The reactors had the control rod inserted okay (apparently) so the normal fission process is pretty much stopped. The continued production of heat is from decay of radioactive fission products. Someone at TOD said this was around 7% of reactor power declining over time.
Just thinking off the top of my head here. So Fukushima I – 1 has an electric output of 430 MW, call it a round 1000 MW thermal (I guess it's a bit more than that). With the full insertion of control rods, there remains 7% or ~70 MW of heat to dissipate. The latent heat of vaporization of water is 2.5 MJ/kg (ignoring energy to boil), so we get through 28 kg of water per second, or 100 tonnes an hour!
Seawater is around 3.5% salt, so using seawater is going to deposit 3.5 tonnes of salt per hour. Wow, is this even remotely right?
Edit: Okay, so I read the Wikipeda page on
decay heat now. The ~7% is the instantaneous rate. After a day it's more like 0.4%, so leaving 4 MW to cool, leaving behind around 200 kg of salt per hour.