cfd modelling of mass transfer with and without chemical ... · pdf fileuniversity of dortmund...

University of Dortmund

CFD modelling of mass transfer with and without chemical reaction

in liquid-liquid slug flow capillary microreactors

M. N. Kashid1,2, D. W. Agar1 and S. Turek2

1Institute of Reaction Engineering (TCB)&

2Institute for Applied Mathematics (LSIII)University of Dortmund

Germany

ISCRE Presentation – 6th September, 2006 Institute of Reaction Engineering&

Institute for Applied Mathematics


Outline

Introduction

Motivation & objectives

CFD model

Model validation

Closing remarks




Introduction - Micoreactor technology

Appeal of small scales to chemical engineers:

Important technique for process intensification

Improved performance due to high specific surface areas enhancing heat and mass transfer

Enhanced mass transfer increases reaction rates & reduces process volumes

Precise control of highly exothermic and hazardous reactions

Numbering-up instead of scale-up




Introduction - slug flow reactor

An alternative to suspended drop or film contactor ?

Uniform, well-defined slug size

High specific interfacial area

Enhanced mass transferRecirculationRecirculation Diffusion

DiffusionSlug Flow

Stratified Flow

PIV Measurement

Velocity vectors

CFD simulations

CFD particle tracingTaylor-like vortices - Internal circulations




Introduction- slug flow reactor (..continued)

Facile temperature profiling along the reactor Straightforward downstream phase separation

Outlet 2 – Teflon

Outlet 1 – steel

InletAqueous phase

Organic phase




Motivation & ObjectivesSlug flow concept & mass transfer performance (Burns and Ramshaw, 2001; Harries et al., 2003)

Elucidation & optimisation of nitration reactions(Dummann et al. 2003; Loebbecke et al, 2003)

Fundamental hydrodynamic modelling (Kashid et. al. 2005; Kashid et. al. 2006; Kashid and Agar, 2006)

Prediction of mass transfer rates and reaction(ISCRE 2006)

Powerful experimental tool for analysing biphasic reactions

Identification of asymptotic limits for technical processes




CFD Modelling - Volume of Fluid (VOF)

Incompressible Navier-Stokes equation

The indicator function

Surface tension + wall adhesion

Assumption: No mass transfer between phasesIsothermal conditions

Commercial CFD software package, Fluent 6.2

. 0α α∂+ ∇ =

∂k

k kut

( ) [ ]( )[ ]

∑∑∑ ==

=∇

+∇+∇⋅∇−∇−=⋅∇+∂∂

kk

kkkkk

SFT

u

Fuupuutu

ραμρα

μραρ

ρμ

ρ

and,where

0

11

Experimental: (ID = 1 mm, Velocity = 20 mm/s)

CFD: (ID = 1 mm, Velocity = 20 mm/s)




CFD model

ρ1, μ1, C1 ρ2,μ2,C2

Assumption: C1’= C1

’’= C1’’’ C2

’= C2’’

Schematic representation:

Reduces computational resources significantly

C1’ C2

’ C1’ ’ C1

’ ’ ’C2’ ’

ρ1,μ1 ρ2,μ2 ρ1,μ1 ρ2,μ2 ρ1,μ1

1 21 2 1




Governing Equations – fluid flow

( ) ( )[ ]0u

T][0,x Ωuuu 2

=∇

ℜ∈∇−∇+∇⋅∇=∇⋅+∂

∂ puut

Tμρρ

Assumptions

Slugs are Newtonian, viscous and imcompressibleShape of the slug and volume invariant Flow is laminar and mass diffusivity constantMass transfer and reaction does not affect the flow patterns within the slugs

Density and viscosity ( ))X(

X

0

0

ff

μμρρ

==

Interface condition 2

22

1

11 n n

uu∂∂

=∂∂ μμ

Flow field



University of DortmundGoverning Equations– Mass transfer & reaction

12

22

11

mCCx

CDxCD

=∂

∂=

∂∂

12

22

11

ˆˆ

ˆˆ

CCx

CmDx

Cm

D

=∂

∂=

∂∂

Species transport

( ) ( ) ikik rCDuCt

CrCDuC

tC

±=∇−⋅∇+∂

∂±=∇−⋅∇+

∂∂

2222

1111 ;

Species transport, if partition coefficient (m) ≠1

Interface condition

Interface condition becomes

( ) ( ) ( ) ikik rCDCumt

m

CrCDCumtm

Cm

CCmCC

ˆˆˆ1

ˆ;ˆˆˆ1ˆ

ˆ;ˆ

2222

1111

2211

±=∇−⋅∇+

⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂±=∇−⋅∇+

∂

∂

==




Boundary conditions

ρ1,μ1,, C1 ρ2,μ2,C2

Moving Wall, Vwall = Vav


Stationay Interface,

Vint = 0


Vint = 0


Vint = 0

No-slip at the moving walls Zero species flux at the moving wallsPeriodic boundary concept to connect the extremities of domainMoving boundary concept to set velocity of interface Interface and periodically connected interface satisfies:

Fluid flow

Species transport

xu

xu

∂∂

=∂∂ 2

21

1 μμ

12

22

11

ˆˆ

ˆˆ

CCx

CmD

xC

mD

=∂

∂=

∂∂




SolutionPhysical properties defined using Heaviside function

Terms in the Convection-diffusion equations for m ≠ 1

⎩⎨⎧

Χ>Χ≤

=xwhenxwhen

yxH01

),(

( ) ( )

( )

( ) ( ) ( ) ( ) ( )yxHCDmCDm

CDmCD

yxHCumCum

CumCu

yxHt

m

Ctm

C

tm

CtC

,ˆˆˆˆ1ˆˆˆˆ

,ˆˆ1ˆˆ

,1

ˆˆ

1

ˆˆ

221122

221122

212

⎟⎠

⎞⎜⎝

⎛ ∇⋅∇−∇⋅∇+∇⋅∇=∇⋅∇

⎟⎠

⎞⎜⎝

⎛ ∇⋅−∇⋅+∇⋅=∇⋅

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎠

⎞⎜⎝

⎛∂

∂−

∂∂

+⎟⎠

⎞⎜⎝

⎛∂

∂=

∂∂

( ) ),(property,Physical 212 yxHφφφφ −+=




Solution (… continued)Reaction solution, straightforward operator splitting strategy, within each time step, Step 1: Solution of convection-diffusion equations, all in parallel

Step 2: Obtained concentration field used as initial data for reaction ODE

Discretisation: time → implicit BE, space → FEMFlux correction → upwindEquations are implemented in FEATFLOWTransient simulations

nn ttt −=Δ +1

( ) 0. =∇∇−∇+∂

∂ikikik

ik CDCut

C

ikik r

dtdC

±=




Results - fluid flow

Phase 1

x

y

Phase 2

T = 0.012 s

T = 0.036 s

T = 0.06 s

T = 0.084 s

Test simulation

m/s0.3x10υm/s0.3x10υ 32

51

−− ==

Slug flow velocity = 10 m/sSlug diameter = 0.5 mmSlug length = 2 mm




Results – mass transfer

0

0.2

0.4

0.6

0.8

1

0 2 4 6 8 10

Time [s]

k La

[s-1]

Mesh Level 3 - 80 x 16Level 4 - 160 x 32Level 5 - 320 x 64Level 6 - 640 x 128

Level 3

Level 4

Level 5

Level 6

0

0.002

0.004

0.006

0.008

0.01

0 2 4 6 8 10Time [s]

kL [m

/s

Level 3

Level 4

Level 5

Level 6

Fig: Mass transfer coefficients

Water – succinic acid – n-butanol Capillary ID = 0.5 mmInitial conc. in aqueous solution = 10 Kg/m3

Volumetric mass transfer coefficient

( )( )⎥⎦

⎤⎢⎣

⎡

−−

=outsat

insatL CC

CCT

ak,2,2

,2,2ln1




Model Validation - Neutralisation Reaction

Neutralisation reaction (Harries et al. 2003)

Rapid, second order (k= 1.35 x 1011 L mol-1 s-1) → implicit treatment for reaction ODEsReaction medium: aqueous phasePartitioning of Acetic Acid in favour of aqueous phase: 85:1Governing equations – for species transport in water slug

Kerosene + Acetic acid Water + KOH/NaOH(Reaction Zone)

3 3 2CH + → +COOH NaOH CH COONa H O

( )

( )

( )

( ) 2212424242242

2212323232232

2212222222222

2212121212212

.

.

.

.

CkCCDCut

C

CkCCDCut

C

CkCCDCut

C

CkCCDCut

C

=∇∇−∇+∂

∂

=∇∇−∇+∂

∂

−=∇∇−∇+∂

∂

−=∇∇−∇+∂

∂




Reaction Simulations

0

0.05

0.1

0.15

0.2

0.25

0.3

0 0.5 1 1.5 2 2.5 3

Time [s]

C[m

ol/

CH3COOHNaOHCH3COONa

Average concentrations in aqueous phase

0

2

4

6

8

Level 3 Level 4 Level 5 Level 6 Level 7

Level of refinement

Titra

tion

time

1.75 mm/s3.33 mm/s5.5 mm/s

Mesh independent solution

Data used for chemical reaction simulation

Flow ratio (aqueous/organic): 1Slug lengths : 1.5-3.8 mmSlug diameter: 0.38 mmSlug flow velocities: 0.6-16.6 mm/s

Density ratio (kerosene/water): 0.8Viscosity ratio (kerosene/water): 1.82 Initial conc. of CH3COOH in kerosene: 0.5 mol/LInitial conc. of CH3COOH in water: 0 mol/LInitial conc. of NaOH in water: 0.25 mol/LInitial conc. of CH3COONa in water: 0 mol/LPartition coefficient for CH3COOH (m): 85

Smallest cell size: 0.008D mmSmallest time step for u and p: 1 x10-4 sTime step for mass transfer & reaction: 1x10-5 s




Results

CH3COOH NaOH CH3COONa

Simulated snapshots for neutralisation reaction (Titration time = 5.24s)

Time

Fig: Velocity vectors




Comparison

0

2

4

6

8

10

0 4 8 12 16 20Flow velocity [mm/s]

Titra

tion

time

Experimental (Harries et al., 2003)Simulation (Harries et. al., 2003)Present work

0

2

4

6

8

10

0 1 2 3 4 5

Slug length [mm]

Titra

tion

time

Experimental (Harries et al., 2003)Simulations (Harries et. al., 2003)Present work

Titration time vs flow velocity Titration time vs slug length

End point of the titration was taken at 95 % base neutralisation




Closing remarksConclusions

The model developed for mass transfer with/without reaction shows good agreement with experimental data of neutralisation reactionVery fine meshes required to discern true behaviour

Future workIncorporate interface curvature (level set method)Integrate wall film in model Detailed experimentation on mass transfer and chemical reaction DFG grant as of Oct. 2006




Thank you for your attention




ReferencesBurns, J. R. and Ramshaw, C., Lab on a Chip, 1,10-15, 2001Harries et al., International Journal of Heat & Mass Transfer, 46, 3313-3322, 2003Dummann et al., Catalysis Today, 79-80, 433-439, 2003Kashid et al., Industrial & Engineering Chemistry Research, 44(14), 5003-5010, 2005 Vandu et al., Chemical Engineering Science, 60(22), 6430-6437, 2005Tamir, A., Impinging Stream Reactors: Fundamentals and Applications, Elsevier: Amsterdam, The Netherlands, 1994Dehkordi Asghar Molaei, Industrial & Engineering Chemistry Research, 40, 681-688, 2001.Berman, Y. and Tamir, A., AIChE Journal, 46 (4), 769, 2000




Slug Flow Generation

Y-Junction FlowExperimental

(Y-junction ID = 1 mm, Capillary ID = 1 mm,Slug Flow Velocity = 20 mm/s)

Y-Junction FlowCFD Simulation (Fluent(R))(Y-junction ID = 1 mm, Capillary ID = 1 mm,Slug Flow Velocity = 2 mm/s )




0

2

4

6

8

10

0 2 4 6 8 10

Time [s]

C [k

g/m3 ]

Conc - Phase 1Conc - Phase 2

Level 3

Level 4

Level 5

Level 6

Level 6

Level 5

Level 4

Level 3

Mesh Level 3 - 80 x 16Level 4 - 160 x 32Level 5 - 320 x 64Level 6 - 640 x 128




Hydrodynamics - Experimentation

P1, P2 - Piston Pumps PT - Pressure TransducerY-jn -Y-junction CM - Capillary MicroreactorL - LightCC - Commercial CameraW - Water CH - Cyclohexane

Operating Conditions:

0-1Pressure Sensor, bar

0.5, 0.75 and 1 Y-junction ID, mm

0.5, 0.75 and 1 Capillary ID, mm

0 – 100 (each phase)Flow rate, ml/hr

Water - CyclohexaneSystem

Experimental Set-up:

P2

P1

Y-jnCM

PTPT

L

CC

CH

W

PT

PT

Slug Flow

Drop Flow

Deformed Interface Flow

Water (+ Brilliant Blue)

Cyclohexane

0

40

80

120

160

0 40 80 120 160

Inlet flow velocity of cyclohexane [mm/s]

Inle

t flo

w v

eloc

ity o

f wat

er [m

m/s

]

Slug flow

Drop Flow

Deformed Interface Flow

ID = 0.5 mm ID = 0.75mm ID = 1 mm

Flow Regime:




Slug Size

b) Unequal inlet flow rates(Water Flow Rate = 10 ml/hr, Y-junction ID = 0.5 mm,

Capillary ID = 0.5 mm)

0

0.5

1

1.5

2

2.5

0 20 40 60 80

Slug Flow Velocity [mm/s]

Slu

g V

olum

e [ μ

l]

ID = 1 mmID = 0.75 mmID = 0.5 mm

0

0.5

1

1.5

2

2.5

3

4 8 12 16 20 24Slug Flow Velocity [mm/s]

Slu

g V

olum

e [ μ

l]

WaterCyclohexane

a) Equal inlet flow rates(Y-junction ID = 0.5 mm)

Photographic measurements




Pressure Drop

U H C

W CH C

ΔP =ΔP PΔP +ΔP P

+

= +

W W CH CHW CH C2 2

8μ V 8μ V 2γΔP = ; ΔP = andP = cosθr r r

l l

lW lCH

θ

WΔP CP CHΔP

Where,

Simplest Model:Pressure Drop = Hydrodynamic Pressure Drop of Individual Phase

+ Capillary Pressure

Pressure Gradient vs Slug Flow Velocity(Y-junction ID = 0.5 mm)

0

20

40

60

0 50 100 150

Slug Flow Velocity [mm/s]

Pre

ssur

e G

radi

ent [

kPa/

m]

ExperimentalTheoratical

ID = 0.5 mm

ID = 0.75 mm

ID = 1 mm




Wall Film

Dynamic experiments confirmpresence of an organic wall film

Experimentation

Initial droplets shrink & disappear

Residual aromatic found in acid

Nitration acid

R1,R2

SS flow

1.2.3.4. No aromatics

Aromatics on

Wall material: PTFE System: Nitration acid (HNO3 + H2SO4) + aromaticFilm not visible under microscope (<10μm)High aromatic wettability

⇐ Step 2: Initial droplets shrink & disappear




Pressure Drop – With Film

4

1 1-

,-

f CH

P PL k L

whereR hk

R

Δ Δ⎛ ⎞ ⎛ ⎞⎛ ⎞=⎜ ⎟ ⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠

=

4CH

ΔP ΔP =1-kL L

α⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

SS equation for velocity profile in the film :2

2

1 c

f

gV V Pr r r Lμ

∂ ∂ Δ⎛ ⎞+ = ⎜ ⎟∂ ∂ ⎝ ⎠

Upon integration:

In terms of inlet flow ratio, α:

Assumptions:One dimensional laminar flowInternal circulations within the slugs are neglected i.e. hard slug Pressure drop due to film region only




Pressure Drop – With Film

0

10

20

30

40

50

60

0 40 80 120 160

Slug Flow velocity [mm/s]

Pre

ssur

e G

radi

ent [

kPa/

m]

Experimental Theo - Without FilmTheo - With Film ID = 0.5 mm

ID = 0.75 mm

ID = 1 mm

Pressure Gradient vs Slug Flow Velocity at equal flow rate of both phases (Y-junction ID = 0.5 mm)




Interfacial Area/Power

1860 -2440

730 –1025

2400 –2510

620 -870

1

2520 -3300

960 –1330

3200 –3330

880 -1330

0.75

3660 -4690

1085 –1770

4500 –4800

1080 -1970

0.5

With Film , m2/m3

W/o Film m2/m3

With Film , m2/m3

W/o Film m2/m3

Unequal Flow Rate

QW = 5 - 100 ml/hr QW = 10 ml/hr

Equal Flow Rate

QW = QCH(5-100 ml/hr)

IDmm

Interfacial area:

Mechanically agitated stirred tank reactors: ~ 500 m2/m3

Presence of wall film offers ~ x 3-4 higher interfacial area

0.2 - 20Liquid-liquid slug flow (Present Work)

850 - 2600Centrifugal Extractor

35 - 1500Impinging Stream Extractor

280Impinging Streams

175 – 250Rotating disk Impinging Streams contactor

150 – 250Mixer-settler

0.5 – 190Agitated extraction column

Power InputkJ/m3 of liquid

Contactor Type

Power input:




Internal Circulations – PIV Experimentation

X-Y TranslationPlatform

ObjectCondenser

Exciter BlueFilter

540 nm

CCD camera

LabChip

ChromaticBeam Splitter

Fig.: Experimental set up

Experimental Snapshot

PIV velocity distributionWater (+ fluorescence) – paraffin oil, V = 0.031 mm/s




CFD SimulationsIncompressible Navier-Stokes equation

Boundary conditions

Numerical mesh

Solver2D, Projected solver, FEATFLOW

0; =∇=∇+Δ−∇⋅+∂∂ ufpuuu

tu υ



Vint = 0

-0,375

-0,3

-0,225

-0,15

-0,075

0

0,075

0,15

0,225

0,3

0,375

-25 -20 -15 -10 -5 0 5 10 15 20

u-velocity [mm/s]

Rad

ius

of s

lug

[mm

]

Vav = 5.64 mm/s

Vav = 11.28 mm/s

Vav = 16.92 mm/s

Vav = 22.56 mm/s

r00

r0

Fig: Parabolic profiles in a slug

Fig: snapshot of CFD simulation




CFD - Recirculation TimeImportant parameter for Mass Transfer and MixingTime required for liquid particles to move from one end of the slug to the other end

( )( )

0

20

0

2nofilm r

av

L r

L U r r drV

τ =

∫

0

1

2

3

4

5

6

0 50 100 150 200 250

Flow Velocity [mm/s]

Circ

ulat

ion

Tim

e [-]

Phase 1 (L = 2.379 mm)Phase 1 (L = 4.758 mm)Phase 2 (L = 0.561 mm)Phase 2 (L = 1.122 mm)

0

1

2

3

4

5

6

0 50 100 150 200 250

Flow Velocity [mm/s]

Circ

ulat

ion

Tim

Phase 1 (L = 2.379 mm)

Phase 1 (L = 4.758 mm)

Phase 2 (L = 0.561 mm)

Phase 2 (L = 1.122 mm)

Fig: Recirculation time without film Fig: Recirculation time with film




CFD - Particle TracingMethod of visualizationConverts Eulerian description of a flow into Langragian description with selected particleIn-house developed algorithm, GMVPT

Phase 1 Phase 2L = 2.379 mm L = 1.12 mmD = 0.75 mm D = 0.75 mmVav = 5.64 mm/s Vav = 11.28 mm/s




Mass Transfer - Experimentation

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.04 0.08 0.12 0.16 0.2Slug flow velocity [m/s]

kLa

[s-1]

375 - 1120Water – succinic acid –n-butanol Present work

775 - 2500Water (c) – succinic acid –n-butanol (d)

1364 - 4456Kerosene – acetic acid – water (c)

1187 - 3975Water (c) – iodine – kerosene (d)Rotating disks impinging streams contactor

560 – 2000Water (c) – iodine – kerosene (d)

500 – 3000Kerosene (d) – acetic acid –water (c)

15 - 2100Water (c) –iodine – kerosene (d)Impinging streams

28.5Water (c) – acetaldehyde – vinyl acetate (d)Perforated plate column

7.4 -24CCl4 (c) – acetone – water (d)Packed column

8 - 60Water (c) –acetone –benzene (d)Spray column

0.15n-hexane(c) – acetone – water (d)Rotated agitated column

57Water (c) – succinic acid – n-butanol (d)Rotated disk contactor

0.16-16.6Water (c) -iodine-CCl4 (d)Agitated vessel

kLa x 104, s-1Chemical systemContactor

Fig.: Volumetric mass transfer coefficient Operating Conditions:

0.5, 0.75 and 1 Y-junction ID, mm

0.5, 0.75 and 1 Capillary ID, mm

Slug flow regimeRegime

Water – succinic acid –n-butanolSystem




Key Issues and Design Parameters

Key Issues:Internal CirculationsHydrodynamics Slug Flow StabilityPresence of Wall Film

Design Parameters:Flow Regimes Flow Patterns within the SlugsCirculation TimeSlug DimensionPressure DropMass Transfer CoefficientFilm Thickness




Hydrophobic wall preferentially wetted by organic phase

Experimentally observed transition behaviour ~ 10 mm

Film thickness (Bretherton Law):

Enhanced interfacial area:

Slug & average flow velocity:

Film not stagnant:

2 31.34h RCa=

2

21 ( )s av

s

V VR R

=+

av film slugQ Q Q= +

π

π

≅

⎡ ⎤= − +⎣ ⎦

2

2

WithoutFilm: 2

WithFilm: 2 ( ) Where,r = Radius of capillary

a r

a r h rl

Wall Film




Introduction - Liquid-liquid contacting

Suspended drop contactors– Difficult to control drop size conditioning– Scale-up is difficult– Efficiency diminishes at low solvent/feed ratio

Film contactors– Ability to optimise solvent/feed ratio

cfd modelling of mass transfer with and without chemical ... · pdf fileuniversity of dortmund...

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