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Introduction The model
Modeling of Non-Isothermal Reacting Flow in Fluidized BedReactors
Vít Orava1,2, Ondřej Souček2, Peter Cendula1
1Institute of Computational Physics, ZHAW, Switzerland2Faculty of Mathematics and Physics, CUNI, Czech Republic
October 15, 2015
Orava et al., Multi-phase modeling of non-isothermal reactiveflow in fluidized bed reactors, J. Comp. App. Math., 2015.
Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 1 / 12
Introduction The model
What is a fluidized bed reactor?
Bubble column reactor:liquid � gas
Dissolution of the gas into the liquid.
Packed bed reactor:gas
solid� gas
Heterogeneous catalysis in porousimmobilized macro-structure
Fluidized bed reactor:liquid
solid� gas
Heterogeneous catalysis on movingmicro-structure.
Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 2 / 12
Introduction The model
The application: Hydrogen generator coupled to PEM FC
Hydrogen (gas) is produced by endothermal decarboxylation of formic acid(liquid) - in presence of a (solid) catalyst.
Figure : Scheme of the HyForm system.
Purpose: Using formic acid as a fuel to generate 1− 5kW .Typical usage: back-up devices, i.e. start-up in a few minutes, works for manyhours, comparable with diesel aggregate.
Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 3 / 12
Introduction The model
Constituents and phase transitions within the reactor
We treat the system, contained in a fixed control volume, as a mixture of 7 const.
FA(l), FA(g), CO2(d), CO2(g), H2(d), H2(g), Cat(s).
Subscripts "(l), (g), (s)" denote liquid, gas, solid phase and "(d)" refers to dissolved phase.Along the decarboxylation of formic acid
FA(l)32.9kJ−→ H2(d) + CO2(d)
we consider four phase transitions (evaporation) mechanisms
FA(l)23.1kJ−→ FA(g)
H2(d) −→ H2(g)
CO2(d) −→ CO2(g).
Other transformation processes are assumed to be negligible.
Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 4 / 12
Introduction The model
Model setting
Distinguishing partial densities and momenta, we consider one commontemperature field - so called Class II model.There is a natural division of the constituent within two groups forming, so called,pseudo phases where:(i) Gaseous phase: denoted by ()g - consists of CO2(g), H2(g) and FA(g) which share
one common velocity field ug and Φg :=ΦCO2(g)=ΦH2(g)
=ΦFA(g).
(ii) Liquid phase: denoted by ()l - consists of FA(l) and dissolved CO2(d), H2(d) whichshare one common velocity field ul and Φl ≈ ΦFA.
(iii) Solid phase: denoted by ()s - consists of Cat(s).
(ii)∗ Suspension: denoted by ()ls - mixture of liquid and solid where Φls := Φl + Φs .
Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 5 / 12
Introduction The model
Mixture theoryhandling mass concentrations ci
no interfacial phenomenausually CPU friendly
Two-phase theoryhandling volume fractions Φi
tracking of interfacesCPU-costly, steady solution (?!)
Our approach: Multi-phase (scale-up averaging) theoryGeometry of interfaces follow the mixture approach.Interfacial phenomena are caught in the model.
Slattery, J. C., Momentum, Energy and Mass Transfer in Continua, McGraw-Hill Book Co., 1972.Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 6 / 12
Introduction The model
Full model∂t (Φlsρ
truels ) + div
(Φlsρ
truels uls
)= −mgl (MaB.1)
∂t (Φgρtrueg ) + div
(Φgρ
trueg ug
)= MCO2(d)
r evCO2(d)
+ MH2(d)r evH2(d)
+ MFAr evFA(l)
(MaB.2)
∂t (Φsρtrues ) + div(Φsρ
trues us ) = 0 (MaB.3)
∂t (ΦCO2(d)ρtrue
CO2(d)) + div(ΦCO2(d)
ρtrueCO2(d)
ul ) + JCO2(d)= MCO2(d)
r ch −MCO2(d)r evCO2(d)
(MaB.4)
∂t (ΦH2(d)ρtrue
H2(d)) + div(ΦH2(d)
ρtrueH2(d)
ul ) + JH2(d)= MH2(d)
r ch −MH2(d)r evH2(d)
(MaB.5)
Φlsρtruels
dlsulsdt
= −Φls∇pls + Φlsρtruels νlsDls + Φlsρ
truel g− mgl uls + Φls Φg
38
Cdρtruels
rg|ulsg
slip |ulsgslip (MoB.1)
∇(
pdynls + Φg
2σrg
)+ (Φlsρ
truels − Φgρ
trueg )g = −ΦlsCd
38ρtrue
lsrg|ulsg
slip |ulsgslip (MoB.2)
(ρtruel − ρtrue
s )∇pdynls + (ρtrue
l − ρtrues )g = −
92
Φlsρtruels νls
r2s
ulsslip (MoB.3)
ρCpduTdt− k∆T = −
Lch
MFAr ch −
LevFA
MFAr evFA −
LdissCO2(d)
MCO2(d)
r evCO2(d)
−Ldiss
H2(d)
MH2r evH2(d)
(EnB)
∂tn + div(nug ) = R (Pop)
Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 7 / 12
Introduction The model
Quasi-steady modelPerforming parameter analysis and neglecting of some minor terms, we look forvariables Φg , Φsl , ug , uls , pls , T and n such that the following holds:
∂t (Φlsρtruels ) + div
(Φlsρ
truels uls
)= −MFAr ch (MaB.1)
∂t (Φgρtrueg ) + div
(Φgρ
trueg ug
)= MFAr ch (MaB.2)
∂t (Φsρtrues ) + div(Φsρ
trues us ) = 0 (MaB.3)
Φlsρtruels
dlsulsdt
=−Φls∇pls +Φlsρtruels νlsDls +Φlsρ
truel g−mgl uls +Φls Φg
38
Cdρtruels
rg|ulsg
slip |ulsgslip (MoB.1)
g = −38
Cdrg|ulsg
slip |ulsgslip (MoB.2)
(ρtruel − ρtrue
s )g = −92
Φlsρtruels νls
r2s
ulsslip (MoB.3)
ρCpduTdt− k∆T = −
Lch
MFAr ch (EnB)
∂tn + div(nug ) = R (Pop)
where Φls + Φg = 1, ulsslip = us − ul , ulsg
slip = usl − ul
Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 8 / 12
Introduction The model
COMSOL implementation
1 Full model:Laminar Bubbly Flow (CFD Module):
MaB.1, MaB.2, MoB.1, MoB.2Heat Transfer in Fluids: EnBCoefficient Form PDE:
MaB.3, MaB.4 + MaB.5, Popexplicit form: MoB.3
2 Quasi-steady model:Laminar Bubbly Flow (CFD Module):
MaB.1, MaB.2, MoB.1, MoB.2Heat Transfer in Fluids: EnBCoefficient Form PDE:
MaB.3, Popexplicit form: MoB.3
Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 9 / 12
Introduction The model
The results: Floating
Figure : Velocity Field Liquid, Temperature, Gas Concentration, Solid Concentration.
Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 10 / 12
Introduction The model
The results: Traffic Jam Effect
Figure : Velocity Field Liquid, Temperature, Gas Concentration, Solid Concentration.Traffic Jam Effect: ρtrue
s < ρtruel
Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 11 / 12
Introduction The model
Game over!
Thank you for your attention!
Details on my poster.
Acknowledgement
We thank M. Grasemann, A. Dalebrook G. Laurenczy a J. Schumacher for providing preliminaryexperimental observations and fruitful discussions during the investigation of the problem.This work was supported by CCEM and Swisselectric Research under project Hy-Form and byMŠMT CZ under project SVV 260220/2015.
Vít Orava (ICP ZHAW, MFF CUNI) COMSOL Conference: Multi-Phase Reactor Modeling October 15, 2015 12 / 12