Estimation of spatial covariance of log conductivity from particle size data

Abstract

We derive analytical relationships between the spatial covariance of the (natural) logarithm of hydraulic conductivity (K) and that of representative soil particle sizes and porosity. The latter quantities can be directly measured during routine sedimentological analyses of soil samples and provide a way of incorporating K estimates into groundwater flow models at a relatively modest experimental cost. Here we rely on widely used empirical formulations requiring measurements of representative particle diameters and, in some cases, of medium porosity. We derive exact formulations relating the spatial covariance of these quantities and K and present workable approximations on the basis of perturbation methods. Our formulations provide a direct link between key geostatistical descriptors of sedimentological and hydraulic parameters of heterogeneous aquifers which can be employed in classical estimation and simulation procedures. The approach and theoretical results are tested on an extensive data set comprising 411 particle size curves collected at 12 boreholes in a small-scale alluvial aquifer.

A Class-Kriging Predictor for Functional Compositions with Application to Particle-Size Curves in Heterogeneous Aquifers

“…These data were adopted by Riva et al (2006Riva et al ( , 2008Riva et al ( , 2010 in numerical Monte Carlo analysis and interpretation of a tracer test, and to provide a probabilistic delineation of well-related capture zones. Riva et al (2014) rely on these data to support their analytical developments leading to a set of relationships between the spatial covariance of the (natural) logarithm of hydraulic conductivity and that of representative soil particle sizes and porosity. A subset of these data was employed by Menafoglio et al (2014) to test their FCK methodology, in a stationary setting.…”

“…The quality of groundwater flow and transport predictions in natural aquifer systems is markedly dependent on the way one can provide a proper representation of the heterogeneous spatial distribution of geomaterials and their associated hydraulic/transport parameters at a given model grid scale. Amongst the set of available analysis techniques, particle-size curves (PSCs) are widely employed to provide relatively inexpensive estimates of the types of geo-materials forming the internal architecture of an aquifer, and the associated values of hydraulic conductivity (Riva et al, 2006(Riva et al, , 2010(Riva et al, , 2014, and references therein).…”

Geostatistical Analysis in Bayes Spaces: Probability Densities and Compositional Data

“…The aquifer system under consideration has been the subject of an extensive series of experimental campaigns and modeling studies. Amongst these, the reader is referred to the works of Riva et al [15,16,17,18], Hoffmann and Dietrich [19], Rein et al [20], Neuman et al [21,22], Lessof et al [23], Barahona-Palomo et al [24], Handel and Dietrich [25], and Menafoglio et al [7,8,9]. Characterization of the site has been based on data acquired through detailed geological, hydrogeological, hydraulic, sedimentological and geophysical investigations.…”

Stochastic simulation of soil particle‐size curves in heterogeneous aquifer systems through a Bayes space approach

“…[], and Riva et al . [] in the context of stochastic modeling studies aimed at (a) providing a probabilistic analysis of solute residence times within well capture zones, (b) interpreting an observed tracer test in a numerical Monte Carlo framework, (c) assessing the link between the spatial covariance functions of the (natural) logarithm of hydraulic conductivity and of soil particle representative diameters, and (d) characterizing the correlation between hydraulic conductivity values estimated through impeller flowmeter downhole measurements and by way of empirical formulations based on PSC representative diameters.…”