Abstract
A variety of methods is available to quantify uncertainties arising
within 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 parameters in constitutive relations,
and of material properties. We consider recent versions of the following
non-intrusive and intrusive uncertainty quantification methods: arbitrary
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.
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