Separatists in the east need revenue if they are to be able to resist the western-based central government in their struggle for autonomy (or independence if the struggle goes violent). The government doesn't want them to have that revenue:
Libyan Prime Minister Ali Zeidan warned oil tankers to stay away from eastern terminals seized by armed protesters or they could be sunk, as a confrontation over control of Libya's crude escalated. ...
In the east, the self-proclaimed Cyrenaica regional government and its armed protesters have taken over three ports: Ras Lanuf, Es Sider and Zueitina, which previously accounted for 600,000 bpd in crude exports.
It isn't a civil war, but my wartime advice to secure oil supplies still applies.