Page 135 - Separation process engineering

Find D, B, Q , Q .
c
R

B. Explore. Since there are only two unknowns in the mass balances, B and D, we can solve for these
variables immediately. Either solve Eqs. (3-1) and (3-2) simultaneously, or use Eqs. (3-3) and (3-
4). For the energy balances, enthalpies must be determined. These can be read from the enthalpy-
composition diagram (Figure 2-4). Then Q can be determined from the balance around the
c
condenser and Q from the overall energy balance.
R
C. Plan. Use Eqs. (3-3) and (3-4) to find D and B, Eq. (3-14) to determine Q , and Eq. (3-15a) to
c
determine Q .
R
D. Do It. From Eq. (3-3),

From Eq. (3-4), B = F − D = 10,000 − 3333 = 6667 kg/h

From Figure 2-4 the enthalpies are

h (x = 0.8, saturated liquid) = 60 kcal/kg
D
D
h (x = 0.05, saturated liquid) = 90 kcal/kg
B
B
h (z = 0.3, 40 ° C) = 30 kcal/kg
f
H (y = x = 0.8, saturated vapor) = 330 kcal/kg
1
1
D
From Eq. (3-14),

From Eq. (3-15a),

Q = Dh + Bh − Fh − Q C
D
B
R
F
Q = (3333)(60) + (6667)(90) − (10,000)(30) − (−3,599,640) = 4,099,650 kcal/h
R
E. Check. The overall balances, Eqs. (3-1) and (3-5), are satisfied. If we set up this problem on a
spreadsheet without explicitly solving for D, B, Q and Q we obtain identical answers.
c,
R
F. Generalize. In this case we could solve the mass and energy balances sequentially. This is not
always the case. Sometimes the equations must be solved simultaneously (see Problem 3.D3).
Also, the mass balances and energy balances derived in the text were for the specific case shown
in Figure 3-8. When the column configuration is changed, the mass and energy balances change (see
Problem 3.D2, 3.D3, and 3.D5). For binary distillation we can usually determine the external
flows and energy requirements from the external balances. Exceptions will be discussed in Chapter
4.