Examples
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 |
