Approximate prediction of gas-solid conversion in FB reactors

Chemical and Environmental Department University of Seville Spain Approximate prediction of gas-solid conversion in FB reactors A. Gómez-Barea, M. Campoy (University of Seville, Spain). B. Leckner (Chalmers University of Technology, Sweden) contact: agomezbarea@esi.us.es The 12 th International Conference on Fluidization May 13-17, 2007. Harrison Hot Springs near Vancouver, B.C. (Canada) 15th May 2007

Content 1. Objective 2. Problem description 3. Model concept 4. Two-step solution Catalytic gas solid reaction (CGSR) Non-catalytic gas solid reactions (NCGSR) 5. Applications 6. Conclusions

1. Objective Development of a method for solution of gas-solid reactions (GSR) in FB CGSR NCGSR (non-catalytic case) The method aims: General but still simple to apply Identification of main governing parameters Simple solutions A BFB case is dealt with here (A CFB case is under development: CFBC Hamburg 2008) 1. Objective

Why another model/method? Simplified gas-solid FB reactor models are mostly applicable for catalytic reactions the solids are unchanged with reaction (no poisoned) no particle discharged Two main parameter govern the problem Lacking in literature a simple method like the one existing for CGSR in FB (Orcutt, 1962) applicable for NCGSR (FB reactor models for NCGSR are devised for specific reactions only) 1. Objective

2. Problem description w c p ( x ) b X g c REACTOR SCALE Gas film layer cr () r N A Particle c s c e F 0 p 0 ( x c ) FEED F 1 p 1 ( x c ) x c,b GAS PARTICE SCALE 2. Problem description

3. Model concept Simplifications: Isothermal (reactor and particle) Only one reaction Particle at the same (uniform) conversion in feed Retained: Fluid-dynamics of the FB (two-phase flow) Population balances General particle model Rate, physical and thermochemical properties varies with conversion 3. Model concept

Model concept: Reactor scale c out REACTION WITHIN A PARTICLE c S DIFFUSION WITHIN A PARTICLE FILM DIFUSSION c e SOLIDS DENSE PHASE (EMULSION) c e EXCHANGE OF CO 2 BETWEEN PHASES GAS (PLUG FLOW) BUBBLE PHASE c b (z) η p η ph c e = cin n c in z GAS 3. Model concept

Model concept: Particle scale Gas film layer N A Evaluation of rate of conversion cr () r Particle c s c e dxc re, i( c) dt = K F x Particle effectiveness factor η ( x ) = p c dx dx c / c / dt dt FDE dx dt c =η ( x ) F( x ) K p c i c r η p << 1 Diffusional regime η 1 Kinetic regime p 3. Model concept

Methodology: Two step solution Step 1: Development of a a CGSR model Step 2: Extension to NCGSR Kintetic particle model varying with conversion Population balance in the FB 3. Model concept

uo umf β = : dimensionless excess flow uo kbε b reactor residence time NTU = : u / L time to flush out the reactant from bubble o 4. Solution Reactor scale: Fluid-dynamics f 1 Fluid-dynamic parameter NTU Na = 1 β exp β N a 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 β=0.25 β=0.5 β=0.75 β=0.95 0.1 0 0.1 1 5 NTU 4. Solution

Reactor scale: Fluid-dynamic vs. Chemical kinetics Kv residence time Da R = : u / L chemical reaction time 0 f Damköhler number at reactor scale 4. Solution

Solution: Particle scale Damköhler number at particle scale Da p = kl k equ G c c e n e rate of reaction : rate of external diffusion Thiele module M s n 1 1/2 1 kc s rate of chemical reaction n + = Lequ : 2 De rate of internal diffusion 4. Solution

4.A: Solution for CGSR N a Da R Da p, in M in Fluid-dynamic parameter Damköhler number at reactor scale Damköhler number at particle scale Thiele module Solution 1/ n X g = (1- η ph )Na η ph =f (Da R /N a, η p, n) η p =f (Da p,in,m in, η ph, n) 4. Solution

Solution of η ph =f (Da R /N a, η p, n) 1 0.9 0.8 n=0.25 n=0.5 0.7 0.6 η ph n=2 n=1.5 n=0.75 0.5 n=1 0.4 0.3 0.2 0.1 0.1 0.5 1 5 Da R /N a 4. Solution

Solution of η p =f (M in, Da p,in, η ph, n) 1 0.9 0.8 0.7 Da pin η (n-1)/n =0 ph Da pin η (n-1)/n =0.5 ph Da pin η (n-1)/n =1 ph n=0.25 n=0.5 n=1 n=1.5 η p 0.6 0.5 Da pin η (n-1)/n =3 ph 0.4 0.3 Da pin η (n-1)/n =10 ph 0.2 0.1 0 0.1 0.5 1 5 10 (n-1)/2n M in η ph 4. Solution

4.B. Solution (NCGSR) The non-catalytic nature of the reaction make the problem more complex: Da R is unknown Diffusion limitations in particles (as in CGSR) Solid reactant in bed is unknown There is a distribution in conversion (or t) M s and Da p,e changes with time (conversion) Known parameters are (Da p,in0 and M in0 ) CONCLUSION: Alternative formulation is needed 4. Solution

Definition of (Da s /λ) Da s = F K 0 re, / w b r c w b : Bed inventory λ = F K re, / 1 w b F 0 F 1 Da s λ = 1 rc F 0 0 complete conversion 1 null conversion 4. Solution

NCGSR: Governing groups at rector scale Three groups govern the problem (at reactor scale): 1. The fluid-dynamic parameter, N a 2. The ratio of reactant gas and solid feed flow rates, α 3. Das/λ (approach to complete solid conversion) * Da s /λ depend on the processes at particle scale and the RTD distribution (obtained from a population balance and kinetic particle model) 4. Solution

4. Solution (NCGSR) Solution 1/ n X g = (1- η ph )Na x c 1 1 Da s = xc0 Yc Yc λ η ph =f (Da s /λ, N a α, n) Da s /λ=f (Da p,in0,m in0, η ph, n, F i (x c )) Y c :%w of solid reactant in the feed; x c0 : initial conversion 4. Solution

4. Solution (Non-catalytic case): Solution of η ph 1/n =f (Das/λ, N a α ) 1 0.9 0.8 N a α=5 1/n η ph 0.7 0.6 0.5 2 1.5 0.4 0.3 0.2 1 0.75 0.5 0.25 0.1 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Da s /λ 4. Solution

4. Solution (Non-catalytic case): Das/λ =f (Das/λ, M in,0,dap in,0, n) 1 0.8 0.6 (Da s /λ) 0.4 0.2 5 15 (n-1)/2n Da pin,0 η ph =0.1 (1-n)/n M in,0 η ph =0.1 1 0 0 1 2 3 Da sin η ph 4. Solution

Exploration of the model capability FB reactor behaviour s analysis as a function of: α, N a, Da s /λ, M in,0,dap in,0 Simple solutions and values of parameters where these simplifications applies 4. Solution

5. Application examples Gasification of char with CO 2 in a labscale FB Conversion in an industrial scale FB zinc roaster (Grace, 1986 *) * Grace, J.R., 1986. Fluid beds as chemical reactors, in Geldart, D. (Ed.), Gas Fluidization Technology, John Wiley & Sons Ltd. 5. Application examples

INPUTS Direct inputs 5. Application: Imputs of examples Units CO 2 -char gasification (C+CO 2 2 CO) (Lab-scale BFB) (Gómez Barea et al. (2006) Zinc Roaster (ZnS + 3/2 O 2 ZnO +SO 2 (Full-scale BFB) (Grace 1986) D t m 2.66 10-2 6.38 H m 0.165 n.a. T b K 1173 1273 u mf m s -1 0.19 0.048 u 0 m s -1 0.8 0.78 c in kmol m -3 2.07 10-3 2.075 10-3 F 0 kg s -1 1.4 10-5 2.48 x c0 0 0 Y c 0.85 1 w b kg 2.5 10-2 30,000 ν 1 3/2 K r s -1 2.3 10-3 7.35 10-3 n 0.4 1 F i (x c ) (1-x c ) 1/2 (1-x c ) 2/3 d c0 m 2.1 10-3 6 10-5? c0 kg m -3 800 4100 d si kg m -3 4.71 10-4 6 10-5? si m 2650 3420 D e m 2 s -1 7.0 10-6 9.0 10-6 g(x c ) (1-x c ) 2.5 1 5. Application examples

5. Application: Calculation of goberning parameters Fluid-dynamic parameters NTU 7 1.40 β 0.76 0.99 Governing parameters N a 0.99 0.76 α 0.2 1.35 Da sin 3.78 88.91 M in,0 2.0 10-2 >>1 Da pin,0 < 1.0 10-3 <<1 5. Application examples

5. Application: Example s solution SOLUTION η ph 0 0.025 (Da s /λ) 0.80 [ =(Da s /λ) crit ] 4.05 10-5 [ 0] Da R >>1 29.08 X g 1 0.74 [ (1/α)] x c,b 0.17 0.99 5. Application examples

6. Conclusions Establishment of a method for solution of isothermal non-catalytic gas-solid reactions in an FB General (fluid-dynamic of a FB and general solution for NCGSR: n th kinetics with respect gas and any with respect to solid) Identification of the main governing parameters Identification of simplifications and limiting cases Easy to use (spreadsheet or even one envelope calculations) 6. Conclusions

More information Proceeding of Fluidization XII. pp. 639-646 (Problem description and catalytic solution) A. Gómez-Barea, B. Leckner, D. Santana A., P. Ollero. Gas-solid conversion in fluidised bed reactors (Submitted for publication Chemical Engineering Journal (May 2007) (Complete solution) Contacting me (Alberto Gómez-Barea): agomezbarea@esi.us.es 0034 954487223