Uncertainty quantification on the macroscopic properties of heterogeneous porous media

Pore-scale simulation is an essential tool to understand complex physical process in many environmental problems. However, structural heterogeneity and data scarcity render the porous medium, and in turn its macroscopic properties, uncertain. Meanwhile, direct numerical simulation of the medium at the fine scale often incurs high computational cost, which further limits efforts to quantify the parametric uncertainty over those macroscopic properties. To address this challenge, we propose a framework to compute the probabilistic density function (PDF) of the macroscopic property based on the generalized polynomial chaos expansion method and the Minkowski functionals. To illustrate the effectiveness of our approach, we conduct numerical experiments for one macroscopic property, namely the permeability, and we compare its PDF with that obtained from Monte Carlo simulations. Both two- and three-dimensional cases show that our framework requires much fewer realizations while maintaining the desired accuracy.