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.

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