A 2400 ft^2 x 8' tall house with 0.5 ACH leaks 160 cfm. At 30% RH and 70 F, Pa = 0.3e^(17.863-9621/(70+460)) = 0.225 "Hg and wa = 0.62198/(29.921/Pa-1) = 0.00470 pounds of water per pound of dry air. Outdoor air has wo = 0.0025 in Phila in January. Air weighs about 0.075 lb/ft^3, so keeping a house at
30% RH requires evaporating 60x160x0.075(wa-wo) = 1.584 pounds of water per hour, which requires about 1584 Btu/h, ie 38016 Btu/day, about 11.1 kWh or $1.11 per day at 10 cents/kWh, with electric heat.
As an alternative, we might use the earth's heat to evaporate water from a basement floorslab and move humid air up into the house as needed. The deep ground temp in Phila is 54.3 F. If the air near the slab is 54.3 F with 60% RH (not higher, to avoid mold) and wb = 0.00541, we might move
1.584/(60(wb-wa)) = 37 cfm of basement air up at an energy cost of about
37(70-55) = 558 Btu/h, ie 35% of the heat energy needed above.
Or maybe less, since humid air diffuses and rises, so some cool water vapor will move upstairs without moving any cool air with a fan and a duct near the floor. We might dampen the floorslab with a soaker hose and solenoid valve whenever the house is less than 40% RH and the slab is less than 60%, and only turn on the fan when the house RH drops to 30%.
Solenoid valves can be scrounged from discarded dishwashers and washing machines. Herbach and Rademan (800) 848-8001
Nick