Heat and Mass Transfer in Fixed-bed Tubular Reactor

Junichiro Kugai

1

Main issue

Continuum plug flow

Particle-scale

Non-uniform flowComplex

Uniformity assumptionSemi-empirical

Purpose

• Simulating velocity, temperature, and mass distributions in a catalytic tubular reactor using COMSOL

• Investigating the effect of the flow rate at inlet, heat of reaction, permeability, and porosity on catalytic activity

• Understanding fluid behavior in particle-scale

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Model and Equations(Axial 2D)

4

A

Fluid flow in porous mediaFluid 　 　 　 　　　　 : Typical syngas Porous media : Catalyst-bed

Axialsym Wall

Outlet

Inlet

EquationsVelocity : Navier-StokesTemperature: Convection-conductionMass (CO conc.) : Convection-diffusion

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Gas ρ 0.258 kg/m3

η 1.0 e-5 Pa s

Solid ρ 1500 (apparent) ε 0.4 κ 1.0 e-7 m2

CO + H2O CO2 + H2 rate = A exp(-Ea/RT)[CO]0.1[H2O]0.8[CO2]-0.2[H2]-0.6(1-β)

A 1.0 e8 mol/m3-cat/s Ea 70 kJ/mol ⊿H -40 kJ/mol

Gas in solid k 0.76 W/m/K (0.1, 1.2) Cp 316 kJ/K/m3 (2, 525) D 1.5 e-5 m2/s (6 e-5)

Parameters and Boundary Conditions

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Axialsym

Wall623.2 K

1 e5 PaConvection

0.085 m/s620 K2.542 mol/m3

0.0025m

0.01mOther properties

Reaction rate expression

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Velocity Temperature CO conc.

Catalyst-bed temperature is determined by the inlet temperatureReaction reaches equilibrium at ~4 mm from the inlet

Distribution of velocity, temperature, and mass

2.54mol/m3

0.6 mol/m3

620 K

623.34 K0.129 m/s

0 m/s

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Effect of U0 (average linear velocity) on z-velocity

r [10-3 m]

0.005 m/s0.01 m/s

0.05 m/s

0.1 m/s

0.2 m/s

0.4 m/s

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Effect of U0 (average linear velocity)

z [m]

0.005 m/s0.01 m/s

0.05 m/s 0.1 m/s 0.2 m/s0.4 m/s

z [m]

0.005 m/s

0.01 m/s0.05 m/s

0.1 m/s

0.2 m/s

0.4 m/s

Large difference in behaviorbtw. 0.01 and 0.05 m/s

Temperature

CO conc.

Equilibrium

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Effect of ⊿H (heat of reaction)

+20 kJ/mol

-400 kJ/mol

Temperature CO conc.

⊿H : Small impact

-80 kJ/mol

Z [m]

10r [10-3 m] r [10-3 m]

Effect of permeability

r [10-3 m]

10-8

10-7

10-6

10-8

10-7

10-6

Temperature CO conc.

Verocity

Homogeneity of fluid

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Z [m]

PressureP

ress

ure

[Pa]

100001

100000

Κ = 10-8

Κ = 10-7

(ε = 0.2-0.5)

Κ = 10-6

Effect of permeability and porosity

Permeability : Larger impact

Fluid behavior in particle-scale (2D)

Velocity (0~0.22 m/s) CO conc. (2.54~1.67 mol/m3)

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0.2 0.6 1.0 1.4 1.8 2.2

2.5

0.12

0.05

2.2

Velocity and mass inside a particle

Ve

loci

ty [m

/s]

CO

co

nc. [

mol

/m3]

z [mm]

Conclusion

• An actual WGS reactor was reproduced by the simulation

• Inlet temperature is crucial to the catalyst-bed temperature in the given condition

• Permeability has large impact on homogeneity of fluid in the reaction condition

• Gas diffusion effectively flatten mass distribution from uneven fluid flow

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15

Effect of porosity

r [10-3 m] r [10-3 m]

r [10-3 m]

0.4

0.3

0.2

0.5

0.2

0.5

Dporous = (ε / τ) Dgas

kporous = kgas ε + ksolid (1- ε)Cpporous = Cpgas ε + Cpsolid (1- ε)

in J/K/m3

Temperature CO conc.

Verocity