A Comparison of Common Methods for Optimal Well Placement

Abstract

The well placement problem is challenging due to the non-linear, discrete and often multi-modal objective function. This is complicated by computationally expensive function evaluations from reservoir simulation, typically producing no gradient information. Heuristics for automated optimisation have been proposed over the past 20 years with minimal comparison or benchmarking of performance. This paper presents a comparison of common methods, including genetic algorithms, simulated annealing, particle swarm optimisation and variants of the hill climbing algorithms. These algorithms were tested in the context of locating a single production or injection well in two reservoir cases. For this class of problem, the genetic algorithm produced good results after 100 evaluations. The particle swarm method performed only slightly worse but was able to improve considerably with the use of 'educated guesses' seeding it's initialisation. For this reason the particle swarm optimiser is arguably the better method for industrial implementation as some idea of optimality would exist through intuition and experience. A recommendation for further development is the investigation of objective function approximations for initialisation seeding as well as sequentially combining algorithms, such as particle swarm and simulated annealing, to find a combination of explorative then exploitative searching. The validity of these results are limited, however, due to the small sample size and to single well problems. In fact, some findings were contradictory to previously published guidelines which illustrates the need for this type of comparison: understanding an algorithm's performance under given conditions is necessary in leveraging its benefits, particularly with such demanding problems such as well placement.