Modelling Fiber Suspensions Flows Using Rheological Data

1. Modelling Fiber Suspensions Flows Using Rheological Data COSt Action FP1005 meeting Nancy, 13-14 October 2011 M. Graça Rasteiro Portugal

2. Overview UNIVERSITY of COIMBRA • Objectives • Overview of work being developed • Rheological characterization • Pilot rig • CFD model • Results • Future work

3. Objectives UNIVERSITY of COIMBRA Flow properties of pulp suspensions are important for the optimization of most unit operations in pulp and paper making. Therefore, it is necessary to understand the specific hydrodynamic features of fibre suspensions.

4. Plug Flow Mixed Flow Turbulent Flow Objectives UNIVERSITY of COIMBRA Pulp suspensions flowing in pipes exhibit three basic types of shear flow mechanisms: water Turbulent flow Transition flow Plug flow

5. Objectives UNIVERSITY of COIMBRA Construction of a flow model able to predict the flow behaviour of pulp fibre suspensions represents an important step in this area. Strategy: Pseudo-Homogeneous Model Knowledge of the rheological behaviour is essential for the construction of a realistic model. The Turbulence Model is one of the simplest and most used turbulence models for industrial applications. Modifications to the k-εmodel can lead to an efficient description of the flow of concentrated fiber suspensions.

6. Overview of the research developed UNIVERSITY of COIMBRA Rheological characterization of fiber suspensions (different fiber types and consistencies). -new rotational rheometer (Searl effect) developed at UCM Development of models for the rheology of fiber suspensions. (Carla A.F. Ventura, A. Blanco, C. Negro, F.A.P. Garcia, P. Ferreira, M.G. Rasteiro, "Modelling Pulp Fibre Suspension Rheology", Tappi J, 6, 7, 17-23 (2007).) Identification of the main parameters with a stronger impact on the rheology of fiber suspensions. (Carla A.F. Ventura, A. Blanco, C. Negro, F.A.P. Garcia, P. Ferreira, M.G. Rasteiro, "Modelling Pulp Fibre Suspension Rheology", Tappi J, 6, 7, 17-23 (2007).)

7. Overview of the research developed UNIVERSITY of COIMBRA Pilot rig for the study of the flow of fiber suspensions in pipes. -Flow tests varying fiber type, suspension consistency, temperature, pipe diameter and material. Identification of the main parameters with a stronger impact on the flow regimen. (Carla Ventura, Fernando Garcia, Paulo Ferreira, Maria Rasteiro; "Flow Dynamics of Pulp Fibre Suspensions", Tappi J, 7, 8, 20-26 (2008).) New set of design correlations for friction factor vs Reynolds number based on a statistical design, showing the dependence on consistency and pipe diameter for two flow regimes. (Carla A.F. Ventura, Fernando Garcia, Paulo Ferreira, Maria Rasteiro, "Modelling Pipe Friction Loss of Pulp Fibre Suspensions", CHERD (2011) – in revision.) Modelling of the flow of fiber suspensions in pipes- turbulent regime – pseudo-homegeneous approach. (Carla A.F. Ventura, Fernando Garcia, Paulo Ferreira, Maria Rasteiro, "Modelling the Turbulent Flow of Pulp Suspensions”, I&ECR, 50,16, 9735–9742(2011).)

8. Rheological characterization UNIVERSITY of COIMBRA New plate rotational Rheometer – Searl effect 5 3 4 2 5 6 1 6 Induces uniform fibre distribution 1 5 Measures shear in the rotor (mobile plate) and in the vessel (fixed plate) Calculates the difference between torque applied by the rotor and torque transmitted by the fluid to the vessel

9. Rheological characterization UNIVERSITY of COIMBRA Suspensions tested:

10. Rheological characterization UNIVERSITY of COIMBRA Typical Rheograms ap (Pa.s)  (Nm-2) C=3.2% C=2.5 % C=2.2 % C=1.9 % C=1.6% C=1.2 % C=0.9 % pine + eucalyptus suspension

11. Rheological characterization UNIVERSITY of COIMBRA Herschel-Bulkley model ty- yield stress k – consistency coefficient n – flow index • Using an experimental design the influence of fibre characteristics (length), consistency and temperature onty were evaluated. • n an k are mainly influenced by consistency • Yield stress increases with consistency and fibre length • Temperature has got a negative effect on yield stress See: Ventura C, Blanco A, Negro C, Ferreira P, Garcia F, Rasteiro M, Tappi J, 6 (7) 17 (2007)

12. Flow model UNIVERSITY of COIMBRA Pseudo-Homogeneous Model Objective: To model the turbulent flow of pulp fibre suspensions in pipes using CFD(FEM). Modified k-ε model. COMSOL Multiphysics Software, version 3.5

13. Pilot rig UNIVERSITY of COIMBRA Pilot Rig

14. Pilot rig UNIVERSITY of COIMBRA Pilot Rig

15. pulp Experimental Results- pressure drop UNIVERSITY of COIMBRA Pipe -3”SS Pulp type effect

16. Details of Governing Equations UNIVERSITY of COIMBRA Equation for k Equation for ε Equations for the turbulence intensity and length scales I – turbulence intensity scaling parameter l - turbulence length scaling parameter Turbulence damping assumed – I and l were adjusted depending on fiber type and consistency. Viscosity was supplied as a function of local shear rate in the pipe cross-section (data extracted from the rheograms).

17. Results - Modelling UNIVERSITY of COIMBRA Experimental data

18. Results - Modelling UNIVERSITY of COIMBRA Turbulence parameters values

19. Results - Modelling UNIVERSITY of COIMBRA Comparison between predicted and experimental pressure drop (Pa/m) for the turbulent regime

20. Results - Modelling UNIVERSITY of COIMBRA Turbulence intensity scaling parameter versus suspension consistency

21. Future work UNIVERSITY of COIMBRA • ▪ Introduce in the model experimental information on the turbulence damping. • ▪ Modify the transport equations for k and ε to include mechanistic damping terms. • Establish quantitative correlations for the turbulence intensity and length scales, as a function of fiber characteristics and consistency. • ▪ Model the intermediate regime (plug of fibers + water annulus). • Acquire experimental information on the fiber plug evolution with Reynolds number (different fiber types and consistencies), using tomographic techniques.

22. UNIVERSITY of COIMBRA Acknowledgments: European Project NODESZELOSS; FCT Project FIBERFLOW; UCM; RAIZ – Instituto Investigação da Floresta e Papel; Gopaca, S.A.; Prado Karton, S.A.; Soporcel - Grupo Portucel Soporcel; CELTEJO - Empresa de Celulose do Tejo, S.A.; Carla Ventura Carla Cotas Joy Iglesias F. Garcia Paulo Ferreira

23. UNIVERSITY of COIMBRA Thank you for your attention

24. Conclusions UNIVERSITY of COIMBRA • ▪ The pressure drop profiles obtained using COMSOL Multiphysics Software agree very well with the experimental results obtained. • ▪ The use of the k-ε Turbulence Model, associated with the rheological data acquired in a specially built viscometer, revealed to be a good strategy for the prediction of pressure drop values for fibre suspension flow. • ▪ For very low consistencies the I value is minimally influenced by the consistency increase. • ▪ For relatively high values of consistency, as consistency increases, the I values decrease for all the pulps tested. This boundary is dependent on the fibre type. • The turbulence damping is higher in the case of the pine suspensions (longer and stiffer fibres), being lower for the recycled fibres suspension.

25. Results - Modelling UNIVERSITY of COIMBRA Comparison with experimental data

26. Numerical Implementation UNIVERSITY of COIMBRA Results and Discussion First, the numerical implementation was validated with water. Then, the pulp’s physical characteristics were introduced in the model. Simulated pressure drop for the flow of the recycled pulp suspension with 2.7% (w/w) consistency, at a velocity of 4.8 m/s.

27. Numerical Implementation UNIVERSITY of COIMBRA Results and Discussion Kinetic energy profile for the recycled fibre suspension 0.72% consistency

28. Numerical Implementation UNIVERSITY of COIMBRA Results and Discussion Kinetic energy profile for the recycled fibre suspension 2.7% consistency

29. Governing Equations UNIVERSITY of COIMBRA Continuity equation Conservation of momentum Standard k-εmodel Transport Equation for k Transport Equation for ε model constants:

30. Numerical Implementation UNIVERSITY of COIMBRA For the CFD modelling the Chemical Engineering module of COMSOL Multiphysics Software version 3.5 was used. Geometry The system to be modelled is basically a linear pipe (3 in diameter and 1 m long) where a pulp fibre suspension is flowing. 2D axial symmetry. 4 m

31. Numerical Implementation UNIVERSITY of COIMBRA 2D axial symmetry: mesh mode In order to reach accurate results for the pressure drop, the mesh selected was a mapped mesh consisting of quadrilateral elements. The mesh is more refined near the wall to resolve the viscous sublayer.

32. Numerical Implementation UNIVERSITY of COIMBRA Physics and Boundaries

33. Friction Factor

34. Friction factor results Friction Factor: Eucalypt pulp Cf Re

35. Friction factor results Friction Factor: distinct pulps

36. Friction Factor Correlations for not only as a function of Reynolds number, but also showing the dependence on consistency and pipe diameter for a range of pulp suspensions and for two different flow regimes were obtained;

37. Rheological characterization UNIVERSITY of COIMBRA Typical rheogram for a pulp fibre suspension τD Newtonian fluid τY

38. Rheological characterization UNIVERSITY of COIMBRA Typical Rheograms  (Nm-2) ap (Pa.s) C=3.6% C=3.3 % C=2.9 % C=2.3 % C=1.9% C=1.5 % C=1.0 % Pine suspension