Gaussian process emulators for quantifying uncertainty in CO2 spreading predictions in heterogeneous media. (August 2017)

• Record Type: Journal Article
• Authors: Tian, Liang; Wilkinson, Richard; Yang, Zhibing; Power, Henry; Fagerlund, Fritjof; Niemi, Auli
• Is Part Of: Computers & geosciences. Volume 105(2017)
• Page Start: 113
• Page End: 119
• Publication Date: 2017-08
• Subjects: Permeability heterogeneity -- Karhunen-Loève expansion -- Monte Carlo -- Uncertainty analysis -- Gaussian process emulator; Environmental policy -- Periodicals; 550.5
• DOI: 10.1016/j.cageo.2017.04.006
• Languages: English
• ISSNs: 0098-3004

Abstract

Abstract: We explore the use of Gaussian process emulators (GPE) in the numerical simulation of CO 2 injection into a deep heterogeneous aquifer. The model domain is a two-dimensional, log-normally distributed stochastic permeability field. We first estimate the cumulative distribution functions (CDFs) of the CO 2 breakthrough time and the total CO 2 mass using a computationally expensive Monte Carlo (MC) simulation. We then show that we can accurately reproduce these CDF estimates with a GPE, using only a small fraction of the computational cost required by traditional MC simulation. In order to build a GPE that can predict the simulator output from a permeability field consisting of 1000s of values, we use a truncated Karhunen-Loève (K-L) expansion of the permeability field, which enables the application of the Bayesian functional regression approach. We perform a cross-validation exercise to give an insight of the optimization of the experiment design for selected scenarios: we find that it is sufficient to use 100s values for the size of training set and that it is adequate to use as few as 15 K-L components. Our work demonstrates that GPE with truncated K-L expansion can be effectively applied to uncertainty analysis associated with modelling of multiphase flow and transport processes in heterogeneous media. Abstract : Highlights: Uncertainty quantification approach developed for predictive modelling of CO 2 spreading in heterogeneous media. Gaussian processes regression with truncated Karhunen-Loève expansion. Excellent ECDF estimate at a fraction of computational cost compared to Monte Carlo simulation.