On the upscaling of mass transfer rate expressions for interpretation of source zone partitioning tracer tests

Abstract

Analysis of partitioning tracer tests conducted in dense nonaqueous phase liquid (DNAPL) source zones relies on conceptual models that describe mass exchange between the DNAPL and aqueous phases. Such analysis, however, is complicated by the complex distribution of entrapped DNAPL mass and formation heterogeneity. Due to parameter uncertainty in heterogeneous regions and the desire to reduce model complexity, the effect of mass transfer limitations is often neglected, and an equilibrium-based model is typically used to interpret test results. This work explores the consequences of that simplifying assumption on test data interpretation and develops an alternative upscaled modeling approach to quantify effective mass transfer rates. To this end, a series of partitioning tracer tests is numerically simulated in heterogeneous two-dimensional PCE-DNAPL source zones, representative of a range of hydraulic conductivity and DNAPL mass distribution characteristics. The effective mass transfer coefficient corresponding to each test is determined by fitting an upscaled model to the simulated data, and regression analysis is performed to explore the correlation between various source zone metrics and the effective mass transfer coefficient. Results suggest that vertical DNAPL spreading, Reynolds number, pool fraction, and the effective organic phase saturation are the most significant parameters controlling tracer partitioning rates. Finally, a correlation for prediction of the effective (upscaled) mass transfer coefficient is proposed and verified using existing experimental data. The developed upscaled model incorporates the influence of physical heterogeneity on the rate of tracer partitioning and, thus, can be used for the estimation of source zone mass distribution characteristics from tracer test results.

Comparison of Two‐Dimensional and Three‐Dimensional Macroscopic Invasion Percolation Simulations with Laboratory Experiments of Gas Bubble Flow in Homogeneous Sands

“…Distributions of non‐wetting fluid saturations are often quantified using spatial moments, in both experiments and numerical simulations (Kueper and Frind, 1991; Essaid and Hess, 1993; Kueper and Gerhard, 1995; Lemke et al, 2004; Christ et al, 2005; Fagerlund et al, 2007; Pantazidou and Liu, 2008; Boroumand and Abriola, 2015). For a porous medium containing water and gas, the spatial moments in two dimensions are defined as where θ is the porosity, ρ g is the gas density, S g is the gas saturation, and x and z are the horizontal and vertical positions in a two‐dimensional domain.…”

Organic contaminant transport and fate in the subsurface: Evolution of knowledge and understanding

“…Partitioning tracer tests are most successfully applied to identify DNAPL residual saturation, although Moreno‐Barbero and Illangasekare [] have shown that incorporating nonequilibrium partitioning can improve results for high‐saturation zones. Inverse modeling has been successfully used to identify the location and dimensions of a single‐component DNAPL pool within a saturated, steady flow field based on observed downgradient aqueous concentrations [ Sciortino et al ., ], however, determining residual saturations in heterogeneous systems is more challenging [ Boroumand and Abriola , ]. Yeh and Zhu [] combined multiwell hydraulic tomography and partitioning tracer tomography to facilitate analysis in heterogeneous settings.…”

“…Indirect, nondestructive methods for evaluating field saturations have been developed to overcome the challenges of direct measurement. Partitioning tracer methods are based on comparing the arrival times in interwell or push-pull tests for multiple tracers with different NAPL partitioning rates [Datta- Gupta et al, 2002;Dugan et al, 2003;Huang et al, 2010;James et al, 1997James et al, , 2000Jawitz et al, 2003;Jin et al, 1995;Moreno-Barbero and Illangasekare, 2006;Zhang and Graham, 2001a,b] [Boroumand and Abriola, 2015]. Yeh and Zhu [2007] combined multiwell hydraulic tomography and partitioning tracer tomography to facilitate analysis in heterogeneous settings.…”

“…Considerable progress has been made in developing noninvasive methods to determine NAPL source zone architecture. Partitioning tracer tests have shown promise for characterizing simple source zones, but their interpretation is difficult for multiconstituent NAPLs in heterogeneous settings [see Boroumand and Abriola , ]. Recent studies have begun to explore the potential of NAPL detection by various geophysical methods, but this work is still in the early stages [ U.S. Environmental Protection Agency , ].…”

Mathematical modeling of organic liquid dissolution in heterogeneous source zones

“…In the past two decades, several different types of simple, upscaled models have been developed and tested, such as equilibrium streamtube methods, power law relationships between concentration and mass, dual-domain models, and other methods with upscaled effective mass transfer rate coefficients (Parker and Park, 2004;Jawitz et al, 2005;Marble et al, 2008;Christ et al, 2010;DiFilippo and Brusseau, 2011a;Boroumand and Abriola, 2015). However, most of these models (e.g., Parker and Park, 2004;Jawitz et al 2005;Basu et al, 2008;Marble et al, 2008;Luciano et al, 2018) produce smooth singular dissolution profiles and thus are not able to capture non-singular dissolution behavior caused by the complexity of the source zone architectures.…”