Thermodynamic Geometry 2

Peter SalamonUdine Advanced School

October 2005

Distillation -- an application

Distillation

• Sequence of K-stages• Min Exergy cost implies

constant distance stages

• Stages need heat input– diabatic column

L1

L2

L3

L4

L5

L6

L7

V7

V6

V5

V4

V3

V2

V1

L7

L6

V7

V6L5

L4

V5

L3

V4

V3 L2

V2 L1

V1

D, XD D, XD

F, Xf F, Xf

Additional

Heat Sinks

And

Heat Sources

QD QD

QB QB

B, XBB, XB

Adiabatic Diabatic

A False Stumbling Block

• Only a semi-metric– Scaling directions have zero length– Change of phase has zero length

Constant distance means that we should choose each Ti such that

Can construct these heat capacities

Heat capacity of

Vi+1

Li

coexistence

Heat capacity that turns distillation problem into a coffee

cup problem

-40

-30

-20

-10

0

10

20

30

40

0 10 20 30 40 50 60 70

Comparison of heat requirements

Plate number

Kilojoules of heat added

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 10 20 30 40 50 60 70

Equal thermodynamic distance heat demand (ends omitted)

Plate number

Heat (in Kilojoules)

Economic Realities

Investment $ vs. Operating $

More trays. Smaller reboiler

More heat exchangers. Smaller condenser

Same total area

More(?) heat pumps There exist clever heat pumps

Saves 75% of the exergy cost

ca. 200% of the capital cost

Political realities: Installation is gathering dust, within $200K of finished after $3M invested. Ricardo Rivero had a physical breakdown over it.

Exercise as prelude to Lecture 3