title: Statistical scaling of pore-scale Lagrangian velocities in natural porous media.
abstract: We investigate the scaling behavior of sample statistics of pore-scale Lagrangian velocities in two different rock samples, Bentheimer sandstone and Estaillades limestone. The samples are imaged using x-ray computer tomography with micron-scale resolution. The scaling analysis relies on the study of the way qth-order sample structure functions (statistical moments of order q of absolute increments) of Lagrangian velocities depend on separation distances, or lags, traveled along the mean flow direction. In the sandstone block, sample structure functions of all orders exhibit a power-law scaling within a clearly identifiable intermediate range of lags. Sample structure functions associated with the limestone block display two diverse power-law regimes, which we infer to be related to two overlapping spatially correlated structures. In both rocks and for all orders q, we observe linear relationships between logarithmic structure functions of successive orders at all lags (a phenomenon that is typically known as extended power scaling, or extended self-similarity). The scaling behavior of Lagrangian velocities is compared with the one exhibited by porosity and specific surface area, which constitute two key pore-scale geometric observables. The statistical scaling of the local velocity field reflects the behavior of these geometric observables, with the occurrence of power-law-scaling regimes within the same range of lags for sample structure functions of Lagrangian velocity, porosity, and specific surface area.
authors.affiliation: Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano, Italy.
authors.forename: M
authors.initials: M
authors.lastname: Siena
authors.affiliation: Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano, Italy and Department of Hydrology and Water Resources, University of Arizona, Tucson, Arizona 85721, USA.
authors.forename: A
authors.initials: A
authors.lastname: Guadagnini
authors.affiliation: Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano, Italy and Department of Hydrology and Water Resources, University of Arizona, Tucson, Arizona 85721, USA.
authors.forename: M
authors.initials: M
authors.lastname: Riva
authors.affiliation: Department of Earth Science and Engineering, Imperial College, London, United Kingdom.
authors.forename: B
authors.initials: B
authors.lastname: Bijeljic
authors.affiliation: Department of Earth Science and Engineering, Imperial College, London, United Kingdom and Reservoir Geophysics Group, Petrobrás, Rio de Janeiro, Rio de Janeiro, Brazil.
authors.forename: J P
authors.initials: JP
authors.lastname: Pereira Nunes
authors.affiliation: Dipartimento di Ingegneria Civile e Ambientale, Politecnico di Milano, Piazza L. Da Vinci 32, 20133 Milano, Italy and Department of Earth Science and Engineering, Imperial College, London, United Kingdom.
authors.forename: M J
authors.initials: MJ
authors.lastname: Blunt
mesh_terms: D003198:Computer Simulation; D055593:Geological Phenomena; D015233:Models, Statistical; D009038:Motion; D016062:Porosity; D014057:Tomography, X-Ray Computed