Selecting Representative Models from a Large Set of Models

Abstract

AbstractIn order to make the field development decision making and planning process tractable, the decision-makers usually need a few representative models (for example, P10, P50, P90 models) selected from a large ensemble of reservoir models. This ensemble of models may have been obtained from a static and/or dynamic modeling process involving uncertainty quantification (ED), history matching, optimization or other workflows. The usual approach to select a few models is using various variants of clustering. This selection process is not only suboptimal, but it could also be quite difficult to do if multiple output responses and/or percentiles are required and the number of models is large. The current approach in most oil companies is even more naïve, wherein, such models are chosen manually or using Excel spreadsheets. Thus, due to the unavailability of good approaches, representative models are usually chosen based on one or two criteria. Use of such models in the decision making process can lead to sub-optimal decisions. As such, there is a need to automatically select a small set of statistically representative models from a larger set based on multiple decision criteria.We propose a new model selection approach, namely minimax approach, which can simultaneously and efficiently select a few reservoir models from a large ensemble of models by matching target percentiles of multiple output responses (for example, matching P10, P50 and P90 of OPC, WPC and OOIP), while also obtaining maximally different models in the input uncertainty space. The approach requires the simultaneous solution of two minimax combinatorial optimization problems. Since this requires the solution a complex multi-objective optimization problem, we instead convert the problem to the solution of a single constrained minimax optimization problem. We propose the solution of this optimization problem using a global exhaustive search (for small problems), and a very efficient greedy method wherein a simpler optimization problem can be solved directly by enumeration or by Markov chain Monte Carlo methods for larger problems with many models, target percentiles and variables. The new approach is implemented in Chevron’s in-house uncertainty quantification software called genOpt and tested with multiple synthetic examples and field cases. The results demonstrate that the proposed approach is much more efficient than clustering and solution quality is generally better than clustering. For some models, minimax was orders of magnitude faster than clustering. The new approach could help business units select P10, P50 and P90 models efficiently for decision making and planning.