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Modeling Nonequilibrium Flow and Transport Processes Using HYDRUS

Jirka imnek^a,* and Martinus Th. van Genuchten^b

^a Dep. of Environmental Sciences, Univ. of California, Riverside, CA 92521
^b USDA-ARS, U.S. Salinity Lab., 450 West Big Springs Rd., Riverside, CA 92507

View larger version (17K): [in this window] [in a new window]   FIG. 1. Conceptual physical nonequilibrium models for water flow and solute transport. In the plots, is the water content, mo and im in (b) and (c) are water contents of the mobile and immobile flow regions, respectively; M and F in (d) are water contents of the matrix and macropore (fracture) regions, respectively, and M,mo, M,im, and F in (e) are water contents of the mobile and immobile flow regions of the matrix domain, and in the macropore (fracture) domain, respectively; c are concentrations of corresponding regions, with subscripts having the same meaning as for water contents, while S is the total solute content of the liquid phase.

View larger version (28K): [in this window] [in a new window]   FIG. 2. Conceptual physical nonequilibrium models for water flow and solute transport.

View larger version (17K): [in this window] [in a new window]   FIG. 3. Conceptual chemical nonequilibrium models for reactive solute transport. In the plots, is the water content, mo and im in (d) are water contents of the mobile and immobile flow regions, respectively; M and F in (e) are water contents of the matrix and macropore (fracture) regions, respectively; c are concentrations of the corresponding regions, se are sorbed concentrations in equilibrium with the liquid concentrations of the corresponding regions, and sk are kinetically sorbed solute concentrations of the corresponding regions.

View larger version (9K): [in this window] [in a new window]   FIG. 4. Breakthrough curves calculated using the Uniform Transport Model for a 10-cm-long soil column and the following parameters: q = 5 cm d–1, = 0.5, and b = 1.5 g cm–3; on the left, Kd = 1 cm3 g–1 and = 0.1, 1, and 10 cm; and on the right, = 1 cm and Kd = 0, 1, and 3 cm3 g–1.

View larger version (10K): [in this window] [in a new window]   FIG. 5. Breakthrough curves calculated using the Mobile–Immobile Water Model for a 10-cm-long soil column and the following parameters: q = 3 cm d–1, = 0.5, mo = 1 cm, Kd = 1 cm3 g–1, b = 1.5 g cm–3. On the left: fmo = 0.6, mo = 0.3, im = 0.2, and mim = 0.1, 0.5, 10 d–1. On the right: mim = 0.5 d–1 and (a) fmo = 0.4, mo = 0.2, im = 0.3; (b) fmo = 0.6, mo = 0.3, im = 0.2; and (c) fmo = 0.8, mo = 0.4, im = 0.1.

View larger version (21K): [in this window] [in a new window]   FIG. 6. Breakthrough curves calculated using the Dual-Permeability Model for a 10-cm-long soil column and the following parameters: qm = 3 cm d–1, qf = 30 cm d–1, = m = f = 0.5, w = 0.1, m = f = 1 cm, Kdm = Kdf = 1 cm3 g–1, b = 1.5 g cm–3, and dp = 0, 0.1, and 0.5 d–1. Matrix, fracture, and total breakthrough curves are represented by thin, medium, and thick lines, respectively.

View larger version (25K): [in this window] [in a new window]   FIG. 7. Breakthrough curves calculated using the Dual-Permeability Model with MIM for a 10-cm-long soil column and the following parameters: qm = 3 cm d–1, qf = 30 cm d–1, = m = f = 0.5, w = 0.1, m = f = 1 cm, Kdm = Kdf = 1 cm3 g–1, b = 1.5 g cm–3, dp = 0.1 d–1, dpm = 0.1 d–1, im,m (thim) = 0.0, 0.1, 0.3, and 0.4, and fm = 1, 0.8, 0.4, and 0.2, respectively. Matrix, fracture, and total breakthrough curves are represented by thin, medium, and thick lines, respectively.

View larger version (13K): [in this window] [in a new window]   FIG. 8. Breakthrough curves calculated using the One Kinetic Site Model for a 10-cm-long soil column and the following parameters: q = 5 cm d–1, = 0.5, = 1 cm, Kd = 1 cm3 g–1, b = 1.5 g cm–3, and k = 0.1, 0.5, and 10 d–1.

View larger version (10K): [in this window] [in a new window]   FIG. 9. Breakthrough curves calculated using the Two-Site Kinetic Model for a 10-cm-long soil column and the following parameters: q = 5 cm d–1, = 0.5, = 1 cm, Kd = 1 cm3 g–1, and b = 1.5 g cm–3; on the left, fe = 0.4 and k = 0.1, 0.5, and 10 d–1; and on the right, k = 0.5 d–1 and fe = 0.1, 0.4, and 0.8.

View larger version (15K): [in this window] [in a new window]   FIG. 10. Breakthrough curves calculated using the Two Kinetic Sites Model for a 10-cm-long soil column and the following parameters: solute pulse duration = 10 d, q = 5 cm d–1, = 0.5, = 1 cm, Kd = 1 cm3 g–1, b = 1.5 g cm–3, ka1 = 1.5 d–1, kd1 = 0.5 d–1, and ka2 = 0.0, 0.3, and 3.0 d–1 with kd2 = 0.0, 0.1, and 1.0 d–1, respectively.

View larger version (13K): [in this window] [in a new window]   FIG. 11. Breakthrough curves calculated using the Dual-Porosity Model with One Kinetic Site for a 10-cm-long soil column and the following parameters: solute pulse duration = 10 d, q = 3 cm d–1, = 0.5, mo = 0.3, im = 0.2, mo = 1 cm, Kd = 1 cm3 g–1, b = 1.5 g cm–3, fmo = 0.6, = 0.1 d–1; on the left, fem = 0.4 and ch = 0.1, 0.5, and 10 d–1 ; and on the right, ch = 0.1 d–1 and fem = 1.0, 0.7, 0.4, and 0.1.

View larger version (29K): [in this window] [in a new window]   FIG. 12. Breakthrough curves calculated using the Dual-Permeability Model with Two-Site Sorption for a 10-cm-long soil column and the following parameters: solute pulse duration = 10 d, qm = 3 cm d–1, qf = 30 cm d–1, = m = f = 0.5, w = 0.1, m = f = 1 cm, Kdm = Kdf = 1 cm3 g–1, b = 1.5 g cm–3, dp = 0.1 d–1, ch,m = ch,f = 0.1 d–1, and ff = fm = 1, 0.7, and 0.4. Matrix, fracture, and total breakthrough curves are represented by thin, medium, and thick lines, respectively.