Batch Distillation - James C. Sutherland · PDF fileSimple Binary Batch Distillation Analysis Q B D, y W, x D! Distillate molar ﬂow rate! W! Moles of “residue” in the still!

Batch DistillationSHR Chapter 13

1 BatchDistillation.key - April 3, 2014

Simple Binary Batch Distillation Analysis

QB

D, y

W, x

D Distillate molar flow rate W Moles of “residue” in the still x Mole fraction of light key in

the still (assumed spatially homogeneous)

y Mole fraction of light key in the distillate (assumed spatially homogeneous)

d (Wx)

dt

= �Dy

Light key mole balance: Overall mole balance:dW

dt= �D

W

dx

dt

+ x

dW

dt

= �Dy

W

dx

dt

=dW

dt

(y � x)Relates time rate of change of x to time rate of change of W.

W dx = dW (y � x)Relates change in x to change in W.

No connection to time evolution. Think “projectile trajectory.”

Sometimes this is referred to as “phase

space” or “state space”

Zx

x0

dx

y � x

=

ZW

W0

dW

W

= lnW

W0

Rayleigh Equation

To integrate the LHS term, we need to know y(x).

SHR §13.1


Zx

x0

dx

y � x

=

ZW

W0

dW

W

= lnW

W0

Rayleigh Equation Consider a single-stage with no reflux.

Option 1: assume that K = y/x is constant.

Option 2: assume that α is constant.

Zx

x0

dx

x (K � 1)= ln

✓W

W0

◆1

K � 1ln

✓x

x0

◆= ln

✓W

W0

◆(constant K)

↵ ⌘ KA

KB

=yA/xA

yB/xB

=y/x

(1�y)/(1�x)y =

↵x

1 + x (↵� 1)

Zx

x0

✓1 + x(↵� 1)

↵x

� x

◆�1

dx = ln

✓W

W0

◆

(constant α)

ln

✓W0

W

◆=

1

↵� 1

ln⇣x0

x

⌘+ ↵ ln

✓1� x

1� x0

◆�

Option 3: if T-x-y data are available, integrate numerically using the trapezoid rule.


Example: Constant BoilupSHR Example 13.1

It is easier to solve for W(x) than x(W)...

How do we connect W and x to t?

A batch still is loaded with 100 kmol of a binary mixture of 50 mol% benzene in toluene. As a function of time, make plots of:

(a) still temperature, (b) instantaneous vapor composition, (c) still-pot composition, and (d) average total-distillate composition.

Assume a constant boilup rate, 10 kmol/h of product, and a constant α of 2.41 at a pressure of 101.3 kPa (1 atm).

dW

dt= �D constant boilup...

W = W0 �Dt ) t =W0 �W

D

ln

✓W0

W

◆=

1

↵� 1

ln⇣x0

x

⌘+ ↵ ln

✓1� x

1� x0

◆�

Total amount distilled: W0 - W Amount of light key distilled: x0W0 - xW

y

avg =x0W0 � xW

W0 �W

average distillate composition (see SHR eq. (13-6))

0 2 4 6 8 100

0.2

0.4

0.6

0.8

1

t(h)

Mol

e Fr

actio

n

x y yavg W/W0

0 2 4 6 8 10

95

100

105

110

t(h)

T (K

)

From the T-x-y data in SHR Table 13.1, we get T

from x.


Example: Using Tabular Data

Zx

x0

dx

y � x

= lnW

W0Z b

af(x)dx ⇡ b�a

2 [f(a) + f(b)] trapz in matlab...

A batch still is loaded with 100 kmol of a binary mixture of 50 mol% benzene in toluene. As a function of time, make plots of:

(a) still temperature, (b) instantaneous vapor composition, (c) still-pot composition, and (d) average total-distillate composition.

Assume a constant boilup rate, 10 kmol/h of product, and use the T-x-y data in SHR Table 13.1.

x y T 0.0 0.0 111

0.10 0.208 105.30.20 0.372 101.50.30 0.507 980.40 0.612 95.10.50 0.713 92.30.60 0.791 89.70.70 0.857 87.30.80 0.912 850.90 0.959 82.70.95 0.980 81.41.0 1.0 80.1

SHR Example 13.2

x decreases in time from 0.5.

Different approach to get this term. Otherwise it is the same as the last example.


Batch Distillation with Constant Reflux Ratio

Assumptions: • McCabe-Thiele analysis (see notes on binary

distillation)

• Total condenser

• Constant molar overflow

• Only heat transfer is in condenser and reboiler (not in the rectifying section)

• Constant V and R (implies constant L and D)

SHR §13.2.1

xD is a nontrivial function of xW, depending on # stages, reflux ratio, equilibrium, etc.

That means that this integral is not easy to get!

ZxW

xW0

dx

W

x

D

� x

W

= lnW

W0

came from the mole balance (see slide 2)

Concept: • Use McCabe-Thiele to get the relationship between xD and xW. • Given the graphically-obtained integrand, carry out the

integration to find W(xW). • Choose xW - find W - find t.

t =W0 �W

V (1� L/V )

=R+ 1

V(W0 �W )

QB

W, xW

D, xDL, xD

V, yD

Time to reach amount W in still.

dW

dt= L� V = �D

Z W

W0

dW = (L� V ) t

W = W0 + (L� V ) t

= W0 + V (L/V � 1) t

= W0 �V

R+ 1t


McCabe-Thiele to get (xD - xW) Assume that the number of theoretical stages

(Nt) and the reflux ratio (R) are known.L

V=

R

R+ 1

adjust xD

ZxW

xW0

dx

W

x

D

� x

W

= lnW

W0

1.Choose xW.

2. Construct an operating line with the prescribed R such that in Nt stages, we hit the intersection of the operating line and the 45º line. This defines xD for the xW chosen in step 1.

3. Repeat steps 1-2 for the desired range of xW, choosing “enough” points to do step 4.

4. Numerically integrate (trapezoid rule) to find ln(W/W0).

5. From W, find t. t =W0 �W

V (1� L/V )

=R+ 1

V(W0 �W )

Calculate average distillate composition over time t as before:

xW(t)

x

avgD =

xW0W0 � xWW

W0 �W


Batch Distillation with Constant xD Idea: constant V and vary R in time to obtain a desired xD.

• More difficult than constant R, but typically more desirable.

• Implies that D is changing in time.

dt = VW0 (xD � xW0)dxW�

1� LV

�(xD � xW )2

t = VW0 (xD

� x

W0)

ZxW

xW0

dx

W�1� L

V

�(x

D

� x

W

)2Use McCabe-Thiele to get values of

the integrand graphically.

Recall that xD is known (constant) and V is constant, but L/V is changing depending on xW.

SHR §13.2.2

x

avgD =

xW0W0 � xWW

W0 �W

) W = W0

xD � xW0

xD � xW

�

dW/dt, assume constant xD and rearrange...

dW

dt

= W0xD � xW0

(xD � xW )2dxW

dt

(V � L) = W0xD � xW0

(xD � xW )2dxW

dt


1. Choose xW.

2. Construct an operating line with R such that in Nt stages, we hit the intersection of the operating line and the 45º line. This defines R for the xW chosen in step 1.

3. Repeat steps 1-2 for the desired range of xW, choosing “enough” points to do step 4.

4. Numerically integrate (trapezoid rule) to find t for a given xW.

t = VW0 (xD

� x

W0)

ZxW

xW0

dx

W�1� L

V

�(x

D

� x

W

)2

x

yx =

y

0 1.0

1.0

xDxW1xW2

W = W0

xD � xW0

xD � xW

�

R(t)

xW(t)


Documents

Batch Distillation - James C. Sutherland · PDF fileSimple Binary Batch Distillation Analysis Q B D, y W, x D! Distillate molar ﬂow rate! W! Moles of “residue” in the still!