f01_11

Seader & Henley, Separation Process Principles 1

Separation Processes • Absorption – Solutes removed from a gas into a liquid

•  Solutes removed from liquid into gas is called stripping or desorption

•  Distillation – Thermal vapor-liquid separation processes (Ch 11); vapor phase generated from liquid

•  Liquid-liquid extraction – Solute extracted from liquid A into an immiscible liquid B (a solvent)

•  Leaching (extraction) – Solute extracted from a solid into a solvent phase (liquid, dense gas, or supercritical fluid)

•  Membrane processing – Molecules separated using a dense (non-porous film) or porous physical barrier

•  Filtration – Suspended solids separated from a liquid or gas phase using a porous membrane

2

Methanol more volatile than water

Pm > Pw

Pm > 1 atm

Vapor-liquid equilibria... (e.g. ideal, methanol-water system)

BP diagram at const P (ideal)

dew-point

bubble-point

x = y (1 component)

x-y diagram at const P

P (= pm + pw) diagram at const T

3

f02_18

Ethanol more volatile γePe > γhPh

Ethanol less volatile γePe < γhPh

x = y at 58oC

Low T

High T

Vapor-liquid equilibria... (e.g. non-ideal, n-hexane-ethanol system)

4

The greater the separation between the equilibrium and 45o

line, the easier the separation

Getting into separations

x = y

x-y diagram at const P

€

α AB =yA / xA

yB / xB

=yA / xA

(1− yA ) /(1− xA )

α AB =PA

PB

€

yA =α AB xA

1+ (α AB −1)xA

if α AB =1, yA = xA

5

The greater the separation between the equilibrium and 45o

line, the easier the separation

Simple flash distillation (single stage; heated to T, phase split)

x = y

x-y diagram at const P

€

F = V + LFxF = Vy + Lx∴ FxF = Vy + (F −V )x

heater separator F, xF

V, y

L, x 6

f01_11

Where liquid is stripped of A by raising vapor from reboiler Stripping section

Binary distillation of components A & B (A is more volatile, e.g. methanol (A)-water (B) system)

Where “cold” reflux liquid condenses some or the vapor Enriching section

Vapor enriched

in A

Liquid depleted of

A

Near yA = 1 @ TB,A (light boiler)

Near xB = 1 @ TB,B (high boiler)

7

€

F = D+W (molar flow)FxF = DxD +WxWDF

=xF − xWxD − xW

, WF

=xD − xFxD − xW

€

Vm+1 = Lm −WVm+1ym+1 = Lmxm -WxW

€

ym+1 =LmVm+1

xm −WVm+1

xW

€

Vn+1 = Ln + DVn+1yn+1 = Lnxn + DxD

€

yn+1 =LnVn+1

xn −DVn+1

xD

W xW

8

Approximation - Constant molal overflow

•  Liquid and vapor flowrates are nearly constant in rectifying (top) and stripping (bottom + feed plate) sections –  Ln=Ln+1=Ln+2… Vn=Vn+1=Vn+2… –  L and V, rectifying; L and V, stripping

•  ΔHv (condensing high boiler) ≈ ΔHv (vaporizing low boiler)

•  Operating equations or lines are linear

€

yn+1 =LnVn+1

xn −DVn+1

xD

€

ym+1 =LmVm+1

xm −WVm+1

xW

9

Variables

•  # Plates, plate design, height of column, etc. (later)

•  Cooling in condenser –  Liquid returned to top of column

(reflux) •  Heating in reboiler

–  Vapor returned to bottom of column

•  Location and conditions of feed –  Cold? Hot? L or V or L-V?

10

€

R =LnD

=Vn+1 −D

D (overhead product, L at B.P.)

€

yn+1 =R

R +1xn −

1R +1

xD

Top plate (1) Total condenser

Partial condenser

11

•  Reboiler with saturated steam

•  Condenser with cooling water

Heating and cooling requirements

€

ms =Vm+1λλ s

€

λ = latent heat steamλs = latent heat vapor mixtureVm +1 = vapor flowrate from reboiler (stripping section)

€

mw =Vn+1 λ

(T2 −T1)c p,w

€

cp,w = heat capacity cooling water(T2 −T1) = Temp change in cooling waterVn+1 = vapor flowrate into condensor

12

q > 1 (sub-cooled L)

q = 1 (@ BP)

0 < q < 1 (L-V)

q = 0 (@ D.P.)

q < 0 (superheated V)

Feed conditions

€

q =moles L in stripping section from feed

moles feed

q =HV (D.P.)−HF

HV (D.P.)−HL (B.P.)

q =(HV −HL ) + cp,L (TB −TF )

HV −HL

€

Lm = Ln + qF (stripping)Vn =Vm + (1− q)F (rectifying)

€

y =q1− q

x − 11− q

xF13

McCabe-Thiele Method - # of ideal plates McCabe & Thiele, Industrial Engineering & Chemistry Research, 17 (1925) 605.

V=L, R→∞ (total reflux)

y=x (P=Pi at each tray)

14

€

yn+1 =R

R +1xn −

1R +1

xD

xD ≡ design condition R ≡ design variable

Rectifying section

15

Stripping section

€

ym+1 =LmVm+1

xm −WVm+1

xW

16

Feed conditions (feed line)

@ D.P.

@ B.P.

€

yn+1 =R

R +1xn −

1R +1

xD

€

ym+1 =LmVm+1

xm −WVm+1

xW

€

y =q1− q

x − 11− q

xF

17

Putting it all together…

€

yn+1 =LnVn+1

xn −DVn+1

xD

€

ym+1 =LmVm+1

xm −WVm+1

xW

€

y =q1− q

x − 11− q

xF

18

Stepping off stages (start at xD)

What we want in overhead product

What we want in bottoms product

(start here)

operating equilibrium

x = xF

4 stages + reboiler

19

x = xW

Minimum # of plates

€

αav = (αAαB )1/ 2

€

Fenske equation :

Nm =

ln xD(1− xD )

(1− xW )xW

lnαav

*includes rebioler

OR

xB xD

V=L (op lines = 45o)

R→∞ (total reflux)

20

Minimum reflux (occurs @ pinch point, P)

€

yn+1 =R

R +1xn −

1R +1

xD€

Rm

Rm +1=xD − y

'

xD − x'

y ',x ' @ pinch point

21