Diffusion and Reaction in Fe-Based Catalyst for Fischer- Tropsch Synthesis Using Micro Kinetic Rate Expressions 3-D CFD Model for Shell & Tube Exchanger with 7 Tubes Ender Ozden and Ilker Tari (2010) Multitubular Reactor Design for Low Temperature Fischer-Tropsch Arvind Nanduri & Patrick L. Mills * Department of Chemical & Natural Gas Engineering Texas A&M University-Kingsville Kingsville, TX 78363-8202 USA * Patrick.Mills@tamuk.edu 10 50 K Tubes Session: Transport Phenomena October 9, 2014
Presentation Outline Introduction Objectives F-T Chemistry, Kinetics & Thermo Multiphysics Model Equations Key Results Catalyst Performance Concentration Profiles Computational Difficulties Conclusions Weight percentage 100 90 80 70 60 50 40 30 20 10 Anderson-Schulz-Flory (ASF) Product Distribution 0 C2-4 C1 C5-11 C12-20 0 0.2 0.4 0.6 0.8 1 Chain growth probability factor, α C20-n CO Dissociation Pathway M. Ojeda et al. (2008)
Introduction Fischer-Tropsch synthesis (FTS) is a highly exothermic polymerization reaction of syngas (CO+H 2 ) in the presence of Fe/Co/Ru-based catalysts to produce a wide range of paraffins, olefins and oxygenates, often known as syncrude Gasification or oxidation CH 4 CO + H 2 (Syn Gas) FTS Paraffins Olefins Oxygenates Etc. Standard large-scale gas conversion Isolated Stranded gas conversion n CO + 2n H 2 -(CH 2 ) n - + n H 2 O David A. Wood, Chikezie Nwaoha, & Brian F. Towler, Journal of Natural Gas Science and Engineering (2012)
Objectives Model the Fischer-Tropsch (FT) reaction network Implement micro-kinetic rate expressions Assess the effect of process parameters on the FT product distribution i. Catalyst particle shape ii. Operating conditions (T, P) Incorporate Soave-Redlich-Kwong (SRK) equation of state (EOS) into the particle-scale transport-kinetics model to more accurately describe the vapor-liquid-equilibrium (VLE) behavior of the FT product distribution within the porous catalyst particle. Bulk gas phase Cylinder Sphere L p Reactants diffusing into the pores Catalyst pores filled with liquid wax Products diffusing into the bulk phase R p Ring/Hollow Cylinder R p L p R i R o
Key F-T Catalytic Reactions Main Reactions 1 Methane CO + 3H 2 CH 4 + H 2 O Conventional Names of F-T Products 2 Paraffins (2n+2) H 2 + n CO C n H 2n+2 + n H 2 O Name Composition 3 Olefins 2n H 2 + n CO C n H 2n + n H 2 O Fuel Gas C 1 -C 2 4 WGS (only on Fe catalyst) CO + H 2 O CO 2 + H 2 Side Reactions 5 Alcohols 2n H 2 + n CO C n H 2n+1 O + n H 2 O 6 Boudouard Reaction 2CO C + CO 2 Catalyst Modifications 7 Catalyst Oxidation/Reduction (a) M x O y + y H 2 y H 2 O + x M LPG C 3 -C 4 Gasoline C 5 -C 12 Naphtha C 8 -C 12 Kerosene C 11 -C 13 Diesel/Gasoil C 13 -C 17 F-T Wax C 20+ (b) M x O y + y CO y CO 2 + x M 8 Bulk Carbide Formation y C + x M M x C y 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 Syn Gas Paraffins (C n H 2n+2 ) Olefins (C n H 2n ) n = 2 to 20 Long Chain Paraffins (C n H 2n+2 ) Re-adsorption of Olefins Wang et al., Fuels (2003)
Thermodynamics of F-T Reaction Mixtures Soave-Redlich-Kwong (SRK) EOS Flash Calculations Rachford-Rice Objective Function Vapor-Liquid Equilibrium ^ ^ f L i = f V i i = 1 to 43 with 43 distinct roots Only the positive roots less than 1 are used for VLE calculations Catalyst Pore Hydrocarbons in Vapor Phase Wilson s Correlation Liquid Wax with Dissolved Hydrocarbons V F Wang et al., Fuels (1999) L
Catalyst Properties & Process Conditions Cylinder Sphere Ring/Hollow Cylinder L p L p R p R p R i Volume sphere = Volume cylinder = Volume ring R o (4/3) R 3 sphere = L cylinder R 2 cylinder= L ring (R 2 o-r 2 i) Dimensions of Cylinder and Ring for R sphere = 1.5 mm Catalyst Properties Cylinder Ring L = 3 mm & R = 1 mm L = 2 mm, R o =1.5 mm & R i =0.3 mm Density of pellet, ρ p 1.95 x 10 6 (gm/m 3 ) Porosity of pellet,ε 0.51 Tortuosity, τ 2.6 Dimensions of Cylinder and Ring for R sphere = 1 mm Cylinder L = 3 mm & R = 0.7 mm Ring L = 2 mm, R o =1.5 mm & R i =1 mm Operating Conditions Temperature, o K 493, 523 & 533 Pressure, bar 20, 25 & 30 H 2 /CO 2
Governing Multiphysics Model Equations 43 species and 43 reactions
Model Assumptions & Boundary Conditions Boundary Conditions Spherical Particle Cylindrical Particle At ξ = -1 and ξ = 1, C i = C i,bulk (CO 2,bulk = eps for convergence) At ξ = -1 and ξ = 1, C i = C i,bulk (CO 2,bulk = eps for convergence) Ring Particle At ξ = 0 and ξ = 1, C i = C i,bulk (CO 2,bulk = eps for convergence) Species Flux Independent of composition C i Dependent on local temperature T Future work: Use multicomponent flux transport models COMSOL Modules Transport of Diluted Species Coefficient Form PDE Solver Key Assumptions i. Concentration is a function of only the radial coordinate, i.e., C i = C i (r) ii. Steady-state iii. All catalyst particle shapes have the same material properties (ε, τ, ρ, k eff ) iv. Isothermal conditions (since ΔT is small) v. Bulk gas phase contains only H 2 and CO (Reactor entrance conditions)
Effectiveness Factor Concentration (mol/m 3 ) Various Catalyst Shapes: h & C i Profiles Effectiveness Factor Concentration (mol/m 3 ) Concentration (mol/m 3 ) Effectiveness Factor Cylinder Ring/Hollow Cylinder Sphere 493 K 513 K 533 K 493 K 513 K 533 K 493 K 513 K 533 K L p = 3 mm R o = 1.5 mm Ri = 0.3 mm L p = 2 mm R p = 1.5 mm Dimensionless Radial Coordinate, ξ = r/r p Dimensionless Radial Coordinate, ξ = (r-r i ) /(R o -R i ) Dimensionless Radial Coordinate, ξ = r/r p H 2 CO CO 2 H 2 O H 2 CO CO 2 H 2 O H 2 CO CO 2 H 2 O Dimensionless Radial Coordinate, ξ = r/r p Dimensionless Radial Coordinate, ξ = (r-r i ) /(R o -R i ) Dimensionless Radial Coordinate, ξ = r/r p
Methane based Intra-particle Diesel Selectivity Methane based Intra-particle Diesel Selectivity Methane based Intra-particle Diesel Selectivity L/V L/V L/V & & & L p = 3 mm R o = 1.5 mm Ri = 0.3 mm L p = 2 mm R p = 1.5 mm H 2 Concentration Profile H 2 Concentration Profile H 2 Concentration Profile R p = 1.5 mm δ = 1.2 mm R p = 0.7 mm δ = 0.5 mm Dimensionless Radial Coordinate, ξ = r/r p Dimensionless Radial Coordinate, ξ = (r-r i ) /(R o -R i ) Dimensionless Radial Coordinate, ξ = r/r p R p = 1.5 mm R p = 0.7 mm δ = 0.5 mm δ = 1.2 mm Dimensionless Radial Coordinate, ξ = r/r p Dimensionless Radial Coordinate, ξ = (r-r i ) /(R o -R i ) Dimensionless Radial Coordinate, ξ = r/r p
Computational Issues To avoid convergence issues, the radius of the particle was set to a very small number and the subsequent solution was stored to be used as initial conditions for higher radius. H 2 CO CO 2 H 2 O Numerical instabilities were encountered in the region where CO and CO 2 concentrations approached zero leading to convergence issues and unrealistic values. Region with numerical instabilities Once the convergence issue was solved the mesh was refined to get smooth curves. The convergence issues were solved by not letting CO and CO 2 concentrations approach zero by using CO=if(CO 0,eps,CO) and CO 2 =if(co 2 0,eps,CO).
Conclusions A 1-D catalyst pellet model can be used to analyze particle-level performance. Catalyst performance on a reactor-scale can be studied by coupling 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 suggest that the cylindrical and spherical catalyst particle shapes are preferred over hollow rings. The presence of more liquid in the spherical particle creates an advantage for the cylindrical catalyst shape due to diffusional limitations in the wax. Micro kinetic rate equations, when coupled with intraparticle transport effects and vapor-liquid equilibrium phenomena, captures the transportkinetic interactions and phase behavior for gas-phase FT catalysts. Convergence can be a major issue in fast reaction-diffusion systems. This can sometimes be easily resolved by using simple built-in operators, such as if () and eps, to avoid negative and other unrealistic values of dependent variables at the boundaries or interior and then refining the mesh in accordance with computational time.
Thank You
References
References (cont d)
Mole Fraction of Diesel in Liquid Phase Mole Fraction of Diesel in Liquid Phase Mole Fraction of Diesel in Liquid Phase Mole Fraction of Wax in Liquid Phase Mole Fraction of Wax in Liquid Phase Mole Fraction of Wax in Liquid Phase Mole Fraction of Wax & Diesel in Liquid Phase Cylinder Ring/Hollow Cylinder Sphere R p = 0.7 mm δ = 1.2 mm δ = 0.5 mm R p = 1.5 mm Dimensionless Radial Coordinate, ξ = r/r p Dimensionless Radial Coordinate, ξ = (r-r i ) /(R o -R i ) Dimensionless Radial Coordinate, ξ = r/r p R p = 0.7 mm δ = 1.2 mm δ = 0.5 mm R p = 1.5 mm Dimensionless Radial Coordinate, ξ = r/r p Dimensionless Radial Coordinate, ξ = (r-r i ) /(R o -R i ) Dimensionless Radial Coordinate, ξ = r/r p
Mole Fraction of Fuel Gas in Vapor Phase Mole Fraction of Fuel Gas in Vapor Phase Mole Fraction of Fuel Gas in Vapor Phase Mole Fraction of Fuel Gas in Vapor Phase Cylinder Ring/Hollow Cylinder Sphere δ = 1.2 mm R p = 1.5 mm 533 K 533 K 533 K 513 K 493 K Dimensionless Radial Coordinate, ξ = r/r p 513 K 493 K Dimensionless Radial Coordinate, ξ = (r-r i ) /(R o -R i ) 513 K 493 K Dimensionless Radial Coordinate, ξ = r/r p