Abstract

In this paper, we investigated truncation effect on transport parameter estimation using a laboratory slug injecting tracer test in two-dimensional homogeneous porous medium. To obtain concentration distribution in space during the test, an image analysis technique was used. Then, in order to evaluate the effect of truncation on estimates of transport parameters, we artificially truncated observed concentration maps, and estimated the parameters including the pore velocity, and the longitudinal and transverse dispersivities. The results showed that the pore velocity does not depend on truncation concentration (i.e., the limit of detection), whereas the dispersivities are underestimated as time or truncation concentration increases.

Introduction

The transport parameters such as pore velocity, longitudinal dispersivity and transverse dispersivity are very important to investigate the fate and transport of the contaminants in porous media and groundwater. The slug injecting tracer test has been widely used to estimate transport parameters (Freyberg, 1986; Chao et al., 2000; Qian et al., 2015; Liang et al., 2018; Kurotori et al., 2019; Zhang et al., 2019; Kurasawa et al., 2020b). In a typical slug test, a prepared tracer solution is instantaneously injected into the aquifer through a test well, and evolution of tracer plume is observed at downstream sampling locations. When detailed concentration distribution in space is measured, the parameters are often inferred by interpretation of spatial moment that represents global features of the transport process (Freyberg, 1986; Adams and Gelhar, 1992; Fernàndez-Garcia et al., 2005; Kurasawa et al., 2020b).

In practice, unfortunately, observed data are often truncated, because of detection-limit constraint, i.e., when the tracer concentration is below the limit of detection of the instrument (Drummond et al., 2012). In this case, only the tracer concentrations above the limits are detected. Thus, inferring transport parameters from spatial moment of truncated concentration data may yield erroneous estimates. In porous media, the hydrodynamic dispersion, which originates from the combined action of molecular diffusion (resulting from concentration gradients) and advection (resulting from velocity variations at the pore scale), leads to the reduction of the peak concentration and the increase of the plume entropy (Bear, 1972; Xu et al., 2019). Thus, as travel time increases, the concentration front of solute becomes smoothed out. As a result, at large travel times, truncation effect on parameter estimation may be more pronounced. Recently, in terms of analysis of an analytical solution for the one-dimensional solute transport in homogeneous porous media, Kurasawa et al. (2020a) have found that the longitudinal dispersivity estimated from spatial moment of concentration distribution exhibits time-dependence, whereas the pore velocity does not depend on time. Yet, an experimental proof of the real occurrence of truncation effect is still missing.

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