COMPRESSIBILITY FACTOR z FOR GASES USING REDLICH-KWONG EQUATION OF STATEBy: Ankur SrivastavaDate: May 09, 2006

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Redlich-Kwong (R-K) Equation & its solution:

The R-K equation is usually written as:

P = ((R*T)/V-b) - (a/V*(V+b)*√T) 1where

2

3

P = pressure in atm absoluteV = molar volume in L/g-molT = Temperature in °KR = universal gas constant = 0.08206 atm*L/g-mol*°K

Eliminating V from eq. 1 & writing it as a cubic equation of the compressibility factor z, yields

4where

5

6

7

8

9wheref = ((-3*q)-1)/3 10g = ((-27*r)-(9*q)-2)/27 11

If C>0, there is one real solution for z: 12z = D+E+1/3where

13

14

If C<0, there are three real solutions:

15where

1617

a = 0.42747*(R2*Tc2.5/Pc)

b = 0.8664*(R*Tc/Pc)

Tc = critical temperature in °K

Pc = critical pressure in atm absolute

f(z) = z3-z2-q*z-r = 0

r = A2*B

q = B2+B-A2

A2 = 0.42747*(Pr/Tr2.5)

B = 0.86664*(Pr/Tr)

Here Pr = reduced pressure (P/Pc) and Tr = reduced temperature (T/Tc).

Eq. 4 can be solved analytically for 3 roots. Some of these roots are complex. Considering only the real roots, the sequence of calculations involves the following steps:

C = (f/3)3 + (g/2)2

D = ((-g/2)+√C)1/3

E = ((-g/2)-√C)1/3

zk = 2*(√-f/3)*cos[(φ/3)+2*p*(k-1)/3]k = 1,2,3

φ = a*cos*SQROOT[(g2/4)/(-f3/27)]r = P*M/R*T*z

COMPRESSIBILITY FACTOR z FOR GASES USING REDLICH-KWONG EQUATION OF STATEBy: Ankur SrivastavaDate: May 09, 2006

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Inputs:Gas: PropaneMolecular Weight, M 44.1 g/g-mol

369.83 °K

41.92 atmA

Oper. temperature, T 333.15 °KOperating Pressure, P 20.414 atmA

Constants Used:Gas Constant, R: 0.08206 L*atm/g-mol*°K

Calculated Parameters:

0.901

0.487

Equations:

0.27028 Eq. 7 sheet 1B = 0.04684 Eq. 8 sheet 1q = -0.22125 Eq. 6 sheet 1r = 0.01266 Eq. 5 sheet 1f = -0.11208 Eq. 10 sheet 1g = -0.01298 Eq. 11 sheet 1C = -0.00001 Eq. 9 sheet 1D = IRRELEVANT Eq. 13 sheet 1E1 = IRRELEVANT Eq. 14 sheet 1φ = 0.45354 Eq. 16 sheet 1E = IRRELEVANT Eq. 14 sheet 1z1 = 0.71550 Eq. 15 sheet 1z2 = 0.09183 Eq. 15 sheet 1z3 = 0.19267 Eq. 15 sheet 1z0 = IRRELEVANT Eq. 12 sheet 1z = 0.71550

r = 46.02

Yellow colored cells are inputs. Blank yellow cells have been provided to add components.Calculation of Pseudocritical Temperature & Pressure for a Natural Gas Mixture:

0.932 190.6 177.64 45.35 42.27 16.04 14.95

0.058 305.33 17.71 48.07 2.79 30.07 1.74

0.01 369.83 3.70 41.92 0.42 44.1 0.44

0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

0.00 0.00 0.00

1.000 199.05 45.47 17.13

Prepared by: Ankur SrivastavaChemical Engineere-mail: ankur2061@yahoo.co.in

Crit. Temperature, Tc: (for gas mixtures use peudocritical values, see example below below for calculating pseudocritical temperature)

Crit. Pressure, Pc: (for gas mixtures use peudocritical values, see example below below for calculating pseudocritical pressure)

Reduced Temperature, Tr (T/Tc)

Reduced Pressure, Pr (P/Pc)

A2 =

g/l or kg/m3

Component description

Mole Fraction, yi

Component Critical Temp.,

Tc1, °K

Pseudo-critical

Temp, Tpc, °K

Component Critical

Pressure, Pci, atmA

Pseudo-critical

Pressure, Ppc, atm

Component Molecular weight, Mi

Mixture Molecular

weight, yi*Mi

CH4

C2H6

C3H8

Tpc = Ppc = Mmix =

COMPRESSIBILITY FACTOR z FOR GASES USING REDLICH-KWONG EQUATION OF STATEBy: Ankur SrivastavaDate: May 09, 2006

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Disclaimer: The information and methods included within this spreadsheet are presented for compressibility factor z calculations. It is intended to be used by technically skilled persons at their own discretion. I do not warrant the suitability or accuracy of these methods.