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A stochastic Galerkin approach to uncertainty quantification in poroelastic media

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  • Delgado, Paul
  • Kumar, Vinod

Abstract

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 and 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 the Galerkin projection with uniform and log-normally distributed material parameters. We analyze accuracy and efficiency of our method and compare it to the Monte Carlo method. We verify exponential convergence of the stochastic Galerkin approach.

Suggested Citation

  • Delgado, Paul & Kumar, Vinod, 2015. "A stochastic Galerkin approach to uncertainty quantification in poroelastic media," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 328-338.
    • Handle: RePEc:eee:apmaco:v:266:y:2015:i:c:p:328-338
    DOI: 10.1016/j.amc.2015.04.127
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    1. Curtis M. Oldenburg, 2012. "The risk of induced seismicity: is cap‐rock integrity on shaky ground?," Greenhouse Gases: Science and Technology, Blackwell Publishing, vol. 2(4), pages 217-218, August.
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