Understanding the Path to High- Efficiency Chemical Engines

Chris F. Edwards

Kwee

Yan Teh, Shannon Miller, Matthew Svrcek, Sankaran

Ramakrishnan, and Adam Simpson

Advanced Energy Systems Laboratory Department of Mechanical Engineering

Stanford University

40%40%

34%34%

>74% of U.S. CO2

is emitted by engines.

Engines•

All

engines have three essential features:

–

they produce work (by definition)–

they require a resource (1st

Law)

–

they reject energy to surroundings (2nd

Law)

Engine WorkEnergy Resource

Rejected Energy

(surroundings)

Efficiency Limits•

Only

four ways to transfer energy:

–

work (entropy free)–

heat (energy transfer due to ΔT )

–

matter (internal and external)•

External:

K.E., gravitational P.E., electrostatic P.E.

•

Internal: thermal, chemical, nuclear

–

radiation (not considered here)

•

It is the combination of energy resource and surroundings that determines the ultimate efficiency limitation of an engine (exergy).

Classifying Engines by Energy Resource

Hydrosphere

Atmosphere

Lithospher

e

Space

Sun

AccumulatedResources

Surface 

Water

Geothermal

Biosphere

HighK.E.

Moon

Anthrosphere

ChemicalEngines

(e.g., ICE)

NuclearEngines

(e.g., BWR)

HeatEngines

(e.g., Geo)

KineticEngines

(e.g., Wind)

RadiationEngines

(e.g., PV)

GravityEngines

(e.g., Hydro)

Chemical Exergy of Some FuelsFuel Chemical Chem. Exergy† ΔH° Reaction* ΔG° Reaction* ΔS° Reaction* Exergy Species+ Formula MJ per fuel MJ per fuel MJ per fuel kJ/K per fuel to LHV kmol kg kmol kg kmol kg kmol kg Ratio Methane CH4 832 51.9 -803 -50.0 -801 -49.9 -5.2 -0.33 1.037 Methanol CH3OH 722 22.5 -676 -21.1 -691 -21.6 50.4 1.57 1.068 Carbon Monoxide CO 275 9.8 -283 -10.1 -254 -9.1 -98.2 -3.51 0.971 Acetylene C2H2 1267 48.7 -1257 -48.3 -1226 -47.1 -104.6 -4.02 1.008 Ethylene C2H4 1361 48.5 -1323 -47.2 -1316 -46.9 -25.2 -0.90 1.029 Ethane C2H6 1497 49.8 -1429 -47.5 -1447 -48.1 60.5 2.01 1.048 Ethanol C2H5OH 1363 29.6 -1278 -27.7 -1313 -28.5 117.7 2.56 1.067 Propylene C3H6 2001 47.6 -1926 -45.8 -1937 -46.0 36.6 0.87 1.039 Propane C3H8 2151 48.8 -2043 -46.3 -2082 -47.2 129.2 2.93 1.053 Butadiene C4H6 2500 46.2 -2410 -44.5 -2421 -44.7 36.9 0.68 1.038 i-Butene C4H8 2644 47.1 -2524 -45.0 -2560 -45.6 120.2 2.14 1.047 i-Butane C4H10 2800 48.2 -2648 -45.6 -2712 -46.7 214.4 3.69 1.058 n-Butane C4H10 2805 48.3 -2657 -45.7 -2717 -46.7 200.0 3.44 1.056 n-Pentane C5H12 3460 48.0 -3272 -45.3 -3353 -46.5 271.3 3.76 1.057 i-Pentane C5H12 3454 47.9 -3265 -45.2 -3347 -46.4 277.0 3.84 1.058 Benzene C6H6 3299 42.2 -3169 -40.6 -3190 -40.8 69.4 0.89 1.041 n-Heptane C7H16 4769 47.6 -4501 -44.9 -4625 -46.2 415.0 4.14 1.060 i-Octane C8H18 5422 47.5 -5100 -44.7 -5259 -46.0 531.4 4.65 1.063 n-Octane C8H18 5424 47.5 -5116 -44.8 -5261 -46.1 487.1 4.26 1.060 Jet-A C12H23 7670 45.8 -7253 -43.4 -7440 -44.5 626.4 3.74 1.057 Hydrogen H2 236 117.2 -242 -120.0 -225 -111.6 -56.2 -27.88 0.977

+All species taken as ideal gases. †Environment taken as: 25°C, 1 bar, 363 ppm CO2, 2% H2O, 20.48% O2, balance N2 .*Reaction with stoichiometric air at 25°C, 1 bar. All products present as ideal gases, including water.

Fuel Conversion Efficiency potential (maximum first-law efficiency based on LHV) of most fuels is ~100%.

Classification & Architecture

Restrained

Reaction

Unrestrained

Reaction

ElectricalWork

(e.g., SOFC)

MechanicalWork

(e.g., None)

ElectricalWork

(e.g., MHD)

MechanicalWork

(e.g., GT)

Chemical

Engines

Architecture: the set of

components & connections, and the corresponding set of thermodynamic idealizations & device limitations that constitute a particular engine.

Classification: (1)

(2)

(3)

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 only in the limit

of infinitesimal rate and constrained chemical pathway (chemical reversibility).

Restrained vs. Unrestrained Architectures

* After Primus, et al. “Proceedings of International Symposium on Diagnostics and Modeling of Combustion in Reciprocating Engines, (1985) p.529-538.

Restrained (SOFC) Unrestrained (DI Diesel*)

•

Efficiency declines with load•

Irreversibility reduced via facile kinetics (reaction and transport)

•

Efficiency improves with load•

Irreversibility reduced by reaction at extreme states

Entropy Generation with Unrestrained Reaction

Stoichiometric

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

Four ways to transfer energy…

100

101

1020

20

40

60

80

100

Compression Ratio

First Law (per LHV)70-80% First LawFuel Exergy/LHV

Efficiency Achievable with Simple- Cycle Extreme Compression

CI

SI

Stoichiometric

propane/air

Firs

t-Law

Eff

icie

ncy

(%)

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!

Must be fast! Must be balanced!

Free-Piston Engines

Example: Junkers Compressor

M. Nakahara and H. Kohama, “Junkers High Pressure Air Compressor-A Case of Technology Transfer through the Imperial Japanese Navy,”

in The 1st international conference on business and technology transfer, 2004.

Van Blarigan/Aichlmayr

Linear Alternator Concept

Experimental Apparatus

16

Operating Space

Combustion VisualizationCR = 30:1 CR = 100:1

1 ms injection duration, finishing at TDC

Combustion Data at CR = 70

10-1100

101

102

Volume (V/V0)

Pres

sure

(bar

)

Air-onlyCombustionIsentrope

φ

= 0.35

19

First-Law Efficiency: Initial Results

10 20 30 40 50 60 70 80 90 100

30

40

50

60

70

80

90

Compression Ratio

Effic

ienc

y (%

)

First law (per LHV), φ = 0.3570-80% first lawCombustion data

20

First-Law Efficiency: Initial Results

10 20 30 40 50 60 70 80 90 100

30

40

50

60

70

80

90

Compression Ratio

Effic

ienc

y (%

)

First law (per LHV), φ = 0.3570-80% first lawCombustion dataTheoretical efficiency with air losses Losses in air

experiments

Additionallosses due tocombustion

21

First-Law Efficiency: Initial Results

10 20 30 40 50 60 70 80 90 100

30

40

50

60

70

80

90

Compression Ratio

Effic

ienc

y (%

)

First law (per LHV), φ = 0.3570-80% first lawCombustion dataTheoretical efficiency with air lossesLow blowby

53%, 20°C walls

Losses in airexperiments

Additionallosses due tocombustion

•

Confident we can demonstrate 60% indicated•

Speculate 70% is achievable regeneratively

Simple-Cycle Steady Flow

What is the optimal action to be taken (transfer or transformation) at each step in order to minimize Sgen

?

Challenges w/Steady Flow•

Irreversibility–

Chemical reaction

–

Reactant mixing–

Rejection of non-equilibrium exhaust

–

Polytropic

compression and expansion (Friction, viscous dissipation)

•

Material Limitations–

Temperature limit

–

Pressure limit

Polytropic

work

-0.5 0 0.5 1 1.5 2-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

s-si(kJ/kgmixK)

h-h i(M

J/kg

mix

)

i

b' c'

b

c

f '

f

Pi

a'a

Reversible WorkCycle

Net WorkOut

Equilibrium Attractor Trajectory

Irreversible Work Cycle

Pi

Premixed Reactants, GRI 3.0Polytropic

efficiency --

0.9

Optimal Pressure Ratio

100 101 102 1030

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Pressure Ratio

Ent

ropy

Gen

erat

ion

(kJ/

kgm

ixK

)

CombustionFluid FrictionTotal

P*

Nonpremixed

reactantsPolytropic

efficiency --

0.8

Effect of Polytropic

Efficiency

Polytropic Efficiency η

Pres

sure

Lim

it P* (b

ar)

0.6 0.65 0.7 0.75 0.8 0.85100

101

102

103

0.6 0.65 0.7 0.75 0.8 0.851500

1750

2000

2250

2500

2750

3000

3250

Max

imum

Tem

pera

ture

Tm

ax (K

)

Nonpremixed

reactants

In the absence of material limitations, the pressure ratio of today’s engines is well below optimum.

Temperature Limit

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8-1.5

-1

-0.5

0

0.5

1

1.5

s-si (kJ/kgmixK)

h-h

i (MJ/

kgm

ix)

Brayton (18.5:1)CT (40:1)CT(160:1)Attractor (160:1)Attractor (40:1)

f

c

i

Increasingwork-output

DecreasingSgenTemperature Limit : 1650K

A temperature-limited, extreme-state cycle gives the optimal simple-cycle GT architecture.

Nonpremixed

reactants Polytropic

efficiency --

0.9

T-Limited Simple-Cycle GT

Take-Home Messages (1 of 2)•

Despite three centuries of effort, engine efficiency remains well below theoretical limits

(resource exergy)—often by more than a factor of two.

•

Misconceptions

about what ultimately limits engine efficiency (e.g., Carnot) are sometimes to blame.

•

Working in the space between the exergy limit and real engines, we have found the ideas of classification and

architecture to be useful.

•

Our approach is to use the principles of optimal control

to identify the most efficient architecture

for any given set of allowable devices, resources, and environment.

•

For chemical engines, a key to understanding is whether the architecture uses restrained or

unrestrained reaction.

Take-Home Messages (2 of 2)•

Irreversibility in restrained reaction

engines can be reduced by improving kinetics. To date, the only examples of restrained reaction engines are electrochemical (i.e., fuel cells).

•

Irreversibility in unrestrained reaction

engines can be reduced by reaction at states of high energy density (extreme-states principle).

•

For simple-cycle engines, we believe that architectures capable of delivering 60% first-law efficiency

are possible.

•

For regenerative engines, we believe a systematic approach to identifying optimal architectures can be developed. We speculate that such engines are capable of 70% first-law efficiency.

•

For combined-cycle engines, we speculate that a systematic approach is again possible and can lead to the development of engines with first-law efficiencies in excess of 80%.

0.1

1.0

10.0

100.0

1600 1700 1800 1900 2000 2100Time (Years A.D.)

Firs

t-Law

Effi

cien

cy (%

) .

Savery, Newcomen (<0.5%)Watt/Boulton Steam EnginesPost-Watt Steam EnginesLenoir, Hugon Coal-Gas EnginesOtto/Langen Coal-Gas EnginesAtkinson, Tangye Coal-Gas EnginesBanki Spirits EnginePriestman's Oil EngineDiesel's Oil EnginesAutomotive SI EnginesTruck Diesel EnginesLarge Bore DI DieselsSteam TurbinesGas Turbine/Steam TurbinePolymer Electrolyte Membrane FCPhosphoric Acid Fuel CellsSOFC/Gas Turbine

Conversion Efficiency of Engines

50%

After three centuries of development, combined-cycle efficiency just exceeds 50%, simple-cycle remains below.

Work Extraction During CombustionOtto Cycle Processes

Detailed Chemical Kinetics Slider-Crank Piston Profile

All complete rxn solutions resulted in increased irreversibility!2nd Law

Conclusions invariant with changes in fuel (methane, methanol, propane), rate, piston profile, etc.

Optimal Control Problems

•

Linear system wrt

control input q ⇒ bang-bang control

•

Sgen is minimized when reactions occur at Vmin

•

The key is to manage the location of the u-v attractor

•

Strategy has no explicit dependence on kinetics

(Pontryagin

Max. Principle)

Optimal Piston Motion

Work Extraction During CombustionOtto Cycle Processes

Detailed Chemical Kinetics Slider-Crank Piston Profile

2nd Law

The key to reducing irreversibility in unrestrained reaction (combustion) is to drive the reactants to the highest u state.

u-v attractorstates

Restrained Reaction w/out Electrochemistry?

2 2

2 2

2 2

2

2 2

( , ) ( , )

( , ) ( , )

( ) ( )

( )

12( , ) ( , )

Transfer Restraint Requires:

Reaction Restraint Requires:

Gib

H g cylinder H aq reactor

O g cylinder O aq reactor

H O cylinder H O reactor

H O reactor

H aq reactor O aq reactor

μ μ

μ μ

μ μ

μ

μ μ

=

=

=

=

+

bs-Duhem Relation:d sdT vdPμ = − +

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 H2

O(l)(kJ/molH2O

)

H2

+ ½

O2 H2O

Po

= 1 bar

Pressure Retarded Osmosis

Sat. NaCl: πο

= 380 atm Dead Sea: πo

> 500 atm

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

Electrochemical Cell w/Losses

ReactantPreparation

TripleJunc.

TripleJunc.

TripleJunc.

TripleJunc.

CathodeReactants

ReactantCrossover

ElectrolyteMembrane

AnodeContact

CathodeContact

Reactants

AnodeContact

CathodeContact

BipolarPlates

-

+

ElectrolyteMembrane

ReactantCrossover

AnodeReactants

CathodeReactantChannel

AnodeReactantChannel

TransportLosses

…

…

ActivationLosses

42

Restrained/Unrestrained Expansion

maxoutW W= maxoutW W<

43

Restrained/Unrestrained Reaction

maxoutW W= maxoutW W<

RestrainedReaction

UnrestrainedReaction

44

Implementing Restrained Reaction

2 2

1 1

0

if is small for a given d

will be small

lost destroyed gen

i ii

gen

piston

gen

W X T S

AS d dT T

dx dAT

S

ξ ξ

ξ ξ

ν μξ ξ

ξ

ξ

= =

−= =

⇒

→

∑∫ ∫

The rate of change of the restraint must be slow compared to the internal relaxation time of the resource

in order to be fully restrained (reversible).

45

•

The reaction pathway must be open•

no constraints or additional restraints on the reaction•

reaction affinity equals zero before work is produced

•

Work must couple to the chemical reaction•

temperature•

pressure•

composition•

electrical potential

Requirements for Restrained Chemical Engines

determining parameters for electrochemical potential of reacting species

Minimum Sgen Solution1. Bang-bang solution, switching at P = Peq

2. Optimal over set of all

possible piston motions

P < Peq ⇒ compressionControl: dV < 01st. law: dU = −P dV

Constant-UV Equilibrium Attractor

Teq dSeq = dUeq + Peq dVeq

= dU + Peq dV= (−P + Peq ) dV

Teq dSeq < 0

V1 + dV

V1

U1

+dU

V

U1

U

S

Seq,1

S1

Seq,1

+dSeq

dSeq

Extracting energy during combustion can only

decrease efficiency. We are going the wrong way!

Exergy Destruction via Reaction

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

Effect of Compression

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

Effect of Heating & Cooling

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

Extreme Compression Concept

•

High compression ratio, ~100:1

•

Multiple pistons (balanced forces, ~unity aspect ratio)

•

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

55

Combustor Design

Combustor tested to 2000 bar

Material stress strategy: Use pressure profile to our advantage

Combustor bore

below 100 bar after 200 mm

Injectors (5)

Exhaust valve

56

Combustor Design and Injection

5 Bosch, diesel injectors (1500

bar) withcustomized

nozzles

57

Volume Measurement

Optical bar code. Outer diameter

reflects light, inner diameter

does not.Graphite bearings

Copper ring for thermally protecting

the rings

Graphitesealing ring

Piston Design

Steel ring for VR sensors

5878 80 82 84 86

20

40

60

80

100

120

140

160

Time (ms)

Pres

sure

(bar

)

800 g piston

58 59 60 61 62 63

20

40

60

80

100

120

140

160

Time (ms)

Pres

sure

(bar

)

350 g piston

30 40 50 60 70 80 90 100

0.2

0.4

0.6

0.8

1

Time (ms)

Vol

ume

(V/V

0)

800 g piston350 g piston

Air Compression: Initial Findings

MPS = 90 m/s

CR = 45

MPS = 60 m/s

CR = 45

59

31.5 32 32.5 33 33.5 34 34.520

40

60

80

100

120

140

160

180

200

Time (ms)

Pres

sure

(bar

)

Method of CharacteristicsExperimental

Simulating Acoustic WavesMethod of Characteristics simulations show that high piston

accelerations cause acoustic waves.

Shock forms due to lack of dissipation in model.

60

Air Data

10-2 10-1 100

100

200

300

400

500

Volume (V/V0)

Pres

sure

(bar

)

CR = 99Isentrope

Compression

Expansion

61

50 60 70 80 90 100-15

-14

-13

-12

-11

-10

-9

-8

Compression Ratio

Wne

t/LH

V (%

)

40 50 60 70 80 90 10085

90

95

100

Compression Ratio

P peak

/Pis

entro

pic (%

)

Total Losses Over an Air CycleLosses consist of heat and mass transfer (~50:50).

Percentage work lost per LHV Percentage isentropic pressure achieved

500 bar

Critical QuestionsCritical Question Extreme

Compression Apparatus

Extreme Compression Engine

Material stress

Wall temperatures and heat transfer

NOx

Seal survivability

Sealing ability

Ignition phasing

Combustioncontrol

solutions available and understood

more research required, but no obvious barriers

high priority for research

? ?

64

Aquifer Sequestration as Commonly Envisioned

65

Potential Problems with Aquifer Sequestration

66

Pre-equilibrated Aquifer Sequestration

Storage Security

Adapted from IPCC Special Report on Carbon Dioxide Capture and Storage 2005, p. 208

Conceptual Plant Schematic

Indirectly FiredCombined-

Cycle Engine

Pre-equilibrated StorageZero Emissions to Atm.42.1% Efficiency(LHV, 1600 K, 38°C)

Modeled System

Thermodynamic AnalysisComponent Power (MW)Brayton Cycle

Compressor -388.4Turbine 659.9

Net 271.5Rankine Cycle

Condensate Pump -0.026Feed Pump -2.27Turbine 331.6

Net 329.3ASU -73.2Water Pumps -27.5Overall Plant 500.0Heat Rate (LHV basis) 1188.4Overall Efficiency 42.1%

Combustor Outlet T=1600 KCondenser T=38°C

Experimental Schematic

Experimental Combustor

Mixing Entropy Generation

Unmixed NG/air at the same temperature and pressure. (~2% of comb. Sgen

)

Next: Regeneration

What is the optimal action to be taken (transfer or transformation) at each step in order to minimize Sgen

?

Work, Heat, and Matter with Closure Constraints and Environmental Interactions

Thermodynamic State-Space

Natural Gas –

Air, Equivalence Ratio 0.5

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.081

1.5

2

2.5

3

3.5

4

Work-Specific Carbon Emission to Atmosphere (kg-C/MJ-Work)

Wor

k-S

peci

fic E

xerg

y C

onsu

mpt

ion

(MJ-

Exe

rgy/

MJ-

Wor

k)

6FB

LM6000

LMS100

STIG

GTCC-H

Sub.Super

Elsam

EUDOE

Super-SFAGE1GE2

GE3Shell-SFAEgas

GTCC-SFA

GTCC-SFA

Super-SFAOxyPC-SFA

GE3Shell-SFA Sub.

Super

EUDOE

Super

ShellUltra

GE

Shell

Super

GE

ShellOxyPC

FGC1FGC2ATR

OxyNG

SI

SI-H

DICI

LBCI

LM6000DSIH2

PEM

PEM

PEM

SIMeOH

SIMeOH

CLSC

CLCC

SOGT-MSOGT-CASOGT-CBSOGT-CB

MC-Ultra-Coal-NG

SOGT-RASOGT-RBSOGT-RC

SOGT-ZSOGT-BA

SOGT-BB

SOGT-BCSOGT-C

MCGC-RAMCGC-RB

MCNG-RA

MCNG-RB

AZEPAZEPGraz

ATR-GTCCWC-K

SOGT-K

WC-GWC-G

CESMAT

100%

67%

50%

40%

33%

29%

25%

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.081

1.5

2

2.5

3

3.5

4

100%

67%

50%

40%

33%

29%

25%

Sub

Super

DOEPCEUPC

Ultra IGCC

SI

SIH

CI

Work-Specific Carbon Emission to Atmosphere(kg-C/MJ-Work)

Work-Specific Exergy Consumption

(MJ-Input-Exergy/MJ-Work)

Exergetic Efficiency

(MJ-Work/MJ-Input-Exergy)

ADGT

ICGT

GTCC

SOGT

RGT

HFGT

SI

SIH

CI

LBCI

ADGT

HCCI

PCCI

Hydrogen

SI

PEM

SIH

|? No Sequestration|? 50% Seq. ? |? | |? 90% Seq.

SI

SIHIGCC

Super

Oxy

GTCC

SOGT

OxyATRCCCLCC

IGCLMat

Graz

SOGT

AZEP

MCUltra

MCCC

IGMC

EC, GCEP

SCWC,

GCEP