Comparison of data-driven uncertainty quantification methods for a carbon dioxide storage benchmark scenario

TL;DR

This paper compares four data-driven uncertainty quantification methods applied to a carbon dioxide storage benchmark, evaluating their accuracy, convergence, and suitability for realistic scenarios with limited data.

Contribution

It provides a comprehensive comparison of recent uncertainty quantification methods for CO2 storage, including implementation details and performance analysis on a benchmark scenario.

Findings

Kernel-based greedy interpolation shows fast convergence.

Spatially adaptive sparse grids provide accurate results with fewer model runs.

All methods' performance varies depending on the uncertainty source.

Abstract

A variety of methods is available to quantify uncertainties arising with\-in the modeling of flow and transport in carbon dioxide storage, but there is a lack of thorough comparisons. Usually, raw data from such storage sites can hardly be described by theoretical statistical distributions since only very limited data is available. Hence, exact information on distribution shapes for all uncertain parameters is very rare in realistic applications. We discuss and compare four different methods tested for data-driven uncertainty quantification based on a benchmark scenario of carbon dioxide storage. In the benchmark, for which we provide data and code, carbon dioxide is injected into a saline aquifer modeled by the nonlinear capillarity-free fractional flow formulation for two incompressible fluid phases, namely carbon dioxide and brine. To cover different aspects of uncertainty quantification, we incorporate various sources of uncertainty such as uncertainty of boundary conditions, of conceptual model definitions and of material properties. We consider recent versions of the following non-intrusive and intrusive uncertainty quantification methods: arbitary polynomial chaos, spatially adaptive sparse grids, kernel-based greedy interpolation and hybrid stochastic Galerkin. The performance of each approach is demonstrated assessing expectation value and standard deviation of the carbon dioxide saturation against a reference statistic based on Monte Carlo sampling. We compare the convergence of all methods reporting on accuracy with respect to the number of model runs and resolution. Finally we offer suggestions about the methods' advantages and disadvantages that can guide the modeler for uncertainty quantification in carbon dioxide storage and beyond.