Few studies have drawn on any systematic research into the energy demand to produce polymer-based nanocomposites. Regarding the problem, it is well-known that single screw extrusion is an energy-intensive process, so the incorporation of energy meters must be considered to examine the energy efficiency of the process. In this study, the effect of a nanoclay addition on the energy demand of the extrusion process was examined by extruding recycled high-density polyethylene (rHDPE) and recycled polypropylene (rPP) with a gradual compression screw with both dispersive and distributive mixers. The rHDPE/rPP was modified by adding commercial organoclay (OMMT) (3 wt%) and olefin block copolymer (OBC) (5 wt%) as compatibilizers. The energy consumption was measured on the total energy of the extruder machine. Mass throughput (MT) and specific energy consumption (SEC) were obtained at different screw speeds (10, 20, 30, 40, 50 RPM). The SEC of OMMT and OMMT/OBC nanocomposites was 25–50% lower than rHDPE/rPP, especially at higher throughputs. X-ray diffraction (XRD) and scanning electron microscope (SEM) illustrated the degree of intercalation and dispersion of the organoclay at different screw speeds. Better organoclay intercalation and dispersion were found at lower temperatures. Rheological curves showed a decrease in the viscosity at extrusion rates of nanocomposite mixtures. Melt temperature measured at die exit was reduced in the presence of organoclay over the screw speeds studied. This work suggests that the processing of rHDPE/rPP based nanocomposites can result in minor costs when processing conditions are carefully selected.