Question

What is the bubble point temperature of a mixture that is 15 mol% i-pentane, 30 mol% n-pentane, and 55 mol% n-hexane? Pressure is 1-atm. K-values may be obtained from DePriester charts. Alternativley, K-values may be calculated from the following empirical equation, equation 2-12, (coefficients given in table 2-4):

ln(K) = a_T1/_T² + a_T2/T + a_T6 + a_p1ln (p) + a_p2/p² + a_p3/p (The first entry has T squared in the denominator)

Table 2-4. Constants for Fit to K Values Using equatin 2-12. Note: T is degree R and p in psia

Compund	aT1	aT2	aT6	ap1	ap2	ap3	Mean Error
Isopentane	-1,481,583	0.00	7.58071	-0.93159	0.00	0.00	4.56
n-Pentane	-1524891.00	0.00	7.33129	-0.89143	0.00	0.00	4.30
n-Hexane	-1778901.00	0.00	6.96783	-0.84634	0.00	0.00	4.90

My professor said this can be done using Newton's Method. How? I'm doing this all in excel if that helps but I just need the calculations for it.

Thank you

Answer 1

Given K-value as a function of Temperature and Pressure,

Assume Isopentane as the reference component, A, and n-pentane and n-hexane as B and C respectively.

Guess a value of temperature,

, where is the boiling point of pure component i at pressure (Can be calculated by setting )

Let,

Determining ,

;

;

;

Now let,

For this value of , find temperature , by substituting in the emperical equation

Since ,

Repeat with new guess value of using newton's method,

We know, at Bubble Point temperature summation of vapor phase molar fraction should be 1.

Therefore we take as follows,

The following table has all iterations,

586.39	2.155	1.65	0.618	1.86	0.15725	0.018	576.619	9.771	577.65
577.65	1.89	1.441	0.528	1.878	6.2 x 10-3	0.016	577.217	0.432	-

Since in the second iteration the value of we stop the iterations.

Thus, the bubble point temperature