06 - compressors

Chapter 6: Fans, Blowers, and CompressorsRules 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

InputsFluid Airflow rate m3/h at inlet conditions 500.0 Inlet pressure kPa-absolute 101.3 Inlet temperature C 25.0 Discharge pressure kPa-absolute 900.0 Number of stages 2

Intermediate Lookup Values and Calculations

Overall compression ratio 8.88 Compression ratio per stage 2.98 Gas constant R 8,314.47 MW 29.0 heat capacity ratio k 1.4 density at inlet kg/m3 1.19 mass flow rate kg/s 0.16

OutputsReciprocating Compressor - GPSA Shortcut Formula

C 0.013 F 1.08 R 2.98 N 2 Q m3/h at 100 kPa 506.5 Adjustment for high speed compressor (see text) 0.1

Brake Power (shaft power) kW 46.6

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

See Text for values

Air Aircfm at inlet conditions 294.0 422psia 14.7 14.7F 77.0 77psia 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

InputsFluid Airflow rate m3/h at inlet conditions 500.0 500.0 Inlet pressure kPa-absolute 101.3 206.8 Inlet temperature C 25.0 40.2 Discharge pressure kPa-absolute 900.0 900.0 Number of stages 2 3 Intercooler temperature approaC 5 5 Polytropic Efficiency 0.70 0.70

Intermediate Lookup Values and Calculations

Overall compression ratio 8.88 4.35 Compression ratio per stage 2.98 1.63 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 0.16 0.50

Outputs

Stage 1Compressibility factor using Redlich-Kwong EOS

Inlet compressibility Z #VALUE! #VALUE!Discharge compressibility #VALUE! #VALUE!Average compressibility #VALUE! #VALUE!

Polytropic compressionPolytropic exponent n 1.69 1.69 Stage discharge pressure kPa-absolute 301.94 337.64 Discharge temperature C 192 110 Polytropic head kN-m/kg #VALUE! 31.07 Polytropic gas power kW #VALUE! 22.27



Polytropic compressionPolytropic exponent n 1.69 1.69

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

Stage inlet temperature C 30.00 45.18 Stage inlet density kg/m3 3.47 5.80 Stage discharge pressure kPa-absolute 900.00 551.25 Discharge temperature C 200 116 Polytropic head kN-m/kg #VALUE! 31.57 Polytropic gas power kW #VALUE! 22.62



Polytropic compressionPolytropic exponent n 1.69 1.69 Stage inlet temperature C 30.00 45.18 Stage inlet density kg/m3 10.35 9.48 Stage discharge pressure kPa-absolute 2,682.62 900.00 Discharge temperature C 200 116 Polytropic head kN-m/kg #VALUE! 31.57 Polytropic gas power kW - 22.62

Total gas power kW #VALUE! 67.51 Add for mechanical losses kW #VALUE! 5.39

Brake power (shaft power) kW #VALUE! 72.91

Aircfm 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 #VALUE!#VALUE!#VALUE!

n 1.69 psia 43.80 F 379 ft-lbf/lbm #VALUE!hp #VALUE!

Z #VALUE!#VALUE!#VALUE!

n 1.69

F 87.00 lb/ft3 0.22 psia 130.50 F 394 ft-lbf/lbm #VALUE!hp #VALUE!

#VALUE!#VALUE!#VALUE!

n 1.69 F 87.00 lb/ft3 0.64 psia 388.83 F 394 ft-lbf/lbm #VALUE!hp -

hp #VALUE!hp #VALUE!

hp #VALUE!

InputsFluid Airflow rate m3/h at inlet conditions 500.0 Inlet pressure kPa-absolute 101.5 Inlet temperature C 25.0 Discharge pressure kPa-absolute 900.0 Number of stages 2 Intercooler temperatu C 5 Isentropic Efficiency 0.80

Intermediate CalculationOverall compression ratio 8.87 Compression ratio per stage 2.98 Density kg/m3 1.19

ResultsEnthalpy of CompressikJ/kg 291.52 Work kJ/h 173,083

kW 48.08

Mechanical losses in the compressor 4.71 Shaft power kW 52.79

Stage-by-Stage Calculations by Interpolating the P-E DataPoint Pressure Enthalpy TemperaturEntropy Comment

1 1.02 298.43 25.00 6.86 Inlet conditionsStage 1 2 3.02 417.78 143.32 6.88 Compress with constant entropy

3 3.02 447.61 177.25 Apply isentropic compression efficiency4 3.02 302.87 30.00 6.56 Cool with intercooler

Stage 2 5 9.00 416.74 142.87 6.56 Compress with constant entropy6 9.00 445.20 174.83 Apply isentropic compression efficiency7 9.00 301.67 30.00 6.24 Cool with intercooler

Stage 3 8 26.80 393.44 121.09 6.20 Compress with constant entropy9 26.80 416.38 144.84 Apply isentropic compression efficiency

10 26.80 297.47 30.00 5.92 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 350Pressure Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy

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

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 P-E tables are interpolated to:a) 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 chart expanded to encompass the full range of enthalpy data, click the "Reset Chart Area" button.

Result

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

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 pressuresStage 1 3.022416 198.3255 218.6317 238.9379 259.1753 279.444 299.68149 350.2189Stage 2 9 195.58 216.404 236.9736 257.528 277.9976 298.4672 349.3216Stage 3 26.79975 191.6445 213.2556 234.14 255.1667 275.9511 296.73556 348.0622

Pressure Entropy Entropy Entropy Entropy Entropy Entropy Entropybar 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 7.0265 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 6.36120 5.568 5.672 5.765 5.849 5.927 5.998 6.15840 5.33 5.444 5.543 5.632 5.712 5.786 5.9560 5.174 5.298 5.404 5.497 5.581 5.657 5.82480 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 5.661150 4.757 4.919 5.051 5.161 5.257 5.343 5.525200 4.631 4.796 4.932 5.048 5.149 5.238 5.426250 4.544 4.706 4.843 4.961 5.064 5.155 5.348300 4.48 4.637 4.773 4.891 4.995 5.088 5.283400 4.386 4.537 4.669 4.786 4.89 4.983 5.181500 4.317 4.463 4.593 4.708 4.811 4.905 5.103600 2.263 4.406 4.533 4.646 4.749 4.842 5.041800 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 TablePressure Interpolatio TemperaturInterpolation Compression enthalpy

1 0.009251Compress with constant entropy 1 0.687232Apply isentropic compression efficiency 8 0.503986 149.18

1 0.687232Compress with constant entropy 2 0.847997Apply isentropic compression efficiency 8 0.479819 142.34

2 0.847997Compress with constant entropy 2 2.42222Apply isentropic compression efficiency 8 0.179888 -

4 0.42222

400 500 600 800 1000 1200 1400 1600 1800Enthalpy 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

Add these values together for total enthalpy of compression

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 P-E tables are interpolated to:a) 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 chart expanded to encompass the full range of enthalpy data, click the "Reset Chart Area" button.

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 2,017.0 400.2 502.9 607.3 822.7 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

400.9251 503.2626 607.4313 822.5687 1046.869 1278.68723 1515.687 1764 2017400.2912 502.9456 607.3152 822.6848 1047.154 1279 1516 1764.848 2017.848399.3467 502.4733 607.1578 822.8422 1047.627 1279 1516 1766.422 2019.422

Entropy Entropy Entropy Entropy Entropy Entropy Entropy Entropy EntropykJ/(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 8.6956.698 6.927 7.116 7.426 7.676 7.887 8.069 8.233 8.2336.497 6.727 6.917 7.226 7.477 7.688 7.87 8.034 8.0346.295 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 7.6365.967 6.202 6.396 6.708 6.96 7.172 7.355 7.52 7.525.878 6.116 6.311 6.624 6.877 7.089 7.273 7.437 7.4375.807 6.048 6.244 6.559 6.812 7.024 7.208 7.373 7.3735.677 5.922 6.121 6.439 6.693 6.906 7.092 7.256 7.2565.581 5.831 6.033 6.353 6.608 6.822 7.009 7.173 7.1735.506 5.76 5.963 6.286 6.542 6.757 6.944 7.108 7.1085.443 5.7 5.906 6.23 6.488 6.703 6.891 7.056 7.2065.344 5.605 5.813 6.142 6.401 6.618 6.808 6.972 7.1235.267 5.531 5.741 6.072 6.333 6.55 6.743 6.907 7.0585.205 5.47 5.681 6.014 6.277 6.495 6.69 6.854 7.0055.108 5.374 5.586 5.922 6.136 6.407 6.605 6.769 6.9215.034 5.3 5.513 5.85 6.115 6.337 6.539 6.703 6.856

Interpolation of the Enthalpy Data Table

Interpolation

Constant Temperature2000 2500 298.15 416.4657 303.15 416.02 303.15 394.24

Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy EnthalpykJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg kJ/kg

Add these values together for total enthalpy of compression

0 50 100 150 200 250 300 350 400 4501

10

Enthalpy-Pressure Diagram for Air

Enthalpy, kJ/kg

Pre

ssu

re,

bar

, ab

solu

te

2,279.0 3,011.0 298.4 418.0 303.5 417.6 303.5 395.4 2,278.0 2,981.0 297.5 417.7 302.6 417.2 302.6 394.9 2,279.0 2,974.0 296.4 417.1 301.5 416.7 301.5 394.3 2,279.0 2,970.0 294.1 416.1 299.3 415.6 299.3 393.2 2,281.0 2,969.0 289.7 414.2 295.0 413.7 295.0 391.0 2,284.0 2,969.0 283.5 411.6 289.1 411.1 289.1 387.8 2,285.0 2,971.0 281.6 410.7 287.2 410.2 287.2 386.9 2,288.0 2,972.0 277.7 409.0 283.5 408.6 283.5 385.0 2,294.0 2,977.0 269.5 405.6 275.5 405.1 275.5 381.0 2,299.0 2,982.0 263.1 403.0 269.3 402.5 269.3 377.8 2,304.0 2,988.0 258.3 401.0 264.7 400.5 264.7 375.5 2,310.0 2,993.0 255.2 399.8 261.7 399.3 261.7 374.0 2,321.0 3,004.0 252.3 399.2 258.9 398.7 258.9 373.0 2,332.0 3,015.0 252.9 400.7 259.5 400.2 259.5 374.2 2,343.0 3,026.0 255.6 403.7 262.2 403.2 262.2 377.1 2,365.0 3,049.0 264.8 413.3 271.4 412.8 271.4 386.6 2,386.0 3,071.0 277.1 424.7 283.5 424.2 283.5 398.0

2278.313 2990.3832278.848 2975.0642280.422 2964.044

Entropy Entropy Entropy Entropy Entropy Entropy Entropy EntropykJ/(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 7.199 6.881 7.198 6.881 7.145 8.52 8.832 6.400 6.736 6.416 6.735 6.416 6.682

8.321 8.63 6.198 6.535 6.214 6.534 6.214 6.481 8.121 8.428 5.991 6.332 6.008 6.331 6.008 6.279 7.922 8.229 5.779 6.128 5.796 6.127 5.796 6.074 7.806 8.112 5.650 6.006 5.668 6.005 5.668 5.951 7.723 8.029 5.555 5.917 5.573 5.916 5.573 5.861 7.659 7.964 5.479 5.847 5.497 5.846 5.497 5.790 7.543 7.848 5.335 5.717 5.354 5.716 5.354 5.659

7.46 7.765 5.230 5.622 5.250 5.621 5.250 5.563 7.396 7.701 5.147 5.548 5.167 5.547 5.167 5.488 7.344 7.648 5.079 5.485 5.100 5.484 5.100 5.425 7.261 7.566 4.974 5.387 4.995 5.386 4.995 5.325 7.196 7.501 4.896 5.310 4.917 5.309 4.917 5.248 7.144 7.449 4.833 5.249 4.855 5.247 4.855 5.186

7.06 7.366 4.736 5.152 4.757 5.151 4.757 5.089 6.995 7.302 4.664 5.078 4.684 5.077 4.684 5.015

Temperature 5 8 6 8 6 7Interpolation 0.9075 0.164657 0.063 0.1602 0.063 0.884837

Interpolation

Constant Entropy 303.15 6.860 6.880 6.561 6.564 6.245 6.20 Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy Enthalpy

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

0 50 100 150 200 250 300 350 400 4501

10

Enthalpy-Pressure Diagram for Air

Enthalpy, kJ/kg

Pre

ssu

re,

bar

, ab

solu

te

303.5 297.2 303.4 220.3 221.0 #N/A #N/A 302.6 473.4 482.4 349.4 350.5 254.5 242.3 301.5 576.2 587.2 428.9 430.3 311.5 295.8 299.3 707.3 721.3 524.5 526.1 380.2 361.7 295.0 854.5 872.5 639.2 641.3 466.3 444.2 289.1 960.7 978.8 722.0 724.2 523.9 497.6 287.2 1036.2 1054.9 781.3 783.5 570.3 543.3 283.5 1105.6 1127.8 827.9 830.6 607.0 579.9 275.5 1239.7 1261.9 937.4 940.2 692.6 658.3 269.3 1343.0 1368.7 1016.8 1019.6 754.4 720.1 264.7 1430.6 1456.5 1083.2 1086.6 803.4 769.1 261.7 1502.8 1528.6 1146.0 1149.4 847.6 810.3 258.9 1632.4 1663.4 1247.8 1251.2 931.5 887.3 259.5 1742.0 1773.1 1332.2 1336.1 999.5 955.2 262.2 1834.7 1868.9 1408.9 1412.8 1056.5 1012.4 271.4 1998.4 2032.5 1533.5 1537.3 1196.2 1152.2 283.5 2129.2 2167.6 1640.9 1645.8 1255.0 1201.1

Entropy TemperaturekJ/(kg-C) deg K deg K deg K deg K deg K deg K 6.881 296.90 303.05 220.52 221.22 #N/A #N/A 6.416 470.88 479.68 349.46 350.51 255.76 243.73 6.214 570.17 580.77 427.95 429.29 312.93 297.52 6.008 692.81 705.77 521.07 522.64 381.60 363.62 5.796 827.34 843.40 629.77 631.75 466.35 445.20 5.668 920.89 936.88 705.95 707.93 521.96 497.15 5.573 986.81 1,003.27 759.93 761.90 565.95 540.67 5.497 1,045.58 1,064.59 801.81 804.25 600.38 575.16 5.354 1,157.10 1,176.03 896.29 898.72 677.73 646.73 5.250 1,240.98 1,262.53 963.36 965.78 732.25 701.44 5.167 1,310.50 1,332.05 1,017.94 1,020.81 774.36 743.84 5.100 1,367.36 1,388.79 1,068.18 1,071.05 811.31 778.59 4.995 1,463.80 1,488.37 1,147.73 1,150.58 879.22 841.16 4.917 1,543.07 1,567.64 1,211.70 1,214.90 932.26 894.49 4.855 1,608.37 1,635.06 1,267.99 1,271.15 975.36 937.88 4.757 1,720.15 1,746.67 1,355.85 1,358.96 1,080.14 1,043.77 4.684 1,806.21 1,835.20 1,427.18 1,430.94 1,116.75 1,072.35

60.063

06 - compressors

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