Fluid trapping characteristics of immiscible displacement in fractures
Résumé
Immiscible displacement of a fluid by another one in rock fractures is relevant for several important underground engineering applications, including hydrocarbon recovery and CO2 sequestration. The spatial distribution of fluid phases and the geometry of fluid-fluid interfaces in fractures cast decisive influence on a range of macroscopic flow parameters. Fluid trapping adds complexity to the analysis of fluid phase distributions and interface geometries. The aperture field of a natural rock fracture exhibits aperture variability, the influence of which on fluid displacement is not yet fully understood. Here we present a numerical investigation of the critical role of aperture variation and spatial correlation on fluid trapping and phase structure. We consider capillary dominated flow in a fracture with normally distributed random apertures. We address both spatially correlated and uncorrelated fracture geometries. The aperture fields are generated by a power spectrum based algorithm. This correlation scale varies among the investigated geometries between L/256 and L/16, L being the fracture largest dimension. The aperture variability is represented by the coefficient of variation (CV), which ranges among the various geometries from 0.05 to 0.25. To simulate fluid displacement we use a newly developed invasion percolation model which has been shown to properly reproduce displacement patterns observed in experiments. We present a quantitative analysis of the size distribution of trapped fluid clusters. The shape of this distribution depends on whether the in-plane curvature, that is, the minor principle component of the interface curvature, parallel to the fracture plane, is taken into account in the numerical model. We show that when the in-plane curvature is not considered, the trapped cluster distribution scales as a power law. 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 smaller than the correlation length. This dampening effect is strongly affected by the CV: the smaller the CV, the smaller the number of trapped clusters and the total mass of trapped fluid.