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Hydrodynamics And Mass Transfer In Taylor Flow
COMSOL Conference 2015 Grenoble - 15/10/15
F. L. Durán Martínez1, A. M. Billet1, C. Julcour-Lebigue1, F. Larachi2
1LGC – Laboratoire de Génie Chimique, Toulouse University, Toulouse, France 2Department of Chemical Engineering, Laval University, Quebec, Canada
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Overview
I. Modelling Strategy
II. Liquid-phase hydrodynamics
III. Gas-liquid mass transfer
IV. Conclusions and Recommendations
COMSOL Conference 2015 Grenoble - 15/10/15
GAS BUBBLES
LIQUIDSLUGS
LIQUID FILM
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Modelling strategy
…
…
Monolith reactor
Aluminium
P C
P: Product C: Coolant
P C
P
Catalyst
Reacting channel
Single-channel approach
COMSOL Conference 2015 Grenoble - 15/10/15
Twall
Twall
Twall
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Modelling strategy
Unit Cell approach (UC):
• Bubble frame of reference. • Bubble fixed shape. • P & u fields as numerical
“platform” to mass transfer. Fully-developed Taylor flow
HALF- LIQUID PLUGS
GAS
BUBBLE
WALLLIQUID FILMT
HALF-LIQUID SLUGS
THIN LIQUID FILM
GAS BUBBLE
WALL
GAS BUBBLES
LIQUIDSLUGS
LIQUID FILM
COMSOL Conference 2015 Grenoble - 15/10/15
wal
l
-UB
usrc,Psrc
udst,Pdst
usrc = udst
Psrc = Pdst + DP Periodic flow
Periodic flow
DP
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Simulation Strategies
1. Periodic UC: Periodic B.C. in the vert. direction usource = udestination, Psource = Pdestination + DP
2. “Open” UC: Parabolic velocity profile (inlet); P = 0, normal flow (outlet) DP evaluation & comparison
Liquid-phase hydrodynamics
uo=2UTP[1-(r/Rc)2] - UB
Po = 0, Normal flow
COMSOL Conference 2015 Grenoble - 15/10/15
Governing equations
Mass conservation:
Momentum conservation (upward flow):
𝛁 ∙ 𝒖𝐿 = 0
𝜌𝐿 𝒖𝐿 ∙ 𝛁 𝒖𝐿 = 𝛁 ∙ −𝑝𝑰 + 𝜇 𝛁𝒖𝐿 + 𝛁𝒖𝐿 𝑇 + 𝑭
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Liquid-phase hydrodynamics
-UB
Moving wall = -UB
usrc = udst
Psrc = Pdst + DP
G-L interface: Slip / No slip
DP
usrc,Psrc
udst,Pdst
Pressure ref.: Po = 0 bar
wal
l
Liquid properties: rL, mL
Fvol : -rL*g
Laminar flow
Periodic flow
Periodic Unit Cell strategy usrc = udst, Psrc-Pdst = DP?
Remarks:
Van Baten & Krishna study case1
Upward concurrent flow Bubble frame of reference Air-water system 1van Baten, J.M., Krishna, R., Chem Eng Sci. 2004, 59, 2535-2545
COMSOL Conference 2015 Grenoble - 15/10/15
Periodic flow
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Mesh details for the sensitivity study
Liquid-phase hydrodynamics
Total mesh element
Smallest element size (µm)
Biggest element size (µm)
N. of elem. in liq. film
DPOpenUC (Pa)
1 33347 3 155 17 283
2 77318 ~0,8 155 19 324
3 151616 ~0,2 87 22 331
4 226798 ~0,2 67 22 325
Mesh 2 with focus on refined zones
COMSOL Conference 2015 Grenoble - 15/10/15
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Liquid-phase hydrodynamics
Results: converged velocity fields in periodic UC, DPcalc
Remarks:
Parabolic profile within the slug. Umax changes by ~15% between DP = 0 and DP calculated in open UC (DPOpenUC).
Fully-developed flow on the liquid film is rapidly observed.
COMSOL Conference 2015 Grenoble - 15/10/15
?
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Comparison of the B.C. at the interface between simulations and Abiev’s1 model
Analysis of a “fully-developed film-bubble flow”:
Liquid-phase hydrodynamics
Gas phase:
Liquid phase:
1Abiev, R.Sh., Theor Found Chem Eng. 2008, 42, 1105-117
d film
buller
z
Bubble
COMSOL Conference 2015 Grenoble - 15/10/15
10 Thèse F. DURÁN MARTÍNEZ 3ème réunion d’avancement 8/06/15
Comparaison simulation COMSOL – modèle d’Abiev
-4,5E-01
-4,0E-01
-3,5E-01
-3,0E-01
-2,5E-01
-2,0E-01
-1,5E-01
-1,0E-01
-5,0E-02
0,0E+00
1,45E-03 1,46E-03 1,47E-03 1,48E-03 1,49E-03 1,50E-03
Vz [m/s]
r [m]
VzL - UB
z=0_Open-Slip
z=0_Open-NoSlip
RB
-0,33
Durán M (Slip Open UC)
Durán M (No slip Open UC)
Abiev (continuity)
Comparison of the B.C. at the interface between simulations and Abiev’s1 model
slip B.C. seems appropriate for the GL interface u
Liquid-phase hydrodynamics
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Mass transfer
Periodicity
Periodicity
.(-Di ci ) + u.ci = Ri Ni = -Di ci + uci Periodic velocity field u Di : 10-9 [m2/s]
Convection & diffusion
Flux: - n . Ni = Kc*c [mol/m2/s]
G-L Interface: c* = 1,3 mol/m3
ci,in = ci,out
-nin . Ni,in = -nout . Ni,out
Stationary mass transfer with reaction at the wall
Remarks:
Bubble: mass source Reactive wall: mass sink Bubble frame of reference Air-water system
Aim:
Stationary: Transfer Rxn kLa evaluation & comparison
COMSOL Conference 2015 Grenoble - 15/10/15
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Mass transfer
Stationary concentration field
COMSOL Conference 2015 Grenoble - 15/10/15
Homogenous bulk concentration
Flux = N = kLa Dc
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Mass transfer
Gas molar flow rate from bubble:
N = Surface integration(chds.bndFlux_c) [mol/s] (1) N = I/Sbubble [mol/m2/s]
Overall average concentration <Coverall>:
<Coverall> = Volume integration(c)/VL [mol/m3] (2)
Methodology for kLa evaluation
(3) 𝑘𝐿𝑎 =𝑁
(𝐶∗ − 𝐶𝑜𝑣𝑒𝑟𝑎𝑙𝑙 )∗𝑏𝑢𝑏𝑏𝑙𝑒 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑎𝑟𝑒𝑎
𝑈𝐶 𝑣𝑜𝑙𝑢𝑚𝑒= 0,078
𝑚𝐿3
𝑚𝑈𝐶3 ∗ 𝑠
COMSOL Conference 2015 Grenoble - 15/10/15
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Conclusions & Recommendations
COMSOL Conference 2015 Grenoble - 15/10/15
Conclusions
Methodology for a relevant DP choice has been developed. Periodic UC DP influence has been shown. Slip B.C. seems appropriate after comparison. kLa has been computed in a reaction study case.
Future work
Complex kinetic equation heterogeneous catalyst on the wall Add heat transport Build a overall monolith reactor model
Acknowledgements
15 COMSOL Conference 2015 Grenoble - 15/10/15
THANK YOU!
Questions
