The Alchemy Well, found in Ayuthay, is powered by water and produces water in vast quantities, and was powered by Alex 20 years before Dark Dawn. For it to work, you need the Luna Mask . You can acquire the Sand Prince Stone here by defeating the Sand Prince, which is one way of reversing the well.
The Alchemy Forge is Found in Passaj and is powered by fire. It distributes the water in the Ei-Jei Region, and is powered By Matthew, Karis, Tyrell, Rief, and Amiti. For it to work, you need the Sol Mask, found in the Ouroboros. To reverse the machine, you need the Ice Queen Stone, which you obtain after defeating the Ice Queen in Harapa. This stone, when equipped, enables the Mercury Adept to use Cold Snap Psynergy.