An improved model for the drying of porous solids with abruptly changing permeability

Abstract

We present the simulation of the drying of porous solids with abruptly changing permeability using the Darcy-Forchheimer equations. This model arises in fluid mechanics through porous media when the flow exhibits moderate to high velocities and can be useful to predict the drying rate of the first drying period, which is usually constant. The presence of abrupt changes in permeability creates strong singularities and makes it difficult to obtain accurate predictions of the fluid flow, velocity, and pressure drop. In order to overcome these difficulties, we apply an adaptive finite element method based on a simple a posteriori error indicator, reliable and locally efficient, that allows us to refine the mesh over the singularities. We also present a semi-analytical method to obtain an accurate measurement of the apparent permeability of a porous medium. Finally, we provide some numerical experiments that illustrate the performance of the method.

Keywords:

• Darcy-Forchheimer
• mixed finite element
• a posteriori error estimates
• porous solids drying
• abruptly changing permeability

Acknowledgments

We acknowledge the Spanish companies Grupo Anta de Construcción y Diseño, SL, for providing us with knowledge about the usual techniques in vacuum wood drying, and Portell Hielo, SL, for providing us with the experimental data.

Disclosure statement

The authors have no conflict of interest to disclose.

Additional information

Funding

The authors wish to acknowledge the financial support of Xunta de Galicia through grant ED431C 2022/47 and the support received from CITIC, a research center funded by Xunta de Galicia and the European Union through the European Regional Development Fund and Galicia 2014-2020 Program, grant ED431G 2019/01. The research of H.V. was partially supported by the Ministerio de Educación grant FPU18/06125.