A percolation theoretically based treatment of the upscaling of the hydraulic conductivity using a uniquely detailed and realistic digital model of the sedimentary structure of a braid belt is proposed. Critical path analysis, based on percolation theory, has been used to address the question of upscaling the hydraulic conductivity for simplified models and generated results in agreement with simulations for isotropic media, and with field results for anisotropic media.
The digital representation of the sedimentary deposit is currently being created by colleagues to incorporate realistic architecture from the scale of centimeters up to the scale of kilometers. As the authors state, a model with this range of scales is unprecedented. The digital deposit will represent the hierarchical sedimentary architecture of fluvial braid-belt deposits, common in both aquifers and petroleum reservoirs. Using such a digital model will allow in principle detailed predictions as well as comparison with simulations as "ground truth," at least as regards the ability of theory to treat the model.
Intellectual merit of the proposal is three-fold. 1) It will be possible to develop a simple numerical routine for generating a distribution of K values as a function of support volume scale. This routine will likely be adaptable to a fairly wide range of realistic media. 2) Verification of the hypotheses proposed relating the isolation of geological and statistical (percolation) effects on spatial correlation will assist in application of critical path analysis to arbitrary and realistic geologic media. 3) The likely combination of multi-scale heterogeneity with (different) anisotropy at every scale will produce a more complex dependence of both K on scale and its spatial correlations than has previously been investigated by the proposed techniques, allowing potentially a quantitative isolation of various effects.
Broader impacts from such a study include an increased understanding of how heterogeneity on multiple scales influences the scale-dependence of the hydraulic conductivity and its distribution. The resulting numerical routine for applying critical path analysis to more arbitrary (and realistic) media will be made available to the community. And a graduate student will be trained at a nexus of physics, hydrogeology, and sedimentology.
