06 - Compressors

Chapter 6: Fans, Blowers, and Compressors

Rules of Thumb for Chemical Engineers, 5th Edition

by Stephen Hall

This Excel workbook includes Visual Basic for Application function subroutines.

Macros must be enabled for them to work.

The following Text Boxes contain the syntax for the functions.

Copy them to the worksheet where you want to use the functions for ready reference.

Function ZSI(P, T, Pc, Tc) ' calculates compressibility factor, Z, using SI units ' P = gas pressure, kPa ' T = gas temperature, C ' Pc = gas pseudo-critical pressure, atm ' Tc = gas pseudo-critical temperature, C

Function ZUS(P, T, Pc, Tc) ' calculates compressibility factor, Z, using US units ' P = gas pressure, psia ' T = gas temperature, F ' Pc = gas pseudo-critical pressure, psia ' Tc = gas pseudo-critical temperature, F

Inputs

Fluid Air

flow rate m3/h at inlet conditions 52.9

Inlet pressure kPa-absolute 100.0

Inlet temperature C 25.0

Discharge pressure kPa-absolute 103.0

Number of stages 1

Intermediate Lookup Values and Calculations

Overall compression ratio 1.03

Compression ratio per stage 1.03

Gas constant R 8,314.47

MW 29.0

heat capacity ratio k 1.4

density at inlet kg/m3 1.17

mass flow rate kg/s 0.02

Outputs

Reciprocating Compressor - GPSA Shortcut Formula

C 0.013

F 1.00

R 1.03

N 1

Q m3/h at 100 kPa 52.9

Adjustment for high speed compressor (see text) 0.1

Brake Power (shaft power) kW 0.8

Problem Statement: Calculate the shaft (brake) power of a reciprocating compressor

See Text for values

Air Air

cfm at inlet conditions 294.0 422

psia 14.7 14.7

F 77.0 77

psia 130.5 140

2 2

8.88 9.52

2.98 3.09

10.73 10.73

29.0 29.0

1.4 1.4

lb/ft3 0.074 0.074 density = (P M) / (R T)

lb/s 0.36 0.52

0.030 0.030

1.08 1.08

2.98 3.09

2 2

cfm at 14.5 psia 298.1 427.8

0.1 0.2

hp 63 103

kw 47.22 76.59

motor efficiency 0.949

80.70

nnppTT 11212

Inputs

Fluid Air

flow rate m3/h at inlet conditions 52.6 52.6

Inlet pressure kPa-absolute 101.3 206.8

Inlet temperature C 25.0 40.2

Discharge pressure kPa-absolute 125.0 125.0

Number of stages 2 3

Intercooler temperature approachC 5 5

Polytropic Efficiency 0.70 0.70

Intermediate Lookup Values and Calculations

Overall compression ratio 1.23 0.60

Compression ratio per stage 1.11 0.85

Gas constant R 8,314.47 8,314.47

MW 29.0 45.5

Critical pressure atm 39.0 41.5

Critical temperature C (140.0) 101.9

heat capacity ratio k 1.4 1.4

density at inlet kg/m3 1.19 3.61

mass flow rate kg/s 0.02 0.05

Outputs

Stage 1

Compressibility factor using Redlich-Kwong EOS

Inlet compressibility Z 0.9995 0.9716

Discharge compressibility 0.9996 0.9709

Average compressibility 0.9996 0.9712

Polytropic compression

Polytropic exponent n 1.69 1.69

Stage discharge pressure kPa-absolute 112.53 174.85

Discharge temperature C 38 19

Polytropic head kN-m/kg 9.18 (9.29)

Polytropic gas power kW 0.23 (0.70)

Stage 2







Stage inlet temperature C 30.00 45.18

Stage inlet density kg/m3 1.29 3.01

Problem Statement: Calculate the hydraulic and shaft (brake) power of a compressor




Polytropic gas power kW 0.23 (0.71)

Stage 3







Stage inlet temperature C 30.00 45.18

Stage inlet density kg/m3 1.44 2.54




Polytropic gas power kW - (0.71)

Total gas power kW 0.46 (2.12)

Add for mechanical losses kW 0.73 #NUM!

Brake power (shaft power) kW 1.19 #NUM!

Air

cfm at inlet conditions 294.0

psia 14.7

F 77.0

psia 130.5

2

F 10

0.70

8.88

2.98

10.73

29.0

psia 573.0

F (220.0)

1.4

lb/ft3 0.074

lb/s 0.36

Z 0.9995

1.0005

1.0000

n 1.69

psia 43.80

F 379

ft-lbf/lbm 39,349

hp 37.06

Z 0.9988

1.0015

1.0001

n 1.69

F 87.00

lb/ft3 0.22

QNRFCPowerBrake

psia 130.50

F 394

ft-lbf/lbm 40,088

hp 37.75

0.9964

1.0048

1.0006

n 1.69

F 87.00

lb/ft3 0.64

psia 388.83

F 394

ft-lbf/lbm 40,108

hp -

hp 74.81

hp 5.62

hp 80.43

Inputs

Fluid Air

flow rate m3/h at inlet conditions 52.9

Inlet pressure kPa-absolute 101.5

Inlet temperature C 25.0

Discharge pressure kPa-absolute 125.0

Number of stages 2

Intercooler temperature approachC 5

Isentropic Efficiency 0.80

Intermediate Calculation

Overall compression ratio 1.23

Compression ratio per stage 1.11

Density kg/m3 1.19

Results

Enthalpy of CompressionkJ/kg 31.58

Work kJ/h 1,984

kW 0.55

Mechanical losses in the compressor 0.79

Shaft power kW 1.34

Stage-by-Stage Calculations by Interpolating the P-E Data

Point Pressure Enthalpy TemperatureEntropy Comment

1 1.02 298.43 25.00 6.86 Inlet conditions

Stage 1 2 1.13 310.08 36.62 6.87 Compress with constant entropy

3 1.13 313.00 40.61 Apply isentropic compression efficiency

4 1.13 303.41 30.00 6.85 Cool with intercooler



7 1.25 303.35 30.00 6.82 Cool with intercooler



10 1.39 303.29 30.00 6.79 Cool with aftercooler

Data Source: Perry's Chemical Engineers' Handbook, 6th Edition, Table 3-212

Fluid: Air

Temperature deg K 200 220 240 260 280 300 350

Pressure Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy

bar kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg

1 199.7 219.8 239.9 260.0 280.2 300.3 350.7

5 197.7 218.1 238.5 258.8 279.1 299.4 350.0

Problem Statement: Calculate the shaft (brake) power of a compressor by interpolating the Pressure-Enthalpy data table

The data tables give enthalpy and entropy at pressure and temperature combinations. Values are in RED text; these are the values to change to enter data for a different ccompound. Beginning with the compressor inlet pressure and temperature, the Pa) follow a constant entropy path from inlet conditions to the stage discharge pressureb) increase the temperature, at constant pressure, by applying the isentropic efficiency to the amount of enthalpy gain in (a) c) capture the enthalpy change for the staged) cool the gas to a temperature near the inlet temperature; this is performed at constant pressuree) look up the new enthalpyf) repeat for stages 2 and 3 The x and y scales on the chart adjust automatically to fit the pressure range entered in the Input section. To see the chartexpanded to encompass the full range of enthalpy data, click the "Reset Chart Area" button.

Result

10 195.2 216.1 236.7 257.3 277.8 298.3 349.2

20 190.1 211.9 233.2 254.3 275.2 296.0 347.7

40 179.7 203.5 226.3 248.5 270.2 291.7 344.6

60 163.9 191.1 216.1 240.0 263.1 285.6 340.4

80 158.7 187.1 212.9 237.3 260.8 283.7 339.0

100 148.8 179.4 206.7 232.2 256.4 279.9 336.5

150 129.2 163.2 193.4 221.0 247.0 271.8 330.9

200 117.6 152.2 183.6 212.5 239.6 265.5 326.5

250 111.7 145.6 177.1 206.6 234.3 260.8 323.2

300 109.0 142.0 173.2 202.7 230.8 257.7 320.9

400 108.5 140.1 170.5 199.7 227.8 254.8 319.1

500 111.4 142.0 171.7 200.5 228.4 255.4 319.9

600 116.0 146.1 175.3 203.6 231.2 258.1 322.6

800 157.4 185.9 213.7 240.3 267.3 331.6

1000 226.4 253.2 279.5 343.4

Interpolated Enthalpy at stage discharge pressures

Stage 1 1.126388 199.5521 219.6743 239.7965 259.9113 280.1187 300.23345 350.6482

Stage 2 1.25 199.4227 219.5643 239.7059 259.8336 280.0475 300.17522 350.6029

Stage 3 1.387177 199.2933 219.4543 239.6153 259.756 279.9763 300.11699 350.5577

Pressure Entropy Entropy Entropy Entropy Entropy Entropy Entropy

bar kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C)

1 6.463 6.559 6.647 6.727 6.802 6.871 7.026

5 5.994 6.092 6.18 6.262 6.337 6.406 6.563

10 5.786 5.885 5.975 6.058 6.134 6.204 6.361

20 5.568 5.672 5.765 5.849 5.927 5.998 6.158

40 5.33 5.444 5.543 5.632 5.712 5.786 5.95

60 5.174 5.298 5.404 5.497 5.581 5.657 5.824

80 5.051 5.186 5.299 5.396 5.484 5.562 5.733

100 4.949 5.095 5.214 5.315 5.406 5.486 5.661

150 4.757 4.919 5.051 5.161 5.257 5.343 5.525

200 4.631 4.796 4.932 5.048 5.149 5.238 5.426

250 4.544 4.706 4.843 4.961 5.064 5.155 5.348

300 4.48 4.637 4.773 4.891 4.995 5.088 5.283

400 4.386 4.537 4.669 4.786 4.89 4.983 5.181

500 4.317 4.463 4.593 4.708 4.811 4.905 5.103

600 2.263 4.406 4.533 4.646 4.749 4.842 5.041

800 4.318 4.442 4.553 4.653 4.745 4.943

1000 4.482 4.582 4.672 4.869

Entry Point into Table and Interpolation Ratio Interpolation of the Enthalpy Data Table

Pressure InterpolationTemperatureInterpolation Compression enthalpy

1 0.009251

Compress with constant entropy 1 0.073949

Apply isentropic compression efficiency 6 0.275102 14.56

1 0.073949


Apply isentropic compression efficiency 6 0.427286 17.02

1 0.138647


Apply isentropic compression efficiency 6 0.464601 -

1 0.203345

400 500 600 800 1000 1200 1400 1600 1800

Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy

kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg

401.2 503.4 607.5 822.5 1,046.8 1,278.0 1,515.0 1,764.0 2,017.0

400.8 503.2 607.4 822.6 1,046.9 1,279.0 1,516.0 1,764.0 2,017.0

Add these values together for total enthalpy of compression

Enthalpy data table

The data tables give enthalpy and entropy at pressure and temperature combinations. Values are in RED text; these are the values to change to enter data for a different ccompound.

Beginning with the compressor inlet pressure and temperature, the P-E tables are interpolated to: a) follow a constant entropy path from inlet conditions to the stage discharge pressure b) increase the temperature, at constant pressure, by applying the isentropic efficiency to the amount of enthalpy gain in

c) capture the enthalpy change for the stage d) cool the gas to a temperature near the inlet temperature; this is performed at constant pressure e) look up the new enthalpy f) repeat for stages 2 and 3

The x and y scales on the chart adjust automatically to fit the pressure range entered in the Input section. To see the chart expanded to encompass the full range of enthalpy data, click the "Reset Chart Area" button.

400.2 502.9 607.3 822.7 1,047.2 1,279.0 1,516.0 1,765.0 2,018.0

399.1 502.4 607.2 823.0 1,047.7 1,280.0 1,517.0 1,766.0 2,019.0

397.0 501.5 606.9 823.7 1,048.8 1,281.0 1,519.0 1,768.0 2,021.0

394.0 500.6 606.8 824.3 1,050.0 1,283.0 1,521.0 1,770.0 2,023.0

393.1 499.8 606.7 825.1 1,051.1 1,284.0 1,522.0 1,772.0 2,025.0

391.3 499.0 606.6 825.8 1,052.4 1,286.0 1,524.0 1,774.0 2,027.0

387.5 497.5 606.6 827.8 1,055.5 1,290.0 1,529.0 1,779.0 2,033.0

384.5 496.6 607.0 829.9 1,058.7 1,294.0 1,533.0 1,783.0 2,038.0

382.3 496.0 607.6 832.2 1,062.0 1,298.0 1,538.0 1,789.0 2,043.0

380.9 495.9 608.5 834.5 1,065.3 1,302.0 1,542.0 1,794.0 2,049.0

380.0 496.8 611.0 839.4 1,072.0 1,310.0 1,552.0 1,804.0 2,059.0

381.3 499.1 614.3 844.6 1,078.8 1,318.0 1,561.0 1,814.0 2,070.0

384.2 502.6 618.5 850.1 1,085.5 1,326.0 1,570.0 1,824.0 2,080.0

393.8 512.3 625.8 862.0 1,099.3 1,341.0 1,588.0 1,844.0 2,101.0

405.1 524.4 641.2 875.1 1,113.3 1,356.0 1,606.0 1,863.0 2,121.0

401.1704 503.3852 607.4926 822.5074 1046.807 1278.07395 1515.074 1764 2017

401.1445 503.3723 607.4861 822.5139 1046.814 1278.13865 1515.139 1764 2017

401.1187 503.3593 607.4797 822.5203 1046.82 1278.20334 1515.203 1764 2017

Entropy Entropy Entropy Entropy Entropy Entropy Entropy Entropy Entropy

kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C)

7.161 7.389 7.579 7.888 8.138 8.349 8.531 8.695 8.695

6.698 6.927 7.116 7.426 7.676 7.887 8.069 8.233 8.233

6.497 6.727 6.917 7.226 7.477 7.688 7.87 8.034 8.034

6.295 6.52 6.716 7.027 7.277 7.489 7.671 7.835 7.835

6.09 6.323 6.515 6.826 7.077 7.289 7.473 7.636 7.636

5.967 6.202 6.396 6.708 6.96 7.172 7.355 7.52 7.52

5.878 6.116 6.311 6.624 6.877 7.089 7.273 7.437 7.437

5.807 6.048 6.244 6.559 6.812 7.024 7.208 7.373 7.373

5.677 5.922 6.121 6.439 6.693 6.906 7.092 7.256 7.256

5.581 5.831 6.033 6.353 6.608 6.822 7.009 7.173 7.173

5.506 5.76 5.963 6.286 6.542 6.757 6.944 7.108 7.108

5.443 5.7 5.906 6.23 6.488 6.703 6.891 7.056 7.206

5.344 5.605 5.813 6.142 6.401 6.618 6.808 6.972 7.123

5.267 5.531 5.741 6.072 6.333 6.55 6.743 6.907 7.058

5.205 5.47 5.681 6.014 6.277 6.495 6.69 6.854 7.005

5.108 5.374 5.586 5.922 6.136 6.407 6.605 6.769 6.921

5.034 5.3 5.513 5.85 6.115 6.337 6.539 6.703 6.856

Interpolation of the Enthalpy Data Table

Interpolation

Constant Temperature

2000 2500 298.15 309.7686 303.15 316.704 303.15 318.21

Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy

kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg

2,279.0 3,011.0 298.4 310.1 303.5 317.1 303.5 318.7

2,278.0 2,981.0 297.5 309.3 302.6 316.3 302.6 317.8

Add these values together for total enthalpy of

1

10

100

1000

0 500 1000 1500 2000 2500

Pre

ss

ure

, b

ar,

ab

so

lute

Enthalpy, kJ/kg

Enthalpy-Pressure Diagram for Air

2,279.0 2,974.0 296.4 308.2 301.5 315.3 301.5 316.8

2,279.0 2,970.0 294.1 306.1 299.3 313.3 299.3 314.8

2,281.0 2,969.0 289.7 302.0 295.0 309.4 295.0 311.0

2,284.0 2,969.0 283.5 296.3 289.1 303.9 289.1 305.6

2,285.0 2,971.0 281.6 294.5 287.2 302.2 287.2 303.8

2,288.0 2,972.0 277.7 291.0 283.5 298.8 283.5 300.5

2,294.0 2,977.0 269.5 283.3 275.5 291.5 275.5 293.3

2,299.0 2,982.0 263.1 277.4 269.3 285.9 269.3 287.7

2,304.0 2,988.0 258.3 273.0 264.7 281.6 264.7 283.5

2,310.0 2,993.0 255.2 270.0 261.7 278.8 261.7 280.7

2,321.0 3,004.0 252.3 267.4 258.9 276.3 258.9 278.2

2,332.0 3,015.0 252.9 268.0 259.5 276.9 259.5 278.9

2,343.0 3,026.0 255.6 270.7 262.2 279.6 262.2 281.6

2,365.0 3,049.0 264.8 279.9 271.4 288.8 271.4 290.7

2,386.0 3,071.0 277.1 292.0 283.5 300.8 283.5 302.8

2278.926 3008.782

2278.861 3006.841

2278.797 3004.9

Entropy Entropy Entropy Entropy Entropy Entropy Entropy Entropy

kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C) kJ/(kg-C)

8.983 9.308 6.865 6.901 6.881 6.923 6.881 6.927

8.52 8.832 6.400 6.437 6.416 6.458 6.416 6.463

8.321 8.63 6.198 6.235 6.214 6.256 6.214 6.261

8.121 8.428 5.991 6.029 6.008 6.051 6.008 6.056

7.922 8.229 5.779 5.818 5.796 5.841 5.796 5.846

7.806 8.112 5.650 5.690 5.668 5.713 5.668 5.718

7.723 8.029 5.555 5.595 5.573 5.619 5.573 5.624

7.659 7.964 5.479 5.520 5.497 5.544 5.497 5.550

7.543 7.848 5.335 5.379 5.354 5.404 5.354 5.409

7.46 7.765 5.230 5.275 5.250 5.301 5.250 5.306

7.396 7.701 5.147 5.193 5.167 5.219 5.167 5.225

7.344 7.648 5.079 5.126 5.100 5.153 5.100 5.159

7.261 7.566 4.974 5.022 4.995 5.049 4.995 5.055

7.196 7.501 4.896 4.944 4.917 4.971 4.917 4.977

7.144 7.449 4.833 4.881 4.855 4.908 4.855 4.914

7.06 7.366 4.736 4.784 4.757 4.811 4.757 4.817

6.995 7.302 4.664 4.710 4.684 4.738 4.684 4.744

Temperature 5 6 6 6 6 6

Interpolation 0.9075 0.195371 0.063 0.33408 0.063 0.364237

Interpolation

Constant Entropy

303.15 6.860 6.867 6.846 6.858 6.816 6.83

Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy

kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg

303.5 297.2 299.1 293.1 296.6 284.4 289.2

302.6 473.4 476.3 467.2 472.5 453.7 461.2

2500 3000 3500

301.5 576.2 579.8 568.5 575.1 552.0 561.2

299.3 707.3 711.9 697.7 706.0 676.8 688.4

295.0 854.5 860.4 842.0 852.8 816.9 830.0

289.1 960.7 966.6 948.2 959.0 921.3 936.3

287.2 1036.2 1042.1 1023.8 1034.5 996.9 1011.8

283.5 1105.6 1112.9 1090.3 1103.5 1057.2 1075.6

275.5 1239.7 1247.0 1224.4 1237.6 1191.3 1209.7

269.3 1343.0 1351.4 1325.2 1340.5 1287.7 1308.1

264.7 1430.6 1439.1 1412.7 1428.1 1374.1 1395.6

261.7 1502.8 1511.3 1485.0 1500.4 1446.7 1468.0

258.9 1632.4 1642.5 1611.0 1629.5 1564.8 1590.5

259.5 1742.0 1752.2 1720.5 1739.0 1674.1 1699.9

262.2 1834.7 1845.9 1812.2 1831.5 1765.6 1791.6

271.4 1998.4 2009.6 1974.8 1995.2 1924.0 1952.3

283.5 2129.2 2141.8 2104.8 2125.6 2054.1 2082.3

Entropy Temperature

kJ/(kg-C) deg K deg K deg K deg K deg K deg K

6.881 296.90 298.82 292.87 296.35 284.15 289.00

6.416 470.88 473.77 464.80 470.05 451.66 458.97

6.214 570.17 573.64 562.84 569.16 547.01 555.82

6.008 692.81 697.06 683.85 691.58 664.51 675.27

5.796 827.34 832.61 816.25 825.82 793.77 805.62

5.668 920.89 926.13 909.83 919.37 885.96 899.25

5.573 986.81 992.04 975.80 985.30 952.03 965.26

5.497 1,045.58 1,051.82 1,032.44 1,043.78 1,004.07 1,019.86

5.354 1,157.10 1,163.31 1,144.03 1,155.31 1,115.79 1,131.50

5.250 1,240.98 1,248.05 1,226.08 1,238.93 1,194.68 1,211.82

5.167 1,310.50 1,317.57 1,295.60 1,308.45 1,263.43 1,281.34

5.100 1,367.36 1,374.39 1,352.54 1,365.32 1,320.54 1,338.35

4.995 1,463.80 1,471.86 1,446.81 1,461.47 1,410.14 1,430.55

4.917 1,543.07 1,551.13 1,526.08 1,540.74 1,489.40 1,509.82

4.855 1,608.37 1,617.12 1,590.72 1,605.83 1,554.04 1,574.45

4.757 1,720.15 1,728.85 1,701.83 1,717.64 1,662.25 1,684.28

4.684 1,806.21 1,815.72 1,787.44 1,803.46 1,748.12 1,770.00

6

0.063

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06 - Compressors