Transport phenomena during drying of deformable, hygroscopic porous media: Fundamentals and applications

A fundamental model of multi-phase flow in deformable, hygroscopic porous media is developed via macroscopic energy and mass conservation equations for application to paper and lumber drying problems. Microscopic effects are included via volume-averaging techniques for three phases present in porous media: liquid, gas, and solid. The model includes convective and capillary transport of free water, convective and diffusive transport of water vapor and air, and diffusive transport of bound water. Porosity variations in deformable media are included during development of the governing equations and a structural model proposed for the deformation of paper during water removal.; Two-phase drainage experiments are conducted for various paper furnishes using a centrifuge method to determine the capillary pressure-moisture relationship required for modeling species transport with Darcy's Law. The irreducible moisture content levels which correspond to the onset of the hygroscopic regime are identified for each furnish. An analytic Wyllie-Gardner relative permeability model modified to account for media deformation is derived and used to extract liquid and gas phase relative permeability correlations from the experimental data.; The model is applied to convective drying of paper and lumber via appropriate boundary conditions and transport parameters. Boundary conditions for conventional multi-cylinder drying of paper webs are also developed. The governing coupled, non-linear equations are rewritten and solved in terms of three governing variables: moisture content, temperature, and gas phase pressure. The conservation equations are reduced to both a one(spatial)-dimensional model and to a two-dimensional model for strongly anisotropic media.; Control-volume formulations are used to discretize the governing partial differential equations and boundary conditions, with a power-law scheme used to proportion the diffusive and convective flux contributions across the control volume interfaces. An uncoupled solution strategy is employed although each conservation equation is solved implicitly. Model results presented for 1-D convective drying problems at different temperatures include predictions of moisture, temperature, and gas phase pressure during drying both as averages over time and as distributions within the lumber board and paper web at any time. Internal flows of individual moisture species are also presented.