Compression Ratio & Multi-Stage Compression

What is the Compression Ratio?

The Compression Ratio ($R_c$) is arguably the single most important parameter in compressor design. It is simply the ratio of the absolute discharge pressure to the absolute suction pressure:

$$ R_c = \frac{P_{discharge}}{P_{suction}} $$

Warning: You MUST use absolute pressure (psia or bar a). If you use gauge pressure, your ratio will be mathematically meaningless!

If a compressor takes atmospheric air (1.0 bar a) and squeezes it to 5.0 bar a, the compression ratio is exactly 5.0.

The Thermodynamic Limit of a Single Stage

In an ideal world, you could use a single compressor to take gas from 1 bar and blast it to 100 bar (a ratio of 100). In the real world, doing this will literally melt the compressor casing.

As gas is compressed, its temperature skyrockets. The discharge temperature is exponentially related to the Compression Ratio (as dictated by the isentropic relation $\frac{T_2}{T_1} = (R_c)^{\frac{k-1}{k}}$).

For standard industrial compressors, metallurgical limits on the rotor, casing, and synthetic lubricating oils restrict the absolute maximum discharge temperature to around 150°C to 170°C (300°F - 340°F).

Because of this strict temperature limit, the Compression Ratio for a single stage is practically limited:

• Centrifugal Compressors: $R_c$ is limited to about 2.0 to 3.0 per stage. (Higher ratios require impellers to spin so fast the tips exceed the speed of sound, causing destructive shockwaves).
• Reciprocating Compressors: $R_c$ is limited to about 3.0 to 5.0 per cylinder (due to discharge temperature limits).

The Solution: Multi-Stage Compression

If a natural gas plant needs to compress gas from 1 bar to 64 bar, it cannot do it in one step. It must be split into multiple stages.

To minimize the total power required, engineers design multi-stage compressors so that the compression ratio is exactly equal across all stages.

$$ R_c = \sqrt[N]{\frac{P_{final}}{P_{initial}}} $$

Where $N$ is the number of stages.

For our example (1 bar to 64 bar), let's try 3 stages ($N=3$):

$$ R_c = \sqrt[3]{\frac{64}{1}} = 4.0 $$

The gas will be compressed from 1 bar $\rightarrow$ 4 bar (Stage 1), then 4 bar $\rightarrow$ 16 bar (Stage 2), then 16 bar $\rightarrow$ 64 bar (Stage 3).

Intercooling: The Secret to Efficiency

Between every single stage, the extremely hot gas must be routed through an Intercooler (a massive shell-and-tube heat exchanger or air-fin cooler) to drop its temperature back down to ambient (e.g., 40°C) before entering the next stage.

This cooling accomplishes two vital goals:

1. It resets the temperature, preventing the next stage from exceeding the 150°C metallurgical limit.
2. It drastically increases the density of the gas. Pumping cold, dense gas takes significantly less mechanical horsepower than pumping hot, expanded gas. Intercooling saves millions of dollars in electricity over the lifecycle of the plant.