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Nicole ReedDepartment of Energy and Mineral EngineeringEGEE 520Penn State University

April 29, 2008

COMSOL Modeling of Liquid Flow Through a Fixed-Bed Packed Reactorfor Adsorptive Desulfurization

Desulfurization approaches require severe conditions and are not suitable for fuel cell applications

Selective Adsorption (SARS) is achieved at ambient pressure and temperature without hydrogen

HydrodesulfurizationHydrodesulfurization (HDS) (HDS)

– High Temp (300-350 °C)High Temp (300-350 °C)

– High Pressure of HHigh Pressure of H22 (30-40 bar) (30-40 bar)

A fixed-bed continuous flow system measures the performance of adsorbents for various fuels

HPLCPump

(X ppm S)

Fixed-bed reactor

2 3

Fuel samples collected at regular intervals

1

0.2513 g

Samples weighed

1

Amount of Treated Fuel

C = C0

This study focuses on liquid fuel flow through a packed bed

Fuel

Diesel Fuel

Density = 800 kg/m3

Flow Rate = 0.05 ml/min 0.0005 m/s

Fixed-bed reactor

Volume = 2.49 mLLength = 0.15 mWidth = 0.0025 m

Packed Bed: Activated Carbon

Porosity(ε) = 0.6 (experimental)Permeability(κ) = 1.88x10-11 m2

22

3

)1( vSK

pv DS

6

5

Darcy’s Law describes flow through porous medium in terms of head gradients

Darcy’s Law:

kggk

x

hK

A

Qq

Term Meaning Units

q Darcy Flux m/s

Q Discharge m3/s

K Hydraulic conductivity m/s

k Permeability m2

µ Absolute viscosity Ns/m2

ρ Density kg/m3

h head m

ν Kinematic viscosity m2/s

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Boundary Conditions

r = 0.0025 m

Insulation BC h = 0.15 m

2-D Axial Symmetry

Inflow/Outflow = 0.005 m/s

Quantity Value Unit Description

ρ 0.8 kg/m3 Density

κ 1.88x10-11 m2 Permeability

µ .0024 Pa·s Dynamic Viscosity

f 0 kg/(m3·s) Source Term

sPasm

kg

m

kg

s

cmx

0024.00024.08.0103

3

22

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Solution

Inflow = 0.0005 m/sΔP = 1.069 atm

Outflow = 0.0005 m/sΔP = 0.975 atm

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Validation

qdx

h

p

32

2)1(180

sm

kg

s

m

mxsm

kg

x

h

2326

2

640000005.06.0)1050(

)6.01(1800024.0

atmPasm

kgm

sm

kg

sm

kgxh 095.9600960015.6400064000

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Darcy’s Law

Column Length

From COMSOL Solution:

Maximum Pressure - Minimum Pressure = Pressure Drop1.069 – 0.974 = 0.095 atm

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Parametric Study

How does particle size and fuel flow rate affect the pressure drop?

Particle Size Permeabilityq

dx

h

p

32

2)1(180

Fuel flow rate Velocity

Case Flow Rate Velocity Particle Size Permeability Max Min P DROP1 0.05 0.0005 5E-05 1.875E-11 1.069 0.974 0.0952 0.20 0.002 5E-05 1.875E-11 1.278 0.9 0.3783 1.00 0.04 5E-05 1.875E-11 6.56 -0.999 7.5594 0.05 0.0005 5E-06 1.875E-13 8.095 -1.34 9.4355 0.20 0.002 5E-06 1.875E-13 29 -8.4 37.46 1.00 0.04 5E-06 1.875E-13 569 -187 7567 0.05 0.0005 5E-07 1.875E-15 770 -174 9448 0.20 0.002 5E-07 1.875E-15 2736 -1042 3778

9 1.00 0.04 5E-07 1.875E-15 5470 -20890 26360

0.05, 0.20, and 1.0 ml/min

50, 5, and 0.5 microns

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Summary

COMSOL can effectively model packed bed reactors

with the following parameters:– Adsorbent: porosity, particle size, density– Fuel: flow rate, density

Particle size and fuel flow rate affect pressure drop across small reactors

COMSOL can be used to find limits for scale-up models and other reactor designs

THANK YOU!THANK YOU!