A Functional Data Analysis Approach to Surrogate Modeling in Reservoir and Geomechanics Uncertainty Quantification

Abstract

Uncertainty quantification for geomechanical and reservoir predictions is in general a computationally intensive problem, especially if a direct Monte Carlo approach with large numbers of full-physics simulations is used. A common solution to this problem, well-known for the fluid flow simulations, is the adoption of surrogate modeling approximating the physical behavior with respect to variations in uncertain parameters. The objective of this work is the quantification of such uncertainty both within geomechanical predictions and fluid-flow predictions using a specific surrogate modeling technique, which is based on a functional approach. The methodology realizes an approximation of full-physics simulated outputs that are varying in time and space when uncertainty parameters are changed, particularly important for the prediction of uncertainty in vertical displacement resulting from geomechanical modeling. The developed methodology has been applied both to a subsidence uncertainty quantification example and to a real reservoir forecast risk assessment. The surrogate quality obtained with these applications confirms that the proposed method makes it possible to perform reliable time–space varying dependent risk assessment with a low computational cost, provided the uncertainty space is low-dimensional.