Prospects for the Development of Low-Exergy-

Loss Chemical Engines

Chris Edwards, Kwee Yan Teh, Shannon Miller,

Matthew Svrcek

Department of Mechanical EngineeringStanford University

40%40%

32%32%

The Carnot MisconceptionReversible, Heat,

Isothermal/AdiabaticReversible, Matter, Isothermal

Reversible, Matter, Adiabatic

(Stirling, Ericsson)

(Fuel Cell+Electric Motor)

(I.C. Engines)

Stoichiometric hydrogen/air, To = 300 K

Fuel Cell Polarization Curve

Electrical Current Density i (A/m2)

Ele

ctric

al P

oten

tial φ

(V)

oE

E ReactantPreparationChannel Loss& UtilizationAnode Polar.Cathode Polar.

Ohmic Loss

Mass DiffusionRate Limit

Open Circuit Potential

Delivered Potential

Delivered PowerII

rev

W iW i

φ φη = = =&

& E E

The Carnot Misconception

CarnotReversible, IsothermalReversible,Adiabatic

Poor kinetics (polarization) is the key irreversibility in fuel cells.

PEM Fuel Cell

ImprovedKinetics

The Carnot MisconceptionReversible, Heat,

Isothermal/AdiabaticReversible, Matter, Isothermal

Reversible, Matter, Adiabatic

(Stirling, Ericsson)

(Fuel Cell+Electric Motor)

(I.C. Engines)

Stoichiometric hydrogen/air, To = 300 K

Nat. Gas

Dry Air Flue Gas

Shaft Work

3m

2a 4m2f

1f 1a 5m

1 2 3 4 5 60

10

20

30

40

50

Conversion Device

Exe

rgy

Loss

(%)

Device Key:1-Fuel Compressor2-Air Compressor3-Premixer4-Combustor5-Turbine6-Exhaust

Efficiency (LHV): 42.7Exergy Efficiency: 41.1

200 300 400 500 600 700 80030

35

40

45

50

55

Air-Specific Work (kJ/kg-air)

Firs

t-Law

Effi

cien

cy (%

LH

V)

10

204060

80100

10

20

4065100125

150

10

20

40

65100150

200

1600 K1800 K2000 K

1 2 3 4 5 60

10

20

30

40

Conversion Device

Exe

rgy

Loss

(%)

Device Key:1-Fuel Compressor2-Air Compressor3-Premixer4-Combustor5-Turbine6-Exhaust

Efficiency (LHV): 48.4Exergy Efficiency: 46.5

GT Exergy Loss

The Carnot Misconception

Unrestrained reaction is the key irreversibility in I.C. engines.

CarnotReversible, IsothermalReversible,Adiabatic

Brayton, 50:1Pressure Ratio

EnergyDensity

The Carnot Misconception

CarnotReversible, IsothermalReversible,Adiabatic

In neither case are conclusions based on Carnot of relevance.

Two Approaches to Reaction• Unrestrained

– Reactants are initially internally restrained, i.e., frozen in chemical non-equilibrium (e.g. combustion, fuel reforming).

– Internal restraint is released, allowing reaction to proceed.– Reaction “stops” when equilibrium is achieved or kinetics are so

slow as to be negligible (frozen again).– Inherently irreversible.

• Restrained– Reactants are initially externally restrained, i.e., in chemical

equilibrium (e.g. electrochemistry, solution chemistry).– External restraints are changed, allowing reaction to proceed.– Never stops; always dynamically balanced.– Reversible in the limit of infinitesimal rate and constrained

chemical pathway (chemical reversibility).

Change of Restraints• Removal of an internal restraint generates entropy.

• Entropy generation from a change of external restraintsdepends on the rate wrt internal equilibration processes.

Inherently irreversible(exergy destroyed)

Irreversibility dependsupon the relative rates

t

S InternalRestraintRemoved

Systemstate(s)

1, 1

Systemstate

2

Systemstate notdefined

S=Sgen

U ,V ,Ni

Phase Phase U ,V ,Ni

t

S ExternalRestraintChanged

Systemstate

1

Systemstate

2

U ,V ,Ni

S - SP,0 (kJ/kg

fuel -K)

U-U

P,0

(MJ/

kgfu

el)

P increases

T increases

Reactants (frozen)

Products (with full

dissociation)

Unrestrained Reaction

Stoichiometric propane/air, adiabaticFrozen reactants (no dissociation)Equilibrium products (full dissociation)

Isobars: 0.1, 1, 10, 100 bar Reactant Isotherms: 1000, 2000 KProduct Isotherms: 1000, 2000, 3000 K

log10 (V/VP,0)

Exergy Destruction via Unrestrained Reaction

Stoichiometric propane/air mixture modeled as ideal gases. Isochoric, adiabatic combustion.Includes the effects of variable specific heats, reaction, & dissociation.

Efficiency by Extreme Compression

?

Extreme-Compression Post-Combustion Conditions

Stoichiometric propane/air mixture modeled as ideal gases. Includes the effects of variable specific heats, reaction, & dissociation.

3300K! 1000 bar!

Extreme Compression Concept

• High compression ratio, ~100:1

• Two pistons (balanced forces)

• High speeds, M~0.3 (reduced time for heat transfer)

- air at 300 K, speed of sound ~ 350 m/s 100 m/s

- for reference: 3000 RPM and 90 mm stroke 9 m/s

Proof-of-Concept Apparatus

Modeling the Concept

0 0.05 0.1 0.15 0.2 0.250

2

4

6

8

10

12

Pisto

n Po

sitio

n (m

)

Time (s)

0 0.05 0.1 0.15 0.2 0.25-200

-150

-100

-50

0

50

100

150

Pisto

n Sp

eed

(m/s)

Time (s)

Single piston, w/out combustion, CR 100:1

0 0.05 0.1 0.15 0.2 0.250

0.5

1

1.5

2

2.5

3

Mas

s (kg

)

Time (s)

0 0.05 0.1 0.15 0.2 0.250

100

200

300

400

500

600

Pres

sure

(bar

)

Time (s)

Combustion ChamberDriverReservoir

Junkers Free-Piston Compressor

Van Blarigan/Aichlmayr Linear Alternator Concept

Prototype Schematic

• Specifications:50:1 CR150 m/s max PSnon-combusting

• Testing: Piston ringsPoppet valve jitterPosition sensing

Restrained Reaction• The objective is a reaction architecture that is reversible

in the limit of infinitesimal rate.• Internal restraints are not permitted.

– The fluid is either chemically frozen throughout the process (inert) or in chemical equilibrium.

• External restraints are absolutely required.– Work provides an entropy-free interaction.– Heat provides an entropic interaction.– Matter provides a mixed mode of interaction.

• By varying the external restraints, the reactants may be “reversibly” transformed to products.

A Restrained Chemical Engine

Heat

HumidAir

Water and�Depleted Air

NafionWork

Protons Electrons

Hydrogen

M

2

2, ,

• 2 2

2

Anode:

2gas a nafion a anodeH H e

H H e

μ μ μ+ −

+ −+

= +% %

2 2

2 2, , ,

• 2 2 0.5

2 2 0.5

Cathode: nafion c cathode gas c gas c

O H OH e

H e O H O

μ μ μ μ+ −

+ −+ +

+ + =% %

2 2 2

2 2 2

(

, ,

, , ,

, ,

Chemical Affinity)

,

•

2 0

Nafion connected, open circuit to motor:

.5 2

0.5r overall

nafion anode nafion cathodeH Hgas a cathode gas c anode gas cH O H Oe e

gas a gas c gas cH O O

G

H

μ μ

μ μ μ μ μ

μ μ

+ +

− −

−Δ =−

=

+ + = +

+ −

% %

% %

14442A

( )( )2

2cathode anode

anode cathodee e

F φ φ

μ μ− −

−

= −% %4443 144424443

A Restrained Reaction Engine w/out Electrochemistry?

)()(

),(),(

),(),(

22

22

22

chamberreactionOHcylinderOH

chamberreactionaqOcylindergO

chamberreactionaqHcylindergH

μμμμμμ

===

122 2 2

Gibbs-Duhem: d sdTH O

PH O

vdμ = − ++

10-2

10-1

100

101

102

103

104

105

106

-350

-300

-250

-200

-150

-100

-50

0

50

P/P0

μ (k

J/m

ol)

Chemical Equilibrium, 300K

H2 (kJ/molH2) O2 (kJ/molO2)

H2 + ½ O2 (kJ/molReaction)

Incompressible H2O(l)(kJ/molH2O)

H2 + ½ O2 H2O

Po = 1 bar

Pressure Retarded Osmosis

Sat. NaCl: πο = 380 atm Dead Sea: πo > 500 atm

Osmotic PotentialsΔμosmotic = VA × π0, where VA is the molar volume of pure solvent A,

and π0 is osmotic pressure of the solution wrt A.Assumes: - constant T and VA

- limit process: osmosis proceeds until the solution is infinitely dilute

For liquid water as solvent A, Vwater(l) = 1.8 ×10−5 m3 [mol water (l)]−1

2.5×10 0241 .1.3×10+5H2 + ½O2 → H2O>9.5×10−3>0.9 .>500Dead Sea

7.2×10−30.6 .380Sat. NaCl4.7×10−40.0425Typ. sea water

(eV)Δμosmotic (kJ mol−1)π0 (atm)

Conclusions• Efficiency of simple-cycle engines can be more than

doubled—current exergy efficiencies are less than 50%.• The key to systematically improving engine efficiency

(both simple and compound) is exergy management.• Exergy destruction due to combustion must be reduced.

This can be achieved by positioning of reactants to states of extreme energy density.

• Restrained reaction is possible electrochemically. Reducing irreversibilities due to slow kinetics (reaction and transport) is the key.

• Possibility exists for a non-electrochemical, restrained reactive engine. Making it practical remains a challenge.