Two-Stage Refrigeration Interstage Pressure

The interstage pressure that splits a two-stage compression equally, and the stage imbalance that setting it anywhere else produces. Compression work per stage follows the pressure RATIO rather than the pressure difference, so the total work is least when both stages carry the same ratio -- and equal ratios put the interstage at the GEOMETRIC mean of the two absolute pressures, sqrt(P_low x P_high), always below the arithmetic mean. On a plant at 15 psig suction and 185 psig discharge the geometric mean is 62.3 psig while the arithmetic mean is 100, and setting the interstage at that halfway point loads the booster with a ratio of 3.86 against the high stage's 1.74, an imbalance that shows up as a hot booster discharge. The equal-ratio optimum is a starting point rather than an answer. Real plants move the interstage deliberately: where there is a substantial intermediate-temperature load, the interstage is set at that load's saturation pressure instead, because feeding it from the intermediate beats pulling it down to the low stage and compressing it all the way back. Compressor selection pulls the setting too, since machines come in discrete sizes and matching real equipment beats matching a theoretical optimum. Pressures are ENTERED as gauge and converted at 14.7 psi; it does not select compressors, size an intercooler, compute discharge temperature, or evaluate whether two-staging is warranted at all. The compressor manufacturer's selection data and the refrigeration engineer of record govern.

interstage pressure = sqrt(P_low_absolute x P_high_absolute), the geometric mean, which makes the ratio equal in both stages; stage ratio = interstage / P_low = P_high / interstage; the arithmetic mean and the ratios it would produce are reported for contrast.

The equal-stage-ratio optimum for multistage compression as refrigeration practice states it. Gauge pressures are converted at the 14.7 psi standard atmosphere the trade uses. It does not select compressors, size an intercooler, compute discharge temperature, or judge whether two-staging is warranted.

One square root on two pressures the reader reads off a gauge.

Estimate. AHJ and licensed professional govern.

Field names used by the API: low_psig, high_psig, intermediate_load_psig, interstage_psia, interstage_psig, stage_ratio, single_stage_ratio, arithmetic_mean_psig

• Gauge to absolute at 14.7 psi the refrigeration convention, not the 14.696 standard atmosphererefrigeration gauge practice
• Equal ratios are the optimum true for ideal isentropic stages with perfect intercoolingthe compressor manufacturer's selection data
• It does not select machines compressors come in discrete sizes and matching real equipment beats matching a theoretical optimumthe refrigeration engineer of record