Modelling Fiber Suspensions Flows Using Rheological Data

M. Graça Rasteiro COSt Action FP1005 meeting Nancy, 13-14 October 2011

Portugal

Objectives

Overview of work being developed

Rheological characterization

Pilot rig

CFD model

Results

Future work

OverviewUNIVERSITY of COIMBRA

Objectives

Flow properties of pulp suspensions are important for the optimization of most unit operations in pulp and paper making. Therefore, it is necessary to understand the specific hydrodynamic features of fibre suspensions.

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Plug Flow

Mixed Flow

Turbulent Flow

Pulp suspensions flowing in pipes exhibit three basic types of shear flow mechanisms:

Objectives

water

Plug flow

Turbulent

flow

Transition

flowL

P

maxV WTV WV redV

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Objectives

Construction of a flow model able to predict the flow behaviour of pulp fibre suspensions represents an important step in this area.

The Turbulence Model is one of the simplest and most used turbulence models for industrial applications. Modifications to the

k- ε model can lead to an efficient description of the flow of concentrated fiber suspensions.

k

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Strategy: Pseudo-Homogeneous Model

Knowledge of the rheological behaviour is essential for the construction of a realistic model.

Overview of the research developed

Rheological characterization of fiber suspensions (different fiber types and consistencies).

-new rotational rheometer (Searl effect) developed at UCM

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Development of models for the rheology of fiber suspensions.(Carla A.F. Ventura, A. Blanco, C. Negro, F.A.P. Garcia, P. Ferreira, M.G. Rasteiro, "Modelling Pulp

Fibre Suspension Rheology", Tappi J, 6, 7, 17-23 (2007).)

Identification of the main parameters with a stronger impact on the rheology of fiber suspensions.(Carla A.F. Ventura, A. Blanco, C. Negro, F.A.P. Garcia, P. Ferreira, M.G. Rasteiro, "Modelling Pulp

Fibre Suspension Rheology", Tappi J, 6, 7, 17-23 (2007).)

Overview of the research developed

Pilot rig for the study of the flow of fiber suspensions in pipes.

-Flow tests varying fiber type, suspension consistency, temperature, pipe diameter and material.

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Identification of the main parameters with a stronger impact on the flow regimen.(Carla Ventura, Fernando Garcia, Paulo Ferreira, Maria Rasteiro; "Flow Dynamics of Pulp Fibre Suspensions", Tappi J, 7, 8, 20-26 (2008).)

New set of design correlations for friction factor vs Reynolds number based on a statistical design, showing the dependence on consistency and pipe diameter for two flow regimes.(Carla A.F. Ventura, Fernando Garcia, Paulo Ferreira, Maria Rasteiro, "Modelling Pipe Friction Loss of Pulp Fibre Suspensions", CHERD (2011) – in revision.)

Modelling of the flow of fiber suspensions in pipes- turbulent regime – pseudo-homegeneous approach. (Carla A.F. Ventura, Fernando Garcia, Paulo Ferreira, Maria Rasteiro, "Modelling the Turbulent Flow of Pulp Suspensions”, I&ECR, 50,16, 9735–9742 (2011).)

Rheological characterization

New plate rotational Rheometer – Searl effect

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Induces uniform fibre distribution

Measures shear in the rotor (mobile plate) and in the vessel (fixed plate)

Calculates the difference between torque applied by the rotor and torque transmitted by

the fluid to the vessel

1

2

34

5

6

1-Analytical scales;2-Arms to measure torque;3-Rotor;4-Vessel;5-Computer connected to the scales;6-device to control velocity.

5

5

1

6

Rheological characterization

Suspensions tested:

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Pulp TypeFibre length

(mm)

Consistencies %

(w/w)

Recycled pulp 1.14±0.04 1.4 – 4.23

Eucalypt bleachedkraft pulp

0.71±0.03 1.45 – 3.5

Eucalypt (90%) + pine (10%) bleached pulp

0.61±0.06 0.9 – 3.2

Pine unbleached kraft pulp 2.56 ±0.14 0.8 – 3.6

Rheological characterization

Typical Rheograms

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(Nm-2)

C=3.2%C=2.5 %C=2.2 %C=1.9 %

C=1.6%C=1.2 %C=0.9 %

pine + eucalyptus suspension

ap (Pa.s)

Rheological characterization

y - yield stress

k – consistency coefficient

n – flow index

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-Using an experimental design the influence of fibre characteristics (length), consistency and temperature on y were evaluated.

- n an k are mainly influenced by consistency

Herschel-Bulkley model

- Yield stress increases with consistency and fibre length- Temperature has got a negative effect on yield stress

See: Ventura C, Blanco A, Negro C, Ferreira P, Garcia F, Rasteiro M, Tappi J, 6 (7) 17 (2007)

Objective:

Flow model

To model the turbulent flow of pulp fibre suspensions in pipes using CFD(FEM).

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Pseudo-Homogeneous Model

COMSOL Multiphysics Software, version 3.5

Modified k-ε model.

Pilot rig

Pilot Rig

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Pilot rig

Pilot Rig

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Pulp type effect Pipe -3”SS

Experimental Results- pressure drop

0

50

100

150

200

250

300

350

400

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Velocity(m/s)

∆P

(mm

H2O

/m p

ipe)

recycled pulp suspension C=4.2% eucalypt pulp suspension C=3.5 %pine Pulp suspension C=3.4%pulp

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Details of Governing Equations

Equations for the turbulence intensity and length scales

Turbulence damping assumed – I and l were adjusted depending on fiber type

and consistency.

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Equation for ε

2TIk

Equation for k

TL

k 23

81

Re

hDT II

hT DlL

I – turbulence intensity scaling parameter

l - turbulence length scaling parameter

Viscosity was supplied as a function of local shear rate in the pipe cross-section (data extracted from the rheograms).

Results - Modelling

Experimental data

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Pulp Type

Consistencies %

SS Pipes and PE Pipes

3” and 4”

Recycled pulp 1.4 – 4.23

Eucalypt bleached kraft pulp 1.45 – 3.5

Eucalypt (90%) + pine (10%) bleached pulp

0.9 – 3.2

Pine unbleached kraft pulp 0.8 – 3.6

Turbulence parameters values

Pulp type Turbulence Parameters very low consistencies low consistencies

Recycled

Consistency (%) 0.72 0.60 0.61 1.40 1.80 2.30 2.70

I 0.01 0.01 0.01 0.009 0.008 0.007 0.005

l 0.005 0.005 0.005 0.005 0.005 0.005 0.005

Eucalypt

Consistency (%) 0.77 0.91 1.4 1.5

I 0.09 0.09 0.007 0.003

l 0.005 0.005 0.005 0.005

Eucalypt + pine

Consistency (%) 0.71 0.77 0.9 1.2 1.3

I 0.07 0.05 0.01 0.005 0.003

l 0.005 0.005 0.005 0.005 0.005

Pine

Consistency (%) 0.66 0.76 0.8 1

I 0.01 0.01 0.0005 0.0003

l 0.005 0.005 0.005 0.005

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Results - Modelling

Comparison between predicted and experimental pressure drop (Pa/m) for the turbulent regime

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0

300

600

900

1200

1500

1800

0 300 600 900 1200 1500 1800

Experimental

Pre

dict

ed

Recycled 0.61%

Recycled 0.76%

Recycled 1.4%

Recycled 1.8%

Recycled 2.3%

Recycled 2.7%

0

400

800

1200

1600

2000

0 400 800 1200 1600 2000

Experimental

Pre

dic

ted

Eucalypt 0.77%

Eucalypt 0.91%

Eucalypt 1.4%

Eucalypt 1.5%

0

300

600

900

1200

1500

1800

0 300 600 900 1200 1500 1800

Experimental

Pre

dic

ted

eucalypt+pine 0.71%

eucalypt+pine 0.90%

eucalypt+pine 0.77%

eucalypt+pine 1.20%

eucalypt+pine 1.30%

0

300

600

900

1200

1500

1800

0 300 600 900 1200 1500 1800Experimental

Pre

dic

ted

pine 0.66%

pine o.76%

pine 0.8%

pine 1%

c) eucalypt+pine d) pine

a) recycled b) eucalypt

Results - Modelling

Turbulence intensity scaling parameter versus suspension consistency

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0.0001

0.001

0.01

0.1

1

0.00 0.50 1.00 1.50 2.00 2.50 3.00

Consistency (%)

I

Recycled Pulp

Eucalypt Pulp

Eucalypt/Pine Pulp

Pine Pulp

Low Consistencies

High Consistencies

Future work

▪ Introduce in the model experimental information on the turbulence damping.

▪ Modify the transport equations for k and ε to include mechanistic damping terms.

Establish quantitative correlations for the turbulence intensity and length scales, as a function of fiber characteristics and consistency.

▪ Model the intermediate regime (plug of fibers + water annulus).

Acquire experimental information on the fiber plug evolution with Reynolds number (different fiber types and consistencies), using tomographic techniques.

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Acknowledgments:

RAIZ – Instituto Investigação da Floresta e Papel;

Gopaca, S.A.;

Prado Karton, S.A.;

Soporcel - Grupo Portucel Soporcel;

CELTEJO - Empresa de Celulose do Tejo, S.A.;

European Project NODESZELOSS;

FCT Project FIBERFLOW;

UCM;

Carla Ventura

Carla Cotas

Joy Iglesias

F. Garcia

Paulo Ferreira

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Thank you for your attention

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Conclusions

▪ The pressure drop profiles obtained using COMSOL Multiphysics Software agree very well with the experimental results obtained.

▪ The use of the k-ε Turbulence Model, associated with the rheological data acquired in a specially built viscometer, revealed to be a good strategy for the prediction of pressure drop values for fibre suspension flow.

▪ For very low consistencies the I value is minimally influenced by the consistency increase.

▪ For relatively high values of consistency, as consistency increases, the I values decrease for all the pulps tested. This boundary is dependent on the fibre type.

The turbulence damping is higher in the case of the pine suspensions (longer and stiffer fibres), being lower for the recycled fibres suspension.

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0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 1 2 3 4 5 6 7

Velocity (m/s)

Pre

ssu

re D

rop

(P

a/m

)

Pine 0.76% - experimental

Pine 0.76% - predicted

Pine 1.0% - experimental

Pine 1.0% - predicted

005.0

0003.0%1

005.0

01.0%76.0

l

IC

l

IC

Results - Modelling

Comparison with experimental data

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Results and Discussion

Simulated pressure drop for the flow of the recycled pulp suspension with 2.7% (w/w) consistency, at a velocity of 4.8 m/s.

Numerical Implementation

First, the numerical implementation was validated with water. Then, the pulp’s physical characteristics were introduced in the model.

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Results and Discussion

Numerical ImplementationUNIVERSITY of COIMBRA

Kinetic energy profile for the recycled fibre suspension

0.72% consistency

Results and Discussion

Numerical ImplementationUNIVERSITY of COIMBRA

Kinetic energy profile for the recycled fibre suspension

2.7% consistency

Governing Equations

0 u

Fuupuut

u T

2

2

1 TT

k

T UUkUkt

k

k

CUUk

CUt

TT

T2

2

2

12

1

C 1C 2C k Constant

Value 0.09 1.44 1.92 1.0 1.3

Continuity equation

Conservation of momentum

Transport Equation for k

Transport Equation for ε

model constants:

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Standard k-ε model

2kCT

Numerical Implementation

For the CFD modelling the Chemical Engineering module of COMSOL Multiphysics Software version 3.5 was used.

Geometry

4 m

The system to be modelled is basically a linear pipe (3 in diameter and 1 m long) where a pulp fibre suspension is flowing.

2D axial symmetry.

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2D axial symmetry: mesh mode

In order to reach accurate results for the pressure drop, the mesh selected was a mapped mesh consisting of quadrilateral elements.

The mesh is more refined near the wall to resolve the viscous sublayer.

Numerical ImplementationUNIVERSITY of COIMBRA

Physics and Boundaries

Numerical Implementation

Inlet Boundary

Plug type cross section velocity profile;

The existence of particles, such as fibres, in a fluid flow induces a turbulence damping, thus the L and I values should be smaller then usually assumed for homogeneous fluids

Since the turbulent length scale is mentioned to be mainly dependent on the system geometry, it’s value was assumed to be constant for all the fibre types and all the consistencies. The intensity scale parameter was adjusted according to the pulp fibre type and concentration.

Outlet Boundary “Normal Stress, Normal Flow” function

Wall Logarithm wall function,

Symmetry Boundary

Axial Symmetry

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Friction Factor

D

uC

L

Hf

2

2

Du

Re

.

RevsC f

Friction factor results

Friction Factor: Eucalypt pulp

Re

Cf

Friction Factor: distinct pulps

0.001

0.010

0.100

1.000

10.000

10 100 1000 10000 100000Re

Cf

recycled pulp suspension C=4.2% eucalypt pulp suspension C=3.5%eucalypt/pine pulp suspension C=3.2% pine pulp suspension C=3.4%water line

Friction factor results

Friction Factor

Correlations for not only as a function of Reynolds number, but also showing the dependence on consistency and pipe diameter for a range of pulp suspensions and for two different flow regimes were obtained;

fC

Rheological characterization

Typical rheogram for a pulp fibre suspension

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Rate of shear, γ

Sh

ear

stre

ss,

δ

Newtonianfluid

τD

τY

Rheological characterization

Typical Rheograms

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C=3.6%C=3.3 %C=2.9 %C=2.3 %

C=1.9%C=1.5 %C=1.0 %

Pine suspension

(Nm-2) ap (Pa.s)

0

50

100

150

200

250

300

350

400

0 2000 4000 6000 8000 10000

(1/s)

(N

/m2)

pine C=3.6%

pine C=3.3%

pine C=2.9%

pine C=2.3%

pine C=1.9%

pine C=1.5%

pine C=1.0%0.01

0.1

1

10

0 2000 4000 6000 8000 10000 12000

dV/dx (1/s)

pine C=3.6%

pine C=3.3%

pine C=2.9%

pine C=2.3%

pine C=1.9%

pine C=1.5%

pine C=1.0%