HYPOTHESIS: Imbibition of a fluid into a porous material involves the invasion of a wetting fluid in the pore space through piston-like displacement, film and corner flow, snap-off and pore bypassing. These processes have been studied extensively in two-dimensional (2D) porous systems; however, their relevance to three-dimensional (3D) natural porous media is poorly understood. Here, we investigate these pore-scale processes in a natural rock sample using time-resolved 3D (i.e., four-dimensional or 4D) X-ray imaging. EXPERIMENTS: We performed a capillary-controlled drainage-imbibition experiment on an initially brine-saturated carbonate rock sample. The sample was imaged continuously during imbibition using 4D X-ray imaging to visualize and analyze fluid displacement and snap-off processes at the pore-scale. FINDINGS: We discover a new type of snap-off that occurs in pores, resulting in the entrapment of a small portion of the non-wetting phase in pore corners. This contrasts with previously-observed snap-off in throats which traps the non-wetting phase in pore centers. We relate the new type of pore-snap-off to the pinning of fluid-fluid interfaces at rough surfaces, creating contact angles close to 90°. Subsequently, we provide correlations for displacement events as a function of pore-throat geometry. Our findings indicate that having a small throat does not necessarily favor snap-off: the key criterion is the throat radius in relation to the pore radius involved in a displacement event, captured by the aspect ratio.