A Network Modeling Approach to Derive Unsaturated Hydraulic Properties of a Rough-Walled Fracture

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The hydraulic properties of a rough-walled fracture in a limestone sample are estimated using a network model based on three-dimensional representations of the fracture apertures. Two different scenarios are considered: drainage of water out of a fracture and infiltration of water into a fracture. Besides capillary effects, the model takes into account an accessibility criterion (invasion percolation) and, in the case of infiltration, the rate dependence of the water movement. A hysteresis effect between drainage and imbibition hydraulic properties can be observed, which increases with increasing capillary number. The measured permeability is overestimated by 15% by the network model. In a sensitivity analysis the influence of the main fracture field characteristics (field size and fracture segment size in relation to correlation length) on the calculated hydraulic properties is investigated. Field size has an important influence on the inverse of the water/air entry value α for imbibition, making it difficult to scale this parameter to other field sizes. A parameter analysis investigating the influence of the main fracture characteristics (mean fracture aperture, roughness, and correlation length) on the hydraulic properties shows that the mean fracture aperture is the most important fracture parameter influencing both strongly the saturated permeability K and α. The effect of varying the variance and the correlation length on K and α is much less than the influence of the mean fracture aperture. The effective permeability of the fracture is also calculated by the geometric mean Kg. Up to σ(loge(K)) = 1, the discrepancy between Kg and Kn (network model result) is less than 15%. At larger correlation lengths (for a constant σ(loge(K))), the discrepancy between Kg and Kn increases.

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