Interpretation:
Estimation of the fugacity for methane/ethane/propane in a mixture. Also estimate fugaciy coefficient for gases in the mixture.
Concept introduction:
The calculation of fugacity and fugacity coefficient of gases in the gas mixture is possible by using different correlation given as follows:
The fugacity coefficient for gas can be calculated by the equation given in the book as follows:
Where,
T = temperature
Where,
Similarly,
The fugacity of gases can be calculated by the definition of fugacity coefficient that is fugacity coefficient is the ratio of fugacity and pressure.
Answer to Problem 10.27P
Fugacity and fugacity coefficient of methane are 7.4896 bar and 1.019, respectively.
Fugacity and fugacity coefficient of ethane are 13.259 bar and 0.881, respectively.
Fugacity and fugacity coefficient of propane are 9.765 bar and 0.775, respectively.
Explanation of Solution
Refer APPENDIX-B and Table-B.1 to determine critical properties and acentric factor of ethylene(1)/Propylene (2) as:
Component | Pc (bar) | Tc (K) | Vc (cm3/mol) |
|
Zc |
Methane (1) | 45.99 | 190.6 | 98.6 | 0.012 | 0.286 |
Ethane (2) | 48.72 | 305.3 | 145.5 | 0.100 | 0.279 |
Propane (3) | 42.48 | 369.8 | 200 | 0.152 | 0.276 |
Where,
Pc = critical pressure
Tc = critical temperature
Vc = critical volume
Zc = critical compressibility factor
From the properties derived above, we can calculate the reduced pressure and temperature as follows:
Pressure P = 35 bar (given in question) and Temperature (T) = 1000C or 373.15K (given)
Y1= 0.21 ; y2 = 0.43 (given)
So,
Reduced temperature of gases can be calculated as:
Similar to the above calculated matrix we will calculate the reduced temperature as follows:
Critical volume of both the gases in the mixture can be calculated as given below:
With the help of critical volume and critical temperature, critical pressure of gases in the mixture can be calculated as follows:
The reduced compressibility factor can be calculated as:
After putting all values in the critical pressure formula, we will get:
At this calculated value of reduced temperature, we can calculate correlation constant as:
Overall correlation constant value in gas mixture can be calculated by equation:
Using above calculated values fugacity coefficient of gases calculated as given below:
Similarly, we can calculate fugacity coefficient for second species ethane and for third one propane as:
Now finally we can estimate the fugacity of all gases by just multiplying P with derived fugacity coefficient values:
Therefore fugacity of methane is 7.4896 bars, fugacity of ethane is 13.259 bar and fugacity of propane is 9.765 bar in the gas mixture.
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Chapter 10 Solutions
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