MoistAirTab™ Example 8 - Multiple Stage Compression
Example 8
Air at 80°F, 740 mm Hg pressure and 55% relative humidity is compressed to 10 atm (gauge) in a 3-stage air compressor. The isentropic efficiency of the air compressor for each stage is 85%. Cooler/condensers are used to reduce the stage discharge temperature to 80°F. The pressure drop for each cooler is 3 psi. The compressed air flowrate is 25,000 lb/hr.
- What is the discharge temperature of the compressor (before any cooling)?
- What is the total brake horsepower required?
Solution
The solution is presented below as a table generated from Excel. The gray shaded areas represent the input data.
| Solution: | | Inlet | 1st Stage | 2nd Stage | 3rd Stage | Overall |
| | | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |
| | Units | Ambient Air | 1st Stage Compressor Outlet | 1st Stage Condenser Outlet | 2nd Stage Compressor Outlet | 2nd Stage Condenser Outlet | 3rd Stage Compressor Outlet | 3rd Stage Condenser Outlet | Summary |
| Flow rate | lb/hr | 25,000 | 25,000 | 25,000 | 25,000 | 25,000 | 25,000 | 25,000 | 25,000 |
| Compression ratio | | | 2.24 | | 2.24 | | 2.24 | | 11.30 |
| Number of stages | | | | | | | | | 3 |
| Pressure | mm Hg | 740 | | | | | | | |
| | atm | 0.97 | 2.18 | 1.98 | 4.90 | 4.70 | 11.00 | 10.80 | |
| | psia | 14.31 | 32.11 | 29.11 | 72.05 | 69.05 | 161.67 | 158.67 | |
| | | | | | | | | | |
| Pressure drop | psia | | | 3.00 | | 3.00 | | 3.00 | |
| Temperature | °F | 80.00 | 240.09 | 80.00 | 247.80 | 80.00 | 284.08 | 80.00 | |
| Relative humidity | % | 55% | 2.5% | 100% | 4.3% | 100% | 2.2% | 100% | |
| Humidity ratio | lbw/lbdry air | 0.0124 | 0.0124 | 0.0111 | 0.0111 | 0.0047 | 0.0047 | 0.0021 | |
| Moisture condensed | lbw/hr | | | 32.76 | | 160.98 | | 65.31 | |
| | | | | | | | | | |
| Isentropic efficiency | | | 87% | | 87% | | 87% | | |
| Entropy of moist air | Btu/(lbdry air.°F) | 0.0517 | 0.0591 | -0.0008 | 0.0024 | -0.0743 | -0.0551 | -0.1379 | |
| Enthalpy of moist air | Btu/lbdry air | 25.15 | 64.57 | 23.61 | 64.80 | 16.28 | 65.89 | 12.82 | |
| | | | | | | | | | |
| Entropy (Ideal) | Btu/lbdry air | | 0.0517 | | -0.0008 | | -0.0743 | | |
| Enthalpy (Ideal) | Btu/lbdry air | | 59.44 | | 59.44 | | 59.44 | | |
| Enthalpy Difference (Ideal) | Btu/lbdry air | | 34.29 | | 35.83 | | 43.16 | | |
| Enthalpy Difference (Real) | Btu/lbdry air | | 39.41 | | 41.19 | | 49.61 | | |
| | | | | | | | | | |
| Specific volume of moist air | ft3/lbdry air | 14.25 | 8.24 | 6.99 | 3.71 | 2.91 | 1.72 | 1.26 | |
| Volumetric flow rate | ACFM | 5,936.19 | 3,432.58 | 2,911.20 | 1,544.19 | 1,213.91 | 717.38 | 525.23 | |
| | | | | | | | | | |
| Power Input | Btu/hr | | 985,361 | | 1,029,698 | | 1,240,239 | | |
| Brake Horsepower | HP | | 391.79 | | 409.42 | | 493.14 | | 1,294.35 |
| Condenser Duty | Btu/hr | | | (1,023,934) | | (1,212,869) | | (1,326,794) | |
| Temp rise in cooling water | oF | | | 15 | | 15 | | 15 | |
| Cooling water consumption | GPM | | | 1,138 | | 1,348 | | 1,474 | 3,960 |