Hydraulic Conductivity Upscaling Method In Heterogeneous Aquifers

Groundwater stochastic modeling calls for the upscaling to reduce the computational cost. The flow and transport behaviors are preserved through advanced upscaling approach to transfer the scale discrepancy between the measurement and the parameter in the numerical model.A non-local three-dimensional hydraulic conductivity full tensor upscaling algorithm and code is presented. The algorithm is capable of transforming very refined cell conductivity models into coarse block conductivity models for quick and accurate solution of the groundwater flow equation. Flow rate and hydraulic head gradient are the variables used to relate the outputs from the fine scale model to the outputs from the coarse scale model. The flows and gradients computed at the coarse scale blocks should match the average values of the corresponding quantities observed at the fine scale. The proposed algorithm is successfully demonstrated in four synthetic examples with spatially isotropic, anisotropic and bimodal conductivities fields at the fine scale.A new three-dimensional steady-state saturated groundwater-flow forward-simulator with full conductivity tensors using a nineteen-points block-centered finite-difference method is developed. Hydraulic conductivity tensors are defined at the block interfaces eliminating the need to average conductivity tensors at adjacent blocks to approximate their values at the interfaces. The capabilities of the code are demonstrated in three heterogeneous formulations, two of the examples are two-dimensional, and the third one is three-dimensional and uses a nonuniform discretization grid.Simple averaging, simple-Laplacian, Laplacian-with-skin, and non-uniform coarsening are the techniques investigated in this comparative study of three-dimensional hydraulic conductivity upscaling. The reference is a fine scale conditional realization of the hydraulic conductivities at the MAcro-Dispersion Experiment site on Columbus Air Force Base in Mississippi (USA). This realization was generated using a hole-effect variogram model and it was shown that flow and transport modeling in this realization (at this scale) can reproduce the observed non-Fickian spreading of the tritium plume. The purpose of this work is twofold, first to compare the effectiveness of different upscaling techniques in yielding upscaled models able to reproduce the observed transport behavior, and second to demonstrate and analyze the conditions under which flow upscaling can provide a coarse model in which the standard advection–dispersion equation can be used to model transport in seemingly non-Fickian scenarios. Specifically, the use of Laplacian-based upscaling technique coupled with a non-uniform coarsening scheme yields the best results both in terms of flow and transport reproduction, for this case study in which the coarse blocks are smaller than the correlation ranges of the fine scale conductivities.