Storing \ce{CO2} in sub-seabed sediment is a promising \ce{CO2} sequestration method to reduce the atmospheric \ce{CO2} concentration and mitigate climate change, with the advantage of self-sealing capability due to formation of \ce{CO2} hydrate in the sediment pore space. Above the sequestration site, enhanced \ce{CO2} migration and supersaturation lead to a zone of coexisting gaseous, hydrate and aqueous phases of \ce{CO2} where curved surfaces of bubbles and hydrate crystals shift the phase equilibria, enabling fast development of the self-sealing capability due to permeability reduction by both hydrates and entrapped bubbles. We simulate the three-phase zone in a shallow seabed using a Monte Carlo method in packed synthetic mono-dispersed spherical sediment grains, and analyze its variations due to temperature and pressure perturbations. Our work demonstrates the difference between \ce{CO2} hydrate-bearing sediment layer and methane hydrate reservoir, and provides insight into the formation mechanisms of the self-sealing cap above sequestration sites.