Storing carbon dioxide (CO₂) underground is a promising way to fight climate change, but it comes with safety concerns—particularly the risk of triggering small earthquakes by increasing pressure near underground faults. This study focuses on better understanding and reducing that risk. We created a computer model to simulate how CO₂ moves and builds up pressure underground after being injected into a rock formation. The model then estimates how likely it is that this pressure could cause a nearby fault to slip over time. By testing this approach at sites like those in the Delaware Basin, we show how it can help identify and manage risks before they become problems. Our work supports safer carbon storage and helps inform decisions by scientists, engineers, and regulators working to make this technology more reliable.