Optimal Well Placement under Uncertainty using a Retrospective Optimization Framework

Abstract

Subsurface geology is highly uncertain, and it is necessary to account for this uncertainty when optimizing the location of new wells. This can be accomplished by evaluating reservoir performance for a particular well configuration over multiple realizations of the reservoir and then optimizing based, for example, on expected net present value (NPV) or expected cumulative oil production. A direct procedure for such an optimization would entail the simulation of all realizations at each iteration of the optimization algorithm. This could be prohibitively expensive when it is necessary to use a large number of realizations to capture geological uncertainty. In this work, we apply a procedure that is new within the context of reservoir management-retrospective optimization (RO)-to address this problem. RO solves a sequence of optimization subproblems that contain increasing numbers of realizations. We introduce the use of k-means clustering for selecting these realizations. Three example cases are presented that demonstrate the performance of the RO procedure. These examples use particle swarm optimization (PSO) and simplex linear interpolation (SLI)-based line search as the core optimizers (the RO framework can be used with any underlying optimization algorithm, either stochastic or deterministic). In the first example, we achieve essentially the same optimum using RO as we do using a direct optimization approach, but RO requires an order of magnitude fewer simulations. The results demonstrate the advantages of cluster-based sampling over random sampling for the examples considered. Taken in total, our findings indicate that RO using cluster sampling represents a promising approach for optimizing well locations under geological uncertainty.

Joint optimization of oil well placement and controls

“…It will also be useful to consider global exploration techniques such as particle swarm optimization (Eberhart et al, 2001) or genetic algorithms (Goldberg, 1989) for the well placement part of the optimization. Uncertainty in the reservoir model should also be included in the optimization using, for example, the stochastic procedure recently presented by Wang et al (2012).…”

“…In closing, this overall topic is also coupled with the possible application of other gradient-based solvers for the specific purpose of decreasing the total number of calls to the reservoir simulator (see Section 3.2.1, page 57). Finally, as previously discussed, if further method developments are to be readily applied within field development operations, we need to take into account reservoir model uncertainty within the optimization process, e.g., by using the method by Wang et al (2012), briefly discussed in Section 2.1, on page 16.…”

“…Another important effect not included in this work is uncertainty in the reservoir model; i.e., the optimization approaches studied here do not involve stochastic programming considerations. A general method for optimizing well location under uncertainty has been developed by Wang et al (2012), and this approach could be extended in a straightforward manner to also include well controls.…”

Optimization of Geothermal-Well-Doublet Placement

“…Gradient-based optimization algorithms are used for optimization purposes throughout the oil and gas industry (e.g., Yeten et al 2003;Bangerth et al 2004;Güyagüler and Horne 2004;Ӧzdögan and Horne 2006;Zandvliet et al 2008;Onwunalu and Durlofsky 2011;Wang et al 2012). These algorithms provide a systematic way to explore a wide range of well positions and have the goal to find the optimal (or at least very good) well positions for given boundary conditions (e.g., restrictions on surface facilities and the reservoir geometry).…”

“…Multiple of such optimization methods have been developed by the oil and gas industry to determine optimal positions for producers and injectors in heterogeneous reservoirs (e.g., Güyagüler and Horne 2004;Kraaijevanger et al 2007;Zandvliet et. al 2008;Kalla and White 2007;Wang et al 2012). This topic will be further discussed in chapter 4.…”