What, exactly do you mean by "be replaced"? If you mean "none used whatsoever", that probably will not happen, at least for the foreseeable future. If you mean replaced to some or a large extent, that has already happened and has been happening for some time. Much of the electricty in The United States, and, I am sure in the rest of the world, is produced by water turbines. A small amount, increasing all the time, is produced by wind turbines, solar panels, and nuclear power plants.
(Even with the problems at Chernyoble and now in Japan, far more people have been killed mining coal for power plants than in nuclear accidents.)