Compress. Cool.
Repeat.

The bike-pump effect, in numbers.

Compression work can raise a gas’s temperature. For an ideal gas compressed reversibly without heat transfer, T₂ / T₁ = (P₂ / P₁)^(k−1)/k. Temperatures in this equation are kelvin and pressures are absolute.

These calculated values use k = 1.4. Real irreversible compression needs more work; heat transfer, gas properties and efficiency change the outlet temperature. NASA’s isentropic relations give the starting equation.

Cool between stages. Lower the next stage’s inlet temperature.

At the same pressure, cooler gas occupies less volume. Compressing it again requires less work. With ideal intercooling and equal efficiencies, equal pressure ratios per stage minimize compression work. Isothermal compression is the limiting reversible case.

This model isolates the effect of staging. A real selection also considers real-gas properties, cylinder and valve losses, cooling performance, rod loads, flow capacity and mechanical limits. A value below a temperature reference alone does not establish a suitable compressor.

A temperature limit is not a universal failure point.

The reel’s “around 150 °C” is a shorthand for a cited reciprocating-compressor standard limit. It does not mean every oil, seal or valve fails at that temperature, or that every compressor type has the same cap.

For the hydrogen case discussed here, Ariel uses 135 °C. Its published application limits vary with gas service and lubrication. Use the applicable standard edition, vendor limits and service requirements for an actual selection. Ariel: limits by service.

Eight stages. One compressor system.

Ariel’s example compresses 50 kg/h of hydrogen from an alkaline electrolyser at 1.01 bar(a) to 200 bar(a). Its selected design is one six-throw compressor with eight stages, requiring 129 kW in that vendor selection.

“Eight machines” in the reel is loose wording: a stage is not a separate machine. Nor does every hydrogen duty at 200 bar require eight stages. In the same article, a 25 bar(a) PEM-electrolyser inlet gives a three-stage selection.

Read the original Ariel case. The interactive table above is our simplified calculation; it is not a reproduction of the vendor’s eight-stage temperature table.

The five-stage train from Reflux Student.

This is the actual CHE480 case export used for the video: five stages with a parallel first stage and an anti-surge recycle. It is a separate simulation example from the eight-stage hydrogen selection.

Download the original editable P&ID (.drawio) · Open the full drawing

Intercooler outlet temperatures in the export are 298.1 K (about 25 °C). The pressure unit is reproduced as the case labels it. These numbers describe this source case, not the simplified hydrogen model above.