Method for separating solids suspended or entrained in a liquid

A method for separating solids and liquids comprising:

• providing a first vessel comprising a solids compactor, a slurry inlet, a filter medium, a fluid outlet, and a solids outlet, wherein the filter medium is outside the solids compactor, the slurry inlet is located towards a first end of the first vessel, and the solids outlet is located towards a second end of the first vessel;
• providing a second vessel in communication with the first vessel through the solids outlet;
• passing a slurry stream, comprising a feed solid and a feed liquid, through the slurry inlet into the first vessel;
• compacting the slurry stream with the solids compactor towards the second end of the first vessel, wherein compacting the slurry stream drives a portion of the feed liquid out of the slurry through the filter medium and out the fluid outlet as a liquid product stream, leaving a solids product stream in the first vessel;
• passing the solids product stream out of the first vessel through the solids outlet into the second vessel;
• and
• melting the solids product stream in the second vessel;
• wherein, as the solids outlet restricts flow of the solids product stream sufficient for a backpressure to be built towards the second end of the first vessel, the solids compactor is enabled to compact the solids without the slurry stream passing through the solids outlet.