Push‐pull tracer tests: Their information content and use for characterizing non‐Fickian, mobile‐immobile behavior

Abstract

Path reversibility and radial symmetry are often assumed in push‐pull tracer test analysis. In reality, heterogeneous flow fields mean that both assumptions are idealizations. To understand their impact, we perform a parametric study which quantifies the scattering effects of ambient flow, local‐scale dispersion, and velocity field heterogeneity on push‐pull breakthrough curves and compares them to the effects of mobile‐immobile mass transfer (MIMT) processes including sorption and diffusion into secondary porosity. We identify specific circumstances in which MIMT overwhelmingly determines the breakthrough curve, which may then be considered uninformative about drift and local‐scale dispersion. Assuming path reversibility, we develop a continuous‐time‐random‐walk‐based interpretation framework which is flow‐field‐agnostic and well suited to quantifying MIMT. Adopting this perspective, we show that the radial flow assumption is often harmless: to the extent that solute paths are reversible, the breakthrough curve is uninformative about velocity field heterogeneity. Our interpretation method determines a mapping function (i.e., subordinator) from travel time in the absence of MIMT to travel time in its presence. A mathematical theory allowing this function to be directly “plugged into” an existing Laplace‐domain transport model to incorporate MIMT is presented and demonstrated. Algorithms implementing the calibration are presented and applied to interpretation of data from a push‐pull test performed in a heterogeneous environment. A successful four‐parameter fit is obtained, of comparable fidelity to one obtained using a million‐node 3‐D numerical model. Finally, we demonstrate analytically and numerically how push‐pull tests quantifying MIMT are sensitive to remobilization, but not immobilization, kinetics.

Inferring subsurface heterogeneity from push‐drift tracer tests

“…(The literature review in Hansen et al . [] contains an extensive discussion of these assumptions.) Background groundwater flow (drift) and heterogeneity cause nonradial, hysteretic flow patterns and violate the LIFO assumption, complicating test interpretation by generating heavy tails that may spuriously be attributed to other causes [ Lessoff and Konikow , ].…”

“…Johnsen and Whitson [] presented analysis quantifying the effect of solute path hysteresis caused by background drift on push‐pull breakthrough curves obtained from homogeneous velocity fields and Hansen et al . [] studied this phenomenon numerically in heterogeneous velocity fields.…”

“…In this note, we further consider the information that can be obtained from an asymmetric (i.e., push-drift) test. We exploit the basic numerical framework originally developed by Hansen et al [2016] to study the robustness of idealized push-pull test interpretation methods under nonideal conditions, and instead apply it to the study of pushdrift tests. In particular, our goal is to assess the degree of heterogeneity from push-drift test breakthrough curves.…”

Biased Estimation of Groundwater Velocity from a Push-Pull Tracer Test Due to Plume Density and Pumping Rate

“…Among various types of tracer test, the single-well push-pull test is a method of easy performance and no more logistical complexity with a modest cost and has been applied to estimate physical parameters such as longitudinal dispersivity, groundwater velocity, and effective porosity of the tested aquifer [8][9][10][11][12]. The push-pull test consists of three phases.…”

The role of eddies in solute transport and recovery in rock fractures: Implication for groundwater remediation

“…Eddy (or recirculation zone) acts as immobile zone and occurs due to the irregularities of apertures in a rough-walled fracture (Cardenas et al, 2009;Raven et al, 1988). Mass exchange between mobile and immobile zones is assumed to be diffusive, which is based on the mobile-immobile conceptual models and their relevant analytical equations that have been suggested to explain non-Fickian process (Cherubini, Giasi, & Pastore, 2013;Gao, Zhan, Feng, Fu, & Huang, 2012;Hansen, Berkowitz, Vesselinov, O 0 Malley, & Karra, 2016;Qian et al, 2011;Raven et al, 1988). Cardenas et al (2009) showed that tailing, due to a large eddy, was more persistent with an increase of the Reynolds number (Re) up to about 10.…”