Hydrodynamic dispersion at the local scale of continuum representation

Abstract

Two types of measurement devices, a fully penetrating dry observation well with a gamma ray detector and a multilevel piezometer with a 7.5‐cm‐long screen, were used for measurement of radiotracer concentrations in three natural gradient dispersion tests performed at the Twin Lake aquifer, Chalk River, Ontario over 20, 40, and 260 m distances. The devices are classified according to the method of measurement of tracer concentration as through‐the‐wall and mixing‐cup measurement devices. The weighting function associated with the through‐the‐wall measurement device is defined by considering the process of interaction of gamma radiation with aquifer materials in a laboratory experiment and is found to follow an exponential attenuation law. As a result, a continuum description of the porous medium is introduced in which the field variable is defined as a convolution product of associated microscopic values with the exponential weighting function. An experimental method for measuring the field variable according to the convolution procedure is proposed. It is shown that in the field tests the weighting function associated with the through‐the‐wall and mixing‐cup measurement devices can be approximated by a “table” function with the scale of support of the order of centimeters. The scale of support is referred to as the local scale of continuum representation. It is postulated that the transport of a tracer at the Twin Lake aquifer can be quantified by means of the local scale advection‐dispersion equation. Dispersivity values obtained from three field‐tracer dispersion experiments using the local scale advection‐dispersion equation are found to be similar to dispersivity values obtained from 23 laboratory columns. The comparison between results of field and laboratory experiments showed that patterns of dispersion observed in field tests at the local scale (using different measurement devices with the same scale of support) are similar to the patterns observed in small‐scale laboratory experiments. The comparison between results of three field tests performed under different experimental and hydrogeological conditions and over different scales showed the universal nature of the local scale characteristics of the dispersion process.