Parameter Screening with Hilbert-Schmidt Independence Statistical Tests for the Design of Saline Aquifer CO2 Storage Sites

Numerical models can be considered to predict the response of CO2 storage sites to various injection scenarios and help to estimate their potential and identify optimal exploitation schemes. For these models to be representative of the considered storage and provide reliable predictions, their input parameters must be characterized using the available data. However, these data are generally not informative enough to determine unique values for these properties, resulting in uncertainties on the predicted dynamics that must be considered for robust decisions. This generally requires to perform many time-consuming flow simulations. These computation times can however be reduced by replacing simulations with calls to meta-models that approximate the relationship between the simulator inputs and outputs and provide fast estimations of these outputs.

In practice, the number of parameters to be considered as inputs to these meta-models can be large, inducing the need for many simulations in the training set to obtain accurate estimations. A preliminary screening of these parameters can help to discard the ones that have a negligible influence on the outputs of interest, thus reducing the complexity of the meta-modeling process. We propose here to investigate the potential of a new screening technique based on the Hilbert-Schmidt independence criterion (HSIC), which proved to be efficient in other applications. This sensitivity approach relies on cross-covariance operators between the input parameters and outputs probability distributions to detect dependencies. The resulting sensitivity indices can be estimated from a limited sample of simulations, and statistical tests can be performed to separate significant parameters from non-significant ones. In addition, this approach makes it possible to compute some global sensitivity indices for temporal or spatial outputs. Finally, the samples used to compute the sensitivity indices can be designed to be re-used for the meta-modeling training step, considering for instance space-filling designs such as Latin Hypercube sampling.

We propose here to study the potential of this approach in the context of CO2 storage, considering the simulation of CO2 injection in a synthetic radial saline aquifer with and without salting-out effect. More precisely, the HSIC indices are computed from samples of varying sizes, and Gaussian process-based predictors are built considering as inputs the parameters identified as influential from the statistical tests. The studied input parameters include physical and geological characteristics as well as operational constraints. Outputs include temporal and spatial simulated properties.