I own a house that was built around 1890 to 1910 located in central Pennsylvania. It is a double boarded house meaning that it has no framing at all, it is a unique type of construction that was used in some parts of the northeast US. More info (https://www.oldhouseweb.com/how-to-advice/boxhouse-plank-construction.shtml)
Long one inch thick boards are stood on end (vertically) and run from the sill plate on the foundation to the roof. Then a layer of paper, similar to tar paper is nailed on then another layer of one inch thick boards are nailed on to the outside vertically. Picture board and batten only the battens are full size boards. The boards used are random width and range from 18 inches to 4 inches wide, all one inch thick rough sawn.
On the outside layer of boards is wooden clapboard and then aluminum siding (no foam backing on it).
The house has no insulation in the walls since they are basically solid wood. What I want to do is the following.
Apply 3/4" rigid foam board insulation to the INTERIOR boarded wall and seal the seams with heat/insulation tape.
Run a 2"x4" stud wall up against the foam board.
Insulate the stud wall with unfaced R-13 Batts.
Cover studs with 1/2" drywall.
Will doing this cause issues with condensation/moisture? If so how can I mitigate the issue? Thank you any thoughts that you have.