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During the planning stages of this project, we had come up with a few strategies to create a thick layer of insulation and a primary air barrier using dense-packed cellulose and a fabric such as Pro Clima’s  Mento Plus.  Using this type of system, it is possible to use cellulose, an environmentally friendly choice for insulation, on the outside of the structural components.  The whole assembly ends up vapor open, and has drying potential both to the exterior and interior.  This creates a great thermal envelope that has long-term durability.  The method is gaining traction, particularly with people looking to achieve Passive House levels of insulation and air tightness, with a relatively low environmental cost.
For my own project, I decide to go another way for the simple reason that I would be doing the work over and extended period of time, and only have a couple of days a week at best to get things done.  I needed a system that I could put on in stages, and keep weather tight while work is on going.  I could not figure out how to do this with the cellulose system, which will readily soak up water.  So I opted for the more “traditional” DER approach using multiple layers of rigid foam.  With this method, multiple layers of insulation are put to the exterior of the structural framing.  This creates an envelope that is vapor closed from the sheathing out, but with such a large fraction of the thermal insulation outside of the sheathing, it is insured that the sheathing is always above the dew point, and liquid water will never form within the wall cavity.  This system keeps the structural framing of the building within the thermal envelope, and at near interior conditions, warm and dry.