Pulp Suspension Rheology James A. Olson, P.Eng. Pulp and Paper Centre Mechanical Engineering Dept. 604.8-5705 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 Pulp Air Fillers Chemicals Debris Newtonian, ~ 60 deg. C mechanical - chemical - recycled operating + quality problems e.g. clay, starch retention aids, defoamers colloidal, pitch, shives, plastic
Poly-disperse Early wood / latewood Juvenile / mature Hardwood / softwood Chemical pulp / mechanical pulp Whole / fragmented Pulp fibres 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 C M V C = consistency M = Mass if dry fibres V = 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 Normalized Fraction 0.15 0.10 0.05 0.00 0 1 3 4 5 Length (mm) Mean Fibre Lengths Definitions Number average Length weighted average (assumes constant coarseness) Weight weighted coarseness (assumes coarseness proportional to length) Ln Lw i i i i i n l i i n n l i i i n l i i 3 nili Lww n l i i i
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 w M L Crowding Factor (N F ) 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 m C v C C V = 3 3 3 4 l Nd l l d N f fibre volume swept volume = 6 3 4 4 4 / w l C N l w N C w d l l d Length Mass w Coarseness m f f m f f Crowding Factor N F < 1 chance collisions 1 < N F < 60 forced collisions 60 < N F continuous contact N n F C 4 n C contacts per fibre
Western Red Cedar N F = 4, 6, 78, 130 C m =.0,.1,.3,.5 % Aspen N F = 1, 3, 17, 34 C m =.0,.1,.5, 1.0 % Types of Flocculation Chemical flocculation (colloidal) Mechanical flocculation mechanical forces elastic fibre bending
Mechanical Forces Elastic Fibre Bending
Elongational Flow Flow Through Grid disruption by stretching (more than 5:1) not shear INCIPIENT PLUG FLOW INTERMEDIATE FLOW TURBULENT FLOW
Refloculation Times C M (%) Velocity (m/s) Time (s) 0.15 0.45 1.0.0 3.0 4.0 0.8-1.0 1. -.0 7.6 10. 0.6 0.01 0.04 0.01 0.001 Shear stress BINGHAM PLASTIC dv dy NEWTONIAN dv dy Velocity gradient
Modes of Flow How does pulp affect piping losses? Friction loss, dp/dx A B PULP D C WATER H A A-B B-C Yield stress Plug flow with wall contact Plug flow with water annulus C-D Annulus becomes turbulent D-H True mixed flow Velocity, V
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 V max H L Vw KC FKV C D 1.C 1.44
Example This example looks at how to estimate the head loss in pulp pipe flow Remember the Energy Balance in one dimension (for example, MECH 80, White Ch. 3.6) P V P V z z h h h g g g g in out friction pump turbine h = head loss/gain (in units of meters) Tank A contains 1% (Cm) consistency softwood, kraft pulp at 75 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 m 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? 10m Tank A 1% SWK Pulp Tank B 100 mm m
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