diffusion and reaction in fe-based catalyst for fischer ...diffusion and reaction in fe-based...

Diffusion and Reaction in Fe-Based Catalyst for Fischer-

Tropsch Synthesis Using Micro Kinetic Rate Expressions

Arvind Nanduri & Patrick L. Mills*

Department of Chemical & Natural Gas Engineering

Texas A&M University-Kingsville

Kingsville, TX 78363-8202 USA*[email protected]

3-D CFD Model for Shell & Tube

Exchanger with 7 Tubes

Multitubular Reactor Design

for Low Temperature Fischer-Tropsch

Session: Transport Phenomena October 9, 2014

Ender Ozden and Ilker Tari (2010)

10 – 50 K Tubes

Presentation Outline

• Introduction

• Objectives

• F-T Chemistry, Kinetics & Thermo

• Multiphysics Model Equations

• Key Results– Catalyst Performance– Concentration Profiles– Computational Difficulties

• Conclusions

M. Ojeda et al. (2008)

CO Dissociation Pathway

Anderson-Schulz-Flory (ASF)

Product Distribution

0

10

20

30

40

50

60

70

80

90

100

0 0.2 0.4 0.6 0.8 1

Weight

perc

ent

age

Chain growth probability factor, α

C1

C2-4

C5-11

C12-20

C20-n

Introduction

• Fischer-Tropsch synthesis (FTS) is ahighly exothermic polymerizationreaction of syngas (CO+H2) in thepresence of Fe/Co/Ru-basedcatalysts to produce a wide range ofparaffins, olefins and oxygenates,often known as syncrude

David A. Wood, Chikezie Nwaoha, & Brian F. Towler, Journal of Natural Gas Science and Engineering (2012)

– Standard large-scale gas conversion– Isolated “Stranded gas” conversion

CH4CO + H2

(Syn Gas)

ParaffinsOlefins

OxygenatesEtc.

FTS

Gasification or

oxidation

n CO + 2n H2 -(CH2)n- + n H2O

Objectives

• Model the Fischer-Tropsch (FT) reaction network– Implement micro-kinetic rate expressions– Assess the effect of process parameters on the FT product

distributioni. Catalyst particle shapeii. Operating conditions (T, P)

• Incorporate Soave-Redlich-Kwong (SRK) equation of state (EOS)into the particle-scale transport-kinetics model to more accuratelydescribe the vapor-liquid-equilibrium (VLE) behavior of the FTproduct distribution within the porous catalyst particle.

Catalyst pores filled with liquid wax

Bulk gas phase

Reactants diffusing into the pores

Products diffusing into the bulk phase

Rp

Lp

Cylinder

Rp

Sphere

Ring/Hollow Cylinder

Lp

Ro

Ri

Key F-T Catalytic Reactions

Name Composition

Fuel Gas C1-C2

LPG C3-C4

Gasoline C5-C12

Naphtha C8-C12

Kerosene C11-C13

Diesel/Gasoil C13-C17

F-T Wax C20+

Conventional Names of F-T Products

Main Reactions

1 Methane CO + 3H2 CH4 + H2O

2 Paraffins (2n+2) H2 + n CO CnH2n+2 + n H2O

3 Olefins 2n H2 + n CO CnH2n + n H2O

4 WGS (only on Fe catalyst) CO + H2O CO2 + H2

Side Reactions

5 Alcohols 2n H2 + n CO CnH2n+1 O + n H2O

6 Boudouard Reaction 2CO C + CO2

Catalyst Modifications

7 Catalyst Oxidation/Reduction (a) MxOy + y H2 y H2O + x M

(b) MxOy + y CO y CO2 + x M

8 Bulk Carbide Formation y C + x M MxCy

David A. Wood, Chikezie Nwaoha, & Brian F. Towler, Journal of Natural Gas Science and Engineering (2012)

Fischer-Tropsch Micro-kinetic Rates

Fe-Based Olefin Readsorption Microkinetic Model

n = 2 to 20

Wang et al., Fuels (2003)

Syn Gas

Paraffins(CnH2n+2)

Olefins(CnH2n)

Long Chain Paraffins(CnH2n+2) Re-adsorption

of Olefins

Soave-Redlich-Kwong (SRK) EOS Flash Calculations

F

V

L

Rachford-Rice Objective Function

Wilson’s Correlation

Liquid Wax with Dissolved

Hydrocarbons

Catalyst Pore Hydrocarbons in

Vapor Phase

i = 1 to 43 with 43 distinct roots

Only the positive roots

less than 1 are used for

VLE calculations

fLi = fV

i

Vapor-Liquid Equilibrium

Thermodynamics of F-T Reaction Mixtures

Wang et al., Fuels (1999)

^ ^

Catalyst Properties & Process Conditions

Cylinder

Rp

Sphere

Rp

Lp

Ring/Hollow Cylinder

Lp

Ro

Ri

Dimensions of Cylinder and Ring for Rsphere = 1.5 mm

Dimensions of Cylinder and Ring for Rsphere = 1 mm

Volumesphere = Volumecylinder = Volumering

(4/3) R3sphere = LcylinderR

2cylinder= Lring(R

2o-R

2i)

Cylinder L = 3 mm & R = 1 mm

Ring L = 2 mm, Ro=1.5 mm & Ri=0.3 mm

Cylinder L = 3 mm & R = 0.7 mm

Ring L = 2 mm, Ro=1.5 mm & Ri=1 mm

Catalyst Properties

Density of pellet, ρp 1.95 x 106 (gm/m3)

Porosity of pellet,ε 0.51

Tortuosity, τ 2.6

Operating Conditions

Temperature, oK 493, 523 & 533

Pressure, bar 20, 25 & 30

H2/CO 2

Governing Multiphysics Model Equations

43 species and 43 reactions

Spherical ParticleAt ξ = -1 and ξ = 1, Ci = Ci,bulk

(CO2,bulk = eps for convergence)

Cylindrical

Particle

At ξ = -1 and ξ = 1, Ci = Ci,bulk


Ring ParticleAt ξ = 0 and ξ = 1, Ci = Ci,bulk


Species Flux

• Independent of composition Ci

• Dependent on local temperature T

• Future work: Use multicomponent

flux transport models

Key Assumptions

i. Concentration is a function of only the

radial coordinate, i.e., Ci = Ci(r)

ii. Steady-state

iii. All catalyst particle shapes have the same

material properties (ε, τ, ρ, keff)

iv. Isothermal conditions (since ΔT is small)

v. Bulk gas phase contains only H2 and CO

(Reactor entrance conditions)

Boundary Conditions

COMSOL Modules

• Transport of Diluted Species

• Coefficient Form PDE Solver

Model Assumptions & Boundary Conditions

Various Catalyst Shapes: h & Ci Profiles

Rp = 1 mm

Lp = 3 mm

P = 25 bar493 K

513 K

533 K

Eff

ecti

ven

ess F

acto

r

493 K

513 K

533 K

493 K

513 K

533 K

P = 25 bar

Rp = 1.5 mmEff

ecti

ven

ess F

acto

r

Dimensionless Radial Coordinate, ξ = r/Rp

Ro = 1.5 mm

Ri = 0.3 mm

Lp = 2 mm

Dimensionless Radial Coordinate, ξ = (r-Ri) /(Ro-Ri)

Eff

ecti

ven

ess F

acto

r


P = 25 bar

Co

nc

en

trati

on

(m

ol/

m3)


T = 493 K

P = 25 bar

H2

CO

CO2

H2O

H2

CO

CO2

H2O

H2

CO

CO2

H2O

T = 493 K

P = 25 barT = 493 K

P = 25 bar

Co

nc

en

trati

on

(m

ol/

m3)

Co

nc

en

trati

on

(m

ol/

m3)

Dimensionless Radial Coordinate, ξ = (r-Ri) /(Ro-Ri) Dimensionless Radial Coordinate, ξ = r/Rp

Cylinder Ring/Hollow Cylinder Sphere

T = 493 K & P = 25 barT = 493 K & P = 25 bar T = 493 K & P = 25 bar

H2 Concentration Profile H2 Concentration ProfileH2 Concentration Profile

Rp = 1 mm

Lp = 3 mmRo = 1.5 mm

Ri = 0.3 mm

Lp = 2 mm

Rp = 1.5 mm

T = 493 K

P = 25 bar

T = 493 K

P = 25 bar

T = 493 K

P = 25 bar

Rp = 1 mm

Rp = 0.7 mm

Rp = 1.5 mm

Rp = 1 mmδ = 1.2 mm

δ = 0.5 mm

L/V L/V

L/V

Dimensionless Radial Coordinate, ξ = r/Rp Dimensionless Radial Coordinate, ξ = (r-Ri) /(Ro-Ri) Dimensionless Radial Coordinate, ξ = r/Rp

Meth

an

e b

ased

In

tra

-pa

rtic

le

Die

sel

Sele

cti

vit

y

Meth

an

e b

ased

In

tra

-pa

rtic

le

Die

sel

Sele

cti

vit

y

Meth

an

e b

ased

In

tra

-pa

rtic

le

Die

sel

Sele

cti

vit

y

Dimensionless Radial Coordinate, ξ = r/Rp Dimensionless Radial Coordinate, ξ = (r-Ri) /(Ro-Ri) Dimensionless Radial Coordinate, ξ = r/Rp

Rp = 1 mm

Rp = 0.7 mm

δ = 1.2 mm

δ = 0.5 mm

Rp = 1 mm

Rp = 1.5 mm

T = 493 K

P = 25 barT = 493 K

P = 25 bar

T = 493 K

P = 25 bar

Computational Issues

Region with numerical instabilities

H2

CO

CO2

H2O

• To avoid convergence issues, theradius of the particle was set toa very small number and thesubsequent solution was stored tobe used as initial conditions forhigher radius.

• Numerical instabilities wereencountered in the region whereCO and CO2 concentrationsapproached zero leading toconvergence issues and unrealisticvalues.

• The convergence issues weresolved by not letting CO and CO2

concentrations approach zero byusing CO=if(CO≤0,eps,CO) andCO2=if(CO2≤0,eps,CO).

Once the convergence issue was solved the mesh was refined to get smooth curves.

Conclusions

• A 1-D catalyst pellet model can be used to analyze particle-levelperformance. Catalyst performance on a reactor-scale can be studied bycoupling the pellet model to the tube & shell-side models for the MTFBR.

• The CO conversion, effectiveness factor, intra-particle liquid to vapor(L/V) fraction, catalyst strength and the diesel selectivity results suggestthat the cylindrical and spherical catalyst particle shapes are preferredover hollow rings. The presence of more liquid in the spherical particlecreates an advantage for the cylindrical catalyst shape due to diffusionallimitations in the wax.

• Micro kinetic rate equations, when coupled with intraparticle transporteffects and vapor-liquid equilibrium phenomena, captures the transport-kinetic interactions and phase behavior for gas-phase FT catalysts.

• Convergence can be a major issue in fast reaction-diffusion systems. Thiscan sometimes be easily resolved by using simple built-in operators, suchas ‘if ()’ and ‘eps’, to avoid negative and other unrealistic values ofdependent variables at the boundaries or interior and then refining themesh in accordance with computational time.

Thank You

References

References (cont’d)


Mo

le F

racti

on

of

Wax in

Liq

uid

Ph

ase

Cylinder SphereRing/Hollow Cylinder


Mo

le F

racti

on

of

Wax in

Liq

uid

Ph

ase

Mo

le F

racti

on

of

Wax in

Liq

uid

Ph

ase


Dimensionless Radial Coordinate, ξ = r/RpDimensionless Radial Coordinate, ξ = (r-Ri) /(Ro-Ri)M

ole

Fra

cti

on

of

Die

sel

in L

iqu

id

Ph

ase

Mo

le F

racti

on

of

Die

sel

in L

iqu

id

Ph

ase

Mo

le F

racti

on

of

Die

sel

in L

iqu

id

Ph

ase


Mole Fraction of Wax & Diesel in Liquid Phase

Rp = 1 mm

Rp = 0.7 mm

T = 493 K

P = 25 barT = 493 K

P = 25 bar

T = 493 K

P = 25 bar

Rp = 1.5 mm

Rp = 1 mm

δ = 1.2 mm

δ = 0.5 mm

Rp = 1 mm

Rp = 0.7 mm

δ = 1.2 mm

δ = 0.5 mm

Rp = 1.5 mm

Rp = 1 mm

T = 493 K

P = 25 barT = 493 K

P = 25 bar

T = 493 K

P = 25 bar

Rp = 1 mm

P = 25 bar

533 K

513 K

493 K

δ = 1.2 mm

P = 25 bar

533 K

513 K

493 K

Rp = 1.5 mm

P = 25 bar

533 K

513 K

493 K

Cylinder Ring/Hollow Cylinder Sphere

Mo

le F

racti

on

of

Fu

el

Gas i

n

Vap

or

Ph

ase


Mo

le F

racti

on

of

Fu

el

Gas i

n

Vap

or

Ph

ase


Mo

le F

racti

on

of

Fu

el

Gas i

n

Vap

or

Ph

ase


Mole Fraction of Fuel Gas in Vapor Phase

diffusion and reaction in fe-based catalyst for fischer ...diffusion and reaction in fe-based...

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