Solute Arrival Time Research Articles

Assessing the validity of the channel model of fracture aperture under field conditions

In recent investigations of fluid and solute movement in discrete fractures, spatial heterogeneity of the fracture aperture has been conceptualized as a series of noninterconnecting constant aperture flow paths, or channels. Two methods of estimating the distribution of the aperture sizes are presented using information from a single‐hole pumping test and a radially converging tracer test. The first method uses the transmissivity of the fracture and mean arrival time of the tracer, while the second method uses the mean and variance of the solute arrival time. If the fracture can be conceptualized as a series of nonintersecting flow paths of constant aperture, the two methods should yield identical estimates for the parameters of the distribution. The validity of the channel model can be assessed by comparing the parameters of the distribution that are estimated by the two methods. This technique was demonstrated using hydraulic and tracer tests conducted in a discrete, areally extensive, horizontal fracture in the Silurian dolomite in the northeastern Illinois. A lognormal and a truncated gamma distribution were used to describe the distribution of constant aperture flow paths. The lognormal distribution could not reproduce the abrupt rising limb and maximum rate of mass arrival that characterized the tracer tests. The gamma distribution more accurately predicted the shape of the breakthrough curves; however, the two methods of estimating the parameters of the distribution provided significantly different estimates of the variances of the aperture sizes. The mean aperture as estimated by the two methods was similar. The difference in the variance of the aperture as estimated by the two methods indicates that alternative conceptual models of aperture heterogeneity are required to more accurately describe both fluid and solute movement in this field situation.

Stochastic analysis of solute arrival time in heterogeneous porous media

Longitudinal advective solute movement in heterogeneous porous media is investigated by considering the solute arrival time at a plane perpendicular to the mean fluid velocity. The moments of the solute arrival time are defined in terms of the stochastic properties of a statistically anisotropic hydraulic conductivity field. The flux‐averaged concentration is specified by introducing the moments of the arrival time into a probability density function for the arrival time. The quadratic dependence of the arrival time variance on position in the vicinity of an injection point is indicative of a nondiffusive process. For the assumed spatial correlation of the hydraulic conductivity, the variance of the arrival time asymptotically approaches a linear dependence on the position from the injection point similar to a diffusion process. The impact of assuming solute movement to be a diffusive process from the onset of the solute injection causes erroneous estimates of flux‐averaged concentrations at distances from the injection point that are of the order of the correlation length of the hydraulic conductivity. The arrival time analysis and the particle position analysis given in Dagan (1982, 1984) are complementary interpretations of advective solute movement that yield different definitions of the solute concentration; the position analysis intrinsically defines the resident or volume‐averaged concentration, while the flux‐averaged concentration is defined from the arrival time analysis. The temporal variation of the resident and flux‐averaged concentration are similar at a given position for small values of the variance of the hydraulic conductivity, or at distances from the solute injection point that are large relative to correlation length of the hydraulic conductivity.