in which SE is denoted in kw per kg/h, kw is kilowatts (the motor rating, kw = hp x 0.746); % torque is the percentage used of the maximum allowable torque; and rpm is the screws' rotations per minute. A lower SE indicates that less mechanical energy is being used, and a larger SE indicates more energy. SE records are particularly important to confirm batch-to-batch consistency, as well as for troubleshooting and scale-up purposes.

Scale-up. Scale-up is useful for estimating rates for production twin-screw extruders based on lab experiments. When comparing different size extruders, the geometries should be nearly identical for this equation to be valid. For processes that scale-up volumetrically, the equation is as follows:

in which Q is the throughput rate (in any units) and OD is the screw outside diameter (each). The greater the difference in OD, the less reliable this calculation becomes. Accuracy is also dependent upon whether the process is restricted by a volume, heat transfer, or mass transfer limitation. For a heat-transfer limited process, the exponent is closer to 2.0. For mass-transfer limited processes, the scale-up exponent is typically between 2.3 and 2.7 (as compared to 3.0).

For rough scaling between different-size machines that share geometric similarities (OD/ID ratio and similar screw designs) the comparative free volumes are a useful benchmark. For instance:

Q _target = Q _reference × (Volume_target/Volume_reference)

For example, assuming geometric similarities, if an 18 mm twin-screw extruder has a SV of 3 cc/dia and is running at 2 kg/h, then it can be inferred that a 30 mm extruder with a specific volume (SV) of 12 cc/dia will process approximately four times the rate, or 8 kg/h.

Residence time. This formula provides the approximate residence time (RT) in the process section of an HSEI twin-screw extruder. As denoted above, the residence time distribution is highly dependent upon the degree of screw fill. The following equation can be used for RT:

RT(s) = (SV × SG × L/D × %fill)/(Q × 0.2777)

where RT is residence time in seconds, SV is specific volume in cc/dia, SG is specific gravity, L/D is the L/D extruder ratio, % fill is the degree of fill expressed as a decimal (i.e., 40% = 0.4), and Q is the kg/h being processed. The RT formula provides insight as to how long materials are exposed to heat and shear in the process section.

Temperature rise during pressure generation. Pressure generation in the front end of the extruder caused by the die restriction results in a temperature rise. The more restrictive the front end, the higher the pressure and melt temperature rise, which may adversely effect the product. The temperature rise equation is as follows:

Δ T (°C) = Δ P (bar) / 2