Yes, the article is sufficiently vague to not really know what it is they're doing. Are they hydrating and dehydrating NaOH? Or are they using geo-heat pump to store heat in earthen thermal mass.
I think to your point, the exact question is whether there is still an exothermic reaction when you keep adding water. A quick google says that 50% is the saturation point for a NaOH solution, so I don't know how they would be further hydrating lye and getting heat out.
Maybe the article is incorrect, and they meant that the solution would be at 50% NaOH after they got as much heat out as they could, and that is the point where heat would be applied to dehydrate the solution and "store" heat for later.
As I type, I realize that would put the solution above 50% and NaOH would begin precipitating out, so how would their solution flow.......
In short, I'm curious to know more about their supposed setup, and I hope the article isn't just bogus.....
EDIT: As always, best to go to the source: https://www.empa.ch/web/s604/naoh-heat-storage
||I think the original article said that the heat was stored in 50% solution and diluted to 30%, but not sure that sodium hydroxide gives out heat at those concentrations.|