Generalized Local Cubic Law for inertial fluid flow and solute transport through tortuous and rough fractures
Abstract
Fundamental understanding of flow and transport processes through single rough-walled fractures remains a challenge to gain insight for interpreting hydrological phenomena at continuum scale. The Generalized Local Cubic Law (GLCL) developed here is based on (1) modifying the aperture field by orienting it with the flow direction accounting for tortuosity, and (2) correcting for roughness changes associated with flow expansion/contraction and inertial effects. We compared its performance in estimating flow rate to results of direct numerical simulations with the Navier-Stokes equations (NSE) and physical flow experiments for real and synthetic three-dimensional rough-walled fractures. We also evaluated the performance of the Local Cubic Law (LCL). The LCL consistently overestimates flow rate with relative error δ ranging from 20% to 100% with arithmetic mean of |δ| (<|δ|>) equal to 45.4% depending on the degree of tortuosity and roughness. However, the GLCL performs well and improves the performance of the LCL, where δ in flow rate range from -3.1% to 11.4% with <|δ|>=4.7%. Furthermore, we generated breakthrough curves (BTCs) through direct numerical simulations based on the advection-diffusion equation with flow field resulting from solving the NSE (which are considered to the true or experimental BTCs). We revisited the applicability of random walk particle tracking (RWPT) to simulate solute transport dynamics through real fractures, where flow fields resulted from the GLCL and LCL, respectively. We found persistent early arrival and heavy tailing in the BTCs from both direct numerical simulations and RWPT, which are the salient characteristics of non-Fickian behavior. The LCL consistently overestimates mean flow velocity; whereas the GLCL improves estimating flow field, and markedly improves fits to the BTCs relative to those fitted with LCL solutions. Therefore, PWPT with flow field resulting from the GLCL is robust in predicting solute transport through tortuous and rough fractures.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2013
- Bibcode:
- 2013AGUFM.H53A1404W
- Keywords:
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- 1829 HYDROLOGY Groundwater hydrology;
- 1832 HYDROLOGY Groundwater transport;
- 1828 HYDROLOGY Groundwater hydraulics;
- 1805 HYDROLOGY Computational hydrology