Effective Conductivity Of Highly Heterogeneous Anisotropic Formations: Does The Self- Consistent Solution Work?
Abstract
Three-dimensional simulations of flow in highly heterogeneous anisotropic porous formations are conducted to estimate horizontal and vertical effective conductivities of aquifer formations. Multi-Indicator conductivity model, developed by Dagan et al (2003), was employed to test validity of the classical self-consistent solution (Dagan 1989) and the solution based on the exponential conjecture (Gelhar and Axness 1983). In a Multi-Indicator model for statistically anisotropic formations, conductivity statistics (mean, variance and 2-point correlation) of the formation are reproduced using spheroidal inclusions of different hydraulic conductivities and sizes. In the present study, hydraulic conductivity of constant-size inclusions follows a log-normal distribution and the anisotropic covariance function has spherical structure with different integral scales in the horizontal (Ih) and vertical (Iv) directions. Using large domain sizes (over 100 conductivity integral scales long) and high volume fraction of inclusions (0.5 and 0.7), we examine accuracy of the self-consistent solution over a range of logconductivity variances (up to 8) and anisotropy ratios (Ih/ Iv up to 20). We present two main findings: 1) effective conductivities (both horizontal and vertical) of the simulated Multi-Indicator Models are exactly equal to those predicted by self-consistent solution; 2) the exponential conjecture is not valid for examined Multi-Indicator model. Modeling technology developed for the present study can be used in other flow and transport studies, including large-scale transport through highly heterogeneous anisotropic formations.
- Publication:
-
AGU Fall Meeting Abstracts
- Pub Date:
- December 2007
- Bibcode:
- 2007AGUFM.H11I..05S
- Keywords:
-
- 1829 Groundwater hydrology;
- 1847 Modeling;
- 1869 Stochastic hydrology