The idea of $CO_2$ sequestration in the ocean is proposed to be an effective mitigation strategy to counteract potential global warming due to the greenhouse effect. Therefore, in the present study, calculations of the dissolution behavior of $CO_2$ hydrate when liquid carbon dioxide is released at 1,000m and 1,500m in depth are performed. The results show the liquid $CO_2$ injected in the ocean becomes $CO_2$ bubble at between 350 m in depth, and the injection from a moving ship is a more effective method of dissolution than through a fixed pipeline. It so also noted that the ultimate plume generated from $CO_2$ bubbles repeats expansion and shrinking due to the peeling from a fixed pipeline.