Page 87 - Separation process engineering

With V/F = 0.1 this is

From Eq. (2-46) the next guess for V/F is (V/F) = 0.1 + 0.8785/4.631 = 0.29. Calculating the value
2
of the Rachford-Rice equation, we have f(0.29) = 0.329. This is still positive and V/F is still too low.

Second Trial:

which gives (V/F) = 0.29 + 0.329/1.891 = 0.46
3
and the Rachford-Rice equation is f(0.46) = 0.066. This is closer, but V/F is still too low. Continue
convergence.

Third Trial:

which gives (V/F) = 0.46 + 0.066/1.32 = 0.51
4
We calculate that f(0.51) = 0.00173, which is close to zero and is within the accuracy of the
DePriester charts. Thus V/F = 0.51.
Now we calculate x from Eq. (2-38) and y from Kx. For example,
i
i
i i

y = K x = (7.0)(0.0739) = 0.5172
1
1 1

since F = 1000 and V/F = 0.51, V = 0.51F = 510 kmol/h, and L = F – V = 1000 – 510 = 490 kmol/h.

E. Check. We can check Σ y and Σ x.
i
i

These are close enough. They aren’t perfect, because V/F wasn’t exact. Essentially the same
answer is obtained if Eq. (2-30) is used for the K values. Note: Equation (2-30) may seem more
accurate since one can produce a lot of digits; however, since it is a fit to the DePriester chart it
can’t be more accurate.

F. Generalize. Since the Rachford-Rice equation is almost linear, the Newtonian convergence routine
gives rapid convergence. Note that the convergence was monotonic and did not oscillate. Faster
convergence would be achieved with a better first guess of V/F. This type of trial-and-error
problem is easy to program on a spreadsheet (see Appendix B in this chapter).