A method of recycling polytrimethylene terephthalate, said method comprising: providing a multi-screw extruder that comprises: (i) a first satellite screw extruder, said first satellite screw extruder comprising a first satellite screw that is mounted to rotate about a central axis of said first satellite screw; (ii) a second satellite screw extruder, said second satellite screw extruder comprising a second satellite screw that is mounted to rotate about a central axis of said second satellite screw; (iii) a third satellite screw extruder, said third satellite screw extruder comprising a third satellite screw that is mounted to rotate about a central axis of said third satellite screw; (iv) a fourth satellite screw extruder, said fourth satellite screw extruder comprising a fourth satellite screw that is mounted to rotate about a central axis of said fourth satellite screw; and (v) a pressure regulation system that is adapted to maintain a pressure within said first, second, third, and fourth satellite screw extruders between about 0 millibars and about 18 millibars; using said pressure regulation system to reduce a pressure within said first, second, third, and fourth satellite screw extruders to between about 0 millibars and about 18 millibars; while maintaining said pressure within said first, second, third, and fourth satellite screw extruders between about 0 millibars and about 18 millibars, passing a melt comprising recycled polytrimethylene terephthalate through said multi-screw extruder so that: 1) a first portion of said melt passes through said first satellite screw extruder, 2) a second portion of said melt passes through said second satellite screw extruder, 3) a third portion of said melt passes through said third satellite screw extruder, and 4) a fourth portion of said melt passes through said fourth satellite screw extruder; and after said step of passing said melt of recycled polytrimethylene terephthalate through said multi-screw extruder, preparing said polymer melt for use in production of one or more new products, wherein prior to step C, said method comprises the step of providing recycled polytrimethylene terephthalate from polytrimethylene terephthalate carpets and/or polytrimethylene terephthalate food containers. providing a multi-screw extruder that comprises: (i) a first satellite screw extruder, said first satellite screw extruder comprising a first satellite screw that is mounted to rotate about a central axis of said first satellite screw; (ii) a second satellite screw extruder, said second satellite screw extruder comprising a second satellite screw that is mounted to rotate about a central axis of said second satellite screw; (iii) a third satellite screw extruder, said third satellite screw extruder comprising a third satellite screw that is mounted to rotate about a central axis of said third satellite screw; (iv) a fourth satellite screw extruder, said fourth satellite screw extruder comprising a fourth satellite screw that is mounted to rotate about a central axis of said fourth satellite screw; and (v) a pressure regulation system that is adapted to maintain a pressure within said first, second, third, and fourth satellite screw extruders between about 0 millibars and about 18 millibars; (i) a first satellite screw extruder, said first satellite screw extruder comprising a first satellite screw that is mounted to rotate about a central axis of said first satellite screw; (ii) a second satellite screw extruder, said second satellite screw extruder comprising a second satellite screw that is mounted to rotate about a central axis of said second satellite screw; (iii) a third satellite screw extruder, said third satellite screw extruder comprising a third satellite screw that is mounted to rotate about a central axis of said third satellite screw; (iv) a fourth satellite screw extruder, said fourth satellite screw extruder comprising a fourth satellite screw that is mounted to rotate about a central axis of said fourth satellite screw; and (v) a pressure regulation system that is adapted to maintain a pressure within said first, second, third, and fourth satellite screw extruders between about 0 millibars and about 18 millibars; using said pressure regulation system to reduce a pressure within said first, second, third, and fourth satellite screw extruders to between about 0 millibars and about 18 millibars; while maintaining said pressure within said first, second, third, and fourth satellite screw extruders between about 0 millibars and about 18 millibars, passing a melt comprising recycled polytrimethylene terephthalate through said multi-screw extruder so that: 1) a first portion of said melt passes through said first satellite screw extruder, 2) a second portion of said melt passes through said second satellite screw extruder, 3) a third portion of said melt passes through said third satellite screw extruder, and 4) a fourth portion of said melt passes through said fourth satellite screw extruder; and 1) a first portion of said melt passes through said first satellite screw extruder, 2) a second portion of said melt passes through said second satellite screw extruder, 3) a third portion of said melt passes through said third satellite screw extruder, and 4) a fourth portion of said melt passes through said fourth satellite screw extruder; and after said step of passing said melt of recycled polytrimethylene terephthalate through said multi-screw extruder, preparing said polymer melt for use in production of one or more new products,