Three-Dimensional, Multi-scale, and Multi-variance Dispersivity Upscaling for Hierarchical Sedimentary Deposit using Parallel Computing
Abstract
A high-resolution non-stationary hydraulic conductivity (K) model, or a fully heterogeneous (FHM), is generated from an experimental stratigraphy which exhibits realistic sedimentary heterogeneity at multiple scales. Based on this model, a set of hierarchical hydrostratigraphic models (HSMs) with decreasing heterogeneity resolutions are created. These models contain 8, 3, and 1 stratigraphic unit(s), respectively, that are irregular in shape and hierarchical in structure. For all models, increasing system ln(K) variances - 0.1, 1.0, 4.5 - are tested, leading to a suite of 12 conceptual aquifer models. Using a numerical upscaling technique, equivalent K tensors are first computed for each unit of the HSMs. For all the variances tested, significant accuracy is achieved with the upscaled K in terms of capturing both the hydraulic head and flow connectivity of the FHM, i.e., mean relative error in head predictions ranging from 1% to 10% (higher error correlates to higher variances). Among the HSMs, the 8-unit model, given its higher stratigraphic resolution, is always the most accurate flow predictor. The same suite of HSMs is then subject to a novel dispersivity scaling analysis whereas upscaled dispersivities are computed with both stochastic and deterministic methods. For this analysis, a parallel random walk particle tracking code (RWPT), which accounts for the divergence of the dispersion tensors, is developed and verified with 100,000 particles (Zhang & Zhang, 2013). This new code leads to significantly improved accuracy and efficiency in modeling transport. Interestingly, for all the HSMs, at all the variances tested, the effect of divergence of the dispersion coefficient on solute plume migration and its spatial moments is negligible, suggesting that this term can be neglected in future simulations. When comparing the transport prediction of the FHM against those of the HSMs with upscaled dispersivities, plume trajectory, breakthrough curve, and the arrival/tailing behavior of the FHM can generally be captured by the HSMs. At all the variances tested, the 8-unit upscaled model is always the most accurate. When the variance is low to moderate, this model can provide accurate to adequate predictions of all the FHM plume moments. In addition, upscaled dispersivities computed with the stochastic versus deterministic techniques yield similar solute predictions, which suggest that in this analysis, an ergodic transport regime has emerged. However, when the variance of ln(k) increases to 4.5, the upscaled dispersivities predicted by the stochastic methods result in significant upstream dispersion that is nonphysical. In this case, the HSMs cannot capture the FHM plume moments for the given ln(K) variance. In summary, simulation results suggest that the upscaling dispersivity can be used to accurately capture solute transport in low ln(K) variance systems but fails to describe the solute motion if system variance is high. Reference: Mingkan Zhang, and Ye Zhang, Multiscale, Multi-variance Dispersivity Upscaling for A Three-Dimensional Hierarchical Aquifer: Developing and Testing a Parallel Random Walk Method with a Drift Term in the Dispersion Tensor, Water Resources Research, in preparation.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2013
- Bibcode:
- 2013AGUFM.H21D1094Z
- Keywords:
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- 1829 HYDROLOGY Groundwater hydrology;
- 1832 HYDROLOGY Groundwater transport;
- 1847 HYDROLOGY Modeling;
- 1869 HYDROLOGY Stochastic hydrology