Fibre water as a key to describe dewatering during wetpressing

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Fibre water as a key to describe dewatering
during wet-pressing
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Paper production
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Wet- pressing

• Water removal line load/speed

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Effect of dewatering on density
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Insight in dewatering enables

• Increase in paper machine speed
• Reduce of losses
• Increase in paper quality

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Insight gained from

• Dewatering Model
• provided that .

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Boundary requirements

• Dewatering model should be
• Independent of paper properties
• Independent of the machine geometry
• Firmly based on physics

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Independent of paper properties

• This implies that the model is applicable
• on all basis weights
• on all pulp recipes

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Pulp recipes

• Large differences with
• fines content type
• filler content type
• fibre origin treatment

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Approach

• Experimental determination
• Permeability
• Structural pressure

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Empirical Rules

• Structural pressure PS PS0? -q
• Permeability K A ? b
• ? porosity
• A
• Ps0 material constants
• q
• b

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Deformation physics

• Hookes law
• PS E e
• e D h/h0

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Deformation physics

• Hookes law
• PS E e
• In fact
• e ? 1/h dh

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Deformation physics

• Hookes law
• PS E e
• In fact
• e ? 1/h dh D h/h0
• small D h

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Deformation physics

• Hookes law
• PS E e
• e ? 1/h dh ln(h/h0)
• D h significant

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Deformation physics

• Hookes law tensile forces
• Wet-pressing compressive forces
• PS E e
• e ln(h/h0)

-
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Deformation physics

• Hookes law tensile forces
• Wet-pressing compressive forces
• or
• PS E e
• e ln(h0 /h)

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Flow dynamics

• Kozeny Carman
• ? void fraction available to flow

K0
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Engineering models

• Hookes Law
• Kozeny Carman

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Paradox

• Empirical rules Engineering models

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Paradox

• Empirical rules Engineering models
• WHY??

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Micro-scale

• Void fraction available to flow ? porosity
• VT Vp Vf
• VT total void volume
• Vp inter-fibre pore volume
• Vf intra-fibre pore volume

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Suggested approach

• Separate equations describing flow
• Intra-fibre volume Inter-fibre volume
• Felt

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Suggested approach

• Separate equations describing flow
• Separate parameters
• Structural pressure
• Permeability

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Deformation of wet sheet

• Two different deformations
• Network deformation Ep
• Fibre deformation Ef

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Extended structural pressure curve

• TMP

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Extended structural pressure curve

• TMP

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Extended structural pressure curve

• Eucalypti cellulose

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Extended structural pressure curve

• Eucalypti cellulose

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Sub-Conclusions

• Hookes law describes deformation due to
  wet-pressing if accounted for
• Compressive force
• Significant deformation
• Two systems under deformation

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Flow in wet sheet

• ? porosity
• ? void fraction available to flow
• Inter-fibre flow Intra-fibre flow
  

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Flow in wet sheet

• Inter-fibre flow
• Eq. 1
• Intra-fibre flow
• Eq. 2

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Permeability test

• Conventional
• K aKp bKf a, b unknown
• At high porosity K ? Kp
• Alternative
• Fit of dewater model to measured compression

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Experimental results
Lindsay Reverdy-Bruas 1.110-15
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Sub-Conclusions

• Porosity in Kozeny-Carman equation Void
  fraction available to flow
• Total void fraction divided over two separate
  systems
• Conventional permeability tests do not account
  for the above

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Conclusion

• Engineering models describe the behaviour of
  paper during wet-pressing

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Conclusion

• Engineering models describe the behaviour of
  paper during wet-pressing
• if
• a double continuous model is used to describe the
  void fractions in the wet sheet

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Next

• Numerical version of the model
• Start fibre dewatering?
• Fibre dewatering ?Pdt ?
• Relation fibre dewatering expansion?

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Challenge

• Steep start gradients

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First approach

• Matlab
• Driving force
• No internal gradients

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Preliminary results
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But..

• Ph (PT - Ps)exp(10-6 PT )
• No physical explanation for exp(10-6 PT )
• Artefact
• First approach too simple!

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Now

• Femlab
• Quadratic finite element approach
• Runge Kutta variable time-step time integration
• Gradients
• Preliminary results promising!

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Future work

• Calculation of pore water alone OK
• Next all parameters simultaneously

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Thank you !

• Questions?