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We study experimentally and numerically slow drainage of a non-wetting fluid in a saturated fracture. Facing surfaces of the experimental fracture (25 cm × 25cm) are obtained from the casting of a brittle fracture of a granite block. They are rough but mated leading to a constant aperture where glass beads (1 mm) are spread in a single layer to mimic the influence of gouge particles trapped within the fracture. During injection, snap off might appear owing to the buoyancy difference between fluids, which splits the non-wetting invader into bubbles. Geometry and connectivity of this new fluid structure are characterized and shown to be significantly controlled by the long range spatial correlations of the fracture topography. Two coexisting types of sub structures emerge along percolating clusters: string-like links and compact blobs. Saturation and trapping are shown to be significantly influenced by the buoyancy effect. A numerical model to describe the experiments is introduced. It is based on an invasion percolation algorithm but includes spatially correlated contributions resulting from the roughness of the crack surfaces and gravity. Numerical results are shown to be consistent with experimental observations. The model allows us to extend the analysis to regimes where gravity forces are completely dominating and to obtain statistical results exploring numerous different fractures with the same properties (roughness statistics, pore size distribution, size). A description of the injection pressure evolution is proposed.