1 Steady-state Packed Bed Reactor Modeling for Methanol Synthesis K. R. Rout*, H. A. Jakobsen NTNU, Norway
2 Contents Motivation of methanol synthesis Types of reactor model Pseudo-homogeneous model Conventional heterogeneous model Simplified heterogeneous model Comparasion of Psedu-homogeneous-, conventional- and simplified heterogeneous model Numerics: least squares spectral element method. Results and Discussion Conclussion
3 Process evaluation for methanol synthesis Reactor Simulation for methanol synthesis Net power Total input Total output Reactor type design/size Best operating conditions Transport phenomena Kinetic study for methanol synthesis Catalyst preparation Kinetic rate Catalytic activity
4 Motivation for the process METHANOL is multipurpose based chemical. It can be used as chemical intermidiates. Easy for transportation. It has high octane number. Good antiknock performance. Future renewable energy sources (Methanol + Gasoline) Fuel combustion engine Methanol: Fuel cell
5 Motivation for steady-state reactor modeling METHANOL synthesis: Feed treatment purification Reforming Methanol synthesis Product purification and storage Intrinsic nonlinerity + complex phenomena = Computer Simulation Dynamic simulation: Start-up and shut down investigation System identification Reactor modeling? Safety, control, optimization Catalytic activity Pseudo-homogeneous Conventional- and simplified Heterogeneous Steady-state model
6 Reactions involved in Methanol synthesis CO + 2H 2 = CH 3 OH (1) CO 2 + H 2 = CO + H 2 O...(2) CO 2 + 3 H 2 = CH 3 OH + H 2 O...(3) The over all reaction is exothermic. Side reactions (even through they are inhibited by high catalyst selectivity under normal operating conditions): CO + 3H 2 = CH 4 + H 2 O.(4) nco + 2nH 2 = C n H 2n+1 OH + (n-1) H 2 O (5) 2CH 3 OH = CH 3 OCH 3 + H 2 O.(6) This reaction occurs at 570 K; might lead to reactor instabilites due to of its high exothermicity. Catalyst: Cu/Zn/Al 2 O 3 (life cycle: 2 year)
7 Packed bed reactor models Derivation of Reactor model Massbasedmodel: Mole basedmodel: C Assumption of total numer of moles along the reactor axis is constant: this is not true Modeling of packed bed reactor Pseudo-homogeneous model Heterogeneous model do not account explicitly the seperate equation for the solid and presence of pellet Simplified interstitial Conventional fluid. Mass transport: 1. Wilke Model Mass transport: Efficiency 2. factors Maxwell-Stefan Multicomponent Model diffusion models 3. Dusty gas model
8 Pseudo-homogeneous reactor model Species Mass balance: Total continuity equation: Energy balance: Ergun Equation: j u (1 ) R g z k k jk k ( u z g ) 0 T 4U gcpguz (1 ) ( Hrk) krk Tw T d 2 P 1 uzg 1 1.75 150 Re 3 dp t
9 Conventional a) Fluid phase equations: i Mass balance: guz kgiavg( is i) Energy: Ergun Eq.: b) Solid phase equations (Wilke, Maxwell-Stefan, Dusty gas model): Mass balance: J (1 ) R where J D ir, is, k k ik ir, gs, ri, r k r Energy: Q r s Heterogeneous Model T 4U Cp u h a ( T T) ( T T) d g g z f v s w t 2 P 1 uzg 1 (1.75 150( )) ( ) 3 Re d p Ts (1 ) ( Hrk ) k Rk where Qs s r a) Fluid phase equations: i Mass balance: u Energy: Ergun Eq.: Simplified g z kgiavg( is i) T 4U gcpguz hfav( Ts T) ( Tw T) dt 2 P 1 uzg 1 (1.75 150( )) ( ) 3 Re d b) Solid phase equations: Mass balance: avgkg, i( i i, s) (1 ) krkik 0 Energy: k ah ( TT) (1 ) ( H ) R 0 v f s rk k k p
10 Numerical scheme Least square spectral method (LSM)*. Because, for a given accuracy the high order spectral method requires only a few collocation points where as the low order methods such as the finite volume method (FVM), require a large number of grid points. The basic idea in the LSM is to minimize the integral of the square of the residual over the computational domain. *Rout K. R., Solsvik J., Nayak A. K., Jakobsen H. A. (2011) A numerical study of multicomponent mass diffusion and convection in porous pellets for the SE-SMR and desorption processes. Chemical Engineering Science 66:4111-4126
11 Overall Purpose Comparison of pseudo-homogeneous reactor model, conventional- and simplified heterogeneous reactor models with experimental data. The proposal of best suitable reactor model under normal operating conditions of fixed bed Lurgi reactor. Comparasion of different multicomponent diffusion models.
12 Comparasion with Rezaie et al. Mole Temperature[K] fraction of CH OH 3 Simplified heterogenous(gas phase) Simplified heterogenous(gas phase) Simplified heterogenous(solid phase) Literature heterogenous(gas phase) Literature heterogenous(gas phase) 530 0.06 525 0.04 520 515 0.02 510 505 5000 0 2 4 Axial direction [m] [m] 6 8 Rezaie N., Jahanmiri A., Moghtaderi B. Rahimpour M.R (2005) A comparasion of homogeneous and heterogeneous dynamic models for industrial methanol Reactors in the presence of catalyst deactivation. Chemical Engineering and Processing 44: 911-921
13 Comparasion with different packed bed reactor models Mole fraction Pressure of [bar] CH OH Temperature[K] 3 Psedu-homogeneous Psedu-homogeneous Simplified Simplified heterogenous(gas heterogenous phase) phase) Simplified heterogenous(solid phase) phase) 7.7 x Conventional heterogenous 106 Conventional heterogenous(gas phase) phase) Conventional heterogenous(solid phase) phase 0.06 530 7.695 0.04 520 7.69 0.02 510 7.685 0 7.68 500 1 3 4 5 6 7 0 2 8 Axial direction 4 [m] 6 8 Axial Axial direction direction [m] [m]
14 Comparasion with Experimental data by Rezaie et al Time (day) Plant (tonne/day) Pseudohomogeneous (tonne /day) Simplified heterogeneous (tonne/day) Conventional heterogeneous (tonne/day) 0 295.0 308.86 308.80 300.00 Rezaie N., Jahanmiri A., Moghtaderi B. Rahimpour M.R (2005) A comparasion of homogeneous and heterogeneous dynamic models for industrial methanol Reactors in the presence of catalyst deactivation. Chemical Engineering and Processing 44: 911-921
15 Comparasion of different multicomponent diffusion models in conventional heterogeneous model Temperature [K] 530 Mole fraction of CH 3 OH 525 520 515 510 0.06 0.04 0.02 Maxwell-Stefan Model Dusty gas Model Wilke Model Maxwell-Stefan Model Dusty gas Model Wilke Model r 0 0 2 4 6 8 Axial direction [m] 505 0 2 4 6 8 Axial direction [m]
16 Conclusion Both Pseudo-homogeneous- and simplified heterogeneous reactor model slightly overestimates with experimental data. However, the percentage of deviation is quite small. Conventional heterogeneous model is computationally expensive. As there is no significant deviation between gas- and solid phase concentrations of different components along the reactor axis, the pseudo-homogeneous reactor model seems to be best choice for methanol synthesis process.
17 Thank You