Page 85 - Separation process engineering

(2-45)

Substituting Eqs. (2-42) and (2-45) into (2-44) and solving for (V/F) k+1 , we obtain

(2-46)

Equation (2-46) gives a good estimate for the next trial. Once (V/F) k+1 is calculated the value of the
Rachford-Rice function can be determined. If it is close enough to zero, the calculation is finished;
otherwise repeat the Newtonian convergence for the next trial.

Newtonian convergence procedures do not always converge. One advantage of using the Rachford-Rice
equation with the Newtonian convergence procedure is that there is always rapid convergence. This is
illustrated in Example 2-2.

Once V/F has been found, x and y are calculated from Eqs. (2-38) and (2-39). L and V are determined
i
i
from the overall mass balance, Eq. (2-5). The enthalpies h and H can now be calculated. For ideal
L
v
solutions the enthalpies can be determined from the sum of the pure component enthalpies multiplied by
the corresponding mole fractions:

(2-47a)

(2-47b)

where and are enthalpies of the pure components. If the solutions are not ideal, heats of mixing
are required. Then the energy balance, Eq. (2-7), is solved for h , and T is determined.
F
F
If V/F and p drum are specified, then T drum must be determined. This can be done by picking a value for
T drum , calculating K, and checking with the Rachford-Rice equation, (2-42). A plot of f(V/F) vs. T drum
i
will help us select the temperature value for the next trial. Alternatively, an approximate convergence
procedure similar to that employed for bubble- and dew-point calculations can be used (see Section 5-4).
The new K can be determined from
ref

(2-48)

where the damping factor d ≤ 1.0. In some cases this may overcorrect unless the initial guess is close to
the correct answer. The calculation when V/F = 0 gives us the bubble-point temperature (liquid starts to
boil) and when V/F = 1.0 gives the dew-point temperature (vapor starts to condense).