title: 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(zeta) with mean displacement (zeta) 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(zeta), 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 sigma(2) of displacement distributions when compared to flow experiments with water.
authors.affiliation: Schlumberger-Cambridge Research, High Cross, Madingley Road, Cambridge CB3 0EL, UK. ums@dq.fct.unl.pt
authors.forename: Ulrich M
authors.initials: UM
authors.lastname: Scheven
authors.forename: John P
authors.initials: JP
authors.lastname: Crawshaw
authors.forename: Valerie J
authors.initials: VJ
authors.lastname: Anderson
authors.forename: Rob
authors.initials: R
authors.lastname: Harris
authors.forename: Mike L
authors.initials: ML
authors.lastname: Johns
authors.forename: Lynn F
authors.initials: LF
authors.lastname: Gladden
mesh_terms: D000465:Algorithms; D005583:Fourier Analysis; D009682:Magnetic Resonance Spectroscopy / Q000379:methods*; D011135:Polysaccharides, Bacterial / Q000737:chemistry; D016062:Porosity; D012212:Rheology / Q000379:methods; D016008:Statistical Distributions; D014867:Water / Q000737:chemistry
chemical_list: D011135:Polysaccharides, Bacterial; D014867:Water; C002563:xanthan gum