Page 312 - Process Equipment and Plant Design Principles and Practices by Subhabrata Ray Gargi Das

314 Chapter 11 Distillation

Variables in the MESH equations are
• Stage temperatures (T j )
• Internal vapour and liquid flow rates (V j and L j )
• Stage compositions (x i,j and y i,j or V i,j and L i,j)
A) The summation/stoichiometric equations are
For the liquid phase
n n n
X
X
X
x i;j 1 ¼ 0or L i;j = L j 1 ¼ 0 or y i;j = K i;j 1 ¼ 0 (11.21a)
i¼1 i¼1 i¼1
For the vapour phase
n n n
X
X
X
y i;j 1 ¼ 0or V i;j = V j 1 ¼ 0or K i;j x i;j 1 ¼ 0 (11.21b)
i¼1 i¼1 i¼1
B) The equilibrium equations are

y i;j ¼ K i;j x i;j or V i;j =V j ¼ K i;j L i;j =L j
The expression of K i;j in a real system will be a complex function of stage temperature, pressure
and compositions derived from thermodynamics:

K i;j ¼ K i;j T j ; P j ; x i;j ; y i;j (11.22)

C) Component balance equations

For a single feed, single distillate and bottom product,
F i B i D i ¼ 0 (11.23)
Balance on a simple stage (no draw or feed on the stage) as shown in Fig. 11.13B,
V i;jþ1 þ L i;j 1 V i;j L i;j ¼ 0 (11.24)
) as shown below
Balance on the feed stage N F contains only the liquid portion of the feed (FL i;N F
¼ 0 (11.24a)
V i;N F þ1 þ L i;N F 1 þ FL i;N F V i;N F L i;N F
The vapour fraction of feed appears in the balance of stage ðN F 1Þ.
Balance on the product draw off stage N P is
¼ 0 (11.24b)
V i;N P þ1 þ L i;N P 1 V i;N P L i;N P w i;N P
is the molar flow rate of the ith component in the side stream draw from tray N P.
where w i;N P
The overall material balance equation for stage j is
V jþ1 þ L j 1 V j L j ¼ 0 (11.25)