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Simulation of Tracer Dispersion in Porous Media Using Lattice Boltzmann and Random Walk Models

^a Dep. of Agronomy, University of Córdoba, P.O. Box 3048, 14080 Córdoba, Spain
^b Dep. of Agronomy, University of Córdoba and Institute of Sustainable Agriculture, CSIC, P.O. Box 3048, 14080 Córdoba, Spain
^c Dep. of Applied Physics, University of Córdoba, P.O. Box 3048, 14080 Córdoba, Spain

View larger version (8K): [in a new window]   Fig. 1. Neighborhood relationships used in the BGK model for the description of advection (d2q9), and diffusion (d2q4), where d is the dimension number and q the number of adopted neighbors.

View larger version (40K): [in a new window]   Fig. 2. Dispersion of a passive tracer in a medium with porosity = 0.76, simulated with the BGK model. The flow was forced from left to right with the parameters Re = 39.7 and Pe = 110.2. The dark and white hues correspond to regions with higher and lower tracer concentration, respectively. The concentration values are normalized with respect to their initial value. The numbers in the figure corresponds to the computed time steps.

View larger version (43K): [in a new window]   Fig. 3. Dispersion of a passive tracer in a medium with porosity = 0.76, simulated with the BGK/RW model. The flow was forced from left to right with the parameters Re = 39.7 and Pe = 110.2. The dark and white hues correspond to regions with higher and lower tracer concentration, respectively. The concentration values are normalized with respect to their initial value. The numbers in the figure corresponds to the computed time steps.

View larger version (12K): [in a new window]   Fig. 4. Breakthrough curves computed with BGK (full line) and the BGK/RW models (dashed line) for simulating the dispersion of a passive tracer in a medium with porosity = 0.76 using the parameters Re = 39.7 and Pe = 110.2.

View larger version (22K): [in a new window]   Fig. 5. Plots of variance (2) vs. time (t) obtained with the BGK (solid line) and BGK/RW models (dashed line) for Taylor–Aris dispersion during flow with Re = Pe = 4.8. The last branch of each curve may be fitted to the indicated values for d2/dt.

View larger version (11K): [in a new window]   Fig. 6. Breakthrough curve computed with the BGK model (solid line), for Taylor–Aris dispersion of a passive tracer during flow with the Re = Pe = 4.8, and comparison with the theoretical solution (dashed line).

View larger version (11K): [in a new window]   Fig. 7. Breakthrough curve computed with the BGK/RW model (solid line), for Taylor–Aris dispersion of a passive tracer during flow with the Re = Pe = 4.8, and comparison with the theoretical solution (dashed line).