Abstract: Methods for purifying an aqueous hydrochloric acid solution waste stream having an impurity fraction comprising an initial Ti fraction, an initial S fraction and an initial Si fraction; that provide purified aqueous hydrochloric acid solutions having a final Ti fraction of less than 250 ppm, a final S fraction of less than 200 ppm, and a final Si fraction of less than 10 ppm, which may be determined with inductively coupled plasma spectroscopy. Process steps in various embodiments include sparging with an gas; mixing the sparged solution with a precipitation agent comprising a sufficient amount of an alkali earth metal salt and, optionally, a phosphoric acid source, to provide a metal salt precipitate; and mixing the initial aqueous acid solution or, optionally, the sparged aqueous acid solution, with a flocculating polymer. A preferred alkali earth metal salt is barium chloride and preferred flocculating polymers are poly(diallyldialkylammonium chloride) homopolymers and copolymers.