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

64 MATHEMATICAL MODELS OF CHEMICAL ENGINEERING SYSTEMS
Let us try to describe some of these phenomena quantitatively. For simplicity,
we will assume isothermal, constant-holdup, constant-pressure, and constant
density conditions and a perfectly mixed liquid phase. The gas feed bubbles are
assumed to be pure component A, which gives a constant equilibrium concentration
of A at the gas-liquid interface of Cx (which would change if pressure and
temperature were not constant). The total mass-transfer area of the bubbles is
A and could depend on the gas feed rate FA. A constant-mass-transfer coetliciF:t
k, (with units of length per time) is used to give the flux of A into the liquid
through the liquid film as a function of the driving force.
N, = kL(CX - C,) (3.72)
Mass transfer is usually limited by diffusion through the stagnant liquid film
because of the low liquid diffusivities.
We will assume the vapor-phase dynamics are very fast and that any unreacted
gas is vented off the top of the reactor.
Component continuity for A :
FY = F, - AM, NA MA (3.73)
PA
Vf%A
N
- FL CA - VkCA CB
dt MT A
Component continuity for B:
V$$=F,C,,-F,C.-VkC&,
(3.74)
(3.75)
Total continuity :
4p VI
-=O=FgpB+MANAAMT-FLp
dt
(3.76)
Equations (3.72) through (3.76) give us five equations. Variables are NA,
C,, C, , F, , and F, . Forcing functions are F,, F, , and CBO .
3.11 IDEAL BINARY DISTILLATION COLUMN
Next to the ubiquitous CSTR, the distillation column is probably the most
popular and important process studied in the chemical engineering literature.
Distillation is used in many chemical processes for separating feed streams and
for purification of final and intermediate product streams.
Most columns handle multicomponent feeds. But many can be approximated
by binary or pseudobinary mixtures. For this example, however, we will
make several additional assumptions and idealizations that are sometimes valid
but more frequently are only crude approximations.