Numerical Modeling of the Medium-Density Fiberboard Hot Pressing Process, Part 1: Coupled Heat and Mass Transfer Model

Authors

  • Zanin Kavazović
  • Jean Deteix
  • Alain Cloutier
  • André Fortin

Keywords:

Mathematical model, hot pressing, coupled heat and mass transfer, finite element method, resin cure kinetics, reference domain

Abstract

A mathematical model describing heat and moisture transfer during hot pressing of medium-density fiberboard mats is presented. The model is based on conservation of energy, air mass, and water vapor mass, resulting in a three-dimensional unsteady-state problem in which mat properties and state variables vary in time and space. The conservation equations are expressed as functions of the three state variables: temperature, air pressure, and vapor pressure. The model includes conductive and convective heat transfer, phase change of water, and convective and diffusive mass transfer. Resin curing kinetics and latent heat associated with phase change of water are also taken into account. The closing of the batch press and development of the density profile are taken into account by imposing a predefined time- and space-dependent density profile. Calculations are carried out on reference geometry, and mathematical details relevant to the transfer from actual to reference geometry are presented. The system is discretized in space by the finite element method and in time by the Euler implicit scheme. The results exhibit good agreement with experimental measurements and provide information on variables of interest such as total gas pressure, temperature, moisture content, RH, and resin cure.

References

Bathe KJ (1982) Finite element procedures in engineering analysis. Prentice-Hall, Upper Saddle River, NJ. 735 pp.nBolton AJ, Humphrey PE (1988) The hot pressing of dry-formed wood-based composites. Part I. A review of the literature identifying the primary physical process and the nature of their interaction. Holzforschung 42(6):403-406.nBolton AJ, Humphrey PE, Kavvouras PK (1989a) The hot pressing of dry-formed wood-based composites. Part III. Predicted pressure and temperature variation with time and compared with experimental data for laboratory board. Holzforschung 43(4):265-274.nBolton AJ, Humphrey PE, Kavvouras PK (1989b) The hot pressing of dry-formed wood-based composites. Part IV. Predicted variation of mattress moisture content with time. Holzforschung 43(5):345-349.nBolton AJ, Humphrey PE, Kavvouras PK (1989c) The hot pressing of dry-formed wood-based composites. Part VI. The importance of stresses in the pressed mattress and their relevance to the minimisation of pressing time and the variability of board properties. Holzforschung 43(6):406-410.nCarvalho LM, Costa CAV (1998) Modeling and simulation of the hot-pressing process in the production of medium density fiberboard (MDF). Chem Eng Commun 170:1-21.nCarvalho LMH, Costa MRN, Costa CAV (2001) Modeling rheology in the hot-pressing of MDF: Comparison of mechanical models. Wood Fiber Sci 33(3):395-411.nCarvalho LMH, Costa MRN, Costa CAV (2003) A global model for the hot-pressing of MDF. Wood Sci Technol 37:241-258.nDai C, Yu C (2004) Heat and mass transfer in wood composite panels during hot-pressing. Part 1. A physical-mathematical model. Wood Fiber Sci 36(4):585-597.nGarcía P (2002) Three-dimensional heat and mass transfer during oriented strandboard hot-pressing. PhD thesis, University of British Columbia, Vancouver, BC, Canada. 254 pp.nHarper DP, Wolcott MP, Rials TG (2001) Evaluation of the cure kinetics of the wood/pMDI bondline. Int J Adhes Adhes 21:137-144.nHumphrey PE (1982) Physical aspects of wood particle-board manufacture. PhD thesis, University of Wales, Bangor, Wales, UK.nHumphrey PE, Bolton AJ (1989) The hot pressing of dry-formed wood-based composites. Part II. A simulation model for heat and moisture transfer and typical results. Holzforschung 43(3):199-206.nKavazović Z (2011) Modélisation mathématique du pressage à chaud des panneaux MDF: Couplage du modeèle mécanique avec le modèle couplé de transfert de chaleur et de masse. PhD thesis, Université Laval, Québec, Canada. 145 pp. http://www.giref.ulaval.ca/publications/memoires-et-theses.html'>http://www.giref.ulaval.ca/publications/memoires-et-theses.htmlnKavazović Z, Deteix J, Cloutier A, Fortin A (2010) Sensitivity study of a numerical model of heat and mass transfer involved during the MDF hot pressing process. Wood Fiber Sci 42(2):1-20.nKavvouras PK (1977) Fundamental process variables in particleboard manufacture. PhD thesis, University of Wales, UK. 156 pp.nLiang G, Chandrashekhara K (2006) Cure kinetics and rheology characterization of soy-based epoxy resin system. J Appl Polym Sci 102:3168-3180.nLoxton C, Thumm A, Grigsby WJ, Adams TA, Ede RM (2003) Resin distribution in medium density fiberboard. Quantification of UF resin distribution on blow line and dry-blended MDF fiber and panels. Wood Fiber Sci 35(3):370-380.nMalmquist L (1958) Sorption a deformation of space. Svenska Traforskningsinstitutet Trateknik Meddelande 983, Stockholm, Sweden.nNelson RM Jr. (1983) A model for sorption of water by cellulosic materials. Wood Fiber Sci 15(1):8-22.nNigro N, Storti M (2001) Hot-pressing process modeling for medium density fiberboard (MDF). Int J Math Sci 26(12):713-729.nPark BD, Kang EC, Park JY (2008) Thermal curing behavior of modified urea-formaldehyde resin adhesives with two formaldehyde scavengers and their influence on adhesion performance. J Appl Polym Sci 110:1573-1580.nPereira C, Carvalho LMH, Costa CAV (2006) Modeling the continuous hot-pressing of MDF. Wood Sci Technol 40:308-326.nReddy JN (2006) An introduction to the finite element method. 3rd ed. McGraw Hill Higher Education. New York. 766 pp.nSiau J (1984) Transport processes in wood. Springer-Verlag. New York. 245 pp.nThömen H (2000) Modeling the physical process in natural fiber composites during batch and continuous pressing. PhD thesis, Oregon State University, Corvallis, OR. 187 pp.nThömen H, Humphrey PE (2003) Modeling the continuous pressing process for wood-based composites. Wood Fiber Sci 35(3):456-468.nThömen H, Humphrey PE (2006) Modeling the physical process relevant during hot pressing of wood-based composites. Part 1. Heat and mass transfer. Holz Roh Werkst 64:1-10.nVidal Bastías M (2006) Modélisation du pressage à chaud des panneaux de fibres de bois (MDF) par la méthode des éléments finis. PhD thesis, Univeristé Laval, Québec, Canada. 158 pp.nVidal Bastías M, Cloutier A (2005) Evolution of wood sorption models for high temperatures. Maderas-Cienc Tecnol 7(2):145-158.nvon Haas G, Steffen A, Fruhwald A (1998) Untersuchungen zur permeabilitat von faser- span- und OSB-Matten fur gase. Holz Roh Werkst 56:386-392.nWang S, Winistorfer PM (2000) Fundamentals of vertical density profile formation in wood composites. Part 2. Methodology of vertical density formation under dynamic conditions. Wood Fiber Sci 32(2):220-238.nWang S, Winistorfer PM, Young TM (2004) Fundamentals of vertical density profile formation in wood composites. Part 3. MDF density formation during hot-pressing. Wood Fiber Sci 36(1):17-25.nWang S, Winistorfer PM, Young TM, Helton C (2001) Step-closing pressing on medium density fiberboard. Part 1. Influences on the vertical density profile. Holz RohWerkst 59:19-26.nWinistorfer PM, Moschler WW Jr., Wang S, DePaula E, Bledsoe BL (2000) Fundamentals of vertical density profile formation in wood composites. Part 1. In-situ density measurement of the consolidation process. Wood Fiber Sci 32(2):209-219.nWu Q (1999) Application of Nelson's sorption isotherm to wood composites and overlays. Wood Fiber Sci 31(2): 187-191.nXing C (2003) Characterization of urea-formaldehyde resin efficiency affected by four factors in the manufacture of medium density fiberboard. PhD thesis, Université Laval, Québec, Canada. 198 pp.nXing C, Riedl B, Cloutier A, He G (2004) The effect of urea-formaldehyde resin pre-cure on the internal bond of medium density fiberboard. Holz Roh Werkst 62:439-444.nYu C, Dai C, Wang BJ (2007) Heat and mass transfer in wood composite panels during hot pressing. Part 3. Predicted variations and interactions of the pressing variables. Holzforschung 61:74-82.nZombori BG (2001) Modeling the transient effects during the hot-pressing of wood-based composites. PhD thesis, Virginia Tech, Blacksburg, VA. 212 pp.nZombori BG, Kamke FA, Watson LT (2003) Simulation of the internal conditions during the hot-pressing process. Wood Fiber Sci 35(1):2-23.nZombori BG, Kamke FA, Watson LT (2004) Sensitivity analysis of internal mat environment during hot pressing. Wood Fiber Sci 36(2):195-209.n

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Published

2012-03-30

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Research Contributions