Modelling of fluid filtration through plastically deformed porous medium in the process of extrusion

Mathematical models of fluid flow through non-deformable or elastically deformable porous media have become widely used. Especially they are common in water resources and oil drilling problems. The proposed hydrodynamic model of fluid filtration through plastically deforming porous skeleton, finds application in the investigation of the rapeseed extrusion extraction process. During this process the porous skeleton undergoes large inelastic deformation, which requires an alternative approach to the material behavior description. The material was presented by a two-component mixture of plastically deformable compressible porous medium saturated by oil. The mixture components were assumed to be nonreactive. According to the polymers extrusion processing theory, the problem was considered in reverse motion, the screw channel was unrolled on the plane, and viscous fluid model was used as governing equation for both mixture components. Further problem formulation was performed in the framework of the Euler motion description approach in a two-dimensional formulation for the plane of screw channel middlesection. Boundary-value problem formulated based on momentum balance and mass conservation equations for each mixture component. The boundary value problem independent variables are the mixture pressure, oil pressure, mixture velocity and oil velocity. The hypothesis of extraction speed proportionality to the oil pressure allows obtaining an approximate analytical solution for a constant filtration and compressibility coefficients.