Fluid trapping during capillary displacement in fractures

The spatial distribution of fluid phases and the geometry of fluid-fluid interfaces resulting from immiscible displacement in fractures cast decisive influence on a range of macroscopic flow parameters. Most importantly, these are the relative permeabilities of the fluids as well as the macroscopic irreducible saturations. They also influence parameters for component (solute) transport, as it usually occurs through one of the fluid phase only. Here, we present a numerical investigation on the critical role of aperture variation and spatial correlation on fluid trapping and the morphology of fluid phase distributions in a geological fracture. We consider drainage in the capillary dominated regime. The correlation scale, that is, the scale over which the two facing fracture walls are matched, varies among the investigated geometries between L/256 and L (self-affine fields), L being the domain/fracture length. The aperture variability is quantified by the coefficient of variation (δ), ranging among the various geometries from 0.05 to 0.25. We use an invasion percolation based model which has been shown to properly reproduce displacement patterns observed in previous experiments. We present a quantitative analysis of the size distribution of trapped fluid clusters. We show that when the in-plane curvature is considered, the amount of trapped fluid mass first increases with increasing correlation scale Lc and then decreases as Lc further increases from some intermediate scale towards the domain length scale L. The in-plane curvature contributes to smoothening the invasion front and to dampening the entrapment of fluid clusters of a certain size range that depends on the combination of random aperture standard deviation and spatial correlation.