Particle Swarm Optimization Algorithm for Optimum Well Placement Subject to Realistic Field Development Constraints
Authors: Jesmani Mansoureh , Bellout Mathias C. , Hanea Remus , Foss Bjarne 
Published: September 2015

Abstract
Well placement optimization has the potential to become an important procedure within field development planning. The main objective of a well placement optimization effort is to provide decision makers with high quality advice on where to place wells. To achieve this task, an optimizer searches for well locations that improve a relevant economic performance measure, or maximize the expected recovery of the hydrocarbon asset. However, the well placement problem is challenging because the relationship between well placement, reservoir geology and resulting fluid flow patterns is, but in the most trivial cases, complex, and therefore the optimizer often needs to rely on computationally expensive reservoir simulations to find the final production volumes associated with a given well configuration. Moreover, besides the efficiency of the optimization effort, the quality of the advice provided relies on how well realistic constraints have been introduced into the optimization problem. In particular, it is important that the design limitations that the field development team operates with, either explicitly or implicitly, are articulated and formalized within the search for optimal well placement.
In this work, we focus on developing constraint formulations to enforce various realistic field development considerations. Furthermore, we apply the Particle Swarm Optimization (PSO) algorithm to iterate on the location of wells for two production cases while using some of the developed constraints. The constraints developed in this work include maintaining a minimum inter-well distance, a minimum and maximum well length, a general orientation of the wells with respect to a set platform location, and keeping the wells within specified reservoir regions. Moreover, we investigate the sensitivity of these constraints with respect to the optimal solution. These various constraint classes have been developed in close collaboration with a major field operator on the Norwegian Continental Shelf.
The PSO algorithm applied in this work is a derivative-free optimizer based on an stochastic search procedure. The procedure consists of a model of the behavior of a swarm. It includes various probabilistic factors, and mimics the collective motion of animals, e.g., the flight of a flock of birds. We incorporate the various well placement constraints into the PSO algorithm using two different constraint-handling techniques: a decoder procedure and the penalty method. The decoder procedure maps the feasible search space onto n-dimensional cubes and has the advantage of not requiring parameter tuning. The penalty method converts the constrained optimization problem into an unconstrained one by introducing an additional term, called a penalty function, to the objective function.
These constraint-handling techniques are applied to two different reservoir production cases. The first case is a simple problem where the PSO algorithm is implemented with a particular bound and a well length constraint to find the optimal location of one horizontal producer. The second case treats a synthetic field model with realistic porosity and permeability data and grid geometry. For this case, using the decoder implementation of the PSO algorithm, we optimize the placement of eight vertical wells to be placed within irregular-shaped reservoir regions determined based on geological considerations, e.g., faults. In terms of economic performance for this case, the PSO with decoder yields an improvement of 16% compared to the initial well configuration.