Page 83 - Separation process engineering

sequential solution for a relatively simple problem.
How does one solve 32 simultaneous equations? In general, the K value relations could be nonlinear

functions of composition. However, we will restrict ourselves to ideal solutions where Eq. (2-29) is
valid and
K = K(T drum , p drum )
i
i
Since T drum and p drum are known, the 10 K can be determined easily [say, from the DePriester charts or
i
Eq. (2-30)]. Now there are only 22 linear equations to solve simultaneously. This can be done, but trial-
and-error procedures are simpler.
To simplify the solution procedure, we first use equilibrium, y = K x, to remove y from Eq. (2-36):
i
i
i i
Solving for x, we have
i

If we solve Eq. (2-5) for L, L = F – V, and substitute this into the last equation we have

(2-37)

Now if the unknown V is determined, all of the x can be determined. It is usual to divide the numerator
i
and denominator of Eq. (2-37) by the feed rate F and work in terms of the variable V/F. Then upon
rearrangement we have

(2-38)
The reason for using V/F, the fraction vaporized, is that it is bounded between 0 and 1.0 for all possible
problems. Since y = Kx, we obtain
i
i i

(2-39)

Once V/F is determined, x and y are easily found from Eqs. (2-38) and (2-39).
i
i
How can we derive an equation that allows us to calculate V/F?

To answer this, first consider what equations have not been used. These are the two stoichiometric
equations, Σ x = 1.0 and Σ y = 1.0. If we substitute Eqs. (2-38) and (2-37) into these equations, we obtain
i
i

(2-40)