Experimental and theoretical investigations of drainage in horizontal rough-walled fractures with different correlation structures

Experiments on the immiscible displacement of water by air were performed in two horizontal artificial open rough-walled fractures with different correlation structures. The aperture field of the first fracture has a Gaussian variogram with a finite correlation length, while that of the second one has a power-law variogram, for which no finite correlation length can be assigned. We simulated the displacement process using an invasion percolation model, which takes the in-plane curvature of the interface between water and air into account. The correlation structure of the aperture field has no effect on the irregularity of the shape of the air clusters. However, the correlation structure in combination with the in-plane curvature influences the density of the air clusters and thus has an impact on characteristic properties of the flow. We analyze the model parameters and properties with respect to the fracture properties. The stochastic average of the air clusters for models with different curvature numbers and fields with different correlation lengths is then calculated in order to analyze their influence on continuum approach models.