Selecting a set of deterministic (e.g., P10, P50 and P90) models is an important and difficult step in any uncertainty quantification workflow. In this paper, we propose to use multi-objective optimization to find a reasonable balance between often conflicting features that must be captured by these models. We embed this approach into a streamlined uncertainty quantification workflow that seamlessly integrates multi-realization history-matching (MHM), production forecasting with uncertainty ranges and representative, deterministic model selection.

Some uncertain parameters strongly impact simulated responses representing historic (production) data and are selected as active parameters for history-matching, whereas others are important only for forecasting. An ensemble of conditional realizations of active history match parameters is generated in the MHM stage using a distributed optimizer, integrated with either randomized-maximum-likelihood (RML) or Gaussian-mixture-model (GMM). This ensemble is extended with unconditional realizations of forecast parameters generated by sampling from their prior distribution. Based on production forecasting results from simulations of this ensemble representing the posterior uncertainty distribution, representative (P10/P50/P90) models are selected using multi-objective optimization.

In addition to matching target values of the primary and a few secondary key performance indicators (e.g., cumulative oil/gas/water production, recovery factor, etc.), selected representative models often must satisfy other requirements or constraints, e.g., the value of some key parameters must be within a user specified tight range. It can be quite difficult to find a set of representative models that satisfy all requirements. Even more challenging, some requirements may be conflicting with others such that no single model can satisfy all requirements. To overcome these technical difficulties, this paper proposes formulating different requirements and constraints as objectives and applying a multi-objective optimization strategy to find a set of Pareto optimal solutions based on the concept of dominance. One or more representative models can then be selected from the set of optimal solutions according to case dependent preferences or requirements.

The proposed method is tested and validated on a realistic example. Our results confirm that the proposed method is robust and efficient and finds acceptable solutions with no violation or minimal violations of constraints (when conflicting constraints are present). These results suggest that our advanced multi-objective optimization technique can select high-quality representative models by striking a balance between conflicting constraints. Thus, a better decision can be made while running much fewer simulations than would be required with traditional methods.

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