An efficient stochastic framework to propagate the effect of the random solid-pore geometry of porous media on the pore-scale flow

Simulating the pore-scale flow-field past porous media samples is a computationally expensive exercise. Uncertainty quantification of such systems can turn out to be a real challenge, especially by employing the available spectral approaches such as the polynomial chaos expansion (PCE) technique and its variants. The present study addresses this problem by combining the strengths of a sampling based method and a spectral characterization technique. This novel approach integrates Monte Carlo Simulations (MCS) and Karhunen-Lòeve (K-L) expansion techniques in order to create a framework for the modelling and reconstruction of the output fields of large order complex systems such as the porous media flow. A pore-scale modelling of flow through porous media samples, by simulating the incompressible Navier-Stokes equation in the pore spaces by employing the Lattice Boltzmann method has been taken up in the present study. The modelling of the input randomness also has an element of novelty in the present work as it directly captures the random solid-pore arrangement of the media geometry instead of any macro-properties. The input random geometries are created digitally using limited statistics of an appropriate discrete valued random process. The resulting process is weakly correlated and needs a very large number of input random variables to capture its higher frequency content. Such large random dimensional problems cannot be practically solved using popular spectral tools like the PCE. The proposed integrated MCS-KL approach has been utilized successfully in the present work to propagate their effect on the pore-scale velocity field. Further, the K-L step provides an efficient means for reconstructing physically realistic samples of the chosen output whose statistics match the target statistics well. This is a significant time saver as it effectively bypasses the need of fresh flow-field simulations through a complex large order system such as the present one.