Pulp Suspension Rheology

James A. Olson, P.Eng.

Pulp and Paper Centre

Mechanical Engineering Dept. 604.822-5705

olson@mech.ubc.ca

General Questions

• What is pulp?

• How do we characterize a pulp suspension?

• What are the key consistency ranges?

• What is the crowding factor?

• What are the regimes of pipe flow?

• How does pulp affect piping head losses?

Why mix pulp fibres with water?

• Pulping process

• Conveying/cleaning media

• Fibre mat

• Hydrogen bonding

Pulp Suspension - The Players

Water Newtonian, ~ 60 deg. C

Pulp mechanical - chemical - recycled

Air operating + quality problems

Fillers e.g. clay, starch

Chemicals retention aids, defoamers

Debris colloidal, pitch, shives, plastic

Pulp fibres• Poly-disperse

– Early wood / latewood

– Juvenile / mature

– Hardwood / softwood

– Chemical pulp / mechanical pulp

– Whole / fragmented

How to characterize a pulp fibre suspension

• Concentration– In pulp and paper the concentration is usually called

the “Consistency” and has a slightly different definition than typical concentration

• Fibre length– Pretty straightforward …

• Coarseness– Mass per unit length of fibre

Pulp Consistency

reflects proportion of fibre and water

V

MC

C = consistency M = Mass if dry fibresV = Mass of Suspension (Water + Fibres)

Range of Consistencies

< 0.1% highly dilute - low fibre interaction (whitewater)

0.1 - 1% dilute suspension - free motion (cleaners, headboxes)

1 - 5% thin stock - substantial flocculation (screening)

5 - 15% medium consistency - semi-solid (storage)

15 - 30% high consistency - wet solid (formed paper)

30 - 70% wet web - damp solid (pressed paper)

70 - 100% paper

Fibre Length

0.00

0.05

0.10

0.15

0 1 2 3 4 5

Length (mm)

No

rmal

ized

Fra

ctio

n

Mean Fibre Lengths

• Definitions– Number average

– Length weighted average (assumes constant coarseness)

– Weight weighted coarseness (assumes coarseness proportional to length)

ii

iii

n

lnLn

iii

iii

ln

lnLw

2

iii

iii

ln

lnLww

2

3

Coarseness• Definition: Mass per unit length

• The lower the coarseness– The more fibres per gram

– The thinner the wall thickness / diameter

– The more area available for bonding

– Smoother stronger paper

Mw

L

Crowding Factor (NF)• The number of fibres in a volume swept out by a fibre length• useful in characterizing frequency of interactions

r = aspect ratio (l/d)

Crowding Factor Derivation

vm CC

CV = 2

2

3

2

2

3

234

2l

Nd

l

ld

N f

fibre volume

swept volume=

6

2

34

4

4/

2

2

2

2

w

lCN

l

NwC

wd

l

ld

LengthMasswCoarseness

mf

fm

f

f

Crowding Factor

NF < 1 chance collisions1 < NF < 60 forced collisions60 < NF continuous contact

N nF C 4 2

nC contacts per fibre

Western Red Cedar

NF = 4, 26, 78, 130Cm = .02, .1, .3, .5 %

Aspen

NF = 1, 3, 17, 34Cm = .02, .1, .5, 1.0 %

Types of Flocculation

• Chemical flocculation (colloidal)• Mechanical flocculation

mechanical forceselastic fibre bending

Mechanical Forces

Elastic Fibre Bending

Elongational Flow

Flow Through Griddisruption by stretching (more than 5:1)

not shear

TU

RB

UL

EN

TF

LO

W

INT

ER

ME

DIA

TE

FL

OW

INC

IPIE

NT

PL

UG

FL

OW

Refloculation Times

CM (%)

0.15

0.45

1.0

2.0

3.0

4.0

Velocity (m/s)

0.8 - 1.0

Time (s)

2

1.2 - 2.0

7.6

10.2

0.6

0.01

0.04

0.01

0.001

Velocity gradient

She

ar s

tres

s

dV

dy

NEWTONIAN

dV

dy

BINGHAM PLASTIC

Modes of Flow

How does pulp affect piping losses?

WATER

Velocity, V

Frict

ion

loss

,dP

/dX

PULP

A

B

CD

H

A Yield stressA-B Plug flow with

wall contactB-C Plug flow with

water annulus C-D Annulus becomes

turbulentD-H True mixed flow

How do we design a pump and pipe systems for such a complex flow?

• Standardized method for pipe design – TAPPI TIS 0410-14

– “Generalized method for determining the pipe friction loss of a flowing pulp suspension”

Tappi TIS 0410-14

• Calc Vmax– Point where annulus starts (B)

• If V < Vmax calc head as …• If V > VMax

– Calc Vw (velocity at which it acts just like water

– If Vmax < V < Vw then use Vmax in above

– If V > Vw then calc friction loss as if it is just water.

• Beware!– D is in mm– C is in %– V in M– DH/L is head (m) per 100 m of length

maxV K CH

FKV C DL

1.441.22wV C

Example

10m

2m100 mm

Tank A1% SWK Pulp

Tank B

This example looks at how to ‘estimate’ the head loss in pulp pipe flow Remember the Energy Balance in one dimension (for example, MECH 280, White Ch. 3.6)

2 2

2 2 friction pump turbine

in out

P V P Vz z h h h

g g g g

h = head loss/gain (in units of meters)Tank A contains 1% (Cm) consistency softwood, kraft pulp at 725 CSF at 35 degrees C. The tank is full to a height of 10m. It is draining through a 100mm diameter smooth stainless steel pipe into a second tank B. The height of the pulp in Tank B is 2m and both are open to the atmosphere. If the mean velocity of the pulp in the pipe is 1 m/s and you neglect minor losses, how long is the pipe connecting the two tanks?

The End