Stochastic macrodispersion models for gravel aquifers

Abstract

Statistical information on sedimentary structures determined from natural gravel deposits in north-eastern Swit zerland is used to characterize transport phenomena of aquifers. These aquifers essentially consist of a back ground 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 experi ments 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. RÉSUMÉDes informations statistiques sur les structures sédimentaires déterminées a partir de depots de graviers dans le nord-est de la Suisse sont utilises pour caractériser les phénomènes de transport dans l'aquifère. Les matrices de ces aquifères sont principalement constituées de graviers avec des lentilles scellées aux propriétés hydrauliques et structures internes variées. Un de ces matériaux constitue un réseau tres permeable au sein de l'aquifère, d'oü l'idée d'utiliser une fonction de densité de probabilité bimodale pour la conductivité hydraulique de l'ensemble du matériau compose de graviers. A partir de l'analyse de cette information, trois approches sont suggérées pour modéliser la macrodispersion. Dans la première, différentes realisations non conditionnelles d'aquifères synthé-tiques caractérisés par des facies en forme de bloc, possédant les mêmes caractéristiques statistiques en terme de facies, de geometrie et de propriétés hydrauliques que les depots étudiés, sont générées numériquement. Des tests numériques simulant le transport et l'écoulement saturé ont été realises a l'aide d'un code 3D aux elements finis et un modèle lagrangien de type ...

On using the equivalent conductivity to characterize solute spreading in environments with low‐permeability lenses

“…Apparent macrodispersivities predicted by stochastic theory for these two environments are the same, however, given the same conductivity contrast and volume ratio of lenses to matrix [cf. Stauffer and Rauber , 1998], since the difference in geologic structure is in the connectedness, not the variance or integral scale of the conductivity field.…”

“…Because of shortcomings such as these, many alternative models and enhancements to stochastic theories have been explored to describe anomalous transport behavior in heterogeneous environments. Stauffer and Rauber [1998] expanded on the theory developed by Rubin [1995] to derive macrodispersion coefficients for anisotropic, bimodal, permeability distributions. They simulated transport through realistic models of a three‐dimensional, bimodal, glaciofluvial environment and compared macrodispersivity predictions from their theory to the simulated results.…”

Transverse mixing in three-dimensional nonstationary anisotropic heterogeneous porous media

“…[]. Stauffer and Rauber [] analyzed macrodispersion in virtual hierarchical sedimentary structures generated by hydrofacies modeling followed by filling the sedimentary structures with blockwise stationary anisotropic log conductivity field.…”

Subsurface flow mixing in coarse, braided river deposits

“…1, coarse, braided river deposits are composed of two main depositional elements, remnants of gravel sheets (Huber and Huggenberger, 2015) and trough fills with clear-cut erosional lower-bounding surfaces (e.g. Siegenthaler and Huggenberger, 1993;Jussel et al, 1994a;Beres et al, 1995Beres et al, , 1999Rauber et al, 1998;Stauffer and Rauber, 1998;Teutsch et al, 1998;Anderson et al, 1999;Klingbeil et al, 1999;Whittaker and Teutsch, 1999;Huggenberger and Regli, 2006;Bayer et al, 2011). The sedimentary structure of the remnants of gravel sheets consists of horizontal to sub-horizontal layers with a poorly sorted gravel texture.…”

“…Most of these studies assessed either macrodispersion processes (e.g. Jussel et al, 1994b;Stauffer and Rauber, 1998), sorption processes (e.g. Rauber et al, 1998; Teutsch et al, 1998), or particle concentrations (e.g.…”