Pulp Suspension Rheology
James A. Olson, P.Eng.
Pulp and Paper Centre
Mechanical Engineering Dept. 604.822-5705
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