A lattice Boltzmann study on the impact of the geometrical properties of porous media on the steady state relative permeabilities on two-phase immiscible flows

• Published in: Advances in water resources 2016-09, Vol.95, p.61-79
• Main Authors: Zhang, Duo, Papadikis, K., Gu, Sai
• Format: Article
• Language: English
• Subjects: Boolean model; Disengaging; Lattices; Media; Minkowski functionals; MRT Lattice Boltzmann method; Permeability; Porosity; Porous media; Relative permeability; Saturation; Solid phases
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2015.12.015

•A MRT LBM is applied to the immiscible two phase flow in artificial porous media.•The effect of porous media properties on the relative permeabilities is studied.•Different non-wetting phase saturations result in different flow structures.•For high non-wetting phase saturations the lubricating effect is observed.•Non-linear flow behaviours are observed at low driving forces. In the current paper, the effect of the geometrical characteristics of 2-D porous media on the relative permeability in immiscible two-phase flows is studied. The generation of the different artificial porous media is performed using a Boolean model based on a random distribution of overlapping circles/ellipses, the size and shape of which are chosen to satisfy the specific Minkowski functionals (i.e. volume fraction, solid line contour length, connectivity). The study aims to identify how each different Minkowski functional affects the relative permeability of each phase at various saturations of the non-wetting phase. A 2-D multi-relaxation time (MRT) lattice Boltzmann model (LBM) that can handle high density ratios is employed in the simulation. The relationship between the driving forces G and the relative permeabilities of the two phases for every artificial structure is quantified. It is found that for high non-wetting phase saturations (fully connected flow), a non-linear relationship exists between the non-wetting phase flow rate and the driving force, whilst this relationship becomes linear at higher magnitudes of the latter. The force magnitude required to approach the linear region is highly influenced by the pore size distribution and the connectivity of the solid phase. For lower non-wetting phase saturation values, its relative permeability in the linear regime decreases as the fraction of small pores in the structure increases and the non-wetting phase flow becomes disconnected. A strong influence of the solid phase connectivity is also observed.