O. Iliev, G. Printsypar, S. Rief

• The paper production is a problem with significant importance for the society and it is a challenging topic for scientific investigations. This study is concerned with the simulations of the pressing section of a paper machine. A two-dimensional model is developed to account for the water flow within the pressing zone. Richards’ type equation is used to describe the flow in the unsaturated zone. The dynamic capillary pressure–saturation relation proposed by Hassanizadeh and co-workers (Hassanizadeh et al., 2002; Hassanizadeh, Gray, 1990, 1993a) is adopted for the paper production process. The mathematical model accounts for the co-existence of saturated and unsaturated zones in a multilayer computational domain. The discretization is performed by the MPFA-O method. The numerical experiments are carried out for parameters which are typical for the production process. The static and dynamic capillary pressure–saturation relations are tested to evaluate the influence of the dynamic capillary effect.