Determining permeability tensors of porous media: A novel ‘vector kinetic’ numerical approach

Abstract

New structurally tailored porous materials are nowadays used in many engineering applications due to several attractive properties. Knowledge of pressure losses or flow structures in such complex media and their relationship with geometrical parameters are thus critical for various applications. Precise determination of local flow behavior and macroscale properties of natural media (soils, biomass....) are increasingly needed. It is therefore important to simulate the complex and unsteady flows by reliable numerical methods and to determine intrinsic macroscopic hydraulic properties on porous structures. The availability of low cost, easy-to use high-performance computational resources lead to generalization of pore scale numerical simulations in various fields. The recent development of innovative scheme like Lattice Boltzmann (LBM) to overcome the classical drawback of commercial softwares (Finite Volume, Finite Element) in achieving high accuracy, shows the potential of kinetic based methods for producing efficient and accurate solvers. An alternative vector kinetic method is proposed to solve incompressible Navier–Stokes equations at pore scale and eventually determine permeability tensors of complex porous media. A moment based (vs discrete velocities), non-diffusive, explicit, parallel implementation was implemented and successfully used on several totally different complex geometries. Excellent results at low Reynolds number (Re) were obtained, the method is thus well suited for permeability tensors determination of complex heterogeneous media. The code was validated against classical benchmark as well as experimental and numerical permeability data obtained on different porous media of variable porosity namely (i) foams (virtual model structures and real samples), (ii) sandstone and (iii) wood.