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Journal of Engineering Mathematics
Published in: Journal of Engineering Mathematics 1/2013

01-12-2013

A two-dimensional model of the pressing section of a paper machine including dynamic capillary effects

Authors: Oleg Iliev, Galina Printsypar, Stefan Rief

Published in: Journal of Engineering Mathematics | Issue 1/2013

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Abstract

Paper production is a problem with significant importance for society; it is also a challenging topic for scientific investigation. This study is concerned with the simulation of the pressing section of a paper machine. A two-dimensional model is developed to account for the water flow within the pressing zone. A Richards-type equation is used to describe the flow in the unsaturated zone. The dynamic capillary pressure–saturation relation is adopted for the paper production process. The mathematical model accounts for the coexistence of saturated and unsaturated zones in a multilayer computational domain. The discretization is performed by the MPFA-O method. Numerical experiments are carried out for parameters that are typical of the production process. The static and dynamic capillary pressure–saturation relations are tested to evaluate the influence of the dynamic capillary effect.
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Literature
1.
2.
3.
Bezanovic D, van Duijn CJ, Kaasschieter EF (2006) Analysis of paper pressing: the saturated one-dimensional case. J Appl Math Mech 86(1):18–36MATH
4.
Bezanovic D, van Duijn CJ, Kaasschieter EF (2007) Analysis of wet pressing of paper: the three-phase model. Part 1: Constant air density. Report CASA 05-16 of the Department of Mathematics and Computer Science, Eindhoven, University of Technology
5.
Bezanovic D, van Duijn CJ, Kaasschieter EF (2007) Analysis of wet pressing of paper: the three-phase model. Part 2: Compressible air case. Transp Porous Med 67:171–187CrossRef
6.
Hiltunen K (1995) Mathematical and numerical modelling of consolidation processes in paper machines. PhD Thesis, University of Jyväskylä, Finland
7.
8.
Kataja M, Hiltunen K, Timonen J (1992) Flow of water and air in a compressible porous medium. A model of wet pressing of paper. J Phys D 25:1053–1063ADSCrossRef
9.
Bermond C (1997) Establishing the scientific base for energy efficiency in emerging pressing and drying technologies. Appl Therm Eng 17(8–10):901–910CrossRef
10.
Rief S (2005) Nonlinear flow in porous media. Dissertation, University of Kaiserslautern, Germany
11.
Rief S (2007) Modeling and simulation of the pressing section of a paper machine. Berichte des Fraunhofer ITWM, Nr 113
12.
Velten K, Best W (2000) Rolling of unsaturated porous materials: evolution of a fully saturated zone. Phys Rev E 62:3891–3899ADSCrossRef
13.
Bear J (1972) Dynamics of fluids in porous media. American Elsevier, New YorkMATH
14.
Bear J, Bachmat Y (1990) Introduction to modeling of transport phenomena in porous media. Kluwer, DordrechtCrossRef
15.
Bear J, Verruijt A (1987) Modeling groundwater flow and pollution. Reidel, Dordrecht
16.
Helmig R (1997) Multiphase flow and transport processes in the subsurface. Springer (Environmental Engineering), Berlin
17.
Broocks RH, Corey AT (1964) Hydraulic properties of porous media. In: Hydrology paper, vol 3. Colorado State University, Fort Collins
18.
Leverett MC (1941) Capillary behavior in porous solids. Trans AIME 142:152–169
19.
Van Genuchten MT (1980) A closed-form equation for predicting the hydraulic conductivity of unsaturated soils. Soil Sci Soc Am J 44:892–898CrossRef
20.
Barenblatt GI, Gilman AA (1987) Nonequilibrium counterflow capillary impregnation. J Eng Phys 52:335–339CrossRef
21.
Barenblatt GI, Patzek TW, Silin DB (2002) The mathematical model of non-equilibrium effects in water–oil displacement. In: SPE/DOE 13th symposium on improved oil recovery, vol SPE 75169, Tusla, USA
22.
Bourgeat A, Panfilov M (1998) Effective two-phase flow through highly heterogeneous porous media: capillary nonequilibrium effects. Comput Geosci 2:191–215MathSciNetCrossRefMATH
23.
Kalaydjian F (1992) Dynamic capillary pressure curve for water/oil displacement in porous media: theory vs. experiment. Soc Petrol Eng SPE 24813:491–506
24.
Ross PJ, Smettem KRJ (2000) A simple treatment of physical nonequilibrium water flow in soils. Soil Sci Soc Am J 64:1926–1930CrossRef
25.
Hassanizadeh SM, Celia MA, Dahle HK (2002) Dynamic effect in the capillary pressure–saturation relationship and its impacts on unsaturated flow. Vadose Zone J 1:38–57
26.
Hassanizadeh SM, Gray WG (1990) Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv Water Resour 13:169–186ADSCrossRef
27.
Hassanizadeh SM, Gray WG (1993) Thermodynamic basis of capillary pressure in porous media. Water Resour Res 29:3389–3405ADSCrossRef
28.
Manthey S (2006) Two-phase flow processes with dynamic effects in porous media—parameter estimation and simulation. Dissertation, Institute of Hydraulic Engineering of Stuttgart, Germany
29.
30.
Aavatsmark I (2007) Multipoint flux approximation methods for quadrilateral grids. In: 9th International forum on reservoir simulation, Abu Dhabi
31.
Edwards MG (2002) Unstructured, control-volume distributed, full-tensor finite-volume schemes with flow based grids. Comput Geosci 2:433–452CrossRef
32.
Herbin R, Hubert F (2008) Benchmark on discretization schemes for anisotropic diffusion problems on general grids for anisotropic heterogeneous diffusion problems. In: Eymard R, Hrard J-M (eds) Finite volumes for complex applications V. Wiley, Hoboken, pp 659–692
33.
Eigestad GT, Klausen RA (2005) On the convergence of the multi-point flux approximation O-method: numerical experiments for discontinuous permeability. Wiley Interscience, New York
34.
35.
Jewett K, Ceckler W, Busker L, Co A (1980) Computer model of a transversal flow nip. AIChE symposium series, New York, vol 76, pp 59–70 (200)
36.
Eymard R, Gallouet T, Herbin R (2006) Finite volume methods. An update of the preprint no. 97-19 du LATP, UMR 6632, Marseille, September 1997
37.
Deuflhard P (2004) Newton methods for nonlinear problems. Affine invariance and adaptive algorithms. Computational mathematics. Springer, New York
38.
Kelley CT (1995) Iterative methods for linear and nonlinear equations. Fundamental algorithms for numerical calculations. SIAM, Philadelphia
39.
Printsypar G (2012) Mathematical modeling and simulation of two-phase flow in porous media with application to the pressing section of a paper machine. Dissertation, University of Kaiserslautern, Germany
40.
Beck D (1983) Fluid pressure in a press nip: measurements and conclusions. In: Engineering conference proceedings, TAPPI, Atlanta, GA, pp 475–487
Metadata
Title
A two-dimensional model of the pressing section of a paper machine including dynamic capillary effects
Authors
Oleg Iliev
Galina Printsypar
Stefan Rief
Publication date
01-12-2013
Publisher
Springer Netherlands
Published in
Journal of Engineering Mathematics / Issue 1/2013
Print ISSN: 0022-0833
Electronic ISSN: 1573-2703
DOI
https://doi.org/10.1007/s10665-012-9619-0

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