Seader & Henley, Separation Process Principles
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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
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Vapor-liquid equilibria...
(e.g. ideal, methanol-water system)
BP diagram at const P (ideal)
x-y diagram at const P
Methanol more
volatile than water
dew-point
x=y
(1 component)
bubble-point
Pm > Pw
Pm > 1 atm
P (= pm + pw) diagram at const T
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Vapor-liquid equilibria...
(e.g. non-ideal, n-hexane-ethanol system)
Low T
Ethanol more
volatile
γePe > γhPh
x=y
at 58oC
Ethanol less
volatile
γePe < γhPh
High T
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Getting into separations
x-y diagram at const P
x=y
The greater the
separation
between the
equilibrium and 45o
line, the easier the
separation
α AB =
yA / xA
yA / xA
=
yB / xB (1− y A ) /(1− x A )
yA =
α AB =
PA
PB
if α AB = 1, y A = x A
α AB x A
1+ (α AB −1)x A
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Simple flash distillation
(single stage; heated to T, phase split)
x-y diagram at const P
F =V + L
FxF = Vy + Lx
x=y
∴ FxF = Vy + (F − V )x
€
The greater the
separation
between the
equilibrium and 45o
line, the easier the
separation
V, y
F, xF
heater
separator
L, x
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Binary distillation of components A & B
(A is more volatile, e.g. methanol (A)-water (B) system)
Near yA = 1 @ TB,A
(light boiler)
Where “cold” reflux
liquid condenses
some or the vapor
Enriching section
Liquid
depleted of
A
Where liquid is
stripped of A by
raising vapor from
reboiler
Stripping section
Vapor
enriched
in A
Near xB = 1 @ TB,B
(high boiler)
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F = D + W (molar flow)
Fx F = Dx D + WxW
D x F − xW
W xD − xF
=
,
=
F x D − xW
F x D − xW
€
Vn +1 = Ln + D
Vn +1y n +1 = Ln x n + Dx D
€
Ln
D
xn −
xD
Vn +1
Vn +1
Vm +1 = Lm − W
Vm +1 y m +1 = Lm x m - WxW
€
W
xW
y n +1 =
€
y m +1 =
Lm
W
xm −
xW
Vm +1
Vm +1
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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
Lm
W
y m +1 =
xm −
xW
Vm +1
Vm +1
Ln
D
y n +1 =
xn −
xD
Vn +1
Vn +1
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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?
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R=
Ln Vn +1 − D
=
(overhead product, L at B.P.)
D
D
y n +1 =
€
R
1
xn −
xD
R +1
R +1
€
Top plate (1)
Total
condenser
Partial
condenser
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Heating and cooling requirements
• Reboiler with saturated steam
λ = latent heat steam
λs = latent heat vapor mixture
Vm +1 = vapor flowrate from reboiler (stripping section)
V λ
ms = m +1
λs
€
• Condenser with cooling water
€
Vn +1 λ
mw =
(T2 − T1 )c p,w
c p,w = heat capacity cooling water
(T2 − T1 ) = Temp change in cooling water
Vn +1 = vapor flowrate into condensor
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Feed conditions
q>1
(sub-cooled L)
q=1
(@ BP)
0<q<1
(L-V)
moles L in stripping section from feed
moles feed
HV (D.P.) − H F
q=
HV (D.P.) − H L (B.P.)
q=
q=
€
(HV − H L ) + c p,L (TB − TF )
HV − H L
Lm = Ln + qF
(stripping)
Vn = Vm + (1− q)F (rectifying)
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q=0
(@ D.P.)
q<0
(superheated V)
y=
q
1
x−
xF
1− q
1− q
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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)
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Rectifying section
xD ≡ design condition
R ≡ design variable
y n +1 =
R
1
xn −
xD
R +1
R +1
€
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Stripping section
Lm
W
y m +1 =
xm −
xW
Vm +1
Vm +1
€
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Feed conditions (feed line)
y n +1 =
R
1
xn −
xD
R +1
R +1
@ B.P.
y=
q
1
x−
xF
1− q
1− q
€
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@ D.P.
y m +1 =
Lm
W
xm −
xW
Vm +1
Vm +1
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Putting it all together…
y n +1 =
Ln
D
xn −
xD
Vn +1
Vn +1
€
y=
q
1
x−
xF
1− q
1− q
€
y m +1 =
Lm
W
xm −
xW
Vm +1
Vm +1
€
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Stepping off stages (start at xD)
operating
equilibrium
x = xF
4 stages + reboiler
x = xW
What we want in
bottoms product
(start here)
What we want
in
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overhead product
Minimum # of plates
Fenske equation :
 x D (1− xW ) 
ln

(1−
x
)
x


D
W
Nm =
ln α av
*includes rebioler
OR
V=L (op lines = 45o)
R→∞ (total reflux)
€
1/ 2
α av = (α Aα B )
€
xB
xD
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Minimum reflux
(occurs @ pinch point, P)
Rm
xD − y'
=
Rm + 1 x D − x '
y ' , x ' @ pinch point
y n +1 =
R€
1
xn −
xD
R +1
R +1
€
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