Assigment

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1. Intro-Start Here

Compressibility Factor Calculator - Choice of U.S. or S.I. Units
Workbook Contents
Click on tabs at the bottom of the screen to access the following: NOTE: The cells containing formulas are locked (protected) to avoid the
possibility of inadvertently typing over any of the formulas. You may,
Tab 1. Contents (current tab) however, adjust the number of decimal places for any of the cells.
Tab 2. Compressibility Factor Calculator - U.S. Units
Tab 3. Compressibility Factor Calculator - S.I. Units Notes on the use of these worksheets:
1. Each of the compressibility factor calculator worksheets allows the user
to either select a gas from a dropdown menu list of 21 gases or else enter
the critical temperature and critical pressure of a gas. In either case the user
must enter the temperature and pressure of the gas.
Copyright © McGraw-Hill Global Education Holdings, LLC. All rights reserved.
2. The worksheet will calculate the compressibility factor of the gas at the
user specified temperature and pressure, using the Redlich-Kwong equation.
3. For accurate calculation of the compressibility factor with the Redlich-Kwong
equation, the reduced pressure should be less than half of the reduced
temperature. That is: P/Pc < T/(2Tc). The worksheet checks on this requirement
and advises changing either P or T if the requirement is not met.

2. U.S. Units

1. For calculations with one of the 21 gases listed in the table below, select the appropriate
Calculation of Gas Compressibility Factor - U.S. Units gas from the dropdown list in cell D12 and enter the gas temperature and pressure in
the indicated yellow cells. The gas critical temperature and critical pressure will be
shown below on this worksheet and those values will be used for calculation of the
FLUID SELECTION Either (i) select a Gas and enter its temperature and pressure in the indicated yellow cells compressibility factor of the gas.
below, so that its critical temperature and critical pressure will be obtained and used, or else,
(ii) enter those parameters in the yellow cells D35, & D50, and those values will be used. 2. For calculations with some other gas, not listed in the table below, the user must enter
values for the gas critical temperature and critical pressure in the indicated yellow
Select a Gas and Enter Temp. and Pressure (Enter Values in yellow cells only) cells in column D. Those user entered property values will be used for calculation of
the compressibility factor of the gas. The gas temperature and pressure must be
Click at right to Select Gas Methane entered in the yellow cells, D14 and D15.
NOTE: For accurate calculation of Z with
Gas Temperature (oF): -40 the Redlich Kwong equation, the reduced 3. For either a gas selected from the dropdown list or user entered gas properties,
Gas Pressure (psia): 400 pressure should be less than half of the the gas compressibility factor is calculated with the Redlich-Kwong Equation
reduced temperature. That is: P/Pc < T/(2Tc) For accurate results P and T values should be such that P/Pc < T/(2Tc).
Check on Gas Temperature and Gas Pressure Values entered above: The source for the Tc and Pc values in this table is:
Table 2-13.2 in Perry's Chemical Engineers' Handbook, 9th Ed.
Is P/Pc < T/(2Tc)? YES P/Pc = 0.600
T/2Tc = 0.612
The entered values for T and P above are ok.
Excel Vlookup results based on selected fluid:
343.0 667.0
CRITICAL TEMP. Critical Temperature from above menu selection: Tc, ºR Pc, psi
343.0 oR Acetylene 554.9 890.2
Air 238.4 547.4
NOTE: If you want to use a gas from the menu Ammonia 730.2 1636
above, then the yellow cell, D35, below must be blank. Argon 271.5 710.4
Butane 765.2 550.6
Use the Critical Temperature value above, OR Carbon Dioxide 547.6 1071
Carbon Monoxide 239.3 507.5
Enter a Critical Temperature obtained elsewhere Chlorine 750.9 1118
Ethane 549.6 706.6
Critical Temperature (oR): Ethylene 508.2 731.1
Helium 9.36 33.00
Critical Temp. Result: 343.0 oR (from menu selection) Hydrogen 59.7 190.4
(This is the Critical Temperature that will be used to calculate compressibility factor.) Hydrogen Chloride 584.4 1205.3
Hydrogen Sulfide 672.4 1300.0
CRITICAL PRESSURE Critical Pressure from above menu selection: Methane 343.0 667.0
667.0 psi Nitric Oxide 324.3 939.8
Nitrogen 227.2 493.1
NOTE: If you want to use a gas from the menu Oxygen 278.2 731.4
above, then the yellow cell, D50, below must be blank. Propane 665.7 616.1
Propylene 656.7 667.2
Use the Critical Pressure value above, OR Sulfur Dioxide 775.3 1143.5
Enter a Critical Pressure obtained elsewhere
Critical Pressure (psi): For the Redlich-Kwong Equation of State (used to calculate the compressibility factor, Z) see:
Handbook of Chemical Engineering Calculations, 4th Ed, Section 1.4. Redlich-Kwong Equation of State
Critical Pressure Result: 667.000 psi (from menu selection) One form of the Redlich-Kwong Eqn of State is:
(This is the Critical Pressure that will be used to calculate compressibility factor.) Where:
P = Gas pressure, atm
COMPRESSIBILITY FACTOR Calculation of Compressibility Factor of the Gas using the Redlich-Kwong Equation of State: T = Gas temperature, K
Tc = critical temperature of gas, K
(Note that P/Pc must be less than T/2Tc for accurate Redlich-Kwong Equation calculations.) Pc = critical pressure of gas, atm Note that the first and second forms of the R-K
V = molar volume of gas, cm3/gmole equation require the S.I. units shown. The third
R = Gas Law Constant, 82.05 atm cm3/gmole K form uses only TR and PR, so either U.S. or S.I.
Is P/Pc < T/(2Tc) ? YES If this answer is "NO", change P and/or T units may be used.
in cell(s) D14 and/or D15 above. A second form of the R-K Equation of State is:
Where:
Reduced Temperature, TR = 1.2235 Equation Constant, r = 6.574E-03 Z = Compressibility Factor
Reduced Pressure, PR = 0.5997 Equation Constant, q = -1.105E-01 T = Gas temperature, K
Equation Constant, D = 0.15481 Equation Constant, f = -2.228E-01 P = Gas pressure, atm
Equation Constant, E = 0.04247 Equation Constant, g = -4.380E-02 Tc = critical temperature of gas, K
Calculated Value of C = 7.006E-05 Pc = critical pressure of gas, atm
Z = 0.883 A third form of the Redlich-Kwong
Equation of State is:
Z1 =
Equation Constant, f = Z2 =
Z3 =
The third form of the Redlich-Kwong equation can be obtained by substituting V = ZRT/P (from the definition
of the compressibility factor, Z = PV/RT) into the first form of the Redlich-Kwong equation given above.
CALCULATION CHECK Calculation of Z using the 2nd Form of the R-K Equation with the value of Z calculated above:
The compressibility factor, Z, can be determined for specified gas temperature, pressure, critical temperature
and critical pressure using either the second form or the third form of the Redlich-Kwong equation, however
Equation Constant, A = 0.0056893 Equation Constant, B = 0.0015606 use of the second form requires an iterative calculation, while an explicit solution for Z can be obtained using
Equation Constant, h = 0.048078 the third form of the R-K equation (as the maximum real root of the cubic equation in Z).
The value for Z is calculated here by finding the maximum real root of the third form of the
Compressibility Factor, Z = 0.883 Redlich-Kwong equation as described at: www.polymath-software.com/ASEE2007/PDF1.pdf:
To find the maximum real root, first the parameter C is calculated, where C = (f/3)3 + (g/2)2, f = (-3q - 1)/3
Equations used for this and g = (-27r - 9q - 2)/27. If C > 0, there is one real root, Z = (-g/2 + C1/2)1/3 + (-g/2 - C1/2)1/3 + 1/3.
Calculation Check are:
If C < 0, then there are three real roots, given by: Zk = 2(-f/3)1/2cos[(f/3) + 2p(k-1)/3] + 1/3, k = 1,2,3
with f = cos-1{[(g2/4)/((-f3)/27)]1/2}
Note that the final calculation check made at the left using the more familiar second form of the Redlich-Kwong
Copyright © McGraw-Hill Global Education Holdings, LLC. All rights reserved. equation uses the value of Z calculated with the third form of the equation, so if the calculated value of Z is the
same, no iteration is required.
http://www.accessengineeringlibrary.com/browse/handbook-of-chemical-engineering-calculations-fourth-edition/c9780071768047ch01 http://www.accessengineeringlibrary.com/browse/handbook-of-chemical-engineering-calculations-fourth-edition/c9780071768047ch01?utm_source=Compressibility%20Factor&utm_medium=Excel&utm_content=HBChemEngCalc%201.4&utm_campaign=USUnits http://accessengineeringlibrary.com/browse/perrys-chemical-engineers-handbook-eighth-edition/p200139d89972_420001 http://accessengineeringlibrary.com/browse/perrys-chemical-engineers-handbook-eighth-edition/p200139d89822_421001 http://www.accessengineeringlibrary.com/browse/perrys-chemical-engineers-handbook-9th-edition/c9780071834087ch02lev1sec13?q=Critical+Constants&book=Perry%27s+Chemical+Engineers%27+Handbook%2C+9th+Edition

3. S.I. Units

1. For calculations with one of the 21 gases listed in the table below, select the appropriate
Calculation of Gas Compressibility Factor - S.I. Units gas from the dropdown list in cell D12 and enter the gas temperature and pressure in
the indicated yellow cells. The gas critical temperature and critical pressure will be
shown below on this worksheet and those values will be used for calculation of the
FLUID SELECTION Either (i) select a Gas and enter its temperature and pressure in the indicated yellow cells compressibility factor of the gas.
below, so that its critical temperature and critical pressure will be obtained and used, or else,
(ii) enter those parameters in the yellow cells D35, & D50, and those values will be used. 2. For calculations with some other gas, not listed in the table below, the user must enter
values for the gas critical temperature and critical pressure in the indicated yellow
Select a Gas and Enter Temperature (Enter Values in yellow cells only) cells in column D. Those user entered property values will be used for calculation of
the compressibility factor of the gas. The gas temperature and pressure must be
Click at right to Select Gas Methane entered in the yellow cells, D14 and D15.
NOTE: For accurate calculation of Z with
Gas Temperature (oC): 20 the Redlich Kwong equation, the reduced 3. For either a gas selected from the dropdown list or user entered gas properties,
Gas Pressure in Pipe (kPa abs): 1013 pressure should be less than half of the the gas compressibility factor is calculated with the Redlich-Kwong Equation
reduced temperature. That is: P/Pc < T/(2Tc) For accurate results P and T values should be such that P/Pc < T/(2Tc).
Check on Gas Temperature and Gas Pressure Values entered above: The source for the Tc and Pc values in this table is:
Table 2-13.2 in Perry's Chemical Engineers' Handbook, 9th Ed.
Is P/Pc < T/(2Tc)? YES P/Pc = 0.200
T/2Tc = 0.288
The entered values for T and P above are ok.
Excel Vlookup results based on selected fluid:
190.6 4599.0
CRITICAL TEMP. Critical Temperature from above menu selection: Tc, K Pc, kPa
190.6 K Acetylene 308.3 6138
Air 132.45 3774
NOTE: If you want to use a gas from the menu Ammonia 405.65 11280
above, then the yellow cell, D35, below must be blank. Argon 150.86 4898
Butane 425.12 3796
Use the Critical Temperature value above, OR Carbon Dioxide 304.21 7383
Carbon Monoxide 132.92 3499
Enter a Critical Temperature obtained elsewhere Chlorine 417.15 7710
Ethane 305.32 4872
Critical Temperature (K): 508.2 Ethylene 282.34 5041
Helium 5.2 227.5
Critical Temp. Result: 508.2 K (manual entry) Hydrogen 33.19 1313
(This is the Critical Temperature that will be used to calculate compressibility factor.) Hydrogen Chloride 324.65 8310
Hydrogen Sulfide 373.53 8963
CRITICAL PRESSURE Critical Pressure from above menu selection: Methane 190.56 4599
4599.0 kPa Nitric Oxide 180.15 6480
Nitrogen 126.2 3400
NOTE: If you want to use a gas from the menu Oxygen 154.58 5043
above, then the yellow cell, D50, below must be blank. Propane 369.83 4248
Propylene 364.85 4600
Use the Critical Pressure value above, OR Sulfur Dioxide 430.75 7884
Enter a Critical Pressure obtained elsewhere
Critical Pressure (kPa): 5066.25 For the Redlich-Kwong Equation of State (used to calculate the compressibility factor, Z) see:
Handbook of Chemical Engineering Calculations, 4th Ed, Section 1.4. Redlich-Kwong Equation of State
Critical Pressure Result: 5066.3 kPa (manual entry) One form of the Redlich-Kwong Eqn of State is:
(This is the Critical Pressure that will be used to calculate compressibility factor.) Where:
P = Gas pressure, atm
COMPRESSIBILITY FACTOR Calculation of Compressibility Factor of the Gas using the Redlich-Kwong Equation of State: T = Gas temperature, K
Tc = critical temperature of gas, K
(Note that P/Pc must be less than T/2Tc for accurate Redlich-Kwong Equation calculations.) Pc = critical pressure of gas, atm
V = molar volume of gas, cm3/gmole
R = Gas Law Constant, 82.05 atm cm3/gmole K
Is P/Pc < T/(2Tc) ? YES If this answer is "NO", change P and/or T
in cell(s) D14 and/or D15 above. A second form of the R-K Equation of State is:
Where:
Reduced Temperature, TR = 0.5768 Equation Constant, r = 1.016E-02 Z = Compressibility Factor
Reduced Pressure, PR = 0.2000 Equation Constant, q = -3.073E-01 T = Gas temperature, K
Equation Constant, D = 0.33821 Equation Constant, f = -2.605E-02 P = Gas pressure, atm
Equation Constant, E = 0.03003 Equation Constant, g = 1.820E-02 Tc = critical temperature of gas, K
Calculated Value of C = 8.211E-05 Pc = critical pressure of gas, atm
Z = 0.037 A third form of the Redlich-Kwong
Equation of State is:
Z1 =
Equation Constant, f = Z2 =
Z3 =
The third form of the Redlich-Kwong equation can be obtained by substituting V = ZRT/P (from the definition
of the compressibility factor, Z = PV/RT) into the first form of the Redlich-Kwong equation given above.
CALCULATION CHECK Calculation of Z using the 2nd Form of the R-K Equation with the value of Z calculated above:
The compressibility factor, Z, can be determined for specified gas temperature, pressure, critical temperature
and critical pressure using either the second form or the third form of the Redlich-Kwong equation, however
Equation Constant, A = 0.0338297 Equation Constant, B = 0.0030040 use of the second form requires an iterative calculation, while an explicit solution for Z can be obtained using
Equation Constant, h = 0.801959 the third form of the R-K equation (as the maximum real root of the cubic equation in Z).
The value for Z is calculated here by finding the maximum real root of the third form of the
Compressibility Factor, Z = 0.037 Redlich-Kwong equation as described at: www.polymath-software.com/ASEE2007/PDF1.pdf:
To find the maximum real root, first the parameter C is calculated, where C = (f/3)3 + (g/2)2, f = (-3q - 1)/3
Equations used for this and g = (-27r - 9q - 2)/27. If C > 0, there is one real root, Z = (-g/2 + C1/2)1/3 + (-g/2 - C1/2)1/3 + 1/3.
Calculation Check are:
If C < 0, then there are three real roots, given by: Zk = 2(-f/3)1/2cos[(f/3) + 2p(k-1)/3] + 1/3, k = 1,2,3
with f = cos-1{[(g2/4)/((-f3)/27)]1/2}
Note that the final calculation check made at the left using the more familiar second form of the Redlich-Kwong
equation uses the value of Z calculated with the third form of the equation, so if the calculated value of Z is the
Copyright © McGraw-Hill Global Education Holdings, LLC. All rights reserved. same, no iteration is required.
http://www.accessengineeringlibrary.com/browse/handbook-of-chemical-engineering-calculations-fourth-edition/c9780071768047ch01 http://www.accessengineeringlibrary.com/browse/handbook-of-chemical-engineering-calculations-fourth-edition/c9780071768047ch01?utm_source=Compressibility%20Factor&utm_medium=Excel&utm_content=HBChemEngCalc%201.4&utm_campaign=USUnits http://accessengineeringlibrary.com/browse/perrys-chemical-engineers-handbook-eighth-edition/p200139d89972_420001 http://accessengineeringlibrary.com/browse/perrys-chemical-engineers-handbook-eighth-edition/p200139d89822_421001 http://www.accessengineeringlibrary.com/browse/perrys-chemical-engineers-handbook-9th-edition/c9780071834087ch02lev1sec13?q=Critical+Constants&book=Perry%27s+Chemical+Engineers%27+Handbook%2C+9th+Edition