Methods and apparatus are provided for the removal and purification of the water and salt by-products from spent BHP emitted from a lasing process. The apparatus comprises a liquid processing system that freezes the water and salt by-products into a slurry, and then separates out the water (as ice) and salt components by filtering in a centrifuge. In order to remove as much residual BHP from the wet mixed ice-salt component as possible, a heat source is used to partially melt ice crystals, thereby generating an aqueous rinsing liquid on the surface of the wet mixed ice-salt crystals. The applied centrifugal force causes a continual displacement of the liquid film wetting the surface, so that it becomes progressively diluted. As such, the purification of the mixture of ice and salt crystals is implemented with an aqueous (water) rinse that is unaffected by the sub-freezing temperatures within the centrifuge. The separation and purification may also be performed with a filter in which the conventional built-in water rinse is replaced with a heat source. The filter's driving force, for example gas pressure or vacuum, would be continuously applied during warming.