Horizontal spatial correlation of hydraulic and reactive transport parameters as related to hierarchical sedimentary architecture at the Borden research site

Abstract

[1] Highly resolved data from the Borden research site provide a unique opportunity to study the horizontal spatial bivariate correlation of hydraulic and reactive attributes affecting subsurface transport. The data also allow quantitatively relating this correlation to the hierarchical sedimentary architecture of the aquifer. The data include collocated samples of log permeability, Y, the log of the perchloroethene sorption distribution coefficient, Ä, and lithologic unit type. The horizontal Y and Ä autosemivariograms and the Ä-Y cross-semivariogram have the same underlying correlation structure (shape and range in the rise to a sill). The common structure is not due to Ä-Y point correlation or in-unit spatial correlation. The common structure is defined by how the proportion of lag transitions crossing different unit types (i.e., the cross-transition probability structure) increases with increasing lag distance. The common underlying cross-transition structure contains two substructures with different correlation ranges corresponding to two scales of unit types within the sedimentary architecture. For each substructure, a large standard deviation in the length of units relative to the mean length gives rise to an exponential-like shape and the proportions and mean length of units define the ranges. The horizontal Ä-Y spatial cross correlation is primarily defined by the larger-scale substructure and the differences in mean Ä and Y between larger-scale unit types.

What have we learned from deterministic geostatistics at highly resolved field sites, as relevant to mass transport processes in sedimentary aquifers?

“…Equation (2) has been expanded by including indicator spatial functions to track the facies sampled by each element of S and thereby track the hierarchy of facies types within the equations (Rubin, 1995(Rubin, , 2003Barrash and Clemo, 2002;Ritzi et al, 2004;Ritzi et al, 2013). While any number of hierarchical levels can be tracked, here we consider a domain comprising facies types defined at each of two scales (a two-level hierarchy), as illustrated in …”

“…are facies specific auto-or cross semivariograms (Ritzi et al, 2013). The ) ( , h t ji ro are the sample transition probabilities which give the fraction of lags of a specific distance and direction that are of a particular transition type (i.e., the fraction with tail in region type ro and head in region type ji).…”

“…These data sets have been taken from sedimentary deposits representing a range of depositional settings including fluvial deposits , alluvial deposits , and lake-shore deposits (Ritzi et al, 2013). Importantly, there are some common aspects to all outcomes thus far.…”

“…This included highly resolved data characterizing the sedimentary architecture in fluvial, alluvial, and lake shoreline deposits. The studies have created a body of literature studying the link between sedimentary architecture and heterogeneity in attributes such as permeability and sorptive properties (e.g., Anderson, 1989Anderson, , 1991aAnderson, , 1991bDavis et al, 1993;Davis et al, 1997;Allen-King et al, 1998;Barrash and Clemo, 2002;Divine, 2002;Guad et al, 2004;Biteman et al, 2004;Kalinovich et al, 2012;Ritzi et al, 2013;Ritzi, 2014, andAllen-King et al, 2015). In these studies, data populations were subdivided according to facies type.…”

“…Statistics for spatial-bivariate correlation in discrete structural hierarchies have been formulated so that any number of hierarchical levels can be represented. These equations have been applied to highly resolved data sets used in a number of deterministic geostatistic studies at different locations (Rubin (1995), Barrash and Clemo (2002), Rubin (2003), Ritzi et al (2004); , Ramanathan et al (2010) and Ritzi et al (2007Ritzi et al ( , 2013). From these collective studies, a more fundamental understanding of the spatial-bivariate correlation for attributes controlling mass transport has emerged and, in turn, we are gaining a more fundamental understanding of those transport processes, as reviewed below.…”