Uncertainty Quantification in Porous Media flows

Bayesian Calibration, Validation and Uncertainty Quantification of Subsurface flow models

Details

Motivation

In this project, we address the mathematical modeling, numerical simulation, and uncertainty quantification of multiphase flow in porous media with a special emphasis on CO2 storage in geological formations. Carbon Capture and Storage (CCS) is a family of technologies and techniques that enable the capture of CO2 from fossil fuel combustion and industrial processes in order to prevent the produced CO2 to be released into the atmosphere without control.

Methodology

This project is characterized by an​ interdisciplinary and multi-scale approach. At each scale, we solve the corresponding PDE model with High Performance Computing techniques. We use the description at fine scales to estimate the unknown parameters at large scales by solving an inverse problem (i.e. statistical calibration and validation of large scale models) based on Bayesian inference. 

Results and ongoing work

We are currently developing a family of multi-scale models for two-phase flows at different scales. We will use these results, from the more detailed and computationally more expensive ones to the simplified ones, to assess the reliability and variability in the prediction of quantities of interests, such as CO2 flow rates.  The overall goal of the project is to obtain a reliable field-scale model by a robust estimation of its parameters. We will extend the approach to other common porous media problems, such as oil recovery and contaminant dispersion. The pictures below show a pore-scale simulation of flow and transport phenomena in a three-dimensional porous medium and the statistical moments of Darcy fluxes in a square domain.

                                                                        
                 


​​Pore scale simulation using Navier-Stokes.

 Statistics of random subsurface flow computed using stochastic collocation. 
 


Collaborators

Participants:
  • Serge Prudhomme (Ecole Polytechnique de Montreal, UT Austin)
  • Raul Tempone (KAUST)
  • J. Tinsley Oden (UT Austin)
  • Masa Prodanovic (UT Austin)
  • Fanis Strouboulis (TAMU)
  • Quan Long (KAUST)
  • Matteo Icardi (KAUST)
  • Bilal Saad (KAUST)
Other collaborators: 
  • Rajandrea Sethi (Politecnico di Torino)
  • Daniele Marchisio (Politecnico di Torino)
  • Gianluca Boccardo (Politecnico di Torino)
  • Francesca Messina (Politecnico di Torino)​

Publications

Journal publications: ​
Conference publication:​​
  • Q. Long, S. Prudhomme, M. Scavino, R. Tempone and S. Wang. Optimal design of model validation procedure with respect to quantity of interest. Stochasitc Modeling Techniques and Data Analysis International Conference, Chania, Crete, Jun. 5-8, 2012.