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Comparison of a Lattice-Boltzmann Model, a Full-Morphology Model, and a Pore Network Model for Determining Capillary Pressure–Saturation Relationships

^a Institute of Environmental Physics, Univ. of Heidelberg, INF 229, 69120 Heidelberg, Germany
^b Institute for Computer Applications in Civil Engineering, TU Braunschweig, Pockelsstr. 3, 38106 Braunschweig, Germany

View larger version (75K): [in a new window]   Fig. 1. (left) Original gray-scale image of reconstructed X-ray absorption coefficients for a horizontal section through the sintered borosilicate glass (natural width 3.2 mm) and (right) three-dimensional representation of the subsample used for further analysis after segmentation (solid phase is white, natural width 1.47 mm). The size of the subsample is also indicated in the horizontal section.

View larger version (19K): [in a new window]   Fig. 2. Porosity (solid line), Euler number (dashed line), and hydraulic conductivity (bars) vs. sample size. The values are normalized to the result for 1503 voxels. The hydraulic conductivity was modeled for pressure gradients along the three main axes. Bars indicate the range of the results.

View larger version (159K): [in a new window]   Fig. 3. Distribution of residual water (blue) and air (red) in the porous medium (gray) at the end of the drainage process simulated with the Lattice-Boltzmann approach.

View larger version (61K): [in a new window]   Fig. 4. Visualization of the wetting and the nonwetting phase distribution at different capillary pressures for a single constricted pore. The connectivity is evaluated for the (left) "eroded" image, the pore-size distribution is obtained by the (middle) "opened" image, and the phase distribution is also obtained from the "opened" image while taking the (right, the air reservoir is on top) connectivity into account. Within the pore the various steps of erosions and openings are illustrated by colors from green to red with increasing radius of the structuring element.

View larger version (47K): [in a new window]   Fig. 5. Distribution of the wetting and the nonwetting phases during the simulated drainage process using the full-morphology model. From the top to bottom the wetting phase in blue is being expelled by the brown nonwetting phase.

View larger version (12K): [in a new window]   Fig. 6. Morphological material functions: (left) pore-size distribution V(r) and (right) connectivity function (r).

View larger version (141K): [in a new window]   Fig. 7. Typical realization of the pore network model showing the distribution of air (red) and water (blue) close to the air entry point. The shown volume represents 2.8 mm3, which is approximately the same as the measured sample of sintered glass (3.18 mm3).

View larger version (22K): [in a new window]   Fig. 8. Capillary pressure–saturation relationship as determined with the different models: Lattice-Boltzmann model, thick dashed line; full-morphology model, two solid lines representing extreme values for simulation of drainage in six principal directions; network model, gray shaded area enclosing 20 independent realizations.