Comparison of Observations from a Laboratory Model with Stochastic Theory: Initial Analysis of Hydraulic and Tracer Experiments

Hydraulic and tracer tests were conducted in a flow cell containing a mixture of sediments designed to mimic a two-dimensional, log-normally distributed, second-order stationary, exponentially correlated random conductivity field. With 60 integral scales in the direction of mean flow and 25 integral scales perpendicular to this direction, behavior of flow and transport in the interior of the flow cell can be compared directly with stochastic solutions for flow and transport. Using 144 piezometers and 361 platinum electrodes, the distribution of hydraulic head and the concentrations of an ionic tracer could be monitored in substantial detail. The present discussion presents the details of the experimental equipment. Results and initial analysis of hydraulic measurements and characterization of a two-dimensional tracer plume are also presented. Analysis using first-order hydraulic theory shows that the flow through the medium was consistent with an effective conductivity equal to the geometric mean of the conductivity distribution. Further, the semivariogram of head increments as observed in the experimental results was consistent with the semivariogram predicted by theory. The chemical transport experiments are here compared with the early solutions presented by Dagan (1984, 1987). The observed rate of longitudinal spread of two tracer plumes was slightly less than that predicted using this theory. Further, the spread in the transverse dimension was observed to decline from the initial plume dimensions and then remain constant or increase slightly, but at a rate lower than predicted by the theory. The difference between the hydraulic and transport results is believed to be related to the fact that the hydraulic results were averaged over a very large portion of the flow cell such that ergodic conditions could be assumed. In contrast, the initial geometry of the plume covered only approximately five integral scales in the transverse direction such that the validity of the assumption of ergodic conditions must be questioned in the analysis of results for the chemical transport.     

A Network Modeling Approach to Derive Unsaturated Hydraulic Properties of a Rough-Walled Fracture

The hydraulic properties of a rough-walled fracture in a limestone sample are estimated using a network model based on three-dimensional representations of the fracture apertures. Two different scenarios are considered: drainage of water out of a fracture and infiltration of water into a fracture. Besides capillary effects, the model takes into account an accessibility criterion (invasion percolation) and, in the case of infiltration, the rate dependence of the water movement. A hysteresis effect between drainage and imbibition hydraulic properties can be observed, which increases with increasing capillary number. The measured permeability is overestimated by 15% by the network model. In a sensitivity analysis the influence of the main fracture field characteristics (field size and fracture segment size in relation to correlation length) on the calculated hydraulic properties is investigated. Field size has an important influence on the inverse of the water/air entry value for imbibition, making it difficult to scale this parameter to other field sizes. A parameter analysis investigating the influence of the main fracture characteristics (mean fracture aperture, roughness, and correlation length) on the hydraulic properties shows that the mean fracture aperture is the most important fracture parameter influencing both strongly the saturated permeability K and . The effect of varying the variance and the correlation length on K and is much less than the influence of the mean fracture aperture. The effective permeability of the fracture is also calculated by the geometric mean K _g . Up to (log_e(K)) = 1, the discrepancy between K _g and K _n (network model result) is less than 15%. At larger correlation lengths (for a constant (log_e(K))), the discrepancy between K _g and K _n increases.