Page 88 - Separation process engineering

If the specified variables are F, z, p drum , and either x or y for one component, we can follow a sequential
i
convergence procedure using Eq. (2-38) or (2-39) to relate to the specified composition (the reference
component) to either K or V/F. We can do this in either of two ways. The first is to guess T drum and use
ref
Eq. (2-38) or (2-39) to solve for V/F. The Rachford-Rice equation is then the check equation on T drum . If
the Rachford-Rice equation is not satisfied, we select a new temperature—using Eq. (2-49)—and repeat
the procedure. In the second approach, we guess V/F and calculate K from Eq. (2-38) or (2-39). We
ref
then determine the drum temperature from this K . The Rachford-Rice equation is again the check. If it is
ref
not satisfied, we select a new V/F and continue the process.

If there are nonvolatile compounds present, the K values for these compounds are zero. The presence of
i
these compounds will cause no difficulties for Eqs. (2-38) to (2-49). However, if there are
noncondensable compounds present, the K for these compounds will be very large, particularly if the
i
solubilities are small. It is tempting to set these K values to infinity, but then Eq. (2-42) becomes
i
undefined. This difficulty is easily handled by rearranging Eq. (2-42) (Hatfield, 2008). If we divide
numerator and denominator of the noncondensable term of Eq. (2-42) by K NC , this term becomes

(2-49)

Substitution of this term into Eq. (2-42) results in a well-behaved equation in the presence of
noncondensable compounds. Equations (2-38) and (2-39) become x NC = 0 and y NC = Fz NC /V.

2.7 Simultaneous Multicomponent Convergence

If the feed rate F, the feed composition consisting of (C – 1) z values, the flash drum pressure p drum , and
i
the feed temperature T are specified, the hot liquid will vaporize when its pressure is dropped. This
F
“flashing” cools the liquid to provide energy to vaporize some of the liquid. The result T drum is unknown;

thus, we must use a simultaneous solution procedure. First, we choose a feed pressure such that the feed
will be liquid. Then we can calculate the feed enthalpy in the same way as Eqs. (2-47) and (2-48):

(2-50)

Although the mass and energy balances, equilibrium relations, and stoichiometric relations could all be
solved simultaneously, it is again easier to use a trial-and-error procedure. This problem is now a double
trial and error.

The first question to ask in setting up a trial-and-error procedure is: What are the possible trial variables

and which ones shall we use? Here we first pick T drum , since it is required to calculate all K, and
i
and since it is difficult to solve for. The second trial variable is V/F, because then we can use the
Rachford-Rice approach with Newtonian convergence.

The second question to ask is: Should we converge on both variables simultaneously (that is change both