Saturation‐Dependent Hydraulic Conductivity Anisotropy for Multifluid Systems in Porous Media

Abstract

The hydraulic conductivity of unsaturated anisotropic soils has recently been described with a tensorial connectivity–tortuosity (TCT) concept. We extend this concept to unsaturated porous media with two or three immiscible fluids. Mathematical expressions to describe the conductivity of each fluid in anisotropic porous media under unsaturated condition are derived in the form of symmetric second order tensors. The theory is applicable to the generalized hydraulic conductivity model and compatible types of saturation–pressure formulation. The extended model shows that the anisotropic coefficient of any one of the fluids is independent of the saturation of other fluids. Synthetic Miller‐similar soils generated to be anisotropic were defined by allowing the saturated hydraulic conductivity to have different correlation ranges for different directions of flow. The extended TCT concept was tested using synthetic soils with four levels of heterogeneity and four levels of anisotropy. Numerical experiments of infiltration of two liquid phases, water and the nonaqueous phase liquid (NAPL) carbon tetrachloride, were performed to test the extended model. The results show that, similar to water in a two‐fluid (air–water) system, NAPL retention curves in a three‐fluid (air–NAPL–water) system were independent of flow direction but dependent on soil heterogeneity, whereas the connectivity–tortuosity coefficients are functions of both soil heterogeneity and anisotropy. The extended TCT model accurately describes unsaturated hydraulic functions of anisotropic soils and can be combined into commonly used relative permeability functions for use in multifluid flow and transport numerical simulations.

Hanford Site Vadose Zone Studies: An Overview

“…Ward and Zhang (2007) describe methods to estimate effective hydraulic properties for anisotropic unsaturated flow. In a companion paper, Zhang et al (2007) describe the use of a pore connectivity–tortuosity concept to model saturation‐dependent anisotropy. Khaleel et al (2007) present an impact assessment of tank farm vadose zone contamination, and Rucker and Fink (2007) show how geophysical characterization can be used in some cases to delineate contaminant plumes and to assist with vadose zone characterization.…”

Relationship between Anisotropy in Soil Hydraulic Conductivity and Saturation

“…The TCT model has advantages over other models—its use of any type of hydraulic function, its simple parameterization, and its easy use in numerical simulators. Zhang et al (2007) further extended the TCT model to multifluid systems. The TCT concept can describe the nonaqueous phase unsaturated hydraulic functions of anisotropic soils and can be combined into commonly used relative permeability functions for use in multifluid flow and transport numerical simulations.…”

Pore‐Scale Explanation of the Archie's Cementation Exponent: Microstructure, Electrical Anisotropy, and Numerical Experiments

“…Although it is believed that the possible causes of resistivity anisotropy mainly include electrical anisotropy of the matrix minerals and connective anisotropy of pore space (Clavaud, ; Emlin et al, ; Zhang et al, ), the anisotropy in matrix minerals can be negligible for reservoirs in the shallow Earth's crust. Therefore, our research is focused on the effects of microscopic pore connectivity and shapes of matrix grain on resistivity anisotropy at the macroscopic scale.…”

“…Moreover, the anisotropic factors at the microscopic scale, such as the anisotropy of the matrix mineral, the distribution of fluid, and pore connectivity, are not involved in these studies. Recently, a number of studies indicate that these microscopic factors may play a significant role in causing the anisotropy of the macroscopic electrical resistivity (Clavaud, ; Emlin et al, ; Minh et al, ; Zhang et al, ).…”