Analysis of Vortex Tube Applications in Hydrogen Liquefaction

Marshall Crenshaw

Washington State UniversityPullman, WANovember 14, 2017

• >80% of global energy comes from fossil fuels.1

• Since 1976, global temperatures warmer than long-term average.2

• 11 of the top 12 hottest years are from 2003-2016.3

Why is Renewable Energy Necessary?

1 International Energy Agency Technical Report. Key World Energy Statistics. 2016 2 https://climate.nasa.gov/scientific-consensus/3 https://www.ncdc.noaa.gov/sotc/global/201613

• 9th most abundant element in earth’s crust

• Photo-biological bacteria produce hydrogen

H2 Production

http://www.fsec.ucf.edu/en/consumer/hydrogen/basics/images/HydrogenProductionPaths.gif

• Lowest volumetric density

• Containers are pressurized or cryogenic to increase density

Difficulties of H2

https://energy.gov/eere/fuelcells/hydrogen-storage

• Double density when liquefying over pressurizing

Liquid vs Pressurized H2

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70

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0 25 50 75 100 125 150 175 200

Den

sity

(kg/

m³)

Pressure of Compressed Hydrogen (MPa)

Pressurized Hydrogen

Liquid Hydrogen

Pressurized Tank @ 70 MPa

Pressurized Tank @ 35 MPa

• Inexpensive cooling device

• 1 high pressure stream 2 low pressure streams

• Transfers cold stream energy hot outer stream

• No moving parts

Diagram of Vortex Tube (VT)

• Low-cost cycle for hydrogen liquefaction

• Low-efficiency method for liquefaction

• Increase cycle efficiency by adding component

Pre-cooled Linde-Hampson Cycle

• Additional compressor and heat exchanger

• Cycle efficiency: Adding compressor > Adding throttle

• 3rd HX reduces O-P ratio of hydrogen

• What is O-P ratio?

Pre-cooled L-H cycle with VT

• Equilibrium O-P ratio depends on temperature of hydrogen

• Normal hydrogen 3:1 O-P ratio

• Liquid hydrogen all parahydrogen

• Catalyst added to HXs to maintain equilibrium O-P ratio

• Why is equilibrium hydrogen important?

Orthohydrogen & Parahydrogen

https://3c1703fe8d.site.internapcdn.net/newman/gfx/news/hires/2011/1-nuclearmagne.jpg

• 50% of normal hydrogen boils away in 200 hours

Importance of Ortho-Para Equilibrium

Gursu, S. et al. An Optimization Study of Liquid Hydrogen Boil-Off Losses,Int. J. Hydrogen Energy., v. 17, p. 227, 1992.

Statistical Thermodynamic Properties of H2

https://3c1703fe8d.site.internapcdn.net/newman/gfx/news/hires/2011/1-nuclearmagne.jpg

Stat Thermo

https://hydrogen.wsu.edu/2015/06/22/why-equilibrium-hydrogen-doesnt-exist/

REFPROP

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7.5

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Idea

l-gas

ent

halp

y [M

J/kg

]

Temperature [K]

Ortho [REFPROP]

Para [REFPROP]

REFPROP with Corrected Orthohydrogen vs. Stat Thermo

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enth

alpy

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Idea

l-gas

ent

halp

y [M

J/kg

]

Temperature [K]

Corrected Ortho

Para [REFPROP]

Stat Thermo

MATLAB

https://hydrogen.wsu.edu/2015/06/22/why-equilibrium-hydrogen-doesnt-exist/

r2 = 0.999996

Equilibrium Ofrac

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Equi

libriu

m O

rthoh

ydro

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tion

Temperature (K)

Piece-Wise Equilibrium H2 Function

Coefficients of equilibrium MATLAB function

a1 1.935x10-4 b1 -2.044 c1 1.111x10-7

a2 -5.832x10-3 b2 -2.724x10-2 c2 -2.243x10-6

a3 3.448x10-2 b3 0.75 c3 -1.886x10-5

c4 6.514x10-4

c5 -3.499x10-3

Ofrac =

a1T2 + a2T + a3 T ≤ 24.82Kb1eb2T + b3 T ≤ 51.51K

�i=1

4

ciTi + c5 T > 51.51K

Approximate Equilibrium O-P Function

0

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0 50 100 150 200 250 300Equi

libriu

m O

rthoh

ydro

gen

Frac

tion

Temperature (K)

Stat ThermoMATLAB

r2 = 0.99986

Liquefaction Components & Cycle Assumptions

• Bath pressure is atmospheric (101.3 kPa) and temperature is 77 K

• LN2 Bath is catalyzed: Ofrac = ~0.5

• Heat extracted:

�̇�𝑄𝐵𝐵𝐵𝐵𝐵𝐵𝐵 = �̇�𝑚𝐻𝐻2 ℎ𝐵𝐵𝐵𝐵𝐵𝐵𝐵,𝑖𝑖𝑖𝑖 − ℎ𝐵𝐵𝐵𝐵𝐵𝐵𝐵,𝑜𝑜𝑜𝑜𝐵𝐵 + Δℎ𝐵𝐵𝐵𝐵𝐵𝐵𝐵,𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐

• Added work to hydrogen liquefaction:

�̇�𝑊𝐵𝐵𝐵𝐵𝐵𝐵𝐵 =�̇�𝑄𝐵𝐵𝐵𝐵𝐵𝐵𝐵 �

𝐿𝐿𝐿𝐿2𝑖𝑖𝑖𝑖𝑖𝑖𝐵𝐵𝑖𝑖𝐿𝐿𝐿𝐿2𝐹𝐹𝐹𝐹𝐹𝐹

�̇�𝑚𝐿𝐿𝐻𝐻2 � Δ𝐻𝐻𝑐𝑐𝐵𝐵𝑣𝑣,𝑁𝑁2

LN2 Bath

𝐿𝐿𝐿𝐿2 𝐵𝐵𝐵𝐵𝐵𝐵ℎ

• Energy balance equation:

�𝑖𝑖=1

𝑖𝑖

∆ℎ𝑖𝑖 + ∆ℎ𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐,𝑖𝑖 = 0

• Minimum temperature approach solves for outlet temperatures

• Hot stream T limit: 𝑇𝑇𝐻𝐻𝑜𝑜𝐵𝐵,𝑜𝑜𝑜𝑜𝐵𝐵,𝑖𝑖𝑖𝑖𝑙𝑙𝑖𝑖𝐵𝐵 = Δ𝑇𝑇𝑙𝑙𝑖𝑖𝑖𝑖 + 𝑇𝑇𝐶𝐶𝑜𝑜𝑖𝑖𝑖𝑖𝑖𝑖𝐶𝐶𝐵𝐵,𝑖𝑖𝑖𝑖

• Cold streams T limit: 𝑇𝑇𝐶𝐶𝑜𝑜𝑖𝑖𝑖𝑖,𝑜𝑜𝑜𝑜𝐵𝐵,𝑖𝑖𝑖𝑖𝑙𝑙𝑖𝑖𝐵𝐵 = 𝑇𝑇𝐻𝐻𝑜𝑜𝐵𝐵,𝑖𝑖𝑖𝑖 − Δ𝑇𝑇𝑙𝑙𝑖𝑖𝑖𝑖

Counter-flow Heat Exchanger

𝐻𝐻𝐻𝐻3

Cold

Nitrogen𝐻𝐻𝐻𝐻2

Hot𝐻𝐻𝐻𝐻4

• Staging compressors decreases their work

• 4 stages is optimal for compressors

Staged Compression with Intercooling

• Pressure Ratio per stage: 𝑃𝑃𝑃𝑃𝐶𝐶𝐵𝐵𝐵𝐵𝑠𝑠𝑖𝑖 =𝑛𝑛

�𝑃𝑃𝑜𝑜𝑜𝑜𝑜𝑜𝑃𝑃𝑖𝑖𝑛𝑛

• Enthalpy of compressor: ℎ2 = 𝐵𝑠𝑠−𝐵1𝜂𝜂𝐶𝐶

+ ℎ1

• Work of compressor: 𝐿𝐿𝑐𝑐 = ∑𝑖𝑖=1𝑖𝑖 �̇�𝑚𝐶𝐶 ℎ2,𝑖𝑖 − ℎ1,𝑖𝑖

• Heat extracted: �̇�𝑄𝐶𝐶 = 𝐿𝐿𝑐𝑐 + ∑𝑖𝑖=1𝑖𝑖 ℎ𝑖𝑖 − ℎ𝑖𝑖−1

• Enthalpy of expander: ℎ2 = 𝜂𝜂𝐸𝐸 ℎ1 − ℎ𝐶𝐶 + ℎ1

Compressor/Expander Component

𝐶𝐶

𝐿𝐿𝐶𝐶

�̇�𝑄𝐶𝐶

𝐿𝐿𝐸𝐸

𝐸𝐸

• Throttle is ideally isenthalpic: ℎ𝑖𝑖𝑖𝑖 = ℎ𝑜𝑜𝑜𝑜𝐵𝐵• Quality of LH2: solved with enthalpy & pressure

• Heat of O-P conversion in tank:�̇�𝑄𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐 = �̇�𝑚𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑖𝑖𝑖𝑖∆ℎ𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐

• Return stream flow:�̇�𝑚𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑜𝑜𝑜𝑜𝐵𝐵 = �̇�𝑚𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑖𝑖𝑖𝑖 � X𝐻𝐻2 +

�̇�𝑄𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑐𝑐 + �̇�𝑄𝑇𝑇𝐵𝐵𝑖𝑖𝑇𝑇,𝐵𝑖𝑖𝐵𝐵𝐵𝐵 𝑖𝑖𝑖𝑖𝐵𝐵𝑇𝑇

ℎ𝐿𝐿𝐻𝐻,𝐻𝐻2

Throttle & Tank

𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿𝐿 𝐻𝐻2 𝑇𝑇𝐵𝐵𝑇𝑇𝑇𝑇

𝐽𝐽𝑇𝑇

• Specific exergy: 𝐻𝐻1 = ℎ0 − ℎ1 − 𝑇𝑇0 𝑠𝑠0 − 𝑠𝑠1

• Exergy destruction: ∆𝐻𝐻𝐷𝐷𝑖𝑖𝐶𝐶𝐵𝐵= � �̇�𝑚𝑖𝑖𝑖𝑖𝐻𝐻𝑖𝑖𝑖𝑖 −� �̇�𝑚𝑜𝑜𝑜𝑜𝐵𝐵𝐻𝐻𝑜𝑜𝑜𝑜𝐵𝐵 −𝑊𝑊

• Limits are set to the exergy destruction of throttle (lower) and expander (higher)

Effectiveness of a VT

• Exergy destruction of devices:∆𝐻𝐻𝑉𝑉𝑇𝑇= �̇�𝑚𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − �̇�𝑚𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖𝐻𝐻𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 − �̇�𝑚𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵𝐻𝐻𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵

∆𝐻𝐻𝐽𝐽𝑇𝑇= �̇�𝑚𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐽𝐽𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 + �̇�𝑚𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐽𝐽𝑇𝑇,𝐵𝑜𝑜𝐵𝐵

∆𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣

= �̇�𝑚𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 − 𝑊𝑊𝐸𝐸𝐸𝐸𝑣𝑣,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖 + �̇�𝑚𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵 𝐻𝐻𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 − 𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣,𝐵𝑜𝑜𝐵𝐵 − 𝑊𝑊𝐸𝐸𝐸𝐸𝑣𝑣,𝐵𝑜𝑜𝐵𝐵

• Exergy destruction using effectiveness• ∆𝐻𝐻𝑉𝑉𝑇𝑇= ∆𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣 + 1 − 𝜀𝜀𝑉𝑉𝑇𝑇 ∆𝐻𝐻𝐽𝐽𝑇𝑇 − ∆𝐻𝐻𝐸𝐸𝐸𝐸𝑣𝑣

Effectiveness of a VT cont.

• Cold fraction: 𝑉𝑉𝑇𝑇𝑐𝑐𝑐𝑐 = �̇�𝑙𝑉𝑉𝑉𝑉,𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐�̇�𝑙𝑉𝑉𝑉𝑉,𝑖𝑖𝑛𝑛

• Pressure Ratio: 𝑉𝑉𝑇𝑇𝑃𝑃𝑃𝑃 = 𝑃𝑃𝑖𝑖𝑛𝑛𝑃𝑃𝑉𝑉𝑉𝑉,𝑐𝑐𝑜𝑜𝑐𝑐𝑐𝑐

• Hot outlet Pressure: 𝑃𝑃𝑉𝑉𝑇𝑇,𝐵𝑜𝑜𝐵𝐵 = ⁄1 3 𝑃𝑃𝑉𝑉𝑇𝑇,𝑖𝑖𝑖𝑖 + ⁄2 3 𝑃𝑃𝑉𝑉𝑇𝑇,𝑐𝑐𝑜𝑜𝑖𝑖𝑖𝑖

• Outlet temperatures are solved with effectiveness

Variables of the VT

Cycle Parameters

Previous Cycle Parameters

Cycle Analysis & Results

• Liquid hydrogen yield: 𝜑𝜑 = �̇�𝑙𝑓𝑓

�̇�𝑙

• Ratio of nitrogen to compressed hydrogen flow: 𝜓𝜓 =�̇�𝑙𝑁𝑁2�̇�𝑙

• Liquid yield maximum: 𝜑𝜑𝑙𝑙𝐵𝐵𝐸𝐸 = 𝐵9−𝐵4𝐵9−𝐵7

• Relating 𝜓𝜓 to 𝜑𝜑𝑙𝑙𝐵𝐵𝐸𝐸: 𝜓𝜓 = 𝐵1−𝐵2𝐵11−𝐵10

+ 𝜑𝜑𝑙𝑙𝐵𝐵𝐸𝐸𝐵7−𝐵1𝐵11−𝐵10

State-Point Analysis of Ideal Cycle

Peschka W. Liquid hydrogen: fuel of the future. Springer Science & Business Media; 2012 Dec 6.

• O-P conversion happens at LN2 Bath and LH2 tank

• �̇�𝑚𝑏𝑏𝑜𝑜𝑖𝑖𝑖𝑖 = �̇�𝑄𝑉𝑉𝑇𝑇𝑛𝑛𝑇𝑇𝐵𝑔𝑔−𝐵𝑓𝑓

• �̇�𝑚∗ = �̇�𝑚 + �̇�𝑙𝑏𝑏𝑜𝑜𝑖𝑖𝑐𝑐𝜑𝜑𝑚𝑚𝑇𝑇𝑚𝑚

• 𝜑𝜑∗ = �̇�𝑙𝑓𝑓

�̇�𝑙∗= 𝜑𝜑𝑚𝑚𝑇𝑇𝑚𝑚

1+ ��̇�𝑄𝑉𝑉𝑇𝑇𝑛𝑛𝑇𝑇 �̇�𝑙𝑓𝑓 𝐵8−𝐵7

• 𝜓𝜓∗ =�̇�𝑙𝑁𝑁2�̇�𝑙∗

O-P conversion at LH2 Tank

• Maximum yield of LN2 Bath: 𝜑𝜑𝑁𝑁2,𝑙𝑙𝐵𝐵𝐸𝐸 =�̇�𝑙𝑁𝑁2,𝑓𝑓

�̇�𝑙𝑁𝑁2= 𝐵𝑁𝑁,1−𝐵𝑁𝑁,2

𝐵𝑁𝑁,1−𝐵𝑁𝑁,5

• Work of LN2 Bath: 𝛼𝛼 = 1𝜑𝜑

�̇�𝑊�̇�𝑙 𝑐𝑐𝑜𝑜𝑙𝑙𝑣𝑣

• Work of compressor: �̇�𝑊�̇�𝑙 𝑐𝑐𝑜𝑜𝑙𝑙𝑣𝑣

= 𝑇𝑇𝑖𝑖𝑖𝑖 � 𝑠𝑠𝑖𝑖𝑖𝑖 − 𝑠𝑠𝑜𝑜𝑜𝑜𝐵𝐵 − ℎ𝑖𝑖𝑖𝑖 − ℎ𝑜𝑜𝑜𝑜𝐵𝐵

• 𝛼𝛼𝑁𝑁2 = 1𝜑𝜑𝑁𝑁2,𝑚𝑚𝑇𝑇𝑚𝑚

𝑇𝑇𝑁𝑁,1 � 𝑠𝑠𝑁𝑁,1 − 𝑠𝑠𝑁𝑁,2 − ℎ𝑁𝑁,1 − ℎ𝑁𝑁,2

Work of LN2 Bath

Peschka W. Liquid hydrogen: fuel of the future. Springer Science & Business Media; 2012 Dec 6.

• State-Point work of liquefaction for pre-cooled L-H cycle:

𝛼𝛼𝐻𝐻2 =1𝜑𝜑∗

𝑇𝑇1 � 𝑠𝑠1 − 𝑠𝑠2 − ℎ1 − ℎ2 + 𝛼𝛼𝑁𝑁2 𝜓𝜓∗ +�̇�𝑄𝐵𝐵𝐵𝐵𝐵𝐵𝐵

ℎ12 − ℎ11

• Peak pressure of LN2 Bath: 100 bar (10 MPa)

• Temperature of LN2 Bath: 63.2 K or 77 K

• State-Point work of liquefaction results:- 𝛼𝛼𝐶𝐶,63.2 𝐾𝐾 = 13.65 kWh∙kg-1

- 𝛼𝛼𝐶𝐶,77 𝐾𝐾 = 19.95 kWh∙kg-1

• Peschka value: 𝛼𝛼𝑃𝑃 = 16.27 kWh∙kg-1

State-Point Results

• Work of liquefaction for component-based model:

- 𝛼𝛼𝑐𝑐,63.2 𝐾𝐾 = 14.82 kWh∙kg-1

- 𝛼𝛼𝑐𝑐,77 𝐾𝐾 = 20.83 kWh∙kg-1

• Percentage error between results:

- 63.2 K: 8.57%

- 77 K: 4.41%

• Error caused by heat exchanger and LN2 components

State-Point vs. Component Results

Vortex Tube Simulation

Reduced Work for L-H w/VT Cycle

Cycle Analysis & Results

Simulation of L-H w/VT Cycle

• Simulate higher complexity cycles e.g. pre-cooled Claude

• Vary the LN2 Bath temperature to 63.2 K

• Higher inlet pressure tests for vortex tube

• Continued tests of vortex tube catalyzation

• Test vortex tube as a final liquefaction component

Recommendations

• Simplified Statistical thermodynamic models created

• Variable components created for the pre-cooled L-H cycle

• Component model verified with state-point model

• Effectiveness introduced as a new VT variable

• Required effectiveness provided for combinations of 𝑉𝑉𝑇𝑇𝑐𝑐𝑐𝑐 and 𝑉𝑉𝑇𝑇𝑃𝑃𝑃𝑃 values

Summary