This paper describes a graphical method for classifying reservoir models of the above type, and for clarifying the connection between permeability (and permeability gradients) and saturation. The theory behind the method is reviewed, and then the technique is applied to the example of a bottom-heated geothermal heatpipe, which is shown to have a maximum length, beyond which the only possible stable continuation (downwards) is into single-phase vapour. A permeability increase (downwards) always acts to induce a liquid saturation increase. A similar conclusion holds for non-zero net mass flow but with no conduction. Our theoretical results agree with those obtained by numerical simulation.