Compression ratio

Why the ratio, and not the pressure rise, is the number that sizes a machine

Compression is governed by the ratio of the pressures, not the difference between them. A machine taking a stream from 100 psia to 900 psia and one taking it from 1000 psia to 1800 psia both add 800 psi, and they are nothing like the same duty: the first has a ratio of nine, the second well under two. The work done per unit of gas follows the ratio, which is why the pressure rise alone says almost nothing about the size of machine required.

Both pressures must be ABSOLUTE, and this is where the calculation most often goes wrong. Field instruments read gauge pressure, measured against the surrounding atmosphere; absolute pressure adds the barometric component back on, roughly 14.7 psi at sea level and noticeably less at altitude. Entering psig where psia is asked for barely moves the answer at high suction and destroys it at low suction: a stream at 5 psig sits at nearly 20 psia, so treating the gauge reading as absolute overstates the ratio fourfold. A ratio wrong at the first step stays wrong through staging, temperature and power.

The result is dimensionless, and that is what makes it portable. It carries no unit, so it is the same number whether the pressures were read in psia, bar or kPa — provided both were read the same way and both were absolute. That is why ratio rather than pressure is the currency of this cluster: stage count and discharge temperature are expressed against it, and neither needs to know how the original gauges were calibrated.

Distinguish the OVERALL ratio from the ratio ACROSS ONE STAGE. This computes the overall duty, from first-stage suction to last-stage discharge. A multi-stage machine divides that duty between its stages, and the per-stage ratio is what actually sets the temperature each cylinder or wheel sees. Feeding an overall ratio into a per-stage relation predicts a discharge temperature no part of the machine will ever reach.

When this calculation is used

• Establishing the duty at the start of a screening calculation, before stage count, temperature or power are looked at.
• Checking whether a stream can plausibly be handled in one stage or whether staging is already implied by the pressures alone.
• Reconciling a vendor datasheet against site conditions, where suction pressure has drifted from the value the machine was selected for.
• Diagnosing a declining wellhead or gathering pressure: as suction falls at fixed discharge, the ratio climbs even though nothing about the discharge side changed.

Worked example

Take the duty this pack uses as its own anchor: a suction pressure of 100 psia and a discharge pressure of 900 psia, both absolute, both at the machine flanges.

The ratio that comes back is the number the rest of this cluster consumes. Read it as a statement about difficulty rather than about pressure: a duty in this range is firmly multi-stage territory, and the ratio is what says so — the same 800 psi of rise would be unremarkable if it started from a high enough suction.

Now hold the discharge at 900 psia and drop the suction to 50 psia. The rise falls by under six per cent and the ratio doubles. That asymmetry is why compression is quoted in ratio, and why a falling suction pressure is a far more serious operating change than a rising discharge pressure of the same size.

What each input represents

Assumptions and limits

• Both pressures are absolute (psia). A gauge reading entered here is not detected as such and produces a confidently wrong ratio.
• Both are taken at the machine flanges for the same operating case, not at different points or different times.
• This is the overall ratio across the whole machine, not the per-stage ratio unless the machine has one stage.
• The relation is purely geometric in the pressures. It knows nothing about the gas, the temperature or the machine type.

What the guards protect against

• Discharge pressure must exceed suction pressure. If it does not, the calculation is refused as a domain error rather than answered: a ratio at or below one describes expansion or no flow, and there is no compressor duty to size.
• Both pressures must be greater than zero. An absolute pressure cannot be zero or negative, which also catches a gauge reading near atmospheric entered as though it were absolute.
• Both are bounded to a range covering ordinary industrial service. A value outside it is refused rather than extrapolated, because a figure that far from the envelope is far more likely to be a unit mistake than a real duty.

Provenance

Standard compression relation, r = Pd / Ps on absolute pressures

Direct quotient of the declared discharge and suction pressures, both absolute, returning a dimensionless ratio.

Screening and reference material, to be checked against the governing standard and a qualified engineer; not a design determination. The signed pack carries its own citation, and the page reports the verification state of the release it mounted.