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

Abstract

In the method of deterministic geostatistics (sensu Issaks and Srivastava, 1988), highlyresolved data sets are used to compute sample spatial-bivariate statistics within a deterministic framework. The general goal is to observe what real, highly resolved, sample spatial-bivariate correlation looks like when it is well-quantified in naturally-occurring sedimentary aquifers.Furthermore, it is to understand how this correlation structure, (i.e. shape and correlation range) is related to independent and physically quantifiable attributes of the sedimentary architecture.The approach has evolved among work by Rubin for sample statistics have been developed which allow tracking the facies types at the heads and tails of lag vectors. The goal is to observe and thereby understand how aspects of the sedimentary architecture affect the well-supported sample statistics. The approach has been used to study heterogeneity at a number of sites, representing a variety of depositional environments, with highly resolved data sets. What have we learned?We offer and support an opinion that the single most important insight derived from these studies is that the structure of spatial-bivariate correlation is essentially the cross-transition probability structure, determined by the sedimentary architecture. More than one scale of hierarchical sedimentary architecture has been represented in these studies, and a hierarchy of cross-transition probability structures was found to define the correlation structure in all cases. This insight allows decomposing contributions from different scales of the sedimentary architecture, and has led to a more fundamental understanding of mass transport processes including mechanical dispersion of solutes within aquifers, and the time-dependent retardation of reactive solutes.These processes can now be described in terms of quantifiable physical attributes of the sedimentary architecture. In addition to discussing the benefits to basic scientific understanding, we also discuss some of the practical benefits derived from this insight.

Data‐Worth Analysis for Heterogeneous Subsurface Structure Identification With a Stochastic Deep Learning Framework

“…Reliable characterization of heterogeneous subsurface structures is crucial for earth sciences and other related applications such as groundwater management and contamination, geological carbon storage, radioactive waste disposal, and geothermal applications (Allen‐King et al., 2015; de Barros et al., 2013; de Barros, 2018; Dentz et al., 2020; Ershadnia et al., 2021; Fernàndez‐Garcia et al., 2005; Fiori et al., 2010; Gómez‐Hernández et al., 2017; Kitanidis, 2015; Ritzi & Soltanian, 2015; Sanchez‐Vila et al., 2006; M. R. Soltanian et al., 2015; Sudicky, 1986; Wallace et al., 2021; Weissmann et al., 2015). The poorly estimated subsurface structure may introduce a larger bias into dynamic responses prediction than inappropriate model parameters (Dai et al., 2020; Fernàndez‐Garcia et al., 2002, 2004, 2005; Harp et al., 2008; Pedretti et al., 2013; Riva et al., 2008; Sanchez‐Vila et al., 2010; Wallace & Soltanian, 2021; Ye et al., 2004).…”

Evaluating the Effects of Multiscale Heterogeneous Sediments on Solute Mixing and Effective Dispersion

“…Using indicator geostatistics, several works have provided a more realistic link between sedimentary architecture data (e.g., mean length and volume proportions of facies types) at different scales and the time‐evolution of solute transport metrics (e.g., Dai et al., 2004; 2019, 2020; Ramanathan et al., 2010; Ritzi & Soltanian, 2015; Soltanian, Ritzi, Dai, et al., 2015a; Soltanian et al., 2020). The most important insight from these studies is that the spatial‐bivariate correlation structure of K is directly defined by the transition probability structure (i.e., probability of transitioning from one facies type to another), with the main contributions from cross‐transition probability.…”

“…Accurate representation of solute transport processes (e.g., dispersion, mixing, and dilution) is important for various porous media‐related applications such as hydrogeology, soil physics, environmental engineering and sciences, water resources management, and petroleum engineering (de Barros et al., 2015; Ershadnia, Hajirezaie, et al., 2021; Ershadnia, Wallace, et al., 2021; Fiori & Dagan, 2000; Fiori, 2001; Jha et al., 2011; Jiménez‐Martínez et al., 2015; Kitanidis and McCarty, 2012). Large‐scale field experiments (e.g., Borden, MADE, Cape Cod) have revealed that spatial heterogeneity in physical and geochemical sediment properties, as well as local‐scale dispersion, are among the primary underlying mechanisms which govern solute transport processes (Anderson & McCray, 2011; Attinger et al., 2004; Bianchi et al., 2011; Dai et al., 2004; Fiori & Dagan, 1999; Freyberg, 1986; Gelhar, 1986; Ritzi & Soltanian, 2015; Salamon et al., 2007; Sudicky & Illman, 2011; Zheng et al., 2011). Heterogeneous aquifer hydraulic conductivity ( K ) results in erratic solute distributions, which increase solute surface area and enhance spreading and mixing (Burr et al., 1994; de Barros et al., 2015; Dentz et al., 2011, 2018; Kitanidis, 1994; Sanchez‐Vila et al., 2006; Werth et al., 2006).…”

Stage‐Wise Stochastic Deep Learning Inversion Framework for Subsurface Sedimentary Structure Identification

“…The structure estimated by sparse geological data typically involves great uncertainty (J. Chen & Rubin, 2003). This uncertainty may introduce significant biases in numerical simulations of flow and solute transport (Carrera, 1993; Carrera et al., 2005; Dai et al., 2014; Dai et al., 2020; Dentz et al., 2020; Geng et al., 2020; Nowak et al., 2010; Rajaram & Gelhar, 1995; Ritzi & Soltanian, 2015; Soltanian et al., 2019; Vrugt et al., 2005). Therefore, how to effectively use sparse observations, direct or indirect, to obtain a more realistic view of subsurface sedimentary structures in practice is an essential issue (Doherty, 2003; Keating et al., 2010).…”