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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
(CO2,bulk = eps for convergence)
Ring ParticleAt ξ = 0 and ξ = 1, Ci = Ci,bulk
(CO2,bulk = eps for convergence)
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
Dimensionless Radial Coordinate, ξ = r/Rp
P = 25 bar
Co
nc
en
trati
on
(m
ol/
m3)
Dimensionless Radial Coordinate, ξ = r/Rp
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)
Dimensionless Radial Coordinate, ξ = r/Rp
Mo
le F
racti
on
of
Wax in
Liq
uid
Ph
ase
Cylinder SphereRing/Hollow Cylinder
Dimensionless Radial Coordinate, ξ = r/Rp
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-Ri) /(Ro-Ri)
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
Dimensionless Radial Coordinate, ξ = r/Rp
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
Dimensionless Radial Coordinate, ξ = r/Rp
Mo
le F
racti
on
of
Fu
el
Gas i
n
Vap
or
Ph
ase
Dimensionless Radial Coordinate, ξ = (r-Ri) /(Ro-Ri)
Mo
le F
racti
on
of
Fu
el
Gas i
n
Vap
or
Ph
ase
Dimensionless Radial Coordinate, ξ = r/Rp
Mole Fraction of Fuel Gas in Vapor Phase