CFD Analysis of Mixing in Polymerization Reactor …...• Effect of impeller speed-100, 500 and 1000 rpm - Conversion analysis and comparison • Effect of residence time - 4 different

CFD Analysis of Mixing in Polymerization Reactor

ByHaresh Patel

Supervisors: Dr. R. Dhib &Dr. F. Ein-MozaffariIP

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Outline• Introduction• Model development• Simulation • Model Setup for Fluent• Results and discussion• Conclusions• Future work• Questions IP

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Introduction

• CFD is a simulation tool to analyze a system having transport equations of mass, momentum and energy.

• Originally developed for aerospace and now it is being expanded to other fields.

• Flow domain is divided into large number of small cells and one equation is written for each cell for each transport equation and then it is solved.

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Introduction• Polymerization is a complex reaction.• Viscosity increase very rapidly during

polymerization.• Mixing plays an important role in deciding the

conversion and the quality of polymer formed.• Several studies are reported to relate mixing

with polymerization but they are of limited use.• CFD has been used for tubular reactors.• No attempt has been reported for

polymerization in CSTR.IP

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Kinetic Model• Styrene can be polymerized in absence of

Initiator.• Thermal initiation• Propagation• Termination

• Steady-state hypothesis

•⎯→⎯ 123 RM Kth

11 ≥⎯→⎯+ •+

• rRMR rKp

r

1, ≥⎯→⎯+ +•• srPRR sr

Ktcsr

tc

th

KMKR

3][2][ =IP

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Kinetic Model

• Propagation rate

whereKp = A p exp(-E p / RT)Similarly for Kth & Ktc

][RMkR pp −=

•Values of A p, A th , A tc , E p , E th and E tc were taken fromDhib.et.al.(2000).

11 ≥⎯→⎯+ •+

• rRMR rKp

r

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Physical Properties

]/)3597

13591327(923.2501.19

032.12[/1109091.11)ln(

3

232

1413.00

TW

WWWW

WMT

p

pppp

pw

+

++−++−

++−=µ

•Zero shear viscosity(Kim and Nauman(1992))

•Shear viscosity (Kim and Nauman(1992)) sPa .)35000/1/( 60.02.1

00 γµµµ +=

3/)605.00.1250()1)(918.07.1174( mKgWTWT pp −+−−=ρ

•Density (Soliman et.al.(1994))

•Cp=1880 J/kg.k•K =0.126 J/m.s.k•Dm=2.0 x 10-9 m2/s

} (Soliman et.al.(1994))IP

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Reactor Geometry

Tank diameter = 14 cm Liquid level = 26 cm Impeller type = pitched blade No. of blades = 4 Impeller diameter = 8.4 cm Impeller speed = 100 to 1000 rpmInlet diameter = 1 cm Outlet diameter = 1.5 cm Reactor temperature = 140oC

• Discretised domain of a reactor• 372,000 cellsIP

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Governing equations

0)( =⋅∇→

vρ

• Continuity Eq.

• Momentum

→→→→

++⋅∇+−∇=⋅∇+∂∂ Fgpvvvt

ρτρρ )()()(

]32)[( Ivvv T

→→→

⋅∇−∇+∇= µτwhere IPR 20

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Governing equations •Energy

heffjjeff SvJhTKPEvEt

+⋅+−∇⋅∇=+⋅∇+∂∂ →→→

∑ ))(())(()( τρρ

2

2vhE +=

jj

jhYh ∑=

∫=T

T

pj

ref

jdTchIP

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Governing equations •Species

iiii RJYvYt

+⋅−∇=⋅∇+∂∂ →→

)()( ρρ

imii YDJ ∇−=→

,ρ

•Only monomer species transport equation was solved andpolymer mass fraction was obtained by (1- wm).IP

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Discretisation• Flow domain was divided into 372,000

small volumes.

dvSAdAdvdvt vv

∫∫∫∫ +⋅∇Γ=⋅+∂∂ →→→

φφρφρφ

∑∑→→→

+⋅∇Γ=⋅+∂∂ faces

ffff

faces

f

N

f

N

ff VSAAvv

tφφφφρρφ

• Integrating on each cell volume

• Discretisation

• For steady state, Above equations result in algebraic equations.

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Discretisation• Finally all equations can be

written as

baa nbnb

nbp += ∑ φφ

• This algebraic equations were solved using Gauss-Seidel with algebraic multigrid (AMG) method.

P

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Model set-up for Fluent• Grid generation in MixSim• Define in Fluent

•Material properties•Boundary conditions•Selecting discretisation techniques•Select under-relaxation factor•Modify Code by hooking UDF•Turn on monitors to check Convergence•Turn on equations to solve•Run Program to solve

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Boundary conditions• Divide flow domain in two regions(for MRF)

-Impeller region(solved in rotating frame)-Far region(solved in stationary frame)

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Boundary conditions •Tank Inlet

-Specified Normal velocity-Species mass fraction of styrene=1.0-Inlet temperature=140o C

•Tank Wall -No slip boundary for momentum-Zero diffusive flux-Fixed temperature=140o C

•Tank Outlet -Zero normal gradient for all the variables

•Liquid level-Symmetry, No normal gradientIP

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Case set up• Discretisation

• Second-order Upwind for all equations• Pressure-Velocity Coupling

• SIMPLEC algorithm • Under-relaxation to control change in variable

φαφφ ∆+= old• Most imp. for species • Started with 0.8 for species

• User-Define function(UDF) was written in C programming language for reaction source term and attached to Fluent.

• Monitored -Surface integral of the outflow of styrene-Residuals for each transport equation-Sum of velocity magnitude on symmetry

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SolverUpdate properties

Solve U,V and W

Solve pressure correction

Update velocity,mass fluxand pressure

Solve species and energy transport

Solution Converged?No Yes

Stop

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Results and Discussion• Computational time

• Computational time is directly related to no. of cells,no. of equations and no. of iterations.

• Our model consists of- approx. 372,000 cells- momentum, energy, species, pressure correction

equations and some other interpolation calculations

- approx. 240,000 iterations for each equationIPR 20

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Results and Discussion• Computational time

• Steady state simulations were run on super-computing facility of HPCVL

•24 to 35 CPUs were used for each simulation

•Flow domain was divided into no. of partitionsequal to no. of CPUs available. Each CPU was assigned one grid.

•It took 4 to 5 days for each run.IPR 20

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Results and Discussion• Convergence Monitor

•Residual monitoring

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•Sum of Velocity magnitude on symmetry

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•Styrene Outflow (kg/h)

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Results and Discussion• Simulations Scenario

• Effect of impeller speed-100, 500 and 1000 rpm - Conversion analysis and comparison

• Effect of residence time- 4 different residence time

• Effect of input-output location- bottom inlet location- 100 rpm & 500 rpmIP

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Results and Discussion• Contours for Styrene mass fraction for 144 min.

residence time

Contours of Mass fraction of styreneFLUENT 6.3 (3d, dp, pbns, spe, lam)

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1.00e+009.70e-019.40e-019.10e-018.80e-018.50e-018.20e-017.90e-017.60e-017.30e-017.00e-016.70e-016.40e-016.10e-015.80e-015.50e-015.20e-014.90e-014.60e-014.30e-014.00e-01

Z

YX

At 100 rpm At 500 RPM

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Results and Discussion• Path lines for the particles entering at inlet (colored by

styrene mass fraction)

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Results and Discussion• Styrene mass fraction contours for 1000rpm and 144 min.

residence time

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Results and Discussion• Conversion Analysis and Comparison

][RMkR pp −=tc

th

KMKR

3][2][ =IP

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Results and Discussion• Reactive flow vs. Non reactive flow

•viscosity rises to approximately 10,000 times the viscosity of styrene

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•Velocity Magnitudes (m/s) for non-reactive mass

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•Velocity Magnitudes (m/s) for reactive mass

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Results and Discussion• Effect of Residence time at 500 rpm

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Results and Discussion• Effect of Bottom inlet

• Contours of Species mass fraction for100rpm and 144 min. residence time


Mar 21, 2007


Z

YX

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Results and Discussion• Effect of Bottom inlet

• Contours of Species mass fraction for500rpm and 144min residence time


Mar 21, 2007


Z

YX

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Results and Discussion• Conversion Analysis for bottom inlet

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Conclusions• CFD was proved to be a good tool to

analyze polymerization reactor.• Conversion predicted by CFD was better

than CSTR model.• Detailed flow visualization was made

possible. IPR 20

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Future work

• To extend the model to analyze initiatorpolymerization in CSTR.

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Thanks

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Questions?

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Documents

CFD Analysis of Mixing in Polymerization Reactor …...• Effect of impeller speed-100, 500 and 1000 rpm - Conversion analysis and comparison • Effect of residence time - 4 different