Abstract
The optimization of large-scale field development is challenging because the number of optimization variables can become excessive. A way to circumvent this difficulty is to constrain wells to exist within patterns and to then optimize parameters associated with the pattern type and geometry. In this paper, we introduce a general framework for accomplishing this type of optimization. The overall procedure, which we refer to as well pattern optimization (WPO), entails a new well pattern description (WPD) incorporated into an underlying optimization method. The WPD encodes potential solutions in terms of pattern types (e.g., five-spot, nine-spot) and pattern operators. The operators define geometric transformations (e.g., stretching, rotating) quantified by appropriate sets of parameters. It is the parameters that specify the well patterns and the pattern operators, along with additional variables that define the sequence of operations, that are optimized by WPO. The well pattern description developed here could be used with a variety of underlying optimization methods. Here we combine it with a particle swarm optimization (PSO) technique, as PSO methods have recently been shown to provide robust and efficient optimizations for well placement problems.
Detailed optimization results are presented for three different example cases using several variants of the WPO algorithm. In one case, multiple reservoir models are considered to account for geological uncertainty. For all examples, significant improvement in the objective function is observed as the algorithm proceeds, particularly at early iterations. A two-stage optimization procedure, in which the first-stage optimization considers multiple well pattern types while the second stage focuses on the most promising pattern, is applied and shown to be effective. Limited comparisons with results using standard well patterns of various sizes demonstrate that the net present values achieved by the WPO algorithm are considerably greater. Taken in total, the optimization results highlight the potential of the WPO procedure for use in practical field development.
