دانلود رایگان مقاله به دام انداختن سیال در طول تغییر مکانی مویرگی در شکستگی

Abstract

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.

5. Conclusions

Geostatistical characteristics of the aperture field in a roughwalled fracture have a strong impact on the two-phase fluid displacement and the resulting fluid entrapment. Our work has elucidated how the aperture correlation length and the coefficient of variation affect the fluid displacement and trapping processes in the capillary dominated regime. We have shown that when the in-plane curvature is not considered, and for the fully uncorrelated case, the trapped cluster distribution scales as a power law. When the in-plane curvature is not considered and spatial correlation exists in the aperture field, the cluster size distribution follows the same power law as in the uncorrelated field case only for clusters of linear size larger than the correlation length Lc. When the in-plane curvature is taken into account and the aperture field is uncorrelated, the cluster size distribution also follows a power law, but with a different exponent. In addition, accounting for the in-plane curvature suppresses the formation of trapped clusters of size below the correlation scale. This dampening effect is strongly affected by the coefficient of variation δ; the smaller the δ, the smaller the number of trapped clusters and the total mass (or saturation) of trapped fluid. The dampening is also affected by the correlation length scale. Interestingly, when the inplane curvature is considered, the trapped phase saturation is highest at some intermediate correlation scale, for a given aperture coef- ficient of variation.