It rainin’ in the cellar …
Its not intuitive that forced outdoor fresh air venting of a damp cellar will make it rain indoors in the summer time. But it sure does. Lots of fan manufacturers willing to sell us ventilation for a wet basement. There is a perpetual summer time dew point in this cellar. RH is 85 and up; its temperature is 75.
The cellar I have in mind has a black ceiling from mildew fed by summer condensation. The walls are sheathed over rigid foam and have no mildew. The ceiling is OSB sheathed (conditioned space above), air-sealed and primed with Bin. The foundation is air and water sealed but the building materials have not had a year to dry out. Some water got in during construction.
Thought is to hang a dehumidifier at top of the wall, drain it into the sewer pipe, and leave it on automatic. This seems energy expensive. What about opening a vent or air channel into the mini-split air conditioned space above? Which approach to this humidification will be the lowest cost?
Its Zone 5 A – what rigid foam R value would stop this problem all together.
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As you realize (and as GBA has pointed out many times), summertime ventilation in a humid climate makes moisture problems in crawl spaces or basements worse. The more you ventilate, the more dripping you get.
The usual solution for cellars, basements, and crawl spaces is, first, to seal the vents; second, the make sure that the floor has a layer of polyethylene; third, to remediate all mold; fourth, to install insulation on the walls; and fifth, to install and operate a dehumidifier, at least on a temporary basis, until the situation stabilizes.
Of course, if there are problems with groundwater, roof gutters, or the exterior grade around the house, these problems have to be fixed as well.
For more detail on all of these steps, see these two articles:
Building an Unvented Crawl Space
Fixing a Wet Basement
To your question about the energy expense of the dehumidifier, if you decrease the amount of air flowing in from outside, you decrease the amount it needs to run. With things sealed as well as you indicate, it might be a one-time expense to dry the building materials out, and then little ongoing expense.
As for venting between the conditioned space above and the basement, that could be circulating between the two spaces, or one way, with a small opening and a small fan pushing air from above down into the basement and out cracks and/or vents to the outdoors. At this point, it seems that circulating would be a bad idea, as you would be bringing moldy basement air into the house. So I'd prefer considering the one-way venting creating positive pressure in the basement. It could be regulated by a humidistat in the basement.
I think I like the dehumidifier plan better for two reasons. One is that the dehumidifier will heat the space as well as remove moisture, and that heat could be beneficial in combating condensation. And the other reason is that the positive pressure ventilation will cause some air leaks from basement to house, which might not be the air you want in the house.