Coupling catalyst/sorbent particle and fluidized bed reactor models to simulate sorption enhanced steam methane reforming

Preliminary simulationsIlaria Aloisi, Andrea Di Carlo, Nader Jand, Pier Ugo Foscolo

University of L'Aquila-Department of Industrial Engineering Via G. Gronchi 18, 67100 L’Aquila Italy

The objective is to simulate Sorption-Enhanced Steam Methane Reforming (SE-SMR) in a fluidized bed of catalyst/sorbent particles

containing CaO (sorbent), Ni (catalyst) and calcium aluminate (inert phase). A particle model is coupled to a CFD reactor model.

1. IntroductionHydrogen is considered a clean energy carrier. It is mainly produced by natural gas reforming.

Carbon dioxide generation is a necessary, undesired side effect. SE-SMR is a potential route for

hydrogen production with CO2 capture and re-use or sequestration:

Steam Methane Reforming (SMR): 𝐶𝐻4 + 𝐻2𝑂 ↔ 3𝐻2 + 𝐶𝑂 ΔH0298 = + 206 𝑘𝐽/𝑚𝑜𝑙

Water Gas Shift (WGS): 𝐶𝑂 + 𝐻2𝑂 ↔ 𝐻2 + 𝐶𝑂2 ΔH0298 = − 41 𝑘𝐽/𝑚𝑜𝑙

Carbonation (CBN): 𝐶𝑎𝑂 + 𝐶𝑂2 →𝐶𝑎𝐶𝑂3 ΔH0298 = − 178 𝑘𝐽/𝑚𝑜𝑙

Conversion of CO2 into a solid carbonate allows shifting the reversible SMR and WGS reactions

beyond their conventional thermodynamic limits up to a hydrogen concentration higher than 95%.

2.1 Particle grain model

3. Preliminary simulationsThe particle grain model was used to calculate the isothermal, overall effectiveness factor of SMR and WGS reactions (Ω𝑆𝑀𝑅,𝑊𝐺𝑆) for a completely carbonated

bi-functional particle, behaving just as a catalyst (휀𝑝 = 0.11; weight fractions: 𝑤𝐶𝑎𝐶𝑂3 = 0.64, 𝑤𝑖𝑛𝑒𝑟𝑡 = 0.29, 𝑤𝑁𝑖 = 0.07) and different bulk gas volumetric

compositions: starting from 25% CH4 and 75% H2O and approaching the equilibrium values at 650°C. These values were implemented in the CFD reactor

model to simulate a lab-scale fluidized bed with average particle diameter of 500 μm.

2 . Physical description and mathematical equations

The particle model was derived from a previously developed solo-sorbent

grain approach (Stendardo and Foscolo, 2009) by adding the catalytic activity

described by means of the Numaguchi and Kikuchi (1988) SMR and WGS

kinetic laws. The main features of the particle model are:

• Spherical grains of calcium oxide and aluminate, with nickel finely dispersed

on their surface and accessible to the gaseous reactants during the whole

reforming and carbonation process.

• The surface reaction rate between CO2 and CaO is described as first order

in carbon dioxide concentration and available active surface, where the

kinetic constant is taken from the literature (Bhatia and Perlmutter, 1983).

• Product layer diffusion of CO2 through the carbonate layer formed around

each calcium oxide grain is expressed as a function of CaO conversion.

2.2 CFD reactor model (Di Carlo et al., 2010)

• Two interpenetrating continua: gas (휀𝑔) and particle (휀𝑠 = 1 − 휀𝑔) phases.

• Rheological properties derived as a function of the granular temperature.

• Granular temperature predicted by a transport equation for the fluctuating

kinetic energy of the particles (Gidaspow, 1994).

Preliminary results of the CFD reactor model at 45 sec

Ω𝑗 = 0

𝑅𝒓𝒋 𝐶𝑖 ∙ 𝑟2𝑑𝑟 0

𝑅𝑟2𝑑𝑟

𝒓𝒋 𝐶𝑖,𝑏𝑢𝑙𝑘𝑗 = 𝑆𝑀𝑅,𝑊𝐺𝑆

Acknowledgment: the financial support of the EU ASCENT 608512 contract is gratefully acknowledged. Address for correspondence: pierugo.foscolo@univaq.it

∂𝑋

𝜕𝑡=

σ0𝐶𝑎𝑂𝑘𝑠 1 − 𝑋)2 3 𝐶𝐶𝑂2− 𝐶𝐶𝑂2 ,𝑒𝑞

1 +𝑁0𝐶𝑎𝑂𝑘𝑠

2𝐷𝑃𝐿𝛿0𝐶𝑎𝑂 1 − 𝑋

3 1 − 1 −𝑋

1 − 𝑋 + 𝑋 𝑧

3

=𝒓𝑪𝑩𝑵𝑁0𝐶𝑎𝑂

𝜕 휀𝑝 ∙ 𝐶𝑖

𝜕𝑡=

1

𝑟2

𝜕

𝜕𝑟 𝐷𝑖 ,𝑒𝑓𝑓 𝑟2

𝜕𝐶𝑖𝜕𝑟

+ 𝒓𝒊

𝐶𝐻2𝑂=

𝑃

𝑅𝑇− 𝐶𝑖

𝑖

𝜕휀𝑝

𝜕𝑡= 1 − 𝑧) 𝑓0𝐶𝑎𝑂

𝜕𝑋

𝜕𝑡

where:

𝑋 = 𝑋 𝑟, 𝑡); 𝐶𝑖 = 𝐶𝑖 𝑟, 𝑡); 휀𝑝 = 휀𝑝 𝑟, 𝑡)

𝒓𝒊 = 𝜈𝑆𝑀𝑅 ,𝑖 ∙ 𝒓𝑺𝑴𝑹 + 𝜈𝑊𝐺𝑆 ,𝑖 ∙ 𝒓𝑾𝑮𝑺 ∙ 𝜌𝑝0 + 𝜈𝐶𝐵𝑁 ,𝑖 ∙ 𝒓𝑪𝑩𝑵

𝜈𝑆𝑀𝑅 ,𝑖 , 𝜈𝑊𝐺𝑆 ,𝑖 , 𝜈𝐶𝐵𝑁 ,𝑖 are the stoichiometric coefficients of

component i (i ≡ CH4, CO2, CO, H2), negative for reactants

and positive for products.

Initial conditions:

𝑋 0 ≤ 𝑟 ≤ R, 𝑡 = 0) = 0

𝐶𝐻2𝑂 0 ≤ 𝑟 ≤ R, 𝑡 = 0) =

𝑃

𝑅𝑇

Boundary conditions:

𝜕𝐶𝑖𝜕𝑟

= 0 𝑎𝑡 𝑟 = 0 𝑎𝑛𝑑 𝑡 > 0

𝐷𝑖 ,𝑒𝑓𝑓 ∙𝜕𝐶𝑖𝜕𝑟

= ℎ𝑖 ∙ 𝐶𝑖 ,𝑏𝑢𝑙𝑘 − 𝐶𝑖 𝑎𝑡 𝑟 = 𝑅 𝑎𝑛𝑑 𝑡 > 0

Schematic drawing of the SE-SMR DFB reactor system (Meyer et al., 2011)

CFD reactor model inputs

Parameter Value

Fluidization Velocity 0.5 m/s (≈3 umf)

T inlet 923 K

T wall 923 K

Inlet Composition (mole fractions)

CH4 0.25

H2O 0.75

ΩSMR remains almost constant (0.12), while ΩWGS was expressed as a function

of the mole fraction of CO2 in the fluidized bed: ΩWGS = 0.069 yCO2-0.212

Mass conservation: 𝑔 = 𝑔𝑎𝑠, 𝑠 = 𝑠𝑜𝑙𝑖𝑑 𝑗 = 𝑆𝑀𝑅,𝑊𝐺𝑆

𝜕

𝜕𝑡 휀𝑔𝜌𝑔 + ∇ ∙ 휀𝑔𝜌𝑔𝑣 𝑔 = 0

𝜕

𝜕𝑡 휀𝑠𝜌𝑠) + ∇ ∙ 휀𝑠𝜌𝑠𝑣 𝑠) = 0

Species balances:

𝜕

𝜕𝑡 휀𝑔𝜌𝑔𝑤𝑖 + ∇ ∙ 휀𝑔𝜌𝑔𝑣 𝑔𝑤𝑖 = ∇ ∙ 휀𝑔𝜌𝑔𝐷𝑖∇𝑤𝑖 + 휀𝑠𝜌𝑠𝑃𝑀𝑖 𝑣𝑗 ,𝑖𝑟𝑗

𝑗

Momentum conservation:

𝜕

𝜕𝑡 휀𝑔𝜌𝑔𝑣 𝑔 + ∇ ∙ 휀𝑔𝜌𝑔𝑣 𝑔𝑣 𝑔 = ∇ ∙ 𝜏𝑔 + 휀𝑔𝜌𝑔𝑔 − 휀𝑔∇𝑝 − 𝛽𝑔𝑠 𝑣 𝑔 − 𝑣 𝑠

𝜕

𝜕𝑡 휀𝑠𝜌𝑠𝑣 𝑠) + ∇ ∙ 휀𝑠𝜌𝑠𝑣 𝑠𝑣 𝑠) = ∇ ∙ 𝜏𝑠 + 휀𝑠𝜌𝑠𝑔 − 휀𝑠∇𝑝 − ∇𝑝𝑠 − 𝛽𝑔𝑠 𝑣 𝑠 − 𝑣 𝑔

Energy conservation:

𝜕

𝜕𝑡 휀𝑔𝜌𝑔𝑐𝑝𝑔𝑇𝑔 + ∇ ∙ 휀𝑔𝜌𝑔𝑣 𝑠𝑐𝑝𝑔𝑇𝑔 = ∇ ∙ 𝑘𝑔∇𝑇𝑔 + ℎ𝑔𝑠 𝑇𝑠 − 𝑇𝑔

𝜕

𝜕𝑡 휀𝑠𝜌𝑠𝑐𝑠𝑇𝑠) + ∇ ∙ 휀𝑠𝜌𝑠𝑣 𝑠𝑐𝑠𝑇𝑠) = ∇ ∙ 𝑘𝑠∇𝑇𝑠) + ℎ𝑔𝑠 𝑇𝑔 − 𝑇𝑠 + 휀𝑠𝜌𝑠 𝑟𝑗Δ𝐻𝑗

𝑗

Granular temperature 𝚯𝒔 balance equation:

3

2 𝜕

𝜕𝑡 휀𝑠𝜌𝑠Θ𝑠) + ∇ ∙ 휀𝑠𝜌𝑠𝑣 𝑠Θ𝑠) = −𝑝𝑠𝐼 + 𝜏 𝑠):∇ ∙ 𝑣 𝑠 + ∇ ∙ 𝑘Θ𝑠∇Θ𝑠) − 𝛾Θ𝑠 − 3𝛽𝑔𝑠Θ𝑠