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

QQ

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

QQ

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

QQ

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