimizers are used with the repair procedure. In the first example (Egg model), for instance, with differential evolution as the core optimizer, we show that the best-case hyperparameters provide feasible solutions and a 30% improvement in objective function value relative to base-case hyperparameters. The best-case hyperparameters from this example are then used directly in the second example, which involves the placement of seven deviated wells in the Brugge model. For this example, with no additional tuning, we achieve feasibility and a 42% improvement in objective function value relative to base-case hyperparameters, suggesting that the tuned hyperparameters are to some extent transferable between problems.