[Luyben] Process Mod.. - Student subdomain for University of Bath

70 MATHEMATICAL MODELS OF CHEMICAL ENGINEERING SYSTEMS
controlled (can be fixed). The two variables that must somehow be specified are
reflux flow R and vapor boilup Y (or heat input to the reboiler). They can be held
constant (an openloop system) or they can be changed by two controllers to try
to hold some other two variables constant. In a digital simulation of this column
in Part II we will assume that two feedback controllers adjust R and V to control
overhead and bottoms compositions xD and xB .
3.12 MULTICOMPONENT NONIDEAL
DISTILLATION COLUMN
As a more realistic distillation example, let us now develop a mathematical model
for a multicomponent, nonideal column with NC components, nonequimolal
overflow, and inehicient trays. The assumptions that we will make are:
1.
2.
3.
4.
Liquid on the tray is perfectly mixed and incompressible.
Tray vapor holdups are negligible.
Dynamics of the condenser and the reboiler will be neglected.
Vapor and liquid are in thermal equilibrium (same temperature) but not in
phase equilibrium. A Murphree vapor-phase efficiency will be used to describe
the departure from equilibrium.
E
,=Ynj-YLI,i
n’ Yn*j-YynT-1.j
(3.96)
where yzj = composition of vapor in phase equilibrium with liquid on nth tray
with composition xnj
ynj = actual composition of vapor leaving nth tray
y,‘_ i, j = actual composition of vapor entering nth tray
Enj = Murphree vapor efficiency forjth component on nth tray
Multiple feeds, both liquid and vapor, and sidestream drawoffs, both liquid
and vapor, are permitted. A general nth tray is sketched in Fig. 3.13. Nomenclature
is summarized in Table 3.1. The equations describing this tray are:
Total continuity (one per tray):
dM
A = L,+1 + F;4 + F,Y-, + v,-, - v, - L, -s; - s.’
dt
(3.97)
Component continuity equations (NC - 1 per tray):
4Mn Xnj) = L
“+I x n+l,j + Fkx$ + FL-d-1.j + K-IYn-1,j
dt
- Vn Y,j - L, Xnj - Sf; X,j - S,’ )‘,I (3.98)