Assigment

Please see attachment 

Use excel to help with the assignment.  assignment must be on word document and please show calculations for problem 

1

ASSIGNMENT-1

PE 5663 Natural Gas Utilization

1- Calculate the Z-factors and the molar volumes for pure CO2 at 150ºC and pressures 10, 20,
40, 60, 100, 300, 400 and 500 bar. Use the RK EoS.

2- Plot the results for Z-factors and molar volumes of CO2 vs P.
3- Plot the gas formation volume factor of CO2 vs P.
4- On the plots, compare the results obtained for the Z-factor and Bg from the RK EoS with

those reported in literature and discuss on the discrepancies.

Experimental data for Z-factor for pure CO2 at 150ºC:

P/bar Z
10 0.985
20 0.970
40 0.942
60 0.913
100 0.869
300 0.762
400 0.824
500 0.910

1. Intro-Start Here

wong equation.

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-

K

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

a):

343.0

343.0 oR

5.3

Methane 343.0 667.0

667.0 psi

NOTE: If you want to use a gas from the menu

psi (from menu selection)

YES

Where:

T = Gas temperature, K

P = Gas pressure, atm

Equation Constant, f =

0.883

Copyright © McGraw-Hill Global Education Holdings, LLC. All rights reserved.

	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 (		psi	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
	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	76	5.2	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:		(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	1	20
	Hydrogen Sulfide	672.4	1300.0
	CRITICAL PRESSURE		Critical Pressure from above menu selection:
	Nitric Oxide	324.3	939.8
	Nitrogen	227.2	493.1
	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		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) ?		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:
	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
	Equation Constant, D =	0.15481			Equation Constant, f =	-2.228E-01
	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 =
	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 =		Redlich-Kwong equation as described at: www.polymath-software.com/ASEE2007/PDF1 :
	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
	same, no iteration is required.

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3. S.I. Units

1. For calculations with one of the 21 gases listed in the table below, select the appropriate

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

(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

20 the Redlich Kwong equation, the reduced 3. For either a gas selected from the dropdown list or user entered gas properties,

abs):

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 = T/2Tc =

The entered values for T and P above are ok.
Excel Vlookup results based on selected fluid:

.0

CRITICAL TEMP. Critical Temperature from above menu selection:

190.6 K Acetylene

Air

NOTE: If you want to use a gas from the menu Ammonia

above, then the yellow cell, D35, below must be blank. Argon

Butane

Use the Critical Temperature value above, OR Carbon Dioxide

Carbon Monoxide

Enter a Critical Temperature obtained elsewhere Chlorine

Ethane

508.2 Ethylene

Helium 5.2

Critical Temp. Result: 508.2 K

Hydrogen

(This is the Critical Temperature that will be used to calculate compressibility factor.) Hydrogen Chloride

Hydrogen Sulfide

CRITICAL PRESSURE Critical Pressure from above menu selection: Methane

4599

kPa Nitric Oxide

Nitrogen

NOTE: If you want to use a gas from the menu Oxygen

above, then the yellow cell, D50, below must be blank. Propane

Propylene

Use the Critical Pressure value above, OR Sulfur Dioxide

Enter a Critical Pressure obtained elsewhere

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:

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 =

Equation Constant, r =

Z = Compressibility Factor

Reduced Pressure, PR =

Equation Constant, q =

T = Gas temperature, K

Equation Constant, D =

P = Gas pressure, atm

Equation Constant, E =

Equation Constant, g =

Tc = critical temperature of gas, K

Calculated Value of C =

Pc = critical pressure of gas, atm

Z =

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 =

Equation Constant, B =

use of the second form requires an iterative calculation, while an explicit solution for Z can be obtained using

Equation Constant, h =

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 :

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.

Calculation of Gas Compressibility Factor – S.I. Units
Select a Gas and Enter Temperature
Gas Temperature (oC):
Gas Pressure in Pipe (		kPa	1013
0.200
0.288
	190.6		4599
Tc, K	Pc, kPa
308.3	6138
132.45	3774
405.65	11280
150.86	4898
425.12	3796
304.21	7383
132.92	3499
417.15	7710
305.32	4872
Critical Temperature (K):	282.34	5041
227.5
	(manual entry)	33.19	1313
324.65	8310
373.53	8963
190.56
4599.0	180.15	6480
126.2	3400
154.58	5043
369.83	4248
364.85	4600
430.75	7884
Critical Pressure (kPa):	5066.25
5066.3
0.5768	1.016E-02
0.2000	-3.073E-01
0.33821	Equation Constant, f =	-2.605E-02
0.03003	1.820E-02
8.211E-05
	0.037
0.0338297	0.0030040
0.801959

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