1. Batch Distillation

2. History Early distillation of alcohol
Alembic still for distillation of brandy

3. Major types of batch distillation
Simple batch distillation
Multistage batch distillation

4. Reasons to use batch distillation
Small capacity (e.g., specialty chemicals)
Intermittent need
Test run for a new product
Up-stream operations are batch (e.g., alcoholic spirits)
Feed inappropriate for continuous distillation (suspended solids)
Feed varies widely in composition

5. Simple batch distillation no rectification ( = no column)
Characteristics:
no column; a single equilibrium stage (= the still pot)
single charge (F) to still pot at time = 0
vapor is withdrawn continuously
composition of liquid in still pot (xW) changes continuously
composition of liquid distillate (xD) changes continuously
time t: W, xW
V, y
D, xD
time 0: F, xF
still pot with heater

6. Rayleigh equation TMB: F = Wfinal + Dtotal
time t: W, xW
y = xD
V, y
D, xD
TMB: F = Wfinal + Dtotal
CMB: FxF = WfinalxW,final + DtotalxD,avg
Specify F, xF and xW,final or xD,avg
Leaves 3 unknowns:
Wfinal, Dtotal and xW,final or xD,avg
Need one more equation:
time 0: F, xF
still pot, with heater
dCMB: - xDdW = - d(WxW)
(vapor withdrawn) = (change in still pot composition)
chain rule: - xDdW = - WdxW - xWdW
WAIT! K is not constant;
K = K(T)
Rayleigh equation
where xD = f(xW)

7. Integration of the Rayleigh equation
1/(xD – xD)
x = xW
Numerical integration:
Constant relative volatility:
xW,final • • xF
Specify F, xF, and either Wfinal or xW,final.
Simpson’s rule:

8. Solvent switching using simple batch distillation
Goal: replace one solvent by another, in order to facilitate crystallization of a non-volatile product, or for a subsequent reaction step.
The Hard Way:
Boil off most of original solvent in a batch still.
Add second solvent.
Perform second batch distillation to remove residual original solvent.
The Easy Way: Constant-level batch distillation
Add second solvent continuously as first solvent vaporizes, keeping W constant; more energy efficient and uses less solvent.
dTMB: dV = dS
(vapor withdrawn) = (new solvent added)
dCMB: ydV = - xDdS = WdxW
(W constant)

9. Batch steam distillation
Used for thermally fragile organics (e.g., essential oils in perfume industry), and for slurries/sludges containing organics.
W, xW
V, y
D, xD = 1
A single charge (F) added to still pot at time = 0. Steam is added continuously.
H2O(l)
(to waste)
still pot,
no heater
steam
If W, D are immiscible with water, we have a heterogeneous azeotrope.
H2O(l)
D.o.F. = 2 components – 3 phases + 2 = 1
Fix Ptotal, then T cannot vary!
constant T < Tbp(H2O)
How much steam is required?
Both H2O and organic vaporize well below their single-component boiling points.
Also, constant vapor composition.
Raoult’s Law: Ptotal = P*WxW + P*H2O
Steam also needed to heat and vaporize the material in the still pot.

10. Batch distillation with rectification
TMB: Vj+1 = Lj + D CMB: Vj+1yj+1 = Ljxj + DxD • both are time-dependent • either D or xD (or both) change over the course of the distillation
time t: W, xW
y1 = x0 = xD
V1, y1
D, xD
L0, x0
stage 1
y1 ≠ K / xW
stage j
CMO: Vj+1 = Vj and Lj = Lj-1
operating line equation:
y = (L/V) x + (1 - (L/V)) xD
y = x = xD slope = L/V
• actually a family of operating lines, since L/V or xD (or both) change over the course of the distillation
• therefore the operating line moves on the M-T diagram
Vj+1, yj+1
Lj, xj
stage N
VN+1, xN+1
LN, xN
time 0: F, xF
still pot, with heater
stage N+1

11. Choice of operating methods
Constant reflux ratio (variable xD)
y=x
Constant distillate composition (variable R)
VLE
y=x
•xD
•xD
total reflux •
time
VLE
time • • •
distillation must end
when (or before) xD,avg = xF
distillation must end
when (or before) R = ∞ (L/V = 1)
Easy to monitor and control.
Harder to monitor and control (need to detect xD on-stream and adjust R accordingly).
Can solve graphically, if we assume no liquid holdup on the column.

12. Multistage batch distillation with constant R
Given F, xF, xW,final, R and N,
find Dtotal, xD,avg
y=x
VLE 1 2
For N = 2 (incl. reboiler) •
xD,4
•xD,1
•xD,2
•xD,3 • •
1. For an arbitrary set of xD values, draw a series of parallel operating lines, each with slope R/(R+1) • 1 2
xW,2 • 1 2
xW,3
2. Step off N stages on each operating line to find its corresponding xW
3. Perform numerical integration:
plot 1/(xD-xW) vs xW
limits: xF, xW,final • 1 2
xW,4
4. Calculate Wfinal using Rayleigh equation
xW,1
5. Solve mass balances for Dtotal and xD,avg
If xD,avg is specified instead of xW,final: guess xW,final, calculate xD,avg, iterate.

13. Operating time at constant R (D)
depends on vapor flow rate (V), which depends on boilup rate
shut down, cleaning and recharging still pot, restart
• if the boilup rate is constant, then V is constant, and D will be constant
condenser TMB:
• V = Vmax when vapor velocity u = uflood
• uflood depends on column diameter
• typically, operate at D = 0.75 Dmax

14. Calculating column diameter
We want to use the smallest diameter that will not cause the column to flood.
where σ is surface tension, ρL and ρV are liquid and vapor densities, respectively.
Csb,flood is the capacity factor, depends on flow parameter FP and tray spacing;
obtain from graphical correlation.
where η is the fraction of the column cross-sectional area available for vapor flow (i.e., column cross-sectional area minus downcomer area).

15. Multistage batch distillation with constant xD
Given F, xF, xD (maybe) xw,final and N,
find Rinitial, Rmin, xW,min
y=x
VLE
N = ∞, R = Rmin •
•xD
(L/V)initial
(L/V)min
1. Draw trial op. lines and step off N stages to end at xF
This is trial-and-error, except for N = 2, or N = ∞ (Rmin) xF • •
xW.min
3. Find xW,min using (L/V) = 1.
Rayleigh equation not needed!
Verify xW,final > xW,min.
Is xWfinal required?
4. Solve mass balance for Wfinal and Dtotal.
N = 2 (incl. reboiler)

16. Operating time with constant xD
mass balance:
x = xW
Numerical integration:
xW,final • xF
1. Draw a series of arbitrary operating lines, each with a different slope L/V
2. Step off N stages on each operating line to find its corresponding xW
3. Perform numerical integration (plot graph, use Simpson’s rule)
4. Calculate toperating

17. Effect of liquid holdup on the column
Optimal control
• use optimal, time-dependent reflux ratio (not constant R, not constant xD)
• more energy-efficient
• useful for difficult separations
Effect of liquid holdup on the column
• usually, we can assume vapor holdup is negligible • liquid holdup causes xw to be lower than it would be in the absence of holdup • causes the degree of separation to decrease To assess the effect on batch distillation: • measure the amount of holdup at total reflux • perform computational simulation
Next year: add heater and condenser duties