On Mathematical Modeling and Simulation of the Pressing Section of a Paper Machine Including Dynamic Capillary Effects: One-Dimensional Model

This study presents the dynamic capillary pressure model (Hassanizadeh and Gray, Adv Water Resour 13:169–186, 1990; Water Resour Res 29:3389–3405, 1993) adapted for the needs of paper manufacturing process simulations. The dynamic capillary pressure–saturation relation is included in a one-dimensional simulation model for the pressing section of a paper machine. The one-dimensional model is derived from a two-dimensional model by averaging with respect to the vertical direction. Then, the model is discretized by the finite volume method and solved by Newton’s method. The numerical experiments are carried out for parameters typical for the paper layer. The dynamic capillary pressure–saturation relation shows significant influence on the distribution of water pressure. The behavior of the solution agrees with laboratory experiments (Beck, Fluid pressure in a press nip: measurements and conclusions, 1983).