「気体分離膜の流体力学計算」
東京大学大学院工学系研究科

高羽洋充

takaba@chemsys.t.u-tokyo.ac.jp

H2 Production by Steam Reforming
Membrane
Buffer tankH2 :H2 : 78 %Steam76 %CO2 : 20 %HO
Natural gas
2CO2 :
CO : 1 %(CH4)
11 %CH4 : 1 %CO :12 %Desulfurizer Steam reforming
CH4 : CO shift reaction Purification
CH4+H2O⇔CO+3H（PSA）
1 % 2 CO+H2O⇔CO2+H2
700~800℃

180~220℃

Pure H2
99.99%

CH4 + H2O

COH2

Concentration Polarization
J H 2 = AH 2 ( PhH 2 − Pl H 2 )J CO = ACO ( PhCO − PlCO )Boundarylayer

xb

JH2
=J COMembrane

Concentration Polarization

yPermeatesideFeedsidexm

Flux and Selectivity DOWN!

Objective
Development of CFD simulator to design agas separation module and check the validity
for concentration polarization prediction
Outline1. Introduction of theory
2. Comparison with the ideal flow calculation
result (plug flow model) to test thevalidation of CFD
3. Comparison with experimental result toinvestigate the concentration polarization
effectTheory in CFD Simulator
Basic Differential Equation for Fluid+ div( u ) = 0t( u ) +  (u  )u = −P + 22 utDifferential Equation for Component
=PMRTY M = 1 /   i  mi 

Finite Volume Method
isothermal operation
Mass Transfer ThroughMembraneYi M
Pi = PTOTAL
miJ i = Ai ( Pi1 − Pi 2 )( Yi ) + div( uYi − Di grad(Yi )) = ( J i A / V )tSolved variables：
Yi(weight fraction), P(pressure drop), u(velocity)Calculation condition
MODEL → H2 separation from H2/CO gas mixture
Feed
H2:CO = 0.75：0.25
773 K
0.8 MPaα(H2/CO) = 1000
D (cm2/s) = 1.46 at 0.8 MPa

Surface area ：0.05 ｍ２

CFD Model(non-ideal flow)

Retantate
Permeate

Permeate side

0.1 MPa

Parallel Plug Flow Model(PFM, ideal flow)

CFD cell size ：0.5 m×0.1 m×0.05 m

Mesh : 40x1x20

Feed side

D： f(T,P)

Permeate sideΘ（non-dimensional parameter)(Membrane Performance)＝ f (surface area(s), permeance (PH2), ΔＰ , flow
volume(F), height of module(d3))
H2 mol/m3
H2 mol/mΘ ＝PH2・S・ΔPFS ： 0.05 ｍ２d : 0.01mConstant!

CO mol/m3

PH2 and u are changed.

ΔP : 7 x105 Pa

Plug flow model →Separation factor and flux are as a function of only Θ!

Calculation condition: F [m3/s]
KH2

Θ=2.010-5
10-6

Θ=0.1

Θ=0.01

Θ=0.001Θ=0.0001

1.406x10-3 2.812x10-3

2.812x10-2

2.812x10-1

2.812x100

2.812x101

1.406x10-4 2.812x10-4

2.812x10-3

2.812x10-2

2.812x10-1

2.812x100

1.406x10-4

1.406x10-3

1.406x10-2

1.406x10-1

1.406x100

10-71.406x10-5 2.812x10-5

2.812x10-4

2.812x10-3

2.812x10-2

2.812x10-110-8

1.406x10-6 2.812x10-6

2.812x10-5

2.812x10-4

2.812x10-3

2.812x10-210-9

1.406x10-7 2.812x10-7

2.812x10-6

2.812x10-5

2.812x10-4

2.812x10-3

5x10-7 7.03x10-5Θ=1.0α(KH2/KCO) ＝１０００

CFD Result （flow volume; F = 2.812x10-8 m3/s)
KH2 = 1.0x10-8

KH2 = 1.0x10-6

Pressure dropPressure drop

Partial pressure of H2

Partial pressure of H2

Partial pressure of CO

Partial pressure of COW eight fraction of H 2 in perm eate

CFD vs PFM -yH210 .9 80 .9 60 .9 40 .9 20 .90 .8 80 .8 6PFMC F D (1 e -5 )C F D (1 e -6 )C F D (1 e -7 )C F D (1 e -8 )C F D (1 e -9 )0 .8 40 .8 2

α＝１０００0 .80 .0 0 10 .0 10 .1

110θ

When permeance of H2 is smaller than 1x10-6mol/m2sPa, CFD agrees with PFM.

CFD vs PFM -RH2R ecovery ratio of H 2PFM
10 .90 .80 .70 .60 .50 .40 .30 .20 .1
00 .0 0 1

C F D (1 e -5 )C F D (1 e -6 )C F D (1 e -8 )C F D (1 e -7 )C F D (1 e -9 )α＝１０００0 .0 10 .1

110θ

When permeance of H2 is smaller than 1x10-6
mol/m2sPa, CFD agrees well with PFM.

CFD Model for Polarization(impermeable section)
Metal plug

Membrane(permeable section)

K. Haraya et al., Sep. Sci. Tech.,
22 (1987) 1425.
Hydrogen and carbon monoxide mixture gas

KH2 (mol/s m2 Pa) = 2.67×10-6
Outer tube

0.45cm

KH2/KCO = 3.74
Ph (MPa) = 1.1
Pl (MPa) = 0.5-0.6

0.87cmD (cm2/s) = 1.06 at 1.1 MPa
Sc = 0.24

Tube membrane(plug flow)

0.10cmFeed (cm/s) = 2.5, 3.75, 5.0
Jv (cm/s) = 0.4

Partial Pressure Distribution
Δｐ

P of H2

P of CO0.34 Pa

0.55 MPa0.55 MPa

Flow

0.41 Pa
0.32 MPa0.25 Pa

0.35 MPa0.55 MPa

Feed velocity = 5 cm/s

0.47 MPa

0.58 MPa0.25 MPa

5.5Permeate
5.0 sideP a rtia l P re ssu re o f H 2 [P a ]Partial Pressure of H2 [Pa]Partial Pressure Distribution

Feed side
0.03 cm
0.12 cm
0.21 cm
0.30 cm
0.39 cm

4.5
4.0
3.5
3.000.2
0.4
0.6
Position [cm]P(H2) along flow direction
Feed velocity is 5 cm/s.

0.8

5 .5
5 .0
5 .0 cm /s
3 .3 cm /s
2 .5 cm /s

4 .5
4 .0
3 .5
00 .2

0 .40 .6

P o sitio n [cm ]Change of P(H2) for different feed
Velocity. Position of flow direction
Is 0.12 cm.

0 .8

Comparison with experiment
1MembranexbFeedside

y0.8

Permeate
side

0.6xm

M

Boundarylayer

0.4
M (Haraya et al. in 1987)
M (CFD)

M is the modulus ofconcentration polarizationy − xb
M=y − xm

0.2012345

Feed velocity [cm/s]

6Conclusion
CFD simulator was developed and tested using a model
based on the separation process of a hydrogen/carbon
monoxide gas mixture in the steam reforming process.
1. CFD results agree with the PFM results when thepermeance of H2 becomes smaller than 1x10-7mol/m2sPa.
2. When the permeance of H2 is larger than 1x10-6
mol/m2sPa, the volume flux and selectivity decreases.
3. The concentration polarization observed in the CFD
simulation results compared well with theexperimental results.

Acknowledgement

Ｔｈｉｓ work has been supported by NEDO as apart of the R&D Project for High Efficiency
Hydrogen Production/Separation System using
Ceramic Membrane promoted by METI, Japan.