Stochastic macrodispersion models for gravel aquifers

Statistical information on sedimentary structures determined from natural gravel deposits in north-eastern Switzerland is used to characterize transport phenomena of aquifers. These aquifers essentially consist of a background gravel matrix with embedded lenses of different hydraulic properties and internal structure. One of the embedded materials is highly conductive open framework gravel which leads to a;bimodal probability density function of the hydraulic conductivity of the overall gravel material. Based on an analysis of this information three approaches to modeling macrodispersion are suggested. in the first one distinct unconditioned realizations of synthetic block shaped facies type aquifers are generated numerically such that they exhibit the same statistical properties with respect to facies geometry and hydraulic properties as the deposits themselves. Numerical experiments simulating saturated flow and transport were subsequently performed with the help of a three-dimensional finite element flow model and a corresponding random walk transport model. A total of 100 experiments allowed estimates of apparent, time dependent macrodispersivity values. In the second approach the statistical parameters characterizing the overall gravel deposit were directly applied to an analytical unimodal stochastic model of apparent macrodispersivity according to Dagan (1988). For the modeling of the bimodal nature of the hydraulic conductivity an analytical anisotropic stochastic model was developed based on the isotropic model of Rubin (1995). This third approach was again applied using the appropriate statistical parameters. Differences in the results of the three models are discussed. They can be attributed mainly to uncertainty in the input parameters, and to the complex sedimentary structure predominant in the natural gravel deposits which were investigated.