A wellhead system for producing hydrocarbons from a subterranean formation that includes concentric tubulars that form an annulus. The annulus is vented by flowing fluid from the annulus through a bleed line having a valve that is selectively opened and closed. Upstream of the bleed line valve, the bleed line is routed adjacent a production flow line. The temperature of the fluid in the production flow line is greater than annulus temperature and warms the bleed line. Hydrate formation in the bleed line is thereby inhibited by the thermal energy it receives from the production flow line.