Page 257 - Separation process engineering

(6-21b)

where 2 ≤ j ≤ N − 1.

Substituting Eqs. (6-21a) and (6-21b) into Eq. (6-20) and rearranging, we obtain

(6-22)

For a total condenser since V = L + D and h = h , the energy balance is
2 1 1 D

(6-23)

which upon rearrangement is

(6-24)

For the partial reboiler (j=N), the energy balance is

(6-25)

and the overall flow rate can be calculated from,

(6-26)

Substituting Eq. (6-26) into (6-25) and rearranging, we have

(6-27)

If Eqs. (6-22), (6-24), and (6-27) are put in matrix form, we have

(6-28)

This matrix again has a tridiagonal form (with A = 0) and can easily be inverted to obtain the vapor flow
j
rates. The B and C coefficients in Eq. (6-28) are easily obtained by comparing Eqs. (6-22), (6-24), and
E
E
(6-27) to Eq. (6-28). For j = 1 these values are