Membrane Dryers
These are based upon ceramic technology which dates back to the 1950's. The best example is the ceramic tube which was used to 'cure' rising damp in brick built structures. In fact you can still buy the same tubes which are inserted into the outer skin of brick walls. The tube sucks moisture from the surrounding brickwork, the water molecules pass through the tube to be carried away by natural air circulation which passes in and out of the centre of the tube. The migration process is caused because of difference in partial pressure which exists on the outside of the tube and on the inside of the tube.
Modern membrane dryers use microscopic tubes which are bundled together inside another much larger tube. The sketch shows a simplified system with just one membrane tube contained within the outer tube. The ends are sealed so that the larger outer tube becomes a small hermetically sealed pressure vessel.
The compressed air passes down the centre of the smaller tube(s), molecules of moisture pass through the tube walls into the 'pressure vessel'. The result is that the water vapour is taken into the larger 'pressure vessel' in an attempt to create an equilibrium. To prevent this happening, purge air is 
introduced from the outlet of the dryer (the dry side), this purge air represents between 20% - 40% of the treated compressed air. The purge air takes away the water molecules and the equilibrium is destroyed. A permanent flow of water molecules is therefore set up from the wet side of the tube to the dry side.
As well as being expensive to run, unfortunately the membranes are highly susceptible to oil and dirt. Compressed air is not usually the cleanest of mediums, therefore the membranes will quickly break down. The structure is microscopic, therefore it cannot be cleaned and has to be replaced.
In terms of performance, a membrane dryer will achieve a pressure dewpoint very similar to, or with high purge rates, better than a refrigerated dryer. Typically between +2 deg C and -8 deg C.
The plus side is that if the compressed air is 100% clean and oil free, then the membrane dryer should last for many years with absolutely no moving parts.
The down side is that it costs as much to run as a heatless desiccant dryer without the advantage of a low pressure dewpoint.