The motion of isothermal vapour in a permeable rock is governed by a nonlinear diffusion equation for the vapour pressure. We analyse vapour flow described by this equation in both bounded and unbounded domains. We then apply these solutions to describe the controls on the rate of vaporization of liquid invading a hot permeable rock. In an unbounded domain, we determine asymptotic similarity solutions describing the motion of vapour when it is either supplied to or removed from the reservoir. Owing to the compressibility, these solutions have the property that vapour surfaces migrate towards the isobar on which the vapour has the maximum speed.
In contrast, if vapour is supplied to or removed from a closed bounded system sufficiently slowly then the vapour density and pressure rapidly become approximately uniform. As more vapour is added, the mean pressure gradually increases and vapour surfaces become compressed. If liquid slowly invades a hot bounded porous layer and vaporizes, the vapour pressure becomes nearly uniform. As more liquid is added, the reservoir gradually becomes vapour saturated and the vaporization ceases.
In an open bounded system, with a constant rate of vapour injection, the flux of vapour across the reservoir becomes uniform. If liquid is injected slowly and vaporizes then again the vapour flux becomes spatially uniform. However, the vapour flux now increases slowly as the liquid invades further into the rock, as a result of the decreased resistance to vapour flow from the interface to the far boundary.