Multi-scale simulation and Bayesian inversion of advection-diffusion-reaction equation in porous media

The mathematical models for particle and contaminant transport in subsurface flows are often limited by a lack of knowledge on the equation parameters. In this work pore scale three dimensional simulations of solute transport in a complex porous structure are analyzed to obtain macro scale averaged quantities. These quantities can be used to select the appropriate model equations for macro scale transport and estimate the parameters of the resulting advection dispersion reaction macro scale equations. The parameters considered are the effective velocity, effective porosity, dispersion and transfer coefficient. Bayesian inversion techniques are used to solve the inverse problem with a collocation approach or with Markov Chain Monte Carlo. The macro scale forward model is solved either by a simplified analytical formulation or by standard finite difference method while the porescale data are obtained from expensive Computational Fluid Dynamics finite volume simulations. Correlation laws that links the inner scale flow properties and porous structures with the macro scale parameters are proposed.