A Stochastic Galerkin Approach to Uncertainty Quantification in Poroelastic Media

Recent concerns over the safety of oil and natural gas extraction, fracking, and carbon sequestration have driven the need to develop methods for uncertainty quantification for coupled subsurface flow & deformation processes. Traditional monte-carlo methods are versatile, but exhibit prohibitively slow convergence. In this work, we develop an intrusive polynomial chaos expansion method for Biot’s Poroelasticity Equations based on galerkin projection with uniform and log-normally distributed material parameters. We analyze accuracy and efficiency of our method and compare it to monte-carlo and anova based probabilistic collocation methods.