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Lecture 8
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Lecture 8 1
Non-Equilibrium Thermodynamicsfor Engineers
” Optimal units in chemical processes”
Signe Kjelstrup, Chair of Engineering Thermodynamics
Department of Process and Energy TU Delft
Lecture 8 2
2. law optimisation: Which path givesminimum total entropy production?*
• The distillation column
• The chemical reactor
Two process unit examples
0)/( 0 >= dtdSTw irrlost
* Use control theory or Euler Lagrange optimisation
Lecture 8 3
The adiabatic distillation column
Feed
Condenser
Reboiler0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.05 0.3 0.55 0.8Mole fraction of benzene in liquid, xB
Mo
lefr
acti
on
of
ben
zen
ein
vap
or,
y B
McCabe-Thiele diagram
Lecture 8 4
Find the minimumtotal entropy production,given the product purity!
Lecture 8 5
Optimal distillation is diabatic
• The entropyproduction is smaller in a diabatic column!
• It is also reducedwhen the numberof trays, N, increases
5 10 15 20 25 30 35 400
1
2
3
4
5
6
7
8
9
N
Tot
al e
ntro
py p
rodu
ctio
n /
(J
/ K s
)
AdiabaticDiabatic
The area for heat transfer was not constrained in this optimisation
Lecture 8 6
The result: Diabatic distillation
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
0.05 0.3 0.55 0.8
Mole fraction of benzene in liquid, xB
Mo
lefr
acti
on
of
ben
zen
ein
vap
or,
y B
iF
reb iB
NN−1
21
condiD
Qx
QQQ
x
Feed
Distillate
Bottom
x
Lecture 8 7
Optimal distillation is diabatic• The amount of heat added
(“duty”) in the stripping and rectifying section can bedetermined: i
F
reb iB
NN−1
21
condiD
Qx
QQQ
x
Feed
Distillate
Bottom
x
Lecture 8 8
Distillation columns with high efficiency
• Left: Heat IntegratedDistillationColumn*
• Right: Solutionfrom optimisationstudy**
*Olujic et al., TU Delft **PhD of Røsjorde, NTNU, 2005
Lecture 8 9
Optimal distillation is diabatic
• The vapor and liquid flowsare no longer constant
iF
reb iB
NN−1
21
condiD
Qx
QQQ
x
Feed
Distillate
Bottom
x
PhD of Gelein de Koeijer, NTNU, 2003PhD of Aris de Rijke, TU Delft, 2007
Lecture 8 10
Steam reforming
CH4 + H2O =CO+ 3H2
CH4+ 2H2O =CO2 + 4H2
CO + H2O =CO2 + 3H2
Lost work in the reformer of an ammonia plant: 5.0 109 / 106 Tonnes
Lecture 8 11
Optimal chemical reactor
• What is the optimal temperature of the heater (coolant) outside the reactor?
D
z0 L
ξ in
ξout
Tin
pin
(z)Ta
T
p(z)
ξ(z)
T out
pout
(z)
Lecture 8 12
The plug flow reactor model
0/
LirrdS dt dz=Ω σ∫
( / ) 1/ 1/( / )( / )
( )i i q ar G T J T Tv T dp dz
σ= −Δ + −
+ −
• No gradients in the radial direction
• The reference system to be optimized is given by Froment et al. -96, -89, Nielsen 1968.
• Rates are highly non-linear functions of the forces
• A constant overall heat transfer coefficient U is used
D
z0 L
ξout
(z)Ta
T
p(z)
ξ(z)
T out
pout
(z)
ξ in
Tin
pin
Lecture 8 13
Lecture 8 14
Optimal reactor performance
• The entropyproduction is constant in a part of the reactor.
• There is a reactionmode and a heat transfer mode of operation
• An optimal length can be determined 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
10−4
10−3
10−2
10−1
100
ξ
σ /
(J
/ K m
s)
Reaction Heat transferTotal
Lecture 8 15
Reformer technologies*
• Prereformer: adiabatic
• Tubular reformer: with heat transfer
•From Haldor Topsoe ASA http://www.topsoe.com/site.nsf/all/BBNN-5PFHXR?OpenDocument
Lecture 8 16
Optimal reactor performance
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9700
900
1100
1300
ξ
T /
K
The optimal solutions are crowdedon a “highway” in state space!
Equilibrium in chemical rx
Access paths
State diagram for SO2 oxidation rx
Line for max rx-rate
When do we prefer a highway?
Lecture 8 17
Energy efficient design
• Optimal distillation columns allow for heat exchange along the column, and a distribution of available heat transfer area
• Optimal chemical reactors have a reactionmode and a heat exchange mode, plus anoptimal length