Do you have to use water to sous vide?
You could use oil, but I don't think it's worth it; realize that you're going to be using additional energy for obtaining, cleaning, and disposal of it.

Regarding using a broth with a porous bag, well, that isn't sous vide. That's more akin to a slow-cooker. The whole point of sous vide is the airtight barrier between food and heat.

Update

Oil does not have a higher thermal mass than water. Ammonia does, but I'd suggest avoiding that. ;)

Source: http://www.engineeringtoolbox.com/specific-heat-fluids-d_151.html