Question

A laboratory cell with volume of 0.007769 ft3 contains 0.001941 lb-moles mixture given in the table below. Temperature is to be raised to 80OF, using Soave-Redlich-Kwong (SRK) equation of state calculate the expected pressure to be. Compare your results with experimental results of 1200 psia + 2 %. Component Composition, mole fraction Acentric factor (?) Methane 0.85 0.0104 Ethane 0.1 0.0979 Propane 0.05 0.1522 use values of zero for binary interaction coefficients

Answer 1

SOLUTION

The Soave-Redlich-Kwong equation of state (SRK-EOS) is given by:

First, we need to calculate the the constants and for each component:

Where, is the acentric factor of the component:

Where:

Where, is the mole fraction of component

Where, is the coeficcient of binary interactions and, in this problem has a value of:

Therefore, equation (8) can be written as:

Now, insert values starting by equations (7) and (3) as follows:

Where:

Now, equation (11) can be written as:

Replacing values:

Solving we obtain:

Now, compute    for each component using equations (2),(4),(5), (5.1) y (6) as follows:

For Methane, we have:

Replacing values we obtain:

Now, is:

Then, from equation (4) we have:

Replacing values:

Solving we obtain:

Then, from equation (5) we have:

Replacing (14) and (16) into equation (17):

Solving we obtain:

Therefore:

Then, compute from equation (6):

Replacing (13) and (20) within (21):

Solving we obtain:

Similarly, for Ethane we have:

Replacing values we obtain:

Now, is:

Then, from equation (4) we have:

Replacing values:

Solving we obtain:

Then, from equation (5) we have:

Replacing (24) and (26) into equation (27):

Solving we obtain:

Therefore:

Then, compute from equation (6):

Replacing (23) and (30) within (31):

Solving we obtain:

Similarly, for Propane we have:

Replacing values we obtain:

Now, is:

Then, from equation (4) we have:

Replacing values:

Solving we obtain:

Then, from equation (5) we have:

Replacing (34) and (36) into equation (37):

Solving we obtain:

Therefore:

Then, compute from equation (6):

Replacing (33) and (40) within (41):

Solving we obtain:

Now, compute the value of    using equation (9) using data given mole fraction and results (22), (32) , (42):

Therefore, equation (9) can be written as:

Replacing values we obtain:

Now, the molar volume is:

Finally, replacing (12), (43), (44) and data given values into equation (1) we get:

Solving we obtain:

While that, the precentage error: