Weather reroutes for an A319 result in a low fuel emergency declaration and a safe landing at their destination.

Narrative

Departed with 28095 LBS of fuel. Estimated burn was 18100 LBS with estimated arrival fuel of approximately 9700 LBS. We were advised enroute that ZZZ Center was shut down due to a severe line of thunderstorms and to expect a reroute. Arrival fuel with the new routing was now at 4200 LBS. We advised ATC we would have to divert if they could not shorten the route. We advised the Dispatcher who also attempted to coordinate with the ATC desk to assist us. The route was changed two or three more times; but each time we were projected to land with insufficient fuel. Our final clearance still showed low projected arrival fuel and insufficient fuel for alternate. We finally declared 'minimum fuel' in hopes that no further delays would allow us to land with about 5;000 LBS. At that point ATC advised us to expect further delays even though we declared minimum fuel. We then declared an emergency for low fuel. In accordance with FOM the Captain deemed that the projected fuel supply suggested the need for traffic priority to ensure a safe landing. Flight was immediately cleared direct to our destination and an uneventful landing was made.