Flow of water and air in a compressible porous medium. A model of wet pressing of paper

Abstract

We have studied the dynamics of two-phase flow in highly compressible porous media. As an application, we consider a (1 + 1)-dimensional 'transverse' flow model of water removal in a paper machine press section. Within the model, the system of water, air and the fibrous solid network is perceived as a homogeneous mixture of three interacting fluids under an external, time-dependent load. The flow of the three components is governed by the continuity equations and the generalized Darcy's laws. The rate of strain of the solid matrix is determined using a phenomenological stress-strain relationship which can include hysteresis and permanent deformation. The effective stress also includes the drag applied to the solid matrix by flowing water and air. The interactions (drag forces) between the three components are determined from either experimental effective permeabilities or interaction terms derived from a simple 'annular plug' capillary flow model.