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

Hydrology Group, Environmental Technology Division, Pacific Northwest National Lab., P.O. Box 999, Richland, WA 99352

View larger version (8K): [in this window] [in a new window]   FIG. 1. Schematic of the water and nonaqueous phase liquid (NAPL) pressure head variation with time at the top and bottom boundaries of the simulation domain. For each simulation set, the water pressure head was kept constant (–2.0, –1.75, –1.5, and –1.25 m) while the NAPL pressure was lowered in steps from zero to a value slightly larger than water pressure head.

View larger version (26K): [in this window] [in a new window]   FIG. 2. Nonaqueous phase liquid (NAPL) retention curves of anisotropic soils (R = 50) with different heterogeneity levels (Soils 3, 7, 11, and 15 in Table 1). R, ratio of correlation length at the direction parallel to soil strata and that normal to soil strata; , inverse macroscopic capillary length; n, pore-size distribution parameter; Y = ln(Ks), with Ks being the saturated hydraulic conductivity; Y2, variance of Y.

View larger version (12K): [in this window] [in a new window]   FIG. 3. Relationship of (a) vs. Y2 and (b) n vs. Y2 for the total liquid retention curves for an air–water (data from Zhang et al., 2003) and air–NAPL–water system. , inverse macroscopic capillary length; n, pore-size distribution parameter; Y = ln(Ks) with Ks being the saturated hydraulic conductivity; Y2, variance of Y.

View larger version (9K): [in this window] [in a new window]   FIG. 4. The ratios of (a) parameter and (b) parameter n of an air–NAPL–water system to those of an air-water system (data from Zhang et al., 2003). The solid line in each plot represents the average. aw, parameter for an air–water system; ao, parameter for an air–NAPL–water system; Y = ln(Ks) with Ks being the saturated hydraulic conductivity; Y2, variance of Y.

View larger version (31K): [in this window] [in a new window]   FIG. 5. Nonaqueous phase liquid (NAPL) permeability as a function of total fluid saturation for anisotropic heterogeneous soils 9–12 in Table 1 and for hw = –2.0 m. Lp, connectivity–tortuosity coefficient in the direction parallel to strata; Ln, connectivity–tortuosity coefficient in the direction normal to strata; R, ratio of correlation lengths of the direction parallel and normal to strata; Y = ln(Ks) with Ks being the saturated hydraulic conductivity; Y2, variance of Y.

View larger version (27K): [in this window] [in a new window]   FIG. 6. Nonaqueous phase liquid (NAPL) anisotropy coefficients as a function of NAPL saturation of soils 9–12 in Table 1 for imposed water pressure head of –2.0 m. Lines: computed relations using Eq. [16] with permeabilities listed in Table 2 and L factors values in plots. Circles: ratio of NAPL permeability values for simulations with flow direction parallel to those normal to soil strata.

View larger version (23K): [in this window] [in a new window]   FIG. 7. Relationships between L vs. ln(R*) of the soils with different levels of heterogeneity. L, tortuosity coefficient; R*, ratio of correlation length in the direction parallel and normal to flow; Y2, variance of Y, where Y = ln(Ks). with Ks being the saturated hydraulic conductivity.

View larger version (10K): [in this window] [in a new window]   FIG. 8. Comparisons of the (a) intercepts and (b) slopes of the relationship between L vs. ln(R*) for an air–water (Zhang et al., 2003) and air–NAPL–water system. Y2, variance of Y, where Y = ln(Ks), with Ks being the saturated hydraulic conductivity.