A cumulant analysis for non-Gaussian displacement distributions in Newtonian and non-Newtonian flows through porous media

Abstract We use displacement encoding pulsed field gradient (PFG) nuclear magnetic resonance to measure Fourier components S q of flow displacement distributions P ( ζ ) with mean displacement 〈 ζ 〉 for Newtonian and non-Newtonian flows through rocks and bead packs. Displacement distributions are non-Gaussian; hence, there are finite terms above second order in the cumulant expansion of ln( S q ). We describe an algorithm for an optimal self-consistent cumulant analysis of data, which can be used to obtain the first three (central) moments of a non-Gaussian P ( ζ ), with error bars. The analysis is applied to Newtonian and non-Newtonian flows in rocks and beads. Flow with shear-thinning xanthan solution produces a 15 . 6±2 . 3% enhancement of the variance σ 2 of displacement distributions when compared to flow experiments with water.