Pulp Suspension Rheology

Transcription

1 Pulp Suspension Rheology James A. Olson, P.Eng. Pulp and Paper Centre Mechanical Engineering Dept 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?

2 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

3 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

4 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) % paper

5 Fibre Length Normalized Fraction 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

6 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)

7 Crowding Factor Derivation m C v C C V = l Nd l l d N f fibre volume swept volume = / 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

8 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

9 Mechanical Forces Elastic Fibre Bending

10 Elongational Flow Flow Through Grid disruption by stretching (more than 5:1) not shear INCIPIENT PLUG FLOW INTERMEDIATE FLOW TURBULENT FLOW

11 Refloculation Times C M (%) Velocity (m/s) Time (s) Shear stress BINGHAM PLASTIC dv dy NEWTONIAN dv dy Velocity gradient

12 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

13 How do we design a pump and pipe systems for such a complex flow? Standardized method for pipe design TAPPI TIS Generalized method for determining the pipe friction loss of a flowing pulp suspension Tappi TIS 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

14 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

15 The End