On Selecting the Intermediate Pressure in Two-stage Compressors

Abstract

The main way to improve the performance of compressors is subjecting the compressed gas to intermediate cooling. In calculating the pressure at which the gas is cooled, a formula for determining the geometric mean value of the inlet and outlet pressures is used. This formula was derived subject to the assumption that the gas temperatures at the inlet to the first and second compression stages are equal, and so are the internal relative efficiencies of the stages. It is also assumed that the pressure loss in the heat exchanger is negligibly small. However, these assumptions introduce an error, and the obtained value is not optimal. A new formula free from these assumptions is derived. With the gas temperatures at the inlets to the compressor first and second stages and their efficiencies being equal, and with the pressure loss being equal to zero, the new formula becomes identical with the commonly used one. The article presents calculations on determining the effects the gas temperatures and compression stage efficiencies have on the intermediate pressure optimal value. In particular (with the efficiencies of the stages being equal and provided that there is no throttling between them), the difference of temperatures upstream the stages equal to 1% (around 3 °C for atmospheric air) causes the intermediate pressure optimal value to alter by k⁄[2(k – 1)] %. For air at k = 1.4 this change makes around 1.75 %. The same change causes the efficiencies of the stages to differ by 1 %. Changing the throttling ratio by 1% causes the intermediate pressure optimal value to vary by 0.5%. A comparison between the results from intermediate pressure calculations carried out using the new formula and commonly applied one has shown that the obtained intermediate pressure optimal values differ from each other by more than 7%.