A new topological model on how gas hydrates form, grow, and agglomerate for oil and water continuous flow, with and without surfactant additives, is presented. A multiscale approach is used to explain how the porous structure of gas hydrates and the affinity between the phases affect the particle morphology and their agglomeration. We propose that gas consumption due to hydrate growth happens mostly in the water trapped inside the capillaries of the hydrate structure near the outer surface of the particles. This approach is herein referred to as the “sponge approach” and is treated as a surface problem, instead of the volume problem often treated in literature (the “shell approach”). Affinity between phases (which in a macro point of view is interpreted as a wetted angle that gives rise to capillarity forces and that can be changed by the use of surfactant additives) describes the preferential entrapment of oil or water inside the hydrate sponge structure. Yet by splitting agglomeration into smaller processes and depending on the morphology of the particles and on the evolution of the porous structure of the hydrates, (i) capillarity bridges may form, causing particles to be sticky, and (ii) water may be available at the outer surface of the particles and may promote consolidation of particle–particle (agglomeration) or particle-wall (deposition). The settling of slurries is treated as a separated solid–liquid flow instability problem once mixture deceleration (due to phase consumption during crystallization) and particle size (due to growth and agglomeration) are known. We also propose a new explanation on how surfactants act as anti-agglomerants in oil continuous flow, differently from the common DLVO theory used in literature, which can only explain anti-agglomeration of particles much smaller than the ones formed over droplets of a very fine dispersion flow.