In one embodiment, a method for drilling a wellbore includes injecting drilling fluid through a drill string disposed in the wellbore and rotating a drill bit disposed on a bottom of the drill string. The drilling fluid includes a liquid and a gas. The drilling fluid is injected at the surface. The drilling fluid exits the drill bit and carries cuttings from the drill bit. The drilling fluid and cuttings (returns) flow to the surface via an annulus formed between the drill string and the wellbore. The liquid is injected at a rate so that a liquid velocity of the returns in the annulus is sufficient to transport the cuttings. The method further includes drilling through at least a portion of a non-productive formation.