Open cell foam makes the wall slightly more air tight than closed cell foam, closed cell foam is slightly tighter than dense-packed BIB, but quite a bit tighter than low-density BIB.
But none of that matters much if they take the time to caulk all the framing to the sheathing, can-foam every electrical & plumbing penetration (including lateral wiring runs through studs), caulk the stud plates to the subfloor (and between doubled-up top plates), and the subfloor to the band joist, the band-joist to the foundation sill, and the foundation sill to the foundation, etc. Use acoustic sealant type caulk, and if they use a powered caulking gun it goes pretty fast. Can-foam guns that take the screw-on cans goes marginally faster and wastes less foam than the plastic-straw throwaways, but if you have a lot of big-gap stuff to seal around plumbing & electrical penetrations a 12 board foot FrothPak kit of 2-part foam goes quite a long way.
Once the insulation cavities are air-tight, cavity fill is cavity fill. With an air tight cavity the difference in "whole-wall" thermal performance after factoring in the thermal bridging of the framing and subfloor is negligible, provided its a blown or sprayed product that truly fills it fully, with no gaps or voids. At a typcial 16" o.c. framing fraction of 25% and R1.2/inch grades of timber a 2x4 wall with R3.5/inch fiberglass comes in at about R9.5 whole-wall, with an R1 allowance for siding & gypsum.
Filling the cavity fully with R6/inch closed cell foam only brings that up to R11.5, but since the best you're really going to do with closed cell is ~3" (you can't easily trim it) it's really closer to R10.
Save the foam budget for the exterior: An inch of foil-faced polyiso on the exterior facing the masonry cavity is usually do-able without custom masonry ties, and brings the whole-wall R from R9.5 to over R15, and in a Georgetown KY climate raises the average wintertime temperature of the sheathing high enough that you won't need an interior side vapor retarder to keep it from accumulating too much moisture. Furthermore, the foil-facers on the polyiso will protects the wall cavity from the intense moisture drives of summertime sun on dew-wetted brick that can cause condensation on the gypsum inside the cavity during the air conditioning season. Tape the seams of the iso with 2" FSK tape (aluminum duct-tape), and foam-seal the edges, and stagger the seams of the iso with those of the sheathing for better overall air tightness. The mold-susceptible wood will remain drier year round and can dry freely to the interior, making the assembly more resilient all around.
Even without interior side air barriers it's worth air-sealing the gypsum side too for both thermal and moisture performance reasons. A square inch of air leakage is worth a whole wall's worth of vapor-diffusion moisture through standard latex paint.
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