Interpretation of multi-scale permeability data through an information theory perspective

Abstract

Abstract. We employ elements of information theory to quantify (i) the information content related to data collected at given measurement scales within the same porous medium domain and (ii) the relationships among information contents of datasets associated with differing scales. We focus on gas permeability data collected over Berea Sandstone and Topopah Spring Tuff blocks, considering four measurement scales. We quantify the way information is shared across these scales through (i) the Shannon entropy of the data associated with each support scale, (ii) mutual information shared between data taken at increasing support scales, and (iii) multivariate mutual information shared within triplets of datasets, each associated with a given scale. We also assess the level of uniqueness, redundancy and synergy (rendering, i.e., information partitioning) of information content that the data associated with the intermediate and largest scales provide with respect to the information embedded in the data collected at the smallest support scale in a triplet. Highlights. Information theory allows characterization of the information content of permeability data related to differing measurement scales. An increase in the measurement scale is associated with quantifiable loss of information about permeability. Redundant, unique and synergetic contributions of information are evaluated for triplets of permeability datasets, each taken at a given scale.

SciKit-GStat Uncertainty: A software extension to cope with uncertain geostatistical estimates

“…Recent geostatistical analyses of these data include the works of Riva et al (2013) andDell'Oca et al (2020).…”

Technical note: Quantification of flow field variability using intrinsic random function theory

“…In many practical applications, the experimental variance of a random variable (function) sampled from a field increases with the size of the field (e.g., Desbarats and Bachu, 1994;Molz et al, 2004;Dell'Oca et al, 2020). This means that the data have an almost unlimited scattering capacity and cannot be properly described by ascribing a finite a priori variance to them.…”