We study, numerically, the behavior of capillary pressure (Pc) during slow immiscible displacement in a rough fracture as a function of the degree of fracture aperture heterogeneity that results from two distinct mechanisms: normal confining stress and fracture surface correlation. We generate synthetic self-affine rough fractures at different correlation scales, solve the elastic contact problem to model the effect of confining stress, and simulate slow immiscible displacement of a wetting fluid by a nonwetting one using a modified invasion percolation model that accounts for in-plane curvature of the fluid-fluid interface. Our modeling results indicate that the power spectral density, S(f), of Pc, can be used to qualitatively characterize fracture aperture heterogeneity. We show that the distribution of forward avalanche sizes follows a power law Nf(Sf) ∝ Sf−α, with exponent α=2, in agreement with previously reported values for porous media and equal to the expected theoretical exponent for a self-organized criticality process.
Bibliographical noteFunding Information:
This work was funded in part by the U.S. Department of Energy (Grant DE-SC0018357 to R. J.). P. K. K. acknowledges a grant from Korea Environment Industry and Technology Institute (KEITI) through Subsurface Environmental Management (SEM) Project, funded by the Korea Ministry of Environment (MOE) (2018002440003). Z. Y. acknowledges financial support from the National Natural Science Foundation of China (41877203). No data were used in producing this manuscript.
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- capillary pressure
- multiphase flow
- self-organized criticality