Project ELOI was the name of a military project, lead by Colonel Wichita, whose goal was to send teams through a series of Time Rips, created by time travel technology invented by Dr. James Radnor, in order to mine the future for technology. The project presumably ended with the destruction of Tempus Flats. ("Morlocks")

Project ELOI is named for the Eloi, another race evolved from humans, originating in the original Time Machine novel that don't appear in this movie.