Wood Science and Technology

, Volume 51, Issue 4, pp 701–719 | Cite as

A relevant and robust vacuum-drying model applied to hardwoods

  • Adam L. RedmanEmail author
  • Henri Bailleres
  • Patrick Perré
  • Elliot Carr
  • Ian Turner


A robust mathematical model was developed to simulate the heat and mass transfer process that evolves during vacuum-drying of four commercially important Australian native hardwood species. The hardwood species investigated were spotted gum (Corymbia citriodora), blackbutt (Eucalyptus pilularis), jarrah (Eucalyptus marginata), and messmate (Eucalyptus obliqua). These species provide a good test for the model based on their extreme diversity between wood properties and drying characteristics. The model uses boundary condition data from a series of vacuum-drying trials, which were also used to validate predictions. By using measured diffusion coefficient values to calibrate empirical formula, the accuracy of the model was greatly improved. Results of a sensitivity analysis showed that the model outputs provide excellent agreement with experimental observation despite the large range of species behaviour and variation in wood properties. This study confirms that the drying rate is significantly improved as a direct result of the enhanced convective and diffusive transfer along the board thickness. Contrary to softwood, it appears that longitudinal migration provides only a secondary effect. Not only is the model able to predict the heat and mass transfer behaviour of a range of hardwood species, it is also flexible enough to predict the behaviour for both conventional and vacuum-drying scenarios. The outcomes of this work provide the hardwood industry with a well-calibrated predictive drying tool that can be used to optimise drying schedules.


Moisture Content Wood Property Hardwood Species Fibre Saturation Point Average Moisture Content 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

Latin letters


Specific heat (J kg−1 K−1)


Molar concentration (mol m−3)


Diffusivity tensor (m2 s−1)


Fibre saturation point


Gravitational acceleration (m s−2)


Specific enthalpy (J kg−1)


Heat transfer coefficient (W m−2 K−1)


Flux expression


Intrinsic permeability (m2)


Absolute permeability tensor (m2)


Relative permeability tensor


Boltzmann’s constant


Air permeability (m2)


Mass transfer coefficient (m s−1)


Relative permeability


Characteristic length (m)


Molecular weight (kg mol−1)


Moisture content


Pressure difference (Pa)


Average pressure (Pa)


Pressure (Pa)


External heat transfer coefficient (W m−2 °C−1)


Gas constant (J mol−1 K−1)


Volume saturation


Time (s)


Temperature (K)


Mass velocity vector (m s−1)


Poisson’s ratio


Green volume (m3)


Molar fraction (mol/mol)


Moisture content (dry basis) (kg kg−1)

Greek symbols


Volume fraction


Thermal conductivity (W m−1 K−1)


Intrinsic averaged density (kg m−2)


Wood density (kg m−2)


Surface tension (N m−1)


Surface tension at temperature T (N m−1)


Dynamic viscosity of air (Pa s)


Phase potential


Porosity (m3 m−3)


Depth scalar (m)


Mass fraction

Superscripts and subscripts










Effective property


Fibre saturation point


Gas phase




Solid phase


Vapour phase


Vapour phase at boundary


Liquid phase

Value outside the boundary layer in the free stream



The substantial contributions of CentraleSupelec, Université Paris-Saclay, Queensland University of Technology (QUT), Forest and Wood Products Australia (FWPA) and the Queensland Government Department of Agriculture and Fisheries (DAF), to the undertaking of this collaborative project are gratefully acknowledged. Authors Turner and Carr wish to acknowledge that this research was partially supported by the Australian Research Council (ARC) via the Discovery Project DP150103675 and DECRA project DE150101137, respectively. Thank you to the reviewers for their comments and suggestions that led to an improved final version of the paper.

Supplementary material

226_2017_908_MOESM1_ESM.docx (50 kb)
Supplementary material 1 (DOCX 50 kb)


  1. Carr E, Turner I, Perré P (2011) A new control-volume finite-element scheme for heterogeneous porous media: application to the drying of softwood chemical. Eng Technol 34:1143–1150CrossRefGoogle Scholar
  2. Carr EJ, Turner IW, Perre P (2013a) A dual-scale modeling approach for drying hygroscopic porous media. Multiscale Model Simul 11:362–384. doi: 10.1137/120873005 CrossRefGoogle Scholar
  3. Carr EJ, Turner IW, Perre P (2013b) A variable-stepsize Jacobian-free exponential integrator for simulating transport in heterogeneous porous media: application to wood drying. J Comput Phys 233:66–82. doi: 10.1016/ CrossRefGoogle Scholar
  4. Hamby DM (1994) A review of techniques for parameter sensitivity analysis of environmental models. Environ Monit Assess 32:135–154CrossRefPubMedGoogle Scholar
  5. Nolan G, Innes TC, Redman AL, McGavin R (2003) Australian hardwood drying best practice manual. Forest and Wood Products Research and Development Corporation,
  6. O’Neill RV, Gardner RH, Mankin JB (1980) Analysis of parameter error in a nonlinear model. Ecol Model 8:297–311CrossRefGoogle Scholar
  7. Pang S (2007) Mathematical modeling of kiln drying of softwood timber: model development, validation and practical application. Dry Technol 25:421–431. doi: 10.1080/07373930601183751 CrossRefGoogle Scholar
  8. Perré P (2007) Fundamentals of wood drying. A.R.BO.LOR, NancyGoogle Scholar
  9. Perré P (2010) Multiscale modeling of drying as a powerful extension of the macroscopic approach: application to solid wood and biomass processing. Dry Technol 28:944–959. doi: 10.1080/07373937.2010.497079 CrossRefGoogle Scholar
  10. Perre P, Moyne C (1991) Processes related to drying: part II use of the same model to solve transfers both in saturated and unsaturated porous media. Dry Technol 9:1153–1179. doi: 10.1080/07373939108916747 CrossRefGoogle Scholar
  11. Perré P, Turner IW (1999a) A 3-D version of TransPore: a comprehensive heat and mass transfer computational model for simulating the drying of porous media. Int J Heat Mass Transf 42:4501–4521. doi: 10.1016/s0017-9310(99)00098-8 CrossRefGoogle Scholar
  12. Perré P, Turner IW (1999b) Transpore: a generic heat and mass transfer computational model for understanding and visualising the drying of porous media. Dry Technol 17:1273–1289. doi: 10.1080/07373939908917614 CrossRefGoogle Scholar
  13. Perré P, Turner JW (2008) A mesoscopic drying model applied to the growth rings of softwood: mesh generation and simulation results. Maderas, Ciencia y technologia 10:251–274. doi: 10.4067/s0718-221x2008000300008 Google Scholar
  14. Perré P, Turner I, Remond R (2007) Chapter 1—comprehensive drying models based on volume-averaging: background, application and perspective. In: Tsotsas E, Mujumdar AS (eds) modern drying technology: volume 1: computational tools at different scalesGoogle Scholar
  15. Redman AL (2011) Evaluation of super-heated steam vacuum drying viability and development of a predictive drying model for four Australian hardwood species. Report for Forest and Wood Products Australia,
  16. Redman AL, Bailleres H, Perré P (2011) Characterization of viscoelastic, shrinkage and transverse anatomy properties of four Australian hardwood species. Wood Mat Sci Eng 6:95–104. doi: 10.1080/17480272.2010.535014 CrossRefGoogle Scholar
  17. Redman AL, Bailleres H, Turner I, Perré P (2012) Mass transfer properties (permeability and mass diffusivity) of four Australian hardwood species. BioResources 7:3410–3424Google Scholar
  18. Redman AL, Bailleres H, Turner I, Perré P (2016) Characterisation of wood-water relationships and transverse anatomy and thier relationship to drying degrade. Wood Sci Technol 50:739–757CrossRefGoogle Scholar
  19. Rozsa A, Mills RG (1997) Index of kiln seasoning schedules. In: Waterson GC (ed) Australian timber seasoning manual, 3rd edn. Australian Furniture Research and Development Institute, Launceston, pp 167–175Google Scholar
  20. Salin JG (1991) Modeling of wood drying: a bibliography. Dry Technol 9(3):775–793CrossRefGoogle Scholar
  21. Salin JG (2010) Problems and solutions in wood drying modelling: history and future. Wood Mat Sci Eng 5:123–134CrossRefGoogle Scholar
  22. Salin JG (2011) Inclusion of the sorption hysteresis phenomenon in future drying models. Some basic considerations. Maderas Ciencia y tecnologia 13:173–182. doi: 10.4067/s0718-221x2011000200005 CrossRefGoogle Scholar
  23. Savard M, Lavoie V, Trembala C (2004) Technical and economical assessment of superheated steam vacuum drying of northern red oak. In: N.A.G.R.E.F. COST E15 conference, Athens, Greece, 22–24 April 2004. Forintek Canada Corp., pp 1–10Google Scholar
  24. Siau JF (1984) Transport processes in wood. Springer, Berlin. doi: 10.1007/978-3-642-69213-0 CrossRefGoogle Scholar
  25. Turner IW, Perré P (2004) Vacuum drying of wood with radiative heating: II comparison between theory and experiment. AIChE J 50:108–118CrossRefGoogle Scholar
  26. Whitaker S (1977) Simultaneous heat, mass and momentum transfer in porous media: a theory of drying. Adv Heat Transf 13:119–203CrossRefGoogle Scholar
  27. Yu C, Cheng JJ, Zielen AJ (1991) Sensitivity analysis of the RESRAD, a dose assessment code. Trans Am Nucl Soc 64:73Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Mathematical Sciences, Science and Engineering FacultyQueensland University of Technology (QUT)BrisbaneAustralia
  2. 2.Agri-Science Queensland, Department of Agriculture and FisheriesQueensland GovernmentSalisburyAustralia
  3. 3.LGPM, CentraleSupelecUniversité Paris-SaclayChâtenay-MalabryFrance
  4. 4.Australian Research Council Centre of Excellence for Mathematical and Statistical Frontiers (ACEMS)Queensland University of Technology (QUT)BrisbaneAustralia

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